%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW316+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:56 EDT 2023

% Result   : Theorem 48.08s 47.14s
% Output   : Proof 48.08s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW316+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 22:22:23 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 48.08/47.14  
% 48.08/47.14  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 48.08/47.14  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.08/47.14  %-----------------------------------------------------
% 48.08/47.14  ncf(matrix, plain, [(52442 ^ _2079533) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs))], !, (47940 ^ _779999) ^ [_1744982, _1744984, _1744986, _1744988] : [class_Orderings_Olinorder(_1744982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744982), _1744984), _1744986)), c_List_Olinorder__class_Osorted(_1744982, hAPP(hAPP(c_List_Olist_OCons(_1744982), _1744986), _1744988)), -(c_List_Olinorder__class_Osorted(_1744982, hAPP(hAPP(c_List_Olist_OCons(_1744982), _1744984), hAPP(hAPP(c_List_Olist_OCons(_1744982), _1744986), _1744988))))], (46616 ^ _779999) ^ [_1715038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1715038)), _1715038 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45432 ^ _779999) ^ [_1689404, _1689406, _1689408, _1689410] : [hAPP(hAPP(c_List_Oappend(_1689404), _1689406), _1689408) = _1689410, 45435 ^ _779999 : [(45438 ^ _779999) ^ [] : [-(_1689408 = hAPP(hAPP(c_List_Odrop(_1689404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689404)), _1689406)), _1689410))], (45436 ^ _779999) ^ [] : [-(_1689406 = hAPP(hAPP(c_List_Otake(_1689404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689404)), _1689406)), _1689410))]]], (5893 ^ _779999) ^ [_873826, _873828, _873830] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873826, tc_HOL_Obool)), _873828), _873830) = _873830, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873826, tc_HOL_Obool)), _873828), _873830)))], (47240 ^ _779999) ^ [_1728884, _1728886, _1728888] : [-(hBOOL(hAPP(hAPP(c_member(_1728884), _1728886), hAPP(c_List_Oset(_1728884), _1728888)))), -(c_List_Oremdups(_1728884, hAPP(hAPP(c_List_Olist_OCons(_1728884), _1728886), _1728888)) = hAPP(hAPP(c_List_Olist_OCons(_1728884), _1728886), c_List_Oremdups(_1728884, _1728888)))], (33881 ^ _779999) ^ [_1413968, _1413970] : [c_Int_OBit1(_1413968) = c_Int_OBit0(_1413970)], (12039 ^ _779999) ^ [_992147, _992149, _992151, _992153, _992155] : [c_Finite__Set_Ofolding__one(_992147, _992149, _992151), hBOOL(hAPP(c_Finite__Set_Ofinite(_992147), _992153)), -(_992153 = c_Orderings_Obot__class_Obot(tc_fun(_992147, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_992147), _992155)), -(_992155 = c_Orderings_Obot__class_Obot(tc_fun(_992147, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_992147, tc_HOL_Obool)), _992153), _992155) = c_Orderings_Obot__class_Obot(tc_fun(_992147, tc_HOL_Obool)), -(hAPP(_992151, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992147, tc_HOL_Obool)), _992153), _992155)) = hAPP(hAPP(_992149, hAPP(_992151, _992153)), hAPP(_992151, _992155)))], (21556 ^ _779999) ^ [_1172460, _1172462, _1172464] : [class_Orderings_Oorder(_1172460), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1172460, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1172460, _1172462, _1172464)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1172460), _1172464)) = c_Orderings_Obot__class_Obot(tc_fun(_1172460, tc_HOL_Obool)))], (20550 ^ _779999) ^ [_1153450] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1153450)))], (40850 ^ _779999) ^ [_1576667, _1576669, _1576671] : [c_Relation_Ototal__on(_1576667, _1576669, hAPP(c_Relation_Oconverse(_1576667, _1576667), _1576671)), -(c_Relation_Ototal__on(_1576667, _1576669, _1576671))], (40423 ^ _779999) ^ [_1566800, _1566802, _1566804, _1566806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566800, _1566800)), hAPP(hAPP(c_Product__Type_OPair(_1566800, _1566800), _1566802), _1566804)), c_Transitive__Closure_Ortrancl(_1566800, _1566806))), -(_1566802 = _1566804), 40430 ^ _779999 : [(40433 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566800, _1566800)), hAPP(hAPP(c_Product__Type_OPair(_1566800, _1566800), _1566802), _1566804)), c_Transitive__Closure_Otrancl(_1566800, _1566806))))], (40431 ^ _779999) ^ [] : [_1566802 = _1566804]]], (45336 ^ _779999) ^ [_1687214, _1687216, _1687218, _1687220] : [-(hAPP(hAPP(c_List_Odrop(_1687214), hAPP(c_Nat_OSuc, _1687216)), hAPP(hAPP(c_List_Olist_OCons(_1687214), _1687218), _1687220)) = hAPP(hAPP(c_List_Odrop(_1687214), _1687216), _1687220))], (52138 ^ _779999) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (6983 ^ _779999) ^ [_894737, _894739, _894741, _894743] : [_894737 = _894739, 6986 ^ _779999 : [(6993 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894741), _894743), _894739)), -(hBOOL(hAPP(hAPP(c_member(_894741), _894743), _894737)))], (6987 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894741), _894743), _894737)), -(hBOOL(hAPP(hAPP(c_member(_894741), _894743), _894739)))]]], (38423 ^ _779999) ^ [_1515981, _1515983, _1515985, _1515987, _1515989, _1515991] : [hBOOL(hAPP(hAPP(c_member(_1515981), _1515983), _1515985)), hBOOL(hAPP(hAPP(c_member(_1515987), _1515989), hAPP(_1515991, _1515983))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515981, _1515987)), hAPP(hAPP(c_Product__Type_OPair(_1515981, _1515987), _1515983), _1515989)), hAPP(hAPP(c_Product__Type_OSigma(_1515981, _1515987), _1515985), _1515991))))], (14798 ^ _779999) ^ [_1045673] : [class_Rings_Olinordered__semidom(_1045673), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045673), c_Groups_Ozero__class_Ozero(_1045673)), c_Groups_Oone__class_Oone(_1045673))))], (39217 ^ _779999) ^ [_1537219, _1537221, _1537223] : [hBOOL(hAPP(hAPP(c_member(_1537221), _1537219), c_Orderings_Obot__class_Obot(tc_fun(_1537221, tc_HOL_Obool)))), -(hBOOL(hAPP(_1537223, _1537219)))], (44518 ^ _779999) ^ [_1668750, _1668752, _1668754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668750), tc_List_Olist(_1668750))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668750), tc_List_Olist(_1668750)), _1668752), c_List_Olist_ONil(_1668750))), c_List_Olistrel(_1668750, _1668754))), -(_1668752 = c_List_Olist_ONil(_1668750))], (2432 ^ _779999) ^ [_815847, _815849] : [_815849 = _815847, -(c_Int_Osucc(_815849) = c_Int_Osucc(_815847))], (33663 ^ _779999) ^ [_1409709, _1409711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409709)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409711))), -(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(_1409711))), 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), _1409709)), c_Int_Onat))))))], (46185 ^ _779999) ^ [_1704616, _1704618, _1704620, _1704622, _1704624, _1704626, _1704628] : [-(hAPP(c_List_Ofoldl(_1704616, _1704618, _1704620, _1704622), hAPP(hAPP(c_List_Omap(_1704624, _1704618), _1704626), _1704628)) = hAPP(c_List_Ofoldl(_1704616, _1704624, hAPP(hAPP(c_COMBC(_1704616, tc_fun(_1704624, _1704618), tc_fun(_1704624, _1704616)), hAPP(hAPP(c_COMBB(tc_fun(_1704618, _1704616), tc_fun(tc_fun(_1704624, _1704618), tc_fun(_1704624, _1704616)), _1704616), c_COMBB(_1704618, _1704616, _1704624)), _1704620)), _1704626), _1704622), _1704628))], (18945 ^ _779999) ^ [_1125671, _1125673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125671), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1125673), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125671), _1125673)))], (7506 ^ _779999) ^ [_905505, _905507, _905509, _905511, _905513, _905515] : [c_Hoare__Mirabelle_Ohoare__derivs(_905505, _905507, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905505)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905505), _905509), _905511), _905513)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905505), tc_HOL_Obool)))), 7513 ^ _779999 : [(7516 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_905515, 7511 ^ [_905505, _905507, _905509, _905511, _905513, _905515]), 7512 ^ [_905505, _905507, _905509, _905511, _905513, _905515]))], (7514 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_905513, 7511 ^ [_905505, _905507, _905509, _905511, _905513, _905515]), 7512 ^ [_905505, _905507, _905509, _905511, _905513, _905515])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_905505, _905507, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905505)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905505), _905509), _905511), _905515)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905505), tc_HOL_Obool)))))], (30595 ^ _779999) ^ [_1353664, _1353666] : [class_Divides_Osemiring__div(_1353664), -(c_Divides_Odiv__class_Omod(_1353664, _1353666, c_Groups_Ozero__class_Ozero(_1353664)) = _1353666)], (7970 ^ _779999) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35161 ^ _779999) ^ [_1438333, _1438335, _1438337, _1438339, _1438341, _1438343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1438333, _1438335)), hAPP(hAPP(c_Product__Type_OPair(_1438333, _1438335), _1438341), _1438343)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool)), _1438337), _1438339))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438333, tc_fun(_1438335, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1438333, tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_fun(_1438335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438335, tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_fun(_1438335, tc_HOL_Obool)), _1438333), c_COMBC(_1438335, tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438335, tc_prod(_1438333, _1438335)), tc_fun(_1438335, tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), _1438333), hAPP(c_COMBB(tc_prod(_1438333, _1438335), tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool), _1438335), c_member(tc_prod(_1438333, _1438335)))), c_Product__Type_OPair(_1438333, _1438335)))), _1438337)), hAPP(hAPP(c_COMBC(_1438333, tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_fun(_1438335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438335, tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_fun(_1438335, tc_HOL_Obool)), _1438333), c_COMBC(_1438335, tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438335, tc_prod(_1438333, _1438335)), tc_fun(_1438335, tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool)), _1438333), hAPP(c_COMBB(tc_prod(_1438333, _1438335), tc_fun(tc_fun(tc_prod(_1438333, _1438335), tc_HOL_Obool), tc_HOL_Obool), _1438335), c_member(tc_prod(_1438333, _1438335)))), c_Product__Type_OPair(_1438333, _1438335)))), _1438339)), _1438341), _1438343)))], (3096 ^ _779999) ^ [_826165, _826167, _826169, _826171] : [-(c_Nitpick_Oint__lcm(_826171, _826167) = c_Nitpick_Oint__lcm(_826169, _826165)), _826171 = _826169, _826167 = _826165], (6803 ^ _779999) ^ [_891518, _891520, _891522] : [-(hBOOL(hAPP(hAPP(c_member(_891518), _891520), hAPP(hAPP(c_Set_Oinsert(_891518), _891520), _891522))))], (50484 ^ _779999) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (46948 ^ _779999) ^ [_1722677, _1722679, _1722681, _1722683, _1722685, _1722687, _1722689] : [c_List_Olist__all2(_1722683, _1722679, hAPP(hAPP(c_COMBB(_1722677, tc_fun(_1722679, tc_HOL_Obool), _1722683), _1722681), _1722685), _1722687, _1722689), -(c_List_Olist__all2(_1722677, _1722679, _1722681, hAPP(hAPP(c_List_Omap(_1722683, _1722677), _1722685), _1722687), _1722689))], (26624 ^ _779999) ^ [_1279060, _1279062] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279060, tc_HOL_Obool)), _1279062) = hAPP(c_Set_OCollect(_1279060), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1279060), c_fNot), hAPP(hAPP(c_COMBC(_1279060, tc_fun(_1279060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1279060)), _1279062))))], (48610 ^ _779999) ^ [_1758454, _1758456, _1758458] : [48612 ^ _779999 : [(48615 ^ _779999) ^ [] : [hBOOL(hAPP(_1758456, 48611 ^ [_1758454, _1758456, _1758458]))], (48613 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758454), 48611 ^ [_1758454, _1758456, _1758458]), hAPP(c_List_Oset(_1758454), _1758458))))]], -(c_List_OtakeWhile(_1758454, _1758456, _1758458) = _1758458)], (6107 ^ _779999) ^ [_877277, _877279, _877281, _877283] : [class_Lattices_Osemilattice__sup(_877277), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877277), _877279), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877277), _877281), _877283)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877277), _877281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877277), _877279), _877283)))], (1634 ^ _779999) ^ [_803532, _803534] : [-(class_Groups_Ocancel__ab__semigroup__add(_803532)), _803534 = _803532, class_Groups_Ocancel__ab__semigroup__add(_803534)], (17763 ^ _779999) ^ [_1103116, _1103118, _1103120, _1103122, _1103124] : [class_Groups_Ocomm__monoid__mult(_1103116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103118), _1103120)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103118), _1103122)), 17777 ^ _779999 : [(17780 ^ _779999) ^ [] : [hAPP(_1103124, 17776 ^ [_1103116, _1103118, _1103120, _1103122, _1103124]) = c_Groups_Oone__class_Oone(_1103116)], (17778 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1103118), 17776 ^ [_1103116, _1103118, _1103120, _1103122, _1103124]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103118, tc_HOL_Obool)), _1103120), _1103122))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1103116, _1103118, c_Groups_Otimes__class_Otimes(_1103116)), _1103124), c_Groups_Oone__class_Oone(_1103116)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1103118, tc_HOL_Obool)), _1103120), _1103122)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103116), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1103116, _1103118, c_Groups_Otimes__class_Otimes(_1103116)), _1103124), c_Groups_Oone__class_Oone(_1103116)), _1103120)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1103116, _1103118, c_Groups_Otimes__class_Otimes(_1103116)), _1103124), c_Groups_Oone__class_Oone(_1103116)), _1103122)))], (36408 ^ _779999) ^ [_1465595, _1465597] : [c_Relation_Oirrefl(_1465595, _1465597), 36411 ^ _779999 : [(36412 ^ _779999) ^ [_1465677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465595, _1465595)), hAPP(hAPP(c_Product__Type_OPair(_1465595, _1465595), _1465677), _1465677)), _1465597))]]], (43317 ^ _779999) ^ [_1637140, _1637142, _1637144, _1637146, _1637148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637140), tc_List_Olist(_1637140))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637140), tc_List_Olist(_1637140)), _1637142), _1637144)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637140), c_List_Olistrel1(_1637140, _1637146)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637140), tc_List_Olist(_1637140))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637140), tc_List_Olist(_1637140)), hAPP(hAPP(c_List_Olist_OCons(_1637140), _1637148), _1637142)), hAPP(hAPP(c_List_Olist_OCons(_1637140), _1637148), _1637144))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637140), c_List_Olistrel1(_1637140, _1637146)))))], (4356 ^ _779999) ^ [_846145, _846147, _846149, _846151, _846153, _846155, _846157, _846159] : [-(c_New__Random__Sequence_Opos__map(_846159, _846155, _846151, _846147) = c_New__Random__Sequence_Opos__map(_846157, _846153, _846149, _846145)), _846159 = _846157, _846155 = _846153, _846151 = _846149, _846147 = _846145], (37471 ^ _779999) ^ [_1490532] : [-(c_Relation_OId__on(_1490532, c_Orderings_Obot__class_Obot(tc_fun(_1490532, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490532, _1490532), tc_HOL_Obool)))], (33251 ^ _779999) ^ [_1402599, _1402601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402599)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402601))), 33254 ^ _779999 : [(33255 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402599), _1402601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1402601)))], (33261 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402599), _1402601)))]]], (13588 ^ _779999) ^ [_1022365, _1022367, _1022369, _1022371, _1022373] : [class_Groups_Ocomm__monoid__add(_1022365), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1022367, _1022365), hAPP(hAPP(c_COMBS(_1022367, _1022365, _1022365), hAPP(hAPP(c_COMBB(_1022365, tc_fun(_1022365, _1022365), _1022367), c_Groups_Oplus__class_Oplus(_1022365)), _1022369)), _1022371)), _1022373) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022365), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1022367, _1022365), _1022369), _1022373)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1022367, _1022365), _1022371), _1022373)))], (44628 ^ _779999) ^ [_1670649, _1670651] : [_1670651 = c_List_Olist_ONil(_1670649), -(hAPP(c_List_Oset(_1670649), _1670651) = c_Orderings_Obot__class_Obot(tc_fun(_1670649, tc_HOL_Obool)))], (30766 ^ _779999) ^ [_1356760, _1356762, _1356764, _1356766] : [class_Divides_Osemiring__div(_1356760), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356760), _1356762), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1356760), _1356764), _1356762))), c_Divides_Odiv__class_Omod(_1356760, _1356764, _1356762))), _1356766) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356760), _1356764), _1356766))], (37674 ^ _779999) ^ [_1497082, _1497084, _1497086, _1497088, _1497090, _1497092, _1497094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497082, _1497084), tc_HOL_Obool)), _1497086), _1497088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497084, _1497090), tc_HOL_Obool)), _1497092), _1497094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497082, _1497090), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1497082, _1497084, _1497090), _1497086), _1497092)), hAPP(hAPP(c_Relation_Orel__comp(_1497082, _1497084, _1497090), _1497088), _1497094))))], (51574 ^ _779999) ^ [_1823939, _1823941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1823939), _1823941)), -(c_Quickcheck_Obeyond(_1823939, _1823941) = _1823941)], (46556 ^ _779999) ^ [] : [-(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))], (3836 ^ _779999) ^ [_837665, _837667, _837669, _837671] : [-(c_List_Olinorder__class_Osorted__list__of__set(_837671, _837667) = c_List_Olinorder__class_Osorted__list__of__set(_837669, _837665)), _837671 = _837669, _837667 = _837665], (46021 ^ _779999) ^ [_1701954, _1701956, _1701958, _1701960] : [-(_1701954 = c_List_Olist_ONil(_1701956)), 46024 ^ _779999 : [(46031 ^ _779999) ^ [] : [-(_1701958 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701956)), _1701954)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1701956, hAPP(hAPP(c_List_Olist__update(_1701956, _1701954), _1701958), _1701960)) = c_List_Olast(_1701956, _1701954))], (46025 ^ _779999) ^ [] : [_1701958 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701956)), _1701954)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1701956, hAPP(hAPP(c_List_Olist__update(_1701956, _1701954), _1701958), _1701960)) = _1701960)]]], (44041 ^ _779999) ^ [_1658380, _1658382] : [class_Groups_Ocomm__monoid__add(_1658380), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1658380), _1658382) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1658380), hAPP(c_List_Onth(_1658380), _1658382)), 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(_1658380)), _1658382))))], (40723 ^ _779999) ^ [_1573209, _1573211, _1573213, _1573215, _1573217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573209, _1573211)), hAPP(hAPP(c_Product__Type_OPair(_1573209, _1573211), _1573213), _1573215)), hAPP(c_Relation_Oconverse(_1573211, _1573209), _1573217))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573211, _1573209)), hAPP(hAPP(c_Product__Type_OPair(_1573211, _1573209), _1573215), _1573213)), _1573217)))], (11819 ^ _779999) ^ [_987756, _987758, _987760, _987762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987756), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987756, tc_HOL_Obool)), _987758), _987762))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987756), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987756, tc_HOL_Obool)), _987758), hAPP(hAPP(c_Set_Oinsert(_987756), _987760), _987762)))))], (21698 ^ _779999) ^ [_1175214, _1175216, _1175218] : [hBOOL(hAPP(hAPP(c_member(_1175214), _1175216), hAPP(c_Set_OCollect(_1175214), _1175218))), -(hBOOL(hAPP(_1175218, _1175216)))], (50589 ^ _779999) ^ [_1802486] : [-(c_Relation_Otrans(_1802486, c_Relation_OId(_1802486)))], (51460 ^ _779999) ^ [_1821125, _1821127, _1821129, _1821131, _1821133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1821125, tc_HOL_Obool)), _1821127), hAPP(c_Set_Oimage(_1821129, _1821125, _1821131), _1821133))), -(c_Fun_Oinj__on(_1821125, _1821129, c_Hilbert__Choice_Oinv__into(_1821129, _1821125, _1821133, _1821131), _1821127))], (19723 ^ _779999) ^ [_1139616, _1139618, _1139620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139616)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1139618), _1139620)), 19730 ^ _779999 : [(19731 ^ _779999) ^ [_1139806] : [19733 ^ _779999 : [(19739 ^ _779999) ^ [] : [-(_1139806 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19735 ^ [_1139616, _1139618, _1139620, _1139806]), 19732 ^ [_1139616, _1139618, _1139620, _1139806]))], (19737 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19735 ^ [_1139616, _1139618, _1139620, _1139806]), _1139620)))], (19734 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19732 ^ [_1139616, _1139618, _1139620, _1139806]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1139616))))]], -(_1139806 = _1139618), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1139806), _1139616) = _1139618]]], (13441 ^ _779999) ^ [_1019407, _1019409, _1019411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019407), _1019409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019409), _1019411))))], (5682 ^ _779999) ^ [_866952, _866954] : [_866954 = _866952, -(tc_Option_Ooption(_866954) = tc_Option_Ooption(_866952))], (2362 ^ _779999) ^ [_814788, _814790, _814792, _814794, _814796, _814798] : [-(c_Power_Opower_Opower(_814798, _814794, _814790) = c_Power_Opower_Opower(_814796, _814792, _814788)), _814798 = _814796, _814794 = _814792, _814790 = _814788], (15165 ^ _779999) ^ [_1052449, _1052451, _1052453, _1052455] : [hBOOL(hAPP(hAPP(_1052453, _1052455), _1052451)), -(hBOOL(hAPP(hAPP(c_member(_1052449), _1052451), c_SetInterval_Oord_OatLeast(_1052449, _1052453, _1052455))))], (9228 ^ _779999) ^ [_937499, _937501, _937503] : [class_Orderings_Olinorder(_937499), 9231 ^ _779999 : [(9238 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937499), _937503), _937501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937499), _937501), _937503))], (9232 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937499), _937501), _937503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937499), _937503), _937501)))]]], (44164 ^ _779999) ^ [_1661179, _1661181, _1661183, _1661185, _1661187, _1661189, _1661191] : [-(hAPP(hAPP(c_List_Ozip(_1661179, _1661181), hAPP(hAPP(c_List_Olist__update(_1661179, _1661183), _1661185), _1661187)), hAPP(hAPP(c_List_Olist__update(_1661181, _1661189), _1661185), _1661191)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1661179, _1661181), hAPP(hAPP(c_List_Ozip(_1661179, _1661181), _1661183), _1661189)), _1661185), hAPP(hAPP(c_Product__Type_OPair(_1661179, _1661181), _1661187), _1661191)))], (10059 ^ _779999) ^ [_953532, _953534] : [class_Complete__Lattice_Ocomplete__lattice(_953532), -(c_Inductive_Ocomplete__lattice__class_Olfp(_953532, hAPP(c_COMBK(_953532, _953532), _953534)) = _953534)], (45039 ^ _779999) ^ [_1680077, _1680079, _1680081, _1680083] : [-(hAPP(hAPP(c_List_Oappend(_1680077), hAPP(hAPP(c_List_Oappend(_1680077), _1680079), _1680081)), _1680083) = hAPP(hAPP(c_List_Oappend(_1680077), _1680079), hAPP(hAPP(c_List_Oappend(_1680077), _1680081), _1680083)))], (34213 ^ _779999) ^ [_1419872, _1419874] : [class_Int_Onumber__ring(_1419872), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1419872), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1419872), c_Groups_Oone__class_Oone(_1419872)), c_Groups_Oone__class_Oone(_1419872))), hAPP(c_Int_Onumber__class_Onumber__of(_1419872), _1419874)) = hAPP(c_Int_Onumber__class_Onumber__of(_1419872), c_Int_OBit0(_1419874)))], (33429 ^ _779999) ^ [_1405370, _1405372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405370), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405370)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405372)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405372))], (30744 ^ _779999) ^ [_1356243, _1356245] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356243, _1356245)), _1356245) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22377 ^ _779999) ^ [_1193945, _1193947] : [class_Orderings_Olinorder(_1193945), -(c_Big__Operators_Olinorder__class_OMin(_1193945, hAPP(hAPP(c_Set_Oinsert(_1193945), _1193947), c_Orderings_Obot__class_Obot(tc_fun(_1193945, tc_HOL_Obool)))) = _1193947)], (10373 ^ _779999) ^ [_958427, _958429, _958431] : [class_Groups_Ocomm__monoid__add(_958427), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958429, _958427), hAPP(c_COMBK(_958427, _958429), c_Groups_Ozero__class_Ozero(_958427))), _958431) = c_Groups_Ozero__class_Ozero(_958427))], (51962 ^ _779999) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52128 ^ _779999) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (20962 ^ _779999) ^ [_1160540, _1160542, _1160544] : [class_Groups_Oordered__ab__group__add__abs(_1160540), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160540), hAPP(c_Groups_Oabs__class_Oabs(_1160540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160540), hAPP(c_Groups_Oabs__class_Oabs(_1160540), _1160542)), hAPP(c_Groups_Oabs__class_Oabs(_1160540), _1160544)))), hAPP(c_Groups_Oabs__class_Oabs(_1160540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160540), _1160542), _1160544)))))], (46966 ^ _779999) ^ [_1723252, _1723254, _1723256, _1723258, _1723260, _1723262, _1723264] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723252)), _1723254) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723256)), _1723258), 46969 ^ _779999 : [(46978 ^ _779999) ^ [] : [-(c_List_Olist__all2(_1723252, _1723256, _1723260, hAPP(hAPP(c_List_Oappend(_1723252), _1723254), _1723262), hAPP(hAPP(c_List_Oappend(_1723256), _1723258), _1723264))), c_List_Olist__all2(_1723252, _1723256, _1723260, _1723254, _1723258), c_List_Olist__all2(_1723252, _1723256, _1723260, _1723262, _1723264)], (46970 ^ _779999) ^ [] : [c_List_Olist__all2(_1723252, _1723256, _1723260, hAPP(hAPP(c_List_Oappend(_1723252), _1723254), _1723262), hAPP(hAPP(c_List_Oappend(_1723256), _1723258), _1723264)), 46973 ^ _779999 : [(46976 ^ _779999) ^ [] : [-(c_List_Olist__all2(_1723252, _1723256, _1723260, _1723262, _1723264))], (46974 ^ _779999) ^ [] : [-(c_List_Olist__all2(_1723252, _1723256, _1723260, _1723254, _1723258))]]]]], (47292 ^ _779999) ^ [_1729841, _1729843, _1729845] : [class_Orderings_Olinorder(_1729841), -(c_List_Olinorder__class_Osort__key(_1729843, _1729841, _1729845, c_List_Olist_ONil(_1729843)) = c_List_Olist_ONil(_1729843))], (44956 ^ _779999) ^ [_1678217, _1678219, _1678221, _1678223] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678217)), hAPP(hAPP(c_List_Oappend(_1678217), _1678219), _1678221)), c_List_Olists(_1678217, _1678223))), 44959 ^ _779999 : [(44962 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678217)), _1678221), c_List_Olists(_1678217, _1678223))))], (44960 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678217)), _1678219), c_List_Olists(_1678217, _1678223))))]]], (18153 ^ _779999) ^ [_1110430, _1110432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110430), _1110432)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110432)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110430)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110432), _1110430)))], (29942 ^ _779999) ^ [_1341367, _1341369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1341367), _1341369)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341367), _1341369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50226 ^ _779999) ^ [_1794033, _1794035, _1794037] : [c_List_Olist__ex1(_1794033, _1794035, _1794037), 50230 ^ _779999 : [(50235 ^ _779999) ^ [_1794279] : [-(_1794279 = 50229 ^ [_1794033, _1794035, _1794037]), hBOOL(hAPP(hAPP(c_member(_1794033), _1794279), hAPP(c_List_Oset(_1794033), _1794037))), hBOOL(hAPP(_1794035, _1794279))], (50233 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1794035, 50229 ^ [_1794033, _1794035, _1794037])))], (50231 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794033), 50229 ^ [_1794033, _1794035, _1794037]), hAPP(c_List_Oset(_1794033), _1794037))))]]], (43712 ^ _779999) ^ [_1648790, _1648792, _1648794] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1648790, _1648790)), hAPP(hAPP(c_Product__Type_OPair(_1648790, _1648790), 43713 ^ [_1648790, _1648792, _1648794]), 43713 ^ [_1648790, _1648792, _1648794])), _1648792))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648790), tc_List_Olist(_1648790))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648790), tc_List_Olist(_1648790)), _1648794), _1648794)), c_List_Olexord(_1648790, _1648792)))], (28420 ^ _779999) ^ [_1314268, _1314270, _1314272, _1314274] : [class_Fields_Olinordered__field(_1314268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314268), _1314270), _1314272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314268), _1314274), c_Groups_Ozero__class_Ozero(_1314268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314268), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314268), _1314272), _1314274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314268), _1314270), _1314274))))], (5811 ^ _779999) ^ [_871892, _871894, _871896, _871898] : [c_Hoare__Mirabelle_Ohoare__derivs(_871892, _871894, _871896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_871892), tc_HOL_Obool)), _871898), _871896)), -(c_Hoare__Mirabelle_Ohoare__derivs(_871892, _871894, _871898))], (48388 ^ _779999) ^ [_1753739, _1753741, _1753743] : [-(hAPP(c_List_Orev(_1753739), hAPP(c_List_Ofilter(_1753739, _1753741), _1753743)) = hAPP(c_List_Ofilter(_1753739, _1753741), hAPP(c_List_Orev(_1753739), _1753743)))], (24580 ^ _779999) ^ [_1240137, _1240139, _1240141] : [class_Orderings_Olinorder(_1240137), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240137), _1240139), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240137), _1240139), _1240141)) = _1240139)], (1304 ^ _779999) ^ [_799407, _799409] : [-(class_Rings_Ocomm__ring__1(_799407)), _799409 = _799407, class_Rings_Ocomm__ring__1(_799409)], (15549 ^ _779999) ^ [_1060390, _1060392, _1060394, _1060396] : [class_Rings_Ocomm__semiring__1(_1060390), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060390), _1060392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060390), _1060394), _1060396)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060390), _1060394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060390), _1060392), _1060396)))], (31594 ^ _779999) ^ [_1372320, _1372322, _1372324] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372320, _1372322) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372324, _1372322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372324), _1372320)), -(_1372320 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1372324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1372322), 31601 ^ [_1372320, _1372322, _1372324])))], (8188 ^ _779999) ^ [_918706, _918708, _918710, _918712, _918714] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_918706, _918708), _918710, _918712, _918714)), 8189 ^ _779999 : [(8190 ^ _779999) ^ [_918761] : [c_Natural_Oevaln(_918706, _918710, _918712, _918761), c_Natural_Oevaln(_918708, _918761, _918712, _918714)]]], (11432 ^ _779999) ^ [_979076, _979078, _979080, _979082] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979076, tc_HOL_Obool)), _979078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979076, tc_HOL_Obool)), _979080), _979082)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979076, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979076, tc_HOL_Obool)), _979078), _979080)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979076, tc_HOL_Obool)), _979078), _979082)))], (30465 ^ _779999) ^ [_1350863, _1350865, _1350867, _1350869] : [class_Divides_Oring__div(_1350863), -(c_Divides_Odiv__class_Omod(_1350863, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350863), _1350865), _1350867), _1350869) = c_Divides_Odiv__class_Omod(_1350863, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350863), c_Divides_Odiv__class_Omod(_1350863, _1350865, _1350869)), c_Divides_Odiv__class_Omod(_1350863, _1350867, _1350869)), _1350869))], (11975 ^ _779999) ^ [_990761, _990763, _990765, _990767, _990769] : [class_Groups_Oordered__comm__monoid__add(_990761), hBOOL(hAPP(c_Finite__Set_Ofinite(_990763), _990765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990763, tc_HOL_Obool)), _990767), _990765)), 11989 ^ _779999 : [(11992 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990761), c_Groups_Ozero__class_Ozero(_990761)), hAPP(_990769, 11988 ^ [_990761, _990763, _990765, _990767, _990769])))], (11990 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_990763), 11988 ^ [_990761, _990763, _990765, _990767, _990769]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990763, tc_HOL_Obool)), _990765), _990767))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990761), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_990763, _990761), _990769), _990767)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_990763, _990761), _990769), _990765))))], (20359 ^ _779999) ^ [_1150501, _1150503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1150501), _1150503)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1150503), _1150501)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1150503)), hAPP(c_Int_Onat, _1150501)))], (46091 ^ _779999) ^ [_1702954, _1702956] : [-(_1702954 = c_List_Olist_ONil(_1702956)), -(hBOOL(hAPP(hAPP(c_member(_1702956), c_List_Olast(_1702956, _1702954)), hAPP(c_List_Oset(_1702956), _1702954))))], (22675 ^ _779999) ^ [_1199933, _1199935, _1199937, _1199939, _1199941] : [22677 ^ _779999 : [(22680 ^ _779999) ^ [] : [hBOOL(hAPP(_1199941, 22676 ^ [_1199933, _1199935, _1199937, _1199939, _1199941]))], (22678 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1199933), 22676 ^ [_1199933, _1199935, _1199937, _1199939, _1199941]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199935, tc_fun(_1199933, tc_HOL_Obool)), _1199937), _1199939))))]], 22681 ^ _779999 : [(22682 ^ _779999) ^ [_1200155] : [hBOOL(hAPP(hAPP(c_member(_1199935), _1200155), _1199937)), 22685 ^ _779999 : [(22686 ^ _779999) ^ [_1200252] : [hBOOL(hAPP(hAPP(c_member(_1199933), _1200252), hAPP(_1199939, _1200155))), -(hBOOL(hAPP(_1199941, _1200252)))]]]]], (39286 ^ _779999) ^ [_1539188, _1539190, _1539192, _1539194, _1539196, _1539198] : [39289 ^ _779999 : [(39292 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1539194), _1539196), hAPP(hAPP(_1539198, 39287 ^ [_1539188, _1539190, _1539192, _1539194, _1539196, _1539198]), 39288 ^ [_1539188, _1539190, _1539192, _1539194, _1539196, _1539198])))], (39290 ^ _779999) ^ [] : [-(_1539188 = hAPP(hAPP(c_Product__Type_OPair(_1539190, _1539192), 39287 ^ [_1539188, _1539190, _1539192, _1539194, _1539196, _1539198]), 39288 ^ [_1539188, _1539190, _1539192, _1539194, _1539196, _1539198]))]], -(hBOOL(hAPP(hAPP(c_member(_1539194), _1539196), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1539190, _1539192, tc_fun(_1539194, tc_HOL_Obool)), _1539198), _1539188))))], (45839 ^ _779999) ^ [_1698211, _1698213, _1698215, _1698217] : [class_Complete__Lattice_Ocomplete__lattice(_1698211), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1698213, _1698211), hAPP(c_List_Oset(_1698213), _1698215)), _1698217) = hAPP(c_List_Ofoldl(_1698211, _1698213, hAPP(c_COMBC(_1698213, _1698211, _1698211), hAPP(hAPP(c_COMBB(_1698211, tc_fun(_1698211, _1698211), _1698213), c_Lattices_Osemilattice__inf__class_Oinf(_1698211)), _1698217)), c_Orderings_Otop__class_Otop(_1698211)), _1698215))], (34345 ^ _779999) ^ [_1422241, _1422243] : [class_Fields_Olinordered__field__inverse__zero(_1422241), class_Int_Onumber__ring(_1422241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422241), c_Groups_Ozero__class_Ozero(_1422241)), _1422243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422241), c_Groups_Ozero__class_Ozero(_1422241)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422241), _1422243), hAPP(c_Int_Onumber__class_Onumber__of(_1422241), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (37809 ^ _779999) ^ [_1500503, _1500505, _1500507, _1500509, _1500511, _1500513] : [c_Typedef_Otype__definition(_1500503, _1500505, _1500507, _1500509, _1500511), -(hBOOL(hAPP(hAPP(c_member(_1500505), hAPP(_1500507, _1500513)), _1500511)))], (34789 ^ _779999) ^ [_1430798] : [c_Int_OMin = _1430798, -(c_Int_OMin = c_Int_OBit1(_1430798))], (1914 ^ _779999) ^ [_807032, _807034] : [-(class_Groups_Ominus(_807032)), _807034 = _807032, class_Groups_Ominus(_807034)], (31632 ^ _779999) ^ [_1373287, _1373289, _1373291, _1373293, _1373295] : [-(hAPP(c_Relation_OImage(_1373287, _1373289, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1373287, _1373289), tc_HOL_Obool)), _1373291), _1373293)), _1373295) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1373289, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1373287, _1373289, _1373291), _1373295)), hAPP(c_Relation_OImage(_1373287, _1373289, _1373293), _1373295)))], (34047 ^ _779999) ^ [_1416811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416811), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1416811)), c_Int_OPls)))], (50078 ^ _779999) ^ [_1790819, _1790821] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1790819), _1790821))), -(c_Lazy__Sequence_Osmall__lazy_H(_1790819, _1790821) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1790821), c_Lazy__Sequence_Osmall__lazy_H(_1790819, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1790821), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42620 ^ _779999) ^ [_1619386, _1619388, _1619390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619386, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619386, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619386, tc_HOL_Obool), _1619388)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619386, tc_HOL_Obool), _1619390))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619386, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1619386, tc_HOL_Obool), tc_HOL_Obool)), _1619388), _1619390)))))], (50571 ^ _779999) ^ [_1802232, _1802234] : [-(c_Relation_Otrans(_1802232, c_Transitive__Closure_Ortrancl(_1802232, _1802234)))], (40043 ^ _779999) ^ [_1557118, _1557120, _1557122] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1557118, _1557120, _1557122)], (13520 ^ _779999) ^ [_1020922, _1020924] : [13521 ^ _779999 : [(13522 ^ _779999) ^ [_1020972] : [_1020924 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020922), _1020972)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020922), _1020924)))], (45646 ^ _779999) ^ [_1694137, _1694139, _1694141] : [-(hAPP(c_List_Oset(_1694137), hAPP(c_List_Orotate(_1694137, _1694139), _1694141)) = hAPP(c_List_Oset(_1694137), _1694141))], (34097 ^ _779999) ^ [_1417704, _1417706] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1417704)), c_Int_OBit1(_1417706)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417704), _1417706)))], (3946 ^ _779999) ^ [_839360, _839362, _839364, _839366] : [-(c_List_Oremdups(_839366, _839362) = c_List_Oremdups(_839364, _839360)), _839366 = _839364, _839362 = _839360], (38734 ^ _779999) ^ [_1526017, _1526019] : [-(c_Fun_Oinj__on(_1526017, _1526017, c_Fun_Oid(_1526017), _1526019))], (42129 ^ _779999) ^ [_1607953, _1607955, _1607957, _1607959, _1607961] : [_1607953 = c_Orderings_Obot__class_Obot(tc_fun(_1607955, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607955, tc_fun(_1607957, tc_HOL_Obool)), _1607953), hAPP(hAPP(c_COMBC(_1607955, tc_fun(_1607957, tc_HOL_Obool), tc_fun(_1607957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1607957, tc_HOL_Obool), tc_fun(tc_fun(_1607957, tc_HOL_Obool), tc_fun(_1607957, tc_HOL_Obool)), _1607955), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607957, tc_HOL_Obool))), _1607959)), _1607961)) = c_Orderings_Otop__class_Otop(tc_fun(_1607957, tc_HOL_Obool)))], (50755 ^ _779999) ^ [_1807544, _1807546] : [c_Relation_Otrans(_1807544, hAPP(c_Set_OCollect(tc_prod(_1807544, _1807544)), hAPP(c_Product__Type_Oprod_Oprod__case(_1807544, _1807544, tc_HOL_Obool), _1807546))), -(c_Predicate_Otransp(_1807544, _1807546))], (5216 ^ _779999) ^ [_859765, _859767, _859769, _859771] : [-(c_Complete__Lattice_OInf__class_OInf(_859771, _859767) = c_Complete__Lattice_OInf__class_OInf(_859769, _859765)), _859771 = _859769, _859767 = _859765], (4550 ^ _779999) ^ [_849136, _849138] : [_849138 = _849136, -(c_List_Onth(_849138) = c_List_Onth(_849136))], (33419 ^ _779999) ^ [_1405185, _1405187] : [class_Groups_Omonoid__mult(_1405185), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1405185), _1405187), 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(_1405185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405185), _1405187), _1405187)), _1405187))], (51396 ^ _779999) ^ [_1819789, _1819791, _1819793, _1819795] : [c_Fun_Oinj__on(_1819789, _1819791, _1819793, c_Orderings_Otop__class_Otop(tc_fun(_1819789, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1819789, _1819791, c_Orderings_Otop__class_Otop(tc_fun(_1819789, tc_HOL_Obool)), _1819793), hAPP(_1819793, _1819795)) = _1819795)], (8490 ^ _779999) ^ [_925279, _925281, _925283] : [class_Groups_Oab__group__add(_925279), 8493 ^ _779999 : [(8500 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925279), _925281), _925283) = c_Groups_Ozero__class_Ozero(_925279), -(_925281 = _925283)], (8494 ^ _779999) ^ [] : [_925281 = _925283, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925279), _925281), _925283) = c_Groups_Ozero__class_Ozero(_925279))]]], (15253 ^ _779999) ^ [_1054027, _1054029, _1054031, _1054033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1054027, _1054029)), c_Sum__Type_OPlus(_1054027, _1054029, _1054031, _1054033))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054029), _1054033)))], (19181 ^ _779999) ^ [_1129706, _1129708] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1129706, _1129708)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1129708), hAPP(c_Nat_OSuc, _1129706)))], (18989 ^ _779999) ^ [_1126327, _1126329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126327), _1126329))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126327), _1126329)), -(_1126327 = _1126329)], (48526 ^ _779999) ^ [_1756740, _1756742, _1756744] : [class_Orderings_Olinorder(_1756740), c_List_Olinorder__class_Osorted(_1756740, hAPP(c_List_Orev(_1756740), _1756742)), 48533 ^ _779999 : [(48540 ^ _779999) ^ [] : [-(_1756742 = c_List_Olist_ONil(_1756740)), -(c_List_Ofoldr(_1756740, _1756740, c_Orderings_Oord__class_Omax(_1756740), _1756742, _1756744) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1756740), hAPP(hAPP(c_List_Onth(_1756740), _1756742), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1756744))], (48534 ^ _779999) ^ [] : [_1756742 = c_List_Olist_ONil(_1756740), -(c_List_Ofoldr(_1756740, _1756740, c_Orderings_Oord__class_Omax(_1756740), _1756742, _1756744) = _1756744)]]], (51664 ^ _779999) ^ [_1825820, _1825822, _1825824, _1825826, _1825828, _1825830, _1825832, _1825834] : [c_Fun_Obij__betw(_1825820, _1825822, _1825824, _1825826, _1825828), c_Fun_Obij__betw(_1825822, _1825830, _1825832, _1825828, _1825834), -(c_Fun_Obij__betw(_1825820, _1825830, hAPP(c_Fun_Ocomp(_1825822, _1825830, _1825820, _1825832), _1825824), _1825826, _1825834))], (27148 ^ _779999) ^ [_1290896, _1290898, _1290900, _1290902] : [class_Rings_Ocomm__semiring__1(_1290896), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1290896), hAPP(hAPP(c_Power_Opower__class_Opower(_1290896), _1290898), _1290900)), _1290902) = hAPP(hAPP(c_Power_Opower__class_Opower(_1290896), _1290898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1290900), _1290902)))], (3478 ^ _779999) ^ [_832030, _832032, _832034, _832036, _832038, _832040, _832042, _832044, _832046, _832048] : [-(c_Fun_Ofun__upd(_832048, _832044, _832040, _832036, _832032) = c_Fun_Ofun__upd(_832046, _832042, _832038, _832034, _832030)), _832048 = _832046, _832044 = _832042, _832040 = _832038, _832036 = _832034, _832032 = _832030], (40827 ^ _779999) ^ [_1575903, _1575905, _1575907] : [-(hAPP(c_Relation_Oconverse(_1575903, _1575905), _1575907) = hAPP(c_Set_OCollect(tc_prod(_1575905, _1575903)), hAPP(c_Product__Type_Oprod_Oprod__case(_1575905, _1575903, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1575905, tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_fun(_1575903, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575903, tc_fun(tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_fun(_1575903, tc_HOL_Obool)), _1575905), c_COMBC(_1575903, tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575903, tc_prod(_1575903, _1575905)), tc_fun(_1575903, tc_fun(tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_HOL_Obool)), _1575905), hAPP(c_COMBB(tc_prod(_1575903, _1575905), tc_fun(tc_fun(tc_prod(_1575903, _1575905), tc_HOL_Obool), tc_HOL_Obool), _1575903), c_member(tc_prod(_1575903, _1575905)))), hAPP(c_COMBC(_1575903, _1575905, tc_prod(_1575903, _1575905)), c_Product__Type_OPair(_1575903, _1575905))))), _1575907))))], (26428 ^ _779999) ^ [_1275145, _1275147] : [class_Lattices_Oboolean__algebra(_1275145), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275145), hAPP(c_Groups_Ouminus__class_Ouminus(_1275145), _1275147)), _1275147) = c_Orderings_Otop__class_Otop(_1275145))], (51762 ^ _779999) ^ [_1827914, _1827916] : [class_Lattices_Obounded__lattice(_1827914), -(class_Lattices_Obounded__lattice(tc_fun(_1827916, _1827914)))], (49102 ^ _779999) ^ [_1769086, _1769088, _1769090, _1769092, _1769094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1769086, _1769088)), hAPP(_1769086, _1769090))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769092, _1769092)), hAPP(hAPP(c_Product__Type_OPair(_1769092, _1769092), _1769088), _1769090)), c_List_Omeasures(_1769092, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1769092, tc_Nat_Onat)), _1769086), _1769094)))))], (39465 ^ _779999) ^ [_1543313, _1543315, _1543317, _1543319, _1543321] : [hAPP(c_Set_Oimage(_1543313, _1543315, _1543317), c_Orderings_Otop__class_Otop(tc_fun(_1543313, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1543315, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1543315, _1543319, _1543321), c_Orderings_Otop__class_Otop(tc_fun(_1543315, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1543319, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1543313, _1543319, hAPP(c_Fun_Ocomp(_1543315, _1543319, _1543313, _1543321), _1543317)), c_Orderings_Otop__class_Otop(tc_fun(_1543313, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1543319, tc_HOL_Obool)))], (21908 ^ _779999) ^ [_1181428, _1181430, _1181432, _1181434, _1181436, _1181438] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1181428), _1181430)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1181432), _1181434)), 21918 ^ _779999 : [(21921 ^ _779999) ^ [] : [hAPP(c_Finite__Set_Ocard(_1181428), hAPP(c_Set_OCollect(_1181428), hAPP(hAPP(c_COMBS(_1181428, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1181428), c_fconj), hAPP(hAPP(c_COMBC(_1181428, tc_fun(_1181428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1181428)), _1181430))), hAPP(hAPP(c_COMBC(_1181428, _1181432, tc_HOL_Obool), _1181436), 21917 ^ [_1181428, _1181430, _1181432, _1181434, _1181436, _1181438])))) = hAPP(_1181438, 21917 ^ [_1181428, _1181430, _1181432, _1181434, _1181436, _1181438])], (21919 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1181432), 21917 ^ [_1181428, _1181430, _1181432, _1181434, _1181436, _1181438]), _1181434)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181428, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1181432, tc_HOL_Obool), tc_Nat_Onat, _1181428), c_Finite__Set_Ocard(_1181432)), hAPP(hAPP(c_COMBB(tc_fun(_1181432, tc_HOL_Obool), tc_fun(_1181432, tc_HOL_Obool), _1181428), c_Set_OCollect(_1181432)), hAPP(hAPP(c_COMBB(tc_fun(_1181432, tc_HOL_Obool), tc_fun(_1181432, tc_HOL_Obool), _1181428), hAPP(c_COMBS(_1181432, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1181432), c_fconj), hAPP(hAPP(c_COMBC(_1181432, tc_fun(_1181432, tc_HOL_Obool), tc_HOL_Obool), c_member(_1181432)), _1181434)))), _1181436)))), _1181430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181432, tc_Nat_Onat), _1181438), _1181434))], (29856 ^ _779999) ^ [_1339881, _1339883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339881)), -(c_SMT_Oz3div(_1339883, _1339881) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1339883), _1339881))], (10339 ^ _779999) ^ [_957848, _957850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957848), _957850)), 10342 ^ _779999 : [(10345 ^ _779999) ^ [] : [_957848 = _957850], (10343 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957848), _957850)))]]], (22205 ^ _779999) ^ [_1190776, _1190778] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1190776, _1190778)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1190776, _1190778), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1190778), c_Orderings_Otop__class_Otop(tc_fun(_1190778, tc_HOL_Obool)))))], (17357 ^ _779999) ^ [_1094674, _1094676, _1094678] : [17358 ^ _779999 : [(17361 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1094676), _1094678))], (17359 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1094674)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094674), _1094676)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094674), _1094678))))], (21389 ^ _779999) ^ [_1169476, _1169478, _1169480, _1169482] : [_1169476 = c_Finite__Set_Ofold1(_1169478, _1169480), -(hAPP(_1169476, hAPP(hAPP(c_Set_Oinsert(_1169478), _1169482), c_Orderings_Obot__class_Obot(tc_fun(_1169478, tc_HOL_Obool)))) = _1169482)], (29182 ^ _779999) ^ [_1328093, _1328095, _1328097, _1328099] : [class_Fields_Olinordered__field__inverse__zero(_1328093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328093), _1328095), _1328097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328093), _1328099), c_Groups_Ozero__class_Ozero(_1328093))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328093), c_Groups_Ozero__class_Ozero(_1328093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328093), _1328095), _1328097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328093), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328093), _1328099), _1328095)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328093), _1328099), _1328097))))], (37694 ^ _779999) ^ [_1497622, _1497624, _1497626, _1497628] : [hAPP(hAPP(c_Relation_Orel__comp(_1497622, _1497622, _1497622), _1497624), _1497626) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497622, _1497622), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1497622, _1497622, _1497622), _1497624), _1497628) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497622, _1497622), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1497622, _1497622, _1497622), _1497624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1497622, _1497622), tc_HOL_Obool)), _1497626), _1497628)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497622, _1497622), tc_HOL_Obool)))], (51968 ^ _779999) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (19175 ^ _779999) ^ [_1129575, _1129577, _1129579, _1129581] : [class_Orderings_Oorder(_1129575), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129575, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1129575, _1129577, _1129579)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1129575, _1129579), _1129581)) = c_Orderings_Obot__class_Obot(tc_fun(_1129575, tc_HOL_Obool)))], (26101 ^ _779999) ^ [_1269567, _1269569, _1269571] : [class_Groups_Ocomm__monoid__mult(_1269567), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269569, _1269567), _1269571), c_Orderings_Obot__class_Obot(tc_fun(_1269569, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1269567))], (10 ^ _779999) ^ [_780122, _780124, _780126] : [-(_780126 = _780122), _780126 = _780124, _780124 = _780122], (10585 ^ _779999) ^ [_962173, _962175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962173)), _962175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962173), _962175)))], (18911 ^ _779999) ^ [_1125090, _1125092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125090), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1125092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125090), _1125092)))], (1494 ^ _779999) ^ [_801782, _801784] : [-(class_Lattices_Olattice(_801782)), _801784 = _801782, class_Lattices_Olattice(_801784)], (5058 ^ _779999) ^ [_857314, _857316, _857318, _857320, _857322, _857324] : [-(c_Random__Sequence_Oempty(_857324, _857320, _857316) = c_Random__Sequence_Oempty(_857322, _857318, _857314)), _857324 = _857322, _857320 = _857318, _857316 = _857314], (42335 ^ _779999) ^ [_1612910, _1612912] : [class_Complete__Lattice_Ocomplete__lattice(_1612910), -(c_Complete__Lattice_OInf__class_OInf(_1612910, _1612912) = c_Complete__Lattice_OSup__class_OSup(_1612910, hAPP(c_Set_OCollect(_1612910), hAPP(hAPP(c_COMBB(tc_fun(_1612910, tc_HOL_Obool), tc_HOL_Obool, _1612910), c_HOL_OAll(_1612910)), hAPP(hAPP(c_COMBB(tc_fun(_1612910, tc_HOL_Obool), tc_fun(_1612910, tc_HOL_Obool), _1612910), hAPP(c_COMBS(_1612910, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1612910), c_fimplies), hAPP(hAPP(c_COMBC(_1612910, tc_fun(_1612910, tc_HOL_Obool), tc_HOL_Obool), c_member(_1612910)), _1612912)))), c_Orderings_Oord__class_Oless__eq(_1612910))))))], (8848 ^ _779999) ^ [_931991, _931993, _931995] : [class_Orderings_Olinorder(_931991), 8851 ^ _779999 : [(8852 ^ _779999) ^ [] : [-(_931993 = _931995), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931991), _931993), _931995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931991), _931995), _931993)))], (8862 ^ _779999) ^ [] : [8863 ^ _779999 : [(8866 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931991), _931995), _931993))], (8864 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931991), _931993), _931995))]], _931993 = _931995]]], (5102 ^ _779999) ^ [_858006, _858008, _858010, _858012, _858014, _858016, _858018, _858020] : [-(c_Random__Sequence_Obind(_858020, _858016, _858012, _858008) = c_Random__Sequence_Obind(_858018, _858014, _858010, _858006)), _858020 = _858018, _858016 = _858014, _858012 = _858010, _858008 = _858006], (31869 ^ _779999) ^ [_1377622, _1377624, _1377626] : [class_Int_Onumber__ring(_1377622), class_Rings_Olinordered__idom(_1377622), 31876 ^ _779999 : [(31883 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377624), _1377626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377622), hAPP(c_Int_Onumber__class_Onumber__of(_1377622), _1377624)), hAPP(c_Int_Onumber__class_Onumber__of(_1377622), _1377626))))], (31877 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377622), hAPP(c_Int_Onumber__class_Onumber__of(_1377622), _1377624)), hAPP(c_Int_Onumber__class_Onumber__of(_1377622), _1377626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377624), _1377626)))]]], (36194 ^ _779999) ^ [_1461316, _1461318, _1461320] : [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), _1461316), _1461318))), -(hBOOL(hAPP(hAPP(_1461320, _1461316), _1461318))), 36201 ^ _779999 : [(36204 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1461320, 36199 ^ [_1461316, _1461318, _1461320]), 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)))), 36200 ^ [_1461316, _1461318, _1461320])))), -(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), 36199 ^ [_1461316, _1461318, _1461320]), 36200 ^ [_1461316, _1461318, _1461320])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36200 ^ [_1461316, _1461318, _1461320]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36214 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1461320, 36199 ^ [_1461316, _1461318, _1461320]), 36200 ^ [_1461316, _1461318, _1461320]))], (36202 ^ _779999) ^ [] : [-(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), 36199 ^ [_1461316, _1461318, _1461320]), 36200 ^ [_1461316, _1461318, _1461320]))))]]], (21730 ^ _779999) ^ [_1176033, _1176035, _1176037] : [-(hAPP(hAPP(c_Set_Oinsert(_1176033), _1176035), _1176037) = hAPP(c_Set_OCollect(_1176033), hAPP(hAPP(c_COMBS(_1176033, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1176033), c_fdisj), hAPP(hAPP(c_COMBC(_1176033, _1176033, tc_HOL_Obool), c_fequal), _1176035))), hAPP(hAPP(c_COMBC(_1176033, tc_fun(_1176033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176033)), _1176037))))], (2572 ^ _779999) ^ [_817935, _817937, _817939, _817941, _817943, _817945, _817947, _817949, _817951, _817953] : [-(c_Product__Type_Oprod_Oprod__size(_817953, _817949, _817945, _817941, _817937) = c_Product__Type_Oprod_Oprod__size(_817951, _817947, _817943, _817939, _817935)), _817953 = _817951, _817949 = _817947, _817945 = _817943, _817941 = _817939, _817937 = _817935], (7334 ^ _779999) ^ [_901663, _901665] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901663, tc_HOL_Obool)), _901665), c_Orderings_Obot__class_Obot(tc_fun(_901663, tc_HOL_Obool))) = _901665)], (47565 ^ _779999) ^ [_1736958, _1736960, _1736962, _1736964] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1736958)), c_List_Otranspose__rel(_1736958)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1736958)), hAPP(hAPP(c_List_Olist_OCons(_1736958), _1736960), _1736962)), _1736964))), -(c_List_Otranspose(_1736958, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1736958)), hAPP(hAPP(c_List_Olist_OCons(_1736958), _1736960), _1736962)), _1736964)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1736958)), hAPP(hAPP(c_List_Olist_OCons(_1736958), _1736960), c_List_Oconcat(_1736958, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736958), tc_List_Olist(_1736958)), c_List_Olist_Olist__case(tc_List_Olist(_1736958), _1736958, c_List_Olist_ONil(_1736958), hAPP(hAPP(c_COMBB(tc_List_Olist(_1736958), tc_fun(tc_List_Olist(_1736958), tc_List_Olist(_1736958)), _1736958), c_COMBK(tc_List_Olist(_1736958), tc_List_Olist(_1736958))), hAPP(hAPP(c_COMBC(_1736958, tc_List_Olist(_1736958), tc_List_Olist(_1736958)), c_List_Olist_OCons(_1736958)), c_List_Olist_ONil(_1736958))))), _1736964)))), c_List_Otranspose(_1736958, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1736958)), _1736962), c_List_Oconcat(tc_List_Olist(_1736958), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736958), tc_List_Olist(tc_List_Olist(_1736958))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1736958)), _1736958, c_List_Olist_ONil(tc_List_Olist(_1736958)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1736958), tc_List_Olist(tc_List_Olist(_1736958))), _1736958), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736958), tc_List_Olist(tc_List_Olist(_1736958)), tc_List_Olist(tc_List_Olist(_1736958))), c_List_Olist_OCons(tc_List_Olist(_1736958))), c_List_Olist_ONil(tc_List_Olist(_1736958)))))), _1736964))))))], (6385 ^ _779999) ^ [_882883, _882885, _882887, _882889] : [class_Lattices_Osemilattice__sup(_882883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882883), _882885), _882887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882883), _882889), _882887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882883), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_882883), _882885), _882889)), _882887)))], (51586 ^ _779999) ^ [_1824072] : [-(c_Quickcheck_Obeyond(_1824072, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (27740 ^ _779999) ^ [_1301626, _1301628, _1301630] : [class_Rings_Olinordered__semidom(_1301626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301626), c_Groups_Ozero__class_Ozero(_1301626)), _1301628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301626), c_Groups_Ozero__class_Ozero(_1301626)), hAPP(hAPP(c_Power_Opower__class_Opower(_1301626), _1301628), _1301630))))], (51878 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (36975 ^ _779999) ^ [_1478506, _1478508, _1478510, _1478512, _1478514, _1478516, _1478518, _1478520, _1478522, _1478524] : [c_Equiv__Relations_Ocongruent2(_1478506, _1478508, _1478510, _1478512, _1478514, _1478516), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478506, _1478506)), hAPP(hAPP(c_Product__Type_OPair(_1478506, _1478506), _1478518), _1478520)), _1478512)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478508, _1478508)), hAPP(hAPP(c_Product__Type_OPair(_1478508, _1478508), _1478522), _1478524)), _1478514)), -(hAPP(hAPP(_1478516, _1478518), _1478522) = hAPP(hAPP(_1478516, _1478520), _1478524))], (13099 ^ _779999) ^ [_1013054, _1013056, _1013058, _1013060, _1013062] : [c_Finite__Set_Ofun__left__comm__idem(_1013054, _1013056, _1013058), -(hAPP(hAPP(_1013058, _1013060), hAPP(hAPP(_1013058, _1013060), _1013062)) = hAPP(hAPP(_1013058, _1013060), _1013062))], (52060 ^ _779999) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (34323 ^ _779999) ^ [_1421821, _1421823] : [class_Rings_Olinordered__idom(_1421821), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421821), hAPP(c_Groups_Oabs__class_Oabs(_1421821), _1421823)), 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(_1421821), _1421823), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37148 ^ _779999) ^ [_1482956] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1482956) = _1482956)], (36907 ^ _779999) ^ [_1476929, _1476931, _1476933, _1476935, _1476937, _1476939] : [c_Equiv__Relations_Oequiv(_1476929, _1476931, _1476933), c_Equiv__Relations_Ocongruent(_1476929, tc_fun(_1476935, tc_HOL_Obool), _1476933, _1476937), hBOOL(hAPP(hAPP(c_member(_1476929), _1476939), _1476931)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476929, tc_fun(_1476935, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1476929, _1476929, _1476933), hAPP(hAPP(c_Set_Oinsert(_1476929), _1476939), c_Orderings_Obot__class_Obot(tc_fun(_1476929, tc_HOL_Obool))))), _1476937) = hAPP(_1476937, _1476939))], (29450 ^ _779999) ^ [_1332958, _1332960, _1332962] : [class_Divides_Osemiring__div(_1332958), -(_1332960 = c_Groups_Ozero__class_Ozero(_1332958)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1332958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332958), _1332960), _1332962)), _1332960) = _1332962)], (47830 ^ _779999) ^ [_1743340] : [class_Orderings_Olinorder(_1743340), -(c_List_Olinorder__class_Osorted(_1743340, c_List_Olist_ONil(_1743340)))], (3440 ^ _779999) ^ [_831439, _831441, _831443, _831445] : [-(c_Big__Operators_Olinorder__class_OMax(_831445, _831441) = c_Big__Operators_Olinorder__class_OMax(_831443, _831439)), _831445 = _831443, _831441 = _831439], (45821 ^ _779999) ^ [_1697770, _1697772, _1697774] : [class_Orderings_Olinorder(_1697770), -(c_Big__Operators_Olattice_OInf__fin(_1697770, c_Orderings_Oord__class_Omin(_1697770), hAPP(c_List_Oset(_1697770), hAPP(hAPP(c_List_Olist_OCons(_1697770), _1697772), _1697774))) = hAPP(c_List_Ofoldl(_1697770, _1697770, c_Orderings_Oord__class_Omin(_1697770), _1697772), _1697774))], (7336 ^ _779999) ^ [_901722, _901724, _901726] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901722, tc_HOL_Obool)), _901724), _901726) = c_Orderings_Obot__class_Obot(tc_fun(_901722, tc_HOL_Obool)), 7339 ^ _779999 : [(7342 ^ _779999) ^ [] : [-(_901726 = c_Orderings_Obot__class_Obot(tc_fun(_901722, tc_HOL_Obool)))], (7340 ^ _779999) ^ [] : [-(_901724 = c_Orderings_Obot__class_Obot(tc_fun(_901722, tc_HOL_Obool)))]]], (49090 ^ _779999) ^ [_1768763, _1768765, _1768767, _1768769, _1768771] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768763, _1768763)), hAPP(hAPP(c_Product__Type_OPair(_1768763, _1768763), _1768765), _1768767)), c_List_Omeasures(_1768763, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1768763, tc_Nat_Onat)), _1768769), _1768771))))), 49091 ^ _779999 : [(49094 ^ _779999) ^ [] : [hAPP(_1768769, _1768765) = hAPP(_1768769, _1768767), hBOOL(hAPP(hAPP(c_member(tc_prod(_1768763, _1768763)), hAPP(hAPP(c_Product__Type_OPair(_1768763, _1768763), _1768765), _1768767)), c_List_Omeasures(_1768763, _1768771)))], (49092 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1768769, _1768765)), hAPP(_1768769, _1768767)))]]], (14690 ^ _779999) ^ [_1043627, _1043629, _1043631] : [-(hAPP(c_Finite__Set_Ocard(_1043627), _1043629) = hAPP(c_Nat_OSuc, _1043631)), 14691 ^ _779999 : [(14692 ^ _779999) ^ [_1043727, _1043729] : [_1043629 = hAPP(hAPP(c_Set_Oinsert(_1043627), _1043729), _1043727), -(hBOOL(hAPP(hAPP(c_member(_1043627), _1043729), _1043727))), hAPP(c_Finite__Set_Ocard(_1043627), _1043727) = _1043631, 14703 ^ _779999 : [(14706 ^ _779999) ^ [] : [_1043727 = c_Orderings_Obot__class_Obot(tc_fun(_1043627, tc_HOL_Obool))], (14704 ^ _779999) ^ [] : [-(_1043631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (15339 ^ _779999) ^ [_1055650, _1055652, _1055654, _1055656] : [class_Rings_Ocomm__semiring__1(_1055650), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055650), _1055652), _1055654)), _1055656) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055650), _1055652), _1055656)), _1055654))], (40667 ^ _779999) ^ [_1571995] : [-(hAPP(c_Relation_Oconverse(_1571995, _1571995), c_Relation_OId(_1571995)) = c_Relation_OId(_1571995))], (39399 ^ _779999) ^ [_1541980, _1541982, _1541984, _1541986, _1541988, _1541990, _1541992, _1541994, _1541996] : [hAPP(c_Fun_Ocomp(_1541980, _1541982, _1541984, _1541986), _1541988) = hAPP(c_Fun_Ocomp(_1541990, _1541982, _1541984, _1541992), _1541994), -(hAPP(_1541986, hAPP(_1541988, _1541996)) = hAPP(_1541992, hAPP(_1541994, _1541996)))], (32925 ^ _779999) ^ [_1397498, _1397500, _1397502] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397498)))), 32928 ^ _779999 : [(32935 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397500)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397498)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397500)), _1397502)) = 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), _1397498), _1397500))), _1397502))], (32929 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397500))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397498)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397500)), _1397502)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397498)), _1397502))]]], (16027 ^ _779999) ^ [_1069326, _1069328, _1069330] : [class_Rings_Oordered__cancel__semiring(_1069326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069326), c_Groups_Ozero__class_Ozero(_1069326)), _1069328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069326), c_Groups_Ozero__class_Ozero(_1069326)), _1069330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069326), c_Groups_Ozero__class_Ozero(_1069326)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069326), _1069328), _1069330))))], (52142 ^ _779999) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (8405 ^ _779999) ^ [_923677, _923679, _923681, _923683, _923685, _923687] : [hBOOL(hAPP(hAPP(c_member(_923677), _923679), _923681)), -(hAPP(c_Fun_Ooverride__on(_923677, _923683, _923685, _923687, _923681), _923679) = hAPP(_923687, _923679))], (49005 ^ _779999) ^ [_1766595, _1766597, _1766599] : [hBOOL(hAPP(hAPP(c_member(_1766595), _1766597), hAPP(c_List_Oset(_1766595), _1766599))), -(c_List_Oinsert(_1766595, _1766597, _1766599) = _1766599)], (45556 ^ _779999) ^ [_1692608, _1692610, _1692612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692608), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692610)), _1692612))), -(hAPP(hAPP(c_List_Oappend(_1692610), hAPP(hAPP(c_List_Otake(_1692610), _1692608), _1692612)), hAPP(hAPP(c_List_Olist_OCons(_1692610), hAPP(c_List_Ohd(_1692610), hAPP(hAPP(c_List_Odrop(_1692610), _1692608), _1692612))), c_List_Olist_ONil(_1692610))) = hAPP(hAPP(c_List_Otake(_1692610), hAPP(c_Nat_OSuc, _1692608)), _1692612))], (8990 ^ _779999) ^ [_933782, _933784, _933786] : [class_Orderings_Opreorder(_933782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933782), _933784), _933786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933782), _933786), _933784))], (14852 ^ _779999) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3042 ^ _779999) ^ [_825308, _825310, _825312, _825314] : [-(c_Relation_ODomain(_825314, _825310) = c_Relation_ODomain(_825312, _825308)), _825314 = _825312, _825310 = _825308], (43866 ^ _779999) ^ [_1652602, _1652604, _1652606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652602), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652604)), _1652606))), -(hBOOL(hAPP(hAPP(c_member(_1652604), hAPP(hAPP(c_List_Onth(_1652604), _1652606), _1652602)), hAPP(c_List_Oset(_1652604), _1652606))))], (31239 ^ _779999) ^ [_1365250, _1365252] : [31240 ^ _779999 : [(31241 ^ _779999) ^ [_1365299] : [_1365250 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1365252), _1365299)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365250, _1365252) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11244 ^ _779999) ^ [_974853, _974855, _974857, _974859] : [class_Lattices_Osemilattice__inf(_974853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974853), _974855), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974853), _974857), _974859))), 11251 ^ _779999 : [(11254 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974853), _974855), _974859)))], (11252 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974853), _974855), _974857)))]]], (27956 ^ _779999) ^ [_1305593, _1305595, _1305597] : [class_Rings_Olinordered__semidom(_1305593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305593), c_Groups_Oone__class_Oone(_1305593)), _1305595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305593), c_Groups_Oone__class_Oone(_1305593)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305593), _1305595), hAPP(hAPP(c_Power_Opower__class_Opower(_1305593), _1305595), _1305597)))))], (40771 ^ _779999) ^ [_1574451, _1574453, _1574455, _1574457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574451, _1574451)), hAPP(hAPP(c_Product__Type_OPair(_1574451, _1574451), _1574453), _1574455)), c_Transitive__Closure_Ortrancl(_1574451, hAPP(c_Relation_Oconverse(_1574451, _1574451), _1574457)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574451, _1574451)), hAPP(hAPP(c_Product__Type_OPair(_1574451, _1574451), _1574455), _1574453)), c_Transitive__Closure_Ortrancl(_1574451, _1574457))))], (24954 ^ _779999) ^ [_1248367, _1248369, _1248371] : [class_Orderings_Olinorder(_1248367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248367), _1248369)), hBOOL(hAPP(hAPP(c_member(_1248367), _1248371), _1248369)), 24965 ^ _779999 : [(24972 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248367, tc_HOL_Obool)), _1248369), hAPP(hAPP(c_Set_Oinsert(_1248367), _1248371), c_Orderings_Obot__class_Obot(tc_fun(_1248367, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1248367, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1248367, c_Orderings_Oord__class_Omax(_1248367), _1248369) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1248367), _1248371), c_Big__Operators_Olattice_OSup__fin(_1248367, c_Orderings_Oord__class_Omax(_1248367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248367, tc_HOL_Obool)), _1248369), hAPP(hAPP(c_Set_Oinsert(_1248367), _1248371), c_Orderings_Obot__class_Obot(tc_fun(_1248367, tc_HOL_Obool)))))))], (24966 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248367, tc_HOL_Obool)), _1248369), hAPP(hAPP(c_Set_Oinsert(_1248367), _1248371), c_Orderings_Obot__class_Obot(tc_fun(_1248367, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1248367, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1248367, c_Orderings_Oord__class_Omax(_1248367), _1248369) = _1248371)]]], (50573 ^ _779999) ^ [_1802260, _1802262] : [c_Relation_Otrans(_1802260, _1802262), -(c_Relation_Otrans(tc_List_Olist(_1802260), c_List_Olexord(_1802260, _1802262)))], (32683 ^ _779999) ^ [_1393143, _1393145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393143), _1393145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393143)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393145))))], (26592 ^ _779999) ^ [_1278310, _1278312, _1278314] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278310, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278310, tc_HOL_Obool)), _1278312), _1278314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278310, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278310, tc_HOL_Obool)), _1278312)), _1278314))], (51956 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (35753 ^ _779999) ^ [_1453764, _1453766] : [-(c_Divides_OnegDivAlg(_1453764, _1453766) = hAPP(c_Divides_Oadjust(_1453766), c_Divides_OnegDivAlg(_1453764, 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)))), _1453766)))), -(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), _1453764), _1453766)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453766), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46378 ^ _779999) ^ [_1709865, _1709867, _1709869, _1709871, _1709873, _1709875] : [-(hAPP(hAPP(c_List_Omap(_1709865, _1709867), _1709869), hAPP(hAPP(c_List_Omap(_1709871, _1709865), _1709873), _1709875)) = hAPP(hAPP(c_List_Omap(_1709871, _1709867), hAPP(c_Fun_Ocomp(_1709865, _1709867, _1709871, _1709869), _1709873)), _1709875))], (51540 ^ _779999) ^ [_1823376, _1823378] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823376), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1823378, hAPP(c_Code__Numeral_Onat__of, 51545 ^ [_1823376, _1823378]))), -(hBOOL(hAPP(_1823378, _1823376)))], (49960 ^ _779999) ^ [_1788723, _1788725, _1788727, _1788729, _1788731] : [-(c_List_Oreplicate(_1788723, _1788725, _1788727) = c_List_Oreplicate(_1788723, _1788729, _1788731)), _1788725 = _1788729, 49965 ^ _779999 : [(49968 ^ _779999) ^ [] : [_1788727 = _1788731], (49966 ^ _779999) ^ [] : [_1788725 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (49579 ^ _779999) ^ [_1780092, _1780094, _1780096] : [c_List_Olist__all(_1780092, _1780094, _1780096), 49582 ^ _779999 : [(49583 ^ _779999) ^ [_1780173] : [hBOOL(hAPP(hAPP(c_member(_1780092), _1780173), hAPP(c_List_Oset(_1780092), _1780096))), -(hBOOL(hAPP(_1780094, _1780173)))]]], (13051 ^ _779999) ^ [_1012214, _1012216, _1012218, _1012220] : [class_Groups_Ocancel__semigroup__add(_1012214), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012214), _1012216), _1012218) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012214), _1012216), _1012220), -(_1012218 = _1012220)], (17840 ^ _779999) ^ [_1104878] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1104878))))], (41966 ^ _779999) ^ [_1603204, _1603206, _1603208, _1603210, _1603212, _1603214] : [class_Complete__Lattice_Ocomplete__lattice(_1603204), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603206, tc_fun(_1603208, _1603204)), _1603210), _1603212), _1603214) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603206, _1603204), _1603210), hAPP(hAPP(c_COMBC(_1603206, _1603208, _1603204), _1603212), _1603214)))], (48572 ^ _779999) ^ [_1757673, _1757675] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1757673), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1757673))), _1757675))), -(c_List_Otranspose(_1757673, c_List_Otranspose(_1757673, _1757675)) = c_List_OtakeWhile(tc_List_Olist(_1757673), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1757673)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1757673), tc_List_Olist(_1757673), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1757673))), _1757675))], (37172 ^ _779999) ^ [_1483626, _1483628, _1483630, _1483632, _1483634, _1483636, _1483638, _1483640] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1483626, _1483628), tc_prod(_1483626, _1483628))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1483626, _1483628), tc_prod(_1483626, _1483628)), hAPP(hAPP(c_Product__Type_OPair(_1483626, _1483628), _1483630), _1483632)), hAPP(hAPP(c_Product__Type_OPair(_1483626, _1483628), _1483634), _1483636))), c_Wellfounded_Olex__prod(_1483626, _1483628, _1483638, _1483640))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483626, _1483626)), hAPP(hAPP(c_Product__Type_OPair(_1483626, _1483626), _1483630), _1483634)), _1483638))), 37179 ^ _779999 : [(37182 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483628, _1483628)), hAPP(hAPP(c_Product__Type_OPair(_1483628, _1483628), _1483632), _1483636)), _1483640)))], (37180 ^ _779999) ^ [] : [-(_1483630 = _1483634)]]], (14347 ^ _779999) ^ [_1036251, _1036253, _1036255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1036251), _1036253)), -(hBOOL(hAPP(hAPP(c_member(_1036251), _1036255), _1036253))), -(hAPP(c_Finite__Set_Ocard(_1036251), hAPP(hAPP(c_Set_Oinsert(_1036251), _1036255), _1036253)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1036251), _1036253)))], (48304 ^ _779999) ^ [_1751905, _1751907, _1751909, _1751911] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751905), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1751905))), _1751907))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751909), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1751905))), c_List_Otranspose(_1751905, _1751907)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751911), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1751905))), hAPP(c_List_Ofilter(tc_List_Olist(_1751905), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1751905)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751909)), c_Nat_Osize__class_Osize(tc_List_Olist(_1751905)))), _1751907)))), -(hAPP(hAPP(c_List_Onth(_1751905), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1751905)), c_List_Otranspose(_1751905, _1751907)), _1751909)), _1751911) = hAPP(hAPP(c_List_Onth(_1751905), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1751905)), _1751907), _1751911)), _1751909))], (41839 ^ _779999) ^ [_1599131, _1599133, _1599135, _1599137, _1599139] : [-(hAPP(c_Relation_Oconverse(_1599131, _1599133), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599135, tc_fun(tc_prod(_1599131, _1599133), tc_HOL_Obool)), _1599137), _1599139)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599135, tc_fun(tc_prod(_1599133, _1599131), tc_HOL_Obool)), _1599137), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1599131, _1599133), tc_HOL_Obool), tc_fun(tc_prod(_1599133, _1599131), tc_HOL_Obool), _1599135), c_Relation_Oconverse(_1599131, _1599133)), _1599139)))], (42032 ^ _779999) ^ [_1605206, _1605208, _1605210, _1605212, _1605214] : [42034 ^ _779999 : [(42037 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605206, tc_HOL_Obool)), _1605208), hAPP(_1605214, 42033 ^ [_1605206, _1605208, _1605210, _1605212, _1605214])))], (42035 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605210), 42033 ^ [_1605206, _1605208, _1605210, _1605212, _1605214]), _1605212)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605206, tc_HOL_Obool)), _1605208), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605210, tc_fun(_1605206, tc_HOL_Obool)), _1605212), _1605214))))], (1164 ^ _779999) ^ [_797657, _797659] : [-(class_Lattices_Obounded__lattice(_797657)), _797659 = _797657, class_Lattices_Obounded__lattice(_797659)], (33031 ^ _779999) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (30345 ^ _779999) ^ [_1348460, _1348462, _1348464] : [-(hBOOL(hAPP(_1348460, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1348462), _1348464)))), 30346 ^ _779999 : [(30353 ^ _779999) ^ [_1348628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1348464), _1348628)), _1348462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1348462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1348464), hAPP(c_Nat_OSuc, _1348628)))), hBOOL(hAPP(_1348460, _1348628))], (30347 ^ _779999) ^ [] : [_1348464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1348460, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (2302 ^ _779999) ^ [_813870, _813872, _813874, _813876] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_813876, _813872) = c_Inductive_Ocomplete__lattice__class_Ogfp(_813874, _813870)), _813876 = _813874, _813872 = _813870], (14766 ^ _779999) ^ [_1045231] : [class_Rings_Ozero__neq__one(_1045231), c_Groups_Oone__class_Oone(_1045231) = c_Groups_Ozero__class_Ozero(_1045231)], (16715 ^ _779999) ^ [_1082386, _1082388, _1082390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082386), _1082388)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082386), _1082390)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082388), _1082390))], (42628 ^ _779999) ^ [_1619607, _1619609, _1619611] : [class_Complete__Lattice_Ocomplete__lattice(_1619607), -(c_Complete__Lattice_OInf__class_OInf(_1619607, hAPP(hAPP(c_Set_Oinsert(_1619607), _1619609), hAPP(hAPP(c_Set_Oinsert(_1619607), _1619611), c_Orderings_Obot__class_Obot(tc_fun(_1619607, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1619607), _1619609), _1619611))], (11372 ^ _779999) ^ [_977563, _977565, _977567] : [11374 ^ _779999 : [(11380 ^ _779999) ^ [] : [-(11373 ^ [_977563, _977565, _977567] = 11376 ^ [_977563, _977565, _977567])], (11378 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977563), 11376 ^ [_977563, _977565, _977567]), _977567)))], (11375 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977563), 11373 ^ [_977563, _977565, _977567]), _977565)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977563, tc_HOL_Obool)), _977565), _977567) = c_Orderings_Obot__class_Obot(tc_fun(_977563, tc_HOL_Obool)))], (32141 ^ _779999) ^ [_1382485, _1382487, _1382489, _1382491] : [class_Int_Onumber__ring(_1382485), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382485), hAPP(c_Int_Onumber__class_Onumber__of(_1382485), _1382487)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382485), hAPP(c_Int_Onumber__class_Onumber__of(_1382485), _1382489)), _1382491)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382485), hAPP(c_Int_Onumber__class_Onumber__of(_1382485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382487), _1382489))), _1382491))], (10573 ^ _779999) ^ [_961954, _961956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961954), _961956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961954), hAPP(c_Nat_OSuc, _961956))))], (37286 ^ _779999) ^ [_1486590, _1486592, _1486594, _1486596, _1486598, _1486600] : [-(hAPP(c_Product__Type_Oapfst(_1486590, _1486592, _1486594, _1486596), hAPP(hAPP(c_Product__Type_OPair(_1486590, _1486594), _1486598), _1486600)) = hAPP(hAPP(c_Product__Type_OPair(_1486592, _1486594), hAPP(_1486596, _1486598)), _1486600))], (34593 ^ _779999) ^ [_1426644, _1426646, _1426648] : [class_Rings_Olinordered__idom(_1426644), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1426644), c_Groups_Ozero__class_Ozero(_1426644)), hAPP(hAPP(c_Power_Opower__class_Opower(_1426644), _1426646), 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)))), _1426648)))))], (39597 ^ _779999) ^ [_1546325, _1546327, _1546329, _1546331, _1546333, _1546335, _1546337] : [class_Groups_Oab__semigroup__mult(_1546325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546327), _1546329)), c_Fun_Oinj__on(_1546327, _1546331, _1546333, _1546329), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1546325, _1546331, c_Groups_Otimes__class_Otimes(_1546325)), _1546335), _1546337), hAPP(c_Set_Oimage(_1546327, _1546331, _1546333), _1546329)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1546325, _1546327, c_Groups_Otimes__class_Otimes(_1546325)), hAPP(c_Fun_Ocomp(_1546331, _1546325, _1546327, _1546335), _1546333)), _1546337), _1546329))], (50022 ^ _779999) ^ [_1789796, _1789798, _1789800, _1789802, _1789804] : [-(hAPP(hAPP(c_List_Omap(_1789796, _1789798), _1789800), c_List_Oreplicate(_1789796, _1789802, _1789804)) = c_List_Oreplicate(_1789798, _1789802, hAPP(_1789800, _1789804)))], (27722 ^ _779999) ^ [_1301247, _1301249, _1301251, _1301253] : [class_Fields_Ofield__inverse__zero(_1301247), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301247), _1301249), _1301251)), _1301253) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301247), hAPP(hAPP(c_Power_Opower__class_Opower(_1301247), _1301249), _1301253)), hAPP(hAPP(c_Power_Opower__class_Opower(_1301247), _1301251), _1301253)))], (38744 ^ _779999) ^ [_1526186, _1526188, _1526190, _1526192] : [class_Groups_Ocomm__monoid__add(_1526186), c_Fun_Oinj__on(_1526188, _1526186, _1526190, _1526192), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526188, _1526186), _1526190), _1526192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526186, _1526186), c_Fun_Oid(_1526186)), hAPP(c_Set_Oimage(_1526188, _1526186, _1526190), _1526192)))], (2772 ^ _779999) ^ [_821089, _821091, _821093, _821095] : [-(c_Nitpick_Onorm__frac(_821095, _821091) = c_Nitpick_Onorm__frac(_821093, _821089)), _821095 = _821093, _821091 = _821089], (4916 ^ _779999) ^ [_855027, _855029, _855031, _855033] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855033, _855029) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855031, _855027)), _855033 = _855031, _855029 = _855027], (7318 ^ _779999) ^ [_901329, _901331, _901333] : [-(hAPP(c_Set_Oimage(_901329, _901331, _901333), c_Orderings_Obot__class_Obot(tc_fun(_901329, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_901331, tc_HOL_Obool)))], (25686 ^ _779999) ^ [_1261584, _1261586] : [class_Lattices_Oboolean__algebra(_1261584), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1261584), hAPP(c_Groups_Ouminus__class_Ouminus(_1261584), _1261586)) = _1261586)], (40221 ^ _779999) ^ [_1561151, _1561153, _1561155, _1561157, _1561159] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561151, _1561151)), hAPP(hAPP(c_Product__Type_OPair(_1561151, _1561151), _1561153), _1561155)), c_Transitive__Closure_Otrancl(_1561151, _1561157))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1561151, _1561151)), hAPP(hAPP(c_Product__Type_OPair(_1561151, _1561151), _1561155), _1561159)), c_Transitive__Closure_Otrancl(_1561151, _1561157))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561151, _1561151)), hAPP(hAPP(c_Product__Type_OPair(_1561151, _1561151), _1561153), _1561159)), c_Transitive__Closure_Otrancl(_1561151, _1561157))))], (49614 ^ _779999) ^ [_1780761, _1780763, _1780765, _1780767] : [-(c_List_Olist__ex1(_1780761, _1780763, hAPP(hAPP(c_List_Olist_OCons(_1780761), _1780765), _1780767))), 49617 ^ _779999 : [(49620 ^ _779999) ^ [] : [c_List_Olist__all(_1780761, hAPP(hAPP(c_COMBS(_1780761, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780761), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1780761), c_fNot), _1780763))), hAPP(c_fequal, _1780765)), _1780767)], (49618 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1780763, _1780765)))]], 49621 ^ _779999 : [(49624 ^ _779999) ^ [] : [c_List_Olist__ex1(_1780761, _1780763, _1780767)], (49622 ^ _779999) ^ [] : [hBOOL(hAPP(_1780763, _1780765))]]], (14037 ^ _779999) ^ [_1030284, _1030286, _1030288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030288), _1030286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030284), _1030286)), _1030288)))], (51940 ^ _779999) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (25562 ^ _779999) ^ [_1259390] : [class_Groups_Ogroup__add(_1259390), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1259390), c_Groups_Ozero__class_Ozero(_1259390)) = c_Groups_Ozero__class_Ozero(_1259390))], (47058 ^ _779999) ^ [_1725062, _1725064, _1725066, _1725068] : [c_List_Olist__all2(_1725062, _1725064, _1725066, _1725068, c_List_Olist_ONil(_1725064)), -(_1725068 = c_List_Olist_ONil(_1725062))], (7631 ^ _779999) ^ [_908247] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _908247)], (39693 ^ _779999) ^ [_1548655, _1548657, _1548659, _1548661, _1548663, _1548665] : [c_Finite__Set_Ofolding(_1548655, _1548657, _1548659, _1548661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548655), _1548663)), -(hAPP(c_Fun_Ocomp(_1548657, _1548657, _1548657, hAPP(_1548659, _1548665)), hAPP(_1548661, _1548663)) = hAPP(c_Fun_Ocomp(_1548657, _1548657, _1548657, hAPP(_1548661, _1548663)), hAPP(_1548659, _1548665)))], (52010 ^ _779999) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (10988 ^ _779999) ^ [_969871, _969873, _969875, _969877, _969879] : [class_Lattices_Olattice(_969871), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969873, _969871)), _969875), _969877), _969879) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969871), hAPP(_969875, _969879)), hAPP(_969877, _969879)))], (6057 ^ _779999) ^ [_876403, _876405, _876407] : [class_Orderings_Oorder(_876403), 6060 ^ _779999 : [(6069 ^ _779999) ^ [] : [-(_876405 = _876407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876403), _876405), _876407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876403), _876407), _876405))], (6061 ^ _779999) ^ [] : [_876405 = _876407, 6064 ^ _779999 : [(6067 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876403), _876407), _876405)))], (6065 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876403), _876405), _876407)))]]]]], (32793 ^ _779999) ^ [_1395123] : [-(c_Int_OBit1(_1395123) = 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)), _1395123)), _1395123))], (52320 ^ _779999) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (34101 ^ _779999) ^ [_1417812] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1417812)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417812))))], (38703 ^ _779999) ^ [_1525155, _1525157, _1525159, _1525161] : [-(c_Fun_Oinj__on(_1525155, tc_prod(_1525157, _1525155), 38701 ^ [_1525155, _1525157, _1525159, _1525161], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525157, tc_fun(_1525155, tc_HOL_Obool)), _1525159), _1525161)))], (25784 ^ _779999) ^ [_1263220, _1263222, _1263224] : [class_Rings_Oring(_1263220), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1263220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263220), _1263222), _1263224)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263220), _1263222), hAPP(c_Groups_Ouminus__class_Ouminus(_1263220), _1263224)))], (16097 ^ _779999) ^ [_1070601, _1070603, _1070605, _1070607] : [class_Rings_Oordered__semiring(_1070601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070601), _1070603), _1070605)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070601), c_Groups_Ozero__class_Ozero(_1070601)), _1070607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070601), _1070603), _1070607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070601), _1070605), _1070607))))], (18325 ^ _779999) ^ [_1113492, _1113494, _1113496, _1113498] : [class_Orderings_Olinorder(_1113492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113492), _1113494), _1113496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113492), _1113496), _1113498)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1113492, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1113492, _1113494), _1113496)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1113492, _1113496), _1113498)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1113492, _1113494), _1113498))], (19601 ^ _779999) ^ [_1137317, _1137319, _1137321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137317)), 19604 ^ _779999 : [(19605 ^ _779999) ^ [_1137451] : [19607 ^ _779999 : [(19613 ^ _779999) ^ [] : [-(_1137451 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19609 ^ [_1137317, _1137319, _1137321, _1137451]), 19606 ^ [_1137317, _1137319, _1137321, _1137451]))], (19611 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19609 ^ [_1137317, _1137319, _1137321, _1137451]), _1137319)))], (19608 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19606 ^ [_1137317, _1137319, _1137321, _1137451]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1137317))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137451), _1137321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1137451), _1137317)), _1137321)))]]], (29544 ^ _779999) ^ [_1334463, _1334465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334463), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29547 ^ _779999 : [(29554 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334465), 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), _1334465), _1334463))))], (29548 ^ _779999) ^ [] : [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), _1334465), _1334463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334465), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15299 ^ _779999) ^ [_1054868, _1054870, _1054872] : [class_Rings_Oring__1(_1054868), hBOOL(hAPP(hAPP(c_member(_1054868), _1054870), c_Int_Oring__1__class_OInts(_1054868))), hBOOL(hAPP(hAPP(c_member(_1054868), _1054872), c_Int_Oring__1__class_OInts(_1054868))), -(hBOOL(hAPP(hAPP(c_member(_1054868), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054868), _1054870), _1054872)), c_Int_Oring__1__class_OInts(_1054868))))], (44616 ^ _779999) ^ [_1670434, _1670436] : [_1670436 = c_List_Olist_ONil(_1670434), -(c_Orderings_Obot__class_Obot(tc_fun(_1670434, tc_HOL_Obool)) = hAPP(c_List_Oset(_1670434), _1670436))], (18869 ^ _779999) ^ [_1124358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124358), 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)), _1124358)), _1124358)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39947 ^ _779999) ^ [_1554509, _1554511, _1554513, _1554515, _1554517, _1554519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554509, tc_HOL_Obool)), _1554511), _1554513)), 39953 ^ _779999 : [(39956 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554515, tc_HOL_Obool)), hAPP(_1554517, 39952 ^ [_1554509, _1554511, _1554513, _1554515, _1554517, _1554519])), hAPP(_1554519, 39952 ^ [_1554509, _1554511, _1554513, _1554515, _1554517, _1554519])))], (39954 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554509), 39952 ^ [_1554509, _1554511, _1554513, _1554515, _1554517, _1554519]), _1554511)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554509, _1554515), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1554509, _1554515), _1554511), _1554517)), hAPP(hAPP(c_Product__Type_OSigma(_1554509, _1554515), _1554513), _1554519))))], (36248 ^ _779999) ^ [_1462434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1462434)), 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), _1462434)) = 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), _1462434))))))], (7179 ^ _779999) ^ [_898373, _898375, _898377] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898373, tc_HOL_Obool)), _898375), hAPP(hAPP(c_Set_Oinsert(_898373), _898377), _898375))))], (23793 ^ _779999) ^ [_1224332, _1224334, _1224336] : [class_Orderings_Olinorder(_1224332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224332), _1224334)), -(hBOOL(hAPP(hAPP(c_member(_1224332), _1224336), _1224334))), -(_1224334 = c_Orderings_Obot__class_Obot(tc_fun(_1224332, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1224332, hAPP(hAPP(c_Set_Oinsert(_1224332), _1224336), _1224334)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224332), _1224336), c_Big__Operators_Olinorder__class_OMin(_1224332, _1224334)))], (29118 ^ _779999) ^ [_1326859, _1326861, _1326863, _1326865] : [class_Fields_Ofield(_1326859), -(_1326861 = c_Groups_Ozero__class_Ozero(_1326859)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1326859), _1326863), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326859), _1326865), _1326861)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1326859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326859), _1326861), _1326863)), _1326865)), _1326861))], (44109 ^ _779999) ^ [_1659873, _1659875, _1659877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659873), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1659875))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1659875), _1659873), _1659877)) = 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), _1659875)), _1659877)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1659875), _1659873)))], (30639 ^ _779999) ^ [_1354436, _1354438] : [-(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, _1354436, _1354438)), _1354438) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354436), _1354438))], (52250 ^ _779999) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40285 ^ _779999) ^ [_1563442, _1563444, _1563446, _1563448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563442, _1563442)), hAPP(hAPP(c_Product__Type_OPair(_1563442, _1563442), _1563444), _1563446)), c_Transitive__Closure_Otrancl(_1563442, _1563448))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563442, _1563442)), hAPP(hAPP(c_Product__Type_OPair(_1563442, _1563442), _1563444), _1563446)), c_Transitive__Closure_Ortrancl(_1563442, _1563448))))], (45352 ^ _779999) ^ [_1687570, _1687572] : [hBOOL(hAPP(c_List_Odistinct(_1687570), hAPP(c_List_Orotate1(_1687570), _1687572))), -(hBOOL(hAPP(c_List_Odistinct(_1687570), _1687572)))], (33791 ^ _779999) ^ [_1412332, _1412334] : [c_Int_Oiszero(_1412332, hAPP(c_Int_Onumber__class_Onumber__of(_1412332), c_Int_OBit1(_1412334))), class_Int_Onumber__ring(_1412332), class_Int_Oring__char__0(_1412332)], (22876 ^ _779999) ^ [_1205028, _1205030, _1205032, _1205034, _1205036] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205028, tc_fun(_1205030, tc_HOL_Obool)), _1205032), hAPP(hAPP(c_COMBS(_1205028, tc_fun(_1205030, tc_HOL_Obool), tc_fun(_1205030, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205030, tc_HOL_Obool), tc_fun(tc_fun(_1205030, tc_HOL_Obool), tc_fun(_1205030, tc_HOL_Obool)), _1205028), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1205030, tc_HOL_Obool))), _1205034)), _1205036)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1205030, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205028, tc_fun(_1205030, tc_HOL_Obool)), _1205032), _1205034)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205028, tc_fun(_1205030, tc_HOL_Obool)), _1205032), _1205036)))], (6544 ^ _779999) ^ [_885729, _885731, _885733, _885735, _885737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885729, tc_HOL_Obool)), _885731), _885733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885735, tc_HOL_Obool)), hAPP(c_Set_Oimage(_885729, _885735, _885737), _885731)), hAPP(c_Set_Oimage(_885729, _885735, _885737), _885733))))], (5560 ^ _779999) ^ [_865149, _865151] : [_865151 = _865149, -(c_Groups_Ouminus__class_Ouminus(_865151) = c_Groups_Ouminus__class_Ouminus(_865149))], (27728 ^ _779999) ^ [_1301406, _1301408, _1301410] : [class_Rings_Olinordered__idom(_1301406), -(hAPP(c_Groups_Oabs__class_Oabs(_1301406), hAPP(hAPP(c_Power_Opower__class_Opower(_1301406), _1301408), _1301410)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301406), hAPP(c_Groups_Oabs__class_Oabs(_1301406), _1301408)), _1301410))], (18705 ^ _779999) ^ [_1121233, _1121235, _1121237] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121233), _1121235))), 18708 ^ _779999 : [(18715 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121237), _1121235))), -(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)), _1121233)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1121237), _1121235)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (18709 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121237), _1121235)), -(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)), _1121233)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1121237), _1121235)) = 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))))]]], (30820 ^ _779999) ^ [_1357793, _1357795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357793)), -(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, _1357795, _1357793))))], (8734 ^ _779999) ^ [_929581, _929583, _929585, _929587] : [c_Orderings_Oorder__class_Omono(tc_fun(_929581, tc_HOL_Obool), tc_fun(_929581, tc_HOL_Obool), _929583), hBOOL(hAPP(hAPP(c_member(_929581), _929585), _929587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929581, tc_HOL_Obool)), _929587), hAPP(_929583, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929581, tc_HOL_Obool)), _929587), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929581, tc_HOL_Obool), _929583))))), -(hBOOL(hAPP(hAPP(c_member(_929581), _929585), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929581, tc_HOL_Obool), _929583))))], (51972 ^ _779999) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (20148 ^ _779999) ^ [_1147021, _1147023] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1147021, _1147023) = 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), _1147021), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147023))))], (14796 ^ _779999) ^ [_1045644] : [-(hAPP(c_Nat_OSuc, _1045644) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1045644))], (13413 ^ _779999) ^ [_1018827, _1018829, _1018831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018827), _1018829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018827), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018831), _1018829))))], (23477 ^ _779999) ^ [_1218373, _1218375, _1218377, _1218379, _1218381] : [hAPP(_1218379, _1218375) = _1218381, -(hBOOL(hAPP(hAPP(c_member(_1218373), _1218375), hAPP(c_Set_Ovimage(_1218373, _1218377, _1218379), hAPP(hAPP(c_Set_Oinsert(_1218377), _1218381), c_Orderings_Obot__class_Obot(tc_fun(_1218377, tc_HOL_Obool)))))))], (36639 ^ _779999) ^ [_1470218, _1470220, _1470222] : [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), _1470218), _1470220))), -(hBOOL(hAPP(hAPP(_1470222, _1470218), _1470220))), 36646 ^ _779999 : [(36649 ^ _779999) ^ [] : [-(36645 ^ [_1470218, _1470220, _1470222] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1470222, 36645 ^ [_1470218, _1470220, _1470222]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36644 ^ [_1470218, _1470220, _1470222], 36645 ^ [_1470218, _1470220, _1470222]))))], (36655 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1470222, 36644 ^ [_1470218, _1470220, _1470222]), 36645 ^ [_1470218, _1470220, _1470222]))], (36647 ^ _779999) ^ [] : [-(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), 36644 ^ [_1470218, _1470220, _1470222]), 36645 ^ [_1470218, _1470220, _1470222]))))]]], (30802 ^ _779999) ^ [_1357505, _1357507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357505)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357505), _1357507)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357505, _1357507) = _1357505)], (51365 ^ _779999) ^ [_1819017, _1819019, _1819021] : [hAPP(_1819021, hAPP(c_Hilbert__Choice_Oinv__into(_1819017, _1819019, c_Orderings_Otop__class_Otop(tc_fun(_1819017, tc_HOL_Obool)), _1819021), 51366 ^ [_1819017, _1819019, _1819021])) = 51366 ^ [_1819017, _1819019, _1819021], -(hAPP(c_Set_Oimage(_1819017, _1819019, _1819021), c_Orderings_Otop__class_Otop(tc_fun(_1819017, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1819019, tc_HOL_Obool)))], (17846 ^ _779999) ^ [_1104966, _1104968, _1104970] : [class_Orderings_Olinorder(_1104966), 17849 ^ _779999 : [(17856 ^ _779999) ^ [] : [_1104968 = _1104970, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1104966), _1104968) = hAPP(c_SetInterval_Oord__class_OlessThan(_1104966), _1104970))], (17850 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1104966), _1104968) = hAPP(c_SetInterval_Oord__class_OlessThan(_1104966), _1104970), -(_1104968 = _1104970)]]], (44021 ^ _779999) ^ [_1658062, _1658064] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1658062, _1658064) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1658062, _1658064)))], (43117 ^ _779999) ^ [_1630709, _1630711, _1630713] : [-(c_Product__Type_Ointernal__split(_1630709, _1630711, _1630713) = c_Product__Type_Oprod_Oprod__case(_1630709, _1630711, _1630713))], (42668 ^ _779999) ^ [_1620290, _1620292] : [class_Complete__Lattice_Ocomplete__lattice(_1620290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620290), _1620292)), -(_1620292 = c_Orderings_Obot__class_Obot(tc_fun(_1620290, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1620290, _1620292) = c_Complete__Lattice_OInf__class_OInf(_1620290, _1620292))], (39523 ^ _779999) ^ [_1544666, _1544668, _1544670, _1544672, _1544674, _1544676] : [class_Groups_Ocomm__monoid__mult(_1544666), c_Fun_Oinj__on(_1544668, _1544670, _1544672, _1544674), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544670, _1544666), _1544676), hAPP(c_Set_Oimage(_1544668, _1544670, _1544672), _1544674)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544668, _1544666), hAPP(c_Fun_Ocomp(_1544670, _1544666, _1544668, _1544676), _1544672)), _1544674))], (47649 ^ _779999) ^ [_1739696, _1739698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1739696), _1739698)), -(c_List_Oupt(_1739696, hAPP(c_Nat_OSuc, _1739698)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1739696, _1739698)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1739698), c_List_Olist_ONil(tc_Nat_Onat))))], (36503 ^ _779999) ^ [_1467684, _1467686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467684), 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)), _1467686)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467684), _1467686) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1467684, _1467686)))], (13375 ^ _779999) ^ [_1018110, _1018112, _1018114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018110), _1018112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018112), _1018114))))], (51029 ^ _779999) ^ [_1812828, _1812830] : [-(c_Relation_Osym(_1812828, c_Relation_OId__on(_1812828, _1812830)))], (3870 ^ _779999) ^ [_838184, _838186, _838188, _838190] : [-(c_List_Olist__update(_838190, _838186) = c_List_Olist__update(_838188, _838184)), _838190 = _838188, _838186 = _838184], (37517 ^ _779999) ^ [_1491643, _1491645, _1491647, _1491649] : [c_Wellfounded_Omax__extp(_1491643, hAPP(hAPP(c_COMBC(_1491643, tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_fun(_1491643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491643, tc_fun(tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_fun(_1491643, tc_HOL_Obool)), _1491643), c_COMBC(_1491643, tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491643, tc_prod(_1491643, _1491643)), tc_fun(_1491643, tc_fun(tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_HOL_Obool)), _1491643), hAPP(c_COMBB(tc_prod(_1491643, _1491643), tc_fun(tc_fun(tc_prod(_1491643, _1491643), tc_HOL_Obool), tc_HOL_Obool), _1491643), c_member(tc_prod(_1491643, _1491643)))), c_Product__Type_OPair(_1491643, _1491643)))), _1491645), _1491647, _1491649), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1491643, tc_HOL_Obool), tc_fun(_1491643, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1491643, tc_HOL_Obool), tc_fun(_1491643, tc_HOL_Obool)), _1491647), _1491649)), c_Wellfounded_Omax__ext(_1491643, _1491645))))], (51644 ^ _779999) ^ [_1825431, _1825433, _1825435, _1825437, _1825439, _1825441, _1825443, _1825445] : [c_Fun_Obij__betw(_1825431, _1825433, _1825435, _1825437, _1825439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1825431, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1825441, _1825431, _1825443), _1825445)), _1825437)), 51651 ^ _779999 : [(51658 ^ _779999) ^ [] : [c_Fun_Obij__betw(_1825441, _1825433, hAPP(c_Fun_Ocomp(_1825431, _1825433, _1825441, _1825435), _1825443), _1825445, _1825439), -(c_Fun_Obij__betw(_1825441, _1825431, _1825443, _1825445, _1825437))], (51652 ^ _779999) ^ [] : [c_Fun_Obij__betw(_1825441, _1825431, _1825443, _1825445, _1825437), -(c_Fun_Obij__betw(_1825441, _1825433, hAPP(c_Fun_Ocomp(_1825431, _1825433, _1825441, _1825435), _1825443), _1825445, _1825439))]]], (4254 ^ _779999) ^ [_844470, _844472, _844474, _844476, _844478, _844480, _844482, _844484] : [-(c_New__DSequence_Opos__decr__bind(_844484, _844480, _844476, _844472) = c_New__DSequence_Opos__decr__bind(_844482, _844478, _844474, _844470)), _844484 = _844482, _844480 = _844478, _844476 = _844474, _844472 = _844470], (50929 ^ _779999) ^ [_1810485, _1810487] : [c_Relation_Oantisym(_1810485, _1810487), 50932 ^ _779999 : [(50933 ^ _779999) ^ [_1810597, _1810599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1810485, _1810485)), hAPP(hAPP(c_Product__Type_OPair(_1810485, _1810485), _1810599), _1810597)), _1810487)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810485, _1810485)), hAPP(hAPP(c_Product__Type_OPair(_1810485, _1810485), _1810597), _1810599)), _1810487)), -(_1810599 = _1810597)]]], (41980 ^ _779999) ^ [_1603646, _1603648, _1603650, _1603652, _1603654] : [-(hAPP(hAPP(c_Set_Oinsert(_1603646), _1603648), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603650, tc_fun(_1603646, tc_HOL_Obool)), _1603652), _1603654)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603650, tc_fun(_1603646, tc_HOL_Obool)), _1603652), hAPP(hAPP(c_COMBB(tc_fun(_1603646, tc_HOL_Obool), tc_fun(_1603646, tc_HOL_Obool), _1603650), hAPP(c_Set_Oinsert(_1603646), _1603648)), _1603654)))], (29922 ^ _779999) ^ [_1341065, _1341067, _1341069] : [class_Int_Oring__char__0(_1341065), 29925 ^ _779999 : [(29932 ^ _779999) ^ [] : [_1341067 = _1341069, -(hAPP(c_Int_Oring__1__class_Oof__int(_1341065), _1341067) = hAPP(c_Int_Oring__1__class_Oof__int(_1341065), _1341069))], (29926 ^ _779999) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1341065), _1341067) = hAPP(c_Int_Oring__1__class_Oof__int(_1341065), _1341069), -(_1341067 = _1341069)]]], (5899 ^ _779999) ^ [_873949, _873951, _873953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873949, tc_HOL_Obool)), _873951), _873953)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873949, tc_HOL_Obool)), _873951), _873953) = _873953)], (21104 ^ _779999) ^ [_1163521, _1163523, _1163525] : [class_Orderings_Oorder(_1163521), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1163521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1163521), _1163523)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1163521, _1163523, _1163525)) = c_Orderings_Obot__class_Obot(tc_fun(_1163521, tc_HOL_Obool)))], (22645 ^ _779999) ^ [_1199143, _1199145, _1199147, _1199149, _1199151] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199143, tc_fun(_1199145, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1199143), _1199147), _1199149)), _1199151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199145, tc_HOL_Obool)), hAPP(_1199151, _1199147)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199143, tc_fun(_1199145, tc_HOL_Obool)), _1199149), _1199151)))], (38293 ^ _779999) ^ [_1512398, _1512400, _1512402, _1512404, _1512406] : [hBOOL(hAPP(hAPP(_1512398, _1512400), _1512402)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1512404, _1512406, _1512398), _1512402)))], (41272 ^ _779999) ^ [_1587501, _1587503, _1587505, _1587507, _1587509, _1587511] : [c_Finite__Set_Ofolding(_1587501, _1587503, _1587505, _1587507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587501), _1587509)), -(hAPP(hAPP(_1587507, _1587509), _1587511) = hAPP(hAPP(c_Finite__Set_Ofold(_1587501, _1587503, _1587505), _1587511), _1587509))], (24646 ^ _779999) ^ [_1241647, _1241649] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1241647), hAPP(c_Nat_OSuc, _1241649)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1241649), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), _1241649)), _1241647))], (26652 ^ _779999) ^ [_1279648, _1279650, _1279652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279648), _1279650)), 26655 ^ _779999 : [(26656 ^ _779999) ^ [] : [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(_1279648, tc_Nat_Onat), _1279652), _1279650))), 26659 ^ _779999 : [(26660 ^ _779999) ^ [_1279816] : [hBOOL(hAPP(hAPP(c_member(_1279648), _1279816), _1279650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1279652, _1279816))))]]], (26666 ^ _779999) ^ [] : [26668 ^ _779999 : [(26671 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1279652, 26667 ^ [_1279648, _1279650, _1279652])))], (26669 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1279648), 26667 ^ [_1279648, _1279650, _1279652]), _1279650)))]], -(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(_1279648, tc_Nat_Onat), _1279652), _1279650))))]]], (47552 ^ _779999) ^ [_1736531, _1736533] : [47554 ^ _779999 : [(47557 ^ _779999) ^ [] : [47553 ^ [_1736531, _1736533] = c_List_Olist_ONil(_1736531)], (47555 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1736531)), 47553 ^ [_1736531, _1736533]), hAPP(c_List_Oset(tc_List_Olist(_1736531)), _1736533))))]], -(c_List_Otranspose(_1736531, _1736533) = c_List_Olist_ONil(tc_List_Olist(_1736531)))], (34161 ^ _779999) ^ [_1418841, _1418843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1418841)), c_Int_OBit1(_1418843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1418841), _1418843)))], (42763 ^ _779999) ^ [_1622686, _1622688, _1622690, _1622692] : [-(_1622686 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1622688, tc_HOL_Obool), tc_HOL_Obool))), 42769 ^ _779999 : [(42772 ^ _779999) ^ [] : [c_Fun_Oinj__on(_1622688, _1622690, _1622692, 42768 ^ [_1622686, _1622688, _1622690, _1622692])], (42770 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1622688, tc_HOL_Obool)), 42768 ^ [_1622686, _1622688, _1622690, _1622692]), _1622686)))]], -(c_Fun_Oinj__on(_1622688, _1622690, _1622692, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1622688, tc_HOL_Obool), _1622686)))], (20228 ^ _779999) ^ [_1148298, _1148300] : [-(hAPP(c_Int_Onat, _1148298) = _1148300), 20231 ^ _779999 : [(20234 ^ _779999) ^ [] : [_1148298 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148300)], (20232 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148298)))]], 20235 ^ _779999 : [(20238 ^ _779999) ^ [] : [_1148300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20236 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148298))]]], (28260 ^ _779999) ^ [_1311214, _1311216, _1311218, _1311220] : [class_Fields_Olinordered__field(_1311214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311214), c_Groups_Ozero__class_Ozero(_1311214)), _1311216)), 28267 ^ _779999 : [(28274 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311214), _1311218), _1311216)), _1311220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311214), _1311218), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311214), _1311220), _1311216))))], (28268 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311214), _1311218), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311214), _1311220), _1311216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311214), _1311218), _1311216)), _1311220)))]]], (18981 ^ _779999) ^ [_1126200, _1126202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126200), _1126202)), 18984 ^ _779999 : [(18987 ^ _779999) ^ [] : [_1126200 = _1126202], (18985 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126200), _1126202)))]]], (29616 ^ _779999) ^ [_1335606, _1335608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335606)), 29619 ^ _779999 : [(29626 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335606), _1335608)), -(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), _1335608), _1335606))))], (29620 ^ _779999) ^ [] : [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), _1335608), _1335606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335606), _1335608)))]]], (46037 ^ _779999) ^ [_1702240, _1702242] : [-(_1702240 = c_List_Olist_ONil(_1702242)), -(c_List_Olast(_1702242, _1702240) = hAPP(hAPP(c_List_Onth(_1702242), _1702240), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702242)), _1702240)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (40717 ^ _779999) ^ [_1573112, _1573114, _1573116] : [c_Relation_Orefl__on(_1573112, _1573114, _1573116), -(c_Relation_Orefl__on(_1573112, _1573114, hAPP(c_Relation_Oconverse(_1573112, _1573112), _1573116)))], (48036 ^ _779999) ^ [_1746522, _1746524, _1746526, _1746528, _1746530] : [class_Orderings_Olinorder(_1746522), 48039 ^ _779999 : [(48046 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1746522, hAPP(hAPP(c_List_Omap(_1746524, _1746522), _1746526), _1746530)), -(c_List_Olinorder__class_Osorted(_1746522, hAPP(hAPP(c_List_Omap(_1746524, _1746522), _1746526), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1746524, _1746522, _1746526), _1746528), _1746530))))], (48040 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1746522, hAPP(hAPP(c_List_Omap(_1746524, _1746522), _1746526), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1746524, _1746522, _1746526), _1746528), _1746530))), -(c_List_Olinorder__class_Osorted(_1746522, hAPP(hAPP(c_List_Omap(_1746524, _1746522), _1746526), _1746530)))]]], (12021 ^ _779999) ^ [_991791, _991793, _991795, _991797, _991799] : [c_Finite__Set_Ofolding__one(_991791, _991793, _991795), hBOOL(hAPP(c_Finite__Set_Ofinite(_991791), _991797)), hBOOL(hAPP(c_Finite__Set_Ofinite(_991791), _991799)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_991791, tc_HOL_Obool)), _991797), _991799) = c_Orderings_Obot__class_Obot(tc_fun(_991791, tc_HOL_Obool))), -(hAPP(hAPP(_991793, hAPP(_991795, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991791, tc_HOL_Obool)), _991797), _991799))), hAPP(_991795, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_991791, tc_HOL_Obool)), _991797), _991799))) = hAPP(hAPP(_991793, hAPP(_991795, _991797)), hAPP(_991795, _991799)))], (40765 ^ _779999) ^ [_1574270, _1574272, _1574274, _1574276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574270, _1574270)), hAPP(hAPP(c_Product__Type_OPair(_1574270, _1574270), _1574272), _1574274)), c_Transitive__Closure_Ortrancl(_1574270, _1574276))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574270, _1574270)), hAPP(hAPP(c_Product__Type_OPair(_1574270, _1574270), _1574274), _1574272)), c_Transitive__Closure_Ortrancl(_1574270, hAPP(c_Relation_Oconverse(_1574270, _1574270), _1574276)))))], (8774 ^ _779999) ^ [_930436, _930438, _930440, _930442] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930436, tc_HOL_Obool)), _930438), hAPP(hAPP(c_Set_Oinsert(_930436), _930440), _930442)))), 8777 ^ _779999 : [(8780 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930436, tc_HOL_Obool)), _930438), _930442))], (8778 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930436), _930440), _930442)))]], 8781 ^ _779999 : [(8784 ^ _779999) ^ [] : [8785 ^ _779999 : [(8788 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930436, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930436, tc_HOL_Obool)), _930438), hAPP(hAPP(c_Set_Oinsert(_930436), _930440), c_Orderings_Obot__class_Obot(tc_fun(_930436, tc_HOL_Obool))))), _930442))], (8786 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930436), _930440), _930438)))]], 8789 ^ _779999 : [(8792 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930436, tc_HOL_Obool)), _930438), _930442))], (8790 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_930436), _930440), _930438))]]], (8782 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_930436), _930440), _930442))]]], (18699 ^ _779999) ^ [_1121081, _1121083, _1121085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121081), _1121083)), -(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)), _1121081)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1121085), _1121083)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121085), _1121081)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121083), _1121081)))], (20120 ^ _779999) ^ [_1146552, _1146554] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146552) = _1146554), _1146552 = hAPP(c_Int_Onat, _1146554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146554))], (44312 ^ _779999) ^ [_1664479, _1664481, _1664483] : [hBOOL(hAPP(c_List_Odistinct(_1664479), hAPP(hAPP(c_List_Olist_OCons(_1664479), _1664481), _1664483))), 44315 ^ _779999 : [(44318 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664479), _1664483)))], (44316 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1664479), _1664481), hAPP(c_List_Oset(_1664479), _1664483)))]]], (40842 ^ _779999) ^ [_1576501, _1576503, _1576505] : [c_Relation_Ototal__on(_1576501, _1576503, _1576505), -(c_Relation_Ototal__on(_1576501, _1576503, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576501, _1576501), tc_HOL_Obool)), _1576505), c_Relation_OId(_1576501))))], (34139 ^ _779999) ^ [_1418392] : [-(c_Int_Osucc(c_Int_OBit0(_1418392)) = c_Int_OBit1(_1418392))], (26566 ^ _779999) ^ [_1277657, _1277659] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277657, tc_HOL_Obool)), _1277659), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277657, tc_HOL_Obool)), _1277659)) = c_Orderings_Otop__class_Otop(tc_fun(_1277657, tc_HOL_Obool)))], (36092 ^ _779999) ^ [_1459549, _1459551, _1459553, _1459555] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459549, _1459551), _1459553)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459549, _1459551), _1459555)), -(_1459553 = _1459555)], (47196 ^ _779999) ^ [_1728056] : [-(c_List_Oremdups(_1728056, c_List_Olist_ONil(_1728056)) = c_List_Olist_ONil(_1728056))], (15817 ^ _779999) ^ [_1065108, _1065110] : [15818 ^ _779999 : [(15821 ^ _779999) ^ [] : [_1065110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15819 ^ _779999) ^ [] : [_1065108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065108), _1065110) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22861 ^ _779999) ^ [_1204527, _1204529, _1204531, _1204533, _1204535] : [22863 ^ _779999 : [(22866 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204527, tc_HOL_Obool)), hAPP(_1204533, 22862 ^ [_1204527, _1204529, _1204531, _1204533, _1204535])), _1204535))], (22864 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1204529), 22862 ^ [_1204527, _1204529, _1204531, _1204533, _1204535]), _1204531)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204527, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204529, tc_fun(_1204527, tc_HOL_Obool)), _1204531), _1204533)), _1204535)))], (46518 ^ _779999) ^ [_1713114, _1713116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1713114)), hAPP(c_Code__Numeral_Oof__nat, _1713116)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1713114), _1713116)))], (22437 ^ _779999) ^ [_1195077, _1195079, _1195081, _1195083] : [c_Fun_Oinj__on(_1195077, _1195079, _1195081, c_Orderings_Otop__class_Otop(tc_fun(_1195077, tc_HOL_Obool))), 22440 ^ _779999 : [(22454 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1195079), _1195083), hAPP(c_Set_Oimage(_1195077, _1195079, _1195081), c_Orderings_Otop__class_Otop(tc_fun(_1195077, tc_HOL_Obool)))))), 22455 ^ _779999 : [(22456 ^ _779999) ^ [_1195480] : [_1195083 = hAPP(_1195081, _1195480), 22460 ^ _779999 : [(22463 ^ _779999) ^ [] : [22459 ^ [_1195077, _1195079, _1195081, _1195083, _1195480] = _1195480], (22461 ^ _779999) ^ [] : [-(_1195083 = hAPP(_1195081, 22459 ^ [_1195077, _1195079, _1195081, _1195083, _1195480]))]]]]], (22441 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1195079), _1195083), hAPP(c_Set_Oimage(_1195077, _1195079, _1195081), c_Orderings_Otop__class_Otop(tc_fun(_1195077, tc_HOL_Obool))))), 22445 ^ _779999 : [(22448 ^ _779999) ^ [_1195342] : [_1195083 = hAPP(_1195081, _1195342), -(_1195342 = 22444 ^ [_1195077, _1195079, _1195081, _1195083])], (22446 ^ _779999) ^ [] : [-(_1195083 = hAPP(_1195081, 22444 ^ [_1195077, _1195079, _1195081, _1195083]))]]]]], (26404 ^ _779999) ^ [_1274685] : [class_Lattices_Oboolean__algebra(_1274685), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1274685), c_Orderings_Otop__class_Otop(_1274685)) = c_Orderings_Obot__class_Obot(_1274685))], (45203 ^ _779999) ^ [_1683510, _1683512, _1683514, _1683516, _1683518, _1683520] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683510), tc_List_Olist(_1683510))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683510), tc_List_Olist(_1683510)), hAPP(hAPP(c_List_Oappend(_1683510), _1683512), _1683518)), hAPP(hAPP(c_List_Oappend(_1683510), _1683514), _1683520))), c_List_Olistrel1(_1683510, _1683516)))), 45204 ^ _779999 : [(45211 ^ _779999) ^ [] : [_1683512 = _1683514, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683510), tc_List_Olist(_1683510))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683510), tc_List_Olist(_1683510)), _1683518), _1683520)), c_List_Olistrel1(_1683510, _1683516)))], (45205 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683510), tc_List_Olist(_1683510))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683510), tc_List_Olist(_1683510)), _1683512), _1683514)), c_List_Olistrel1(_1683510, _1683516))), _1683518 = _1683520]]], (15363 ^ _779999) ^ [_1056222, _1056224, _1056226] : [class_Rings_Ocomm__semiring__1(_1056222), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056222), _1056224), _1056226) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056222), _1056226), _1056224))], (44600 ^ _779999) ^ [_1670194, _1670196] : [-(_1670194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1670196, _1670194, c_List_Olist_ONil(_1670196)) = c_List_Olist_ONil(tc_List_Olist(_1670196)))], (33317 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (49746 ^ _779999) ^ [_1783671, _1783673, _1783675] : [-(hAPP(c_New__DSequence_Oneg__single(_1783671, _1783673), _1783675) = c_Lazy__Sequence_Ohb__single(_1783671, _1783673))], (52026 ^ _779999) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (15135 ^ _779999) ^ [_1051850, _1051852, _1051854, _1051856] : [hBOOL(hAPP(hAPP(c_member(_1051850), _1051852), c_SetInterval_Oord_OgreaterThan(_1051850, _1051854, _1051856))), -(hBOOL(hAPP(hAPP(_1051854, _1051856), _1051852)))], (37529 ^ _779999) ^ [] : [-(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)))], (49406 ^ _779999) ^ [_1776454, _1776456, _1776458, _1776460] : [49407 ^ _779999 : [(49410 ^ _779999) ^ [] : [c_List_Olist__ex(_1776454, _1776456, _1776460)], (49408 ^ _779999) ^ [] : [c_List_Olist__ex(_1776454, _1776456, _1776458)]], -(c_List_Olist__ex(_1776454, _1776456, hAPP(hAPP(c_List_Oappend(_1776454), _1776458), _1776460)))], (16733 ^ _779999) ^ [_1082707, _1082709] : [-(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), _1082707), _1082709)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082709))], (47581 ^ _779999) ^ [_1737856, _1737858] : [-(c_Random_Opick(_1737856, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1737856), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1737856, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1737856, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1737856)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1737858)) = c_Random_Opick(_1737856, _1737858))], (3172 ^ _779999) ^ [_827309, _827311, _827313, _827315, _827317, _827319] : [-(c_Nitpick_Oplus__frac(_827319, _827315, _827311) = c_Nitpick_Oplus__frac(_827317, _827313, _827309)), _827319 = _827317, _827315 = _827313, _827311 = _827309], (36563 ^ _779999) ^ [_1468817, _1468819, _1468821, _1468823, _1468825] : [hBOOL(hAPP(hAPP(_1468817, _1468819), _1468821)), -(hBOOL(hAPP(hAPP(_1468817, hAPP(c_Product__Type_Osnd(_1468823, _1468825), hAPP(hAPP(c_Product__Type_OPair(_1468823, _1468825), _1468821), _1468819))), hAPP(c_Product__Type_Ofst(_1468823, _1468825), hAPP(hAPP(c_Product__Type_OPair(_1468823, _1468825), _1468821), _1468819)))))], (7683 ^ _779999) ^ [_909023, _909025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909023), _909025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909023), hAPP(c_Nat_OSuc, _909025))))], (46151 ^ _779999) ^ [_1704005, _1704007, _1704009] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704005)), _1704007), c_List_Olists(_1704005, _1704009)))), 46152 ^ _779999 : [(46155 ^ _779999) ^ [_1704133, _1704135] : [_1704007 = hAPP(hAPP(c_List_Olist_OCons(_1704005), _1704135), _1704133), hBOOL(hAPP(hAPP(c_member(_1704005), _1704135), _1704009)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704005)), _1704133), c_List_Olists(_1704005, _1704009)))], (46153 ^ _779999) ^ [] : [_1704007 = c_List_Olist_ONil(_1704005)]]], (8110 ^ _779999) ^ [_917087, _917089] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917087, tc_HOL_Obool)), _917089), c_Orderings_Obot__class_Obot(tc_fun(_917087, tc_HOL_Obool))) = _917089)], (14959 ^ _779999) ^ [_1048433] : [14961 ^ _779999 : [(14964 ^ _779999) ^ [_1048543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 14960 ^ [_1048433, _1048543]), _1048543))], (14962 ^ _779999) ^ [_1048509] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14960 ^ [_1048433, _1048509]), _1048433)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1048433)))], (37994 ^ _779999) ^ [_1505038, _1505040] : [c_Wellfounded_Owf(_1505038, _1505040), -(c_Wellfounded_Owf(tc_fun(_1505038, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1505038, _1505040)))], (42310 ^ _779999) ^ [_1612085, _1612087, _1612089, _1612091, _1612093] : [42312 ^ _779999 : [(42315 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1612091, 42311 ^ [_1612085, _1612087, _1612089, _1612091, _1612093]), _1612093))], (42313 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612085), 42311 ^ [_1612085, _1612087, _1612089, _1612091, _1612093]), _1612089)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612085, tc_fun(_1612087, tc_HOL_Obool)), _1612089), _1612091), _1612093)))], (40679 ^ _779999) ^ [_1572246, _1572248] : [c_Wellfounded_Oacyclic(_1572246, _1572248), -(c_Wellfounded_Oacyclic(_1572246, hAPP(c_Relation_Oconverse(_1572246, _1572246), _1572248)))], (35554 ^ _779999) ^ [_1449339, _1449341, _1449343, _1449345, _1449347, _1449349, _1449351] : [hBOOL(hAPP(hAPP(c_member(_1449339), _1449341), hAPP(hAPP(_1449343, _1449345), _1449347))), -(hBOOL(hAPP(hAPP(c_member(_1449339), _1449341), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1449349, _1449351, tc_fun(_1449339, tc_HOL_Obool)), _1449343), hAPP(hAPP(c_Product__Type_OPair(_1449349, _1449351), _1449345), _1449347)))))], (25180 ^ _779999) ^ [_1252640, _1252642, _1252644] : [class_Orderings_Olinorder(_1252640), hAPP(_1252642, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1252640), 25185 ^ [_1252640, _1252642, _1252644]), 25186 ^ [_1252640, _1252642, _1252644])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1252640), hAPP(_1252642, 25185 ^ [_1252640, _1252642, _1252644])), hAPP(_1252642, 25186 ^ [_1252640, _1252642, _1252644])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1252640), _1252644)), -(_1252644 = c_Orderings_Obot__class_Obot(tc_fun(_1252640, tc_HOL_Obool))), -(hAPP(_1252642, c_Big__Operators_Olattice_OSup__fin(_1252640, c_Orderings_Oord__class_Omax(_1252640), _1252644)) = c_Big__Operators_Olattice_OSup__fin(_1252640, c_Orderings_Oord__class_Omax(_1252640), hAPP(c_Set_Oimage(_1252640, _1252640, _1252642), _1252644)))], (1644 ^ _779999) ^ [_803657, _803659] : [-(class_Rings_Oordered__cancel__semiring(_803657)), _803659 = _803657, class_Rings_Oordered__cancel__semiring(_803659)], (14978 ^ _779999) ^ [_1048770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1048770)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048770), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1048770)], (35566 ^ _779999) ^ [_1449639, _1449641, _1449643, _1449645, _1449647] : [hBOOL(hAPP(hAPP(_1449639, _1449641), _1449643)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1449645, _1449647, tc_HOL_Obool), _1449639), hAPP(hAPP(c_Product__Type_OPair(_1449645, _1449647), _1449641), _1449643))))], (1954 ^ _779999) ^ [_807532, _807534] : [-(class_Groups_Oone(_807532)), _807534 = _807532, class_Groups_Oone(_807534)], (20932 ^ _779999) ^ [_1159921, _1159923] : [class_Groups_Oordered__ab__group__add__abs(_1159921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159921), c_Groups_Ozero__class_Ozero(_1159921)), _1159923)), -(hAPP(c_Groups_Oabs__class_Oabs(_1159921), _1159923) = _1159923)], (51992 ^ _779999) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (50401 ^ _779999) ^ [_1798051, _1798053, _1798055] : [c_List_Olist__ex(tc_Int_Oint, _1798051, c_List_Oupto(_1798053, _1798055)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1798051), _1798053, _1798055)], (11520 ^ _779999) ^ [_981332, _981334, _981336, _981338] : [hBOOL(hAPP(hAPP(c_member(_981332), _981334), _981336)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981332, tc_HOL_Obool)), _981336), hAPP(hAPP(c_Set_Oinsert(_981332), _981334), _981338)) = hAPP(hAPP(c_Set_Oinsert(_981332), _981334), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981332, tc_HOL_Obool)), _981336), _981338)))], (23509 ^ _779999) ^ [_1219038, _1219040, _1219042, _1219044, _1219046] : [class_Lattices_Osemilattice__inf(_1219038), class_Orderings_Olinorder(_1219040), c_Orderings_Oorder__class_Omono(_1219040, _1219038, _1219042), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219038), hAPP(_1219042, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1219040), _1219044), _1219046))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1219038), hAPP(_1219042, _1219044)), hAPP(_1219042, _1219046)))))], (1194 ^ _779999) ^ [_798032, _798034] : [-(class_Groups_Olinordered__ab__group__add(_798032)), _798034 = _798032, class_Groups_Olinordered__ab__group__add(_798034)], (40397 ^ _779999) ^ [_1566238, _1566240] : [-(c_Transitive__Closure_Ortrancl(_1566238, _1566240) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566238, _1566238), tc_HOL_Obool)), c_Relation_OId(_1566238)), hAPP(hAPP(c_Relation_Orel__comp(_1566238, _1566238, _1566238), c_Transitive__Closure_Ortrancl(_1566238, _1566240)), _1566240)))], (33883 ^ _779999) ^ [_1414009, _1414011] : [c_Int_OBit0(_1414009) = c_Int_OBit1(_1414011)], (7143 ^ _779999) ^ [_897614, _897616, _897618] : [-(hAPP(hAPP(c_Set_Oinsert(_897614), _897616), _897618) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897614, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897614), _897616), c_Orderings_Obot__class_Obot(tc_fun(_897614, tc_HOL_Obool)))), _897618))], (33427 ^ _779999) ^ [_1405326] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1405326))) = 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)))), _1405326))], (45706 ^ _779999) ^ [_1695327, _1695329, _1695331] : [-(hAPP(c_List_Orotate(_1695327, _1695329), _1695331) = hAPP(hAPP(c_List_Oappend(_1695327), hAPP(hAPP(c_List_Odrop(_1695327), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1695329, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695327)), _1695331))), _1695331)), hAPP(hAPP(c_List_Otake(_1695327), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1695329, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695327)), _1695331))), _1695331)))], (40950 ^ _779999) ^ [_1579174, _1579176, _1579178, _1579180] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579174, _1579174), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1579176), _1579178)), _1579180) = hAPP(hAPP(c_Relation_Orel__comp(_1579174, _1579174, _1579174), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579174, _1579174), tc_HOL_Obool), _1579176), _1579180)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579174, _1579174), tc_HOL_Obool), _1579178), _1579180)))], (30722 ^ _779999) ^ [_1355898, _1355900] : [30723 ^ _779999 : [(30724 ^ _779999) ^ [_1355947] : [_1355898 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1355900), _1355947)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355898, _1355900) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13365 ^ _779999) ^ [_1017913, _1017915] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1017913)), _1017915) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017913), _1017915)))], (42484 ^ _779999) ^ [_1616221, _1616223, _1616225, _1616227] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1616221, _1616223), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616221, tc_HOL_Obool), _1616225)), _1616227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1616221, tc_HOL_Obool), tc_fun(tc_prod(_1616221, _1616223), tc_HOL_Obool)), _1616225), hAPP(hAPP(c_COMBC(tc_fun(_1616221, tc_HOL_Obool), tc_fun(_1616221, tc_fun(_1616223, tc_HOL_Obool)), tc_fun(tc_prod(_1616221, _1616223), tc_HOL_Obool)), c_Product__Type_OSigma(_1616221, _1616223)), _1616227)))], (36523 ^ _779999) ^ [_1468012] : [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), _1468012))), -(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), _1468012)) = 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), _1468012))))], (40659 ^ _779999) ^ [_1571766, _1571768, _1571770] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1571766, _1571766), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1571766, _1571766), _1571768)), c_Transitive__Closure_Ortrancl(_1571766, _1571768)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1571766, _1571766), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571766, _1571766)), hAPP(hAPP(c_Product__Type_OPair(_1571766, _1571766), _1571770), _1571770)), c_Transitive__Closure_Otrancl(_1571766, _1571768)))], (52068 ^ _779999) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (24004 ^ _779999) ^ [_1228515, _1228517] : [class_Orderings_Olinorder(_1228515), -(c_Big__Operators_Olattice_OInf__fin(_1228515, c_Orderings_Oord__class_Omin(_1228515), hAPP(hAPP(c_Set_Oinsert(_1228515), _1228517), c_Orderings_Obot__class_Obot(tc_fun(_1228515, tc_HOL_Obool)))) = _1228517)], (46640 ^ _779999) ^ [_1715603, _1715605] : [-(c_Random_Oselect__weight(_1715603, _1715605) = 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(_1715603, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1715603), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1715603)), _1715605)))), hAPP(hAPP(c_COMBB(_1715603, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1715603, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1715603, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1715603, _1715605))))], (41398 ^ _779999) ^ [_1590175, _1590177, _1590179, _1590181] : [class_Orderings_Olinorder(_1590175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590175), _1590177)), hBOOL(hAPP(hAPP(c_member(_1590175), _1590179), _1590177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1590175), hAPP(hAPP(c_Finite__Set_Ofold(_1590175, _1590175, c_Orderings_Oord__class_Omin(_1590175)), _1590181), _1590177)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1590175), _1590179), _1590181))))], (34199 ^ _779999) ^ [_1419513, _1419515] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1419513)), _1419515) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1419513), _1419515))), _1419515))], (23403 ^ _779999) ^ [_1216726] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1216726) = c_Orderings_Oord__class_Omin(_1216726)), class_Lattices_Osemilattice__inf(_1216726), class_Orderings_Olinorder(_1216726)], (9128 ^ _779999) ^ [_935960, _935962, _935964, _935966, _935968] : [c_Fun_Ofun__upd(_935960, _935962, _935964, _935966, _935968) = _935964, -(hAPP(_935964, _935966) = _935968)], (37473 ^ _779999) ^ [_1490571, _1490573, _1490575] : [-(hAPP(c_Relation_OImage(_1490571, _1490571, c_Relation_OId__on(_1490571, _1490573)), _1490575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490571, tc_HOL_Obool)), _1490573), _1490575))], (33063 ^ _779999) ^ [_1399690, _1399692] : [class_Int_Onumber__ring(_1399690), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1399690), _1399692), hAPP(c_Int_Onumber__class_Onumber__of(_1399690), c_Int_OPls)) = _1399692)], (17311 ^ _779999) ^ [_1093844, _1093846] : [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), _1093844), _1093846))), 17314 ^ _779999 : [(17317 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093846)))], (17315 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093844)))]]], (1874 ^ _779999) ^ [_806532, _806534] : [-(class_Rings_Omult__zero(_806532)), _806534 = _806532, class_Rings_Omult__zero(_806534)], (15759 ^ _779999) ^ [_1064259, _1064261] : [class_Rings_Ocomm__semiring__1(_1064259), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064259), c_Groups_Oone__class_Oone(_1064259)), _1064261) = _1064261)], (30098 ^ _779999) ^ [_1344080, _1344082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344080)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344082), _1344080)), _1344080) = _1344082)], (50357 ^ _779999) ^ [_1797144, _1797146, _1797148, _1797150, _1797152, _1797154, _1797156] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1797144, tc_fun(_1797146, tc_fun(_1797148, tc_HOL_Obool))), _1797150), _1797152), _1797154), _1797156)), 50361 ^ _779999 : [(50364 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1797152, 50360 ^ [_1797144, _1797146, _1797148, _1797150, _1797152, _1797154, _1797156]), _1797154), _1797156)))], (50362 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797144), 50360 ^ [_1797144, _1797146, _1797148, _1797150, _1797152, _1797154, _1797156]), _1797150)))]]], (33669 ^ _779999) ^ [_1409854, _1409856] : [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(_1409856))), 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), _1409854)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409854)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409856))))], (18931 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (39795 ^ _779999) ^ [_1550849, _1550851, _1550853, _1550855, _1550857, _1550859, _1550861] : [c_Hoare__Mirabelle_Ohoare__derivs(_1550849, _1550851, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1550849)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1550849), c_Hoare__Mirabelle_Opeek__and(_1550849, _1550853, _1550855)), _1550857), _1550859)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1550849), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1550849, _1550851, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1550849)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1550849), c_Hoare__Mirabelle_Opeek__and(_1550849, _1550853, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1550855))), _1550861), _1550859)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1550849), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1550849, _1550851, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1550849)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1550849), _1550853), c_Com_Ocom_OCond(_1550855, _1550857, _1550861)), _1550859)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1550849), tc_HOL_Obool)))))], (34461 ^ _779999) ^ [_1424220, _1424222] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1424220), hAPP(c_Int_Onumber__class_Onumber__of(_1424220), _1424222)), 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(_1424220), hAPP(c_Int_Onumber__class_Onumber__of(_1424220), _1424222)), hAPP(c_Int_Onumber__class_Onumber__of(_1424220), _1424222))), class_Groups_Omonoid__mult(_1424220), class_Int_Onumber(_1424220)], (38550 ^ _779999) ^ [_1519840, _1519842] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519840, _1519842), c_Orderings_Otop__class_Otop(tc_fun(_1519840, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1519842, tc_HOL_Obool), _1519840), c_Orderings_Otop__class_Otop(tc_fun(_1519842, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1519840, _1519842), tc_HOL_Obool)))], (44766 ^ _779999) ^ [_1673330, _1673332] : [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), _1673330), _1673332))), 44769 ^ _779999 : [(44776 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1673330), _1673332))), -(c_List_Oupto(_1673330, _1673332) = c_List_Olist_ONil(tc_Int_Oint))], (44770 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1673330), _1673332)), -(c_List_Oupto(_1673330, _1673332) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1673330), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1673330), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1673332)))]]], (27176 ^ _779999) ^ [_1291542, _1291544] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291542)), _1291544) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1291542), _1291544)))], (51073 ^ _779999) ^ [_1813503, _1813505] : [c_Relation_Osym(_1813503, _1813505), -(c_Relation_Osym(_1813503, hAPP(c_Relation_Oconverse(_1813503, _1813503), _1813505)))], (39677 ^ _779999) ^ [_1548175, _1548177, _1548179, _1548181, _1548183, _1548185] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1548175, _1548177), _1548175, tc_prod(_1548179, _1548181), c_Product__Type_Ofst(_1548175, _1548177)), c_Product__Type_Omap__pair(_1548179, _1548175, _1548181, _1548177, _1548183, _1548185)) = hAPP(c_Fun_Ocomp(_1548179, _1548175, tc_prod(_1548179, _1548181), _1548183), c_Product__Type_Ofst(_1548179, _1548181)))], (20098 ^ _779999) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28538 ^ _779999) ^ [_1316416, _1316418, _1316420] : [class_Fields_Olinordered__field__inverse__zero(_1316416), 28541 ^ _779999 : [(28556 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316416), _1316418), _1316420)))), 28557 ^ _779999 : [(28564 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), _1316418), c_Groups_Ozero__class_Ozero(_1316416))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), _1316420), c_Groups_Ozero__class_Ozero(_1316416)))], (28558 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), _1316418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), _1316420))]]], (28542 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316416), _1316418), _1316420))), 28547 ^ _779999 : [(28550 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), _1316420)))], (28548 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), c_Groups_Ozero__class_Ozero(_1316416)), _1316418)))]], 28551 ^ _779999 : [(28554 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), _1316420), c_Groups_Ozero__class_Ozero(_1316416))))], (28552 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316416), _1316418), c_Groups_Ozero__class_Ozero(_1316416))))]]]]], (26364 ^ _779999) ^ [_1274049, _1274051] : [class_Rings_Oring__1__no__zero__divisors(_1274049), 26367 ^ _779999 : [(26368 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274049), _1274051), _1274051) = c_Groups_Oone__class_Oone(_1274049), -(_1274051 = c_Groups_Oone__class_Oone(_1274049)), -(_1274051 = hAPP(c_Groups_Ouminus__class_Ouminus(_1274049), c_Groups_Oone__class_Oone(_1274049)))], (26378 ^ _779999) ^ [] : [26379 ^ _779999 : [(26382 ^ _779999) ^ [] : [_1274051 = hAPP(c_Groups_Ouminus__class_Ouminus(_1274049), c_Groups_Oone__class_Oone(_1274049))], (26380 ^ _779999) ^ [] : [_1274051 = c_Groups_Oone__class_Oone(_1274049)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274049), _1274051), _1274051) = c_Groups_Oone__class_Oone(_1274049))]]], (35580 ^ _779999) ^ [_1449979, _1449981, _1449983] : [-(c_Fun_Oinj__on(tc_prod(_1449979, _1449981), tc_prod(_1449981, _1449979), hAPP(c_Product__Type_Oprod_Oprod__case(_1449979, _1449981, tc_prod(_1449981, _1449979)), hAPP(c_COMBC(_1449981, _1449979, tc_prod(_1449981, _1449979)), c_Product__Type_OPair(_1449981, _1449979))), _1449983))], (22966 ^ _779999) ^ [_1207857, _1207859, _1207861, _1207863, _1207865] : [_1207857 = c_Orderings_Obot__class_Obot(tc_fun(_1207859, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207861, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207859, tc_fun(_1207861, tc_HOL_Obool)), _1207857), _1207863)), _1207865) = _1207865)], (17629 ^ _779999) ^ [_1100239, _1100241, _1100243, _1100245, _1100247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100239), _1100241)), -(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), _1100239), _1100243)), _1100245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100241), _1100243)), _1100247)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100245), 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), _1100241), _1100239)), _1100243)), _1100247)))], (27180 ^ _779999) ^ [_1291628, _1291630, _1291632, _1291634] : [class_Rings_Odivision__ring(_1291628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291628), _1291630), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291628), _1291632), _1291634)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291628), _1291630), _1291632)), _1291634))], (44066 ^ _779999) ^ [_1658849, _1658851, _1658853] : [class_Groups_Omonoid__add(_1658849), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1658849), hAPP(hAPP(c_List_Olist_OCons(_1658849), _1658851), _1658853)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1658849), _1658851), hAPP(c_List_Omonoid__add__class_Olistsum(_1658849), _1658853)))], (47621 ^ _779999) ^ [_1738960, _1738962, _1738964] : [-(c_List_Osublist(_1738960, _1738962, _1738964) = hAPP(hAPP(c_List_Omap(tc_prod(_1738960, tc_Nat_Onat), _1738960), c_Product__Type_Ofst(_1738960, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1738960, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1738960, 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(_1738960, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1738960, tc_Nat_Onat))), _1738964)), hAPP(hAPP(c_List_Ozip(_1738960, tc_Nat_Onat), _1738962), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738960)), _1738962))))))], (1184 ^ _779999) ^ [_797907, _797909] : [-(class_Groups_Oordered__ab__group__add__abs(_797907)), _797909 = _797907, class_Groups_Oordered__ab__group__add__abs(_797909)], (17467 ^ _779999) ^ [_1096834, _1096836, _1096838, _1096840, _1096842] : [class_Groups_Ocomm__monoid__add(_1096834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1096836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096838), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1096834), _1096840), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1096836, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096838), _1096842))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096834), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1096834), _1096840), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1096836, _1096838))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1096834), _1096840), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096838), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096838), _1096842)))))], (38970 ^ _779999) ^ [_1531823, _1531825, _1531827] : [c_Wellfounded_OwfP(_1531823, _1531825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531823, tc_fun(_1531823, tc_HOL_Obool))), _1531827), _1531825)), -(c_Wellfounded_OwfP(_1531823, _1531827))], (46073 ^ _779999) ^ [_1702737, _1702739, _1702741] : [-(_1702737 = c_List_Olist_ONil(_1702739)), -(c_List_Olast(_1702739, hAPP(hAPP(c_List_Olist_OCons(_1702739), _1702741), _1702737)) = c_List_Olast(_1702739, _1702737))], (5943 ^ _779999) ^ [_874636, _874638, _874640, _874642] : [class_Orderings_Opreorder(_874636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874636), _874638), _874640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874636), _874640), _874642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874636), _874638), _874642)))], (6161 ^ _779999) ^ [_878408, _878410] : [class_Lattices_Osemilattice__sup(_878408), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878408), _878410), _878410) = _878410)], (38868 ^ _779999) ^ [_1529356, _1529358, _1529360, _1529362, _1529364, _1529366] : [-(c_Product__Type_Omap__pair(_1529356, _1529358, _1529360, _1529362, _1529364, _1529366) = hAPP(c_Product__Type_Oprod_Oprod__case(_1529356, _1529360, tc_prod(_1529358, _1529362)), hAPP(hAPP(c_COMBC(_1529356, tc_fun(_1529360, _1529362), tc_fun(_1529360, tc_prod(_1529358, _1529362))), hAPP(hAPP(c_COMBB(tc_fun(_1529362, tc_prod(_1529358, _1529362)), tc_fun(tc_fun(_1529360, _1529362), tc_fun(_1529360, tc_prod(_1529358, _1529362))), _1529356), c_COMBB(_1529362, tc_prod(_1529358, _1529362), _1529360)), hAPP(hAPP(c_COMBB(_1529358, tc_fun(_1529362, tc_prod(_1529358, _1529362)), _1529356), c_Product__Type_OPair(_1529358, _1529362)), _1529364))), _1529366)))], (9989 ^ _779999) ^ [_952384, _952386, _952388, _952390, _952392] : [c_Fun_Oinj__on(_952384, _952386, _952388, _952390), hBOOL(hAPP(hAPP(c_member(_952384), _952392), _952390)), -(hAPP(c_Fun_Othe__inv__into(_952384, _952386, _952390, _952388), hAPP(_952388, _952392)) = _952392)], (13473 ^ _779999) ^ [_1020002, _1020004, _1020006, _1020008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020002), _1020004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020006), _1020008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020002), _1020006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020004), _1020008))))], (27218 ^ _779999) ^ [_1292373, _1292375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292373)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1292373), _1292375)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1292373)), _1292375))], (51868 ^ _779999) ^ [_1829307, _1829309] : [-(class_Enum_Oenum(tc_fun(_1829307, _1829309))), class_Enum_Oenum(_1829307), class_Enum_Oenum(_1829309)], (34241 ^ _779999) ^ [_1420476, _1420478] : [class_Int_Onumber__ring(_1420476), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420476), _1420478), hAPP(c_Int_Onumber__class_Onumber__of(_1420476), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420476), _1420478), _1420478))], (9254 ^ _779999) ^ [_937826, _937828, _937830] : [class_Orderings_Oorder(_937826), 9257 ^ _779999 : [(9266 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937826), _937828), _937830))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937826), _937828), _937830)), -(_937828 = _937830)], (9258 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937826), _937828), _937830)), 9261 ^ _779999 : [(9264 ^ _779999) ^ [] : [_937828 = _937830], (9262 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937826), _937828), _937830)))]]]]], (48766 ^ _779999) ^ [_1761742, _1761744, _1761746] : [hBOOL(hAPP(c_List_Odistinct(_1761742), _1761744)), -(hBOOL(hAPP(c_List_Odistinct(_1761742), c_List_OdropWhile(_1761742, _1761746, _1761744))))], (12487 ^ _779999) ^ [_1000926, _1000928, _1000930] : [class_Lattices_Olattice(_1000926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000926), _1000928)), -(_1000930 = c_Orderings_Obot__class_Obot(tc_fun(_1000926, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000926, tc_HOL_Obool)), _1000930), _1000928)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1000926), c_Big__Operators_Olattice__class_OInf__fin(_1000926, _1000930)), c_Big__Operators_Olattice__class_OInf__fin(_1000926, _1000928)) = c_Big__Operators_Olattice__class_OInf__fin(_1000926, _1000928))], (50135 ^ _779999) ^ [_1791899, _1791901, _1791903] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1791899)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1791899, _1791901, _1791903)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1791899)), _1791903)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46404 ^ _779999) ^ [_1710430, _1710432] : [class_Groups_Oordered__ab__group__add__abs(_1710430), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710430), hAPP(c_Groups_Oabs__class_Oabs(_1710430), hAPP(c_List_Omonoid__add__class_Olistsum(_1710430), _1710432))), hAPP(c_List_Omonoid__add__class_Olistsum(_1710430), hAPP(hAPP(c_List_Omap(_1710430, _1710430), c_Groups_Oabs__class_Oabs(_1710430)), _1710432)))))], (52308 ^ _779999) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (51816 ^ _779999) ^ [_1828625, _1828627] : [-(class_Finite__Set_Ofinite(tc_fun(_1828625, _1828627))), class_Finite__Set_Ofinite(_1828625), class_Finite__Set_Ofinite(_1828627)], (39747 ^ _779999) ^ [_1549832, _1549834, _1549836, _1549838, _1549840, _1549842, _1549844] : [c_Finite__Set_Ofolding__image(_1549832, _1549834, _1549836, _1549838, _1549840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549834), _1549842)), -(hAPP(hAPP(_1549840, _1549844), _1549842) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1549832, _1549834, _1549836), _1549844), _1549838), _1549842))], (2630 ^ _779999) ^ [_818856, _818858, _818860, _818862, _818864, _818866, _818868, _818870, _818872, _818874] : [-(c_Product__Type_Oprod_Oprod__rec(_818874, _818870, _818866, _818862, _818858) = c_Product__Type_Oprod_Oprod__rec(_818872, _818868, _818864, _818860, _818856)), _818874 = _818872, _818870 = _818868, _818866 = _818864, _818862 = _818860, _818858 = _818856], (20258 ^ _779999) ^ [_1148729, _1148731] : [-(_1148729 = hAPP(c_Int_Onat, _1148731)), 20261 ^ _779999 : [(20264 ^ _779999) ^ [] : [_1148731 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148729)], (20262 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148731)))]], 20265 ^ _779999 : [(20268 ^ _779999) ^ [] : [_1148729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20266 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148731))]]], (50496 ^ _779999) ^ [_1800422, _1800424, _1800426, _1800428, _1800430] : [c_Relation_Otrans(_1800422, _1800424), hBOOL(hAPP(hAPP(c_member(tc_prod(_1800422, _1800422)), hAPP(hAPP(c_Product__Type_OPair(_1800422, _1800422), _1800426), _1800428)), _1800424)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1800422, _1800422)), hAPP(hAPP(c_Product__Type_OPair(_1800422, _1800422), _1800428), _1800430)), _1800424)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800422, _1800422)), hAPP(hAPP(c_Product__Type_OPair(_1800422, _1800422), _1800426), _1800430)), _1800424)))], (42053 ^ _779999) ^ [_1606160, _1606162, _1606164, _1606166, _1606168] : [class_Complete__Lattice_Ocomplete__lattice(_1606160), class_Orderings_Olinorder(_1606160), 42060 ^ _779999 : [(42070 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606160), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606162, _1606160), _1606164), _1606166)), _1606168))), 42071 ^ _779999 : [(42072 ^ _779999) ^ [_1606508] : [hBOOL(hAPP(hAPP(c_member(_1606162), _1606508), _1606164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606160), hAPP(_1606166, _1606508)), _1606168))]]], (42061 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606160), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606162, _1606160), _1606164), _1606166)), _1606168)), 42065 ^ _779999 : [(42068 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606160), hAPP(_1606166, 42064 ^ [_1606160, _1606162, _1606164, _1606166, _1606168])), _1606168)))], (42066 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606162), 42064 ^ [_1606160, _1606162, _1606164, _1606166, _1606168]), _1606164)))]]]]], (19053 ^ _779999) ^ [_1127371, _1127373, _1127375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127371), _1127373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127371), _1127375)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127373), _1127375))))], (41610 ^ _779999) ^ [_1594030, _1594032, _1594034, _1594036, _1594038, _1594040] : [c_Finite__Set_Ofun__left__comm(_1594030, _1594032, _1594034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594030), _1594036)), hBOOL(hAPP(hAPP(c_member(_1594030), _1594038), _1594036)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594030, _1594032, _1594034), _1594040), _1594036) = hAPP(hAPP(_1594034, _1594038), hAPP(hAPP(c_Finite__Set_Ofold(_1594030, _1594032, _1594034), _1594040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594030, tc_HOL_Obool)), _1594036), hAPP(hAPP(c_Set_Oinsert(_1594030), _1594038), c_Orderings_Obot__class_Obot(tc_fun(_1594030, tc_HOL_Obool)))))))], (27230 ^ _779999) ^ [_1292673, _1292675, _1292677, _1292679] : [class_Rings_Odivision__ring(_1292673), -(_1292675 = c_Groups_Ozero__class_Ozero(_1292673)), 27237 ^ _779999 : [(27244 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292673), _1292677), _1292675) = _1292679, -(_1292677 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292673), _1292679), _1292675))], (27238 ^ _779999) ^ [] : [_1292677 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292673), _1292679), _1292675), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292673), _1292677), _1292675) = _1292679)]]], (41081 ^ _779999) ^ [_1582382, _1582384] : [-(c_Relation_Osingle__valued(_1582382, _1582382, c_Relation_OId__on(_1582382, _1582384)))], (16041 ^ _779999) ^ [_1069581, _1069583, _1069585] : [class_Rings_Oordered__cancel__semiring(_1069581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069581), c_Groups_Ozero__class_Ozero(_1069581)), _1069583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069581), _1069585), c_Groups_Ozero__class_Ozero(_1069581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069581), _1069583), _1069585)), c_Groups_Ozero__class_Ozero(_1069581))))], (22145 ^ _779999) ^ [_1189540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189540), c_Orderings_Otop__class_Otop(tc_fun(_1189540, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1189540)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1189540), tc_HOL_Obool)))))], (24706 ^ _779999) ^ [_1242928, _1242930, _1242932, _1242934] : [class_Orderings_Olinorder(_1242928), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242928, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1242928), _1242930)), c_SetInterval_Oord__class_OatLeastAtMost(_1242928, _1242932, _1242934)) = c_SetInterval_Oord__class_OatLeastAtMost(_1242928, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242928), _1242930), _1242932), _1242934))], (25220 ^ _779999) ^ [_1253458, _1253460, _1253462, _1253464] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1253458), _1253460)), 25226 ^ _779999 : [(25229 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1253462), hAPP(_1253464, 25225 ^ [_1253458, _1253460, _1253462, _1253464])))], (25227 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253458), 25225 ^ [_1253458, _1253460, _1253462, _1253464]), _1253460)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1253462), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1253458, tc_fun(_1253462, tc_HOL_Obool)), _1253460), _1253464))))], (51988 ^ _779999) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11600 ^ _779999) ^ [_983260, _983262, _983264] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_983260), _983262)), 11603 ^ _779999 : [(11604 ^ _779999) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_983260, tc_Nat_Onat), _983264), _983262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11607 ^ _779999 : [(11608 ^ _779999) ^ [_983422] : [hBOOL(hAPP(hAPP(c_member(_983260), _983422), _983262)), -(hAPP(_983264, _983422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11614 ^ _779999) ^ [] : [11616 ^ _779999 : [(11619 ^ _779999) ^ [] : [hAPP(_983264, 11615 ^ [_983260, _983262, _983264]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11617 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_983260), 11615 ^ [_983260, _983262, _983264]), _983262)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_983260, tc_Nat_Onat), _983264), _983262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45528 ^ _779999) ^ [_1691804, _1691806, _1691808, _1691810] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1691804) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1691806), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1691804)), hAPP(hAPP(c_List_Olist_OCons(_1691806), _1691808), _1691810)) = hAPP(hAPP(c_List_Odrop(_1691806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1691804)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1691810))], (35133 ^ _779999) ^ [_1436261, _1436263] : [class_Int_Onumber__ring(_1436261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436263)), -(hBOOL(hAPP(hAPP(c_member(_1436261), hAPP(c_Int_Onumber__class_Onumber__of(_1436261), _1436263)), c_Nat_Osemiring__1__class_ONats(_1436261))))], (25950 ^ _779999) ^ [_1266658, _1266660, _1266662, _1266664, _1266666, _1266668] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_1266658, _1266660, _1266662), _1266664, _1266666, _1266668)), 25951 ^ _779999 : [(25958 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1266658, _1266664))), c_Natural_Oevaln(_1266662, _1266664, _1266666, _1266668)], (25952 ^ _779999) ^ [] : [hBOOL(hAPP(_1266658, _1266664)), c_Natural_Oevaln(_1266660, _1266664, _1266666, _1266668)]]], (49569 ^ _779999) ^ [_1779878, _1779880, _1779882] : [c_List_Olist__all(_1779878, _1779882, _1779880), 49572 ^ _779999 : [(49573 ^ _779999) ^ [_1779959] : [hBOOL(hAPP(hAPP(c_member(_1779878), _1779959), hAPP(c_List_Oset(_1779878), _1779880))), -(hBOOL(hAPP(_1779882, _1779959)))]]], (50452 ^ _779999) ^ [_1799278, _1799280, _1799282, _1799284] : [-(c_Random__Sequence_Omap(_1799278, _1799280, _1799282, _1799284) = c_Random__Sequence_Obind(_1799278, _1799280, _1799284, hAPP(c_Fun_Ocomp(_1799280, 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(_1799280)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1799278, c_Random__Sequence_Osingle(_1799280)), _1799282)))], (45732 ^ _779999) ^ [_1695916, _1695918, _1695920] : [class_Groups_Omonoid__add(_1695916), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1695916), _1695918), hAPP(c_List_Ofoldl(_1695916, _1695916, c_Groups_Oplus__class_Oplus(_1695916), c_Groups_Ozero__class_Ozero(_1695916)), _1695920)) = hAPP(c_List_Ofoldl(_1695916, _1695916, c_Groups_Oplus__class_Oplus(_1695916), _1695918), _1695920))], (16463 ^ _779999) ^ [_1077413, _1077415, _1077417, _1077419] : [class_Rings_Olinordered__semiring__strict(_1077413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077413), _1077415), _1077417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077413), c_Groups_Ozero__class_Ozero(_1077413)), _1077419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077413), _1077415), _1077419)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077413), _1077417), _1077419))))], (47280 ^ _779999) ^ [_1729615, _1729617, _1729619, _1729621] : [class_Orderings_Olinorder(_1729615), -(hAPP(c_List_Oset(_1729617), c_List_Olinorder__class_Osort__key(_1729617, _1729615, _1729619, _1729621)) = hAPP(c_List_Oset(_1729617), _1729621))], (52048 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (40291 ^ _779999) ^ [_1563611, _1563613] : [-(c_Transitive__Closure_Otrancl(_1563611, _1563613) = hAPP(hAPP(c_Relation_Orel__comp(_1563611, _1563611, _1563611), _1563613), c_Transitive__Closure_Ortrancl(_1563611, _1563613)))], (27364 ^ _779999) ^ [_1294723, _1294725, _1294727] : [class_Rings_Ocomm__semiring__1(_1294723), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294723), hAPP(hAPP(c_Power_Opower__class_Opower(_1294723), _1294725), _1294727)), _1294725) = hAPP(hAPP(c_Power_Opower__class_Opower(_1294723), _1294725), hAPP(c_Nat_OSuc, _1294727)))], (15573 ^ _779999) ^ [_1060858, _1060860] : [class_Lattices_Oab__semigroup__idem__mult(_1060858), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060858), _1060860), _1060860) = _1060860)], (24268 ^ _779999) ^ [_1234618] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1234618) = c_Orderings_Oord__class_Omax(_1234618)), class_Lattices_Osemilattice__sup(_1234618), class_Orderings_Olinorder(_1234618)], (42457 ^ _779999) ^ [_1615342, _1615344, _1615346] : [42459 ^ _779999 : [(42462 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615342, tc_HOL_Obool)), 42458 ^ [_1615342, _1615344, _1615346]), _1615346) = c_Orderings_Obot__class_Obot(tc_fun(_1615342, tc_HOL_Obool))], (42460 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1615342, tc_HOL_Obool)), 42458 ^ [_1615342, _1615344, _1615346]), _1615344)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615342, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615342, tc_HOL_Obool), _1615344)), _1615346) = c_Orderings_Obot__class_Obot(tc_fun(_1615342, tc_HOL_Obool)))], (35536 ^ _779999) ^ [_1448963, _1448965, _1448967, _1448969, _1448971, _1448973] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448963, tc_fun(_1448965, tc_HOL_Obool))), _1448967), _1448969), _1448971), _1448973)), 35539 ^ _779999 : [(35542 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1448969, _1448971), _1448973)))], (35540 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1448967, _1448971), _1448973)))]]], (20482 ^ _779999) ^ [_1152538, _1152540] : [c_Nat__Transfer_Onat__set(_1152538), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1152540), _1152538)), -(c_Nat__Transfer_Ois__nat(_1152540))], (19475 ^ _779999) ^ [_1135072, _1135074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1135072), _1135074)), -(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)), _1135072)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1135074))))], (19397 ^ _779999) ^ [_1133655, _1133657] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133655)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133657)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1133655), _1133657)))], (28606 ^ _779999) ^ [_1317617, _1317619, _1317621, _1317623] : [class_Fields_Ofield__inverse__zero(_1317617), -(_1317619 = c_Groups_Ozero__class_Ozero(_1317617)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317617), _1317621), _1317619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317617), _1317623), _1317619)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317617), _1317621), _1317623))], (19429 ^ _779999) ^ [_1134283, _1134285] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134283)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134285))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1134283), _1134285)))], (35608 ^ _779999) ^ [_1450552, _1450554, _1450556, _1450558, _1450560, _1450562] : [hBOOL(hAPP(hAPP(_1450552, _1450554), _1450556)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450558, tc_fun(_1450560, tc_HOL_Obool))), _1450562), _1450552), _1450554), _1450556)))], (43598 ^ _779999) ^ [_1645794, _1645796, _1645798, _1645800] : [43601 ^ _779999 : [(43606 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645794, _1645794)), hAPP(hAPP(c_Product__Type_OPair(_1645794, _1645794), 43600 ^ [_1645794, _1645796, _1645798, _1645800]), 43599 ^ [_1645794, _1645796, _1645798, _1645800])), _1645796))], (43604 ^ _779999) ^ [] : [43599 ^ [_1645794, _1645796, _1645798, _1645800] = 43600 ^ [_1645794, _1645796, _1645798, _1645800]], (43602 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645794, _1645794)), hAPP(hAPP(c_Product__Type_OPair(_1645794, _1645794), 43599 ^ [_1645794, _1645796, _1645798, _1645800]), 43600 ^ [_1645794, _1645796, _1645798, _1645800])), _1645796))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645794), tc_List_Olist(_1645794))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645794), tc_List_Olist(_1645794)), _1645798), _1645800)), c_List_Olexord(_1645794, _1645796)))), -(_1645798 = _1645800), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645794), tc_List_Olist(_1645794))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645794), tc_List_Olist(_1645794)), _1645800), _1645798)), c_List_Olexord(_1645794, _1645796))))], (20621 ^ _779999) ^ [_1154480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154480)), -(c_Nat__Transfer_Ois__nat(_1154480))], (35262 ^ _779999) ^ [_1443193, _1443195, _1443197, _1443199, _1443201, _1443203] : [hBOOL(hAPP(hAPP(c_member(_1443193), _1443195), _1443197)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1443193, _1443199)), hAPP(hAPP(c_Product__Type_OPair(_1443193, _1443199), _1443195), _1443201)), _1443203)), -(hBOOL(hAPP(hAPP(c_member(_1443199), _1443201), hAPP(c_Relation_OImage(_1443193, _1443199, _1443203), _1443197))))], (50192 ^ _779999) ^ [_1793356] : [-(c_List_Omember(_1793356) = c_List_Oset(_1793356))], (52244 ^ _779999) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (31251 ^ _779999) ^ [_1365460, _1365462] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1365460), _1365462))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365460, _1365462) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1365460), _1365462), _1365462))], (38016 ^ _779999) ^ [_1505459, _1505461, _1505463, _1505465] : [c_Wellfounded_Owf(_1505459, _1505461), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505459, _1505459)), hAPP(hAPP(c_Product__Type_OPair(_1505459, _1505459), _1505463), _1505465)), _1505461)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505459, _1505459)), hAPP(hAPP(c_Product__Type_OPair(_1505459, _1505459), _1505465), _1505463)), _1505461))], (3546 ^ _779999) ^ [_833170, _833172, _833174, _833176] : [-(c_Enum_Osublists(_833176, _833172) = c_Enum_Osublists(_833174, _833170)), _833176 = _833174, _833172 = _833170], (3244 ^ _779999) ^ [_828389, _828391, _828393, _828395] : [-(c_List_Olenlex(_828395, _828391) = c_List_Olenlex(_828393, _828389)), _828395 = _828393, _828391 = _828389], (28138 ^ _779999) ^ [_1308969, _1308971, _1308973, _1308975] : [class_Rings_Olinordered__semidom(_1308969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308971), _1308973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308969), c_Groups_Ozero__class_Ozero(_1308969)), _1308975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308969), _1308975), c_Groups_Oone__class_Oone(_1308969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308969), hAPP(hAPP(c_Power_Opower__class_Opower(_1308969), _1308975), _1308973)), hAPP(hAPP(c_Power_Opower__class_Opower(_1308969), _1308975), _1308971))))], (42534 ^ _779999) ^ [_1617516, _1617518, _1617520, _1617522] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617516, tc_fun(_1617518, tc_HOL_Obool)), _1617520), _1617522) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617518, tc_HOL_Obool), hAPP(c_Set_Oimage(_1617516, tc_fun(_1617518, tc_HOL_Obool), _1617522), _1617520)))], (12815 ^ _779999) ^ [_1007061, _1007063, _1007065, _1007067] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007061), _1007063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007061, tc_HOL_Obool)), _1007063), _1007065)), hBOOL(hAPP(_1007067, c_Orderings_Obot__class_Obot(tc_fun(_1007061, tc_HOL_Obool)))), 12830 ^ _779999 : [(12831 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007061), 12829 ^ [_1007061, _1007063, _1007065, _1007067])))], (12835 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1007061), 12828 ^ [_1007061, _1007063, _1007065, _1007067]), 12829 ^ [_1007061, _1007063, _1007065, _1007067]))], (12839 ^ _779999) ^ [] : [hBOOL(hAPP(_1007067, hAPP(hAPP(c_Set_Oinsert(_1007061), 12828 ^ [_1007061, _1007063, _1007065, _1007067]), 12829 ^ [_1007061, _1007063, _1007065, _1007067])))], (12837 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1007067, 12829 ^ [_1007061, _1007063, _1007065, _1007067])))], (12833 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007061), 12828 ^ [_1007061, _1007063, _1007065, _1007067]), _1007065)))]], -(hBOOL(hAPP(_1007067, _1007063)))], (10671 ^ _779999) ^ [_963750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _963750)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963750), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _963750)], (50579 ^ _779999) ^ [_1802347, _1802349] : [-(c_Relation_Otrans(_1802347, c_Relation_OId__on(_1802347, _1802349)))], (1984 ^ _779999) ^ [_807903, _807905, _807907, _807909, _807911, _807913] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807911, _807907, _807903)), c_Hoare__Mirabelle_Ohoare__derivs(_807913, _807909, _807905), _807913 = _807911, _807909 = _807907, _807905 = _807903], (2396 ^ _779999) ^ [_815307, _815309, _815311, _815313] : [-(c_SMT_Oz3mod(_815313, _815309) = c_SMT_Oz3mod(_815311, _815307)), _815313 = _815311, _815309 = _815307], (45815 ^ _779999) ^ [_1697641, _1697643, _1697645] : [class_Orderings_Olinorder(_1697641), -(c_Big__Operators_Olinorder__class_OMax(_1697641, hAPP(c_List_Oset(_1697641), hAPP(hAPP(c_List_Olist_OCons(_1697641), _1697643), _1697645))) = hAPP(c_List_Ofoldl(_1697641, _1697641, c_Orderings_Oord__class_Omax(_1697641), _1697643), _1697645))], (34093 ^ _779999) ^ [_1417628] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1417628)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1417628)))], (46558 ^ _779999) ^ [_1713825, _1713827, _1713829] : [-(hAPP(hAPP(c_List_Ozip(_1713825, _1713827), hAPP(hAPP(c_List_Omap(tc_prod(_1713825, _1713827), _1713825), c_Product__Type_Ofst(_1713825, _1713827)), _1713829)), hAPP(hAPP(c_List_Omap(tc_prod(_1713825, _1713827), _1713827), c_Product__Type_Osnd(_1713825, _1713827)), _1713829)) = _1713829)], (2176 ^ _779999) ^ [_811865, _811867, _811869, _811871, _811873, _811875, _811877, _811879] : [-(c_SetInterval_Oord_OatLeastAtMost(_811879, _811875, _811871, _811867) = c_SetInterval_Oord_OatLeastAtMost(_811877, _811873, _811869, _811865)), _811879 = _811877, _811875 = _811873, _811871 = _811869, _811867 = _811865], (26133 ^ _779999) ^ [_1270033, _1270035, _1270037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270033), _1270035)), 26136 ^ _779999 : [(26137 ^ _779999) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270033, tc_Nat_Onat), _1270037), _1270035) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 26140 ^ _779999 : [(26141 ^ _779999) ^ [_1270195] : [hBOOL(hAPP(hAPP(c_member(_1270033), _1270195), _1270035)), -(hAPP(_1270037, _1270195) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (26147 ^ _779999) ^ [] : [26149 ^ _779999 : [(26152 ^ _779999) ^ [] : [hAPP(_1270037, 26148 ^ [_1270033, _1270035, _1270037]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (26150 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270033), 26148 ^ [_1270033, _1270035, _1270037]), _1270035)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270033, tc_Nat_Onat), _1270037), _1270035) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (48159 ^ _779999) ^ [_1748956, _1748958, _1748960] : [class_Orderings_Olinorder(_1748956), 48162 ^ _779999 : [(48175 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1748956, hAPP(hAPP(c_List_Olist_OCons(_1748956), _1748958), _1748960))), 48179 ^ _779999 : [(48182 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748956), _1748958), 48178 ^ [_1748956, _1748958, _1748960]))], (48180 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748956), 48178 ^ [_1748956, _1748958, _1748960]), hAPP(c_List_Oset(_1748956), _1748960))))]], c_List_Olinorder__class_Osorted(_1748956, _1748960)], (48163 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1748956, hAPP(hAPP(c_List_Olist_OCons(_1748956), _1748958), _1748960)), 48166 ^ _779999 : [(48167 ^ _779999) ^ [_1749124] : [hBOOL(hAPP(hAPP(c_member(_1748956), _1749124), hAPP(c_List_Oset(_1748956), _1748960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748956), _1748958), _1749124)))], (48173 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1748956, _1748960))]]]]], (52256 ^ _779999) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (37951 ^ _779999) ^ [] : [-(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)))))], (39387 ^ _779999) ^ [_1541638, _1541640, _1541642, _1541644, _1541646, _1541648] : [-(hAPP(c_Set_Ovimage(_1541638, _1541640, hAPP(c_Fun_Ocomp(_1541642, _1541640, _1541638, _1541644), _1541646)), _1541648) = hAPP(c_Set_Ovimage(_1541638, _1541642, _1541646), hAPP(c_Set_Ovimage(_1541642, _1541640, _1541644), _1541648)))], (3332 ^ _779999) ^ [_829789, _829791, _829793, _829795, _829797, _829799] : [-(c_List_Oset__Cons(_829799, _829795, _829791) = c_List_Oset__Cons(_829797, _829793, _829789)), _829799 = _829797, _829795 = _829793, _829791 = _829789], (23263 ^ _779999) ^ [_1214032, _1214034, _1214036, _1214038] : [class_Orderings_Olinorder(_1214032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214032), _1214034), _1214036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214032), _1214034), _1214038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214032), _1214034), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214032), _1214036), _1214038))))], (31062 ^ _779999) ^ [_1362260, _1362262] : [-(_1362260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31065 ^ _779999 : [(31072 ^ _779999) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362262, _1362260) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1362262), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1362260)) = 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), _1362262), _1362260))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31066 ^ _779999) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362262, _1362260) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1362262), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1362260)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1362262), _1362260)))]]], (13031 ^ _779999) ^ [_1011880, _1011882, _1011884, _1011886] : [class_Groups_Ocancel__semigroup__add(_1011880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011880), _1011882), _1011884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011880), _1011886), _1011884), -(_1011882 = _1011886)], (8704 ^ _779999) ^ [_929010, _929012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _929010)), _929012)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _929010), _929012)))], (31178 ^ _779999) ^ [_1364304, _1364306] : [class_Rings_Olinordered__idom(_1364304), -(c_Groups_Osgn__class_Osgn(_1364304, c_Groups_Osgn__class_Osgn(_1364304, _1364306)) = c_Groups_Osgn__class_Osgn(_1364304, _1364306))], (20431 ^ _779999) ^ [] : [-(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))))], (33189 ^ _779999) ^ [_1401616] : [class_Int_Onumber__ring(_1401616), -(c_Groups_Oone__class_Oone(_1401616) = hAPP(c_Int_Onumber__class_Onumber__of(_1401616), c_Int_OBit1(c_Int_OPls)))], (6783 ^ _779999) ^ [_891138, _891140, _891142] : [hAPP(hAPP(c_Set_Oinsert(_891138), _891140), _891142) = c_Orderings_Obot__class_Obot(tc_fun(_891138, tc_HOL_Obool))], (44374 ^ _779999) ^ [_1665985, _1665987, _1665989, _1665991] : [hBOOL(hAPP(c_List_Odistinct(_1665985), _1665987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665989), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665985)), _1665987))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665991), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665985)), _1665987))), 44385 ^ _779999 : [(44392 ^ _779999) ^ [] : [_1665989 = _1665991, -(hAPP(hAPP(c_List_Onth(_1665985), _1665987), _1665989) = hAPP(hAPP(c_List_Onth(_1665985), _1665987), _1665991))], (44386 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Onth(_1665985), _1665987), _1665989) = hAPP(hAPP(c_List_Onth(_1665985), _1665987), _1665991), -(_1665989 = _1665991)]]], (50032 ^ _779999) ^ [_1790011, _1790013, _1790015, _1790017] : [-(hBOOL(hAPP(hAPP(c_member(_1790011), _1790013), hAPP(c_List_Oset(_1790011), c_List_Oreplicate(_1790011, _1790015, _1790017))))), _1790013 = _1790017, -(_1790015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43297 ^ _779999) ^ [_1636645, _1636647, _1636649, _1636651] : [hBOOL(hAPP(hAPP(c_member(_1636645), _1636647), c_Wellfounded_Oacc(_1636645, _1636649))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1636645)), _1636651), c_Wellfounded_Oacc(tc_List_Olist(_1636645), c_List_Olistrel1(_1636645, _1636649)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1636645)), hAPP(hAPP(c_List_Olist_OCons(_1636645), _1636647), _1636651)), c_Wellfounded_Oacc(tc_List_Olist(_1636645), c_List_Olistrel1(_1636645, _1636649)))))], (24728 ^ _779999) ^ [_1243371] : [class_Orderings_Olinorder(_1243371), -(c_Orderings_Oord_Omin(_1243371, hAPP(c_COMBC(_1243371, _1243371, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1243371))) = c_Orderings_Oord__class_Omax(_1243371))], (8512 ^ _779999) ^ [_925615, _925617] : [class_Groups_Ogroup__add(_925615), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925615), _925617), c_Groups_Ozero__class_Ozero(_925615)) = _925617)], (46878 ^ _779999) ^ [_1720476, _1720478] : [-(c_List_Opartition(_1720476, _1720478, c_List_Olist_ONil(_1720476)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720476), tc_List_Olist(_1720476)), c_List_Olist_ONil(_1720476)), c_List_Olist_ONil(_1720476)))], (48326 ^ _779999) ^ [_1752467, _1752469] : [_1752469 = c_List_Olist_ONil(_1752467), -(hAPP(c_List_Orev(_1752467), _1752469) = c_List_Olist_ONil(_1752467))], (41340 ^ _779999) ^ [_1588994, _1588996, _1588998, _1589000, _1589002, _1589004] : [c_Finite__Set_Ofun__left__comm__idem(_1588994, _1588996, _1588998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588994), _1589000)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1588994, _1588996, _1588998), _1589002), hAPP(hAPP(c_Set_Oinsert(_1588994), _1589004), _1589000)) = hAPP(hAPP(c_Finite__Set_Ofold(_1588994, _1588996, _1588998), hAPP(hAPP(_1588998, _1589004), _1589002)), _1589000))], (37208 ^ _779999) ^ [_1484989, _1484991, _1484993, _1484995, _1484997] : [c_Equiv__Relations_Oequivp(_1484989, _1484991), hBOOL(hAPP(hAPP(_1484991, _1484993), _1484995)), hBOOL(hAPP(hAPP(_1484991, _1484995), _1484997)), -(hBOOL(hAPP(hAPP(_1484991, _1484993), _1484997)))], (37515 ^ _779999) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (25842 ^ _779999) ^ [_1264333, _1264335, _1264337] : [class_Groups_Ogroup__add(_1264333), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264333), _1264335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264333), hAPP(c_Groups_Ouminus__class_Ouminus(_1264333), _1264335)), _1264337)) = _1264337)], (31275 ^ _779999) ^ [_1365814, _1365816, _1365818] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1365814), _1365816)), _1365818) = 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), _1365814), _1365818)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1365816), _1365818))), 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, _1365814, _1365818)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365816, _1365818))), _1365818)))], (34971 ^ _779999) ^ [_1433584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1433584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1433584)))], (50145 ^ _779999) ^ [_1792095, _1792097, _1792099, _1792101, _1792103] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1792095, _1792097, _1792099) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1792095, _1792101, _1792103)), _1792097 = _1792101, _1792099 = _1792103], (51906 ^ _779999) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (15661 ^ _779999) ^ [_1062220, _1062222, _1062224, _1062226, _1062228] : [class_Rings_Osemiring(_1062220), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062220), _1062222), _1062224)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062220), _1062226), _1062224)), _1062228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062220), _1062222), _1062226)), _1062224)), _1062228))], (40569 ^ _779999) ^ [_1570182, _1570184, _1570186, _1570188] : [-(c_Wellfounded_Oacyclic(_1570182, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1570182, _1570182)), hAPP(hAPP(c_Product__Type_OPair(_1570182, _1570182), _1570184), _1570186)), _1570188))), c_Wellfounded_Oacyclic(_1570182, _1570188), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570182, _1570182)), hAPP(hAPP(c_Product__Type_OPair(_1570182, _1570182), _1570186), _1570184)), c_Transitive__Closure_Ortrancl(_1570182, _1570188))))], (35864 ^ _779999) ^ [_1455583, _1455585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455583)), 35867 ^ _779999 : [(35874 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1455585), _1455583))), -(c_Divides_OposDivAlg(_1455585, _1455583) = hAPP(c_Divides_Oadjust(_1455583), c_Divides_OposDivAlg(_1455585, 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)))), _1455583))))], (35868 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1455585), _1455583)), -(c_Divides_OposDivAlg(_1455585, _1455583) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455585))]]], (8634 ^ _779999) ^ [_927786, _927788] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927786), _927788) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927786), _927788)))], (30687 ^ _779999) ^ [_1355326, _1355328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355326, _1355328)), _1355326)))], (30070 ^ _779999) ^ [_1343540, _1343542] : [class_Rings_Oring__1(_1343540), -(hBOOL(hAPP(hAPP(c_member(_1343540), hAPP(c_Int_Oring__1__class_Oof__int(_1343540), _1343542)), c_Int_Oring__1__class_OInts(_1343540))))], (17503 ^ _779999) ^ [_1097557, _1097559, _1097561, _1097563, _1097565, _1097567] : [class_Rings_Olinordered__semiring__1__strict(_1097557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097557), _1097559), _1097561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097557), _1097563), _1097561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097557), c_Groups_Ozero__class_Ozero(_1097557)), _1097565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097557), c_Groups_Ozero__class_Ozero(_1097557)), _1097567)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097557), _1097565), _1097567) = c_Groups_Oone__class_Oone(_1097557), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097557), _1097565), _1097559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097557), _1097567), _1097563))), _1097561)))], (33611 ^ _779999) ^ [_1408480, _1408482] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1408480), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408482)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1408480), 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)))), _1408482)))], (11937 ^ _779999) ^ [_989914, _989916, _989918, _989920, _989922] : [c_Finite__Set_Ofolding__one(_989914, _989916, _989918), hBOOL(hAPP(c_Finite__Set_Ofinite(_989914), _989920)), hBOOL(hAPP(hAPP(c_member(_989914), _989922), _989920)), 11948 ^ _779999 : [(11955 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989914, tc_HOL_Obool)), _989920), hAPP(hAPP(c_Set_Oinsert(_989914), _989922), c_Orderings_Obot__class_Obot(tc_fun(_989914, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_989914, tc_HOL_Obool))), -(hAPP(_989918, _989920) = hAPP(hAPP(_989916, _989922), hAPP(_989918, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989914, tc_HOL_Obool)), _989920), hAPP(hAPP(c_Set_Oinsert(_989914), _989922), c_Orderings_Obot__class_Obot(tc_fun(_989914, tc_HOL_Obool)))))))], (11949 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989914, tc_HOL_Obool)), _989920), hAPP(hAPP(c_Set_Oinsert(_989914), _989922), c_Orderings_Obot__class_Obot(tc_fun(_989914, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_989914, tc_HOL_Obool)), -(hAPP(_989918, _989920) = _989922)]]], (24052 ^ _779999) ^ [_1229343, _1229345, _1229347] : [class_Orderings_Olinorder(_1229343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229343), _1229345)), -(_1229345 = c_Orderings_Obot__class_Obot(tc_fun(_1229343, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229343), _1229347)), -(_1229347 = c_Orderings_Obot__class_Obot(tc_fun(_1229343, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1229343, c_Orderings_Oord__class_Omin(_1229343), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229343, tc_HOL_Obool)), _1229345), _1229347)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229343), c_Big__Operators_Olattice_OInf__fin(_1229343, c_Orderings_Oord__class_Omin(_1229343), _1229345)), c_Big__Operators_Olattice_OInf__fin(_1229343, c_Orderings_Oord__class_Omin(_1229343), _1229347)))], (11324 ^ _779999) ^ [_976507, _976509, _976511, _976513] : [hBOOL(hAPP(hAPP(c_member(_976507), _976509), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976507, tc_HOL_Obool)), _976511), _976513))), 11327 ^ _779999 : [(11330 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976507), _976509), _976513)))], (11328 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976507), _976509), _976511)))]]], (914 ^ _779999) ^ [_793962, _793964, _793966, _793968, _793970, _793972] : [-(c_List_Olist__ex(_793970, _793966, _793962)), c_List_Olist__ex(_793972, _793968, _793964), _793972 = _793970, _793968 = _793966, _793964 = _793962], (17561 ^ _779999) ^ [_1098883, _1098885] : [17569 ^ _779999 : [(17572 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1098885, 17568 ^ [_1098883, _1098885])))], (17570 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17568 ^ [_1098883, _1098885]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1098883))))]], 17562 ^ _779999 : [(17563 ^ _779999) ^ [_1098952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098952), _1098883)), hBOOL(hAPP(_1098885, _1098952))]]], (5040 ^ _779999) ^ [_857013, _857015, _857017, _857019, _857021, _857023, _857025, _857027] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_857027, _857023, _857019, _857015) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_857025, _857021, _857017, _857013)), _857027 = _857025, _857023 = _857021, _857019 = _857017, _857015 = _857013], (10561 ^ _779999) ^ [_961735, _961737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961735), _961737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961735)), _961737)))], (25830 ^ _779999) ^ [_1264055, _1264057, _1264059] : [class_Groups_Oab__group__add(_1264055), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1264055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264055), _1264057), _1264059)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264055), hAPP(c_Groups_Ouminus__class_Ouminus(_1264055), _1264057)), hAPP(c_Groups_Ouminus__class_Ouminus(_1264055), _1264059)))], (11881 ^ _779999) ^ [_988886, _988888, _988890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988886), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988886, tc_HOL_Obool)), _988888), _988890))), 11884 ^ _779999 : [(11887 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_988886), _988890)))], (11885 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_988886), _988888)))]]], (27540 ^ _779999) ^ [_1297927, _1297929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297927), _1297929)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1297927, tc_HOL_Obool)), hAPP(c_Set_OPow(_1297927), _1297929)) = 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(_1297927), _1297929)))], (10053 ^ _779999) ^ [_953419, _953421, _953423, _953425] : [c_Fun_Oinj__on(_953419, _953421, _953423, _953425), -(c_Fun_Oinj__on(_953421, _953419, c_Fun_Othe__inv__into(_953419, _953421, _953425, _953423), hAPP(c_Set_Oimage(_953419, _953421, _953423), _953425)))], (8086 ^ _779999) ^ [_916572, _916574, _916576, _916578] : [-(hBOOL(hAPP(hAPP(c_member(_916572), _916574), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916572, tc_HOL_Obool)), _916576), _916578)))), hBOOL(hAPP(hAPP(c_member(_916572), _916574), _916576)), -(hBOOL(hAPP(hAPP(c_member(_916572), _916574), _916578)))], (36278 ^ _779999) ^ [_1463165, _1463167] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1463165, _1463167) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1463165, _1463167)))], (2066 ^ _779999) ^ [_810046, _810048, _810050, _810052, _810054, _810056] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_810056, _810052, _810048) = c_Hoare__Mirabelle_Otriple_Otriple__size(_810054, _810050, _810046)), _810056 = _810054, _810052 = _810050, _810048 = _810046], (15030 ^ _779999) ^ [_1049778, _1049780] : [class_Groups_Olinordered__ab__group__add(_1049778), 15033 ^ _779999 : [(15040 ^ _779999) ^ [] : [_1049780 = c_Groups_Ozero__class_Ozero(_1049778), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049778), _1049780), _1049780) = c_Groups_Ozero__class_Ozero(_1049778))], (15034 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049778), _1049780), _1049780) = c_Groups_Ozero__class_Ozero(_1049778), -(_1049780 = c_Groups_Ozero__class_Ozero(_1049778))]]], (34983 ^ _779999) ^ [_1433756] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1433756, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29098 ^ _779999) ^ [_1326503, _1326505, _1326507, _1326509] : [class_Fields_Ofield(_1326503), -(_1326505 = c_Groups_Ozero__class_Ozero(_1326503)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326503), _1326507), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326503), _1326509), _1326505)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326503), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326503), _1326505), _1326507)), _1326509)), _1326505))], (4140 ^ _779999) ^ [_842389, _842391, _842393, _842395, _842397, _842399, _842401, _842403, _842405, _842407, _842409, _842411, _842413, _842415] : [-(c_New__Random__Sequence_Oneg__decr__bind(_842415, _842411, _842407, _842403, _842399, _842395, _842391) = c_New__Random__Sequence_Oneg__decr__bind(_842413, _842409, _842405, _842401, _842397, _842393, _842389)), _842415 = _842413, _842411 = _842409, _842407 = _842405, _842403 = _842401, _842399 = _842397, _842395 = _842393, _842391 = _842389], (34505 ^ _779999) ^ [_1424830, _1424832, _1424834] : [class_Rings_Ocomm__semiring__1(_1424830), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424830), _1424832), 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)))), _1424834)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424830), hAPP(hAPP(c_Power_Opower__class_Opower(_1424830), _1424832), _1424834)), hAPP(hAPP(c_Power_Opower__class_Opower(_1424830), _1424832), _1424834)))], (7209 ^ _779999) ^ [_899091, _899093, _899095, _899097] : [hBOOL(hAPP(hAPP(c_member(_899091), _899093), _899095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899091, tc_HOL_Obool)), _899095), _899097)), -(hBOOL(hAPP(hAPP(c_member(_899091), _899093), _899097)))], (11054 ^ _779999) ^ [_971321, _971323, _971325, _971327] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971321, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971321, tc_HOL_Obool)), _971323), _971325)), _971327) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971321, tc_HOL_Obool)), _971323), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971321, tc_HOL_Obool)), _971325), _971327)))], (22231 ^ _779999) ^ [_1191344, _1191346, _1191348, _1191350, _1191352] : [c_Fun_Oinj__on(_1191344, _1191346, _1191348, c_Orderings_Otop__class_Otop(tc_fun(_1191344, tc_HOL_Obool))), 22234 ^ _779999 : [(22241 ^ _779999) ^ [] : [_1191350 = _1191352, -(hAPP(_1191348, _1191350) = hAPP(_1191348, _1191352))], (22235 ^ _779999) ^ [] : [hAPP(_1191348, _1191350) = hAPP(_1191348, _1191352), -(_1191350 = _1191352)]]], (51590 ^ _779999) ^ [_1824156, _1824158, _1824160, _1824162] : [c_Fun_Obij__betw(_1824156, _1824158, _1824160, c_Orderings_Otop__class_Otop(tc_fun(_1824156, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1824158, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1824156, _1824158, _1824160), hAPP(c_Set_OCollect(_1824156), _1824162)) = hAPP(c_Set_OCollect(_1824158), hAPP(hAPP(c_COMBB(_1824156, tc_HOL_Obool, _1824158), _1824162), c_Hilbert__Choice_Oinv__into(_1824156, _1824158, c_Orderings_Otop__class_Otop(tc_fun(_1824156, tc_HOL_Obool)), _1824160))))], (27142 ^ _779999) ^ [_1290805, _1290807] : [class_Rings_Ocomm__semiring__1(_1290805), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1290805), _1290807), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1290807)], (3450 ^ _779999) ^ [_831588, _831590, _831592, _831594, _831596, _831598] : [-(c_Big__Operators_Olattice_OInf__fin(_831598, _831594, _831590) = c_Big__Operators_Olattice_OInf__fin(_831596, _831592, _831588)), _831598 = _831596, _831594 = _831592, _831590 = _831588], (17915 ^ _779999) ^ [_1106028, _1106030] : [17916 ^ _779999 : [(17917 ^ _779999) ^ [_1106084] : [_1106030 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106028), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1106084)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106028), _1106030)))], (19901 ^ _779999) ^ [_1143067, _1143069, _1143071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143067)), 19907 ^ _779999 : [(19910 ^ _779999) ^ [] : [hBOOL(hAPP(_1143069, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19906 ^ [_1143067, _1143069, _1143071]), _1143067)))], (19908 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1143069, 19906 ^ [_1143067, _1143069, _1143071])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143071)), 19915 ^ _779999 : [(19916 ^ _779999) ^ [_1143356] : [hBOOL(hAPP(_1143069, _1143356)), -(hBOOL(hAPP(_1143069, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143071), _1143067)))))]]], (4820 ^ _779999) ^ [_853429, _853431, _853433, _853435, _853437, _853439, _853441, _853443, _853445, _853447] : [-(c_Nitpick_Opair__box_Opair__box__case(_853447, _853443, _853439, _853435, _853431) = c_Nitpick_Opair__box_Opair__box__case(_853445, _853441, _853437, _853433, _853429)), _853447 = _853445, _853443 = _853441, _853439 = _853437, _853435 = _853433, _853431 = _853429], (33875 ^ _779999) ^ [_1413833, _1413835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413833)), -(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)))), _1413835))), 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)))), _1413833)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1413835), _1413833))], (51998 ^ _779999) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (4556 ^ _779999) ^ [_849221, _849223, _849225, _849227] : [-(c_List_Ofilter(_849227, _849223) = c_List_Ofilter(_849225, _849221)), _849227 = _849225, _849223 = _849221], (35109 ^ _779999) ^ [_1435782, _1435784] : [-(c_Divides_Odivmod__int__rel(_1435782, _1435784) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fequal, _1435782))), 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), _1435784)))))), 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)), _1435784))), 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)), _1435784))))), 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)), _1435784)))), 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), _1435784))), 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))))))))], (10421 ^ _779999) ^ [_959419, _959421, _959423, _959425, _959427] : [c_Fun_Oinj__on(_959419, _959421, _959423, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959419, tc_HOL_Obool)), _959425), _959427)), 10424 ^ _779999 : [(10431 ^ _779999) ^ [] : [_959425 = _959427, -(hAPP(c_Set_Oimage(_959419, _959421, _959423), _959425) = hAPP(c_Set_Oimage(_959419, _959421, _959423), _959427))], (10425 ^ _779999) ^ [] : [hAPP(c_Set_Oimage(_959419, _959421, _959423), _959425) = hAPP(c_Set_Oimage(_959419, _959421, _959423), _959427), -(_959425 = _959427)]]], (42480 ^ _779999) ^ [_1616097, _1616099, _1616101] : [-(hAPP(c_Relation_ORange(_1616097, _1616099), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1616097, _1616099), tc_HOL_Obool), _1616101)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1616097, _1616099), tc_HOL_Obool), tc_fun(_1616099, tc_HOL_Obool)), _1616101), c_Relation_ORange(_1616097, _1616099)))], (41568 ^ _779999) ^ [_1593382, _1593384, _1593386] : [class_Orderings_Olinorder(_1593382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593382), _1593384)), -(hBOOL(hAPP(hAPP(c_member(_1593382), _1593386), _1593384))), -(c_Big__Operators_Olinorder__class_OMin(_1593382, hAPP(hAPP(c_Set_Oinsert(_1593382), _1593386), _1593384)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593382, _1593382, c_Orderings_Oord__class_Omin(_1593382)), _1593386), _1593384))], (46452 ^ _779999) ^ [_1711581, _1711583, _1711585, _1711587, _1711589] : [class_Groups_Ocomm__monoid__add(_1711581), hBOOL(hAPP(hAPP(c_member(_1711583), _1711585), hAPP(c_List_Oset(_1711583), _1711587))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711581), hAPP(hAPP(c_List_Omap(_1711583, _1711581), _1711589), _1711587)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1711581), hAPP(_1711589, _1711585)), hAPP(c_List_Omonoid__add__class_Olistsum(_1711581), hAPP(hAPP(c_List_Omap(_1711583, _1711581), _1711589), c_List_Oremove1(_1711583, _1711585, _1711587)))))], (42325 ^ _779999) ^ [_1612545, _1612547, _1612549, _1612551] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1612545, tc_HOL_Obool), hAPP(c_Set_Oimage(_1612547, tc_fun(_1612545, tc_HOL_Obool), _1612549), _1612551)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612547, tc_fun(_1612545, tc_HOL_Obool)), _1612551), _1612549))], (17143 ^ _779999) ^ [_1090212, _1090214, _1090216] : [class_Rings_Olinordered__ring__strict(_1090212), 17146 ^ _779999 : [(17147 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090212), c_Groups_Ozero__class_Ozero(_1090212)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090212), _1090214), _1090214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090212), _1090216), _1090216)))), _1090214 = c_Groups_Ozero__class_Ozero(_1090212), _1090216 = c_Groups_Ozero__class_Ozero(_1090212)], (17157 ^ _779999) ^ [] : [17158 ^ _779999 : [(17161 ^ _779999) ^ [] : [-(_1090216 = c_Groups_Ozero__class_Ozero(_1090212))], (17159 ^ _779999) ^ [] : [-(_1090214 = c_Groups_Ozero__class_Ozero(_1090212))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090212), c_Groups_Ozero__class_Ozero(_1090212)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090212), _1090214), _1090214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090212), _1090216), _1090216)))))]]], (20290 ^ _779999) ^ [_1149269, _1149271] : [hBOOL(hAPP(_1149269, hAPP(c_Int_Onat, _1149271))), 20293 ^ _779999 : [(20300 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149271), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1149269, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20294 ^ _779999) ^ [_1149369] : [_1149271 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149369), -(hBOOL(hAPP(_1149269, _1149369)))]]], (51079 ^ _779999) ^ [_1813594, _1813596, _1813598] : [c_Relation_Osym(_1813594, _1813596), c_Relation_Osym(_1813594, _1813598), -(c_Relation_Osym(_1813594, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1813594, _1813594), tc_HOL_Obool)), _1813596), _1813598)))], (52296 ^ _779999) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (31395 ^ _779999) ^ [_1368070, _1368072, _1368074, _1368076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1368070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368072), _1368074)), -(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), _1368074), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1368076, _1368070))), _1368072)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368074), _1368070))))], (49752 ^ _779999) ^ [_1783793, _1783795, _1783797] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783793)), c_List_Osplice(_1783793, _1783795, _1783797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783793)), _1783795)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783793)), _1783797)))], (50434 ^ _779999) ^ [_1798626, _1798628, _1798630, _1798632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1798626), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1798628, _1798630, _1798626, _1798632) = 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(_1798628)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1798628)))], (48839 ^ _779999) ^ [_1763354, _1763356] : [class_Orderings_Olinorder(_1763354), 48846 ^ _779999 : [(48851 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763354), hAPP(hAPP(c_List_Onth(_1763354), _1763356), 48844 ^ [_1763354, _1763356])), hAPP(hAPP(c_List_Onth(_1763354), _1763356), 48845 ^ [_1763354, _1763356])))], (48849 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48845 ^ [_1763354, _1763356]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763354)), _1763356))))], (48847 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48844 ^ [_1763354, _1763356]), 48845 ^ [_1763354, _1763356])))]], -(c_List_Olinorder__class_Osorted(_1763354, _1763356))], (24492 ^ _779999) ^ [_1238650, _1238652, _1238654, _1238656] : [class_Orderings_Olinorder(_1238650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238650), _1238652), _1238654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238650), _1238652), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238650), _1238654), _1238656))))], (22940 ^ _779999) ^ [_1207241, _1207243, _1207245, _1207247, _1207249] : [_1207241 = c_Orderings_Obot__class_Obot(tc_fun(_1207243, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207243, tc_fun(_1207245, tc_HOL_Obool)), _1207241), hAPP(hAPP(c_COMBB(tc_fun(_1207245, tc_HOL_Obool), tc_fun(_1207245, tc_HOL_Obool), _1207243), hAPP(c_Set_Oinsert(_1207245), _1207247)), _1207249)) = c_Orderings_Obot__class_Obot(tc_fun(_1207245, tc_HOL_Obool)))], (22851 ^ _779999) ^ [_1204269, _1204271, _1204273, _1204275, _1204277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204269, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204271, tc_fun(_1204269, tc_HOL_Obool)), _1204273), _1204275)), _1204277)), 22854 ^ _779999 : [(22855 ^ _779999) ^ [_1204402] : [hBOOL(hAPP(hAPP(c_member(_1204271), _1204402), _1204273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204269, tc_HOL_Obool)), hAPP(_1204275, _1204402)), _1204277)))]]], (40699 ^ _779999) ^ [_1572767, _1572769, _1572771] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572767, _1572769)), hAPP(c_Relation_Oconverse(_1572769, _1572767), _1572771))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572769, _1572767)), _1572771)))], (19393 ^ _779999) ^ [] : [-(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)))], (51402 ^ _779999) ^ [_1819916, _1819918, _1819920, _1819922, _1819924, _1819926] : [c_Fun_Oinj__on(_1819916, _1819918, _1819920, _1819922), hBOOL(hAPP(hAPP(c_member(_1819916), _1819924), _1819922)), hAPP(_1819920, _1819924) = _1819926, -(hAPP(c_Hilbert__Choice_Oinv__into(_1819916, _1819918, _1819922, _1819920), _1819926) = _1819924)], (26044 ^ _779999) ^ [_1268515, _1268517, _1268519, _1268521, _1268523] : [c_Com_Ocom_OCond(_1268515, _1268517, _1268519) = c_Com_Ocom_OSemi(_1268521, _1268523)], (33605 ^ _779999) ^ [_1408331, _1408333] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1408331, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408333)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1408331, 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)))), _1408333)))], (30471 ^ _779999) ^ [_1351006, _1351008, _1351010, _1351012] : [class_Divides_Oring__div(_1351006), -(c_Divides_Odiv__class_Omod(_1351006, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351006), _1351008), _1351010), _1351012) = c_Divides_Odiv__class_Omod(_1351006, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351006), c_Divides_Odiv__class_Omod(_1351006, _1351008, _1351012)), _1351010), _1351012))], (31375 ^ _779999) ^ [_1367661, _1367663, _1367665] : [-(hBOOL(hAPP(_1367661, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1367663, _1367665)))), 31378 ^ _779999 : [(31381 ^ _779999) ^ [] : [hBOOL(hAPP(_1367661, _1367663))], (31379 ^ _779999) ^ [] : [-(_1367665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 31382 ^ _779999 : [(31387 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31385 ^ [_1367661, _1367663, _1367665]), _1367665)))], (31389 ^ _779999) ^ [] : [-(_1367663 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1367665), 31384 ^ [_1367661, _1367663, _1367665])), 31385 ^ [_1367661, _1367663, _1367665]))], (31391 ^ _779999) ^ [] : [hBOOL(hAPP(_1367661, 31385 ^ [_1367661, _1367663, _1367665]))], (31383 ^ _779999) ^ [] : [_1367665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31556 ^ _779999) ^ [_1371058, _1371060, _1371062] : [_1371060 = c_Orderings_Obot__class_Obot(tc_fun(_1371058, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1371058, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371058), _1371060), _1371062))], (40132 ^ _779999) ^ [_1559074, _1559076, _1559078, _1559080, _1559082, _1559084, _1559086] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1559074, _1559076, _1559078, _1559080), _1559082), _1559084), _1559086) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559076, _1559078, _1559080), _1559084), hAPP(_1559082, _1559086)))], (20942 ^ _779999) ^ [_1160076, _1160078, _1160080] : [class_Groups_Oordered__ab__group__add__abs(_1160076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160076), hAPP(c_Groups_Oabs__class_Oabs(_1160076), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160076), _1160078), _1160080))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160076), hAPP(c_Groups_Oabs__class_Oabs(_1160076), _1160078)), hAPP(c_Groups_Oabs__class_Oabs(_1160076), _1160080)))))], (38392 ^ _779999) ^ [_1514664, _1514666] : [-(hAPP(c_Relation_OField(_1514664), _1514666) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514664, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1514664, _1514664), _1514666)), hAPP(c_Relation_ORange(_1514664, _1514664), _1514666)))], (40948 ^ _779999) ^ [_1579110, _1579112, _1579114] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579110, _1579110), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1579112)), _1579114) = hAPP(hAPP(c_Relation_Orel__comp(_1579110, _1579110, _1579110), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579110, _1579110), tc_HOL_Obool), _1579112), _1579114)), _1579114))], (11288 ^ _779999) ^ [_975632, _975634, _975636] : [class_Lattices_Olattice(_975632), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975632), _975634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975632), _975634), _975636)) = _975634)], (37929 ^ _779999) ^ [_1503886, _1503888] : [c_Wellfounded_Owf(_1503886, hAPP(hAPP(c_Relation_Orel__comp(_1503886, _1503886, _1503886), _1503888), _1503888)), -(c_Wellfounded_Owf(_1503886, _1503888))], (25412 ^ _779999) ^ [_1256926, _1256928, _1256930] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1256926, tc_Nat_Onat), _1256928), _1256930) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1256926, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1256926), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1256928)), _1256930)))], (9578 ^ _779999) ^ [_942787, _942789, _942791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942787, tc_HOL_Obool)), _942789), _942791)), 9581 ^ _779999 : [(9584 ^ _779999) ^ [] : [_942789 = _942791], (9582 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942787, tc_HOL_Obool)), _942789), _942791)))]]], (24574 ^ _779999) ^ [_1240028, _1240030, _1240032] : [class_Orderings_Olinorder(_1240028), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240028), _1240030), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240028), _1240030), _1240032)) = _1240030)], (21784 ^ _779999) ^ [_1177392, _1177394, _1177396] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1177392, tc_HOL_Obool)), _1177394), _1177396) = hAPP(c_Set_OCollect(_1177392), hAPP(hAPP(c_COMBS(_1177392, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177392), c_fconj), hAPP(hAPP(c_COMBC(_1177392, tc_fun(_1177392, tc_HOL_Obool), tc_HOL_Obool), c_member(_1177392)), _1177394))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1177392), c_fNot), hAPP(hAPP(c_COMBC(_1177392, tc_fun(_1177392, tc_HOL_Obool), tc_HOL_Obool), c_member(_1177392)), _1177396)))))], (17689 ^ _779999) ^ [_1101553, _1101555, _1101557, _1101559] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101553), _1101555)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101557), _1101555)), _1101559)) = 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), _1101553), _1101557)), _1101555)), _1101559))], (42195 ^ _779999) ^ [_1609604, _1609606, _1609608, _1609610, _1609612] : [-(_1609604 = c_Orderings_Obot__class_Obot(tc_fun(_1609606, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609606, tc_fun(_1609608, tc_HOL_Obool)), _1609604), hAPP(hAPP(c_COMBB(tc_fun(_1609608, tc_HOL_Obool), tc_fun(_1609608, tc_HOL_Obool), _1609606), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609608, tc_HOL_Obool)), _1609610)), _1609612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609608, tc_HOL_Obool)), _1609610), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609606, tc_fun(_1609608, tc_HOL_Obool)), _1609604), _1609612)))], (1594 ^ _779999) ^ [_803032, _803034] : [-(class_Groups_Olinordered__ab__semigroup__add(_803032)), _803034 = _803032, class_Groups_Olinordered__ab__semigroup__add(_803034)], (49074 ^ _779999) ^ [_1768309, _1768311, _1768313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768309, _1768309)), hAPP(hAPP(c_Product__Type_OPair(_1768309, _1768309), _1768311), _1768313)), c_List_Omeasures(_1768309, c_List_Olist_ONil(tc_fun(_1768309, tc_Nat_Onat)))))], (5700 ^ _779999) ^ [_867207, _867209, _867211, _867213, _867215, _867217] : [-(c_Set_Oimage(_867217, _867213, _867209) = c_Set_Oimage(_867215, _867211, _867207)), _867217 = _867215, _867213 = _867211, _867209 = _867207], (39625 ^ _779999) ^ [_1546949, _1546951, _1546953, _1546955, _1546957, _1546959, _1546961, _1546963] : [c_Finite__Set_Ofolding__image(_1546949, _1546951, _1546953, _1546955, _1546957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546951), _1546959)), c_Fun_Oinj__on(_1546951, _1546951, _1546961, _1546959), -(hAPP(hAPP(_1546957, _1546963), hAPP(c_Set_Oimage(_1546951, _1546951, _1546961), _1546959)) = hAPP(hAPP(_1546957, hAPP(c_Fun_Ocomp(_1546951, _1546949, _1546951, _1546963), _1546961)), _1546959))], (28030 ^ _779999) ^ [_1306895, _1306897, _1306899, _1306901] : [class_Rings_Olinordered__semidom(_1306895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306897), _1306899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306895), c_Groups_Oone__class_Oone(_1306895)), _1306901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306895), hAPP(hAPP(c_Power_Opower__class_Opower(_1306895), _1306901), _1306897)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306895), _1306901), _1306899))))], (33047 ^ _779999) ^ [_1399469] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1399469), c_Int_OPls) = _1399469)], (44093 ^ _779999) ^ [_1659502, _1659504, _1659506] : [hBOOL(hAPP(hAPP(c_member(_1659502), _1659504), hAPP(c_List_Oset(_1659502), c_List_Obutlast(_1659502, _1659506)))), -(hBOOL(hAPP(hAPP(c_member(_1659502), _1659504), hAPP(c_List_Oset(_1659502), _1659506))))], (11765 ^ _779999) ^ [_986731, _986733, _986735, _986737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986731), _986733)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_986735), hAPP(c_Set_Oimage(_986731, _986735, _986737), _986733))))], (27888 ^ _779999) ^ [_1304217, _1304219, _1304221] : [class_Fields_Ofield__inverse__zero(_1304217), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304217), c_Groups_Oone__class_Oone(_1304217)), hAPP(hAPP(c_Power_Opower__class_Opower(_1304217), _1304219), _1304221)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1304217), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304217), c_Groups_Oone__class_Oone(_1304217)), _1304219)), _1304221))], (9010 ^ _779999) ^ [_934102, _934104, _934106, _934108] : [class_Orderings_Oord(_934102), _934104 = _934106, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934102), _934106), _934108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934102), _934104), _934108)))], (21387 ^ _779999) ^ [_1169430, _1169432, _1169434] : [-(hAPP(c_Finite__Set_Ofold1(_1169430, _1169432), hAPP(hAPP(c_Set_Oinsert(_1169430), _1169434), c_Orderings_Obot__class_Obot(tc_fun(_1169430, tc_HOL_Obool)))) = _1169434)], (13708 ^ _779999) ^ [_1024513, _1024515, _1024517, _1024519] : [class_Groups_Oordered__comm__monoid__add(_1024513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024513), c_Groups_Ozero__class_Ozero(_1024513)), _1024515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024513), _1024517), _1024519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024513), _1024517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024513), _1024519), _1024515))))], (9276 ^ _779999) ^ [_938162, _938164, _938166] : [class_Orderings_Opreorder(_938162), 9279 ^ _779999 : [(9288 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938162), _938164), _938166))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938162), _938164), _938166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938162), _938166), _938164)))], (9280 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938162), _938164), _938166)), 9283 ^ _779999 : [(9286 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938162), _938166), _938164))], (9284 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938162), _938164), _938166)))]]]]], (24308 ^ _779999) ^ [_1235282, _1235284, _1235286] : [class_Orderings_Olinorder(_1235282), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235282), _1235284), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235282), _1235284), _1235286)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235282), _1235284), _1235286))], (3740 ^ _779999) ^ [_836129, _836131, _836133, _836135] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_836135, _836131) = c_SetInterval_Oord__class_OatLeastLessThan(_836133, _836129)), _836135 = _836133, _836131 = _836129], (27750 ^ _779999) ^ [_1301809, _1301811, _1301813, _1301815] : [class_Rings_Olinordered__semidom(_1301809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301809), _1301811), _1301813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301809), c_Groups_Ozero__class_Ozero(_1301809)), _1301811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301809), hAPP(hAPP(c_Power_Opower__class_Opower(_1301809), _1301811), _1301815)), hAPP(hAPP(c_Power_Opower__class_Opower(_1301809), _1301813), _1301815))))], (43147 ^ _779999) ^ [_1631401, _1631403, _1631405] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631401)), _1631403) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631401)), _1631405)), _1631403 = _1631405], (22978 ^ _779999) ^ [_1208135, _1208137, _1208139, _1208141, _1208143] : [_1208135 = c_Orderings_Obot__class_Obot(tc_fun(_1208137, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1208139, tc_HOL_Obool)), _1208141), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1208137, tc_fun(_1208139, tc_HOL_Obool)), _1208135), _1208143)) = _1208141)], (11172 ^ _779999) ^ [_973583, _973585, _973587, _973589] : [class_Lattices_Osemilattice__inf(_973583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973583), _973585), _973587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973583), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973583), _973589), _973585)), _973587)))], (10806 ^ _779999) ^ [_966652, _966654, _966656, _966658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_966652), _966654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966652, tc_HOL_Obool)), _966654), _966656)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966652, tc_Nat_Onat), _966658), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966652, tc_HOL_Obool)), _966656), _966654)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966652, tc_Nat_Onat), _966658), _966656)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966652, tc_Nat_Onat), _966658), _966654)))], (41926 ^ _779999) ^ [_1602144, _1602146, _1602148, _1602150] : [c_Orderings_Otop__class_Otop(tc_fun(_1602144, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602146, tc_fun(_1602144, tc_HOL_Obool)), _1602148), _1602150), 41929 ^ _779999 : [(41930 ^ _779999) ^ [_1602260] : [hBOOL(hAPP(hAPP(c_member(_1602146), _1602260), _1602148)), -(hAPP(_1602150, _1602260) = c_Orderings_Otop__class_Otop(tc_fun(_1602144, tc_HOL_Obool)))]]], (40611 ^ _779999) ^ [_1571139, _1571141] : [40612 ^ _779999 : [(40615 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571141), _1571139))], (40613 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1571139), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1571139, _1571141) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (52400 ^ _779999) ^ [_1834840, _1834842] : [hBOOL(hAPP(hAPP(c_fdisj, _1834840), _1834842)), -(hBOOL(_1834840)), -(hBOOL(_1834842))], (40962 ^ _779999) ^ [_1579495, _1579497, _1579499, _1579501, _1579503, _1579505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579495, _1579495)), hAPP(hAPP(c_Product__Type_OPair(_1579495, _1579495), _1579497), _1579499)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579495, _1579495), tc_HOL_Obool), _1579501), _1579503))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1579495, _1579495)), hAPP(hAPP(c_Product__Type_OPair(_1579495, _1579495), _1579499), _1579505)), _1579503)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579495, _1579495)), hAPP(hAPP(c_Product__Type_OPair(_1579495, _1579495), _1579497), _1579505)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579495, _1579495), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1579501)), _1579503))))], (32953 ^ _779999) ^ [_1397979, _1397981] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397979))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397979), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397981)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26596 ^ _779999) ^ [_1278432, _1278434, _1278436] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278432, tc_HOL_Obool)), _1278434), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278432, tc_HOL_Obool)), _1278436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278432, tc_HOL_Obool)), _1278434), _1278436))], (50450 ^ _779999) ^ [_1799217, _1799219, _1799221, _1799223] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1799217), _1799219), _1799221), _1799223) = 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(_1799217)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1799217), _1799219)))], (43551 ^ _779999) ^ [_1644418, _1644420, _1644422, _1644424] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644418)), hAPP(hAPP(c_List_Olist_OCons(_1644418), _1644420), _1644422)), c_List_Olists(_1644418, _1644424)))), hBOOL(hAPP(hAPP(c_member(_1644418), _1644420), _1644424)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644418)), _1644422), c_List_Olists(_1644418, _1644424)))], (38209 ^ _779999) ^ [_1509976, _1509978] : [-(hAPP(c_List_Olexn(_1509976, _1509978), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1509976), tc_List_Olist(_1509976)), tc_HOL_Obool)))], (47753 ^ _779999) ^ [_1741487, _1741489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741487), _1741489)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1741487, _1741489)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1741489), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (41183 ^ _779999) ^ [_1585276, _1585278, _1585280, _1585282, _1585284] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585276, _1585276)), hAPP(hAPP(c_Product__Type_OPair(_1585276, _1585276), _1585278), _1585280)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585276, _1585276), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585282)), _1585284))), 41187 ^ _779999 : [(41190 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585276, _1585276)), hAPP(hAPP(c_Product__Type_OPair(_1585276, _1585276), 41186 ^ [_1585276, _1585278, _1585280, _1585282, _1585284]), _1585280)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585276, _1585276), tc_HOL_Obool), _1585282), _1585284))))], (41188 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585276, _1585276)), hAPP(hAPP(c_Product__Type_OPair(_1585276, _1585276), _1585278), 41186 ^ [_1585276, _1585278, _1585280, _1585282, _1585284])), _1585284)))]]], (17115 ^ _779999) ^ [_1089673, _1089675, _1089677] : [class_Rings_Olinordered__ring__strict(_1089673), 17118 ^ _779999 : [(17127 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089673), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089673), _1089675), _1089675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089673), _1089677), _1089677))), c_Groups_Ozero__class_Ozero(_1089673)))), _1089675 = c_Groups_Ozero__class_Ozero(_1089673), _1089677 = c_Groups_Ozero__class_Ozero(_1089673)], (17119 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089673), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089673), _1089675), _1089675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089673), _1089677), _1089677))), c_Groups_Ozero__class_Ozero(_1089673))), 17122 ^ _779999 : [(17125 ^ _779999) ^ [] : [-(_1089677 = c_Groups_Ozero__class_Ozero(_1089673))], (17123 ^ _779999) ^ [] : [-(_1089675 = c_Groups_Ozero__class_Ozero(_1089673))]]]]], (48346 ^ _779999) ^ [_1752817, _1752819, _1752821] : [hAPP(hAPP(c_List_Olist_OCons(_1752817), _1752819), c_List_Olist_ONil(_1752817)) = hAPP(c_List_Orev(_1752817), _1752821), -(_1752821 = hAPP(hAPP(c_List_Olist_OCons(_1752817), _1752819), c_List_Olist_ONil(_1752817)))], (40763 ^ _779999) ^ [_1574225, _1574227, _1574229] : [-(hAPP(c_Relation_ORange(_1574225, _1574227), _1574229) = hAPP(c_Relation_ODomain(_1574227, _1574225), hAPP(c_Relation_Oconverse(_1574225, _1574227), _1574229)))], (44864 ^ _779999) ^ [_1676206, _1676208, _1676210, _1676212, _1676214] : [hAPP(hAPP(c_List_Oappend(_1676206), _1676208), _1676210) = hAPP(hAPP(c_List_Olist_OCons(_1676206), _1676212), _1676214), 44869 ^ _779999 : [(44872 ^ _779999) ^ [] : [-(_1676210 = hAPP(hAPP(c_List_Olist_OCons(_1676206), _1676212), _1676214))], (44870 ^ _779999) ^ [] : [-(_1676208 = c_List_Olist_ONil(_1676206))]], 44874 ^ _779999 : [(44877 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1676206), 44873 ^ [_1676206, _1676208, _1676210, _1676212, _1676214]), _1676210) = _1676214)], (44875 ^ _779999) ^ [] : [-(_1676208 = hAPP(hAPP(c_List_Olist_OCons(_1676206), _1676212), 44873 ^ [_1676206, _1676208, _1676210, _1676212, _1676214]))]]], (29490 ^ _779999) ^ [_1333524, _1333526, _1333528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1333524), _1333526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333528), 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), _1333526), _1333528)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333524), _1333528))))], (48985 ^ _779999) ^ [_1766268, _1766270, _1766272, _1766274] : [_1766268 = _1766270, -(hAPP(c_List_OremoveAll(_1766272, _1766268), hAPP(hAPP(c_List_Olist_OCons(_1766272), _1766270), _1766274)) = hAPP(c_List_OremoveAll(_1766272, _1766268), _1766274))], (22934 ^ _779999) ^ [_1207050, _1207052, _1207054, _1207056, _1207058] : [hBOOL(hAPP(hAPP(c_member(_1207050), _1207052), _1207054)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207056, tc_HOL_Obool)), hAPP(_1207058, _1207052)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207050, tc_fun(_1207056, tc_HOL_Obool)), _1207054), _1207058)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207050, tc_fun(_1207056, tc_HOL_Obool)), _1207054), _1207058))], (48474 ^ _779999) ^ [_1755623, _1755625] : [-(_1755623 = c_List_Olist_ONil(_1755625)), -(c_List_Olast(_1755625, hAPP(c_List_Orev(_1755625), _1755623)) = hAPP(c_List_Ohd(_1755625), _1755623))], (198 ^ _779999) ^ [_783144, _783146] : [-(c_Nat__Transfer_Ois__nat(_783144)), _783146 = _783144, c_Nat__Transfer_Ois__nat(_783146)], (41254 ^ _779999) ^ [_1587184, _1587186, _1587188] : [class_Orderings_Olinorder(_1587184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587184), _1587186)), -(hBOOL(hAPP(hAPP(c_member(_1587184), _1587188), _1587186))), -(c_Big__Operators_Olattice_OSup__fin(_1587184, c_Orderings_Oord__class_Omax(_1587184), hAPP(hAPP(c_Set_Oinsert(_1587184), _1587188), _1587186)) = hAPP(hAPP(c_Finite__Set_Ofold(_1587184, _1587184, c_Orderings_Oord__class_Omax(_1587184)), _1587188), _1587186))], (3120 ^ _779999) ^ [_826535, _826537, _826539, _826541, _826543, _826545] : [-(c_Nitpick_Oof__frac(_826545, _826541, _826537) = c_Nitpick_Oof__frac(_826543, _826539, _826535)), _826545 = _826543, _826541 = _826539, _826537 = _826535], (15251 ^ _779999) ^ [_1053989, _1053991] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1053989, _1053991)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1053991)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22419 ^ _779999) ^ [_1194818, _1194820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1194818, _1194820)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1194818, _1194820), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1194820), c_Orderings_Otop__class_Otop(tc_fun(_1194820, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1194818), c_Orderings_Otop__class_Otop(tc_fun(_1194818, tc_HOL_Obool)))))], (45275 ^ _779999) ^ [_1685331, _1685333, _1685335, _1685337, _1685339, _1685341, _1685343, _1685345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685331, _1685331)), hAPP(hAPP(c_Product__Type_OPair(_1685331, _1685331), _1685333), _1685335)), _1685337)), _1685339 = hAPP(hAPP(c_List_Oappend(_1685331), _1685341), hAPP(hAPP(c_List_Olist_OCons(_1685331), _1685333), _1685343)), _1685345 = hAPP(hAPP(c_List_Oappend(_1685331), _1685341), hAPP(hAPP(c_List_Olist_OCons(_1685331), _1685335), _1685343)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1685331), tc_List_Olist(_1685331))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1685331), tc_List_Olist(_1685331)), _1685339), _1685345)), c_List_Olistrel1(_1685331, _1685337))))], (46067 ^ _779999) ^ [_1702636, _1702638, _1702640] : [_1702636 = c_List_Olist_ONil(_1702638), -(c_List_Olast(_1702638, hAPP(hAPP(c_List_Olist_OCons(_1702638), _1702640), _1702636)) = _1702640)], (44304 ^ _779999) ^ [_1664320, _1664322] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1664320, _1664322))))], (23579 ^ _779999) ^ [_1220497, _1220499, _1220501, _1220503] : [-(hBOOL(hAPP(hAPP(c_member(_1220497), _1220499), _1220501))), -(hAPP(c_Set_Ovimage(_1220503, _1220497, hAPP(c_COMBK(_1220497, _1220503), _1220499)), _1220501) = c_Orderings_Obot__class_Obot(tc_fun(_1220503, tc_HOL_Obool)))], (13975 ^ _779999) ^ [_1029117, _1029119, _1029121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029117), _1029119)), 13978 ^ _779999 : [(13985 ^ _779999) ^ [] : [_1029119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029121), _1029117), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029119), _1029117) = _1029121)], (13979 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029119), _1029117) = _1029121, -(_1029119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029121), _1029117))]]], (32103 ^ _779999) ^ [_1381875, _1381877, _1381879, _1381881] : [class_Fields_Ofield__inverse__zero(_1381875), class_Int_Onumber(_1381875), 32110 ^ _779999 : [(32111 ^ _779999) ^ [] : [_1381877 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381875), _1381879), hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881)), 32114 ^ _779999 : [(32121 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881) = c_Groups_Ozero__class_Ozero(_1381875), -(_1381877 = c_Groups_Ozero__class_Ozero(_1381875))], (32115 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881) = c_Groups_Ozero__class_Ozero(_1381875)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381875), _1381877), hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881)) = _1381879)]]], (32127 ^ _779999) ^ [] : [-(_1381877 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381875), _1381879), hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881))), 32130 ^ _779999 : [(32133 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381875), _1381877), hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881)) = _1381879], (32131 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881) = c_Groups_Ozero__class_Ozero(_1381875)]], 32134 ^ _779999 : [(32137 ^ _779999) ^ [] : [_1381877 = c_Groups_Ozero__class_Ozero(_1381875)], (32135 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1381875), _1381881) = c_Groups_Ozero__class_Ozero(_1381875))]]]]], (3410 ^ _779999) ^ [_830992, _830994, _830996, _830998] : [-(c_Big__Operators_Olattice__class_OSup__fin(_830998, _830994) = c_Big__Operators_Olattice__class_OSup__fin(_830996, _830992)), _830998 = _830996, _830994 = _830992], (39203 ^ _779999) ^ [_1536989, _1536991] : [39205 ^ _779999 : [(39208 ^ _779999) ^ [] : [hBOOL(hAPP(_1536989, hAPP(c_Int_OAbs__Integ, 39204 ^ [_1536989, _1536991])))], (39206 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39204 ^ [_1536989, _1536991]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1536989, _1536991)))], (33759 ^ _779999) ^ [_1411874, _1411876] : [class_Rings_Osemiring__1(_1411874), 33762 ^ _779999 : [(33769 ^ _779999) ^ [] : [_1411876 = c_Groups_Ozero__class_Ozero(_1411874), -(c_Int_Oiszero(_1411874, _1411876))], (33763 ^ _779999) ^ [] : [c_Int_Oiszero(_1411874, _1411876), -(_1411876 = c_Groups_Ozero__class_Ozero(_1411874))]]], (24648 ^ _779999) ^ [_1241695] : [class_Orderings_Oord(_1241695), -(c_Orderings_Oord__class_Omax(_1241695) = c_Orderings_Oord_Omax(_1241695, c_Orderings_Oord__class_Oless__eq(_1241695)))], (30601 ^ _779999) ^ [_1353751, _1353753] : [class_Divides_Osemiring__div(_1353751), -(c_Divides_Odiv__class_Omod(_1353751, c_Groups_Ozero__class_Ozero(_1353751), _1353753) = c_Groups_Ozero__class_Ozero(_1353751))], (47004 ^ _779999) ^ [_1724032, _1724034, _1724036, _1724038, _1724040, _1724042, _1724044] : [c_List_Olist__all2(_1724032, _1724034, _1724036, hAPP(hAPP(c_List_Olist_OCons(_1724032), _1724038), _1724040), hAPP(hAPP(c_List_Olist_OCons(_1724034), _1724042), _1724044)), 47007 ^ _779999 : [(47010 ^ _779999) ^ [] : [-(c_List_Olist__all2(_1724032, _1724034, _1724036, _1724040, _1724044))], (47008 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1724036, _1724038), _1724042)))]]], (24630 ^ _779999) ^ [_1241210, _1241212, _1241214, _1241216] : [class_Orderings_Olinorder(_1241210), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241210), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241210), _1241212), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1241210), _1241214), _1241216))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1241210), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241210), _1241212), _1241214)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241210), _1241212), _1241216)))))], (31263 ^ _779999) ^ [_1365568, _1365570, _1365572] : [-(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), _1365568), _1365570)), _1365572), _1365570) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365572, _1365570))], (40503 ^ _779999) ^ [_1568738] : [-(c_Relation_Orefl__on(_1568738, c_Orderings_Otop__class_Otop(tc_fun(_1568738, tc_HOL_Obool)), c_Relation_OId(_1568738)))], (48651 ^ _779999) ^ [_1759272, _1759274] : [-(c_List_OtakeWhile(_1759272, _1759274, c_List_Olist_ONil(_1759272)) = c_List_Olist_ONil(_1759272))], (15313 ^ _779999) ^ [_1055123, _1055125, _1055127] : [class_Rings_Oring__1(_1055123), hBOOL(hAPP(hAPP(c_member(_1055123), _1055125), c_Int_Oring__1__class_OInts(_1055123))), hBOOL(hAPP(hAPP(c_member(_1055123), _1055127), c_Int_Oring__1__class_OInts(_1055123))), -(hBOOL(hAPP(hAPP(c_member(_1055123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055123), _1055125), _1055127)), c_Int_Oring__1__class_OInts(_1055123))))], (2194 ^ _779999) ^ [_812166, _812168, _812170, _812172, _812174, _812176] : [-(c_SetInterval_Oord_OgreaterThan(_812176, _812172, _812168) = c_SetInterval_Oord_OgreaterThan(_812174, _812170, _812166)), _812176 = _812174, _812172 = _812170, _812168 = _812166], (4694 ^ _779999) ^ [_851452, _851454] : [_851454 = _851452, -(c_Lazy__Sequence_Oempty(_851454) = c_Lazy__Sequence_Oempty(_851452))], (38624 ^ _779999) ^ [_1521723, _1521725, _1521727, _1521729] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521723, _1521725)), hAPP(hAPP(c_Product__Type_OSigma(_1521723, _1521725), _1521727), hAPP(c_COMBK(tc_fun(_1521725, tc_HOL_Obool), _1521723), _1521729)))), -(_1521727 = c_Orderings_Obot__class_Obot(tc_fun(_1521723, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521725), _1521729)))], (12119 ^ _779999) ^ [_993891, _993893, _993895, _993897] : [c_Finite__Set_Ofolding__one(_993891, _993893, _993895), -(hAPP(_993895, hAPP(hAPP(c_Set_Oinsert(_993891), _993897), c_Orderings_Obot__class_Obot(tc_fun(_993891, tc_HOL_Obool)))) = _993897)], (31607 ^ _779999) ^ [_1372608, _1372610, _1372612, _1372614, _1372616] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372608, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1372610, _1372608, _1372612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372610, tc_HOL_Obool)), _1372614), _1372616))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372608, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1372610, _1372608, _1372612), _1372614)), hAPP(c_Relation_OImage(_1372610, _1372608, _1372612), _1372616)))))], (48390 ^ _779999) ^ [_1753788, _1753790, _1753792, _1753794] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753788)), _1753790) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753792)), _1753794), -(hAPP(hAPP(c_List_Ozip(_1753788, _1753792), hAPP(c_List_Orev(_1753788), _1753790)), hAPP(c_List_Orev(_1753792), _1753794)) = hAPP(c_List_Orev(tc_prod(_1753788, _1753792)), hAPP(hAPP(c_List_Ozip(_1753788, _1753792), _1753790), _1753794)))], (7860 ^ _779999) ^ [_912787, _912789, _912791, _912793] : [-(hBOOL(hAPP(_912787, _912789))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_912787, _912791), _912789, _912793, _912789))], (11490 ^ _779999) ^ [_980848, _980850, _980852, _980854] : [-(hBOOL(hAPP(hAPP(c_member(_980848), _980850), _980852))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980848, tc_HOL_Obool)), _980852), hAPP(hAPP(c_Set_Oinsert(_980848), _980850), _980854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980848, tc_HOL_Obool)), _980852), _980854))], (26123 ^ _779999) ^ [_1269909, _1269911, _1269913, _1269915] : [class_Groups_Ocomm__monoid__mult(_1269909), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269911), _1269913))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269911, _1269909), _1269915), _1269913) = c_Groups_Oone__class_Oone(_1269909))], (20112 ^ _779999) ^ [_1146437, _1146439] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146437) = _1146439, 20115 ^ _779999 : [(20118 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146439)))], (20116 ^ _779999) ^ [] : [-(_1146437 = hAPP(c_Int_Onat, _1146439))]]], (51251 ^ _779999) ^ [_1816331, _1816333] : [-(c_Equiv__Relations_Opart__equivp(_1816331, _1816333)), 51254 ^ _779999 : [(51255 ^ _779999) ^ [_1816451] : [hBOOL(hAPP(hAPP(_1816333, _1816451), _1816451))]], 51272 ^ _779999 : [(51275 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1816333, 51257 ^ [_1816331, _1816333]), 51257 ^ [_1816331, _1816333])))], (51277 ^ _779999) ^ [] : [-(hAPP(_1816333, 51256 ^ [_1816331, _1816333]) = hAPP(_1816333, 51257 ^ [_1816331, _1816333]))], (51279 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1816333, 51256 ^ [_1816331, _1816333]), 51257 ^ [_1816331, _1816333]))], (51273 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1816333, 51256 ^ [_1816331, _1816333]), 51256 ^ [_1816331, _1816333])))]], 51260 ^ _779999 : [(51263 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1816333, 51256 ^ [_1816331, _1816333]), 51256 ^ [_1816331, _1816333])), hBOOL(hAPP(hAPP(_1816333, 51257 ^ [_1816331, _1816333]), 51257 ^ [_1816331, _1816333])), hAPP(_1816333, 51256 ^ [_1816331, _1816333]) = hAPP(_1816333, 51257 ^ [_1816331, _1816333])], (51261 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1816333, 51256 ^ [_1816331, _1816333]), 51257 ^ [_1816331, _1816333])))]]], (31574 ^ _779999) ^ [_1371439, _1371441, _1371443, _1371445] : [c_Fun_Oinj__on(_1371439, tc_fun(tc_fun(_1371439, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1371439, tc_fun(tc_prod(_1371439, _1371439), tc_HOL_Obool), tc_fun(tc_fun(_1371439, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1371439, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1371439, _1371439), tc_HOL_Obool), tc_fun(tc_fun(_1371439, tc_HOL_Obool), tc_HOL_Obool)), _1371439), c_Equiv__Relations_Oquotient(_1371439)), hAPP(hAPP(c_COMBC(_1371439, tc_fun(_1371439, tc_HOL_Obool), tc_fun(_1371439, tc_HOL_Obool)), c_Set_Oinsert(_1371439)), c_Orderings_Obot__class_Obot(tc_fun(_1371439, tc_HOL_Obool))))), _1371441), _1371443), hBOOL(hAPP(hAPP(c_member(_1371439), _1371445), _1371443)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371439, tc_HOL_Obool)), _1371443), hAPP(hAPP(c_Set_Oinsert(_1371439), _1371445), c_Orderings_Obot__class_Obot(tc_fun(_1371439, tc_HOL_Obool))))), _1371441) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1371439, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371439), _1371443), _1371441)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371439), hAPP(hAPP(c_Set_Oinsert(_1371439), _1371445), c_Orderings_Obot__class_Obot(tc_fun(_1371439, tc_HOL_Obool)))), _1371441)))], (7834 ^ _779999) ^ [_912298, _912300, _912302, _912304] : [hBOOL(hAPP(hAPP(c_member(_912298), _912300), _912302)), -(hBOOL(hAPP(hAPP(c_member(_912298), _912300), _912304))), -(hBOOL(hAPP(hAPP(c_member(_912298), _912300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912298, tc_HOL_Obool)), _912302), _912304))))], (31411 ^ _779999) ^ [_1368382, _1368384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368384)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368382, _1368384)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1368382), hAPP(c_Int_Onat, _1368384)))], (8292 ^ _779999) ^ [_920887, _920889, _920891] : [hAPP(c_Com_Ocom_OBODY, _920887) = c_Com_Ocom_OWhile(_920889, _920891)], (25694 ^ _779999) ^ [_1261720, _1261722, _1261724, _1261726] : [class_Groups_Ouminus(_1261720), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261722, _1261720)), _1261724), _1261726) = hAPP(c_Groups_Ouminus__class_Ouminus(_1261720), hAPP(_1261724, _1261726)))], (52440 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (24524 ^ _779999) ^ [_1239209, _1239211, _1239213, _1239215] : [class_Orderings_Olinorder(_1239209), 24527 ^ _779999 : [(24528 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239209), _1239213), _1239215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), _1239213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), _1239215)))], (24538 ^ _779999) ^ [] : [24539 ^ _779999 : [(24542 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), _1239215))], (24540 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), _1239213))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239209), _1239211), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239209), _1239213), _1239215))))]]], (43634 ^ _779999) ^ [_1646745, _1646747, _1646749] : [-(_1646745 = _1646747), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646749)), _1646745) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646749)), _1646747), 43640 ^ _779999 : [(43643 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Onth(_1646749), _1646745), 43639 ^ [_1646745, _1646747, _1646749]) = hAPP(hAPP(c_List_Onth(_1646749), _1646747), 43639 ^ [_1646745, _1646747, _1646749])], (43641 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43639 ^ [_1646745, _1646747, _1646749]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646749)), _1646745))))]]], (42580 ^ _779999) ^ [_1618393, _1618395, _1618397, _1618399, _1618401] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618393, tc_fun(_1618395, tc_HOL_Obool)), _1618397), hAPP(hAPP(c_COMBS(_1618393, tc_fun(_1618395, tc_HOL_Obool), tc_fun(_1618395, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618395, tc_HOL_Obool), tc_fun(tc_fun(_1618395, tc_HOL_Obool), tc_fun(_1618395, tc_HOL_Obool)), _1618393), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618395, tc_HOL_Obool))), _1618399)), _1618401)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618395, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618395, tc_HOL_Obool), hAPP(c_Set_Oimage(_1618393, tc_fun(_1618395, tc_HOL_Obool), _1618399), _1618397))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618395, tc_HOL_Obool), hAPP(c_Set_Oimage(_1618393, tc_fun(_1618395, tc_HOL_Obool), _1618401), _1618397))))], (22997 ^ _779999) ^ [_1208706, _1208708, _1208710, _1208712] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208706, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22998 ^ [_1208706, _1208708, _1208710, _1208712])), _1208708) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208706, 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), 22998 ^ [_1208706, _1208708, _1208710, _1208712]), _1208710))), _1208712), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208706, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1208708) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208706, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1208712))], (44926 ^ _779999) ^ [_1677534, _1677536, _1677538, _1677540, _1677542] : [hAPP(hAPP(c_List_Oappend(_1677534), _1677536), hAPP(hAPP(c_List_Olist_OCons(_1677534), _1677538), c_List_Olist_ONil(_1677534))) = hAPP(hAPP(c_List_Oappend(_1677534), _1677540), hAPP(hAPP(c_List_Olist_OCons(_1677534), _1677542), c_List_Olist_ONil(_1677534))), 44929 ^ _779999 : [(44932 ^ _779999) ^ [] : [-(_1677538 = _1677542)], (44930 ^ _779999) ^ [] : [-(_1677536 = _1677540)]]], (49923 ^ _779999) ^ [_1788104, _1788106, _1788108, _1788110] : [49925 ^ _779999 : [(49928 ^ _779999) ^ [] : [hBOOL(hAPP(_1788110, 49924 ^ [_1788104, _1788106, _1788108, _1788110]))], (49926 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788104), 49924 ^ [_1788104, _1788106, _1788108, _1788110]), hAPP(c_List_Oset(_1788104), c_List_Oreplicate(_1788104, _1788106, _1788108)))))]], -(hBOOL(hAPP(_1788110, _1788108))), -(_1788106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44132 ^ _779999) ^ [_1660451, _1660453, _1660455, _1660457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660451)), _1660453)), _1660455)), -(hAPP(hAPP(c_List_Olist__update(_1660451, _1660453), _1660455), _1660457) = _1660453)], (30365 ^ _779999) ^ [_1348858, _1348860] : [-(c_Nitpick_Onat__lcm(_1348858, _1348860) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1348858), _1348860)), c_Nitpick_Onat__gcd(_1348858, _1348860)))], (46197 ^ _779999) ^ [_1704960, _1704962, _1704964, _1704966] : [_1704966 = c_List_Olist_ONil(_1704960), -(hAPP(hAPP(c_List_Omap(_1704960, _1704962), _1704964), _1704966) = c_List_Olist_ONil(_1704962))], (29534 ^ _779999) ^ [_1334298, _1334300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334298), 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)), _1334300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1334298), _1334300)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22503 ^ _779999) ^ [_1196409, _1196411, _1196413, _1196415, _1196417] : [c_Fun_Oinj__on(_1196409, _1196411, _1196413, c_Orderings_Otop__class_Otop(tc_fun(_1196409, tc_HOL_Obool))), 22506 ^ _779999 : [(22513 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196409, tc_HOL_Obool)), _1196415), _1196417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196411, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1196409, _1196411, _1196413), _1196415)), hAPP(c_Set_Oimage(_1196409, _1196411, _1196413), _1196417))))], (22507 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196411, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1196409, _1196411, _1196413), _1196415)), hAPP(c_Set_Oimage(_1196409, _1196411, _1196413), _1196417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196409, tc_HOL_Obool)), _1196415), _1196417)))]]], (27818 ^ _779999) ^ [_1302936, _1302938] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1302936), c_Groups_Ozero__class_Ozero(_1302936)), hAPP(c_Nat_OSuc, _1302938)) = c_Groups_Ozero__class_Ozero(_1302936)), class_Power_Opower(_1302936), class_Rings_Osemiring__0(_1302936)], (4814 ^ _779999) ^ [_853344, _853346] : [_853346 = _853344, -(c_Groups_Oplus__class_Oplus(_853346) = c_Groups_Oplus__class_Oplus(_853344))], (11080 ^ _779999) ^ [_971960, _971962, _971964, _971966] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971960, tc_HOL_Obool)), _971962), _971964), _971966)), -(hBOOL(hAPP(_971962, _971966)))], (41716 ^ _779999) ^ [_1596184, _1596186, _1596188, _1596190, _1596192, _1596194] : [c_Finite__Set_Ofun__left__comm(_1596184, _1596186, _1596188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596184), _1596190)), -(hBOOL(hAPP(hAPP(c_member(_1596184), _1596192), _1596190))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1596184, _1596186, _1596188), _1596194), hAPP(hAPP(c_Set_Oinsert(_1596184), _1596192), _1596190)) = hAPP(hAPP(_1596188, _1596192), hAPP(hAPP(c_Finite__Set_Ofold(_1596184, _1596186, _1596188), _1596194), _1596190)))], (6461 ^ _779999) ^ [_884192, _884194, _884196] : [class_Lattices_Osemilattice__sup(_884192), 6464 ^ _779999 : [(6471 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884192), _884194), _884196) = _884196, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884192), _884194), _884196)))], (6465 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884192), _884194), _884196)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884192), _884194), _884196) = _884196)]]], (2312 ^ _779999) ^ [_814019, _814021, _814023, _814025, _814027, _814029, _814031, _814033] : [-(c_Sum__Type_OPlus(_814033, _814029, _814025, _814021) = c_Sum__Type_OPlus(_814031, _814027, _814023, _814019)), _814033 = _814031, _814029 = _814027, _814025 = _814023, _814021 = _814019], (17949 ^ _779999) ^ [_1106722, _1106724] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106722), _1106724)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106722)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106724)))], (37475 ^ _779999) ^ [_1490640, _1490642, _1490644, _1490646] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490640, _1490640)), hAPP(hAPP(c_Product__Type_OPair(_1490640, _1490640), _1490642), _1490644)), c_Relation_OId__on(_1490640, _1490646))), 37478 ^ _779999 : [(37481 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490640), _1490642), _1490646)))], (37479 ^ _779999) ^ [] : [-(_1490642 = _1490644)]]], (40118 ^ _779999) ^ [_1558705, _1558707, _1558709, _1558711, _1558713, _1558715, _1558717] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1558705, _1558707, _1558709, _1558711), _1558713), _1558715), _1558717) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1558707, _1558709, _1558711), _1558715), hAPP(_1558713, _1558717)))], (5865 ^ _779999) ^ [_873179, _873181, _873183, _873185, _873187] : [class_Lattices_Olattice(_873179), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873181, _873179)), _873183), _873185), _873187) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_873179), hAPP(_873183, _873187)), hAPP(_873185, _873187)))], (37455 ^ _779999) ^ [_1490149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1490149)), -(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))), _1490149)), c_FunDef_Omax__weak)))], (42879 ^ _779999) ^ [_1625134, _1625136, _1625138, _1625140] : [class_Lattices_Osemilattice__sup(_1625134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625134), _1625136)), 42889 ^ _779999 : [(42892 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625134), 42888 ^ [_1625134, _1625136, _1625138, _1625140]), _1625138))], (42890 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625134), 42888 ^ [_1625134, _1625136, _1625138, _1625140]), _1625136)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625134), hAPP(hAPP(c_Finite__Set_Ofold(_1625134, _1625134, c_Lattices_Osemilattice__sup__class_Osup(_1625134)), _1625140), _1625136)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1625134), _1625138), _1625140))))], (52242 ^ _779999) ^ [_1833009] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1833009)))], (48818 ^ _779999) ^ [_1762776, _1762778, _1762780, _1762782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762776), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762778)), c_List_OdropWhile(_1762778, _1762780, _1762782)))), -(hAPP(hAPP(c_List_Onth(_1762778), c_List_OdropWhile(_1762778, _1762780, _1762782)), _1762776) = hAPP(hAPP(c_List_Onth(_1762778), _1762782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1762776), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762778)), c_List_OtakeWhile(_1762778, _1762780, _1762782)))))], (7725 ^ _779999) ^ [_909693, _909695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909695)), _909693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909693), _909695))], (23585 ^ _779999) ^ [_1220564, _1220566, _1220568, _1220570] : [-(hAPP(c_Set_Ovimage(_1220564, _1220566, _1220568), _1220570) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1220566, tc_fun(_1220564, tc_HOL_Obool)), _1220570), hAPP(hAPP(c_COMBB(tc_fun(_1220566, tc_HOL_Obool), tc_fun(_1220564, tc_HOL_Obool), _1220566), c_Set_Ovimage(_1220564, _1220566, _1220568)), hAPP(hAPP(c_COMBC(_1220566, tc_fun(_1220566, tc_HOL_Obool), tc_fun(_1220566, tc_HOL_Obool)), c_Set_Oinsert(_1220566)), c_Orderings_Obot__class_Obot(tc_fun(_1220566, tc_HOL_Obool))))))], (36489 ^ _779999) ^ [_1467240, _1467242, _1467244] : [-(hAPP(hAPP(c_Product__Type_OPair(_1467240, _1467242), hAPP(c_Product__Type_Ofst(_1467240, _1467242), _1467244)), hAPP(c_Product__Type_Osnd(_1467240, _1467242), _1467244)) = _1467244)], (38662 ^ _779999) ^ [_1522633, _1522635, _1522637, _1522639, _1522641, _1522643] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522633, _1522635), hAPP(hAPP(c_Set_Oinsert(_1522633), _1522637), _1522639)), hAPP(c_COMBK(tc_fun(_1522635, tc_HOL_Obool), _1522633), hAPP(hAPP(c_Set_Oinsert(_1522635), _1522641), _1522643))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1522633, _1522635)), hAPP(hAPP(c_Product__Type_OPair(_1522633, _1522635), _1522637), _1522641)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1522633, _1522635), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522633, _1522635), _1522639), hAPP(c_COMBK(tc_fun(_1522635, tc_HOL_Obool), _1522633), hAPP(hAPP(c_Set_Oinsert(_1522635), _1522641), _1522643)))), hAPP(hAPP(c_Product__Type_OSigma(_1522633, _1522635), hAPP(hAPP(c_Set_Oinsert(_1522633), _1522637), _1522639)), hAPP(c_COMBK(tc_fun(_1522635, tc_HOL_Obool), _1522633), _1522643)))))], (36126 ^ _779999) ^ [_1460140, _1460142, _1460144, _1460146, _1460148, _1460150, _1460152] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1460140, _1460142), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460144), _1460146))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1460148, _1460142), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460150), _1460152))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1460142)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1460140), _1460148), _1460142), 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), _1460144), _1460150)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1460146), _1460152)), _1460142))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1460146), _1460152), _1460142)))))], (47204 ^ _779999) ^ [_1728214, _1728216] : [c_List_Oremdups(_1728214, _1728216) = _1728216, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728214)), c_List_Oremdups(_1728214, _1728216)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728214)), _1728216))], (49013 ^ _779999) ^ [_1766755, _1766757] : [-(c_List_Oinsert(_1766755, _1766757, c_List_Olist_ONil(_1766755)) = hAPP(hAPP(c_List_Olist_OCons(_1766755), _1766757), c_List_Olist_ONil(_1766755)))], (39309 ^ _779999) ^ [_1539811, _1539813, _1539815] : [c_Hoare__Mirabelle_Ohoare__valids(_1539811, _1539813, _1539815), 39312 ^ _779999 : [(39313 ^ _779999) ^ [_1539920] : [39315 ^ _779999 : [(39318 ^ _779999) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1539811, _1539920, 39314 ^ [_1539811, _1539813, _1539815, _1539920])], (39316 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1539811)), 39314 ^ [_1539811, _1539813, _1539815, _1539920]), _1539813)))]], 39319 ^ _779999 : [(39320 ^ _779999) ^ [_1540092] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1539811)), _1540092), _1539815)), -(c_Hoare__Mirabelle_Otriple__valid(_1539811, _1539920, _1540092))]]]]], (25808 ^ _779999) ^ [_1263736, _1263738, _1263740] : [class_Rings_Oidom(_1263736), 25811 ^ _779999 : [(25812 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263736), _1263738), _1263738) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263736), _1263740), _1263740), -(_1263738 = _1263740), -(_1263738 = hAPP(c_Groups_Ouminus__class_Ouminus(_1263736), _1263740))], (25822 ^ _779999) ^ [] : [25823 ^ _779999 : [(25826 ^ _779999) ^ [] : [_1263738 = hAPP(c_Groups_Ouminus__class_Ouminus(_1263736), _1263740)], (25824 ^ _779999) ^ [] : [_1263738 = _1263740]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263736), _1263738), _1263738) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263736), _1263740), _1263740))]]], (5586 ^ _779999) ^ [_865540, _865542] : [_865542 = _865540, -(c_Finite__Set_Ofinite(_865542) = c_Finite__Set_Ofinite(_865540))], (36364 ^ _779999) ^ [_1464765, _1464767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464765), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464767), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1464765, _1464767) = 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), _1464765), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464767)))))], (45738 ^ _779999) ^ [_1696053, _1696055, _1696057, _1696059] : [class_Groups_Osemigroup__add(_1696053), -(hAPP(c_List_Ofoldl(_1696053, _1696053, c_Groups_Oplus__class_Oplus(_1696053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1696053), _1696055), _1696057)), _1696059) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1696053), _1696055), hAPP(c_List_Ofoldl(_1696053, _1696053, c_Groups_Oplus__class_Oplus(_1696053), _1696057), _1696059)))], (7922 ^ _779999) ^ [_913721, _913723] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_913721, tc_HOL_Obool)), _913723), hAPP(c_Set_OPow(_913721), _913723))))], (18119 ^ _779999) ^ [_1109843, _1109845, _1109847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109843), _1109845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109847)), -(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), _1109847)), _1109843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1109847)), _1109845))))], (29418 ^ _779999) ^ [_1332484] : [-(_1332484 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332484), _1332484) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35364 ^ _779999) ^ [_1445443, _1445445] : [-(c_Divides_Odivmod__int(_1445443, _1445445) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1445443), _1445445)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1445443, _1445445)))], (18461 ^ _779999) ^ [_1116060, _1116062, _1116064] : [class_Orderings_Olinorder(_1116060), 18464 ^ _779999 : [(18471 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116060), _1116062), _1116064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116060, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1116060), _1116062)), hAPP(c_SetInterval_Oord__class_OlessThan(_1116060), _1116064))))], (18465 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116060, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1116060), _1116062)), hAPP(c_SetInterval_Oord__class_OlessThan(_1116060), _1116064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116060), _1116062), _1116064)))]]], (40035 ^ _779999) ^ [_1556898, _1556900, _1556902, _1556904, _1556906, _1556908] : [c_Com_Ocom_OCond(_1556898, _1556900, _1556902) = c_Com_Ocom_OLocal(_1556904, _1556906, _1556908)], (19189 ^ _779999) ^ [_1129874, _1129876, _1129878, _1129880] : [class_Orderings_Olinorder(_1129874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129874), _1129876), _1129878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129874), _1129878), _1129880)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1129874, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1129874, _1129876, _1129878)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1129874, _1129878), _1129880)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1129874, _1129876, _1129880))], (47643 ^ _779999) ^ [_1739647, _1739649] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1739647), _1739649))), -(c_List_Oupt(_1739647, hAPP(c_Nat_OSuc, _1739649)) = c_List_Olist_ONil(tc_Nat_Onat))], (52052 ^ _779999) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (34141 ^ _779999) ^ [_1418421] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1418421)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418421)), 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))))], (5384 ^ _779999) ^ [_862373, _862375] : [_862375 = _862373, -(c_Groups_Oone__class_Oone(_862375) = c_Groups_Oone__class_Oone(_862373))], (26757 ^ _779999) ^ [_1281833, _1281835, _1281837] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281833, tc_HOL_Obool)), _1281835), _1281837) = c_Orderings_Obot__class_Obot(tc_fun(_1281833, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281833, tc_HOL_Obool)), _1281835), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1281833, tc_HOL_Obool)), _1281837))))], (44288 ^ _779999) ^ [_1664040, _1664042, _1664044] : [hBOOL(hAPP(c_List_Odistinct(_1664040), _1664042)), -(hBOOL(hAPP(c_List_Odistinct(_1664040), c_List_Osublist(_1664040, _1664042, _1664044))))], (29286 ^ _779999) ^ [_1330111, _1330113, _1330115] : [29288 ^ _779999 : [(29291 ^ _779999) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1330115, 29287 ^ [_1330111, _1330113, _1330115]))], (29289 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330111), 29287 ^ [_1330111, _1330113, _1330115]), _1330113)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330111, tc_Int_Oint), _1330115), _1330113) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330111, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1330111), c_Int_Onat), _1330115)), _1330113)))], (49818 ^ _779999) ^ [_1785290, _1785292, _1785294, _1785296, _1785298] : [hBOOL(hAPP(hAPP(_1785290, _1785292), _1785294)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1785296, _1785298, _1785290), _1785294), _1785292)))], (31909 ^ _779999) ^ [_1378345, _1378347, _1378349] : [class_Int_Onumber(_1378345), class_Orderings_Oord(_1378345), 31916 ^ _779999 : [(31923 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378345), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378347)), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378349)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1378345), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378347)), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378349)) = hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378347))], (31917 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378345), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378347)), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378349))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1378345), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378347)), hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378349)) = hAPP(c_Int_Onumber__class_Onumber__of(_1378345), _1378349))]]], (10645 ^ _779999) ^ [_963235] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963235) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963235)))], (30754 ^ _779999) ^ [_1356494, _1356496, _1356498] : [class_Divides_Osemiring__div(_1356494), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356494), _1356496), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1356494), _1356498), _1356496))), c_Divides_Odiv__class_Omod(_1356494, _1356498, _1356496)) = _1356498)], (8372 ^ _779999) ^ [_922841, _922843, _922845, _922847, _922849] : [8375 ^ _779999 : [(8381 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_922849, 8373 ^ [_922841, _922843, _922845, _922847, _922849]), 8377 ^ [_922841, _922843, _922845, _922847, _922849]))], (8379 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_922847, 8374 ^ [_922841, _922843, _922845, _922847, _922849], _922843, 8377 ^ [_922841, _922843, _922845, _922847, _922849]))], (8376 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_922845, 8373 ^ [_922841, _922843, _922845, _922847, _922849]), 8374 ^ [_922841, _922843, _922845, _922847, _922849])))]], -(c_Hoare__Mirabelle_Otriple__valid(_922841, _922843, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_922841), _922845), _922847), _922849)))], (36270 ^ _779999) ^ [_1462956, _1462958, _1462960, _1462962, _1462964, _1462966] : [hAPP(_1462962, hAPP(c_Product__Type_Osnd(_1462960, _1462956), _1462964)) = hAPP(_1462966, hAPP(c_Product__Type_Osnd(_1462960, _1462956), _1462964)), -(hAPP(c_Product__Type_Oapsnd(_1462956, _1462958, _1462960, _1462962), _1462964) = hAPP(c_Product__Type_Oapsnd(_1462956, _1462958, _1462960, _1462966), _1462964))], (40729 ^ _779999) ^ [_1573380, _1573382, _1573384, _1573386, _1573388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573380, _1573382)), hAPP(hAPP(c_Product__Type_OPair(_1573380, _1573382), _1573384), _1573386)), _1573388)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573382, _1573380)), hAPP(hAPP(c_Product__Type_OPair(_1573382, _1573380), _1573386), _1573384)), hAPP(c_Relation_Oconverse(_1573380, _1573382), _1573388))))], (8298 ^ _779999) ^ [_921039, _921041, _921043, _921045] : [c_Com_Ocom_OWhile(_921039, _921041) = c_Com_Ocom_OSemi(_921043, _921045)], (44934 ^ _779999) ^ [_1677711, _1677713, _1677715, _1677717, _1677719] : [-(hAPP(hAPP(c_List_Oappend(_1677711), _1677713), hAPP(hAPP(c_List_Olist_OCons(_1677711), _1677715), c_List_Olist_ONil(_1677711))) = hAPP(hAPP(c_List_Oappend(_1677711), _1677717), hAPP(hAPP(c_List_Olist_OCons(_1677711), _1677719), c_List_Olist_ONil(_1677711)))), _1677713 = _1677717, _1677715 = _1677719], (52018 ^ _779999) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (26530 ^ _779999) ^ [_1276987, _1276989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276987), _1276989)), 26533 ^ _779999 : [(26540 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276987), c_Orderings_Otop__class_Otop(tc_fun(_1276987, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276987), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276987, tc_HOL_Obool)), _1276989))))], (26534 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276987), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276987, tc_HOL_Obool)), _1276989))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276987), c_Orderings_Otop__class_Otop(tc_fun(_1276987, tc_HOL_Obool)))))]]], (40533 ^ _779999) ^ [_1569303, _1569305, _1569307, _1569309] : [hBOOL(hAPP(hAPP(c_member(_1569303), _1569305), c_Wellfounded_Oacc(_1569303, _1569307))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569303, _1569303)), hAPP(hAPP(c_Product__Type_OPair(_1569303, _1569303), _1569309), _1569305)), c_Transitive__Closure_Ortrancl(_1569303, _1569307))), -(hBOOL(hAPP(hAPP(c_member(_1569303), _1569309), c_Wellfounded_Oacc(_1569303, _1569307))))], (37594 ^ _779999) ^ [_1493933, _1493935] : [-(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), _1493933), _1493935)), 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), _1493933), _1493935))], (51015 ^ _779999) ^ [_1812601, _1812603, _1812605, _1812607] : [c_Relation_Osym(_1812601, _1812603), -(c_Relation_Osym(_1812605, hAPP(hAPP(c_Relation_Oinv__image(_1812601, _1812605), _1812603), _1812607)))], (37325 ^ _779999) ^ [_1487582, _1487584, _1487586] : [-(c_Wellfounded_Omlex__prod(_1487582, _1487584, _1487586) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1487582), _1487582), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1487582, c_Wellfounded_Oless__than, _1487586)), hAPP(hAPP(c_COMBS(_1487582, _1487582, tc_prod(tc_Nat_Onat, _1487582)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1487582, tc_prod(tc_Nat_Onat, _1487582)), _1487582), c_Product__Type_OPair(tc_Nat_Onat, _1487582)), _1487584)), c_COMBI(_1487582))))], (33023 ^ _779999) ^ [_1399095, _1399097] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1399095)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399097)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1399097))), 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), _1399095)), c_Int_Onat)))))], (50068 ^ _779999) ^ [_1790624, _1790626] : [-(c_Predicate_Opred__comp(_1790624, _1790624, _1790624, c_fequal, c_Predicate_Opred__comp(_1790624, _1790624, _1790624, _1790626, c_fequal)) = _1790626)], (5598 ^ _779999) ^ [_865710, _865712] : [_865712 = _865710, -(c_Orderings_Obot__class_Obot(_865712) = c_Orderings_Obot__class_Obot(_865710))], (38080 ^ _779999) ^ [_1506943, _1506945] : [38082 ^ _779999 : [(38083 ^ _779999) ^ [_1506968] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506943, _1506943)), hAPP(hAPP(c_Product__Type_OPair(_1506943, _1506943), hAPP(38081 ^ [_1506943, _1506945], hAPP(c_Nat_OSuc, _1506968))), hAPP(38081 ^ [_1506943, _1506945], _1506968))), _1506945)))]], -(c_Wellfounded_Owf(_1506943, _1506945))], (2726 ^ _779999) ^ [_820384, _820386] : [_820386 = _820384, -(c_Int_Oint__ge__less__than(_820386) = c_Int_Oint__ge__less__than(_820384))], (8302 ^ _779999) ^ [_921126, _921128] : [c_Com_Ocom_OWhile(_921126, _921128) = c_Com_Ocom_OSKIP], (19043 ^ _779999) ^ [_1127180, _1127182, _1127184, _1127186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127180), _1127182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127184), _1127186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127180), _1127184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127182), _1127186))))], (11731 ^ _779999) ^ [_985941, _985943, _985945, _985947, _985949] : [class_Groups_Ocomm__monoid__add(_985941), hBOOL(hAPP(c_Finite__Set_Ofinite(_985943), _985945)), 11738 ^ _779999 : [(11745 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985943), _985947), _985945))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985943, _985941), hAPP(hAPP(c_COMBC(_985943, _985941, _985941), hAPP(hAPP(c_COMBS(_985943, _985941, tc_fun(_985941, _985941)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_985941, tc_fun(_985941, _985941)), _985943), c_If(_985941)), hAPP(c_fequal, _985947))), _985949)), c_Groups_Ozero__class_Ozero(_985941))), _985945) = c_Groups_Ozero__class_Ozero(_985941))], (11739 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_985943), _985947), _985945)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985943, _985941), hAPP(hAPP(c_COMBC(_985943, _985941, _985941), hAPP(hAPP(c_COMBS(_985943, _985941, tc_fun(_985941, _985941)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_985941, tc_fun(_985941, _985941)), _985943), c_If(_985941)), hAPP(c_fequal, _985947))), _985949)), c_Groups_Ozero__class_Ozero(_985941))), _985945) = hAPP(_985949, _985947))]]], (38922 ^ _779999) ^ [_1530866, _1530868, _1530870] : [-(c_Relation_Orefl__on(_1530866, _1530868, _1530870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530866, _1530866), tc_HOL_Obool)), _1530870), hAPP(hAPP(c_Product__Type_OSigma(_1530866, _1530866), _1530868), hAPP(c_COMBK(tc_fun(_1530866, tc_HOL_Obool), _1530866), _1530868)))), 38928 ^ _779999 : [(38931 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530866, _1530866)), hAPP(hAPP(c_Product__Type_OPair(_1530866, _1530866), 38927 ^ [_1530866, _1530868, _1530870]), 38927 ^ [_1530866, _1530868, _1530870])), _1530870))], (38929 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530866), 38927 ^ [_1530866, _1530868, _1530870]), _1530868)))]]], (40583 ^ _779999) ^ [_1570584, _1570586] : [-(c_Relation_Oirrefl(_1570584, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1570584, _1570584), tc_HOL_Obool)), _1570586), c_Relation_OId(_1570584))))], (49291 ^ _779999) ^ [_1774191, _1774193, _1774195] : [class_Orderings_Olinorder(_1774191), 49297 ^ _779999 : [(49300 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1774191), _1774195), 49296 ^ [_1774191, _1774193, _1774195]))], (49298 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774191), 49296 ^ [_1774191, _1774193, _1774195]), hAPP(c_List_Oset(_1774191), _1774193))))]], c_List_Olinorder__class_Osorted(_1774191, _1774193), -(c_List_Olinorder__class_Osorted(_1774191, hAPP(hAPP(c_List_Olist_OCons(_1774191), _1774195), _1774193)))], (52334 ^ _779999) ^ [_1833915, _1833917, _1833919, _1833921, _1833923, _1833925] : [-(hAPP(hAPP(hAPP(c_COMBC(_1833915, _1833917, _1833919), _1833921), _1833923), _1833925) = hAPP(hAPP(_1833921, _1833925), _1833923))], (44342 ^ _779999) ^ [_1665093, _1665095] : [hBOOL(hAPP(c_List_Odistinct(_1665093), _1665095)), 44345 ^ _779999 : [(44346 ^ _779999) ^ [_1665225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665225), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665093)), _1665095))), 44349 ^ _779999 : [(44350 ^ _779999) ^ [_1665352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665352), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665093)), _1665095))), -(_1665225 = _1665352), hAPP(hAPP(c_List_Onth(_1665093), _1665095), _1665225) = hAPP(hAPP(c_List_Onth(_1665093), _1665095), _1665352)]]]]], (36046 ^ _779999) ^ [_1458626, _1458628, _1458630, _1458632, _1458634] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1458626, _1458628), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1458630), _1458632))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1458628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1458634)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1458626, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1458628), _1458634)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1458630), _1458634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1458628), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1458630, _1458634))), _1458632)))))], (38312 ^ _779999) ^ [_1512757, _1512759, _1512761] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1512757), _1512759), _1512761) = c_Nitpick_OAbs__Frac(_1512757, c_Nitpick_Onorm__frac(_1512759, _1512761)))], (30856 ^ _779999) ^ [_1358389, _1358391, _1358393] : [-(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), _1358389), _1358391)), _1358391)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358389, _1358391))), _1358393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358389), _1358393))], (39252 ^ _779999) ^ [_1538104, _1538106, _1538108, _1538110] : [39254 ^ _779999 : [(39257 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1538104, _1538104, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1538104, tc_fun(_1538104, _1538106), tc_fun(_1538104, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538106, tc_HOL_Obool), tc_fun(tc_fun(_1538104, _1538106), tc_fun(_1538104, tc_HOL_Obool)), _1538104), c_COMBB(_1538106, tc_HOL_Obool, _1538104)), hAPP(hAPP(c_COMBB(_1538106, tc_fun(_1538106, tc_HOL_Obool), _1538104), c_fequal), _1538110))), _1538110)), 39253 ^ [_1538104, _1538106, _1538108, _1538110]))], (39255 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538104, _1538104)), 39253 ^ [_1538104, _1538106, _1538108, _1538110]), _1538108)))]], -(c_Equiv__Relations_Ocongruent(_1538104, _1538106, _1538108, _1538110))], (9620 ^ _779999) ^ [_943538, _943540, _943542, _943544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943538, tc_HOL_Obool)), _943540), _943542)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943538, tc_HOL_Obool)), _943542), _943544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943538, tc_HOL_Obool)), _943540), _943544)))], (22647 ^ _779999) ^ [_1199238, _1199240, _1199242, _1199244, _1199246] : [_1199238 = c_Orderings_Obot__class_Obot(tc_fun(_1199240, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199240, tc_fun(_1199242, tc_HOL_Obool)), _1199238), hAPP(hAPP(c_COMBB(tc_fun(_1199242, tc_HOL_Obool), tc_fun(_1199242, tc_HOL_Obool), _1199240), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199242, tc_HOL_Obool)), _1199244)), _1199246)) = c_Orderings_Obot__class_Obot(tc_fun(_1199242, tc_HOL_Obool)))], (43062 ^ _779999) ^ [_1629562, _1629564, _1629566] : [-(c_Nitpick_Oof__frac(_1629564, _1629562, _1629566) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1629562), hAPP(c_Int_Oring__1__class_Oof__int(_1629562), hAPP(c_Nitpick_Onum(_1629564), _1629566))), hAPP(c_Int_Oring__1__class_Oof__int(_1629562), hAPP(c_Nitpick_Odenom(_1629564), _1629566)))), class_Rings_Oinverse(_1629562), class_Rings_Oring__1(_1629562)], (30058 ^ _779999) ^ [_1343328, _1343330] : [class_Rings_Oring__1(_1343328), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343328), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1343330)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1343328), _1343330))], (7645 ^ _779999) ^ [_908455] : [_908455 = hAPP(c_Nat_OSuc, _908455)], (10137 ^ _779999) ^ [_954842, _954844, _954846, _954848, _954850] : [c_Fun_Oinj__on(_954842, _954844, _954846, _954848), -(c_Fun_Oinj__on(_954842, _954844, _954846, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954842, tc_HOL_Obool)), _954848), _954850)))], (17894 ^ _779999) ^ [_1105699] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105699) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1105699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10159 ^ _779999) ^ [_955182, _955184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955182), _955184)), _955184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15835 ^ _779999) ^ [_1065421, _1065423, _1065425] : [_1065423 = _1065425, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065421)), _1065423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065421)), _1065425))], (19978 ^ _779999) ^ [_1144348] : [hBOOL(hAPP(_1144348, 19979 ^ [_1144348])), 19982 ^ _779999 : [(19983 ^ _779999) ^ [_1144442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144442)), -(hBOOL(hAPP(_1144348, hAPP(c_Int_Onat, _1144442))))]]], (13369 ^ _779999) ^ [_1017999, _1018001, _1018003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017999), _1018001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017999), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018003), _1018001))))], (31989 ^ _779999) ^ [_1380075, _1380077, _1380079, _1380081] : [class_Fields_Ofield__inverse__zero(_1380075), class_Int_Onumber(_1380075), 31996 ^ _779999 : [(31997 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380075), _1380077), hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079)) = _1380081, 32000 ^ _779999 : [(32007 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079) = c_Groups_Ozero__class_Ozero(_1380075), -(_1380081 = c_Groups_Ozero__class_Ozero(_1380075))], (32001 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079) = c_Groups_Ozero__class_Ozero(_1380075)), -(_1380077 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380075), _1380081), hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079)))]]], (32013 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380075), _1380077), hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079)) = _1380081), 32016 ^ _779999 : [(32019 ^ _779999) ^ [] : [_1380077 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380075), _1380081), hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079))], (32017 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079) = c_Groups_Ozero__class_Ozero(_1380075)]], 32020 ^ _779999 : [(32023 ^ _779999) ^ [] : [_1380081 = c_Groups_Ozero__class_Ozero(_1380075)], (32021 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1380075), _1380079) = c_Groups_Ozero__class_Ozero(_1380075))]]]]], (25514 ^ _779999) ^ [_1258700, _1258702] : [class_Groups_Ogroup__add(_1258700), 25517 ^ _779999 : [(25524 ^ _779999) ^ [] : [_1258702 = c_Groups_Ozero__class_Ozero(_1258700), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1258700), _1258702) = c_Groups_Ozero__class_Ozero(_1258700))], (25518 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1258700), _1258702) = c_Groups_Ozero__class_Ozero(_1258700), -(_1258702 = c_Groups_Ozero__class_Ozero(_1258700))]]], (9188 ^ _779999) ^ [_936860, _936862, _936864, _936866] : [-(c_Nitpick_Ofold__graph_H(_936860, _936862, _936864, _936866, c_Orderings_Obot__class_Obot(tc_fun(_936860, tc_HOL_Obool)), _936866))], (2750 ^ _779999) ^ [_820770, _820772] : [_820772 = _820770, -(c_Nitpick_Ozero__frac(_820772) = c_Nitpick_Ozero__frac(_820770))], (23551 ^ _779999) ^ [_1219914, _1219916, _1219918, _1219920] : [class_Orderings_Olinorder(_1219914), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1219914, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1219914), _1219916)), c_SetInterval_Oord__class_OatLeastAtMost(_1219914, _1219918, _1219920)) = c_SetInterval_Oord__class_OatLeastAtMost(_1219914, _1219918, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1219914), _1219916), _1219920)))], (25796 ^ _779999) ^ [_1263478, _1263480, _1263482] : [class_Rings_Oring(_1263478), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263478), hAPP(c_Groups_Ouminus__class_Ouminus(_1263478), _1263480)), _1263482) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263478), _1263480), hAPP(c_Groups_Ouminus__class_Ouminus(_1263478), _1263482)))], (31829 ^ _779999) ^ [_1376805, _1376807, _1376809, _1376811] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1376805), _1376807), _1376809)), hAPP(c_Int_Onumber__class_Onumber__of(_1376805), _1376811)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1376805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376805), _1376807), hAPP(c_Int_Onumber__class_Onumber__of(_1376805), _1376811))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376805), _1376809), hAPP(c_Int_Onumber__class_Onumber__of(_1376805), _1376811)))), class_Int_Onumber(_1376805), class_Rings_Oring(_1376805)], (13329 ^ _779999) ^ [_1017348, _1017350, _1017352] : [class_Groups_Ogroup__add(_1017348), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1017348), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017348), _1017350), _1017352)), _1017352) = _1017350)], (32799 ^ _779999) ^ [_1395227] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395227))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1395227)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18477 ^ _779999) ^ [_1116352, _1116354, _1116356, _1116358, _1116360] : [class_Groups_Ocomm__monoid__add(_1116352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116354), _1116356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116356), _1116358)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116352), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116352), _1116360), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116354), _1116356))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116352), _1116360), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116356), _1116358))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116352), _1116360), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116354), _1116358)))], (37787 ^ _779999) ^ [_1500139, _1500141, _1500143, _1500145, _1500147, _1500149, _1500151] : [c_Typedef_Otype__definition(_1500139, _1500141, _1500143, _1500145, _1500147), 37790 ^ _779999 : [(37797 ^ _779999) ^ [] : [_1500149 = _1500151, -(hAPP(_1500143, _1500149) = hAPP(_1500143, _1500151))], (37791 ^ _779999) ^ [] : [hAPP(_1500143, _1500149) = hAPP(_1500143, _1500151), -(_1500149 = _1500151)]]], (22531 ^ _779999) ^ [_1197116, _1197118, _1197120] : [class_Orderings_Olinorder(_1197116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197116), _1197118)), hBOOL(hAPP(hAPP(c_member(_1197116), _1197120), _1197118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197116), _1197120), c_Big__Operators_Olinorder__class_OMax(_1197116, _1197118))))], (15747 ^ _779999) ^ [_1064069, _1064071] : [class_Groups_Ocomm__monoid__mult(_1064069), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064069), c_Groups_Oone__class_Oone(_1064069)), _1064071) = _1064071)], (36921 ^ _779999) ^ [_1477230, _1477232, _1477234, _1477236, _1477238, _1477240, _1477242, _1477244, _1477246, _1477248] : [c_Equiv__Relations_Oequiv(_1477230, _1477232, _1477234), c_Equiv__Relations_Oequiv(_1477236, _1477238, _1477240), c_Equiv__Relations_Ocongruent2(_1477230, _1477236, tc_fun(_1477242, tc_HOL_Obool), _1477234, _1477240, _1477244), hBOOL(hAPP(hAPP(c_member(_1477230), _1477246), _1477232)), hBOOL(hAPP(hAPP(c_member(_1477236), _1477248), _1477238)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477230, tc_fun(_1477242, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477230, _1477230, _1477234), hAPP(hAPP(c_Set_Oinsert(_1477230), _1477246), c_Orderings_Obot__class_Obot(tc_fun(_1477230, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1477236, tc_fun(_1477242, tc_HOL_Obool)), tc_fun(_1477242, tc_HOL_Obool), _1477230), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477236, tc_fun(_1477242, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477236, _1477236, _1477240), hAPP(hAPP(c_Set_Oinsert(_1477236), _1477248), c_Orderings_Obot__class_Obot(tc_fun(_1477236, tc_HOL_Obool)))))), _1477244)) = hAPP(hAPP(_1477244, _1477246), _1477248))], (4350 ^ _779999) ^ [_846060, _846062] : [_846062 = _846060, -(c_New__Random__Sequence_Oneg__single(_846062) = c_New__Random__Sequence_Oneg__single(_846060))], (26825 ^ _779999) ^ [_1283332, _1283334, _1283336, _1283338, _1283340] : [class_Groups_Ocomm__monoid__mult(_1283332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283334), _1283336)), -(hBOOL(hAPP(hAPP(c_member(_1283334), _1283338), _1283336))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283334, _1283332), _1283340), hAPP(hAPP(c_Set_Oinsert(_1283334), _1283338), _1283336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283332), hAPP(_1283340, _1283338)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283334, _1283332), _1283340), _1283336)))], (10181 ^ _779999) ^ [_955473, _955475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955473), _955475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955475), hAPP(c_Nat_OSuc, _955473))))], (51942 ^ _779999) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (16345 ^ _779999) ^ [_1075247, _1075249, _1075251] : [class_Rings_Olinordered__semiring__strict(_1075247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075247), c_Groups_Ozero__class_Ozero(_1075247)), _1075249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075247), c_Groups_Ozero__class_Ozero(_1075247)), _1075251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075247), c_Groups_Ozero__class_Ozero(_1075247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075247), _1075249), _1075251))))], (47502 ^ _779999) ^ [_1735163, _1735165, _1735167] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1735163), tc_List_Olist(_1735163)), c_List_Opartition(_1735163, _1735165, _1735167)) = hAPP(c_List_Ofilter(_1735163, _1735165), _1735167))], (22467 ^ _779999) ^ [_1195708, _1195710, _1195712, _1195714, _1195716] : [c_Fun_Oinj__on(_1195708, _1195710, _1195712, c_Orderings_Otop__class_Otop(tc_fun(_1195708, tc_HOL_Obool))), 22470 ^ _779999 : [(22477 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1195708), _1195714), _1195716)), -(hBOOL(hAPP(hAPP(c_member(_1195710), hAPP(_1195712, _1195714)), hAPP(c_Set_Oimage(_1195708, _1195710, _1195712), _1195716))))], (22471 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1195710), hAPP(_1195712, _1195714)), hAPP(c_Set_Oimage(_1195708, _1195710, _1195712), _1195716))), -(hBOOL(hAPP(hAPP(c_member(_1195708), _1195714), _1195716)))]]], (51047 ^ _779999) ^ [_1813100] : [-(c_Relation_Osym(_1813100, c_Relation_OId(_1813100)))], (38287 ^ _779999) ^ [_1512041, _1512043, _1512045, _1512047] : [hBOOL(hAPP(hAPP(c_member(_1512043), _1512047), hAPP(c_Relation_ORange(_1512041, _1512043), _1512045))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1512041, _1512043, hAPP(hAPP(c_COMBC(_1512041, tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_fun(_1512043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512043, tc_fun(tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_fun(_1512043, tc_HOL_Obool)), _1512041), c_COMBC(_1512043, tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512043, tc_prod(_1512041, _1512043)), tc_fun(_1512043, tc_fun(tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_HOL_Obool)), _1512041), hAPP(c_COMBB(tc_prod(_1512041, _1512043), tc_fun(tc_fun(tc_prod(_1512041, _1512043), tc_HOL_Obool), tc_HOL_Obool), _1512043), c_member(tc_prod(_1512041, _1512043)))), c_Product__Type_OPair(_1512041, _1512043)))), _1512045)), _1512047)))], (42147 ^ _779999) ^ [_1608512, _1608514, _1608516, _1608518, _1608520] : [-(_1608512 = c_Orderings_Obot__class_Obot(tc_fun(_1608514, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608514, tc_fun(_1608516, tc_HOL_Obool)), _1608512), hAPP(hAPP(c_COMBC(_1608514, tc_fun(_1608516, tc_HOL_Obool), tc_fun(_1608516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608516, tc_HOL_Obool), tc_fun(tc_fun(_1608516, tc_HOL_Obool), tc_fun(_1608516, tc_HOL_Obool)), _1608514), c_Groups_Ominus__class_Ominus(tc_fun(_1608516, tc_HOL_Obool))), _1608518)), _1608520)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608516, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608514, tc_fun(_1608516, tc_HOL_Obool)), _1608512), _1608518)), _1608520))], (46243 ^ _779999) ^ [_1706156, _1706158, _1706160, _1706162, _1706164] : [class_Groups_Ocomm__monoid__add(_1706156), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1706156), hAPP(hAPP(c_List_Omap(_1706158, _1706156), hAPP(hAPP(c_COMBS(_1706158, _1706156, _1706156), hAPP(hAPP(c_COMBB(_1706156, tc_fun(_1706156, _1706156), _1706158), c_Groups_Oplus__class_Oplus(_1706156)), _1706160)), _1706162)), _1706164)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706156), hAPP(c_List_Omonoid__add__class_Olistsum(_1706156), hAPP(hAPP(c_List_Omap(_1706158, _1706156), _1706160), _1706164))), hAPP(c_List_Omonoid__add__class_Olistsum(_1706156), hAPP(hAPP(c_List_Omap(_1706158, _1706156), _1706162), _1706164))))], (3290 ^ _779999) ^ [_829172, _829174, _829176, _829178] : [-(c_Wellfounded_Oacc(_829178, _829174) = c_Wellfounded_Oacc(_829176, _829172)), _829178 = _829176, _829174 = _829172], (27704 ^ _779999) ^ [_1300884, _1300886] : [class_Groups_Omonoid__mult(_1300884), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300884), c_Groups_Oone__class_Oone(_1300884)), _1300886) = c_Groups_Oone__class_Oone(_1300884))], (24280 ^ _779999) ^ [_1234776] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1234776) = _1234776)], (17339 ^ _779999) ^ [_1094317, _1094319, _1094321] : [17340 ^ _779999 : [(17343 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1094317), _1094321))], (17341 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1094319)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094317), _1094319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094321), _1094319))))], (20373 ^ _779999) ^ [_1150797] : [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, _1150797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1150797)))], (12171 ^ _779999) ^ [_994828, _994830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994828), _994830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994828), _994830)))], (36493 ^ _779999) ^ [_1467347, _1467349] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467347), _1467349) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1467347, _1467349)))], (19301 ^ _779999) ^ [_1131900, _1131902, _1131904, _1131906, _1131908, _1131910] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131900), _1131902)), _1131904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131906), _1131908)), _1131910), 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), _1131906), _1131908)), _1131910))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131910), _1131906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131906), _1131900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131902), _1131908)))], (47308 ^ _779999) ^ [_1730157, _1730159] : [47310 ^ _779999 : [(47313 ^ _779999) ^ [] : [47309 ^ [_1730157, _1730159] = c_List_Olist_ONil(_1730157)], (47311 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730157)), 47309 ^ [_1730157, _1730159]), hAPP(c_List_Oset(tc_List_Olist(_1730157)), _1730159))))]], -(c_List_Oconcat(_1730157, _1730159) = c_List_Olist_ONil(_1730157))], (21080 ^ _779999) ^ [_1163022, _1163024, _1163026] : [class_Groups_Ocomm__monoid__add(_1163022), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1163022), _1163024), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163026))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163022), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1163022), _1163024), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1163026))), hAPP(_1163024, hAPP(c_Nat_OSuc, _1163026))))], (6013 ^ _779999) ^ [_875739, _875741, _875743, _875745] : [class_Orderings_Oord(_875739), _875741 = _875743, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875739), _875743), _875745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875739), _875741), _875745)))], (29920 ^ _779999) ^ [_1341029, _1341031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341029), _1341031)), _1341029)))], (44246 ^ _779999) ^ [_1663040, _1663042, _1663044, _1663046] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663040), tc_List_Olist(_1663040))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663040), tc_List_Olist(_1663040)), _1663042), _1663044)), c_List_Olistrel1(_1663040, _1663046)))), 44247 ^ _779999 : [(44248 ^ _779999) ^ [_1663173, _1663175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1663040, _1663040)), hAPP(hAPP(c_Product__Type_OPair(_1663040, _1663040), hAPP(hAPP(c_List_Onth(_1663040), _1663042), _1663173)), _1663175)), _1663046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663173), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663040)), _1663042))), _1663044 = hAPP(hAPP(c_List_Olist__update(_1663040, _1663042), _1663173), _1663175)]]], (128 ^ _779999) ^ [_782147, _782149, _782151, _782153, _782155, _782157] : [-(c_Big__Operators_Osemilattice__big(_782155, _782151, _782147)), c_Big__Operators_Osemilattice__big(_782157, _782153, _782149), _782157 = _782155, _782153 = _782151, _782149 = _782147], (34295 ^ _779999) ^ [_1421338] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1421338), 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, _1421338)))], (34481 ^ _779999) ^ [] : [-(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))))], (15921 ^ _779999) ^ [_1066949, _1066951, _1066953, _1066955] : [class_Groups_Ocomm__monoid__add(_1066949), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1066949), _1066951), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1066953), hAPP(c_Nat_OSuc, _1066955))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1066949), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1066949, tc_Nat_Onat), _1066951), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1066953, _1066955)))], (19163 ^ _779999) ^ [_1129321, _1129323, _1129325, _1129327] : [class_Orderings_Oorder(_1129321), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129321, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1129321, _1129323, _1129325)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1129321, _1129325, _1129327)) = c_Orderings_Obot__class_Obot(tc_fun(_1129321, tc_HOL_Obool)))], (646 ^ _779999) ^ [_789942, _789944] : [-(c_Nat__Transfer_Onat__set(_789942)), _789944 = _789942, c_Nat__Transfer_Onat__set(_789944)], (3994 ^ _779999) ^ [_840100, _840102, _840104, _840106, _840108, _840110, _840112, _840114] : [-(c_List_Omaps(_840114, _840110, _840106, _840102) = c_List_Omaps(_840112, _840108, _840104, _840100)), _840114 = _840112, _840110 = _840108, _840106 = _840104, _840102 = _840100], (44148 ^ _779999) ^ [_1660733, _1660735, _1660737, _1660739, _1660741] : [-(hAPP(hAPP(c_List_Olist__update(_1660733, hAPP(hAPP(c_List_Olist_OCons(_1660733), _1660735), _1660737)), hAPP(c_Nat_OSuc, _1660739)), _1660741) = hAPP(hAPP(c_List_Olist_OCons(_1660733), _1660735), hAPP(hAPP(c_List_Olist__update(_1660733, _1660737), _1660739), _1660741)))], (44072 ^ _779999) ^ [_1658978, _1658980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658978), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1658980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1658980), _1658978)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1658980))))], (15153 ^ _779999) ^ [_1052204, _1052206, _1052208, _1052210] : [hBOOL(hAPP(hAPP(_1052208, _1052206), _1052210)), -(hBOOL(hAPP(hAPP(c_member(_1052204), _1052206), c_SetInterval_Oord_OlessThan(_1052204, _1052208, _1052210))))], (40635 ^ _779999) ^ [_1571471, _1571473, _1571475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571471), _1571473))), -(c_Random_Ominus__shift(_1571475, _1571471, _1571473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1571471), _1571473))], (16689 ^ _779999) ^ [_1081887, _1081889, _1081891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081887), _1081889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081891), _1081889))), 16692 ^ _779999 : [(16695 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1081887), _1081891)))], (16693 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1081889)))]]], (52070 ^ _779999) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (47488 ^ _779999) ^ [_1734929, _1734931, _1734933, _1734935] : [-(hBOOL(hAPP(_1734929, _1734931))), -(hAPP(c_List_Ofilter(_1734933, _1734929), hAPP(hAPP(c_List_Olist_OCons(_1734933), _1734931), _1734935)) = hAPP(c_List_Ofilter(_1734933, _1734929), _1734935))], (23535 ^ _779999) ^ [_1219610, _1219612, _1219614, _1219616] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219610), _1219612)), c_Fun_Oinj__on(_1219614, _1219610, _1219616, c_Orderings_Otop__class_Otop(tc_fun(_1219614, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1219614), hAPP(c_Set_Ovimage(_1219614, _1219610, _1219616), _1219612))))], (22824 ^ _779999) ^ [_1203639, _1203641, _1203643, _1203645] : [-(_1203639 = c_Orderings_Obot__class_Obot(tc_fun(_1203641, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203641, tc_fun(_1203643, tc_HOL_Obool)), _1203639), hAPP(c_COMBK(tc_fun(_1203643, tc_HOL_Obool), _1203641), _1203645)) = _1203645)], (27894 ^ _779999) ^ [_1304366, _1304368, _1304370] : [class_Rings_Olinordered__idom(_1304366), -(hAPP(c_Groups_Oabs__class_Oabs(_1304366), hAPP(hAPP(c_Power_Opower__class_Opower(_1304366), hAPP(c_Groups_Ouminus__class_Ouminus(_1304366), _1304368)), _1304370)) = hAPP(c_Groups_Oabs__class_Oabs(_1304366), hAPP(hAPP(c_Power_Opower__class_Opower(_1304366), _1304368), _1304370)))], (35689 ^ _779999) ^ [_1452420, _1452422, _1452424, _1452426] : [-(c_HOL_OThe(tc_prod(_1452420, _1452422), hAPP(c_Product__Type_Oprod_Oprod__case(_1452420, _1452422, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1452420, tc_fun(_1452422, tc_HOL_Obool), tc_fun(_1452422, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1452422, tc_HOL_Obool), tc_fun(_1452422, tc_HOL_Obool)), _1452420), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1452422)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452420), c_fconj), hAPP(c_fequal, _1452424)))), hAPP(c_fequal, _1452426)))) = hAPP(hAPP(c_Product__Type_OPair(_1452420, _1452422), _1452424), _1452426))], (33999 ^ _779999) ^ [_1415961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1415961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1415961))))], (37945 ^ _779999) ^ [_1504144, _1504146] : [c_Wellfounded_Owf(_1504144, _1504146), -(c_Wellfounded_Owf(tc_fun(_1504144, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1504144, _1504146)))], (6733 ^ _779999) ^ [_890140, _890142, _890144, _890146] : [6734 ^ _779999 : [(6737 ^ _779999) ^ [] : [_890142 = _890146], (6735 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890140), _890142), _890144))]], -(hBOOL(hAPP(hAPP(c_member(_890140), _890142), hAPP(hAPP(c_Set_Oinsert(_890140), _890146), _890144))))], (30507 ^ _779999) ^ [_1351832, _1351834, _1351836, _1351838] : [class_Divides_Osemiring__div(_1351832), -(c_Divides_Odiv__class_Omod(_1351832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351832), _1351834), _1351836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351832), _1351838), _1351836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351832), c_Divides_Odiv__class_Omod(_1351832, _1351834, _1351838)), _1351836))], (24978 ^ _779999) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (48450 ^ _779999) ^ [_1755008, _1755010, _1755012, _1755014, _1755016] : [c_List_Olist__all2(_1755008, _1755010, _1755012, _1755014, _1755016), -(c_List_Olist__all2(_1755008, _1755010, _1755012, hAPP(c_List_Orev(_1755008), _1755014), hAPP(c_List_Orev(_1755010), _1755016)))], (49994 ^ _779999) ^ [_1789331, _1789333] : [-(c_List_Oconcat(_1789331, c_List_Oreplicate(tc_List_Olist(_1789331), _1789333, c_List_Olist_ONil(_1789331))) = c_List_Olist_ONil(_1789331))], (4412 ^ _779999) ^ [_847045, _847047] : [_847047 = _847045, -(c_New__Random__Sequence_Opos__single(_847047) = c_New__Random__Sequence_Opos__single(_847045))], (23187 ^ _779999) ^ [_1212754, _1212756, _1212758, _1212760] : [class_Orderings_Olinorder(_1212754), 23190 ^ _779999 : [(23191 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212754), _1212756), _1212758)), _1212760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), _1212756), _1212760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), _1212758), _1212760)))], (23201 ^ _779999) ^ [] : [23202 ^ _779999 : [(23205 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), _1212758), _1212760))], (23203 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), _1212756), _1212760))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212754), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212754), _1212756), _1212758)), _1212760)))]]], (16491 ^ _779999) ^ [_1077951, _1077953, _1077955, _1077957] : [class_Rings_Olinordered__comm__semiring__strict(_1077951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077951), _1077953), _1077955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077951), c_Groups_Ozero__class_Ozero(_1077951)), _1077957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077951), _1077957), _1077953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077951), _1077957), _1077955))))], (19347 ^ _779999) ^ [_1132785, _1132787] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1132785), _1132787))))], (47190 ^ _779999) ^ [_1727963, _1727965] : [_1727965 = c_List_Olist_ONil(_1727963), -(c_List_Olist_ONil(_1727963) = c_List_Oremdups(_1727963, _1727965))], (44704 ^ _779999) ^ [_1672033, _1672035, _1672037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672033), tc_List_Olist(_1672033))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672033), tc_List_Olist(_1672033)), _1672035), c_List_Olist_ONil(_1672033))), c_List_Olexord(_1672033, _1672037)))], (48320 ^ _779999) ^ [_1752376, _1752378] : [hAPP(c_List_Orev(_1752376), _1752378) = c_List_Olist_ONil(_1752376), -(_1752378 = c_List_Olist_ONil(_1752376))], (17329 ^ _779999) ^ [_1094140, _1094142, _1094144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094140), _1094142)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094144), _1094142))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1094142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1094140), _1094144)))], (25980 ^ _779999) ^ [_1267209, _1267211, _1267213, _1267215, _1267217] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1267209, _1267211, _1267213)), _1267215), _1267217))), 25981 ^ _779999 : [(25988 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1267209, _1267215))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267213), _1267215), _1267217))], (25982 ^ _779999) ^ [] : [hBOOL(hAPP(_1267209, _1267215)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267211), _1267215), _1267217))]]], (18129 ^ _779999) ^ [_1110048] : [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), _1110048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110048)))], (45470 ^ _779999) ^ [_1690285, _1690287, _1690289, _1690291, _1690293] : [hAPP(hAPP(c_List_Oappend(_1690285), _1690287), _1690289) = hAPP(hAPP(c_List_Oappend(_1690285), _1690291), _1690293), 45473 ^ _779999 : [(45482 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690287)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690291)))), 45485 ^ _779999 : [(45488 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1690285), hAPP(hAPP(c_List_Odrop(_1690285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690291)), _1690287)), _1690289) = _1690293)], (45486 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1690285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690291)), _1690287) = _1690291)]]], (45474 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690287)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690291))), 45477 ^ _779999 : [(45480 ^ _779999) ^ [] : [-(_1690289 = hAPP(hAPP(c_List_Oappend(_1690285), hAPP(hAPP(c_List_Odrop(_1690285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690287)), _1690291)), _1690293))], (45478 ^ _779999) ^ [] : [-(_1690287 = hAPP(hAPP(c_List_Otake(_1690285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690285)), _1690287)), _1690291))]]]]], (47184 ^ _779999) ^ [_1727876, _1727878] : [c_List_Olist_ONil(_1727876) = c_List_Oremdups(_1727876, _1727878), -(_1727878 = c_List_Olist_ONil(_1727876))], (44138 ^ _779999) ^ [_1660570, _1660572, _1660574, _1660576, _1660578] : [-(_1660570 = _1660572), -(hAPP(hAPP(c_List_Onth(_1660574), hAPP(hAPP(c_List_Olist__update(_1660574, _1660576), _1660570), _1660578)), _1660572) = hAPP(hAPP(c_List_Onth(_1660574), _1660576), _1660572))], (52240 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (6761 ^ _779999) ^ [_890683, _890685, _890687, _890689] : [hBOOL(hAPP(hAPP(c_member(_890683), _890685), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890683, tc_HOL_Obool)), _890687), _890689))), -(hBOOL(hAPP(hAPP(c_member(_890683), _890685), _890687))), -(hBOOL(hAPP(hAPP(c_member(_890683), _890685), _890689)))], (27438 ^ _779999) ^ [_1296147, _1296149, _1296151, _1296153, _1296155] : [class_Fields_Ofield__inverse__zero(_1296147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296149), _1296151)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296149, _1296147), hAPP(hAPP(c_COMBS(_1296149, _1296147, _1296147), hAPP(hAPP(c_COMBB(_1296147, tc_fun(_1296147, _1296147), _1296149), c_Rings_Oinverse__class_Odivide(_1296147)), _1296153)), _1296155)), _1296151) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296147), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296149, _1296147), _1296153), _1296151)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296149, _1296147), _1296155), _1296151)))], (10954 ^ _779999) ^ [_969307, _969309, _969311] : [10955 ^ _779999 : [(10958 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_969311, _969309), _969307))], (10956 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969307), _969309)))]], 10961 ^ _779999 : [(10964 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_969311, _969309), _969307))], (10962 ^ _779999) ^ [] : [-(_969307 = _969309)]], 10967 ^ _779999 : [(10970 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_969311, _969309), _969307))], (10968 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969309), _969307)))]], -(hBOOL(hAPP(hAPP(_969311, _969309), _969307)))], (45574 ^ _779999) ^ [_1693045, _1693047, _1693049] : [-(_1693045 = c_List_Olist_ONil(_1693047)), -(hAPP(c_List_Ohd(_1693047), hAPP(hAPP(c_List_Oappend(_1693047), _1693045), _1693049)) = hAPP(c_List_Ohd(_1693047), _1693045))], (18237 ^ _779999) ^ [_1111962, _1111964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1111962), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111964), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1111962))))), -(_1111962 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111964), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1111962))))], (38870 ^ _779999) ^ [_1529479, _1529481, _1529483, _1529485, _1529487, _1529489, _1529491, _1529493, _1529495, _1529497] : [hAPP(c_Set_Oimage(_1529479, _1529481, _1529483), _1529485) = _1529487, hAPP(c_Set_Oimage(_1529489, _1529491, _1529493), _1529495) = _1529497, -(hAPP(c_Set_Oimage(tc_prod(_1529479, _1529489), tc_prod(_1529481, _1529491), c_Product__Type_Omap__pair(_1529479, _1529481, _1529489, _1529491, _1529483, _1529493)), hAPP(hAPP(c_Product__Type_OSigma(_1529479, _1529489), _1529485), hAPP(c_COMBK(tc_fun(_1529489, tc_HOL_Obool), _1529479), _1529495))) = hAPP(hAPP(c_Product__Type_OSigma(_1529481, _1529491), _1529487), hAPP(c_COMBK(tc_fun(_1529491, tc_HOL_Obool), _1529481), _1529497)))], (1624 ^ _779999) ^ [_803407, _803409] : [-(class_Groups_Oordered__comm__monoid__add(_803407)), _803409 = _803407, class_Groups_Oordered__comm__monoid__add(_803409)], (41964 ^ _779999) ^ [_1603083, _1603085, _1603087, _1603089, _1603091] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603083, tc_fun(_1603085, tc_HOL_Obool)), _1603087), hAPP(hAPP(c_COMBS(_1603083, tc_fun(_1603085, tc_HOL_Obool), tc_fun(_1603085, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603085, tc_HOL_Obool), tc_fun(tc_fun(_1603085, tc_HOL_Obool), tc_fun(_1603085, tc_HOL_Obool)), _1603083), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603085, tc_HOL_Obool))), _1603089)), _1603091)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603085, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603083, tc_fun(_1603085, tc_HOL_Obool)), _1603087), _1603089)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603083, tc_fun(_1603085, tc_HOL_Obool)), _1603087), _1603091)))], (26717 ^ _779999) ^ [_1280767, _1280769, _1280771, _1280773, _1280775] : [class_Groups_Ocomm__monoid__mult(_1280767), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280769), _1280771)), 26724 ^ _779999 : [(26731 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280769), _1280773), _1280771))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280769, _1280767), hAPP(hAPP(c_COMBC(_1280769, _1280767, _1280767), hAPP(hAPP(c_COMBS(_1280769, _1280767, tc_fun(_1280767, _1280767)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1280767, tc_fun(_1280767, _1280767)), _1280769), c_If(_1280767)), hAPP(hAPP(c_COMBC(_1280769, _1280769, tc_HOL_Obool), c_fequal), _1280773))), _1280775)), c_Groups_Oone__class_Oone(_1280767))), _1280771) = c_Groups_Oone__class_Oone(_1280767))], (26725 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1280769), _1280773), _1280771)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280769, _1280767), hAPP(hAPP(c_COMBC(_1280769, _1280767, _1280767), hAPP(hAPP(c_COMBS(_1280769, _1280767, tc_fun(_1280767, _1280767)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1280767, tc_fun(_1280767, _1280767)), _1280769), c_If(_1280767)), hAPP(hAPP(c_COMBC(_1280769, _1280769, tc_HOL_Obool), c_fequal), _1280773))), _1280775)), c_Groups_Oone__class_Oone(_1280767))), _1280771) = hAPP(_1280775, _1280773))]]], (32647 ^ _779999) ^ [_1392394, _1392396, _1392398] : [class_Int_Onumber__ring(_1392394), 32650 ^ _779999 : [(32657 ^ _779999) ^ [] : [-(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), _1392396)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1392394), hAPP(c_Int_Onumber__class_Onumber__of(_1392394), _1392398)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1392396))) = c_Groups_Oone__class_Oone(_1392394))], (32651 ^ _779999) ^ [] : [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), _1392396))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1392394), hAPP(c_Int_Onumber__class_Onumber__of(_1392394), _1392398)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1392396))) = hAPP(hAPP(c_HOL_OLet(_1392394, _1392394), hAPP(hAPP(c_Power_Opower__class_Opower(_1392394), hAPP(c_Int_Onumber__class_Onumber__of(_1392394), _1392398)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392396))), hAPP(hAPP(c_COMBS(_1392394, _1392394, _1392394), hAPP(hAPP(c_COMBB(_1392394, tc_fun(_1392394, _1392394), _1392394), c_Groups_Otimes__class_Otimes(_1392394)), hAPP(c_Groups_Otimes__class_Otimes(_1392394), hAPP(c_Int_Onumber__class_Onumber__of(_1392394), _1392398)))), c_COMBI(_1392394))))]]], (41282 ^ _779999) ^ [_1587690, _1587692, _1587694, _1587696, _1587698] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1587690, _1587692, _1587694), _1587696), _1587698) = c_HOL_OThe(_1587692, c_Finite__Set_Ofold__graph(_1587690, _1587692, _1587694, _1587696, _1587698)))], (32743 ^ _779999) ^ [_1394272, _1394274] : [c_Int_OBit1(_1394272) = c_Int_OBit1(_1394274), -(_1394272 = _1394274)], (23545 ^ _779999) ^ [_1219791, _1219793, _1219795, _1219797] : [c_Fun_Oinj__on(_1219791, _1219793, _1219795, c_Orderings_Otop__class_Otop(tc_fun(_1219791, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1219791, _1219793, _1219795), hAPP(c_Set_Oimage(_1219791, _1219793, _1219795), _1219797)) = _1219797)], (48855 ^ _779999) ^ [_1763725, _1763727, _1763729] : [48857 ^ _779999 : [(48860 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1763727, 48856 ^ [_1763725, _1763727, _1763729])))], (48858 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763725), 48856 ^ [_1763725, _1763727, _1763729]), hAPP(c_List_Oset(_1763725), c_List_OdropWhile(_1763725, _1763727, _1763729)))))]], -(c_List_OtakeWhile(_1763725, _1763727, _1763729) = hAPP(c_List_Ofilter(_1763725, _1763727), _1763729))], (52294 ^ _779999) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (21050 ^ _779999) ^ [_1162495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1162495)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1162495 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34813 ^ _779999) ^ [_1431119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1431119)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431119), c_Int_OMin)))], (30838 ^ _779999) ^ [_1358056, _1358058] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358056, _1358058) = 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), _1358056), _1358058) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42000 ^ _779999) ^ [_1604349, _1604351, _1604353, _1604355] : [_1604349 = c_Orderings_Obot__class_Obot(tc_fun(_1604351, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604351, tc_fun(_1604353, tc_HOL_Obool)), _1604349), hAPP(c_COMBK(tc_fun(_1604353, tc_HOL_Obool), _1604351), _1604355)) = c_Orderings_Otop__class_Otop(tc_fun(_1604353, tc_HOL_Obool)))], (49790 ^ _779999) ^ [_1784740] : [-(c_Predicate_Oconversep(_1784740, _1784740, c_fequal) = c_fequal)], (47226 ^ _779999) ^ [_1728598, _1728600] : [hBOOL(hAPP(c_List_Odistinct(_1728598), _1728600)), -(c_List_Oremdups(_1728598, _1728600) = _1728600)], (1244 ^ _779999) ^ [_798657, _798659] : [-(class_Groups_Oordered__ab__group__add(_798657)), _798659 = _798657, class_Groups_Oordered__ab__group__add(_798659)], (43237 ^ _779999) ^ [_1634479, _1634481, _1634483] : [_1634479 = hAPP(hAPP(c_List_Olist_OCons(_1634481), _1634483), _1634479)], (38566 ^ _779999) ^ [_1520267, _1520269, _1520271, _1520273, _1520275, _1520277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520267, _1520269)), hAPP(hAPP(c_Product__Type_OPair(_1520267, _1520269), _1520271), _1520273)), hAPP(hAPP(c_Product__Type_OSigma(_1520267, _1520269), _1520275), _1520277))), -(hBOOL(hAPP(hAPP(c_member(_1520267), _1520271), _1520275)))], (48786 ^ _779999) ^ [_1762068, _1762070, _1762072, _1762074, _1762076] : [-(c_List_OdropWhile(_1762068, _1762070, hAPP(hAPP(c_List_Omap(_1762072, _1762068), _1762074), _1762076)) = hAPP(hAPP(c_List_Omap(_1762072, _1762068), _1762074), c_List_OdropWhile(_1762072, hAPP(c_Fun_Ocomp(_1762068, tc_HOL_Obool, _1762072, _1762070), _1762074), _1762076)))], (32715 ^ _779999) ^ [_1393741, _1393743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393741)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393741), _1393743)))], (38754 ^ _779999) ^ [_1526379, _1526381, _1526383, _1526385] : [class_Groups_Ocomm__monoid__mult(_1526379), c_Fun_Oinj__on(_1526381, _1526379, _1526383, _1526385), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526381, _1526379), _1526383), _1526385) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526379, _1526379), c_Fun_Oid(_1526379)), hAPP(c_Set_Oimage(_1526381, _1526379, _1526383), _1526385)))], (23099 ^ _779999) ^ [_1211106, _1211108, _1211110, _1211112] : [class_Orderings_Olinorder(_1211106), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211106), _1211108), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211106), _1211110), _1211112)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211106), _1211110), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211106), _1211108), _1211112)))], (27428 ^ _779999) ^ [_1295964, _1295966, _1295968] : [class_Rings_Oring__1(_1295964), hBOOL(hAPP(hAPP(c_member(_1295964), _1295966), c_Int_Oring__1__class_OInts(_1295964))), -(hBOOL(hAPP(hAPP(c_member(_1295964), hAPP(hAPP(c_Power_Opower__class_Opower(_1295964), _1295966), _1295968)), c_Int_Oring__1__class_OInts(_1295964))))], (47779 ^ _779999) ^ [_1742002, _1742004, _1742006, _1742008] : [class_Groups_Ocomm__monoid__add(_1742002), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1742002), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1742002), _1742004), c_List_Oupt(_1742006, _1742008))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1742002), _1742004), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1742006, _1742008))))], (49800 ^ _779999) ^ [_1784933, _1784935, _1784937, _1784939, _1784941] : [hBOOL(hAPP(hAPP(_1784937, _1784941), _1784939)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1784933, _1784935, _1784937), _1784939), _1784941)))], (30916 ^ _779999) ^ [_1359443, _1359445, _1359447, _1359449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1359445), _1359447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1359447), 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), _1359445), _1359443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359445), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359449, _1359443))), _1359447))))], (9408 ^ _779999) ^ [_940111, _940113, _940115] : [class_Orderings_Olinorder(_940111), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940111), _940113), _940115)), 9415 ^ _779999 : [(9422 ^ _779999) ^ [] : [_940113 = _940115, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940111), _940113), _940115))], (9416 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940111), _940113), _940115))), -(_940113 = _940115)]]], (23011 ^ _779999) ^ [_1209212, _1209214] : [-(hBOOL(hAPP(hAPP(c_member(_1209212), _1209214), c_Orderings_Otop__class_Otop(tc_fun(_1209212, tc_HOL_Obool)))))], (11034 ^ _779999) ^ [_970819, _970821, _970823, _970825] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970819, tc_HOL_Obool)), _970821), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970819, tc_HOL_Obool)), _970823), _970825)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970819, tc_HOL_Obool)), _970823), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970819, tc_HOL_Obool)), _970821), _970825)))], (34235 ^ _779999) ^ [_1420359, _1420361] : [class_Int_Onumber__ring(_1420359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420359), hAPP(c_Int_Onumber__class_Onumber__of(_1420359), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1420361) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420359), _1420361), _1420361))], (44820 ^ _779999) ^ [_1674773, _1674775, _1674777, _1674779, _1674781] : [_1674773 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1674775, _1674777, _1674779), _1674773), _1674781) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1674777), _1674775), c_List_Olist_ONil(_1674777)), _1674781))], (49450 ^ _779999) ^ [_1777537, _1777539, _1777541] : [c_List_Olist__all(_1777537, _1777539, _1777541), 49453 ^ _779999 : [(49454 ^ _779999) ^ [_1777626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1777626), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777537)), _1777541))), -(hBOOL(hAPP(_1777539, hAPP(hAPP(c_List_Onth(_1777537), _1777541), _1777626))))]]], (43769 ^ _779999) ^ [_1650335, _1650337, _1650339, _1650341] : [hBOOL(hAPP(hAPP(c_member(_1650335), _1650337), hAPP(c_List_Oset(_1650335), c_List_Osublist(_1650335, _1650339, _1650341)))), -(hBOOL(hAPP(hAPP(c_member(_1650335), _1650337), hAPP(c_List_Oset(_1650335), _1650339))))], (11426 ^ _779999) ^ [_978769, _978771, _978773, _978775] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978769, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978769, tc_HOL_Obool)), _978771), _978773)), _978775) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978769, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978769, tc_HOL_Obool)), _978771), _978775)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978769, tc_HOL_Obool)), _978773), _978775)))], (47262 ^ _779999) ^ [_1729327, _1729329, _1729331, _1729333] : [class_Orderings_Olinorder(_1729327), 47265 ^ _779999 : [(47272 ^ _779999) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1729329), _1729333)), -(hBOOL(hAPP(c_List_Odistinct(_1729329), c_List_Olinorder__class_Osort__key(_1729329, _1729327, _1729331, _1729333))))], (47266 ^ _779999) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1729329), c_List_Olinorder__class_Osort__key(_1729329, _1729327, _1729331, _1729333))), -(hBOOL(hAPP(c_List_Odistinct(_1729329), _1729333)))]]], (43309 ^ _779999) ^ [_1636942, _1636944, _1636946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636942, _1636942), tc_HOL_Obool)), _1636944), _1636946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636942), tc_List_Olist(_1636942)), tc_HOL_Obool)), c_List_Olistrel1(_1636942, _1636944)), c_List_Olistrel1(_1636942, _1636946))))], (2870 ^ _779999) ^ [_822652, _822654, _822656, _822658, _822660, _822662, _822664, _822666] : [-(c_Fun_Othe__inv__into(_822666, _822662, _822658, _822654) = c_Fun_Othe__inv__into(_822664, _822660, _822656, _822652)), _822666 = _822664, _822662 = _822660, _822658 = _822656, _822654 = _822652], (47689 ^ _779999) ^ [_1740426, _1740428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1740426), _1740428)), -(c_List_Oupt(_1740428, _1740426) = c_List_Olist_ONil(tc_Nat_Onat))], (34905 ^ _779999) ^ [_1432509] : [class_Int_Onumber__ring(_1432509), c_Int_Oiszero(_1432509, hAPP(c_Int_Onumber__class_Onumber__of(_1432509), c_Int_OMin))], (19031 ^ _779999) ^ [_1126918, _1126920, _1126922] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126918), _1126920)), _1126922) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126918), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126920), _1126922)))], (26514 ^ _779999) ^ [_1276661, _1276663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276661, tc_HOL_Obool)), _1276663), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276661, tc_HOL_Obool)), _1276663))), -(_1276663 = c_Orderings_Obot__class_Obot(tc_fun(_1276661, tc_HOL_Obool)))], (42510 ^ _779999) ^ [_1616864, _1616866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1616864), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616864, tc_HOL_Obool), _1616866))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1616864, tc_HOL_Obool)), _1616866)))], (26638 ^ _779999) ^ [_1279345, _1279347, _1279349] : [-(hAPP(c_Set_OCollect(_1279345), hAPP(hAPP(c_COMBS(_1279345, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1279345), c_fimplies), _1279347)), _1279349)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279345, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279345, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1279345), _1279347))), hAPP(c_Set_OCollect(_1279345), _1279349)))], (52238 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52254 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (12733 ^ _779999) ^ [_1005446, _1005448] : [class_Lattices_Olattice(_1005446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005446), _1005448)), -(_1005448 = c_Orderings_Obot__class_Obot(tc_fun(_1005446, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1005446), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005446), 12746 ^ [_1005446, _1005448]), 12747 ^ [_1005446, _1005448])), hAPP(hAPP(c_Set_Oinsert(_1005446), 12746 ^ [_1005446, _1005448]), hAPP(hAPP(c_Set_Oinsert(_1005446), 12747 ^ [_1005446, _1005448]), c_Orderings_Obot__class_Obot(tc_fun(_1005446, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1005446), c_Big__Operators_Olattice__class_OSup__fin(_1005446, _1005448)), _1005448)))], (21738 ^ _779999) ^ [_1176410, _1176412, _1176414, _1176416] : [hBOOL(hAPP(hAPP(c_member(_1176410), _1176412), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1176410, tc_HOL_Obool)), _1176414), hAPP(c_Set_OCollect(_1176410), _1176416)))), 21741 ^ _779999 : [(21744 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1176416, _1176412)))], (21742 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1176410), _1176412), _1176414)))]]], (10635 ^ _779999) ^ [_963048, _963050, _963052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963048), _963050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963052), _963048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963048), _963052)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963050), _963052))))], (35779 ^ _779999) ^ [_1454184, _1454186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1454184)), 35782 ^ _779999 : [(35789 ^ _779999) ^ [] : [-(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), _1454186), _1454184)))), -(c_Divides_OnegDivAlg(_1454186, _1454184) = hAPP(c_Divides_Oadjust(_1454184), c_Divides_OnegDivAlg(_1454186, 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)))), _1454184))))], (35783 ^ _779999) ^ [] : [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), _1454186), _1454184))), -(c_Divides_OnegDivAlg(_1454186, _1454184) = 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), _1454186), _1454184)))]]], (7880 ^ _779999) ^ [_913067, _913069, _913071, _913073, _913075] : [hBOOL(hAPP(_913067, _913069)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_913071), _913069), _913073)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_913067, _913071)), _913073), _913075)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_913067, _913071)), _913069), _913075)))], (1574 ^ _779999) ^ [_802782, _802784] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_802782)), _802784 = _802782, class_Groups_Oordered__ab__semigroup__add__imp__le(_802784)], (38552 ^ _779999) ^ [_1519901, _1519903, _1519905, _1519907, _1519909, _1519911] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519901, _1519903)), hAPP(hAPP(c_Product__Type_OPair(_1519901, _1519903), _1519905), _1519907)), hAPP(hAPP(c_Product__Type_OSigma(_1519901, _1519903), _1519909), _1519911))), 38555 ^ _779999 : [(38558 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519903), _1519907), hAPP(_1519911, _1519905))))], (38556 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519901), _1519905), _1519909)))]]], (14840 ^ _779999) ^ [_1046347, _1046349] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046347), _1046349)), -(hAPP(c_Finite__Set_Ocard(_1046347), _1046349) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1046347, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1046347), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046349))], (10265 ^ _779999) ^ [_956732, _956734, _956736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956732), _956734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956734), _956736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956732)), _956736)))], (9374 ^ _779999) ^ [_939576, _939578, _939580] : [class_Orderings_Oorder(_939576), -(_939578 = _939580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939576), _939580), _939578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939576), _939580), _939578)))], (17189 ^ _779999) ^ [_1091054, _1091056, _1091058] : [class_Rings_Olinordered__idom(_1091054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091054), c_Groups_Ozero__class_Ozero(_1091054)), _1091056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091054), c_Groups_Ozero__class_Ozero(_1091054)), _1091058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091054), _1091058), c_Groups_Oone__class_Oone(_1091054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091054), _1091058), _1091056)), _1091056)))], (37837 ^ _779999) ^ [_1502097, _1502099, _1502101] : [c_Wellfounded_Owf(_1502097, _1502099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502097, _1502097), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1502097, _1502097, _1502097), _1502099), _1502101)), _1502099)), -(c_FunDef_Oreduction__pair(_1502097, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1502097, _1502097), tc_HOL_Obool), tc_fun(tc_prod(_1502097, _1502097), tc_HOL_Obool)), _1502099), _1502101)))], (37288 ^ _779999) ^ [_1486652, _1486654, _1486656, _1486658, _1486660] : [-(hAPP(c_Product__Type_Ofst(_1486652, _1486654), hAPP(c_Product__Type_Oapfst(_1486656, _1486652, _1486654, _1486658), _1486660)) = hAPP(_1486658, hAPP(c_Product__Type_Ofst(_1486656, _1486654), _1486660)))], (37465 ^ _779999) ^ [] : [-(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)))))], (7412 ^ _779999) ^ [_903412, _903414] : [class_Lattices_Obounded__lattice__bot(_903412), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903412), _903414), c_Orderings_Obot__class_Obot(_903412)) = _903414)], (2250 ^ _779999) ^ [_813050, _813052, _813054, _813056, _813058, _813060, _813062, _813064] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_813064, _813060, _813056, _813052) = c_Nat_Osemiring__1__class_Oof__nat__aux(_813062, _813058, _813054, _813050)), _813064 = _813062, _813060 = _813058, _813056 = _813054, _813052 = _813050], (21299 ^ _779999) ^ [_1167758, _1167760] : [class_Orderings_Olinorder(_1167758), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1167758, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1167758), _1167760), c_Orderings_Obot__class_Obot(tc_fun(_1167758, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1167758), _1167760)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1167758), _1167760))], (5016 ^ _779999) ^ [_856627, _856629, _856631, _856633, _856635, _856637, _856639, _856641] : [-(c_Random__Sequence_ORandom(_856641, _856637, _856633, _856629) = c_Random__Sequence_ORandom(_856639, _856635, _856631, _856627)), _856641 = _856639, _856637 = _856635, _856633 = _856631, _856629 = _856627], (19111 ^ _779999) ^ [_1128306, _1128308] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128306), _1128308) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128308), _1128306))], (7854 ^ _779999) ^ [_912662, _912664, _912666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912662, tc_HOL_Obool)), _912664), _912666)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_912662, tc_HOL_Obool)), _912664), hAPP(c_Set_OPow(_912662), _912666))))], (47918 ^ _779999) ^ [_1744596, _1744598, _1744600, _1744602] : [class_Orderings_Olinorder(_1744596), 47921 ^ _779999 : [(47930 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744596, hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744598), hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744600), _1744602)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744596), _1744598), _1744600)), c_List_Olinorder__class_Osorted(_1744596, hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744600), _1744602))], (47922 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1744596, hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744598), hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744600), _1744602))), 47925 ^ _779999 : [(47928 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744596, hAPP(hAPP(c_List_Olist_OCons(_1744596), _1744600), _1744602)))], (47926 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744596), _1744598), _1744600)))]]]]], (40641 ^ _779999) ^ [_1571535, _1571537] : [_1571535 = _1571537, -(c_Random_Oinc__shift(_1571535, _1571537) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (8842 ^ _779999) ^ [_931901, _931903] : [class_Orderings_Opreorder(_931901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931901), _931903), _931903))], (22659 ^ _779999) ^ [_1199533, _1199535, _1199537, _1199539, _1199541] : [_1199533 = c_Orderings_Obot__class_Obot(tc_fun(_1199535, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199535, tc_fun(_1199537, tc_HOL_Obool)), _1199533), hAPP(hAPP(c_COMBC(_1199535, tc_fun(_1199537, tc_HOL_Obool), tc_fun(_1199537, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199537, tc_HOL_Obool), tc_fun(tc_fun(_1199537, tc_HOL_Obool), tc_fun(_1199537, tc_HOL_Obool)), _1199535), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199537, tc_HOL_Obool))), _1199539)), _1199541)) = c_Orderings_Obot__class_Obot(tc_fun(_1199537, tc_HOL_Obool)))], (33107 ^ _779999) ^ [_1400362, _1400364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1400362)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1400364)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400364), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1400362))))], (50706 ^ _779999) ^ [_1805586, _1805588, _1805590, _1805592] : [class_Complete__Lattice_Ocomplete__lattice(_1805586), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1805588, _1805586), _1805590), _1805592) = c_Complete__Lattice_OSup__class_OSup(_1805586, hAPP(c_Set_OCollect(_1805586), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool), tc_HOL_Obool, _1805586), c_HOL_OEx(tc_fun(_1805588, _1805586))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool), tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool), _1805586), hAPP(c_COMBS(tc_fun(_1805588, _1805586), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1805588, _1805586)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1805588, _1805586), tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1805588, _1805586))), _1805590)))), hAPP(hAPP(c_COMBC(_1805586, tc_fun(tc_fun(_1805588, _1805586), _1805586), tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1805586, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1805588, _1805586), _1805586), tc_fun(tc_fun(_1805588, _1805586), tc_HOL_Obool)), _1805586), c_COMBB(_1805586, tc_HOL_Obool, tc_fun(_1805588, _1805586))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1805588, _1805586), _1805588, _1805586), c_COMBI(tc_fun(_1805588, _1805586))), _1805592)))))))], (2462 ^ _779999) ^ [_816318, _816320] : [_816320 = _816318, -(c_Enum_Oenum__class_Oenum__ex(_816320) = c_Enum_Oenum__class_Oenum__ex(_816318))], (45424 ^ _779999) ^ [_1689176, _1689178, _1689180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689176)), _1689180)), _1689178)), -(hAPP(hAPP(c_List_Odrop(_1689176), _1689178), _1689180) = c_List_Olist_ONil(_1689176))], (45572 ^ _779999) ^ [_1693009, _1693011, _1693013] : [-(hAPP(c_List_Ohd(_1693009), hAPP(hAPP(c_List_Olist_OCons(_1693009), _1693011), _1693013)) = _1693011)], (19145 ^ _779999) ^ [_1128953, _1128955, _1128957, _1128959] : [class_Rings_Osemiring__1(_1128953), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1128953, _1128955, hAPP(c_Nat_OSuc, _1128957), _1128959) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1128953, _1128955, _1128957, hAPP(_1128955, _1128959)))], (34229 ^ _779999) ^ [_1420168, _1420170, _1420172] : [class_Int_Onumber__ring(_1420168), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1420168), hAPP(c_Int_Onumber__class_Onumber__of(_1420168), _1420170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1420172))) = hAPP(hAPP(c_HOL_OLet(_1420168, _1420168), hAPP(hAPP(c_Power_Opower__class_Opower(_1420168), hAPP(c_Int_Onumber__class_Onumber__of(_1420168), _1420170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420172))), hAPP(hAPP(c_COMBS(_1420168, _1420168, _1420168), c_Groups_Otimes__class_Otimes(_1420168)), c_COMBI(_1420168))))], (35117 ^ _779999) ^ [_1435937, _1435939, _1435941, _1435943, _1435945] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435937, _1435939), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435941), _1435943))), -(_1435939 = 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)), _1435945)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1435939), _1435945)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435941), _1435945)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1435939), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1435941, _1435945))), _1435943)))))], (31220 ^ _779999) ^ [_1364972, _1364974] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364972, _1364974)) = _1364974), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1364972), _1364974) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364972, _1364974)))], (17921 ^ _779999) ^ [_1106169, _1106171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106169)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106169), _1106171)))], (43102 ^ _779999) ^ [_1630378] : [-(c_Nitpick_Onum(_1630378) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1630378, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1630378)))], (52066 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (1234 ^ _779999) ^ [_798532, _798534] : [-(class_Rings_Olinordered__semiring__1(_798532)), _798534 = _798532, class_Rings_Olinordered__semiring__1(_798534)], (4296 ^ _779999) ^ [_845157, _845159, _845161, _845163, _845165, _845167, _845169, _845171] : [-(c_New__DSequence_Opos__bind(_845171, _845167, _845163, _845159) = c_New__DSequence_Opos__bind(_845169, _845165, _845161, _845157)), _845171 = _845169, _845167 = _845165, _845163 = _845161, _845159 = _845157], (45676 ^ _779999) ^ [_1694683, _1694685, _1694687] : [-(hAPP(c_List_Orotate(_1694683, _1694685), _1694687) = hAPP(c_List_Orotate(_1694683, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1694685, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694683)), _1694687))), _1694687))], (46988 ^ _779999) ^ [_1723674, _1723676, _1723678, _1723680, _1723682, _1723684, _1723686] : [c_List_Olist__all2(_1723674, _1723676, _1723678, _1723680, _1723682), c_List_Olist__all2(_1723674, _1723676, _1723678, _1723684, _1723686), -(c_List_Olist__all2(_1723674, _1723676, _1723678, hAPP(hAPP(c_List_Oappend(_1723674), _1723680), _1723684), hAPP(hAPP(c_List_Oappend(_1723676), _1723682), _1723686)))], (33133 ^ _779999) ^ [_1400765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400765), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400765)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1400765)))], (7248 ^ _779999) ^ [_899887, _899889, _899891, _899893, _899895] : [hBOOL(hAPP(hAPP(c_member(_899887), _899889), _899891)), -(hBOOL(hAPP(hAPP(c_member(_899893), hAPP(_899895, _899889)), hAPP(c_Set_Oimage(_899887, _899893, _899895), _899891))))], (1214 ^ _779999) ^ [_798282, _798284] : [-(class_Rings_Olinordered__ring__strict(_798282)), _798284 = _798282, class_Rings_Olinordered__ring__strict(_798284)], (37270 ^ _779999) ^ [_1486106] : [-(c_Equiv__Relations_Oequivp(_1486106, c_fequal))], (5971 ^ _779999) ^ [_875082, _875084, _875086, _875088] : [class_Orderings_Oorder(_875082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875082), _875084), _875086)), _875084 = _875088, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875082), _875088), _875086)))], (30709 ^ _779999) ^ [_1355679, _1355681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355681, _1355679)), _1355679)))], (29986 ^ _779999) ^ [_1342056, _1342058] : [class_Int_Oring__char__0(_1342056), 29989 ^ _779999 : [(29996 ^ _779999) ^ [] : [_1342058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1342056), _1342058) = c_Groups_Ozero__class_Ozero(_1342056))], (29990 ^ _779999) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1342056), _1342058) = c_Groups_Ozero__class_Ozero(_1342056), -(_1342058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (22068 ^ _779999) ^ [_1187630, _1187632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1187630), _1187632)), -(_1187632 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1187630, 22072 ^ [_1187630, _1187632]), 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)), 22071 ^ [_1187630, _1187632]))))], (2002 ^ _779999) ^ [_808970, _808972, _808974, _808976, _808978, _808980, _808982, _808984] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808984, _808980, _808976, _808972) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808982, _808978, _808974, _808970)), _808984 = _808982, _808980 = _808978, _808976 = _808974, _808972 = _808970], (23533 ^ _779999) ^ [_1219544, _1219546, _1219548, _1219550] : [-(hAPP(c_Set_Oimage(_1219544, _1219546, _1219548), hAPP(c_Set_Ovimage(_1219544, _1219546, _1219548), _1219550)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1219546, tc_HOL_Obool)), _1219550), hAPP(c_Set_Oimage(_1219544, _1219546, _1219548), c_Orderings_Otop__class_Otop(tc_fun(_1219544, tc_HOL_Obool)))))], (40079 ^ _779999) ^ [_1557845, _1557847, _1557849, _1557851, _1557853, _1557855, _1557857, _1557859] : [class_Groups_Ocomm__monoid__add(_1557845), class_Orderings_Oord(_1557847), _1557849 = _1557851, _1557853 = _1557855, 40097 ^ _779999 : [(40102 ^ _779999) ^ [] : [hAPP(_1557857, 40096 ^ [_1557845, _1557847, _1557849, _1557851, _1557853, _1557855, _1557857, _1557859]) = hAPP(_1557859, 40096 ^ [_1557845, _1557847, _1557849, _1557851, _1557853, _1557855, _1557857, _1557859])], (40100 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1557847), 40096 ^ [_1557845, _1557847, _1557849, _1557851, _1557853, _1557855, _1557857, _1557859]), _1557855)))], (40098 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1557847), _1557851), 40096 ^ [_1557845, _1557847, _1557849, _1557851, _1557853, _1557855, _1557857, _1557859])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557847, _1557845), _1557857), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1557847, _1557849), _1557853)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557847, _1557845), _1557859), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1557847, _1557851), _1557855)))], (22653 ^ _779999) ^ [_1199407, _1199409, _1199411, _1199413, _1199415] : [-(_1199407 = c_Orderings_Obot__class_Obot(tc_fun(_1199409, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199409, tc_fun(_1199411, tc_HOL_Obool)), _1199407), hAPP(hAPP(c_COMBB(tc_fun(_1199411, tc_HOL_Obool), tc_fun(_1199411, tc_HOL_Obool), _1199409), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199411, tc_HOL_Obool)), _1199413)), _1199415)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199411, tc_HOL_Obool)), _1199413), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199409, tc_fun(_1199411, tc_HOL_Obool)), _1199407), _1199415)))], (46468 ^ _779999) ^ [_1711979, _1711981, _1711983, _1711985] : [class_Groups_Ocomm__monoid__add(_1711979), 46471 ^ _779999 : [(46478 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1711981), _1711983))), -(c_Nitpick_Osetsum_H(_1711981, _1711979, _1711985, _1711983) = c_Groups_Ozero__class_Ozero(_1711979))], (46472 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1711981), _1711983)), -(c_Nitpick_Osetsum_H(_1711981, _1711979, _1711985, _1711983) = hAPP(c_List_Omonoid__add__class_Olistsum(_1711979), hAPP(hAPP(c_List_Omap(_1711981, _1711979), _1711985), c_Hilbert__Choice_OEps(tc_List_Olist(_1711981), hAPP(hAPP(c_COMBS(tc_List_Olist(_1711981), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1711981)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711981), tc_fun(_1711981, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1711981, tc_HOL_Obool), tc_fun(tc_fun(_1711981, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1711981)), c_fequal), c_List_Oset(_1711981))), _1711983))), c_List_Odistinct(_1711981))))))]]], (15599 ^ _779999) ^ [_1061264, _1061266, _1061268] : [class_Rings_Ono__zero__divisors(_1061264), -(_1061266 = c_Groups_Ozero__class_Ozero(_1061264)), -(_1061268 = c_Groups_Ozero__class_Ozero(_1061264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061264), _1061266), _1061268) = c_Groups_Ozero__class_Ozero(_1061264)], (43860 ^ _779999) ^ [_1652481, _1652483, _1652485] : [hBOOL(hAPP(hAPP(c_member(_1652481), _1652483), hAPP(c_List_Oset(_1652481), _1652485))), -(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(_1652481)), _1652485))))], (45450 ^ _779999) ^ [_1689798, _1689800, _1689802, _1689804] : [-(hAPP(hAPP(c_List_Odrop(_1689798), _1689800), hAPP(hAPP(c_List_Olist_OCons(_1689798), _1689802), _1689804)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1689798), hAPP(hAPP(c_List_Olist_OCons(_1689798), _1689802), _1689804), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1689798), tc_List_Olist(_1689798)), c_List_Odrop(_1689798)), _1689804), _1689800))], (17223 ^ _779999) ^ [_1091816, _1091818, _1091820, _1091822, _1091824, _1091826] : [class_Rings_Oordered__ring(_1091816), 17226 ^ _779999 : [(17233 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1091816), _1091818), _1091824)), _1091820)), _1091822)), _1091826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), _1091818), _1091820)), _1091822)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), _1091824), _1091820)), _1091826))))], (17227 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), _1091818), _1091820)), _1091822)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), _1091824), _1091820)), _1091826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1091816), _1091818), _1091824)), _1091820)), _1091822)), _1091826)))]]], (47675 ^ _779999) ^ [_1740135, _1740137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740135), _1740137)), -(c_List_Oupt(_1740135, _1740137) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1740135), c_List_Oupt(hAPP(c_Nat_OSuc, _1740135), _1740137)))], (27156 ^ _779999) ^ [_1291086, _1291088, _1291090, _1291092] : [class_Rings_Odivision__ring(_1291086), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291086), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1291086), _1291088), _1291090)), _1291092) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1291086), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291086), _1291088), _1291092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291086), _1291090), _1291092)))], (35518 ^ _779999) ^ [_1448622, _1448624, _1448626, _1448628, _1448630, _1448632] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448622, tc_fun(_1448624, tc_HOL_Obool))), _1448626), _1448628), _1448630), _1448632)), -(hBOOL(hAPP(hAPP(_1448626, _1448630), _1448632))), -(hBOOL(hAPP(hAPP(_1448628, _1448630), _1448632)))], (38396 ^ _779999) ^ [_1514806, _1514808, _1514810, _1514812] : [hBOOL(hAPP(c_Predicate_ODomainP(_1514806, _1514808, hAPP(hAPP(c_COMBC(_1514806, tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_fun(_1514808, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514808, tc_fun(tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_fun(_1514808, tc_HOL_Obool)), _1514806), c_COMBC(_1514808, tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514808, tc_prod(_1514806, _1514808)), tc_fun(_1514808, tc_fun(tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_HOL_Obool)), _1514806), hAPP(c_COMBB(tc_prod(_1514806, _1514808), tc_fun(tc_fun(tc_prod(_1514806, _1514808), tc_HOL_Obool), tc_HOL_Obool), _1514808), c_member(tc_prod(_1514806, _1514808)))), c_Product__Type_OPair(_1514806, _1514808)))), _1514810)), _1514812)), -(hBOOL(hAPP(hAPP(c_member(_1514806), _1514812), hAPP(c_Relation_ODomain(_1514806, _1514808), _1514810))))], (42730 ^ _779999) ^ [_1621784, _1621786] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621784, tc_HOL_Obool), _1621786) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1621784, tc_HOL_Obool), tc_fun(_1621784, tc_HOL_Obool)), _1621786), c_COMBI(tc_fun(_1621784, tc_HOL_Obool))))], (34921 ^ _779999) ^ [_1432753, _1432755] : [class_Int_Onumber__ring(_1432753), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432753), _1432755), hAPP(c_Int_Onumber__class_Onumber__of(_1432753), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1432753), _1432755))], (52422 ^ _779999) ^ [_1835061, _1835063] : [hBOOL(hAPP(hAPP(c_fimplies, _1835061), _1835063)), hBOOL(_1835061), -(hBOOL(_1835063))], (8558 ^ _779999) ^ [_926402, _926404, _926406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926402), _926404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926402), _926406)), 8565 ^ _779999 : [(8572 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926404), _926406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926404), _926402)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926406), _926402))))], (8566 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926404), _926402)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926406), _926402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926404), _926406)))]]], (49896 ^ _779999) ^ [_1787513, _1787515, _1787517, _1787519, _1787521, _1787523] : [-(hAPP(hAPP(c_List_Ozip(_1787513, _1787515), c_List_Oreplicate(_1787513, _1787517, _1787519)), c_List_Oreplicate(_1787515, _1787521, _1787523)) = c_List_Oreplicate(tc_prod(_1787513, _1787515), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1787517), _1787521), hAPP(hAPP(c_Product__Type_OPair(_1787513, _1787515), _1787519), _1787523)))], (23325 ^ _779999) ^ [_1215155, _1215157, _1215159, _1215161] : [class_Orderings_Olinorder(_1215155), 23328 ^ _779999 : [(23329 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215155), _1215157), _1215159)), _1215161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), _1215157), _1215161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), _1215159), _1215161)))], (23339 ^ _779999) ^ [] : [23340 ^ _779999 : [(23343 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), _1215159), _1215161))], (23341 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), _1215157), _1215161))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215155), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215155), _1215157), _1215159)), _1215161)))]]], (12886 ^ _779999) ^ [_1008587, _1008589, _1008591, _1008593, _1008595] : [c_Finite__Set_Ofolding__one__idem(_1008587, _1008589, _1008591), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008587), _1008593)), -(_1008593 = c_Orderings_Obot__class_Obot(tc_fun(_1008587, tc_HOL_Obool))), -(hAPP(_1008591, hAPP(hAPP(c_Set_Oinsert(_1008587), _1008595), _1008593)) = hAPP(hAPP(_1008589, _1008595), hAPP(_1008591, _1008593)))], (10179 ^ _779999) ^ [_955436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955436), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10912 ^ _779999) ^ [_968858, _968860] : [-(_968858 = _968860), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968858), _968860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968860), _968858)))], (20032 ^ _779999) ^ [_1145194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145194), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1145194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19009 ^ _779999) ^ [_1126630, _1126632, _1126634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126630), _1126632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126632), _1126634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126630), _1126634)))], (16943 ^ _779999) ^ [_1086367, _1086369, _1086371, _1086373, _1086375] : [class_Rings_Olinordered__semiring__strict(_1086367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086367), _1086369), _1086371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086367), _1086373), _1086375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086367), c_Groups_Ozero__class_Ozero(_1086367)), _1086371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086367), c_Groups_Ozero__class_Ozero(_1086367)), _1086373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086367), _1086369), _1086373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086367), _1086371), _1086375))))], (39657 ^ _779999) ^ [_1547611, _1547613, _1547615, _1547617, _1547619, _1547621, _1547623, _1547625, _1547627, _1547629, _1547631] : [c_Finite__Set_Ofolding(_1547611, _1547613, _1547615, _1547617), -(hAPP(c_Fun_Ocomp(_1547619, _1547621, _1547623, _1547625), hAPP(c_Fun_Ocomp(_1547627, _1547619, _1547623, _1547629), _1547631)) = hAPP(c_Fun_Ocomp(_1547627, _1547621, _1547623, hAPP(c_Fun_Ocomp(_1547619, _1547621, _1547627, _1547625), _1547629)), _1547631))], (3394 ^ _779999) ^ [_830758, _830760] : [_830760 = _830758, -(c_List_Orotate1(_830760) = c_List_Orotate1(_830758))], (23075 ^ _779999) ^ [_1210604, _1210606, _1210608] : [class_Orderings_Olinorder(_1210604), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210604), _1210606), _1210608) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210604), _1210608), _1210606))], (43675 ^ _779999) ^ [_1647590, _1647592, _1647594, _1647596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647590), tc_List_Olist(_1647590))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647590), tc_List_Olist(_1647590)), _1647592), _1647594)), c_List_Olexord(_1647590, _1647596))), 43680 ^ _779999 : [(43683 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1647590), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647590)), _1647592)), _1647594) = _1647592)], (43681 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647590)), _1647592)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647590)), _1647594))))]], 43685 ^ _779999 : [(43690 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647590, _1647590)), hAPP(hAPP(c_Product__Type_OPair(_1647590, _1647590), hAPP(hAPP(c_List_Onth(_1647590), _1647592), 43684 ^ [_1647590, _1647592, _1647594, _1647596])), hAPP(hAPP(c_List_Onth(_1647590), _1647594), 43684 ^ [_1647590, _1647592, _1647594, _1647596]))), _1647596)))], (43688 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1647590), 43684 ^ [_1647590, _1647592, _1647594, _1647596]), _1647592) = hAPP(hAPP(c_List_Otake(_1647590), 43684 ^ [_1647590, _1647592, _1647594, _1647596]), _1647594))], (43686 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43684 ^ [_1647590, _1647592, _1647594, _1647596]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647590)), _1647592)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647590)), _1647594)))))]]], (36012 ^ _779999) ^ [_1458088, _1458090] : [_1458088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1458090, _1458088) = 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), _1458090)))], (38390 ^ _779999) ^ [_1514582, _1514584, _1514586, _1514588] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514582, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514582, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1514582, _1514584), _1514586)), hAPP(c_Relation_ODomain(_1514582, _1514584), _1514588))), hAPP(c_Relation_ODomain(_1514582, _1514584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1514582, _1514584), tc_HOL_Obool)), _1514586), _1514588)))))], (33781 ^ _779999) ^ [_1412163, _1412165, _1412167] : [-(hAPP(c_Nat_Onat_Onat__rec(_1412163, _1412165, _1412167), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1412165)], (40942 ^ _779999) ^ [_1578946, _1578948, _1578950] : [40943 ^ _779999 : [(40944 ^ _779999) ^ [_1579022] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578946, _1578946)), _1578948), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578946, _1578946), tc_HOL_Obool), _1579022), _1578950)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578946, _1578946)), _1578948), c_Transitive__Closure_Ortrancl(_1578946, _1578950))))], (21405 ^ _779999) ^ [_1169760, _1169762, _1169764] : [class_Orderings_Oord(_1169760), 21408 ^ _779999 : [(21415 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169760), _1169764), _1169762)), -(hBOOL(hAPP(hAPP(c_member(_1169760), _1169762), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169760), _1169764))))], (21409 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1169760), _1169762), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169760), _1169764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169760), _1169764), _1169762)))]]], (51301 ^ _779999) ^ [_1817520, _1817522, _1817524] : [c_Fun_Oinj__on(_1817520, _1817522, _1817524, c_Orderings_Otop__class_Otop(tc_fun(_1817520, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1817522, _1817520, _1817520, c_Hilbert__Choice_Oinv__into(_1817520, _1817522, c_Orderings_Otop__class_Otop(tc_fun(_1817520, tc_HOL_Obool)), _1817524)), _1817524) = c_Fun_Oid(_1817520))], (48502 ^ _779999) ^ [_1756204, _1756206, _1756208, _1756210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756204), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756206)), _1756208))), -(hAPP(c_List_Orev(_1756206), hAPP(hAPP(c_List_Olist__update(_1756206, _1756208), _1756204), _1756210)) = hAPP(hAPP(c_List_Olist__update(_1756206, hAPP(c_List_Orev(_1756206), _1756208)), 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(_1756206)), _1756208)), _1756204)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1756210))], (45023 ^ _779999) ^ [_1679689, _1679691, _1679693, _1679695, _1679697] : [-(hAPP(hAPP(c_List_Oappend(_1679689), _1679691), _1679693) = hAPP(hAPP(c_List_Oappend(_1679689), _1679695), _1679697)), 45024 ^ _779999 : [(45031 ^ _779999) ^ [_1679913] : [hAPP(hAPP(c_List_Oappend(_1679689), _1679691), _1679913) = _1679695, _1679693 = hAPP(hAPP(c_List_Oappend(_1679689), _1679913), _1679697)], (45025 ^ _779999) ^ [_1679801] : [_1679691 = hAPP(hAPP(c_List_Oappend(_1679689), _1679695), _1679801), hAPP(hAPP(c_List_Oappend(_1679689), _1679801), _1679693) = _1679697]]], (16811 ^ _779999) ^ [_1084102, _1084104, _1084106] : [class_Orderings_Oorder(_1084102), 16814 ^ _779999 : [(16821 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084102), _1084104), _1084106))), -(c_Orderings_Obot__class_Obot(tc_fun(_1084102, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1084102, _1084104, _1084106))], (16815 ^ _779999) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1084102, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1084102, _1084104, _1084106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084102), _1084104), _1084106))]]], (43789 ^ _779999) ^ [_1650825, _1650827, _1650829] : [43791 ^ _779999 : [(43794 ^ _779999) ^ [] : [hBOOL(hAPP(_1650829, 43790 ^ [_1650825, _1650827, _1650829]))], (43792 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1650825), 43790 ^ [_1650825, _1650827, _1650829]), hAPP(c_List_Oset(_1650825), _1650827))))]], 43795 ^ _779999 : [(43796 ^ _779999) ^ [_1651009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651009), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650825)), _1650827))), -(hBOOL(hAPP(_1650829, hAPP(hAPP(c_List_Onth(_1650825), _1650827), _1651009))))]]], (31184 ^ _779999) ^ [_1364397, _1364399] : [class_Rings_Olinordered__idom(_1364397), 31187 ^ _779999 : [(31194 ^ _779999) ^ [] : [_1364399 = c_Groups_Ozero__class_Ozero(_1364397), -(c_Groups_Osgn__class_Osgn(_1364397, _1364399) = c_Groups_Ozero__class_Ozero(_1364397))], (31188 ^ _779999) ^ [] : [c_Groups_Osgn__class_Osgn(_1364397, _1364399) = c_Groups_Ozero__class_Ozero(_1364397), -(_1364399 = c_Groups_Ozero__class_Ozero(_1364397))]]], (10902 ^ _779999) ^ [_968637, _968639, _968641, _968643] : [hBOOL(hAPP(hAPP(c_member(_968637), _968639), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968637, tc_HOL_Obool)), _968641), _968643))), 10905 ^ _779999 : [(10908 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968637), _968639), _968643)))], (10906 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968637), _968639), _968641)))]]], (33285 ^ _779999) ^ [_1403163, _1403165] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403163), _1403165), hAPP(c_Int_Onumber__class_Onumber__of(_1403163), c_Int_OBit1(c_Int_OPls))) = _1403165), class_Fields_Ofield(_1403163), class_Int_Onumber__ring(_1403163)], (44974 ^ _779999) ^ [_1678635, _1678637, _1678639, _1678641, _1678643, _1678645] : [hAPP(hAPP(c_List_Oappend(_1678635), _1678637), _1678639) = _1678641, _1678643 = hAPP(hAPP(c_List_Oappend(_1678635), _1678639), _1678645), -(hAPP(hAPP(c_List_Oappend(_1678635), _1678637), _1678643) = hAPP(hAPP(c_List_Oappend(_1678635), _1678641), _1678645))], (47589 ^ _779999) ^ [_1738046, _1738048] : [-(c_List_Ofoldr(tc_List_Olist(_1738046), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1738046)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1738046))), c_List_Otranspose(_1738046, _1738048), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738046))), hAPP(c_List_Ofilter(tc_List_Olist(_1738046), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1738046)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738046), tc_List_Olist(_1738046), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1738046)))), _1738048)))], (11014 ^ _779999) ^ [_970384, _970386, _970388] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970384, tc_HOL_Obool)), _970386), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970384, tc_HOL_Obool)), _970386), _970388)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970384, tc_HOL_Obool)), _970386), _970388))], (39811 ^ _779999) ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439] : [class_Groups_Ocomm__monoid__add(_1551429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551431), _1551433)), 39821 ^ _779999 : [(39822 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551431), 39820 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439]), _1551433)))], (39827 ^ _779999) ^ [] : [39820 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439] = 39823 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439]], (39831 ^ _779999) ^ [] : [hAPP(_1551437, hAPP(_1551435, 39820 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439])) = c_Groups_Ozero__class_Ozero(_1551429)], (39829 ^ _779999) ^ [] : [-(hAPP(_1551435, 39820 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439]) = hAPP(_1551435, 39823 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439]))], (39825 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551431), 39823 ^ [_1551429, _1551431, _1551433, _1551435, _1551437, _1551439]), _1551433)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1551439, _1551429), _1551437), hAPP(c_Set_Oimage(_1551431, _1551439, _1551435), _1551433)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1551431, _1551429), hAPP(c_Fun_Ocomp(_1551439, _1551429, _1551431, _1551437), _1551435)), _1551433))], (19423 ^ _779999) ^ [_1134178, _1134180] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1134178), _1134180)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134178)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134180))))], (29338 ^ _779999) ^ [_1331214, _1331216] : [class_Divides_Osemiring__div(_1331214), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1331214), c_Groups_Ozero__class_Ozero(_1331214)), _1331216) = c_Groups_Ozero__class_Ozero(_1331214))], (25618 ^ _779999) ^ [_1260388, _1260390, _1260392, _1260394] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1260388), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260390, tc_Nat_Onat), _1260392), _1260394)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260390, _1260388), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1260388, _1260390), c_Nat_Osemiring__1__class_Oof__nat(_1260388)), _1260392)), _1260394)), class_Groups_Ocomm__monoid__mult(_1260388), class_Rings_Osemiring__1(_1260388)], (44498 ^ _779999) ^ [_1668352, _1668354, _1668356, _1668358] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1668354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668352)), hAPP(hAPP(c_List_Olist_OCons(_1668354), _1668356), _1668358)) = c_List_Olist_ONil(_1668354))], (8646 ^ _779999) ^ [_927982, _927984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927982), _927984)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _927984)), _927982) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927984), _927982)))], (31351 ^ _779999) ^ [_1367228, _1367230, _1367232] : [hBOOL(hAPP(_1367228, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1367230, _1367232))), 31354 ^ _779999 : [(31361 ^ _779999) ^ [] : [-(_1367232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31364 ^ _779999 : [(31365 ^ _779999) ^ [_1367476, _1367478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1367476), _1367232)), _1367230 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1367232), _1367478)), _1367476), -(hBOOL(hAPP(_1367228, _1367476)))]]], (31355 ^ _779999) ^ [] : [_1367232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1367228, _1367230)))]]], (50893 ^ _779999) ^ [_1809867, _1809869] : [c_Relation_Oantisym(_1809867, _1809869), -(c_Relation_Oantisym(_1809867, hAPP(c_Relation_Oconverse(_1809867, _1809867), _1809869)))], (18507 ^ _779999) ^ [_1117036, _1117038] : [class_Rings_Osemiring__1(_1117036), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117036), hAPP(c_Nat_OSuc, _1117038)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117036), c_Groups_Oone__class_Oone(_1117036)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117036), _1117038)))], (40339 ^ _779999) ^ [_1564777, _1564779, _1564781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564777, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1564777, _1564777, _1564779), _1564781)), _1564781)), -(hAPP(c_Relation_OImage(_1564777, _1564777, c_Transitive__Closure_Ortrancl(_1564777, _1564779)), _1564781) = _1564781)], (21626 ^ _779999) ^ [_1173885, _1173887] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173885)), -(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)), _1173885))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1173887))))) = 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)), _1173885))), 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, _1173887))))))], (17878 ^ _779999) ^ [_1105448] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1105448), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (16125 ^ _779999) ^ [_1071139, _1071141, _1071143, _1071145] : [class_Rings_Oordered__comm__semiring(_1071139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071139), _1071141), _1071143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071139), c_Groups_Ozero__class_Ozero(_1071139)), _1071145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071139), _1071145), _1071141)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071139), _1071145), _1071143))))], (35974 ^ _779999) ^ [_1457486] : [-(c_Divides_Odivmod__nat(_1457486, 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)), _1457486))], (37232 ^ _779999) ^ [_1485375, _1485377, _1485379] : [c_Equiv__Relations_Oequivp(_1485375, _1485377), -(hBOOL(hAPP(hAPP(_1485377, _1485379), _1485379)))], (42341 ^ _779999) ^ [_1613137, _1613139, _1613141] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1613137, tc_HOL_Obool)), _1613139), _1613141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1613137, tc_HOL_Obool)), _1613139), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1613137, tc_HOL_Obool), _1613141))))], (46678 ^ _779999) ^ [] : [-(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))))], (19405 ^ _779999) ^ [_1133821, _1133823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1133821), _1133823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133821)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133823))))], (30533 ^ _779999) ^ [_1352393, _1352395, _1352397] : [class_Divides_Osemiring__div(_1352393), -(c_Divides_Odiv__class_Omod(_1352393, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352393), _1352395), _1352397), _1352397) = c_Divides_Odiv__class_Omod(_1352393, _1352395, _1352397))], (18491 ^ _779999) ^ [_1116675, _1116677, _1116679, _1116681, _1116683] : [class_Groups_Oab__group__add(_1116675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116677), _1116679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116679), _1116681)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116675), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116675), _1116683), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116677), _1116681))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116675), _1116683), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116677), _1116679))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1116675), _1116683), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1116679), _1116681)))], (5640 ^ _779999) ^ [_866327, _866329] : [_866329 = _866327, -(tc_Lazy__Sequence_Olazy__sequence(_866329) = tc_Lazy__Sequence_Olazy__sequence(_866327))], (11572 ^ _779999) ^ [_982749, _982751, _982753, _982755] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982749, tc_HOL_Obool)), _982751), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982749, tc_HOL_Obool)), _982753), _982755)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982749, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982749, tc_HOL_Obool)), _982751), _982753)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982749, tc_HOL_Obool)), _982751), _982755)))], (30944 ^ _779999) ^ [_1359979, _1359981, _1359983, _1359985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1359981), _1359983)), -(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), _1359983), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359985, _1359979))), _1359981))))], (47876 ^ _779999) ^ [_1744013] : [class_Orderings_Olinorder(_1744013), -(c_List_Olinorder__class_Osorted(_1744013, c_List_Olist_ONil(_1744013)))], (16083 ^ _779999) ^ [_1070346, _1070348, _1070350] : [class_Rings_Oordered__ring(_1070346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070346), _1070348), c_Groups_Ozero__class_Ozero(_1070346))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070346), _1070350), c_Groups_Ozero__class_Ozero(_1070346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070346), c_Groups_Ozero__class_Ozero(_1070346)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070346), _1070348), _1070350))))], (48806 ^ _779999) ^ [_1762512, _1762514, _1762516, _1762518, _1762520] : [-(c_List_OdropWhile(_1762512, _1762514, _1762516) = hAPP(hAPP(c_List_Olist_OCons(_1762512), _1762518), _1762520)), _1762516 = hAPP(hAPP(c_List_Oappend(_1762512), c_List_OtakeWhile(_1762512, _1762514, _1762516)), hAPP(hAPP(c_List_Olist_OCons(_1762512), _1762518), _1762520)), -(hBOOL(hAPP(_1762514, _1762518)))], (52260 ^ _779999) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (20717 ^ _779999) ^ [_1155923, _1155925, _1155927] : [20719 ^ _779999 : [(20722 ^ _779999) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1155927, 20718 ^ [_1155923, _1155925, _1155927]))], (20720 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1155923), 20718 ^ [_1155923, _1155925, _1155927]), _1155925)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1155923, tc_Int_Oint), _1155927), _1155925) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1155923, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1155923), c_Int_Onat), _1155927)), _1155925)))], (14872 ^ _779999) ^ [_1046887, _1046889, _1046891] : [class_Rings_Olinordered__idom(_1046887), -(_1046889 = _1046891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046887), _1046889), _1046891))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046887), _1046891), _1046889)))], (39491 ^ _779999) ^ [_1543864, _1543866, _1543868, _1543870, _1543872, _1543874] : [c_Fun_Oinj__on(_1543864, _1543866, _1543868, _1543870), c_Fun_Oinj__on(_1543866, _1543872, _1543874, hAPP(c_Set_Oimage(_1543864, _1543866, _1543868), _1543870)), -(c_Fun_Oinj__on(_1543864, _1543872, hAPP(c_Fun_Ocomp(_1543866, _1543872, _1543864, _1543874), _1543868), _1543870))], (23013 ^ _779999) ^ [_1209249, _1209251, _1209253, _1209255] : [c_Fun_Oinj__on(_1209249, _1209251, _1209253, c_Orderings_Otop__class_Otop(tc_fun(_1209249, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1209249, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1209249, _1209251, _1209253), hAPP(hAPP(c_Set_Oinsert(_1209251), _1209255), c_Orderings_Obot__class_Obot(tc_fun(_1209251, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1209249), c_HOL_OThe(_1209249, hAPP(hAPP(c_COMBC(_1209249, _1209251, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1209251, tc_fun(_1209251, tc_HOL_Obool), _1209249), c_fequal), _1209253)), _1209255))), c_Orderings_Obot__class_Obot(tc_fun(_1209249, tc_HOL_Obool))))))], (1314 ^ _779999) ^ [_799532, _799534] : [-(class_Groups_Ogroup__add(_799532)), _799534 = _799532, class_Groups_Ogroup__add(_799534)], (21564 ^ _779999) ^ [_1172634, _1172636, _1172638, _1172640] : [c_Big__Operators_Osemilattice__big(_1172634, _1172636, _1172638), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172634), _1172640)), -(hAPP(_1172638, _1172640) = hAPP(c_Finite__Set_Ofold1(_1172634, _1172636), _1172640))], (37739 ^ _779999) ^ [_1498758, _1498760, _1498762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498758, _1498758), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1498758, _1498758, _1498758), _1498760), _1498762)), _1498760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1498758, _1498760)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1498758, _1498762)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1498758, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1498758, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1498758, tc_HOL_Obool), tc_fun(_1498758, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1498758, _1498760))))], (37847 ^ _779999) ^ [_1502339, _1502341, _1502343, _1502345] : [c_Wellfounded_Omax__extp(_1502339, _1502341, _1502343, _1502345), 37850 ^ _779999 : [(37853 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502339), _1502345)))], (37855 ^ _779999) ^ [] : [_1502345 = c_Orderings_Obot__class_Obot(tc_fun(_1502339, tc_HOL_Obool))], (37857 ^ _779999) ^ [_1502555] : [hBOOL(hAPP(hAPP(c_member(_1502339), _1502555), _1502343)), 37861 ^ _779999 : [(37864 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1502341, _1502555), 37860 ^ [_1502339, _1502341, _1502343, _1502345, _1502555])))], (37862 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502339), 37860 ^ [_1502339, _1502341, _1502343, _1502345, _1502555]), _1502345)))]]], (37851 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502339), _1502343)))]]], (10315 ^ _779999) ^ [_957478, _957480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957478), _957480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957478), _957480)))], (15454 ^ _779999) ^ [_1057918, _1057920, _1057922, _1057924, _1057926] : [class_Groups_Ocomm__monoid__mult(_1057918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057920), _1057922)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057920), _1057924)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057920, tc_HOL_Obool)), _1057922), _1057924) = c_Orderings_Obot__class_Obot(tc_fun(_1057920, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057918, _1057920, c_Groups_Otimes__class_Otimes(_1057918)), _1057926), c_Groups_Oone__class_Oone(_1057918)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057920, tc_HOL_Obool)), _1057922), _1057924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057918), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057918, _1057920, c_Groups_Otimes__class_Otimes(_1057918)), _1057926), c_Groups_Oone__class_Oone(_1057918)), _1057922)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057918, _1057920, c_Groups_Otimes__class_Otimes(_1057918)), _1057926), c_Groups_Oone__class_Oone(_1057918)), _1057924)))], (13437 ^ _779999) ^ [_1019323, _1019325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019323), _1019325)), _1019325))], (46712 ^ _779999) ^ [_1716926, _1716928] : [-(c_Code__Numeral_Onat__of__aux(_1716926, _1716928) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716926)), _1716928))], (33069 ^ _779999) ^ [_1399791, _1399793] : [class_Int_Onumber__ring(_1399791), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1399791), hAPP(c_Int_Onumber__class_Onumber__of(_1399791), c_Int_OPls)), _1399793) = _1399793)], (46765 ^ _779999) ^ [_1718007, _1718009, _1718011] : [-(c_List_Olistsp(_1718007, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1718007, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1718007, tc_fun(_1718007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718007)), _1718009)), hAPP(hAPP(c_COMBC(_1718007, tc_fun(_1718007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718007)), _1718011))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1718007), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1718007), tc_fun(tc_List_Olist(_1718007), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1718007))), c_List_Olists(_1718007, _1718009))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1718007), tc_fun(tc_List_Olist(_1718007), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1718007))), c_List_Olists(_1718007, _1718011))))], (4206 ^ _779999) ^ [_843580, _843582, _843584, _843586, _843588, _843590, _843592, _843594] : [-(c_New__DSequence_Oneg__bind(_843594, _843590, _843586, _843582) = c_New__DSequence_Oneg__bind(_843592, _843588, _843584, _843580)), _843594 = _843592, _843590 = _843588, _843586 = _843584, _843582 = _843580], (22874 ^ _779999) ^ [_1204951, _1204953, _1204955, _1204957, _1204959, _1204961] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204951, tc_fun(_1204953, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1204955, _1204951, _1204957), _1204959)), _1204961) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204955, tc_fun(_1204953, tc_HOL_Obool)), _1204959), hAPP(hAPP(c_COMBB(_1204951, tc_fun(_1204953, tc_HOL_Obool), _1204955), _1204961), _1204957)))], (29734 ^ _779999) ^ [_1337547, _1337549, _1337551] : [class_Divides_Osemiring__div(_1337547), -(_1337549 = c_Groups_Ozero__class_Ozero(_1337547)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337547), _1337549), _1337551)), _1337549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337547), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337547), _1337551), _1337549)), c_Groups_Oone__class_Oone(_1337547)))], (38523 ^ _779999) ^ [_1518911, _1518913, _1518915, _1518917, _1518919] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518911, _1518913), _1518915), hAPP(hAPP(c_COMBS(_1518911, tc_fun(_1518913, tc_HOL_Obool), tc_fun(_1518913, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518913, tc_HOL_Obool), tc_fun(tc_fun(_1518913, tc_HOL_Obool), tc_fun(_1518913, tc_HOL_Obool)), _1518911), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518913, tc_HOL_Obool))), _1518917)), _1518919)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518911, _1518913), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518911, _1518913), _1518915), _1518917)), hAPP(hAPP(c_Product__Type_OSigma(_1518911, _1518913), _1518915), _1518919)))], (2288 ^ _779999) ^ [_813649, _813651, _813653, _813655, _813657, _813659] : [-(c_Finite__Set_Ofold1Set(_813659, _813655, _813651) = c_Finite__Set_Ofold1Set(_813657, _813653, _813649)), _813659 = _813657, _813655 = _813653, _813651 = _813649], (38614 ^ _779999) ^ [_1521559, _1521561, _1521563, _1521565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521559, _1521561)), hAPP(hAPP(c_Product__Type_OSigma(_1521559, _1521561), _1521563), hAPP(c_COMBK(tc_fun(_1521561, tc_HOL_Obool), _1521559), _1521565)))), -(_1521565 = c_Orderings_Obot__class_Obot(tc_fun(_1521561, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521559), _1521563)))], (49011 ^ _779999) ^ [_1766706, _1766708, _1766710] : [-(hAPP(c_List_Oset(_1766706), c_List_Oinsert(_1766706, _1766708, _1766710)) = hAPP(hAPP(c_Set_Oinsert(_1766706), _1766708), hAPP(c_List_Oset(_1766706), _1766710)))], (4128 ^ _779999) ^ [_842219, _842221] : [_842221 = _842219, -(c_Nat_Osemiring__1__class_Oof__nat(_842221) = c_Nat_Osemiring__1__class_Oof__nat(_842219))], (688 ^ _779999) ^ [_790545, _790547, _790549, _790551, _790553, _790555] : [-(c_Finite__Set_Ofun__left__comm__idem(_790553, _790549, _790545)), c_Finite__Set_Ofun__left__comm__idem(_790555, _790551, _790547), _790555 = _790553, _790551 = _790549, _790547 = _790545], (1814 ^ _779999) ^ [_805782, _805784] : [-(class_Orderings_Opreorder(_805782)), _805784 = _805782, class_Orderings_Opreorder(_805784)], (10047 ^ _779999) ^ [_953296, _953298, _953300, _953302] : [c_Fun_Oinj__on(_953296, _953298, _953300, _953302), -(hAPP(c_Set_Oimage(_953298, _953296, c_Fun_Othe__inv__into(_953296, _953298, _953302, _953300)), hAPP(c_Set_Oimage(_953296, _953298, _953300), _953302)) = _953302)], (39423 ^ _779999) ^ [_1542478, _1542480, _1542482, _1542484, _1542486, _1542488, _1542490] : [hAPP(c_Fun_Ocomp(_1542478, _1542480, _1542482, _1542484), _1542486) = _1542488, -(hAPP(_1542484, hAPP(_1542486, _1542490)) = hAPP(_1542488, _1542490))], (45690 ^ _779999) ^ [_1695030, _1695032, _1695034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695030)), _1695032)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1695030, _1695034), _1695032) = _1695032)], (37316 ^ _779999) ^ [_1487358, _1487360, _1487362, _1487364, _1487366] : [hBOOL(hAPP(hAPP(c_member(_1487358), _1487360), hAPP(c_Relation_OImage(_1487362, _1487358, _1487364), _1487366))), 37320 ^ _779999 : [(37323 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487362), 37319 ^ [_1487358, _1487360, _1487362, _1487364, _1487366]), _1487366)))], (37321 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487362, _1487358)), hAPP(hAPP(c_Product__Type_OPair(_1487362, _1487358), 37319 ^ [_1487358, _1487360, _1487362, _1487364, _1487366]), _1487360)), _1487364)))]]], (9558 ^ _779999) ^ [_942411, _942413, _942415, _942417] : [class_Lattices_Osemilattice__sup(_942411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942411), _942413), _942415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942411), _942413), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942411), _942415), _942417))))], (46622 ^ _779999) ^ [_1715120, _1715122, _1715124, _1715126] : [class_Groups_Ocomm__monoid__add(_1715120), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1715120), _1715122), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1715124, _1715126))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1715120), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1715120), _1715122), c_List_Oupto(_1715124, _1715126))))], (3420 ^ _779999) ^ [_831141, _831143, _831145, _831147] : [-(c_Big__Operators_Olattice__class_OInf__fin(_831147, _831143) = c_Big__Operators_Olattice__class_OInf__fin(_831145, _831141)), _831147 = _831145, _831143 = _831141], (2952 ^ _779999) ^ [_823927, _823929, _823931, _823933, _823935, _823937] : [-(c_Com_Ocom_OLocal(_823937, _823933, _823929) = c_Com_Ocom_OLocal(_823935, _823931, _823927)), _823937 = _823935, _823933 = _823931, _823929 = _823927], (26781 ^ _779999) ^ [_1282455, _1282457, _1282459] : [class_Groups_Oordered__ab__group__add(_1282455), -(hAPP(c_Set_Oimage(_1282455, _1282455, c_Groups_Ouminus__class_Ouminus(_1282455)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1282455, _1282457), _1282459)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1282455, hAPP(c_Groups_Ouminus__class_Ouminus(_1282455), _1282459), hAPP(c_Groups_Ouminus__class_Ouminus(_1282455), _1282457)))], (494 ^ _779999) ^ [_787574, _787576, _787578, _787580, _787582, _787584, _787586, _787588] : [-(c_Finite__Set_Ofolding(_787586, _787582, _787578, _787574)), c_Finite__Set_Ofolding(_787588, _787584, _787580, _787576), _787588 = _787586, _787584 = _787582, _787580 = _787578, _787576 = _787574], (37202 ^ _779999) ^ [_1484662, _1484664] : [c_Equiv__Relations_Oequivp(_1484662, hAPP(hAPP(c_COMBC(_1484662, tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_fun(_1484662, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484662, tc_fun(tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_fun(_1484662, tc_HOL_Obool)), _1484662), c_COMBC(_1484662, tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484662, tc_prod(_1484662, _1484662)), tc_fun(_1484662, tc_fun(tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_HOL_Obool)), _1484662), hAPP(c_COMBB(tc_prod(_1484662, _1484662), tc_fun(tc_fun(tc_prod(_1484662, _1484662), tc_HOL_Obool), tc_HOL_Obool), _1484662), c_member(tc_prod(_1484662, _1484662)))), c_Product__Type_OPair(_1484662, _1484662)))), _1484664)), -(c_Equiv__Relations_Oequiv(_1484662, c_Orderings_Otop__class_Otop(tc_fun(_1484662, tc_HOL_Obool)), _1484664))], (2542 ^ _779999) ^ [_817488, _817490, _817492, _817494] : [-(c_Divides_Odivmod__int(_817494, _817490) = c_Divides_Odivmod__int(_817492, _817488)), _817494 = _817492, _817490 = _817488], (46694 ^ _779999) ^ [_1716616] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1716616)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1716616))], (32271 ^ _779999) ^ [_1385123, _1385125, _1385127, _1385129] : [class_Fields_Olinordered__field__inverse__zero(_1385123), class_Int_Onumber(_1385123), 32278 ^ _779999 : [(32279 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385123), _1385127), _1385129))), 32282 ^ _779999 : [(32289 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), c_Groups_Ozero__class_Ozero(_1385123)), _1385129))), 32292 ^ _779999 : [(32299 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385129), c_Groups_Ozero__class_Ozero(_1385123)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), c_Groups_Ozero__class_Ozero(_1385123))))], (32293 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385129), c_Groups_Ozero__class_Ozero(_1385123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), _1385129))))]]], (32283 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), c_Groups_Ozero__class_Ozero(_1385123)), _1385129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), _1385129)), _1385127)))]]], (32305 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385123), _1385127), _1385129)))), 32308 ^ _779999 : [(32311 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), _1385129)), _1385127))], (32309 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), c_Groups_Ozero__class_Ozero(_1385123)), _1385129)))]], 32312 ^ _779999 : [(32315 ^ _779999) ^ [] : [32316 ^ _779999 : [(32319 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), _1385129)))], (32317 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385129), c_Groups_Ozero__class_Ozero(_1385123))))]], 32320 ^ _779999 : [(32323 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), hAPP(c_Int_Onumber__class_Onumber__of(_1385123), _1385125)), c_Groups_Ozero__class_Ozero(_1385123)))], (32321 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), _1385129), c_Groups_Ozero__class_Ozero(_1385123)))]]], (32313 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385123), c_Groups_Ozero__class_Ozero(_1385123)), _1385129))]]]]], (44662 ^ _779999) ^ [_1671196] : [class_Groups_Omonoid__add(_1671196), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671196), c_List_Olist_ONil(_1671196)) = c_Groups_Ozero__class_Ozero(_1671196))], (18403 ^ _779999) ^ [_1115046, _1115048, _1115050] : [class_Orderings_Oorder(_1115046), 18406 ^ _779999 : [(18413 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115046), _1115048), _1115050))), -(c_Orderings_Obot__class_Obot(tc_fun(_1115046, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1115046, _1115048, _1115050))], (18407 ^ _779999) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1115046, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1115046, _1115048, _1115050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115046), _1115048), _1115050))]]], (41071 ^ _779999) ^ [_1582215, _1582217, _1582219, _1582221, _1582223] : [c_Relation_Osingle__valued(_1582215, _1582217, _1582219), c_Relation_Osingle__valued(_1582217, _1582221, _1582223), -(c_Relation_Osingle__valued(_1582215, _1582221, hAPP(hAPP(c_Relation_Orel__comp(_1582215, _1582217, _1582221), _1582219), _1582223)))], (47095 ^ _779999) ^ [_1725950, _1725952, _1725954, _1725956, _1725958, _1725960] : [c_List_Olist__all2(_1725950, _1725952, _1725954, _1725956, _1725958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725960), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725950)), _1725956))), -(hBOOL(hAPP(hAPP(_1725954, hAPP(hAPP(c_List_Onth(_1725950), _1725956), _1725960)), hAPP(hAPP(c_List_Onth(_1725952), _1725958), _1725960))))], (13387 ^ _779999) ^ [_1018332, _1018334, _1018336, _1018338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018332), _1018334)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018336), _1018334) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018332), _1018338), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018336), _1018338)))], (50272 ^ _779999) ^ [_1795049, _1795051, _1795053, _1795055, _1795057, _1795059] : [-(c_Nitpick_Opair__box_OPairBox(_1795049, _1795051, _1795053, _1795055) = c_Nitpick_Opair__box_OPairBox(_1795049, _1795051, _1795057, _1795059)), _1795053 = _1795057, _1795055 = _1795059], (47844 ^ _779999) ^ [_1743540, _1743542] : [class_Orderings_Olinorder(_1743540), -(c_List_Olinorder__class_Osorted(_1743540, c_List_Olinorder__class_Osort__key(_1743540, _1743540, c_COMBI(_1743540), _1743542)))], (30772 ^ _779999) ^ [_1356927, _1356929, _1356931, _1356933] : [class_Divides_Osemiring__div(_1356927), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356927), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356927), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1356927), _1356929), _1356931)), _1356931)), c_Divides_Odiv__class_Omod(_1356927, _1356929, _1356931))), _1356933) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356927), _1356929), _1356933))], (33451 ^ _779999) ^ [] : [-(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)))))], (6314 ^ _779999) ^ [_881382, _881384, _881386, _881388] : [6328 ^ _779999 : [(6331 ^ _779999) ^ [] : [-(hBOOL(hAPP(_881388, 6327 ^ [_881382, _881384, _881386, _881388])))], (6329 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881382), 6327 ^ [_881382, _881384, _881386, _881388]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881382, tc_HOL_Obool)), _881384), _881386))))]], 6315 ^ _779999 : [(6322 ^ _779999) ^ [_881591] : [hBOOL(hAPP(hAPP(c_member(_881382), _881591), _881386)), hBOOL(hAPP(_881388, _881591))], (6316 ^ _779999) ^ [_881495] : [hBOOL(hAPP(hAPP(c_member(_881382), _881495), _881384)), hBOOL(hAPP(_881388, _881495))]]], (50042 ^ _779999) ^ [_1790185, _1790187, _1790189] : [-(hAPP(hAPP(c_List_Oappend(_1790185), c_List_Oreplicate(_1790185, _1790187, _1790189)), hAPP(hAPP(c_List_Olist_OCons(_1790185), _1790189), c_List_Olist_ONil(_1790185))) = hAPP(hAPP(c_List_Olist_OCons(_1790185), _1790189), c_List_Oreplicate(_1790185, _1790187, _1790189)))], (22341 ^ _779999) ^ [_1193253, _1193255, _1193257, _1193259, _1193261] : [_1193253 = hAPP(_1193255, _1193257), -(hBOOL(hAPP(hAPP(c_member(_1193259), _1193253), hAPP(c_Set_Oimage(_1193261, _1193259, _1193255), c_Orderings_Otop__class_Otop(tc_fun(_1193261, tc_HOL_Obool))))))], (25936 ^ _779999) ^ [_1266426, _1266428, _1266430, _1266432, _1266434, _1266436] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_1266426, _1266428, _1266430), _1266432, _1266434, _1266436), 25941 ^ _779999 : [(25944 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1266428, _1266432, _1266434, _1266436))], (25942 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1266426, _1266432)))]], 25945 ^ _779999 : [(25948 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1266430, _1266432, _1266434, _1266436))], (25946 ^ _779999) ^ [] : [hBOOL(hAPP(_1266426, _1266432))]]], (6113 ^ _779999) ^ [_877420, _877422, _877424, _877426] : [class_Lattices_Olattice(_877420), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877420), _877422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877420), _877424), _877426)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877420), _877424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877420), _877422), _877426)))], (23417 ^ _779999) ^ [_1216910, _1216912] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1216910)), hAPP(c_Nat_OSuc, _1216912)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1216910), _1216912)))], (18371 ^ _779999) ^ [_1114515, _1114517, _1114519] : [class_Orderings_Oorder(_1114515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114515), _1114517), _1114519)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1114515, _1114519, _1114517) = c_Orderings_Obot__class_Obot(tc_fun(_1114515, tc_HOL_Obool)))], (50288 ^ _779999) ^ [_1795370, _1795372, _1795374] : [-(c_FunDef_OTHE__default(_1795372, _1795374, _1795370) = c_HOL_OThe(_1795372, _1795370)), 50289 ^ _779999 : [(50290 ^ _779999) ^ [_1795434] : [hBOOL(hAPP(_1795370, _1795434)), 50294 ^ _779999 : [(50297 ^ _779999) ^ [] : [50293 ^ [_1795370, _1795372, _1795374, _1795434] = _1795434], (50295 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1795370, 50293 ^ [_1795370, _1795372, _1795374, _1795434])))]]]]], (15927 ^ _779999) ^ [_1067112, _1067114, _1067116] : [-(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)), _1067112)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1067114, _1067116)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067114), _1067112), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067116), _1067112)))], (30146 ^ _779999) ^ [_1344949, _1344951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344949)), 30149 ^ _779999 : [(30156 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344951), _1344949))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344951), _1344949) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1344951), _1344949)), _1344949)))], (30150 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344951), _1344949)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344951), _1344949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (14025 ^ _779999) ^ [_1030024, _1030026, _1030028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030024), _1030026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030028), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030026), _1030028)), _1030024))))], (23485 ^ _779999) ^ [_1218602, _1218604, _1218606, _1218608] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218602), hAPP(c_Set_Ovimage(_1218602, _1218604, _1218606), _1218608))), hAPP(c_Set_Oimage(_1218602, _1218604, _1218606), c_Orderings_Otop__class_Otop(tc_fun(_1218602, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1218604, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1218604), _1218608)))], (20492 ^ _779999) ^ [_1152673, _1152675] : [c_Nat__Transfer_Ois__nat(_1152673), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1152673, _1152675)))], (35358 ^ _779999) ^ [_1445348] : [class_Rings_Osemiring__1(_1445348), -(hBOOL(hAPP(hAPP(c_member(_1445348), c_Groups_Ozero__class_Ozero(_1445348)), c_Nat_Osemiring__1__class_ONats(_1445348))))], (44696 ^ _779999) ^ [_1671758, _1671760, _1671762] : [-(hAPP(hAPP(c_List_Otake(_1671758), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1671758), _1671760), _1671762)) = hAPP(hAPP(c_List_Olist_OCons(_1671758), _1671760), c_List_Olist_ONil(_1671758)))], (6818 ^ _779999) ^ [_891717, _891719] : [_891719 = c_Orderings_Obot__class_Obot(tc_fun(_891717, tc_HOL_Obool)), 6821 ^ _779999 : [(6822 ^ _779999) ^ [_891797] : [hBOOL(hAPP(hAPP(c_member(_891717), _891797), _891719))]]], (35707 ^ _779999) ^ [_1452931] : [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), _1452931))), 35710 ^ _779999 : [(35717 ^ _779999) ^ [] : [-(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), _1452931))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1452931)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1452931)), 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), _1452931)))))], (35711 ^ _779999) ^ [] : [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), _1452931)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1452931)) = 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), _1452931))))]]], (3762 ^ _779999) ^ [_836448, _836450, _836452, _836454, _836456, _836458] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_836458, _836454, _836450) = c_SetInterval_Oord__class_OgreaterThanAtMost(_836456, _836452, _836448)), _836458 = _836456, _836454 = _836452, _836450 = _836448], (19928 ^ _779999) ^ [_1143544, _1143546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143546)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1143544)), hAPP(c_Int_Onat, _1143546)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1143544, _1143546)))], (42644 ^ _779999) ^ [_1619933, _1619935] : [class_Complete__Lattice_Ocomplete__lattice(_1619933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619933), _1619935)), -(_1619935 = c_Orderings_Obot__class_Obot(tc_fun(_1619933, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1619933, _1619935) = c_Complete__Lattice_OSup__class_OSup(_1619933, _1619935))], (1046 ^ _779999) ^ [_795894, _795896, _795898, _795900] : [-(c_Relation_Osym(_795898, _795894)), c_Relation_Osym(_795900, _795896), _795900 = _795898, _795896 = _795894], (37704 ^ _779999) ^ [_1497895, _1497897, _1497899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497895, _1497895), tc_HOL_Obool)), _1497897), _1497899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497895, tc_HOL_Obool)), c_Wellfounded_Oacc(_1497895, _1497899)), c_Wellfounded_Oacc(_1497895, _1497897))))], (51730 ^ _779999) ^ [_1827301, _1827303, _1827305, _1827307] : [c_Fun_Obij__betw(_1827301, _1827303, _1827305, c_Orderings_Otop__class_Otop(tc_fun(_1827301, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1827303, tc_HOL_Obool))), 51733 ^ _779999 : [(51740 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1827303), _1827307)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1827301), hAPP(c_Set_Ovimage(_1827301, _1827303, _1827305), _1827307))))], (51734 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1827301), hAPP(c_Set_Ovimage(_1827301, _1827303, _1827305), _1827307))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1827303), _1827307)))]]], (16837 ^ _779999) ^ [_1084484, _1084486, _1084488, _1084490, _1084492] : [class_Orderings_Oorder(_1084484), 16840 ^ _779999 : [(16853 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084484, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1084484, _1084486, _1084488)), c_SetInterval_Oord__class_OatLeastAtMost(_1084484, _1084490, _1084492)))), 16854 ^ _779999 : [(16857 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084490), _1084486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084488), _1084492))], (16855 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084486), _1084488)))]]], (16841 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084484, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1084484, _1084486, _1084488)), c_SetInterval_Oord__class_OatLeastAtMost(_1084484, _1084490, _1084492))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084486), _1084488)), 16848 ^ _779999 : [(16851 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084488), _1084492)))], (16849 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084484), _1084490), _1084486)))]]]]], (42401 ^ _779999) ^ [_1614188, _1614190, _1614192] : [class_Complete__Lattice_Ocomplete__lattice(_1614188), 42404 ^ _779999 : [(42405 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614188), c_Complete__Lattice_OSup__class_OSup(_1614188, _1614190)), _1614192)), 42408 ^ _779999 : [(42409 ^ _779999) ^ [_1614346] : [hBOOL(hAPP(hAPP(c_member(_1614188), _1614346), _1614190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614188), _1614346), _1614192)))]]], (42415 ^ _779999) ^ [] : [42417 ^ _779999 : [(42420 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614188), 42416 ^ [_1614188, _1614190, _1614192]), _1614192))], (42418 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614188), 42416 ^ [_1614188, _1614190, _1614192]), _1614190)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614188), c_Complete__Lattice_OSup__class_OSup(_1614188, _1614190)), _1614192)))]]], (38087 ^ _779999) ^ [_1507044, _1507046, _1507048] : [c_Wellfounded_Owf(_1507044, _1507046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507044, tc_HOL_Obool)), _1507048), hAPP(c_Relation_OImage(_1507044, _1507044, _1507046), _1507048))), -(_1507048 = c_Orderings_Obot__class_Obot(tc_fun(_1507044, tc_HOL_Obool)))], (28156 ^ _779999) ^ [_1309308, _1309310, _1309312, _1309314] : [class_Fields_Olinordered__field__inverse__zero(_1309308), 28159 ^ _779999 : [(28160 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309310), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309308), _1309312), _1309314))), 28163 ^ _779999 : [(28170 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), c_Groups_Ozero__class_Ozero(_1309308)), _1309314))), 28173 ^ _779999 : [(28180 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), _1309314), c_Groups_Ozero__class_Ozero(_1309308)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309310), c_Groups_Ozero__class_Ozero(_1309308))))], (28174 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), _1309314), c_Groups_Ozero__class_Ozero(_1309308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309308), _1309310), _1309314))))]]], (28164 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), c_Groups_Ozero__class_Ozero(_1309308)), _1309314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309308), _1309310), _1309314)), _1309312)))]]], (28186 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309310), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309308), _1309312), _1309314)))), 28189 ^ _779999 : [(28192 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309308), _1309310), _1309314)), _1309312))], (28190 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), c_Groups_Ozero__class_Ozero(_1309308)), _1309314)))]], 28193 ^ _779999 : [(28196 ^ _779999) ^ [] : [28197 ^ _779999 : [(28200 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309308), _1309310), _1309314)))], (28198 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), _1309314), c_Groups_Ozero__class_Ozero(_1309308))))]], 28201 ^ _779999 : [(28204 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309308), _1309310), c_Groups_Ozero__class_Ozero(_1309308)))], (28202 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), _1309314), c_Groups_Ozero__class_Ozero(_1309308)))]]], (28194 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309308), c_Groups_Ozero__class_Ozero(_1309308)), _1309314))]]]]], (48378 ^ _779999) ^ [_1753519, _1753521] : [hBOOL(hAPP(c_List_Odistinct(_1753519), _1753521)), -(hBOOL(hAPP(c_List_Odistinct(_1753519), hAPP(c_List_Orev(_1753519), _1753521))))], (37017 ^ _779999) ^ [_1479469] : [-(c_Wellfounded_Ofinite__psubset(_1479469) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1479469, tc_HOL_Obool), tc_fun(_1479469, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1479469, tc_HOL_Obool), tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1479469, tc_HOL_Obool), tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1479469, tc_HOL_Obool)), c_COMBS(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1479469, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1479469, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1479469, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1479469, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1479469)))))], (51882 ^ _779999) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (304 ^ _779999) ^ [_784719, _784721, _784723, _784725] : [-(c_FunDef_Oreduction__pair(_784723, _784719)), c_FunDef_Oreduction__pair(_784725, _784721), _784725 = _784723, _784721 = _784719], (1444 ^ _779999) ^ [_801157, _801159] : [-(class_Lattices_Obounded__lattice__bot(_801157)), _801159 = _801157, class_Lattices_Obounded__lattice__bot(_801159)], (44460 ^ _779999) ^ [_1667642, _1667644, _1667646, _1667648] : [_1667642 = _1667644, -(c_List_Oremove1(_1667646, _1667642, hAPP(hAPP(c_List_Olist_OCons(_1667646), _1667644), _1667648)) = _1667648)], (52234 ^ _779999) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (37124 ^ _779999) ^ [_1482560, _1482562] : [c_Code__Numeral_OSuc__code__numeral(_1482560) = c_Code__Numeral_OSuc__code__numeral(_1482562), -(_1482560 = _1482562)], (34303 ^ _779999) ^ [_1421470, _1421472] : [class_Rings_Oring__1(_1421470), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421470), hAPP(c_Groups_Ouminus__class_Ouminus(_1421470), _1421472)), 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(_1421470), _1421472), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (10395 ^ _779999) ^ [_958914, _958916, _958918, _958920, _958922, _958924] : [c_Fun_Oinj__on(_958914, _958916, _958918, _958920), hBOOL(hAPP(hAPP(c_member(_958916), _958922), hAPP(c_Set_Oimage(_958914, _958916, _958918), _958920))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958914, tc_HOL_Obool)), _958920), _958924)), -(hBOOL(hAPP(hAPP(c_member(_958914), hAPP(c_Fun_Othe__inv__into(_958914, _958916, _958920, _958918), _958922)), _958924)))], (42165 ^ _779999) ^ [_1608967, _1608969, _1608971, _1608973, _1608975] : [_1608967 = c_Orderings_Obot__class_Obot(tc_fun(_1608969, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608971, tc_HOL_Obool)), _1608973), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1608969, tc_fun(_1608971, tc_HOL_Obool)), _1608967), _1608975)) = _1608973)], (18098 ^ _779999) ^ [_1109427, _1109429] : [18106 ^ _779999 : [(18109 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1109429, 18105 ^ [_1109427, _1109429])))], (18107 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18105 ^ [_1109427, _1109429]), _1109427)))]], 18099 ^ _779999 : [(18100 ^ _779999) ^ [_1109495] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1109495), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109427))), hBOOL(hAPP(_1109429, _1109495))]]], (33263 ^ _779999) ^ [_1402802, _1402804] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402802)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402804)))), 33266 ^ _779999 : [(33269 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1402804))], (33267 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402802), _1402804)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402802), _1402804))], (33027 ^ _779999) ^ [_1399224] : [c_Int_OBit1(_1399224) = c_Int_OPls], (40375 ^ _779999) ^ [_1565643, _1565645, _1565647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565643, _1565643), tc_HOL_Obool)), c_Relation_OId(_1565643)), _1565645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565643, _1565643), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565643, _1565643, _1565643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1565643, _1565643), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565643, _1565647)), _1565645)), _1565647)), _1565645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565643, _1565643), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565643, _1565647)), _1565645)))], (3074 ^ _779999) ^ [_825776, _825778, _825780, _825782, _825784, _825786, _825788, _825790, _825792, _825794] : [-(c_Finite__Set_Ofold__graph(_825794, _825790, _825786, _825782, _825778) = c_Finite__Set_Ofold__graph(_825792, _825788, _825784, _825780, _825776)), _825794 = _825792, _825790 = _825788, _825786 = _825784, _825782 = _825780, _825778 = _825776], (35003 ^ _779999) ^ [_1434033, _1434035] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434033), _1434035) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35004 ^ _779999 : [(35011 ^ _779999) ^ [] : [_1434033 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1434035 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (35005 ^ _779999) ^ [] : [_1434033 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1434035 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (36000 ^ _779999) ^ [_1457958, _1457960] : [-(c_Divides_Odivmod__nat(_1457960, _1457958) = 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), _1457960), _1457958), _1457958))), -(_1457958 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457960), _1457958)))], (6875 ^ _779999) ^ [_892741, _892743, _892745] : [-(hAPP(hAPP(c_Set_Oinsert(_892741), _892743), hAPP(hAPP(c_Set_Oinsert(_892741), _892743), _892745)) = hAPP(hAPP(c_Set_Oinsert(_892741), _892743), _892745))], (37911 ^ _779999) ^ [_1503595, _1503597, _1503599, _1503601] : [c_Wellfounded_Owf(_1503595, _1503597), c_Wellfounded_Owf(_1503599, _1503601), -(c_Wellfounded_Owf(tc_prod(_1503595, _1503599), c_Wellfounded_Olex__prod(_1503595, _1503599, _1503597, _1503601)))], (18905 ^ _779999) ^ [_1124964, _1124966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124964), _1124966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124966), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (19129 ^ _779999) ^ [_1128703, _1128705, _1128707] : [class_Orderings_Oorder(_1128703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128703), _1128705), _1128707)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1128703, _1128707, _1128705) = c_Orderings_Obot__class_Obot(tc_fun(_1128703, tc_HOL_Obool)))], (33075 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19269 ^ _779999) ^ [_1131312, _1131314, _1131316] : [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), _1131312), _1131314)), _1131316)), 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)), _1131316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131314), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34343 ^ _779999) ^ [_1422206] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1422206), _1422206)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1422206)], (44895 ^ _779999) ^ [_1676870, _1676872, _1676874, _1676876, _1676878] : [hAPP(hAPP(c_List_Olist_OCons(_1676870), _1676872), _1676874) = hAPP(hAPP(c_List_Oappend(_1676870), _1676876), _1676878), 44900 ^ _779999 : [(44903 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1676870), _1676872), _1676874) = _1676878)], (44901 ^ _779999) ^ [] : [-(_1676876 = c_List_Olist_ONil(_1676870))]], 44905 ^ _779999 : [(44908 ^ _779999) ^ [] : [-(_1676874 = hAPP(hAPP(c_List_Oappend(_1676870), 44904 ^ [_1676870, _1676872, _1676874, _1676876, _1676878]), _1676878))], (44906 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1676870), _1676872), 44904 ^ [_1676870, _1676872, _1676874, _1676876, _1676878]) = _1676876)]]], (27394 ^ _779999) ^ [_1295366, _1295368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1295366)), -(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), _1295366), _1295368))))], (7450 ^ _779999) ^ [_904087, _904089, _904091, _904093] : [class_Orderings_Oorder(_904087), class_Orderings_Oorder(_904089), c_Orderings_Oorder__class_Omono(_904089, _904087, _904091), -(c_Orderings_Oord__class_OLeast(_904087, hAPP(hAPP(c_COMBC(_904087, tc_fun(_904087, tc_HOL_Obool), tc_HOL_Obool), c_member(_904087)), hAPP(c_Set_Oimage(_904089, _904087, _904091), _904093))) = hAPP(_904091, c_Orderings_Oord__class_OLeast(_904089, hAPP(hAPP(c_COMBC(_904089, tc_fun(_904089, tc_HOL_Obool), tc_HOL_Obool), c_member(_904089)), _904093)))), 7463 ^ _779999 : [(7464 ^ _779999) ^ [_904371] : [hBOOL(hAPP(hAPP(c_member(_904089), _904371), _904093)), 7468 ^ _779999 : [(7471 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904089), _904371), 7467 ^ [_904087, _904089, _904091, _904093, _904371]))], (7469 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_904089), 7467 ^ [_904087, _904089, _904091, _904093, _904371]), _904093)))]]]]], (18249 ^ _779999) ^ [_1112196] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1112196), hAPP(c_Nat_OSuc, _1112196)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1112196), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (50915 ^ _779999) ^ [_1810201, _1810203, _1810205, _1810207] : [c_Relation_Oantisym(_1810201, _1810203), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810201, _1810201)), hAPP(hAPP(c_Product__Type_OPair(_1810201, _1810201), _1810205), _1810207)), _1810203)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810201, _1810201)), hAPP(hAPP(c_Product__Type_OPair(_1810201, _1810201), _1810207), _1810205)), _1810203)), -(_1810205 = _1810207)], (20068 ^ _779999) ^ [_1145787, _1145789] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1145787)), hAPP(c_Int_Onat, _1145789)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145787), _1145789))], (7613 ^ _779999) ^ [_907861, _907863, _907865, _907867] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_907861, _907863)), _907865), _907867))), 7614 ^ _779999 : [(7615 ^ _779999) ^ [_907929] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907861), _907865), _907929)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907863), _907929), _907867))]]], (27382 ^ _779999) ^ [_1295116, _1295118] : [class_Rings_Ocomm__semiring__1(_1295116), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1295116), _1295118), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1295116))], (1116 ^ _779999) ^ [_796859, _796861, _796863, _796865, _796867, _796869, _796871, _796873] : [-(c_Fun_Oinj__on(_796871, _796867, _796863, _796859)), c_Fun_Oinj__on(_796873, _796869, _796865, _796861), _796873 = _796871, _796869 = _796867, _796865 = _796863, _796861 = _796859], (5738 ^ _779999) ^ [_867798, _867800, _867802, _867804, _867806, _867808] : [-(c_COMBB(_867808, _867804, _867800) = c_COMBB(_867806, _867802, _867798)), _867808 = _867806, _867804 = _867802, _867800 = _867798], (37447 ^ _779999) ^ [_1489973, _1489975, _1489977] : [-(hAPP(c_Relation_OField(_1489973), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489973, _1489973), tc_HOL_Obool)), _1489975), _1489977)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489973, tc_HOL_Obool)), hAPP(c_Relation_OField(_1489973), _1489975)), hAPP(c_Relation_OField(_1489973), _1489977)))], (36883 ^ _779999) ^ [_1476375, _1476377, _1476379, _1476381, _1476383] : [c_Equiv__Relations_Oequiv(_1476375, _1476377, _1476379), hBOOL(hAPP(hAPP(c_member(_1476375), _1476381), _1476377)), hBOOL(hAPP(hAPP(c_member(_1476375), _1476383), _1476377)), 36894 ^ _779999 : [(36901 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476375, _1476375)), hAPP(hAPP(c_Product__Type_OPair(_1476375, _1476375), _1476381), _1476383)), _1476379)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1476375), hAPP(hAPP(c_Set_Oinsert(_1476375), _1476381), c_Orderings_Obot__class_Obot(tc_fun(_1476375, tc_HOL_Obool)))), _1476379) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1476375), hAPP(hAPP(c_Set_Oinsert(_1476375), _1476383), c_Orderings_Obot__class_Obot(tc_fun(_1476375, tc_HOL_Obool)))), _1476379))], (36895 ^ _779999) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1476375), hAPP(hAPP(c_Set_Oinsert(_1476375), _1476381), c_Orderings_Obot__class_Obot(tc_fun(_1476375, tc_HOL_Obool)))), _1476379) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1476375), hAPP(hAPP(c_Set_Oinsert(_1476375), _1476383), c_Orderings_Obot__class_Obot(tc_fun(_1476375, tc_HOL_Obool)))), _1476379), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476375, _1476375)), hAPP(hAPP(c_Product__Type_OPair(_1476375, _1476375), _1476381), _1476383)), _1476379)))]]], (10785 ^ _779999) ^ [_966160, _966162, _966164, _966166, _966168, _966170, _966172, _966174] : [class_Groups_Ocomm__monoid__add(_966160), c_Fun_Oinj__on(_966162, _966164, _966166, _966168), _966170 = hAPP(c_Set_Oimage(_966162, _966164, _966166), _966168), 10799 ^ _779999 : [(10802 ^ _779999) ^ [] : [hAPP(_966172, 10798 ^ [_966160, _966162, _966164, _966166, _966168, _966170, _966172, _966174]) = hAPP(_966174, hAPP(_966166, 10798 ^ [_966160, _966162, _966164, _966166, _966168, _966170, _966172, _966174]))], (10800 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_966162), 10798 ^ [_966160, _966162, _966164, _966166, _966168, _966170, _966172, _966174]), _966168)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966164, _966160), _966174), _966170) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966162, _966160), _966172), _966168))], (25760 ^ _779999) ^ [_1262792, _1262794, _1262796] : [hBOOL(hAPP(hAPP(c_member(_1262792), _1262794), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262792, tc_HOL_Obool)), _1262796))), hBOOL(hAPP(hAPP(c_member(_1262792), _1262794), _1262796))], (43307 ^ _779999) ^ [_1636886, _1636888] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636886), tc_List_Olist(_1636886)), tc_HOL_Obool)), c_List_Olistrel1(_1636886, c_Transitive__Closure_Ortrancl(_1636886, _1636888))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636886), c_List_Olistrel1(_1636886, _1636888)))))], (31609 ^ _779999) ^ [_1372692, _1372694, _1372696, _1372698, _1372700, _1372702] : [-(hAPP(c_Relation_OImage(_1372692, _1372694, _1372696), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372698, tc_fun(_1372692, tc_HOL_Obool)), _1372700), _1372702)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372698, tc_fun(_1372694, tc_HOL_Obool)), _1372700), hAPP(hAPP(c_COMBB(tc_fun(_1372692, tc_HOL_Obool), tc_fun(_1372694, tc_HOL_Obool), _1372698), c_Relation_OImage(_1372692, _1372694, _1372696)), _1372702)))], (28306 ^ _779999) ^ [_1312153, _1312155, _1312157] : [class_Fields_Ofield__inverse__zero(_1312153), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1312153), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312153), _1312155), _1312157)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312153), _1312155), hAPP(c_Groups_Ouminus__class_Ouminus(_1312153), _1312157)))], (14794 ^ _779999) ^ [_1045612] : [-(hAPP(c_Nat_OSuc, _1045612) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045612), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (20615 ^ _779999) ^ [_1154407] : [c_Nat__Transfer_Ois__nat(_1154407), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154407)))], (37373 ^ _779999) ^ [_1488565, _1488567, _1488569, _1488571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1488565), _1488567)), 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)), _1488569), _1488565)), 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)), _1488571), _1488567)), 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)), _1488569), _1488571)), _1488567)), c_FunDef_Omax__strict)))], (28280 ^ _779999) ^ [_1311595, _1311597, _1311599, _1311601] : [class_Fields_Olinordered__field(_1311595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311595), c_Groups_Ozero__class_Ozero(_1311595)), _1311597)), 28287 ^ _779999 : [(28294 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311595), _1311599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311595), _1311601), _1311597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311595), _1311599), _1311597)), _1311601)))], (28288 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311595), _1311599), _1311597)), _1311601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311595), _1311599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311595), _1311601), _1311597))))]]], (34679 ^ _779999) ^ [_1428452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1428452)), -(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), _1428452), 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)))))))], (15519 ^ _779999) ^ [_1059607, _1059609, _1059611, _1059613, _1059615] : [class_Rings_Ocomm__semiring__1(_1059607), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), _1059609), _1059611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), _1059613), _1059615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), _1059613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059607), _1059609), _1059611)), _1059615)))], (24074 ^ _779999) ^ [_1229710, _1229712, _1229714] : [class_Orderings_Olinorder(_1229710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229710), _1229712)), -(hBOOL(hAPP(hAPP(c_member(_1229710), _1229714), _1229712))), -(_1229712 = c_Orderings_Obot__class_Obot(tc_fun(_1229710, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1229710, c_Orderings_Oord__class_Omin(_1229710), hAPP(hAPP(c_Set_Oinsert(_1229710), _1229714), _1229712)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229710), _1229714), c_Big__Operators_Olattice_OInf__fin(_1229710, c_Orderings_Oord__class_Omin(_1229710), _1229712)))], (47414 ^ _779999) ^ [_1733463, _1733465, _1733467, _1733469, _1733471, _1733473] : [class_Orderings_Olinorder(_1733463), -(hBOOL(hAPP(_1733465, _1733467))), -(hAPP(c_List_Ofilter(_1733469, _1733465), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733469, _1733463, _1733471), _1733467), _1733473)) = hAPP(c_List_Ofilter(_1733469, _1733465), _1733473))], (39507 ^ _779999) ^ [_1544174, _1544176, _1544178, _1544180, _1544182, _1544184, _1544186, _1544188, _1544190, _1544192, _1544194] : [-(hAPP(c_Product__Type_Omap__pair(_1544174, _1544176, _1544178, _1544180, _1544182, _1544184), hAPP(c_Product__Type_Omap__pair(_1544186, _1544174, _1544188, _1544178, _1544190, _1544192), _1544194)) = hAPP(c_Product__Type_Omap__pair(_1544186, _1544176, _1544188, _1544180, hAPP(c_Fun_Ocomp(_1544174, _1544176, _1544186, _1544182), _1544190), hAPP(c_Fun_Ocomp(_1544178, _1544180, _1544188, _1544184), _1544192)), _1544194))], (38728 ^ _779999) ^ [_1525923, _1525925] : [-(hAPP(c_Fun_Oid(_1525923), _1525925) = _1525925)], (52044 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (14051 ^ _779999) ^ [_1030576, _1030578, _1030580, _1030582, _1030584] : [class_Groups_Ocomm__monoid__add(_1030576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030578), _1030580)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030578, _1030576), hAPP(hAPP(c_COMBS(_1030578, _1030576, _1030576), hAPP(hAPP(c_COMBB(_1030576, tc_fun(_1030576, _1030576), _1030578), c_Groups_Oplus__class_Oplus(_1030576)), _1030582)), _1030584)), _1030580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030576), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030578, _1030576), _1030582), _1030580)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030578, _1030576), _1030584), _1030580)))], (9536 ^ _779999) ^ [_942016, _942018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942016, tc_HOL_Obool)), _942018), c_Orderings_Obot__class_Obot(tc_fun(_942016, tc_HOL_Obool))))], (29684 ^ _779999) ^ [_1336638, _1336640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1336640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336638), _1336640)), _1336638)))], (39663 ^ _779999) ^ [_1547774, _1547776, _1547778, _1547780, _1547782, _1547784] : [c_Finite__Set_Ofolding(_1547774, _1547776, _1547778, _1547780), -(hAPP(c_Fun_Ocomp(_1547776, _1547776, _1547776, hAPP(_1547778, _1547782)), hAPP(_1547778, _1547784)) = hAPP(c_Fun_Ocomp(_1547776, _1547776, _1547776, hAPP(_1547778, _1547784)), hAPP(_1547778, _1547782)))], (45827 ^ _779999) ^ [_1697905, _1697907, _1697909] : [class_Orderings_Olinorder(_1697905), -(c_Big__Operators_Olattice_OSup__fin(_1697905, c_Orderings_Oord__class_Omax(_1697905), hAPP(c_List_Oset(_1697905), hAPP(hAPP(c_List_Olist_OCons(_1697905), _1697907), _1697909))) = hAPP(c_List_Ofoldl(_1697905, _1697905, c_Orderings_Oord__class_Omax(_1697905), _1697907), _1697909))], (17545 ^ _779999) ^ [_1098477, _1098479, _1098481, _1098483, _1098485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098477), _1098479)), 17548 ^ _779999 : [(17555 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1098483), 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), _1098479), _1098477)), _1098481)), _1098485))), -(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), _1098477), _1098481)), _1098483)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1098479), _1098481)), _1098485))))], (17549 ^ _779999) ^ [] : [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), _1098477), _1098481)), _1098483)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1098479), _1098481)), _1098485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1098483), 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), _1098479), _1098477)), _1098481)), _1098485))))]]], (4500 ^ _779999) ^ [_848413, _848415] : [_848415 = _848413, -(c_List_Orev(_848415) = c_List_Orev(_848413))], (7320 ^ _779999) ^ [_901394, _901396, _901398, _901400] : [hAPP(c_Set_Oimage(_901394, _901396, _901398), _901400) = c_Orderings_Obot__class_Obot(tc_fun(_901396, tc_HOL_Obool)), -(_901400 = c_Orderings_Obot__class_Obot(tc_fun(_901394, tc_HOL_Obool)))], (26156 ^ _779999) ^ [_1270453, _1270455] : [class_Groups_Oordered__ab__group__add(_1270453), 26159 ^ _779999 : [(26166 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270453), _1270455), c_Groups_Ozero__class_Ozero(_1270453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270453), c_Groups_Ozero__class_Ozero(_1270453)), hAPP(c_Groups_Ouminus__class_Ouminus(_1270453), _1270455))))], (26160 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270453), c_Groups_Ozero__class_Ozero(_1270453)), hAPP(c_Groups_Ouminus__class_Ouminus(_1270453), _1270455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270453), _1270455), c_Groups_Ozero__class_Ozero(_1270453))))]]], (33045 ^ _779999) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46894 ^ _779999) ^ [_1721245, _1721247, _1721249, _1721251] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1721245)), _1721247), c_List_Olists(_1721245, _1721249))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1721245)), _1721247), c_List_Olists(_1721245, _1721251))), -(hBOOL(hAPP(c_List_Olistsp(_1721245, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1721245, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1721245, tc_fun(_1721245, tc_HOL_Obool), tc_HOL_Obool), c_member(_1721245)), _1721249)), hAPP(hAPP(c_COMBC(_1721245, tc_fun(_1721245, tc_HOL_Obool), tc_HOL_Obool), c_member(_1721245)), _1721251))), _1721247)))], (8200 ^ _779999) ^ [_918915, _918917] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_918915, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_918915, tc_HOL_Obool))), hAPP(c_Set_OPow(_918915), _918917))))], (41807 ^ _779999) ^ [_1598094, _1598096, _1598098, _1598100, _1598102, _1598104, _1598106, _1598108] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598094, tc_fun(_1598096, tc_fun(_1598098, tc_HOL_Obool))), _1598100), _1598102), _1598104), _1598106)), -(hBOOL(hAPP(hAPP(hAPP(_1598102, _1598108), _1598104), _1598106))), hBOOL(hAPP(hAPP(c_member(_1598094), _1598108), _1598100))], (12373 ^ _779999) ^ [_999054, _999056] : [class_Lattices_Olattice(_999054), -(c_Big__Operators_Olattice__class_OInf__fin(_999054, hAPP(hAPP(c_Set_Oinsert(_999054), _999056), c_Orderings_Obot__class_Obot(tc_fun(_999054, tc_HOL_Obool)))) = _999056)], (2136 ^ _779999) ^ [_811175, _811177, _811179, _811181, _811183, _811185, _811187, _811189, _811191, _811193] : [-(c_SetInterval_Oord_OatLeastLessThan(_811193, _811189, _811185, _811181, _811177) = c_SetInterval_Oord_OatLeastLessThan(_811191, _811187, _811183, _811179, _811175)), _811193 = _811191, _811189 = _811187, _811185 = _811183, _811181 = _811179, _811177 = _811175], (10771 ^ _779999) ^ [_965821, _965823, _965825, _965827, _965829] : [-(c_Fun_Oinj__on(_965821, _965823, _965825, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965821, tc_HOL_Obool)), _965827), _965829))), c_Fun_Oinj__on(_965821, _965823, _965825, _965827), c_Fun_Oinj__on(_965821, _965823, _965825, _965829), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965823, tc_HOL_Obool)), hAPP(c_Set_Oimage(_965821, _965823, _965825), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965821, tc_HOL_Obool)), _965827), _965829))), hAPP(c_Set_Oimage(_965821, _965823, _965825), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965821, tc_HOL_Obool)), _965829), _965827))) = c_Orderings_Obot__class_Obot(tc_fun(_965823, tc_HOL_Obool))], (178 ^ _779999) ^ [_782894, _782896] : [-(class_Rings_Odivision__ring(_782894)), _782896 = _782894, class_Rings_Odivision__ring(_782896)], (28016 ^ _779999) ^ [_1306630, _1306632, _1306634, _1306636] : [class_Rings_Olinordered__semidom(_1306630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306630), c_Groups_Oone__class_Oone(_1306630)), _1306632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306630), hAPP(hAPP(c_Power_Opower__class_Opower(_1306630), _1306632), _1306634)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306630), _1306632), _1306636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306634), _1306636)))], (13209 ^ _779999) ^ [_1015143, _1015145] : [class_Groups_Olinordered__ab__group__add(_1015143), 13212 ^ _779999 : [(13219 ^ _779999) ^ [] : [_1015145 = c_Groups_Ozero__class_Ozero(_1015143), -(c_Groups_Ozero__class_Ozero(_1015143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015143), _1015145), _1015145))], (13213 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_1015143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015143), _1015145), _1015145), -(_1015145 = c_Groups_Ozero__class_Ozero(_1015143))]]], (48462 ^ _779999) ^ [_1755323, _1755325, _1755327, _1755329] : [hAPP(c_List_Orev(_1755323), _1755325) = hAPP(hAPP(c_List_Olist_OCons(_1755323), _1755327), _1755329), -(_1755325 = hAPP(hAPP(c_List_Oappend(_1755323), hAPP(c_List_Orev(_1755323), _1755329)), hAPP(hAPP(c_List_Olist_OCons(_1755323), _1755327), c_List_Olist_ONil(_1755323))))], (41829 ^ _779999) ^ [_1598631, _1598633, _1598635, _1598637] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598631, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598633, tc_fun(_1598631, tc_HOL_Obool)), _1598635), _1598637)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598633, tc_fun(_1598631, tc_HOL_Obool)), _1598635), hAPP(hAPP(c_COMBB(tc_fun(_1598631, tc_HOL_Obool), tc_fun(_1598631, tc_HOL_Obool), _1598633), c_Groups_Ouminus__class_Ouminus(tc_fun(_1598631, tc_HOL_Obool))), _1598637)))], (22413 ^ _779999) ^ [_1194691, _1194693, _1194695, _1194697] : [c_Fun_Oinj__on(_1194691, _1194693, _1194695, c_Orderings_Otop__class_Otop(tc_fun(_1194691, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1194691, _1194693, c_Orderings_Otop__class_Otop(tc_fun(_1194691, tc_HOL_Obool)), _1194695), hAPP(_1194695, _1194697)) = _1194697)], (7986 ^ _779999) ^ [_914780, _914782, _914784, _914786] : [c_Com_Ocom_OWhile(_914780, _914782) = c_Com_Ocom_OWhile(_914784, _914786), 7989 ^ _779999 : [(7992 ^ _779999) ^ [] : [-(_914782 = _914786)], (7990 ^ _779999) ^ [] : [-(_914780 = _914784)]]], (8870 ^ _779999) ^ [_932245, _932247, _932249] : [class_Orderings_Olinorder(_932245), 8873 ^ _779999 : [(8874 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932245), _932247), _932249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932245), _932249), _932247))), -(_932247 = _932249)], (8884 ^ _779999) ^ [] : [8885 ^ _779999 : [(8888 ^ _779999) ^ [] : [_932247 = _932249], (8886 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932245), _932249), _932247))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932245), _932247), _932249))]]], (41426 ^ _779999) ^ [_1590709, _1590711, _1590713] : [class_Lattices_Oab__semigroup__idem__mult(_1590709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590709), _1590711)), -(hAPP(c_Finite__Set_Ofold1(_1590709, c_Groups_Otimes__class_Otimes(_1590709)), hAPP(hAPP(c_Set_Oinsert(_1590709), _1590713), _1590711)) = hAPP(hAPP(c_Finite__Set_Ofold(_1590709, _1590709, c_Groups_Otimes__class_Otimes(_1590709)), _1590713), _1590711))], (36491 ^ _779999) ^ [_1467288, _1467290, _1467292, _1467294, _1467296] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1467288, _1467290, _1467292), _1467294), _1467296) = hAPP(hAPP(_1467294, hAPP(c_Product__Type_Ofst(_1467288, _1467290), _1467296)), hAPP(c_Product__Type_Osnd(_1467288, _1467290), _1467296)))], (40327 ^ _779999) ^ [_1564470, _1564472, _1564474, _1564476, _1564478] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564470, _1564470)), hAPP(hAPP(c_Product__Type_OPair(_1564470, _1564470), _1564472), _1564474)), c_Transitive__Closure_Ortrancl(_1564470, _1564476))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564470, _1564470)), hAPP(hAPP(c_Product__Type_OPair(_1564470, _1564470), _1564474), _1564478)), c_Transitive__Closure_Ortrancl(_1564470, _1564476))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564470, _1564470)), hAPP(hAPP(c_Product__Type_OPair(_1564470, _1564470), _1564472), _1564478)), c_Transitive__Closure_Ortrancl(_1564470, _1564476))))], (36030 ^ _779999) ^ [_1458314, _1458316] : [-(_1458314 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36033 ^ _779999 : [(36040 ^ _779999) ^ [] : [-(_1458316 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1458314, _1458316) = 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, _1458316))), 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, _1458314)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1458316))), c_Divides_Opdivmod(_1458314, _1458316)), 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), _1458316))))), c_Divides_Opdivmod(_1458314, _1458316)))))], (36034 ^ _779999) ^ [] : [_1458316 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1458314, _1458316) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1458314))]]], (10193 ^ _779999) ^ [_955639, _955641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955639), hAPP(c_Nat_OSuc, _955641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955639), _955641))), -(_955639 = _955641)], (40211 ^ _779999) ^ [_1560884, _1560886, _1560888, _1560890, _1560892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560884, _1560884)), hAPP(hAPP(c_Product__Type_OPair(_1560884, _1560884), _1560886), _1560888)), c_Transitive__Closure_Otrancl(_1560884, _1560890))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560884, _1560884)), hAPP(hAPP(c_Product__Type_OPair(_1560884, _1560884), _1560888), _1560892)), _1560890)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560884, _1560884)), hAPP(hAPP(c_Product__Type_OPair(_1560884, _1560884), _1560886), _1560892)), c_Transitive__Closure_Otrancl(_1560884, _1560890))))], (42043 ^ _779999) ^ [_1605559, _1605561, _1605563, _1605565, _1605567] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605559, tc_fun(_1605561, tc_HOL_Obool)), _1605563), hAPP(hAPP(c_COMBC(_1605559, tc_fun(_1605561, tc_HOL_Obool), tc_fun(_1605561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605561, tc_HOL_Obool), tc_fun(tc_fun(_1605561, tc_HOL_Obool), tc_fun(_1605561, tc_HOL_Obool)), _1605559), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605561, tc_HOL_Obool))), _1605565)), _1605567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605561, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605559, tc_fun(_1605561, tc_HOL_Obool)), _1605563), _1605565)), _1605567))], (44017 ^ _779999) ^ [_1657945, _1657947, _1657949, _1657951] : [-(hAPP(c_List_Oset(tc_prod(_1657945, _1657947)), c_Enum_Oproduct(_1657945, _1657947, _1657949, _1657951)) = hAPP(hAPP(c_Product__Type_OSigma(_1657945, _1657947), hAPP(c_List_Oset(_1657945), _1657949)), hAPP(c_COMBK(tc_fun(_1657947, tc_HOL_Obool), _1657945), hAPP(c_List_Oset(_1657947), _1657951))))], (35685 ^ _779999) ^ [_1452274, _1452276, _1452278, _1452280] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1452274, _1452276, _1452278), hAPP(hAPP(c_COMBB(tc_fun(_1452276, tc_prod(_1452274, _1452276)), tc_fun(_1452276, _1452278), _1452274), hAPP(c_COMBB(tc_prod(_1452274, _1452276), _1452278, _1452276), _1452280)), c_Product__Type_OPair(_1452274, _1452276))) = _1452280)], (51294 ^ _779999) ^ [_1817159, _1817161] : [c_Equiv__Relations_Opart__equivp(_1817159, _1817161), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1817159, tc_HOL_Obool)), 51297 ^ [_1817159, _1817161]), hAPP(hAPP(c_COMBB(tc_fun(_1817159, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1817159, tc_HOL_Obool)), c_HOL_OEx(_1817159)), hAPP(hAPP(c_COMBB(tc_fun(_1817159, tc_HOL_Obool), tc_fun(_1817159, tc_HOL_Obool), tc_fun(_1817159, tc_HOL_Obool)), hAPP(c_COMBS(_1817159, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1817159), c_fconj), hAPP(hAPP(c_COMBS(_1817159, _1817159, tc_HOL_Obool), _1817161), c_COMBI(_1817159))))), hAPP(hAPP(c_COMBC(tc_fun(_1817159, tc_HOL_Obool), tc_fun(_1817159, tc_fun(_1817159, tc_HOL_Obool)), tc_fun(_1817159, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1817159, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1817159, tc_fun(_1817159, tc_HOL_Obool)), tc_fun(_1817159, tc_HOL_Obool)), tc_fun(_1817159, tc_HOL_Obool)), c_COMBB(tc_fun(_1817159, tc_HOL_Obool), tc_HOL_Obool, _1817159)), c_fequal)), _1817161))))))], (24546 ^ _779999) ^ [_1239558, _1239560, _1239562] : [class_Orderings_Olinorder(_1239558), 24549 ^ _779999 : [(24556 ^ _779999) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239558), _1239560), _1239562) = _1239562, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239558), _1239560), _1239562)))], (24550 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239558), _1239560), _1239562)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239558), _1239560), _1239562) = _1239562)]]], (2386 ^ _779999) ^ [_815158, _815160, _815162, _815164] : [-(c_Nitpick_Onat__lcm(_815164, _815160) = c_Nitpick_Onat__lcm(_815162, _815158)), _815164 = _815162, _815160 = _815158], (3928 ^ _779999) ^ [_839105, _839107] : [_839107 = _839105, -(c_List_Oreturn__list(_839107) = c_List_Oreturn__list(_839105))], (3238 ^ _779999) ^ [_828304, _828306] : [_828306 = _828304, -(c_HOL_Obool_Obool__size(_828306) = c_HOL_Obool_Obool__size(_828304))], (13536 ^ _779999) ^ [_1021261, _1021263] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021261), _1021263)), _1021261) = _1021263)], (7300 ^ _779999) ^ [_900961, _900963] : [_900963 = c_Orderings_Obot__class_Obot(tc_fun(_900961, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900961, tc_HOL_Obool)), _900963), c_Orderings_Obot__class_Obot(tc_fun(_900961, tc_HOL_Obool)))))], (6595 ^ _779999) ^ [_886938, _886940] : [-(hAPP(c_Set_Oimage(_886938, _886938, c_COMBI(_886938)), _886940) = _886940)], (8212 ^ _779999) ^ [_919246, _919248, _919250] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_919246, tc_HOL_Obool)), _919248), hAPP(c_Set_OPow(_919246), _919250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919246, tc_HOL_Obool)), _919248), _919250)))], (40022 ^ _779999) ^ [_1556524, _1556526, _1556528] : [c_Wellfounded_Owf(_1556524, _1556526), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556524, _1556524)), hAPP(hAPP(c_Product__Type_OPair(_1556524, _1556524), hAPP(_1556528, hAPP(c_Nat_OSuc, 40025 ^ [_1556524, _1556526, _1556528]))), hAPP(_1556528, 40025 ^ [_1556524, _1556526, _1556528]))), _1556526))], (49824 ^ _779999) ^ [_1785401, _1785403, _1785405, _1785407, _1785409] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1785401, _1785403, _1785405), _1785407), _1785409)), -(hBOOL(hAPP(hAPP(_1785405, _1785409), _1785407)))], (49540 ^ _779999) ^ [_1779370, _1779372, _1779374, _1779376] : [c_List_Olist__all(_1779370, _1779372, hAPP(hAPP(c_List_Oappend(_1779370), _1779374), _1779376)), 49543 ^ _779999 : [(49546 ^ _779999) ^ [] : [-(c_List_Olist__all(_1779370, _1779372, _1779376))], (49544 ^ _779999) ^ [] : [-(c_List_Olist__all(_1779370, _1779372, _1779374))]]], (49840 ^ _779999) ^ [_1786057, _1786059, _1786061, _1786063, _1786065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786059, _1786057)), hAPP(hAPP(c_Product__Type_OPair(_1786059, _1786057), _1786063), _1786065)), hAPP(c_Relation_Oconverse(_1786057, _1786059), _1786061))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1786057, _1786059, hAPP(hAPP(c_COMBC(_1786057, tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_fun(_1786059, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1786059, tc_fun(tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_fun(_1786059, tc_HOL_Obool)), _1786057), c_COMBC(_1786059, tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1786059, tc_prod(_1786057, _1786059)), tc_fun(_1786059, tc_fun(tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_HOL_Obool)), _1786057), hAPP(c_COMBB(tc_prod(_1786057, _1786059), tc_fun(tc_fun(tc_prod(_1786057, _1786059), tc_HOL_Obool), tc_HOL_Obool), _1786059), c_member(tc_prod(_1786057, _1786059)))), c_Product__Type_OPair(_1786057, _1786059)))), _1786061)), _1786063), _1786065)))], (47064 ^ _779999) ^ [_1725153, _1725155, _1725157, _1725159] : [_1725159 = c_List_Olist_ONil(_1725153), -(c_List_Olist__all2(_1725153, _1725155, _1725157, _1725159, c_List_Olist_ONil(_1725155)))], (15827 ^ _779999) ^ [_1065266] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32781 ^ _779999) ^ [_1394927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1394927)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394927), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35808 ^ _779999) ^ [_1454750] : [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), _1454750))), 35811 ^ _779999 : [(35818 ^ _779999) ^ [] : [-(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), _1454750)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454750)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454750)), 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), _1454750)))))], (35812 ^ _779999) ^ [] : [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), _1454750))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454750)) = 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)))]]], (52350 ^ _779999) ^ [] : [hBOOL(c_fFalse)], (5791 ^ _779999) ^ [_871530, _871532, _871534, _871536, _871538, _871540, _871542] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871530), _871532), _871534), _871536) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871530), _871538), _871540), _871542)), _871532 = _871538, _871534 = _871540, _871536 = _871542], (11584 ^ _779999) ^ [_982957, _982959, _982961, _982963] : [class_Groups_Ocomm__monoid__add(_982957), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_982959), _982961))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_982959, _982957), _982963), _982961) = c_Groups_Ozero__class_Ozero(_982957))], (52130 ^ _779999) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (38415 ^ _779999) ^ [_1515679, _1515681, _1515683, _1515685, _1515687, _1515689] : [-(hAPP(c_Set_Oimage(_1515679, tc_prod(_1515681, _1515683), hAPP(hAPP(c_COMBS(_1515679, _1515683, tc_prod(_1515681, _1515683)), hAPP(hAPP(c_COMBB(_1515681, tc_fun(_1515683, tc_prod(_1515681, _1515683)), _1515679), c_Product__Type_OPair(_1515681, _1515683)), _1515685)), _1515687)), _1515689) = hAPP(hAPP(c_Product__Type_OSigma(_1515681, _1515683), hAPP(c_Set_Oimage(_1515679, _1515681, _1515685), _1515689)), hAPP(hAPP(c_COMBB(tc_fun(_1515679, tc_HOL_Obool), tc_fun(_1515683, tc_HOL_Obool), _1515681), c_Set_Oimage(_1515679, _1515683, _1515687)), hAPP(hAPP(c_COMBC(_1515681, tc_fun(_1515679, tc_HOL_Obool), tc_fun(_1515679, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515679, tc_HOL_Obool), tc_fun(tc_fun(_1515679, tc_HOL_Obool), tc_fun(_1515679, tc_HOL_Obool)), _1515681), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515679, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515681, tc_HOL_Obool), tc_fun(_1515679, tc_HOL_Obool), _1515681), c_Set_Ovimage(_1515679, _1515681, _1515685)), hAPP(hAPP(c_COMBC(_1515681, tc_fun(_1515681, tc_HOL_Obool), tc_fun(_1515681, tc_HOL_Obool)), c_Set_Oinsert(_1515681)), c_Orderings_Obot__class_Obot(tc_fun(_1515681, tc_HOL_Obool)))))), _1515689))))], (2994 ^ _779999) ^ [_824598, _824600, _824602, _824604, _824606, _824608] : [-(c_Random_Ominus__shift(_824608, _824604, _824600) = c_Random_Ominus__shift(_824606, _824602, _824598)), _824608 = _824606, _824604 = _824602, _824600 = _824598], (30617 ^ _779999) ^ [_1354049, _1354051, _1354053] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1354049), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354051, _1354053)), _1354053) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1354049), _1354051), _1354053))], (37984 ^ _779999) ^ [_1504905] : [-(c_Wellfounded_Owf(tc_fun(_1504905, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1504905)))], (21385 ^ _779999) ^ [_1169398] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1169398)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1169398))], (38036 ^ _779999) ^ [_1505856, _1505858] : [c_Wellfounded_Owf(_1505856, _1505858), 38039 ^ _779999 : [(38040 ^ _779999) ^ [_1505925] : [-(hBOOL(hAPP(hAPP(c_member(_1505856), _1505925), c_Wellfounded_Oacc(_1505856, _1505858))))]]], (12843 ^ _779999) ^ [_1007726, _1007728, _1007730, _1007732, _1007734] : [c_Finite__Set_Ofolding__one__idem(_1007726, _1007728, _1007730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007726), _1007732)), -(_1007734 = c_Orderings_Obot__class_Obot(tc_fun(_1007726, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007726, tc_HOL_Obool)), _1007734), _1007732)), -(hAPP(hAPP(_1007728, hAPP(_1007730, _1007734)), hAPP(_1007730, _1007732)) = hAPP(_1007730, _1007732))], (47775 ^ _779999) ^ [_1741918] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1741918) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1741918))))], (8970 ^ _779999) ^ [_933490, _933492, _933494] : [class_Orderings_Oorder(_933490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933490), _933492), _933494)), _933492 = _933494], (26681 ^ _779999) ^ [_1280197, _1280199] : [class_Groups_Oordered__ab__group__add__abs(_1280197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), c_Groups_Ozero__class_Ozero(_1280197))), -(hAPP(c_Groups_Oabs__class_Oabs(_1280197), _1280199) = hAPP(c_Groups_Ouminus__class_Ouminus(_1280197), _1280199))], (18057 ^ _779999) ^ [_1108635] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1108635)) = _1108635)], (43495 ^ _779999) ^ [_1643014, _1643016, _1643018, _1643020, _1643022, _1643024] : [-(c_List_Olistrelp(_1643014, _1643016, hAPP(hAPP(c_List_Olist_OCons(_1643014), _1643018), _1643020), hAPP(hAPP(c_List_Olist_OCons(_1643014), _1643022), _1643024))), hBOOL(hAPP(hAPP(_1643016, _1643018), _1643022)), c_List_Olistrelp(_1643014, _1643016, _1643020, _1643024)], (45696 ^ _779999) ^ [_1695145, _1695147] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695145)), hAPP(c_List_Otl(_1695145), _1695147)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695145)), _1695147)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (37449 ^ _779999) ^ [_1490040, _1490042] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1490040, _1490040)), _1490042)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1490040), hAPP(c_Relation_OField(_1490040), _1490042))))], (31737 ^ _779999) ^ [_1375217, _1375219, _1375221] : [class_Int_Onumber__ring(_1375217), class_Int_Oring__char__0(_1375217), 31744 ^ _779999 : [(31751 ^ _779999) ^ [] : [_1375219 = _1375221, -(hAPP(c_Int_Onumber__class_Onumber__of(_1375217), _1375219) = hAPP(c_Int_Onumber__class_Onumber__of(_1375217), _1375221))], (31745 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1375217), _1375219) = hAPP(c_Int_Onumber__class_Onumber__of(_1375217), _1375221), -(_1375219 = _1375221)]]], (20629 ^ _779999) ^ [_1154584, _1154586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154584)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1154584, _1154586)))], (11092 ^ _779999) ^ [_972182, _972184] : [class_Lattices_Olattice(_972182), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972182), _972184), _972184) = _972184)], (20142 ^ _779999) ^ [_1146910, _1146912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146910)), _1146912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146910), hAPP(c_Int_Onat, _1146912))))], (7695 ^ _779999) ^ [_909246, _909248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909246), _909248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909246)), hAPP(c_Nat_OSuc, _909248))))], (39002 ^ _779999) ^ [_1532413, _1532415, _1532417, _1532419, _1532421] : [c_Relation_Orefl__on(_1532413, _1532415, _1532417), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532413, _1532413)), hAPP(hAPP(c_Product__Type_OPair(_1532413, _1532413), _1532419), _1532421)), _1532417)), -(hBOOL(hAPP(hAPP(c_member(_1532413), _1532421), _1532415)))], (29964 ^ _779999) ^ [_1341743] : [class_Rings_Oring__1(_1341743), -(hAPP(c_Int_Oring__1__class_Oof__int(_1341743), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1341743))], (51964 ^ _779999) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (46680 ^ _779999) ^ [_1716369, _1716371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1716369), _1716371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716369)), hAPP(c_Code__Numeral_Onat__of, _1716371))))], (6477 ^ _779999) ^ [_884448, _884450, _884452] : [class_Lattices_Osemilattice__sup(_884448), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884448), _884450), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884448), _884452), _884450))))], (40039 ^ _779999) ^ [_1557019, _1557021, _1557023, _1557025, _1557027] : [c_Com_Ocom_OSemi(_1557019, _1557021) = c_Com_Ocom_OLocal(_1557023, _1557025, _1557027)], (11282 ^ _779999) ^ [_975533, _975535] : [class_Lattices_Obounded__lattice__bot(_975533), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975533), _975535), c_Orderings_Obot__class_Obot(_975533)) = c_Orderings_Obot__class_Obot(_975533))], (16707 ^ _779999) ^ [_1082237, _1082239, _1082241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082237), _1082239)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082237), _1082241))), 16710 ^ _779999 : [(16713 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082239), _1082241)))], (16711 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082237)))]]], (21028 ^ _779999) ^ [_1162110] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162110)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1162110))], (48864 ^ _779999) ^ [_1763846, _1763848, _1763850, _1763852] : [48866 ^ _779999 : [(48871 ^ _779999) ^ [] : [hBOOL(hAPP(_1763852, hAPP(hAPP(c_List_Onth(_1763848), _1763850), 48865 ^ [_1763846, _1763848, _1763850, _1763852])))], (48869 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48865 ^ [_1763846, _1763848, _1763850, _1763852]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763848)), _1763850))))], (48867 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48865 ^ [_1763846, _1763848, _1763850, _1763852]), _1763846)))]], 48874 ^ _779999 : [(48877 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1763852, hAPP(hAPP(c_List_Onth(_1763848), _1763850), _1763846))))], (48875 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763846), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763848)), _1763850))))]], -(c_List_OtakeWhile(_1763848, _1763852, _1763850) = hAPP(hAPP(c_List_Otake(_1763848), _1763846), _1763850))], (13664 ^ _779999) ^ [_1023789, _1023791, _1023793] : [class_Groups_Oordered__comm__monoid__add(_1023789), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023789), c_Groups_Ozero__class_Ozero(_1023789)), _1023791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023789), c_Groups_Ozero__class_Ozero(_1023789)), _1023793)), 13675 ^ _779999 : [(13684 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023789), _1023791), _1023793) = c_Groups_Ozero__class_Ozero(_1023789)), _1023791 = c_Groups_Ozero__class_Ozero(_1023789), _1023793 = c_Groups_Ozero__class_Ozero(_1023789)], (13676 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023789), _1023791), _1023793) = c_Groups_Ozero__class_Ozero(_1023789), 13679 ^ _779999 : [(13682 ^ _779999) ^ [] : [-(_1023793 = c_Groups_Ozero__class_Ozero(_1023789))], (13680 ^ _779999) ^ [] : [-(_1023791 = c_Groups_Ozero__class_Ozero(_1023789))]]]]], (14131 ^ _779999) ^ [_1032155, _1032157, _1032159] : [class_Groups_Oordered__comm__monoid__add(_1032155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032155), c_Groups_Ozero__class_Ozero(_1032155)), _1032157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032155), c_Groups_Ozero__class_Ozero(_1032155)), _1032159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032155), c_Groups_Ozero__class_Ozero(_1032155)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032155), _1032157), _1032159))))], (51021 ^ _779999) ^ [_1812700, _1812702] : [-(c_Relation_Osym(_1812700, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812700, _1812700), tc_HOL_Obool)), _1812702), hAPP(c_Relation_Oconverse(_1812700, _1812700), _1812702))))], (2652 ^ _779999) ^ [_819245, _819247, _819249, _819251] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819251, _819247) = c_Inductive_Ocomplete__lattice__class_Olfp(_819249, _819245)), _819251 = _819249, _819247 = _819245], (43930 ^ _779999) ^ [_1655395, _1655397, _1655399, _1655401, _1655403] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1655395, _1655397)), _1655399), hAPP(hAPP(c_List_Ozip(_1655395, _1655397), _1655401), _1655403)) = hAPP(hAPP(c_List_Ozip(_1655395, _1655397), hAPP(hAPP(c_List_Otake(_1655395), _1655399), _1655401)), hAPP(hAPP(c_List_Otake(_1655397), _1655399), _1655403)))], (39141 ^ _779999) ^ [_1535247, _1535249] : [-(c_Nitpick_Owf_H(_1535247, _1535249)), c_Wellfounded_Oacyclic(_1535247, _1535249), 39146 ^ _779999 : [(39149 ^ _779999) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (39147 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535247, _1535247)), _1535249))]]], (20594 ^ _779999) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (968 ^ _779999) ^ [_794777, _794779, _794781, _794783] : [-(c_Wellfounded_Oacyclic(_794781, _794777)), c_Wellfounded_Oacyclic(_794783, _794779), _794783 = _794781, _794779 = _794777], (30495 ^ _779999) ^ [_1351546, _1351548, _1351550, _1351552] : [class_Divides_Osemiring__div(_1351546), -(c_Divides_Odiv__class_Omod(_1351546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351546), _1351548), _1351550), _1351552) = c_Divides_Odiv__class_Omod(_1351546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351546), c_Divides_Odiv__class_Omod(_1351546, _1351548, _1351552)), c_Divides_Odiv__class_Omod(_1351546, _1351550, _1351552)), _1351552))], (27042 ^ _779999) ^ [_1288432, _1288434, _1288436, _1288438, _1288440] : [class_Groups_Ocomm__monoid__mult(_1288432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288434), _1288436)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288434), _1288438)), 27056 ^ _779999 : [(27059 ^ _779999) ^ [] : [hAPP(_1288440, 27055 ^ [_1288432, _1288434, _1288436, _1288438, _1288440]) = c_Groups_Oone__class_Oone(_1288432)], (27057 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288434), 27055 ^ [_1288432, _1288434, _1288436, _1288438, _1288440]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288434, tc_HOL_Obool)), _1288436), _1288438))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288434, _1288432), _1288440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288434, tc_HOL_Obool)), _1288436), _1288438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288432), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288434, _1288432), _1288440), _1288436)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288434, _1288432), _1288440), _1288438)))], (46672 ^ _779999) ^ [_1716245, _1716247] : [_1716245 = _1716247, -(hAPP(c_Code__Numeral_Onat__of, _1716245) = hAPP(c_Code__Numeral_Onat__of, _1716247))], (14860 ^ _779999) ^ [_1046745, _1046747] : [_1046745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046745), _1046747) = _1046747)], (24320 ^ _779999) ^ [_1235550, _1235552, _1235554, _1235556] : [class_Orderings_Olinorder(_1235550), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235550), _1235552), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235550), _1235554), _1235556)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235550), _1235554), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235550), _1235552), _1235556)))], (44712 ^ _779999) ^ [_1672338, _1672340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1672338), _1672340)), -(c_List_Oupto(_1672338, _1672340) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1672338), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1672338), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1672340)))], (38860 ^ _779999) ^ [_1529188, _1529190] : [-(c_Product__Type_Omap__pair(_1529188, _1529188, _1529190, _1529190, c_COMBI(_1529188), c_COMBI(_1529190)) = c_Fun_Oid(tc_prod(_1529188, _1529190)))], (3464 ^ _779999) ^ [_831809, _831811, _831813, _831815, _831817, _831819] : [-(c_Big__Operators_Olattice_OSup__fin(_831819, _831815, _831811) = c_Big__Operators_Olattice_OSup__fin(_831817, _831813, _831809)), _831819 = _831817, _831815 = _831813, _831811 = _831809], (17477 ^ _779999) ^ [_1097125, _1097127, _1097129, _1097131, _1097133, _1097135] : [class_Groups_Oab__semigroup__mult(_1097125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097127), _1097129)), -(hBOOL(hAPP(hAPP(c_member(_1097127), _1097131), _1097129))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097125, _1097127, c_Groups_Otimes__class_Otimes(_1097125)), _1097133), _1097135), hAPP(hAPP(c_Set_Oinsert(_1097127), _1097131), _1097129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097125), hAPP(_1097133, _1097131)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097125, _1097127, c_Groups_Otimes__class_Otimes(_1097125)), _1097133), _1097135), _1097129)))], (40753 ^ _779999) ^ [_1574022, _1574024, _1574026] : [c_Equiv__Relations_Oequiv(_1574022, _1574024, _1574026), -(hAPP(hAPP(c_Relation_Orel__comp(_1574022, _1574022, _1574022), hAPP(c_Relation_Oconverse(_1574022, _1574022), _1574026)), _1574026) = _1574026)], (30812 ^ _779999) ^ [_1357656, _1357658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357656)), 30815 ^ _779999 : [(30818 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357658, _1357656)), _1357656)))], (30816 ^ _779999) ^ [] : [-(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, _1357658, _1357656))))]]], (14043 ^ _779999) ^ [_1030409, _1030411, _1030413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030409), _1030411)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030411), _1030409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030413), _1030409)), _1030411))], (13764 ^ _779999) ^ [_1025563, _1025565] : [class_Groups_Olinordered__ab__group__add(_1025563), 13767 ^ _779999 : [(13774 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025563), c_Groups_Ozero__class_Ozero(_1025563)), _1025565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025563), c_Groups_Ozero__class_Ozero(_1025563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025563), _1025565), _1025565))))], (13768 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025563), c_Groups_Ozero__class_Ozero(_1025563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025563), _1025565), _1025565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025563), c_Groups_Ozero__class_Ozero(_1025563)), _1025565)))]]], (3796 ^ _779999) ^ [_836975, _836977, _836979, _836981, _836983, _836985, _836987, _836989] : [-(c_List_Olinorder__class_Osort__key(_836989, _836985, _836981, _836977) = c_List_Olinorder__class_Osort__key(_836987, _836983, _836979, _836975)), _836989 = _836987, _836985 = _836983, _836981 = _836979, _836977 = _836975], (40387 ^ _779999) ^ [_1565962, _1565964] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1565962, _1565962, _1565962), _1565964), c_Transitive__Closure_Ortrancl(_1565962, _1565964)) = hAPP(hAPP(c_Relation_Orel__comp(_1565962, _1565962, _1565962), c_Transitive__Closure_Ortrancl(_1565962, _1565964)), _1565964))], (47162 ^ _779999) ^ [_1727472, _1727474] : [-(hBOOL(hAPP(c_List_Odistinct(_1727472), c_List_Oremdups(_1727472, _1727474))))], (36685 ^ _779999) ^ [_1471479, _1471481] : [-(c_FunDef_Orp__inv__image(_1471479, _1471481) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))))), tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))), tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)), tc_fun(tc_fun(_1471481, _1471479), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool)), c_COMBS(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)), tc_fun(tc_fun(_1471481, _1471479), tc_fun(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), tc_fun(tc_prod(_1471479, _1471479), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool))), tc_fun(_1471481, _1471479)), c_Product__Type_OPair(tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool), tc_fun(tc_prod(_1471481, _1471481), tc_HOL_Obool)))), c_Relation_Oinv__image(_1471479, _1471481))))), c_Relation_Oinv__image(_1471479, _1471481))))], (39348 ^ _779999) ^ [_1540834, _1540836, _1540838] : [-(hAPP(c_Fun_Ocomp(_1540834, _1540836, _1540834, _1540838), c_Fun_Oid(_1540834)) = _1540838)], (39703 ^ _779999) ^ [_1548868, _1548870, _1548872, _1548874, _1548876, _1548878, _1548880, _1548882] : [c_Finite__Set_Ofolding(_1548868, _1548870, _1548872, _1548874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548868), _1548876)), -(hAPP(c_Fun_Ocomp(_1548870, _1548870, _1548878, hAPP(_1548872, _1548880)), hAPP(c_Fun_Ocomp(_1548870, _1548870, _1548878, hAPP(_1548874, _1548876)), _1548882)) = hAPP(c_Fun_Ocomp(_1548870, _1548870, _1548878, hAPP(_1548874, _1548876)), hAPP(c_Fun_Ocomp(_1548870, _1548870, _1548878, hAPP(_1548872, _1548880)), _1548882)))], (34783 ^ _779999) ^ [_1430723] : [c_Int_OMin = c_Int_OBit1(_1430723), -(c_Int_OMin = _1430723)], (25906 ^ _779999) ^ [_1265898, _1265900, _1265902, _1265904, _1265906, _1265908] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_1265898, _1265900, _1265902), _1265904, _1265906, _1265908), 25911 ^ _779999 : [(25914 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1265900, _1265904, _1265906, _1265908))], (25912 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1265898, _1265904)))]], 25915 ^ _779999 : [(25918 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1265902, _1265904, _1265906, _1265908))], (25916 ^ _779999) ^ [] : [hBOOL(hAPP(_1265898, _1265904))]]], (14417 ^ _779999) ^ [_1037648, _1037650, _1037652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037648), _1037650)), -(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(_1037648), _1037652)), hAPP(c_Finite__Set_Ocard(_1037648), _1037650))), hAPP(c_Finite__Set_Ocard(_1037648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037648, tc_HOL_Obool)), _1037652), _1037650)))))], (15435 ^ _779999) ^ [_1057528, _1057530] : [-(hBOOL(hAPP(_1057528, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1057528, _1057530)), 15443 ^ _779999 : [(15446 ^ _779999) ^ [_1057766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057766), 15442 ^ [_1057528, _1057530])), hBOOL(hAPP(_1057528, _1057766))], (15452 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1057528, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 15442 ^ [_1057528, _1057530]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (15444 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15442 ^ [_1057528, _1057530]), _1057530)))]]], (11162 ^ _779999) ^ [_973404, _973406, _973408, _973410] : [class_Lattices_Osemilattice__inf(_973404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973404), _973406), _973408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973404), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973404), _973406), _973410)), _973408)))], (31289 ^ _779999) ^ [_1366031, _1366033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366033, _1366031)), _1366031)))], (14273 ^ _779999) ^ [_1034779, _1034781, _1034783] : [-(hBOOL(hAPP(_1034779, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034781), _1034783)))), 14276 ^ _779999 : [(14279 ^ _779999) ^ [] : [hBOOL(hAPP(_1034779, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14277 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034781), _1034783)))]], 14281 ^ _779999 : [(14284 ^ _779999) ^ [] : [hBOOL(hAPP(_1034779, 14280 ^ [_1034779, _1034781, _1034783]))], (14282 ^ _779999) ^ [] : [-(_1034781 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034783), 14280 ^ [_1034779, _1034781, _1034783]))]]], (25245 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8433 ^ _779999) ^ [_924259, _924261, _924263] : [class_Groups_Oordered__ab__group__add(_924259), 8436 ^ _779999 : [(8443 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924259), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_924259), _924261), _924263)), c_Groups_Ozero__class_Ozero(_924259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924259), _924261), _924263)))], (8437 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924259), _924261), _924263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924259), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_924259), _924261), _924263)), c_Groups_Ozero__class_Ozero(_924259))))]]], (34685 ^ _779999) ^ [_1428559, _1428561] : [class_Rings_Osemiring__1(_1428559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428561)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1428559), 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)))), _1428561))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428559), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1428559), hAPP(c_Int_Onat, _1428561))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1428559), hAPP(c_Int_Onat, _1428561))))], (9498 ^ _779999) ^ [_941353, _941355, _941357, _941359] : [class_Orderings_Opreorder(_941353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941353), _941355), _941357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941353), _941357), _941359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941353), _941355), _941359)))], (28050 ^ _779999) ^ [_1307281, _1307283, _1307285, _1307287] : [class_Rings_Olinordered__semidom(_1307281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1307283), _1307285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307281), c_Groups_Oone__class_Oone(_1307281)), _1307287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307281), hAPP(hAPP(c_Power_Opower__class_Opower(_1307281), _1307287), _1307283)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307281), _1307287), _1307285))))], (20872 ^ _779999) ^ [_1158918, _1158920, _1158922, _1158924] : [class_Groups_Oordered__ab__group__add__abs(_1158918), -(hAPP(c_Groups_Oabs__class_Oabs(_1158918), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1158920, _1158918), hAPP(hAPP(c_COMBB(_1158918, _1158918, _1158920), c_Groups_Oabs__class_Oabs(_1158918)), _1158922)), _1158924)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1158920, _1158918), hAPP(hAPP(c_COMBB(_1158918, _1158918, _1158920), c_Groups_Oabs__class_Oabs(_1158918)), _1158922)), _1158924))], (34809 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (45127 ^ _779999) ^ [_1681845, _1681847, _1681849] : [-(hAPP(hAPP(c_List_Oappend(_1681845), _1681847), _1681849) = c_List_Olist_ONil(_1681845)), _1681847 = c_List_Olist_ONil(_1681845), _1681849 = c_List_Olist_ONil(_1681845)], (34653 ^ _779999) ^ [_1427931, _1427933, _1427935] : [class_Rings_Olinordered__idom(_1427931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427931), c_Groups_Ozero__class_Ozero(_1427931)), hAPP(hAPP(c_Power_Opower__class_Opower(_1427931), _1427933), 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)))), _1427935))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427931), c_Groups_Ozero__class_Ozero(_1427931)), _1427933)))], (38273 ^ _779999) ^ [_1511451, _1511453, _1511455, _1511457, _1511459] : [-(hAPP(c_Relation_ORange(_1511451, _1511453), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1511451, _1511453)), hAPP(hAPP(c_Product__Type_OPair(_1511451, _1511453), _1511455), _1511457)), _1511459)) = hAPP(hAPP(c_Set_Oinsert(_1511453), _1511457), hAPP(c_Relation_ORange(_1511451, _1511453), _1511459)))], (26885 ^ _779999) ^ [_1284856, _1284858, _1284860, _1284862] : [class_Groups_Ocomm__monoid__mult(_1284856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284858), _1284860)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284858, _1284856), _1284862), _1284860) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1284856, _1284858, c_Groups_Otimes__class_Otimes(_1284856)), _1284862), c_Groups_Oone__class_Oone(_1284856)), _1284860))], (52432 ^ _779999) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), 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))), v_Q)), v_Procs)))], (33453 ^ _779999) ^ [] : [-(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)))))], (14095 ^ _779999) ^ [_1031453, _1031455, _1031457] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031453), _1031455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1031453), _1031455)), hAPP(c_Finite__Set_Ocard(_1031453), hAPP(hAPP(c_Set_Oinsert(_1031453), _1031457), _1031455)))))], (21788 ^ _779999) ^ [_1177556, _1177558] : [-(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), _1177556)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1177558))))))], (39938 ^ _779999) ^ [_1554312, _1554314] : [39940 ^ _779999 : [(39943 ^ _779999) ^ [] : [39939 ^ [_1554312, _1554314] = c_Orderings_Obot__class_Obot(tc_fun(_1554312, tc_HOL_Obool))], (39941 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554312, tc_HOL_Obool)), 39939 ^ [_1554312, _1554314]), hAPP(c_Relation_OImage(_1554312, _1554312, _1554314), 39939 ^ [_1554312, _1554314]))))]], -(c_Wellfounded_Owf(_1554312, _1554314))], (47797 ^ _779999) ^ [_1742451, _1742453, _1742455] : [47798 ^ _779999 : [(47801 ^ _779999) ^ [] : [_1742455 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47799 ^ _779999) ^ [] : [-(_1742451 = c_List_Olist_ONil(tc_List_Olist(_1742453)))]], 47805 ^ _779999 : [(47808 ^ _779999) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742453)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1742453)), _1742451), 47804 ^ [_1742451, _1742453, _1742455])) = _1742455], (47806 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47804 ^ [_1742451, _1742453, _1742455]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1742453))), _1742451))))]], -(c_List_Otranspose(_1742453, _1742451) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1742453)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1742453)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1742453), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1742453)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1742453)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1742453), hAPP(hAPP(c_COMBB(tc_List_Olist(_1742453), tc_fun(tc_Nat_Onat, _1742453), tc_Nat_Onat), c_List_Onth(_1742453)), hAPP(c_List_Onth(tc_List_Olist(_1742453)), _1742451))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1742453))), _1742451)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1742455)))], (51924 ^ _779999) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (14505 ^ _779999) ^ [_1039552, _1039554, _1039556, _1039558, _1039560] : [class_Groups_Ocomm__monoid__add(_1039552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039554), _1039556)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039554, _1039552), _1039558), hAPP(hAPP(c_Set_Oinsert(_1039554), _1039560), _1039556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039552), hAPP(_1039558, _1039560)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039554, _1039552), _1039558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039554, tc_HOL_Obool)), _1039556), hAPP(hAPP(c_Set_Oinsert(_1039554), _1039560), c_Orderings_Obot__class_Obot(tc_fun(_1039554, tc_HOL_Obool)))))))], (13061 ^ _779999) ^ [_1012381, _1012383, _1012385, _1012387] : [class_Groups_Ocancel__semigroup__add(_1012381), 13064 ^ _779999 : [(13071 ^ _779999) ^ [] : [_1012383 = _1012387, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012381), _1012383), _1012385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012381), _1012387), _1012385))], (13065 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012381), _1012383), _1012385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012381), _1012387), _1012385), -(_1012383 = _1012387)]]], (35984 ^ _779999) ^ [_1457657, _1457659] : [-(c_Divides_Odivmod__nat(_1457657, _1457659) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1457657), _1457659)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1457657, _1457659)))], (22587 ^ _779999) ^ [_1197930, _1197932, _1197934, _1197936] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1197930, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1197932)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1197930, tc_HOL_Obool), tc_Nat_Onat), _1197934), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1197936))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1197930, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1197936, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1197932), _1197936))), _1197934))], (40986 ^ _779999) ^ [_1580247, _1580249] : [-(hAPP(hAPP(c_Nat_Ocompow(_1580247, _1580247), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1580249) = c_Fun_Oid(_1580247))], (364 ^ _779999) ^ [_785583, _785585, _785587, _785589] : [-(c_Wellfounded_OwfP(_785587, _785583)), c_Wellfounded_OwfP(_785589, _785585), _785589 = _785587, _785585 = _785583], (11062 ^ _779999) ^ [_971537, _971539, _971541, _971543] : [class_Lattices_Olattice(_971537), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971537), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971537), _971539), _971541)), _971543) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971537), _971539), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971537), _971541), _971543)))], (6723 ^ _779999) ^ [_890000, _890002, _890004, _890006] : [hBOOL(hAPP(hAPP(c_member(_890000), _890002), hAPP(hAPP(c_Set_Oinsert(_890000), _890004), _890006))), -(_890002 = _890004), -(hBOOL(hAPP(hAPP(c_member(_890000), _890002), _890006)))], (36018 ^ _779999) ^ [_1458177, _1458179] : [-(_1458177 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1458179, _1458177) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458179), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458177)))], (21822 ^ _779999) ^ [_1178963, _1178965, _1178967, _1178969, _1178971, _1178973] : [class_Groups_Ocomm__monoid__add(_1178963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178965), _1178967)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178965, _1178963), _1178969), _1178967) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178971, _1178963), hAPP(hAPP(c_COMBB(tc_fun(_1178965, tc_HOL_Obool), _1178963, _1178971), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178965, _1178963), _1178969)), hAPP(hAPP(c_COMBB(tc_fun(_1178965, tc_HOL_Obool), tc_fun(_1178965, tc_HOL_Obool), _1178971), c_Set_OCollect(_1178965)), hAPP(hAPP(c_COMBB(tc_fun(_1178965, tc_HOL_Obool), tc_fun(_1178965, tc_HOL_Obool), _1178971), hAPP(c_COMBS(_1178965, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1178965), c_fconj), hAPP(hAPP(c_COMBC(_1178965, tc_fun(_1178965, tc_HOL_Obool), tc_HOL_Obool), c_member(_1178965)), _1178967)))), hAPP(c_COMBC(_1178965, _1178971, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1178971, tc_fun(_1178971, tc_HOL_Obool), _1178965), c_fequal), _1178973)))))), hAPP(c_Set_Oimage(_1178965, _1178971, _1178973), _1178967)))], (40862 ^ _779999) ^ [_1576873, _1576875, _1576877] : [c_Relation_Ototal__on(_1576873, _1576875, _1576877), 40865 ^ _779999 : [(40866 ^ _779999) ^ [_1577017] : [hBOOL(hAPP(hAPP(c_member(_1576873), _1577017), _1576875)), 40869 ^ _779999 : [(40870 ^ _779999) ^ [_1577157] : [hBOOL(hAPP(hAPP(c_member(_1576873), _1577157), _1576875)), -(_1577017 = _1577157), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576873, _1576873)), hAPP(hAPP(c_Product__Type_OPair(_1576873, _1576873), _1577017), _1577157)), _1576877))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576873, _1576873)), hAPP(hAPP(c_Product__Type_OPair(_1576873, _1576873), _1577157), _1577017)), _1576877)))]]]]], (24284 ^ _779999) ^ [_1234848, _1234850] : [class_Orderings_Olinorder(_1234848), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234848), _1234850), _1234850) = _1234850)], (27692 ^ _779999) ^ [_1300584, _1300586, _1300588, _1300590] : [class_Groups_Ocomm__monoid__mult(_1300584), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300584), _1300586), _1300588)), _1300590) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300584), hAPP(hAPP(c_Power_Opower__class_Opower(_1300584), _1300586), _1300590)), hAPP(hAPP(c_Power_Opower__class_Opower(_1300584), _1300588), _1300590)))], (10521 ^ _779999) ^ [_961071, _961073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961071)), _961073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961071), _961073)))], (13461 ^ _779999) ^ [_1019780, _1019782, _1019784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019780), _1019782)), _1019784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019780), _1019784)))], (52162 ^ _779999) ^ [_1832019, _1832021] : [-(class_Finite__Set_Ofinite(tc_sum(_1832019, _1832021))), class_Finite__Set_Ofinite(_1832019), class_Finite__Set_Ofinite(_1832021)], (47629 ^ _779999) ^ [_1739342, _1739344] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1739342, _1739344))))], (25311 ^ _779999) ^ [_1255153, _1255155, _1255157] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1255153, _1255155, _1255157)) = 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(_1255155)), c_Com_Ocom_Ocom__size(_1255157))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44420 ^ _779999) ^ [_1666888, _1666890, _1666892] : [hBOOL(hAPP(c_List_Odistinct(_1666888), _1666890)), -(hAPP(c_List_Oset(_1666888), c_List_Oremove1(_1666888, _1666892, _1666890)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1666888, tc_HOL_Obool)), hAPP(c_List_Oset(_1666888), _1666890)), hAPP(hAPP(c_Set_Oinsert(_1666888), _1666892), c_Orderings_Obot__class_Obot(tc_fun(_1666888, tc_HOL_Obool)))))], (2594 ^ _779999) ^ [_818324, _818326, _818328, _818330] : [-(c_Divides_Odivmod__nat(_818330, _818326) = c_Divides_Odivmod__nat(_818328, _818324)), _818330 = _818328, _818326 = _818324], (36569 ^ _779999) ^ [_1468980, _1468982] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1468980), _1468982) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1468980, _1468982)))], (11861 ^ _779999) ^ [_988520, _988522, _988524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988520), _988522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_988520, tc_HOL_Obool)), _988524), _988522)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988520), _988524)))], (49278 ^ _779999) ^ [_1773905, _1773907, _1773909, _1773911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773905), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773907)), _1773909))), 49284 ^ _779999 : [(49287 ^ _779999) ^ [] : [hBOOL(hAPP(_1773911, 49283 ^ [_1773905, _1773907, _1773909, _1773911]))], (49285 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773907), 49283 ^ [_1773905, _1773907, _1773909, _1773911]), hAPP(c_List_Oset(_1773907), _1773909))))]], -(hBOOL(hAPP(_1773911, hAPP(hAPP(c_List_Onth(_1773907), _1773909), _1773905))))], (46734 ^ _779999) ^ [_1717325] : [-(_1717325 = 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, _1717325)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1717325))))], (4592 ^ _779999) ^ [_849753, _849755, _849757, _849759] : [-(c_List_Oupt(_849759, _849755) = c_List_Oupt(_849757, _849753)), _849759 = _849757, _849755 = _849753], (8267 ^ _779999) ^ [_920380, _920382, _920384] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_920380, _920382)), _920384), _920384)), hBOOL(hAPP(_920380, _920384)), 8275 ^ _779999 : [(8278 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_920380, _920382)), 8274 ^ [_920380, _920382, _920384]), _920384)))], (8276 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_920382), _920384), 8274 ^ [_920380, _920382, _920384])))]]], (51139 ^ _779999) ^ [_1814483, _1814485] : [c_Predicate_Osymp(_1814483, _1814485), -(c_Relation_Osym(_1814483, hAPP(c_Set_OCollect(tc_prod(_1814483, _1814483)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814483, _1814483, tc_HOL_Obool), _1814485))))], (38980 ^ _779999) ^ [_1531982] : [-(c_Relation_Orefl__on(_1531982, c_Orderings_Obot__class_Obot(tc_fun(_1531982, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531982, _1531982), tc_HOL_Obool))))], (49712 ^ _779999) ^ [_1782642, _1782644, _1782646, _1782648, _1782650, _1782652, _1782654] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1782642, _1782644, _1782646, _1782648, _1782650, _1782652, _1782654) = c_New__DSequence_Oneg__decr__bind(_1782642, _1782644, hAPP(hAPP(hAPP(_1782646, _1782650), _1782652), _1782654), hAPP(hAPP(c_COMBC(_1782642, 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(_1782644)))), hAPP(hAPP(c_COMBC(_1782642, 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(_1782644))))), hAPP(hAPP(c_COMBC(_1782642, 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(_1782644)))))), _1782648), _1782650)), _1782652)), _1782654)))], (47607 ^ _779999) ^ [_1738647, _1738649] : [class_Groups_Omonoid__add(_1738647), -(hAPP(c_List_Ofoldl(_1738647, _1738647, c_Groups_Oplus__class_Oplus(_1738647), c_Groups_Ozero__class_Ozero(_1738647)), _1738649) = c_List_Ofoldr(_1738647, _1738647, c_Groups_Oplus__class_Oplus(_1738647), _1738649, c_Groups_Ozero__class_Ozero(_1738647)))], (52098 ^ _779999) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (38373 ^ _779999) ^ [_1514112, _1514114, _1514116, _1514118] : [hBOOL(hAPP(hAPP(c_member(_1514112), _1514114), hAPP(c_Relation_ODomain(_1514112, _1514116), _1514118))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514112, _1514116)), hAPP(hAPP(c_Product__Type_OPair(_1514112, _1514116), _1514114), 38376 ^ [_1514112, _1514114, _1514116, _1514118])), _1514118)))], (30844 ^ _779999) ^ [_1358149, _1358151] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358149, _1358151) = 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), _1358149), _1358151) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358151), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358149, _1358151)))], (50899 ^ _779999) ^ [_1809958] : [-(c_Relation_Oantisym(_1809958, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1809958, _1809958), tc_HOL_Obool))))], (46771 ^ _779999) ^ [_1718221, _1718223, _1718225] : [hBOOL(hAPP(c_List_Olistsp(_1718221, _1718223), _1718225)), 46774 ^ _779999 : [(46775 ^ _779999) ^ [_1718310] : [hBOOL(hAPP(hAPP(c_member(_1718221), _1718310), hAPP(c_List_Oset(_1718221), _1718225))), -(hBOOL(hAPP(_1718223, _1718310)))]]], (13349 ^ _779999) ^ [_1017672, _1017674] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017672), _1017674) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1017672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1017674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27664 ^ _779999) ^ [_1300145, _1300147, _1300149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1300145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1300145), _1300147)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1300145), _1300149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300147), _1300149)))], (49760 ^ _779999) ^ [_1783984, _1783986, _1783988] : [-(c_List_Osplice(_1783984, hAPP(hAPP(c_List_Olist_OCons(_1783984), _1783986), _1783988), c_List_Olist_ONil(_1783984)) = hAPP(hAPP(c_List_Olist_OCons(_1783984), _1783986), _1783988))], (5432 ^ _779999) ^ [_863083, _863085, _863087, _863089, _863091, _863093, _863095, _863097, _863099, _863101] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_863101, _863097, _863093, _863089, _863085) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_863099, _863095, _863091, _863087, _863083)), _863101 = _863099, _863097 = _863095, _863093 = _863091, _863089 = _863087, _863085 = _863083], (40579 ^ _779999) ^ [_1570408, _1570410] : [-(c_Relation_Orefl__on(_1570408, c_Orderings_Otop__class_Otop(tc_fun(_1570408, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570408, _1570408), tc_HOL_Obool)), _1570410), c_Relation_OId(_1570408))))], (40201 ^ _779999) ^ [_1560617, _1560619, _1560621, _1560623, _1560625] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560617, _1560617)), hAPP(hAPP(c_Product__Type_OPair(_1560617, _1560617), _1560619), _1560621)), _1560623)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560617, _1560617)), hAPP(hAPP(c_Product__Type_OPair(_1560617, _1560617), _1560621), _1560625)), c_Transitive__Closure_Otrancl(_1560617, _1560623))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560617, _1560617)), hAPP(hAPP(c_Product__Type_OPair(_1560617, _1560617), _1560619), _1560625)), c_Transitive__Closure_Otrancl(_1560617, _1560623))))], (8029 ^ _779999) ^ [_915525, _915527, _915529, _915531, _915533] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_915525, _915527), _915529, _915531, _915533), 8034 ^ _779999 : [(8037 ^ _779999) ^ [] : [hBOOL(hAPP(_915525, _915529))], (8035 ^ _779999) ^ [] : [-(_915533 = _915529)]], 8038 ^ _779999 : [(8044 ^ _779999) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_915525, _915527), 8040 ^ [_915525, _915527, _915529, _915531, _915533], _915531, _915533))], (8042 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_915527, _915529, _915531, 8040 ^ [_915525, _915527, _915529, _915531, _915533]))], (8039 ^ _779999) ^ [] : [-(hBOOL(hAPP(_915525, _915529)))]]], (31715 ^ _779999) ^ [_1374855, _1374857, _1374859] : [_1374855 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1374857, _1374857), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374857, _1374857), tc_HOL_Obool)), _1374855), _1374859)))], (49560 ^ _779999) ^ [_1779702, _1779704, _1779706] : [49562 ^ _779999 : [(49565 ^ _779999) ^ [] : [hBOOL(hAPP(_1779706, 49561 ^ [_1779702, _1779704, _1779706]))], (49563 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779702), 49561 ^ [_1779702, _1779704, _1779706]), hAPP(c_List_Oset(_1779702), _1779704))))]], -(c_List_Olist__all(_1779702, _1779706, _1779704))], (6131 ^ _779999) ^ [_877831, _877833, _877835] : [class_Lattices_Olattice(_877831), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877831), _877833), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877831), _877833), _877835)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877831), _877833), _877835))], (23397 ^ _779999) ^ [_1216595, _1216597, _1216599, _1216601, _1216603] : [hBOOL(hAPP(hAPP(c_member(_1216595), hAPP(_1216597, _1216599)), _1216601)), -(hBOOL(hAPP(hAPP(c_member(_1216603), _1216599), hAPP(c_Set_Ovimage(_1216603, _1216595, _1216597), _1216601))))], (552 ^ _779999) ^ [_788465, _788467, _788469, _788471, _788473, _788475] : [-(c_Relation_Osingle__valued(_788473, _788469, _788465)), c_Relation_Osingle__valued(_788475, _788471, _788467), _788475 = _788473, _788471 = _788469, _788467 = _788465], (18043 ^ _779999) ^ [_1108359, _1108361, _1108363, _1108365, _1108367] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1108359, _1108361, _1108363, _1108365, c_Orderings_Obot__class_Obot(tc_fun(_1108359, tc_HOL_Obool))), _1108367)), -(_1108367 = _1108365)], (2080 ^ _779999) ^ [_810267, _810269, _810271, _810273] : [-(c_Enum_Oenum__the(_810273, _810269) = c_Enum_Oenum__the(_810271, _810267)), _810273 = _810271, _810269 = _810267], (50901 ^ _779999) ^ [_1809989, _1809991] : [-(c_Relation_Oantisym(_1809989, c_Relation_OId__on(_1809989, _1809991)))], (47605 ^ _779999) ^ [_1738580, _1738582, _1738584, _1738586, _1738588, _1738590, _1738592] : [-(c_List_Ofoldr(_1738580, _1738582, _1738584, hAPP(hAPP(c_List_Omap(_1738586, _1738580), _1738588), _1738590), _1738592) = c_List_Ofoldr(_1738586, _1738582, hAPP(c_Fun_Ocomp(_1738580, tc_fun(_1738582, _1738582), _1738586, _1738584), _1738588), _1738590, _1738592))], (17927 ^ _779999) ^ [_1106274, _1106276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106274), _1106276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106274)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106276))))], (24198 ^ _779999) ^ [_1232881, _1232883, _1232885] : [class_Orderings_Olinorder(_1232881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1232881), _1232883)), -(_1232883 = c_Orderings_Obot__class_Obot(tc_fun(_1232881, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1232881), _1232885), c_Big__Operators_Olattice_OInf__fin(_1232881, c_Orderings_Oord__class_Omin(_1232881), _1232883)) = c_Big__Operators_Olattice_OInf__fin(_1232881, c_Orderings_Oord__class_Omin(_1232881), hAPP(c_Set_OCollect(_1232881), hAPP(hAPP(c_COMBB(tc_fun(_1232881, tc_HOL_Obool), tc_HOL_Obool, _1232881), c_HOL_OEx(_1232881)), hAPP(hAPP(c_COMBC(_1232881, tc_fun(_1232881, tc_HOL_Obool), tc_fun(_1232881, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1232881, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1232881, tc_HOL_Obool), tc_fun(_1232881, tc_HOL_Obool)), _1232881), c_COMBS(_1232881, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1232881, tc_HOL_Obool), tc_fun(_1232881, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1232881), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1232881), c_fconj)), hAPP(hAPP(c_COMBC(_1232881, tc_fun(_1232881, _1232881), tc_fun(_1232881, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1232881, tc_HOL_Obool), tc_fun(tc_fun(_1232881, _1232881), tc_fun(_1232881, tc_HOL_Obool)), _1232881), c_COMBB(_1232881, tc_HOL_Obool, _1232881)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1232881), _1232885))))), hAPP(hAPP(c_COMBC(_1232881, tc_fun(_1232881, tc_HOL_Obool), tc_HOL_Obool), c_member(_1232881)), _1232883))))))], (41672 ^ _779999) ^ [_1595343, _1595345, _1595347, _1595349, _1595351, _1595353] : [c_Finite__Set_Ofun__left__comm(_1595343, _1595345, _1595347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595343), _1595349)), -(hAPP(hAPP(_1595347, _1595351), hAPP(hAPP(c_Finite__Set_Ofold(_1595343, _1595345, _1595347), _1595353), _1595349)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595343, _1595345, _1595347), hAPP(hAPP(_1595347, _1595351), _1595353)), _1595349))], (25638 ^ _779999) ^ [_1260765, _1260767, _1260769, _1260771, _1260773, _1260775] : [-(c_Com_Ocom_OCond(_1260765, _1260767, _1260769) = c_Com_Ocom_OCond(_1260771, _1260773, _1260775)), _1260765 = _1260771, _1260767 = _1260773, _1260769 = _1260775], (43622 ^ _779999) ^ [_1646458, _1646460, _1646462] : [_1646458 = _1646460, 43625 ^ _779999 : [(43628 ^ _779999) ^ [_1646606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1646606), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646462)), _1646458))), -(hAPP(hAPP(c_List_Onth(_1646462), _1646458), _1646606) = hAPP(hAPP(c_List_Onth(_1646462), _1646460), _1646606))], (43626 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646462)), _1646458) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646462)), _1646460))]]], (22954 ^ _779999) ^ [_1207584, _1207586, _1207588, _1207590, _1207592] : [_1207584 = c_Orderings_Obot__class_Obot(tc_fun(_1207586, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1207588), _1207590), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207586, tc_fun(_1207588, tc_HOL_Obool)), _1207584), _1207592)) = hAPP(hAPP(c_Set_Oinsert(_1207588), _1207590), c_Orderings_Obot__class_Obot(tc_fun(_1207588, tc_HOL_Obool))))], (43145 ^ _779999) ^ [_1631294, _1631296] : [-(c_List_Olenlex(_1631294, _1631296) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1631294)), tc_List_Olist(_1631294)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1631294), c_Wellfounded_Oless__than, c_List_Olex(_1631294, _1631296))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1631294), tc_List_Olist(_1631294), tc_prod(tc_Nat_Onat, tc_List_Olist(_1631294))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1631294), tc_prod(tc_Nat_Onat, tc_List_Olist(_1631294))), tc_List_Olist(_1631294)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1631294))), c_Nat_Osize__class_Osize(tc_List_Olist(_1631294)))), c_COMBI(tc_List_Olist(_1631294)))))], (13920 ^ _779999) ^ [_1028047, _1028049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028047), _1028049)), -(_1028049 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028047), 13923 ^ [_1028047, _1028049])))], (39881 ^ _779999) ^ [_1553054, _1553056, _1553058, _1553060, _1553062, _1553064] : [c_Finite__Set_Ofolding__idem(_1553054, _1553056, _1553058, _1553060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553054), _1553062)), -(hAPP(_1553060, hAPP(hAPP(c_Set_Oinsert(_1553054), _1553064), _1553062)) = hAPP(c_Fun_Ocomp(_1553056, _1553056, _1553056, hAPP(_1553060, _1553062)), hAPP(_1553058, _1553064)))], (10502 ^ _779999) ^ [_960781] : [_960781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960781), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (50903 ^ _779999) ^ [_1810017] : [-(c_Relation_Oantisym(_1810017, c_Relation_OId(_1810017)))], (15117 ^ _779999) ^ [_1051493, _1051495, _1051497, _1051499, _1051501] : [hBOOL(hAPP(hAPP(c_member(_1051493), _1051495), c_SetInterval_Oord_OatLeastAtMost(_1051493, _1051497, _1051499, _1051501))), 15120 ^ _779999 : [(15123 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1051497, _1051495), _1051501)))], (15121 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1051497, _1051499), _1051495)))]]], (5178 ^ _779999) ^ [_859212, _859214] : [_859214 = _859212, -(c_Set_OBex(_859214) = c_Set_OBex(_859212))], (7015 ^ _779999) ^ [_895259, _895261, _895263, _895265] : [_895259 = _895261, hBOOL(hAPP(hAPP(c_member(_895263), _895261), _895265)), -(hBOOL(hAPP(hAPP(c_member(_895263), _895259), _895265)))], (6977 ^ _779999) ^ [_894628, _894630, _894632] : [hBOOL(hAPP(hAPP(c_member(_894628), _894630), _894632)), -(hAPP(hAPP(c_Set_Oinsert(_894628), _894630), _894632) = _894632)], (43058 ^ _779999) ^ [_1629360, _1629362, _1629364] : [-(c_Nitpick_Oplus__frac(_1629360, _1629362, _1629364) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1629360), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1629360), _1629362), hAPP(c_Nitpick_Odenom(_1629360), _1629364))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1629360), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1629360), tc_Int_Oint), c_Nitpick_Ofrac(_1629360)), 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(_1629360), _1629362))), 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(_1629360), _1629362))))), 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(_1629360), _1629364))), 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(_1629360), _1629364)))))), c_COMBI(tc_Int_Oint))))], (10211 ^ _779999) ^ [_955909, _955911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955909)), hAPP(c_Nat_OSuc, _955911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955909), _955911)))], (36603 ^ _779999) ^ [_1469571, _1469573, _1469575] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1469571, _1469573), _1469575))), _1469571 = 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), _1469575)), _1469573)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469575)), 36610 ^ _779999 : [(36613 ^ _779999) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1469575) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36611 ^ _779999) ^ [] : [-(_1469573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 36614 ^ _779999 : [(36617 ^ _779999) ^ [] : [36618 ^ _779999 : [(36621 ^ _779999) ^ [] : [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), _1469575))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469575)), _1469573))], (36619 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469573)))]], 36626 ^ _779999 : [(36629 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1469573), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469575))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469575)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36627 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469573))]]], (36615 ^ _779999) ^ [] : [_1469573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6945 ^ _779999) ^ [_894054, _894056, _894058, _894060] : [-(hBOOL(hAPP(hAPP(c_member(_894054), _894056), _894058))), -(hBOOL(hAPP(hAPP(c_member(_894054), _894056), _894060))), 6952 ^ _779999 : [(6959 ^ _779999) ^ [] : [_894058 = _894060, -(hAPP(hAPP(c_Set_Oinsert(_894054), _894056), _894058) = hAPP(hAPP(c_Set_Oinsert(_894054), _894056), _894060))], (6953 ^ _779999) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_894054), _894056), _894058) = hAPP(hAPP(c_Set_Oinsert(_894054), _894056), _894060), -(_894058 = _894060)]]], (44472 ^ _779999) ^ [_1667807, _1667809, _1667811, _1667813] : [-(c_List_Oremove1(_1667807, _1667809, c_List_Oremove1(_1667807, _1667811, _1667813)) = c_List_Oremove1(_1667807, _1667811, c_List_Oremove1(_1667807, _1667809, _1667813)))], (4716 ^ _779999) ^ [_851771, _851773, _851775, _851777] : [-(c_Wellfounded_Oaccp(_851777, _851773) = c_Wellfounded_Oaccp(_851775, _851771)), _851777 = _851775, _851773 = _851771], (23636 ^ _779999) ^ [_1221560, _1221562, _1221564] : [class_Orderings_Olinorder(_1221560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1221560), _1221562)), -(_1221562 = c_Orderings_Obot__class_Obot(tc_fun(_1221560, tc_HOL_Obool))), 23647 ^ _779999 : [(23657 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221560), hAPP(c_Finite__Set_Ofold1(_1221560, c_Orderings_Oord__class_Omin(_1221560)), _1221562)), _1221564))), 23658 ^ _779999 : [(23659 ^ _779999) ^ [_1221949] : [hBOOL(hAPP(hAPP(c_member(_1221560), _1221949), _1221562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221560), _1221949), _1221564))]]], (23648 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221560), hAPP(c_Finite__Set_Ofold1(_1221560, c_Orderings_Oord__class_Omin(_1221560)), _1221562)), _1221564)), 23652 ^ _779999 : [(23655 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221560), 23651 ^ [_1221560, _1221562, _1221564]), _1221564)))], (23653 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1221560), 23651 ^ [_1221560, _1221562, _1221564]), _1221562)))]]]]], (8628 ^ _779999) ^ [_927672, _927674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927672), _927674)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927672), _927674) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7751 ^ _779999) ^ [_910349, _910351, _910353, _910355, _910357] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_910349, _910351, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910349)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910349), hAPP(hAPP(c_COMBC(_910349, 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)), _910349), 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)), _910349), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _910353))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _910355))), c_Com_Ocom_OWhile(_910355, _910357)), _910353)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910349), tc_HOL_Obool)))))], (47504 ^ _779999) ^ [_1735210, _1735212, _1735214] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1735210), tc_List_Olist(_1735210)), c_List_Opartition(_1735210, _1735212, _1735214)) = hAPP(c_List_Ofilter(_1735210, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1735210, c_fNot), _1735212)), _1735214))], (43783 ^ _779999) ^ [_1650654, _1650656, _1650658] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1650654, tc_HOL_Obool)), hAPP(c_List_Oset(_1650654), _1650656)), hAPP(c_List_Oset(_1650654), hAPP(hAPP(c_List_Olist_OCons(_1650654), _1650658), _1650656)))))], (10892 ^ _779999) ^ [_968436, _968438, _968440, _968442] : [hBOOL(hAPP(hAPP(c_member(_968436), _968438), _968440)), hBOOL(hAPP(hAPP(c_member(_968436), _968438), _968442)), -(hBOOL(hAPP(hAPP(c_member(_968436), _968438), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968436, tc_HOL_Obool)), _968440), _968442))))], (8552 ^ _779999) ^ [_926276] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _926276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15871 ^ _779999) ^ [_1066163, _1066165, _1066167] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066163), _1066165)), _1066167) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066163), _1066167)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066165), _1066167)))], (40954 ^ _779999) ^ [_1579294, _1579296, _1579298] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579294, _1579294)), hAPP(hAPP(c_Product__Type_OPair(_1579294, _1579294), _1579296), _1579296)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579294, _1579294), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1579298))))], (37592 ^ _779999) ^ [_1493832, _1493834, _1493836, _1493838] : [-(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), _1493832), _1493834)), 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), _1493836), _1493838)), 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), _1493832), _1493836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493834), _1493838))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (18633 ^ _779999) ^ [_1119615, _1119617, _1119619] : [class_Groups_Ocomm__monoid__add(_1119615), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1119615), _1119617), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1119619))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119615), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1119615), _1119617), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1119619))), hAPP(_1119617, _1119619)))], (48643 ^ _779999) ^ [_1759164, _1759166, _1759168, _1759170] : [-(hBOOL(hAPP(_1759164, _1759166))), -(c_List_OtakeWhile(_1759168, _1759164, hAPP(hAPP(c_List_Olist_OCons(_1759168), _1759166), _1759170)) = c_List_Olist_ONil(_1759168))], (27083 ^ _779999) ^ [_1289539, _1289541, _1289543, _1289545, _1289547] : [class_Fields_Ofield(_1289539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1289541), _1289543)), -(hAPP(_1289545, _1289547) = c_Groups_Ozero__class_Ozero(_1289539)), 27094 ^ _779999 : [(27101 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1289541), _1289547), _1289543))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289541, _1289539), _1289545), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289541, tc_HOL_Obool)), _1289543), hAPP(hAPP(c_Set_Oinsert(_1289541), _1289547), c_Orderings_Obot__class_Obot(tc_fun(_1289541, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289541, _1289539), _1289545), _1289543))], (27095 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1289541), _1289547), _1289543)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289541, _1289539), _1289545), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289541, tc_HOL_Obool)), _1289543), hAPP(hAPP(c_Set_Oinsert(_1289541), _1289547), c_Orderings_Obot__class_Obot(tc_fun(_1289541, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289539), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1289541, _1289539), _1289545), _1289543)), hAPP(_1289545, _1289547)))]]], (20574 ^ _779999) ^ [_1153757, _1153759] : [c_Nat__Transfer_Ois__nat(_1153757), c_Nat__Transfer_Onat__set(_1153759), 20581 ^ _779999 : [(20588 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1153757)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153759))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1153757), _1153759)))], (20582 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1153757), _1153759)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1153757)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153759))))]]], (18851 ^ _779999) ^ [_1124037, _1124039] : [_1124037 = _1124039, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124039))], (45724 ^ _779999) ^ [_1695762, _1695764, _1695766, _1695768] : [-(hAPP(c_List_Ofoldl(_1695762, _1695764, _1695766, _1695768), c_List_Olist_ONil(_1695764)) = _1695768)], (396 ^ _779999) ^ [_786045, _786047, _786049, _786051, _786053, _786055] : [-(c_Hoare__Mirabelle_Otriple__valid(_786053, _786049, _786045)), c_Hoare__Mirabelle_Otriple__valid(_786055, _786051, _786047), _786055 = _786053, _786051 = _786049, _786047 = _786045], (46231 ^ _779999) ^ [_1705848, _1705850, _1705852, _1705854, _1705856] : [class_Rings_Osemiring__0(_1705848), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705848), hAPP(hAPP(c_List_Omap(_1705850, _1705848), hAPP(hAPP(c_COMBB(_1705848, _1705848, _1705850), hAPP(c_Groups_Otimes__class_Otimes(_1705848), _1705852)), _1705854)), _1705856)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1705848), _1705852), hAPP(c_List_Omonoid__add__class_Olistsum(_1705848), hAPP(hAPP(c_List_Omap(_1705850, _1705848), _1705854), _1705856))))], (8838 ^ _779999) ^ [_931812, _931814, _931816, _931818] : [-(c_Fun_Ofun__upd(_931812, _931814, _931816, _931818, hAPP(_931816, _931818)) = _931816)], (12934 ^ _779999) ^ [_1009470, _1009472, _1009474, _1009476, _1009478] : [class_Groups_Ocomm__monoid__add(_1009470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009472), _1009474)), hBOOL(hAPP(hAPP(c_member(_1009472), _1009476), _1009474)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009472, _1009470), _1009478), _1009474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009470), hAPP(_1009478, _1009476)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009472, _1009470), _1009478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009472, tc_HOL_Obool)), _1009474), hAPP(hAPP(c_Set_Oinsert(_1009472), _1009476), c_Orderings_Obot__class_Obot(tc_fun(_1009472, tc_HOL_Obool)))))))], (33115 ^ _779999) ^ [_1400519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400519), 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), _1400519)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30748 ^ _779999) ^ [_1356361, _1356363, _1356365] : [class_Divides_Osemiring__div(_1356361), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356361), c_Divides_Odiv__class_Omod(_1356361, _1356363, _1356365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356361), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1356361), _1356363), _1356365)), _1356365)) = _1356363)], (37409 ^ _779999) ^ [_1489134, _1489136, _1489138, _1489140] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1489134), _1489136)), 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)), _1489138), _1489134)), 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)), _1489140), _1489136)), 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)), _1489138), _1489140)), _1489136)), c_FunDef_Omax__weak)))], (17045 ^ _779999) ^ [_1088328, _1088330, _1088332, _1088334] : [class_Rings_Olinordered__semiring__strict(_1088328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088328), _1088330), _1088332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088328), _1088334), _1088332))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088328), c_Groups_Ozero__class_Ozero(_1088328)), _1088332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088328), _1088330), _1088334)))], (51966 ^ _779999) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (15081 ^ _779999) ^ [_1050763, _1050765, _1050767, _1050769, _1050771, _1050773] : [hBOOL(hAPP(hAPP(c_member(_1050763), _1050765), c_SetInterval_Oord_OatLeastLessThan(_1050763, _1050767, _1050769, _1050771, _1050773))), 15084 ^ _779999 : [(15087 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1050769, _1050765), _1050773)))], (15085 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1050767, _1050771), _1050765)))]]], (33923 ^ _779999) ^ [_1414728, _1414730] : [_1414728 = _1414730, -(c_Int_OBit0(_1414728) = c_Int_OBit0(_1414730))], (48468 ^ _779999) ^ [_1755472, _1755474, _1755476, _1755478] : [_1755474 = hAPP(hAPP(c_List_Oappend(_1755472), hAPP(c_List_Orev(_1755472), _1755478)), hAPP(hAPP(c_List_Olist_OCons(_1755472), _1755476), c_List_Olist_ONil(_1755472))), -(hAPP(c_List_Orev(_1755472), _1755474) = hAPP(hAPP(c_List_Olist_OCons(_1755472), _1755476), _1755478))], (52300 ^ _779999) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (38560 ^ _779999) ^ [_1520106, _1520108, _1520110, _1520112, _1520114, _1520116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520106, _1520108)), hAPP(hAPP(c_Product__Type_OPair(_1520106, _1520108), _1520110), _1520112)), hAPP(hAPP(c_Product__Type_OSigma(_1520106, _1520108), _1520114), _1520116))), -(hBOOL(hAPP(hAPP(c_member(_1520108), _1520112), hAPP(_1520116, _1520110))))], (45181 ^ _779999) ^ [_1683012, _1683014, _1683016, _1683018] : [hBOOL(hAPP(hAPP(c_member(_1683012), _1683014), hAPP(c_List_Oset(_1683012), _1683016))), -(c_List_Oremove1(_1683012, _1683014, hAPP(hAPP(c_List_Oappend(_1683012), _1683016), _1683018)) = hAPP(hAPP(c_List_Oappend(_1683012), c_List_Oremove1(_1683012, _1683014, _1683016)), _1683018))], (31819 ^ _779999) ^ [_1376562, _1376564, _1376566, _1376568] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376562), hAPP(c_Int_Onumber__class_Onumber__of(_1376562), _1376564)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376562), _1376566), _1376568)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376562), hAPP(c_Int_Onumber__class_Onumber__of(_1376562), _1376564)), _1376566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376562), hAPP(c_Int_Onumber__class_Onumber__of(_1376562), _1376564)), _1376568))), class_Int_Onumber(_1376562), class_Rings_Osemiring(_1376562)], (43138 ^ _779999) ^ [_1631134, _1631136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 43139 ^ [_1631134, _1631136]), hAPP(_1631134, 43139 ^ [_1631134, _1631136]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1631134)), _1631136)))))], (28318 ^ _779999) ^ [_1312411, _1312413, _1312415] : [class_Fields_Olinordered__field__inverse__zero(_1312411), -(hAPP(c_Groups_Oabs__class_Oabs(_1312411), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312411), _1312413), _1312415)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312411), hAPP(c_Groups_Oabs__class_Oabs(_1312411), _1312413)), hAPP(c_Groups_Oabs__class_Oabs(_1312411), _1312415)))], (34629 ^ _779999) ^ [_1427433] : [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, _1427433, 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, _1427433, 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))], (22952 ^ _779999) ^ [_1207506, _1207508] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207506, tc_fun(_1207506, tc_HOL_Obool)), _1207508), hAPP(hAPP(c_COMBC(_1207506, tc_fun(_1207506, tc_HOL_Obool), tc_fun(_1207506, tc_HOL_Obool)), c_Set_Oinsert(_1207506)), c_Orderings_Obot__class_Obot(tc_fun(_1207506, tc_HOL_Obool)))) = _1207508)], (49598 ^ _779999) ^ [_1780485, _1780487, _1780489, _1780491] : [c_List_Olist__ex1(_1780485, _1780487, hAPP(hAPP(c_List_Olist_OCons(_1780485), _1780489), _1780491)), 49601 ^ _779999 : [(49608 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1780487, _1780489))), -(c_List_Olist__ex1(_1780485, _1780487, _1780491))], (49602 ^ _779999) ^ [] : [hBOOL(hAPP(_1780487, _1780489)), -(c_List_Olist__all(_1780485, hAPP(hAPP(c_COMBS(_1780485, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780485), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1780485), c_fNot), _1780487))), hAPP(c_fequal, _1780489)), _1780491))]]], (52310 ^ _779999) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (39960 ^ _779999) ^ [_1554900, _1554902, _1554904] : [39962 ^ _779999 : [(39965 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1554900), 39961 ^ [_1554900, _1554902, _1554904]), c_Wellfounded_Oacc(_1554900, _1554904)))], (39963 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1554900, _1554900)), hAPP(hAPP(c_Product__Type_OPair(_1554900, _1554900), 39961 ^ [_1554900, _1554902, _1554904]), _1554902)), _1554904)))]], -(hBOOL(hAPP(hAPP(c_member(_1554900), _1554902), c_Wellfounded_Oacc(_1554900, _1554904))))], (33631 ^ _779999) ^ [_1408921, _1408923] : [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(_1408921))), 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)), _1408923))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408921) = hAPP(c_Nat_OSuc, _1408923))], (9973 ^ _779999) ^ [_951963, _951965, _951967, _951969] : [9975 ^ _779999 : [(9979 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_951963), 9977 ^ [_951963, _951965, _951967, _951969]), _951969)))], (9981 ^ _779999) ^ [] : [-(hAPP(_951967, 9974 ^ [_951963, _951965, _951967, _951969]) = hAPP(_951967, 9977 ^ [_951963, _951965, _951967, _951969]))], (9983 ^ _779999) ^ [] : [9974 ^ [_951963, _951965, _951967, _951969] = 9977 ^ [_951963, _951965, _951967, _951969]], (9976 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_951963), 9974 ^ [_951963, _951965, _951967, _951969]), _951969)))]], -(c_Fun_Oinj__on(_951963, _951965, _951967, _951969))], (9586 ^ _779999) ^ [_942936, _942938, _942940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942936, tc_HOL_Obool)), _942938), _942940))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942936, tc_HOL_Obool)), _942938), _942940)), -(_942938 = _942940)], (18381 ^ _779999) ^ [_1114678, _1114680, _1114682, _1114684] : [class_Rings_Osemiring__1(_1114678), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1114678), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1114680, tc_Nat_Onat), _1114682), _1114684)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1114680, _1114678), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1114678, _1114680), c_Nat_Osemiring__1__class_Oof__nat(_1114678)), _1114682)), _1114684))], (49029 ^ _779999) ^ [_1767084, _1767086, _1767088, _1767090] : [-(c_List_Omaps(_1767084, _1767086, _1767088, _1767090) = c_List_Oconcat(_1767086, hAPP(hAPP(c_List_Omap(_1767084, tc_List_Olist(_1767086)), _1767088), _1767090)))], (21437 ^ _779999) ^ [_1170320, _1170322, _1170324] : [-(hAPP(c_Finite__Set_Ofold1(_1170320, _1170322), _1170324) = c_HOL_OThe(_1170320, c_Finite__Set_Ofold1Set(_1170320, _1170322, _1170324)))], (45430 ^ _779999) ^ [_1689301, _1689303, _1689305, _1689307] : [-(hAPP(hAPP(c_List_Odrop(_1689301), _1689303), hAPP(hAPP(c_List_Oappend(_1689301), _1689305), _1689307)) = hAPP(hAPP(c_List_Oappend(_1689301), hAPP(hAPP(c_List_Odrop(_1689301), _1689303), _1689305)), hAPP(hAPP(c_List_Odrop(_1689301), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1689303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689301)), _1689305))), _1689307)))], (1944 ^ _779999) ^ [_807407, _807409] : [-(class_Int_Onumber(_807407)), _807409 = _807407, class_Int_Onumber(_807409)], (47286 ^ _779999) ^ [_1729724, _1729726, _1729728, _1729730] : [class_Orderings_Olinorder(_1729724), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729726)), c_List_Olinorder__class_Osort__key(_1729726, _1729724, _1729728, _1729730)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729726)), _1729730))], (21279 ^ _779999) ^ [_1167368, _1167370, _1167372] : [class_Orderings_Olinorder(_1167368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167368), _1167370), _1167372)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1167368, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1167368, _1167370, _1167372)), hAPP(c_SetInterval_Oord__class_OatLeast(_1167368), _1167372)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1167368), _1167370))], (21161 ^ _779999) ^ [_1164862, _1164864, _1164866, _1164868, _1164870] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1164862, _1164864, hAPP(hAPP(c_Set_Oinsert(_1164862), _1164866), _1164868)), _1164870))), 21162 ^ _779999 : [(21163 ^ _779999) ^ [_1164966, _1164968] : [hAPP(hAPP(c_Set_Oinsert(_1164862), _1164866), _1164868) = hAPP(hAPP(c_Set_Oinsert(_1164862), _1164968), _1164966), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1164862, _1164862, _1164864, _1164968, _1164966), _1164870)), -(hBOOL(hAPP(hAPP(c_member(_1164862), _1164968), _1164966)))]]], (52298 ^ _779999) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (22383 ^ _779999) ^ [_1194052, _1194054] : [class_Orderings_Olinorder(_1194052), -(c_Big__Operators_Olinorder__class_OMax(_1194052, hAPP(hAPP(c_Set_Oinsert(_1194052), _1194054), c_Orderings_Obot__class_Obot(tc_fun(_1194052, tc_HOL_Obool)))) = _1194054)], (33775 ^ _779999) ^ [_1412085] : [class_Rings_Osemiring__1(_1412085), c_Int_Oiszero(_1412085, c_Groups_Oone__class_Oone(_1412085))], (44444 ^ _779999) ^ [_1667326, _1667328, _1667330, _1667332] : [-(_1667326 = _1667328), 44447 ^ _779999 : [(44454 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1667330), _1667326), hAPP(c_List_Oset(_1667330), _1667332))), -(hBOOL(hAPP(hAPP(c_member(_1667330), _1667326), hAPP(c_List_Oset(_1667330), c_List_Oremove1(_1667330, _1667328, _1667332)))))], (44448 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1667330), _1667326), hAPP(c_List_Oset(_1667330), c_List_Oremove1(_1667330, _1667328, _1667332)))), -(hBOOL(hAPP(hAPP(c_member(_1667330), _1667326), hAPP(c_List_Oset(_1667330), _1667332))))]]], (5532 ^ _779999) ^ [_864699, _864701, _864703, _864705, _864707, _864709, _864711, _864713] : [-(c_Product__Type_Ocurry(_864713, _864709, _864705, _864701) = c_Product__Type_Ocurry(_864711, _864707, _864703, _864699)), _864713 = _864711, _864709 = _864707, _864705 = _864703, _864701 = _864699], (9700 ^ _779999) ^ [_944888, _944890, _944892, _944894] : [hBOOL(hAPP(hAPP(c_member(_944888), _944890), _944892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944888, tc_HOL_Obool)), _944892), hAPP(_944894, _944892))), -(hBOOL(hAPP(hAPP(c_member(_944888), _944890), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_944888, tc_HOL_Obool), _944894))))], (43731 ^ _779999) ^ [_1649223, _1649225, _1649227] : [-(c_List_Osublist(_1649223, _1649225, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1649227)) = hAPP(hAPP(c_List_Otake(_1649223), _1649227), _1649225))], (34891 ^ _779999) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7731 ^ _779999) ^ [_909808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909808)), _909808))], (15741 ^ _779999) ^ [_1063974, _1063976] : [class_Groups_Omonoid__mult(_1063974), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063974), _1063976), c_Groups_Oone__class_Oone(_1063974)) = _1063976)], (48747 ^ _779999) ^ [_1761350, _1761352, _1761354] : [c_List_OdropWhile(_1761350, _1761352, _1761354) = c_List_Olist_ONil(_1761350), 48750 ^ _779999 : [(48751 ^ _779999) ^ [_1761441] : [hBOOL(hAPP(hAPP(c_member(_1761350), _1761441), hAPP(c_List_Oset(_1761350), _1761354))), -(hBOOL(hAPP(_1761352, _1761441)))]]], (37053 ^ _779999) ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609, _1480611, _1480613, _1480615, _1480617, _1480619] : [c_Equiv__Relations_Oequiv(_1480599, _1480601, _1480603), c_Equiv__Relations_Oequiv(_1480605, _1480607, _1480609), c_Equiv__Relations_Ocongruent2(_1480599, _1480605, tc_fun(_1480611, tc_HOL_Obool), _1480603, _1480609, _1480613), hBOOL(hAPP(hAPP(c_member(tc_fun(_1480599, tc_HOL_Obool)), _1480615), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1480599), _1480601), _1480603))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1480605, tc_HOL_Obool)), _1480617), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1480605), _1480607), _1480609))), 37075 ^ _779999 : [(37081 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1480611, tc_HOL_Obool)), hAPP(hAPP(_1480613, 37074 ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609, _1480611, _1480613, _1480615, _1480617, _1480619]), 37077 ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609, _1480611, _1480613, _1480615, _1480617, _1480619])), _1480619))], (37079 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480605), 37077 ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609, _1480611, _1480613, _1480615, _1480617, _1480619]), _1480607)))], (37076 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480599), 37074 ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609, _1480611, _1480613, _1480615, _1480617, _1480619]), _1480601)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1480611, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480599, tc_fun(_1480611, tc_HOL_Obool)), _1480615), hAPP(hAPP(c_COMBB(tc_fun(_1480605, tc_fun(_1480611, tc_HOL_Obool)), tc_fun(_1480611, tc_HOL_Obool), _1480599), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480605, tc_fun(_1480611, tc_HOL_Obool)), _1480617)), _1480613))), _1480619)))], (20321 ^ _779999) ^ [_1149795, _1149797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149797)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149795), _1149797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1149795)), hAPP(c_Int_Onat, _1149797)))], (35626 ^ _779999) ^ [_1450969, _1450971, _1450973] : [hBOOL(hAPP(_1450969, 35627 ^ [_1450969, _1450971, _1450973])), 35630 ^ _779999 : [(35631 ^ _779999) ^ [_1451080, _1451082] : [-(hBOOL(hAPP(_1450969, hAPP(hAPP(c_Product__Type_OPair(_1450971, _1450973), _1451082), _1451080))))]]], (8320 ^ _779999) ^ [_921448, _921450, _921452, _921454] : [-(hBOOL(hAPP(hAPP(c_member(_921448), _921450), _921452))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921448, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_921448), _921450), _921454)), _921452) = hAPP(hAPP(c_Set_Oinsert(_921448), _921450), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921448, tc_HOL_Obool)), _921454), _921452)))], (37130 ^ _779999) ^ [_1482641, _1482643] : [_1482641 = _1482643, -(c_Code__Numeral_OSuc__code__numeral(_1482641) = c_Code__Numeral_OSuc__code__numeral(_1482643))], (21004 ^ _779999) ^ [_1161505, _1161507, _1161509] : [class_Rings_Olinordered__idom(_1161505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161505), c_Groups_Ozero__class_Ozero(_1161505)), _1161507)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161505), hAPP(c_Groups_Oabs__class_Oabs(_1161505), _1161509)), _1161507) = hAPP(c_Groups_Oabs__class_Oabs(_1161505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161505), _1161509), _1161507)))], (17101 ^ _779999) ^ [_1089404, _1089406, _1089408, _1089410] : [class_Rings_Olinordered__semiring__strict(_1089404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089404), _1089406), _1089408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089404), _1089406), _1089410))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089404), c_Groups_Ozero__class_Ozero(_1089404)), _1089406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089404), _1089408), _1089410)))], (52302 ^ _779999) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (31605 ^ _779999) ^ [_1372517, _1372519, _1372521, _1372523] : [-(hAPP(c_Relation_OImage(_1372517, _1372519, _1372521), _1372523) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372517, tc_fun(_1372519, tc_HOL_Obool)), _1372523), hAPP(hAPP(c_COMBB(tc_fun(_1372517, tc_HOL_Obool), tc_fun(_1372519, tc_HOL_Obool), _1372517), c_Relation_OImage(_1372517, _1372519, _1372521)), hAPP(hAPP(c_COMBC(_1372517, tc_fun(_1372517, tc_HOL_Obool), tc_fun(_1372517, tc_HOL_Obool)), c_Set_Oinsert(_1372517)), c_Orderings_Obot__class_Obot(tc_fun(_1372517, tc_HOL_Obool))))))], (21187 ^ _779999) ^ [_1165616, _1165618, _1165620] : [21189 ^ _779999 : [(21192 ^ _779999) ^ [] : [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(_1165618, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21188 ^ [_1165616, _1165618, _1165620]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1165618, 21188 ^ [_1165616, _1165618, _1165620])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21190 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21188 ^ [_1165616, _1165618, _1165620]), _1165616)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1165618, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1165620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1165620), hAPP(_1165618, _1165616))), 21202 ^ _779999 : [(21205 ^ _779999) ^ [] : [-(hAPP(_1165618, 21201 ^ [_1165616, _1165618, _1165620]) = _1165620)], (21203 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21201 ^ [_1165616, _1165618, _1165620]), _1165616)))]]], (46173 ^ _779999) ^ [_1704429, _1704431, _1704433] : [c_Fun_Oinj__on(_1704429, _1704431, _1704433, c_Orderings_Otop__class_Otop(tc_fun(_1704429, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1704429), tc_List_Olist(_1704431), hAPP(c_List_Omap(_1704429, _1704431), _1704433), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1704429), tc_HOL_Obool))))], (7534 ^ _779999) ^ [_906363, _906365, _906367, _906369, _906371, _906373, _906375] : [c_Hoare__Mirabelle_Ohoare__derivs(_906363, _906365, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906363)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906363), _906367), _906369), _906371)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906363), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_906363, _906365, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906363)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906363), _906371), _906373), _906375)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906363), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_906363, _906365, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906363)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906363), _906367), c_Com_Ocom_OSemi(_906369, _906373)), _906375)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906363), tc_HOL_Obool)))))], (51706 ^ _779999) ^ [_1826658, _1826660, _1826662, _1826664, _1826666] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1826658, _1826660, tc_HOL_Obool, _1826662), _1826664), _1826666)), -(hBOOL(hAPP(_1826662, hAPP(hAPP(c_Product__Type_OPair(_1826658, _1826660), _1826664), _1826666))))], (30082 ^ _779999) ^ [_1343768, _1343770, _1343772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1343768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1343768), _1343770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1343772), _1343770)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1343772), _1343768))))], (10942 ^ _779999) ^ [_969131, _969133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969131), _969133)), _969133 = _969131], (52190 ^ _779999) ^ [_1832379] : [class_Enum_Oenum(_1832379), -(class_Enum_Oenum(tc_Option_Ooption(_1832379)))], (10275 ^ _779999) ^ [_956901, _956903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956901), hAPP(c_Nat_OSuc, _956903))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956901), _956903))), -(_956901 = _956903)], (31166 ^ _779999) ^ [_1364060, _1364062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1364060), _1364062)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364060, _1364062) = _1364060)], (18697 ^ _779999) ^ [_1121031] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121031)) = 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), _1121031))))], (43335 ^ _779999) ^ [_1637799, _1637801, _1637803, _1637805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637799), tc_List_Olist(_1637799))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637799), tc_List_Olist(_1637799)), _1637801), _1637803)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637799), c_List_Olistrel1(_1637799, _1637805)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637799)), _1637801) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637799)), _1637803))], (43134 ^ _779999) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47342 ^ _779999) ^ [_1730932, _1730934, _1730936, _1730938, _1730940] : [class_Orderings_Olinorder(_1730932), -(c_List_Olinorder__class_Osort__key(_1730934, _1730932, _1730936, hAPP(hAPP(c_List_Olist_OCons(_1730934), _1730938), _1730940)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1730934, _1730932, _1730936), _1730938), c_List_Olinorder__class_Osort__key(_1730934, _1730932, _1730936, _1730940)))], (12968 ^ _779999) ^ [_1010389, _1010391, _1010393] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010389), _1010391)), hBOOL(hAPP(hAPP(c_member(_1010389), _1010393), _1010391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1010389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010389, tc_HOL_Obool)), _1010391), hAPP(hAPP(c_Set_Oinsert(_1010389), _1010393), c_Orderings_Obot__class_Obot(tc_fun(_1010389, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1010389), _1010391))))], (16749 ^ _779999) ^ [_1083011, _1083013, _1083015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083013), _1083015)), -(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, _1083011)), _1083013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1083011)), _1083015))))], (20968 ^ _779999) ^ [_1160703, _1160705, _1160707] : [class_Groups_Oordered__ab__group__add__abs(_1160703), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160703), hAPP(c_Groups_Oabs__class_Oabs(_1160703), _1160705)), hAPP(c_Groups_Oabs__class_Oabs(_1160703), _1160707))), hAPP(c_Groups_Oabs__class_Oabs(_1160703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160703), _1160705), _1160707)))))], (19035 ^ _779999) ^ [_1127020, _1127022] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127020), _1127022) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127022), _1127020))], (19512 ^ _779999) ^ [_1135669] : [19513 ^ _779999 : [(19514 ^ _779999) ^ [_1135726] : [hBOOL(hAPP(_1135669, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1135726)))]], 19516 ^ _779999 : [(19519 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1135669, 19515 ^ [_1135669])))], (19517 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19515 ^ [_1135669])))]]], (41992 ^ _779999) ^ [_1604080, _1604082, _1604084, _1604086, _1604088, _1604090] : [hBOOL(hAPP(hAPP(c_member(_1604080), _1604082), _1604084)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604080, tc_fun(_1604086, tc_HOL_Obool)), _1604084), hAPP(hAPP(c_COMBB(tc_fun(_1604086, tc_HOL_Obool), tc_fun(_1604086, tc_HOL_Obool), _1604080), hAPP(c_Set_Oinsert(_1604086), _1604088)), _1604090)) = hAPP(hAPP(c_Set_Oinsert(_1604086), _1604088), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604080, tc_fun(_1604086, tc_HOL_Obool)), _1604084), _1604090)))], (41270 ^ _779999) ^ [_1587448, _1587450, _1587452, _1587454] : [-(hAPP(c_Finite__Set_Ofold__image(_1587448, _1587450, _1587452), _1587454) = c_Finite__Set_Ofold(_1587450, _1587448, hAPP(hAPP(c_COMBB(_1587448, tc_fun(_1587448, _1587448), _1587450), _1587452), _1587454)))], (47398 ^ _779999) ^ [_1732725, _1732727, _1732729] : [-(c_Enum_On__lists(_1732725, hAPP(c_Nat_OSuc, _1732727), _1732729) = c_List_Oconcat(tc_List_Olist(_1732725), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732725), tc_List_Olist(tc_List_Olist(_1732725))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732725), tc_List_Olist(_1732725), tc_List_Olist(tc_List_Olist(_1732725))), hAPP(hAPP(c_COMBB(tc_fun(_1732725, tc_List_Olist(_1732725)), tc_fun(tc_List_Olist(_1732725), tc_List_Olist(tc_List_Olist(_1732725))), tc_List_Olist(_1732725)), c_List_Omap(_1732725, tc_List_Olist(_1732725))), hAPP(c_COMBC(_1732725, tc_List_Olist(_1732725), tc_List_Olist(_1732725)), c_List_Olist_OCons(_1732725)))), _1732729)), c_Enum_On__lists(_1732725, _1732727, _1732729))))], (49732 ^ _779999) ^ [_1783249, _1783251] : [-(hAPP(c_New__DSequence_Opos__empty(_1783249), _1783251) = c_Lazy__Sequence_Oempty(_1783249))], (6649 ^ _779999) ^ [_888347, _888349, _888351, _888353, _888355] : [c_Hoare__Mirabelle_Otriple__valid(_888347, hAPP(c_Nat_OSuc, _888349), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888347), _888351), hAPP(c_Com_Ocom_OBODY, _888353)), _888355)), -(c_Hoare__Mirabelle_Otriple__valid(_888347, _888349, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888347), _888351), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888353))), _888355)))], (50167 ^ _779999) ^ [_1792743, _1792745, _1792747, _1792749, _1792751, _1792753] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1792743, _1792745, _1792747, _1792749, c_Lazy__Sequence_Olazy__sequence_OInsert(_1792745, _1792751, _1792753)) = hAPP(hAPP(_1792749, _1792751), _1792753))], (16573 ^ _779999) ^ [_1079471, _1079473] : [hAPP(_1079471, 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), _1079471), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1079473)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1079471), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1079473)))], (35948 ^ _779999) ^ [_1456968, _1456970] : [_1456968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1456968, _1456970) = 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)))], (28476 ^ _779999) ^ [_1315316, _1315318, _1315320] : [class_Fields_Olinordered__field(_1315316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315316), c_Groups_Ozero__class_Ozero(_1315316)), _1315318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315316), _1315320), c_Groups_Ozero__class_Ozero(_1315316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315316), _1315318), _1315320)), c_Groups_Ozero__class_Ozero(_1315316))))], (44790 ^ _779999) ^ [_1673694, _1673696, _1673698, _1673700, _1673702] : [-(hAPP(hAPP(c_List_Ozip(_1673694, _1673696), _1673698), hAPP(hAPP(c_List_Olist_OCons(_1673696), _1673700), _1673702)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1673694, _1673696)), _1673694, c_List_Olist_ONil(tc_prod(_1673694, _1673696)), hAPP(hAPP(c_COMBC(_1673694, tc_fun(tc_List_Olist(_1673694), tc_List_Olist(tc_prod(_1673694, _1673696))), tc_fun(tc_List_Olist(_1673694), tc_List_Olist(tc_prod(_1673694, _1673696)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1673694, _1673696)), tc_List_Olist(tc_prod(_1673694, _1673696))), tc_fun(tc_fun(tc_List_Olist(_1673694), tc_List_Olist(tc_prod(_1673694, _1673696))), tc_fun(tc_List_Olist(_1673694), tc_List_Olist(tc_prod(_1673694, _1673696)))), _1673694), c_COMBB(tc_List_Olist(tc_prod(_1673694, _1673696)), tc_List_Olist(tc_prod(_1673694, _1673696)), tc_List_Olist(_1673694))), hAPP(hAPP(c_COMBB(tc_prod(_1673694, _1673696), tc_fun(tc_List_Olist(tc_prod(_1673694, _1673696)), tc_List_Olist(tc_prod(_1673694, _1673696))), _1673694), c_List_Olist_OCons(tc_prod(_1673694, _1673696))), hAPP(hAPP(c_COMBC(_1673694, _1673696, tc_prod(_1673694, _1673696)), c_Product__Type_OPair(_1673694, _1673696)), _1673700)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1673694), tc_List_Olist(_1673696), tc_List_Olist(tc_prod(_1673694, _1673696))), c_List_Ozip(_1673694, _1673696)), _1673702))), _1673698))], (40120 ^ _779999) ^ [_1558767, _1558769] : [c_Wellfounded_Owf(_1558767, _1558769), -(c_Wellfounded_Owf(_1558767, c_Transitive__Closure_Otrancl(_1558767, _1558769)))], (11526 ^ _779999) ^ [_981503, _981505, _981507, _981509] : [hBOOL(hAPP(hAPP(c_member(_981503), _981505), _981507)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981503, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_981503), _981505), _981509)), _981507) = hAPP(hAPP(c_Set_Oinsert(_981503), _981505), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981503, tc_HOL_Obool)), _981509), _981507)))], (47451 ^ _779999) ^ [_1734146, _1734148, _1734150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734146, tc_HOL_Obool)), hAPP(c_List_Oset(_1734146), hAPP(c_List_Ofilter(_1734146, _1734148), _1734150))), hAPP(c_List_Oset(_1734146), _1734150))))], (7193 ^ _779999) ^ [_898708, _898710, _898712, _898714, _898716] : [-(hAPP(c_Set_Oimage(_898708, _898710, _898712), hAPP(hAPP(c_Set_Oinsert(_898708), _898714), _898716)) = hAPP(hAPP(c_Set_Oinsert(_898710), hAPP(_898712, _898714)), hAPP(c_Set_Oimage(_898708, _898710, _898712), _898716)))], (39103 ^ _779999) ^ [_1534748, _1534750] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1534748, _1534748)), _1534750)), c_Wellfounded_Oacyclic(_1534748, _1534750), -(c_Wellfounded_Owf(_1534748, _1534750))], (10727 ^ _779999) ^ [_964735, _964737, _964739, _964741, _964743] : [class_Groups_Oab__group__add(_964735), hBOOL(hAPP(c_Finite__Set_Ofinite(_964737), _964739)), 10734 ^ _779999 : [(10741 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_964737), _964741), _964739))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964737, _964735), _964743), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964737, tc_HOL_Obool)), _964739), hAPP(hAPP(c_Set_Oinsert(_964737), _964741), c_Orderings_Obot__class_Obot(tc_fun(_964737, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964737, _964735), _964743), _964739))], (10735 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_964737), _964741), _964739)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964737, _964735), _964743), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964737, tc_HOL_Obool)), _964739), hAPP(hAPP(c_Set_Oinsert(_964737), _964741), c_Orderings_Obot__class_Obot(tc_fun(_964737, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_964735), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964737, _964735), _964743), _964739)), hAPP(_964743, _964741)))]]], (28386 ^ _779999) ^ [_1313678, _1313680, _1313682] : [class_Fields_Olinordered__field__inverse__zero(_1313678), 28389 ^ _779999 : [(28404 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313678), _1313680), _1313682)))), 28405 ^ _779999 : [(28412 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), _1313680), c_Groups_Ozero__class_Ozero(_1313678))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), _1313682), c_Groups_Ozero__class_Ozero(_1313678)))], (28406 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), _1313680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), _1313682))]]], (28390 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313678), _1313680), _1313682))), 28395 ^ _779999 : [(28398 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), _1313682)))], (28396 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), c_Groups_Ozero__class_Ozero(_1313678)), _1313680)))]], 28399 ^ _779999 : [(28402 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), _1313682), c_Groups_Ozero__class_Ozero(_1313678))))], (28400 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313678), _1313680), c_Groups_Ozero__class_Ozero(_1313678))))]]]]], (6621 ^ _779999) ^ [_887391, _887393, _887395, _887397, _887399, _887401] : [c_Hoare__Mirabelle_Ohoare__derivs(_887391, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_887391), tc_HOL_Obool)), _887393), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_887391), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391))), hAPP(hAPP(c_COMBB(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_887391)), _887395)), c_Com_Ocom_OBODY)), _887397)), _887399)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_887391), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391))), hAPP(hAPP(c_COMBB(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_887391, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_887391))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_887391)), _887395)), 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))), _887397)), _887399)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _887401), _887399)), -(c_Hoare__Mirabelle_Ohoare__derivs(_887391, _887393, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_887391)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887391), hAPP(_887395, _887401)), hAPP(c_Com_Ocom_OBODY, _887401)), hAPP(_887397, _887401))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_887391), tc_HOL_Obool)))))], (9038 ^ _779999) ^ [_934540, _934542, _934544, _934546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934540, tc_HOL_Obool)), _934542), _934544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934540, tc_HOL_Obool)), _934544), _934546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934540, tc_HOL_Obool)), _934542), _934546)))], (44622 ^ _779999) ^ [_1670552, _1670554] : [hAPP(c_List_Oset(_1670552), _1670554) = c_Orderings_Obot__class_Obot(tc_fun(_1670552, tc_HOL_Obool)), -(_1670554 = c_List_Olist_ONil(_1670552))], (6274 ^ _779999) ^ [_880498, _880500, _880502, _880504] : [6278 ^ _779999 : [(6281 ^ _779999) ^ [] : [hBOOL(hAPP(_880504, 6277 ^ [_880498, _880500, _880502, _880504]))], (6279 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880498), 6277 ^ [_880498, _880500, _880502, _880504]), _880500)))]], 6283 ^ _779999 : [(6286 ^ _779999) ^ [] : [hBOOL(hAPP(_880504, 6282 ^ [_880498, _880500, _880502, _880504]))], (6284 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880498), 6282 ^ [_880498, _880500, _880502, _880504]), _880502)))]], 6287 ^ _779999 : [(6288 ^ _779999) ^ [_880831] : [hBOOL(hAPP(hAPP(c_member(_880498), _880831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880498, tc_HOL_Obool)), _880500), _880502))), -(hBOOL(hAPP(_880504, _880831)))]]], (13650 ^ _779999) ^ [_1023534, _1023536, _1023538] : [class_Groups_Oordered__comm__monoid__add(_1023534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023534), c_Groups_Ozero__class_Ozero(_1023534)), _1023536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023534), c_Groups_Ozero__class_Ozero(_1023534)), _1023538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023534), c_Groups_Ozero__class_Ozero(_1023534)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023534), _1023536), _1023538))))], (35173 ^ _779999) ^ [_1439566, _1439568, _1439570, _1439572] : [_1439570 = _1439572, -(hAPP(hAPP(c_COMBC(_1439566, tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_fun(_1439568, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439568, tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_fun(_1439568, tc_HOL_Obool)), _1439566), c_COMBC(_1439568, tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439568, tc_prod(_1439566, _1439568)), tc_fun(_1439568, tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), _1439566), hAPP(c_COMBB(tc_prod(_1439566, _1439568), tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool), _1439568), c_member(tc_prod(_1439566, _1439568)))), c_Product__Type_OPair(_1439566, _1439568)))), _1439570) = hAPP(hAPP(c_COMBC(_1439566, tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_fun(_1439568, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439568, tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_fun(_1439568, tc_HOL_Obool)), _1439566), c_COMBC(_1439568, tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439568, tc_prod(_1439566, _1439568)), tc_fun(_1439568, tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool)), _1439566), hAPP(c_COMBB(tc_prod(_1439566, _1439568), tc_fun(tc_fun(tc_prod(_1439566, _1439568), tc_HOL_Obool), tc_HOL_Obool), _1439568), c_member(tc_prod(_1439566, _1439568)))), c_Product__Type_OPair(_1439566, _1439568)))), _1439572))], (44013 ^ _779999) ^ [_1657667, _1657669, _1657671] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1657667))), c_Enum_On__lists(_1657667, _1657669, _1657671)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657667)), _1657671)), _1657669))], (46704 ^ _779999) ^ [_1716786, _1716788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716786)), hAPP(c_Code__Numeral_Onat__of, _1716788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1716786), _1716788)))], (22117 ^ _779999) ^ [_1188774, _1188776, _1188778, _1188780] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1188774, tc_fun(_1188776, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1188774, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1188776, tc_HOL_Obool), tc_fun(_1188776, tc_HOL_Obool), _1188774), hAPP(c_COMBC(_1188776, tc_fun(_1188776, tc_HOL_Obool), tc_HOL_Obool), c_member(_1188776))), _1188778)), _1188780)), -(hBOOL(hAPP(hAPP(c_member(_1188776), _1188780), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1188774, tc_fun(_1188776, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1188774, tc_HOL_Obool))), _1188778))))], (22770 ^ _779999) ^ [_1202416, _1202418, _1202420, _1202422, _1202424] : [hBOOL(hAPP(hAPP(c_member(_1202416), _1202418), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1202420, tc_fun(_1202416, tc_HOL_Obool)), _1202422), _1202424))), 22774 ^ _779999 : [(22777 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1202416), _1202418), hAPP(_1202424, 22773 ^ [_1202416, _1202418, _1202420, _1202422, _1202424]))))], (22775 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1202420), 22773 ^ [_1202416, _1202418, _1202420, _1202422, _1202424]), _1202422)))]]], (22076 ^ _779999) ^ [_1187761, _1187763] : [22077 ^ _779999 : [(22078 ^ _779999) ^ [_1187825, _1187827] : [_1187763 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1187761, _1187825), 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)), _1187827)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1187761), _1187763)))], (50366 ^ _779999) ^ [_1797370, _1797372] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1797370)), _1797372)), 50370 ^ _779999 : [(50371 ^ _779999) ^ [_1797471] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1797370)), _1797471), _1797372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797370)), _1797471)), 50369 ^ [_1797370, _1797372])))]]], (38535 ^ _779999) ^ [_1519471, _1519473, _1519475, _1519477, _1519479] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519471, _1519473), _1519475), hAPP(hAPP(c_COMBS(_1519471, tc_fun(_1519473, tc_HOL_Obool), tc_fun(_1519473, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519473, tc_HOL_Obool), tc_fun(tc_fun(_1519473, tc_HOL_Obool), tc_fun(_1519473, tc_HOL_Obool)), _1519471), c_Groups_Ominus__class_Ominus(tc_fun(_1519473, tc_HOL_Obool))), _1519477)), _1519479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1519471, _1519473), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519471, _1519473), _1519475), _1519477)), hAPP(hAPP(c_Product__Type_OSigma(_1519471, _1519473), _1519475), _1519479)))], (2852 ^ _779999) ^ [_822351, _822353, _822355, _822357, _822359, _822361, _822363, _822365] : [-(c_Product__Type_Oapfst(_822365, _822361, _822357, _822353) = c_Product__Type_Oapfst(_822363, _822359, _822355, _822351)), _822365 = _822363, _822361 = _822359, _822357 = _822355, _822353 = _822351], (27284 ^ _779999) ^ [_1293559, _1293561, _1293563, _1293565] : [class_Rings_Odivision__ring(_1293559), -(_1293561 = c_Groups_Ozero__class_Ozero(_1293559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293559), _1293563), _1293561) = _1293565, -(_1293563 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293559), _1293565), _1293561))], (52038 ^ _779999) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (37664 ^ _779999) ^ [_1496715, _1496717, _1496719, _1496721] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496715, _1496717, _1496719), _1496721), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1496717, _1496719), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1496715, _1496719), tc_HOL_Obool)))], (40817 ^ _779999) ^ [_1575748, _1575750] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575748, _1575748)), _1575750)), c_Wellfounded_Oacyclic(_1575748, _1575750), -(c_Wellfounded_Owf(_1575748, hAPP(c_Relation_Oconverse(_1575748, _1575748), _1575750)))], (38201 ^ _779999) ^ [_1509831, _1509833, _1509835] : [c_Wellfounded_Owf(_1509831, _1509833), -(c_Wellfounded_Owf(tc_List_Olist(_1509831), hAPP(c_List_Olexn(_1509831, _1509833), _1509835)))], (20728 ^ _779999) ^ [_1156189, _1156191, _1156193] : [class_Orderings_Olinorder(_1156189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156189), _1156191), _1156193)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1156189, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1156189), _1156191)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1156189, _1156191, _1156193)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1156189), _1156193))], (2806 ^ _779999) ^ [_821608, _821610, _821612, _821614, _821616, _821618] : [-(c_Predicate_ODomainP(_821618, _821614, _821610) = c_Predicate_ODomainP(_821616, _821612, _821608)), _821618 = _821616, _821614 = _821612, _821610 = _821608], (24568 ^ _779999) ^ [_1239921, _1239923, _1239925] : [class_Orderings_Olinorder(_1239921), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239921), _1239923), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239921), _1239923), _1239925))))], (516 ^ _779999) ^ [_787927, _787929, _787931, _787933, _787935, _787937] : [-(c_Finite__Set_Ofolding__one__idem(_787935, _787931, _787927)), c_Finite__Set_Ofolding__one__idem(_787937, _787933, _787929), _787937 = _787935, _787933 = _787931, _787929 = _787927], (7562 ^ _779999) ^ [_907017, _907019, _907021, _907023] : [c_Com_Ocom_OSemi(_907017, _907019) = c_Com_Ocom_OSemi(_907021, _907023), 7565 ^ _779999 : [(7568 ^ _779999) ^ [] : [-(_907019 = _907023)], (7566 ^ _779999) ^ [] : [-(_907017 = _907021)]]], (21638 ^ _779999) ^ [_1174169, _1174171, _1174173] : [21639 ^ _779999 : [(21642 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1174169), hAPP(c_Set_OCollect(_1174169), _1174173)))], (21640 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1174169), hAPP(c_Set_OCollect(_1174169), _1174171)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1174169), hAPP(c_Set_OCollect(_1174169), hAPP(hAPP(c_COMBS(_1174169, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1174169), c_fconj), _1174171)), _1174173)))))], (50010 ^ _779999) ^ [_1789616, _1789618, _1789620] : [c_List_Oreplicate(_1789616, _1789618, _1789620) = c_List_Olist_ONil(_1789616), -(_1789618 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7264 ^ _779999) ^ [_900232, _900234, _900236, _900238] : [hBOOL(hAPP(hAPP(c_member(_900232), _900234), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900232, tc_HOL_Obool)), _900236), _900238))), -(hBOOL(hAPP(hAPP(c_member(_900232), _900234), _900236))), -(hBOOL(hAPP(hAPP(c_member(_900232), _900234), _900238)))], (36348 ^ _779999) ^ [_1464467] : [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), _1464467))), -(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), _1464467)) = 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), _1464467))))], (45041 ^ _779999) ^ [_1680138, _1680140, _1680142] : [-(hAPP(c_List_Oset(_1680138), hAPP(hAPP(c_List_Oappend(_1680138), _1680140), _1680142)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1680138, tc_HOL_Obool)), hAPP(c_List_Oset(_1680138), _1680140)), hAPP(c_List_Oset(_1680138), _1680142)))], (46550 ^ _779999) ^ [_1713650, _1713652, _1713654, _1713656] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713650)), _1713652) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713654)), _1713656), -(hAPP(hAPP(c_List_Omap(tc_prod(_1713650, _1713654), _1713654), c_Product__Type_Osnd(_1713650, _1713654)), hAPP(hAPP(c_List_Ozip(_1713650, _1713654), _1713652), _1713656)) = _1713656)], (12567 ^ _779999) ^ [_1002175, _1002177, _1002179] : [class_Lattices_Olattice(_1002175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002175), _1002177)), -(hBOOL(hAPP(hAPP(c_member(_1002175), _1002179), _1002177))), -(_1002177 = c_Orderings_Obot__class_Obot(tc_fun(_1002175, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1002175, hAPP(hAPP(c_Set_Oinsert(_1002175), _1002179), _1002177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1002175), _1002179), c_Big__Operators_Olattice__class_OInf__fin(_1002175, _1002177)))], (50809 ^ _779999) ^ [_1808366, _1808368] : [c_Equiv__Relations_Oequivp(_1808366, _1808368), 50812 ^ _779999 : [(50817 ^ _779999) ^ [] : [-(c_Predicate_Otransp(_1808366, _1808368))], (50815 ^ _779999) ^ [] : [-(c_Predicate_Osymp(_1808366, _1808368))], (50813 ^ _779999) ^ [] : [-(c_Predicate_Oreflp(_1808366, _1808368))]]], (51580 ^ _779999) ^ [_1824026, _1824028] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1824026), _1824028))), -(c_Quickcheck_Obeyond(_1824026, _1824028) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (30539 ^ _779999) ^ [_1352502, _1352504, _1352506] : [class_Divides_Osemiring__div(_1352502), -(c_Divides_Odiv__class_Omod(_1352502, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352502), _1352504), _1352506), _1352504) = c_Divides_Odiv__class_Omod(_1352502, _1352506, _1352504))], (18577 ^ _779999) ^ [_1118540, _1118542, _1118544, _1118546] : [class_Orderings_Olinorder(_1118540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118540), _1118542), _1118544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118540), _1118544), _1118546)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1118540, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1118540, _1118542), _1118544)), c_SetInterval_Oord__class_OatLeastAtMost(_1118540, _1118544, _1118546)) = c_SetInterval_Oord__class_OatLeastAtMost(_1118540, _1118542, _1118546))], (4616 ^ _779999) ^ [_850123, _850125] : [_850125 = _850123, -(c_Set_Oinsert(_850125) = c_Set_Oinsert(_850123))], (33583 ^ _779999) ^ [_1407957, _1407959, _1407961] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407957), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407959)), _1407961)) = 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), _1407957), _1407959))), _1407961))], (52338 ^ _779999) ^ [_1834022, _1834024] : [hBOOL(hAPP(hAPP(c_fequal, _1834022), _1834024)), -(_1834022 = _1834024)], (48246 ^ _779999) ^ [_1750668, _1750670, _1750672, _1750674] : [class_Orderings_Olinorder(_1750668), c_List_Olinorder__class_Osorted(_1750668, _1750670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1750672), _1750674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750674), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750668)), _1750670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750668), hAPP(hAPP(c_List_Onth(_1750668), _1750670), _1750672)), hAPP(hAPP(c_List_Onth(_1750668), _1750670), _1750674))))], (44510 ^ _779999) ^ [_1668564, _1668566] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1668564)), c_List_Olist_ONil(_1668564)), c_List_Olists(_1668564, _1668566))))], (47198 ^ _779999) ^ [_1728101, _1728103] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728101)), c_List_Oremdups(_1728101, _1728103)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728101)), _1728103), -(c_List_Oremdups(_1728101, _1728103) = _1728103)], (6439 ^ _779999) ^ [_883812, _883814, _883816, _883818] : [class_Lattices_Osemilattice__sup(_883812), 6442 ^ _779999 : [(6451 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883812), _883814), _883816)), _883818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), _883814), _883818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), _883816), _883818))], (6443 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883812), _883814), _883816)), _883818)), 6446 ^ _779999 : [(6449 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), _883816), _883818)))], (6447 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883812), _883814), _883818)))]]]]], (23978 ^ _779999) ^ [_1227997, _1227999, _1228001, _1228003, _1228005, _1228007, _1228009] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1227997, tc_fun(_1227999, tc_fun(_1228001, tc_HOL_Obool))), _1228003), _1228005), _1228007), _1228009))), 23979 ^ _779999 : [(23980 ^ _779999) ^ [_1228082] : [hBOOL(hAPP(hAPP(c_member(_1227997), _1228082), _1228003)), hBOOL(hAPP(hAPP(hAPP(_1228005, _1228082), _1228007), _1228009))]]], (2662 ^ _779999) ^ [_819394, _819396, _819398, _819400] : [-(c_FunDef_Orp__inv__image(_819400, _819396) = c_FunDef_Orp__inv__image(_819398, _819394)), _819400 = _819398, _819396 = _819394], (50688 ^ _779999) ^ [_1804763, _1804765, _1804767] : [-(c_List_Olist__ex(_1804763, _1804765, _1804767)), 50689 ^ _779999 : [(50690 ^ _779999) ^ [_1804820] : [hBOOL(hAPP(hAPP(c_member(_1804763), _1804820), hAPP(c_List_Oset(_1804763), _1804767))), hBOOL(hAPP(_1804765, _1804820))]]], (41284 ^ _779999) ^ [_1587740, _1587742, _1587744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1587740), _1587742)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587740, tc_HOL_Obool)), _1587742), _1587744) = hAPP(hAPP(c_Finite__Set_Ofold(_1587740, tc_fun(_1587740, tc_HOL_Obool), c_Set_Oinsert(_1587740)), _1587744), _1587742))], (30760 ^ _779999) ^ [_1356627, _1356629, _1356631] : [class_Divides_Osemiring__div(_1356627), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356627), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1356627), _1356629), _1356631)), _1356631)), c_Divides_Odiv__class_Omod(_1356627, _1356629, _1356631)) = _1356629)], (7502 ^ _779999) ^ [_905393, _905395, _905397] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_905393, _905395, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905393)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905393), _905397), c_Com_Ocom_OSKIP), _905397)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905393), tc_HOL_Obool)))))], (13307 ^ _779999) ^ [_1016932, _1016934, _1016936, _1016938] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1016932), 13310 ^ _779999 : [(13317 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016932), _1016934), _1016938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016932), _1016934), _1016936)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016932), _1016938), _1016936))))], (13311 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016932), _1016934), _1016936)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016932), _1016938), _1016936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016932), _1016934), _1016938)))]]], (49078 ^ _779999) ^ [_1768484, _1768486, _1768488, _1768490, _1768492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768484, _1768484)), hAPP(hAPP(c_Product__Type_OPair(_1768484, _1768484), _1768486), _1768488)), c_List_Omeasures(_1768484, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1768484, tc_Nat_Onat)), _1768490), _1768492)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1768490, _1768486)), hAPP(_1768490, _1768488)))), 49085 ^ _779999 : [(49088 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768484, _1768484)), hAPP(hAPP(c_Product__Type_OPair(_1768484, _1768484), _1768486), _1768488)), c_List_Omeasures(_1768484, _1768492))))], (49086 ^ _779999) ^ [] : [-(hAPP(_1768490, _1768486) = hAPP(_1768490, _1768488))]]], (37140 ^ _779999) ^ [_1482796] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1482796)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1482796)], (22247 ^ _779999) ^ [_1191601, _1191603, _1191605, _1191607, _1191609] : [c_Fun_Oinj__on(_1191601, _1191603, _1191605, c_Orderings_Otop__class_Otop(tc_fun(_1191601, tc_HOL_Obool))), hAPP(_1191605, _1191607) = hAPP(_1191605, _1191609), -(_1191607 = _1191609)], (41330 ^ _779999) ^ [_1588771, _1588773, _1588775, _1588777, _1588779, _1588781] : [c_Finite__Set_Ofun__left__comm__idem(_1588771, _1588773, _1588775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588771), _1588777)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1588771, _1588773, _1588775), _1588779), hAPP(hAPP(c_Set_Oinsert(_1588771), _1588781), _1588777)) = hAPP(hAPP(_1588775, _1588781), hAPP(hAPP(c_Finite__Set_Ofold(_1588771, _1588773, _1588775), _1588779), _1588777)))], (14557 ^ _779999) ^ [_1040870, _1040872, _1040874, _1040876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040870), _1040872)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040874), _1040876)), 14564 ^ _779999 : [(14565 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1040870), _1040872)), hAPP(c_Finite__Set_Ocard(_1040874), _1040876)))), 14566 ^ _779999 : [(14567 ^ _779999) ^ [_1041081] : [c_Fun_Oinj__on(_1040870, _1040874, _1041081, _1040872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1040874, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1040870, _1040874, _1041081), _1040872)), _1040876))]]], (14575 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1040870), _1040872)), hAPP(c_Finite__Set_Ocard(_1040874), _1040876))), 14579 ^ _779999 : [(14582 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1040874, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1040870, _1040874, 14578 ^ [_1040870, _1040872, _1040874, _1040876]), _1040872)), _1040876)))], (14580 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_1040870, _1040874, 14578 ^ [_1040870, _1040872, _1040874, _1040876], _1040872))]]]]], (8066 ^ _779999) ^ [_916159, _916161, _916163, _916165, _916167] : [c_Natural_Oevaln(_916159, _916161, _916163, _916165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _916163), _916167)), -(c_Natural_Oevaln(_916159, _916161, _916167, _916165))], (9090 ^ _779999) ^ [_935408, _935410, _935412, _935414] : [class_Orderings_Oorder(_935408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935408), _935410), _935412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935408), _935414), _935410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935408), _935414), _935412)))], (47571 ^ _779999) ^ [_1737491, _1737493] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1737491)), c_List_Otranspose__rel(_1737491)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1737491)), c_List_Olist_ONil(_1737491)), _1737493))), -(c_List_Otranspose(_1737491, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1737491)), c_List_Olist_ONil(_1737491)), _1737493)) = c_List_Otranspose(_1737491, _1737493))], (46410 ^ _779999) ^ [_1710571, _1710573, _1710575, _1710577] : [class_Groups_Oab__group__add(_1710571), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1710571), hAPP(c_List_Omonoid__add__class_Olistsum(_1710571), hAPP(hAPP(c_List_Omap(_1710573, _1710571), _1710575), _1710577))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1710571), hAPP(hAPP(c_List_Omap(_1710573, _1710571), hAPP(c_Fun_Ocomp(_1710571, _1710571, _1710573, c_Groups_Ouminus__class_Ouminus(_1710571)), _1710575)), _1710577)))], (17691 ^ _779999) ^ [_1101624, _1101626, _1101628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101624)), 17694 ^ _779999 : [(17701 ^ _779999) ^ [] : [_1101626 = _1101628, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101624), _1101626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101624), _1101628))], (17695 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101624), _1101626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101624), _1101628), -(_1101626 = _1101628)]]], (27946 ^ _779999) ^ [_1305382, _1305384, _1305386] : [class_Rings_Olinordered__semidom(_1305382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305382), c_Groups_Oone__class_Oone(_1305382)), _1305384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305382), hAPP(hAPP(c_Power_Opower__class_Opower(_1305382), _1305384), _1305386)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305382), _1305384), hAPP(hAPP(c_Power_Opower__class_Opower(_1305382), _1305384), _1305386)))))], (14928 ^ _779999) ^ [_1047868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1047868)), 14932 ^ _779999 : [(14933 ^ _779999) ^ [_1047948] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1047948), _1047868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047948), 14931 ^ [_1047868])))]]], (35620 ^ _779999) ^ [_1450818, _1450820, _1450822, _1450824, _1450826, _1450828] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450818, tc_fun(_1450820, tc_HOL_Obool))), _1450822), _1450824), _1450826), _1450828)), -(hBOOL(hAPP(hAPP(_1450822, _1450826), _1450828)))], (42582 ^ _779999) ^ [_1618522] : [class_Complete__Lattice_Ocomplete__lattice(_1618522), -(c_Complete__Lattice_OSup__class_OSup(_1618522, c_Orderings_Otop__class_Otop(tc_fun(_1618522, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1618522))], (21790 ^ _779999) ^ [_1177598, _1177600, _1177602, _1177604, _1177606, _1177608, _1177610] : [class_Groups_Ocomm__monoid__add(_1177598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177600), _1177602)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177604), _1177606)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177600, _1177598), hAPP(hAPP(c_COMBS(_1177600, tc_fun(_1177604, tc_HOL_Obool), _1177598), hAPP(hAPP(c_COMBB(tc_fun(_1177604, _1177598), tc_fun(tc_fun(_1177604, tc_HOL_Obool), _1177598), _1177600), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177604, _1177598)), _1177608)), hAPP(hAPP(c_COMBB(tc_fun(_1177604, tc_HOL_Obool), tc_fun(_1177604, tc_HOL_Obool), _1177600), c_Set_OCollect(_1177604)), hAPP(hAPP(c_COMBB(tc_fun(_1177604, tc_HOL_Obool), tc_fun(_1177604, tc_HOL_Obool), _1177600), hAPP(c_COMBS(_1177604, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177604), c_fconj), hAPP(hAPP(c_COMBC(_1177604, tc_fun(_1177604, tc_HOL_Obool), tc_HOL_Obool), c_member(_1177604)), _1177606)))), _1177610)))), _1177602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177604, _1177598), hAPP(hAPP(c_COMBS(_1177604, tc_fun(_1177600, tc_HOL_Obool), _1177598), hAPP(hAPP(c_COMBB(tc_fun(_1177600, _1177598), tc_fun(tc_fun(_1177600, tc_HOL_Obool), _1177598), _1177604), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177600, _1177598)), hAPP(c_COMBC(_1177600, _1177604, _1177598), _1177608))), hAPP(hAPP(c_COMBB(tc_fun(_1177600, tc_HOL_Obool), tc_fun(_1177600, tc_HOL_Obool), _1177604), c_Set_OCollect(_1177600)), hAPP(hAPP(c_COMBB(tc_fun(_1177600, tc_HOL_Obool), tc_fun(_1177600, tc_HOL_Obool), _1177604), hAPP(c_COMBS(_1177600, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177600), c_fconj), hAPP(hAPP(c_COMBC(_1177600, tc_fun(_1177600, tc_HOL_Obool), tc_HOL_Obool), c_member(_1177600)), _1177602)))), hAPP(c_COMBC(_1177600, _1177604, tc_HOL_Obool), _1177610))))), _1177606))], (38824 ^ _779999) ^ [_1528150, _1528152, _1528154, _1528156, _1528158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528150, _1528152)), _1528154), hAPP(hAPP(c_Product__Type_OSigma(_1528150, _1528152), _1528156), _1528158))), 38828 ^ _779999 : [(38834 ^ _779999) ^ [] : [-(_1528154 = hAPP(hAPP(c_Product__Type_OPair(_1528150, _1528152), 38827 ^ [_1528150, _1528152, _1528154, _1528156, _1528158]), 38830 ^ [_1528150, _1528152, _1528154, _1528156, _1528158]))], (38832 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528152), 38830 ^ [_1528150, _1528152, _1528154, _1528156, _1528158]), hAPP(_1528158, 38827 ^ [_1528150, _1528152, _1528154, _1528156, _1528158]))))], (38829 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528150), 38827 ^ [_1528150, _1528152, _1528154, _1528156, _1528158]), _1528156)))]]], (34197 ^ _779999) ^ [] : [-(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))))], (3602 ^ _779999) ^ [_834008, _834010] : [_834010 = _834008, -(c_Lazy__Sequence_Ohb__not__seq(_834010) = c_Lazy__Sequence_Ohb__not__seq(_834008))], (11434 ^ _779999) ^ [_979160, _979162, _979164, _979166] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979160, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979160, tc_HOL_Obool)), _979162), _979164)), _979166) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979160, tc_HOL_Obool)), _979162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979160, tc_HOL_Obool)), _979164), _979166)))], (29948 ^ _779999) ^ [_1341478, _1341480, _1341482] : [_1341478 = 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), _1341478), _1341480)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1341478), _1341482)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27734 ^ _779999) ^ [_1301535, _1301537] : [class_Groups_Omonoid__mult(_1301535), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301535), _1301537), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1301537)], (34483 ^ _779999) ^ [_1424523, _1424525] : [class_Rings_Oring__1__no__zero__divisors(_1424523), 34486 ^ _779999 : [(34487 ^ _779999) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1424523), _1424525), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1424523), -(_1424525 = c_Groups_Oone__class_Oone(_1424523)), -(_1424525 = hAPP(c_Groups_Ouminus__class_Ouminus(_1424523), c_Groups_Oone__class_Oone(_1424523)))], (34497 ^ _779999) ^ [] : [34498 ^ _779999 : [(34501 ^ _779999) ^ [] : [_1424525 = hAPP(c_Groups_Ouminus__class_Ouminus(_1424523), c_Groups_Oone__class_Oone(_1424523))], (34499 ^ _779999) ^ [] : [_1424525 = c_Groups_Oone__class_Oone(_1424523)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424523), _1424525), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1424523))]]], (42496 ^ _779999) ^ [_1616545, _1616547, _1616549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1616545, tc_HOL_Obool), tc_HOL_Obool)), _1616547), _1616549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616545, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616545, tc_HOL_Obool), _1616547)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616545, tc_HOL_Obool), _1616549))))], (7852 ^ _779999) ^ [_912637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _912637)))], (6489 ^ _779999) ^ [_884662, _884664, _884666] : [class_Lattices_Osemilattice__sup(_884662), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884662), _884664), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884662), _884664), _884666))))], (33783 ^ _779999) ^ [_1412197, _1412199, _1412201, _1412203] : [-(hAPP(c_Nat_Onat_Onat__rec(_1412197, _1412199, _1412201), hAPP(c_Nat_OSuc, _1412203)) = hAPP(hAPP(_1412201, _1412203), hAPP(c_Nat_Onat_Onat__rec(_1412197, _1412199, _1412201), _1412203)))], (15701 ^ _779999) ^ [_1063149, _1063151, _1063153, _1063155] : [class_Rings_Ocomm__semiring__1(_1063149), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063149), _1063151), _1063153)), _1063155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063149), _1063151), _1063155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063149), _1063153), _1063155)))], (24386 ^ _779999) ^ [_1236808, _1236810, _1236812, _1236814] : [class_Orderings_Olinorder(_1236808), 24389 ^ _779999 : [(24390 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236808), _1236812), _1236814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), _1236812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), _1236814)))], (24400 ^ _779999) ^ [] : [24401 ^ _779999 : [(24404 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), _1236814))], (24402 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), _1236812))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236808), _1236810), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236808), _1236812), _1236814))))]]], (34911 ^ _779999) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (29884 ^ _779999) ^ [_1340291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340291), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1340291 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 29887 ^ [_1340291]))))], (37563 ^ _779999) ^ [_1493158, _1493160, _1493162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493158, _1493158)), _1493160), c_Relation_OId__on(_1493158, _1493162))), 37567 ^ _779999 : [(37570 ^ _779999) ^ [] : [-(_1493160 = hAPP(hAPP(c_Product__Type_OPair(_1493158, _1493158), 37566 ^ [_1493158, _1493160, _1493162]), 37566 ^ [_1493158, _1493160, _1493162]))], (37568 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493158), 37566 ^ [_1493158, _1493160, _1493162]), _1493162)))]]], (3918 ^ _779999) ^ [_838956, _838958, _838960, _838962] : [-(c_List_Obutlast(_838962, _838958) = c_List_Obutlast(_838960, _838956)), _838962 = _838960, _838958 = _838956], (3312 ^ _779999) ^ [_829491, _829493, _829495, _829497] : [-(c_Product__Type_OSigma(_829497, _829493) = c_Product__Type_OSigma(_829495, _829491)), _829497 = _829495, _829493 = _829491], (8304 ^ _779999) ^ [_921154, _921156] : [hBOOL(hAPP(_921154, _921156)), -(hBOOL(hAPP(_921154, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _921154) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _921154), c_Nat_OSuc))))], (8608 ^ _779999) ^ [_927279, _927281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927279), _927281)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927281), _927279)) = _927279)], (23415 ^ _779999) ^ [_1216881] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1216881), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32999 ^ _779999) ^ [_1398725, _1398727] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398725))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398725)), _1398727)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1398727))], (14437 ^ _779999) ^ [_1038059, _1038061, _1038063, _1038065, _1038067] : [class_Groups_Ocomm__monoid__add(_1038059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038061), _1038063)), -(hBOOL(hAPP(hAPP(c_member(_1038061), _1038065), _1038063))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038061, _1038059), _1038067), hAPP(hAPP(c_Set_Oinsert(_1038061), _1038065), _1038063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038059), hAPP(_1038067, _1038065)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038061, _1038059), _1038067), _1038063)))], (34011 ^ _779999) ^ [_1416157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416157), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416157)), c_Int_OPls)))], (9140 ^ _779999) ^ [_936160, _936162, _936164, _936166, _936168, _936170] : [-(c_Fun_Ofun__upd(_936160, _936162, c_Fun_Ofun__upd(_936160, _936162, _936164, _936166, _936168), _936166, _936170) = c_Fun_Ofun__upd(_936160, _936162, _936164, _936166, _936170))], (38226 ^ _779999) ^ [_1510325, _1510327, _1510329, _1510331, _1510333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510325, _1510327)), hAPP(hAPP(c_Product__Type_OPair(_1510325, _1510327), _1510329), _1510331)), _1510333)), -(hBOOL(hAPP(hAPP(c_member(_1510327), _1510331), hAPP(c_Relation_ORange(_1510325, _1510327), _1510333))))], (40031 ^ _779999) ^ [_1556768, _1556770, _1556772] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1556768, _1556770, _1556772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1556772)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51359 ^ _779999) ^ [_1818867, _1818869, _1818871] : [hAPP(c_Set_Oimage(_1818867, _1818869, _1818871), c_Orderings_Otop__class_Otop(tc_fun(_1818867, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1818869, tc_HOL_Obool)), 51362 ^ _779999 : [(51363 ^ _779999) ^ [_1818978] : [-(hAPP(_1818871, hAPP(c_Hilbert__Choice_Oinv__into(_1818867, _1818869, c_Orderings_Otop__class_Otop(tc_fun(_1818867, tc_HOL_Obool)), _1818871), _1818978)) = _1818978)]]], (37730 ^ _779999) ^ [_1498518, _1498520, _1498522] : [37732 ^ _779999 : [(37735 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1498518), 37731 ^ [_1498518, _1498520, _1498522]), c_Wellfounded_Oacc(_1498518, _1498522)))], (37733 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498518, _1498518)), hAPP(hAPP(c_Product__Type_OPair(_1498518, _1498518), 37731 ^ [_1498518, _1498520, _1498522]), _1498520)), _1498522)))]], -(hBOOL(hAPP(hAPP(c_member(_1498518), _1498520), c_Wellfounded_Oacc(_1498518, _1498522))))], (25886 ^ _779999) ^ [_1265405, _1265407, _1265409] : [class_Groups_Ocomm__monoid__mult(_1265405), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265407, _1265405), hAPP(c_COMBK(_1265405, _1265407), c_Groups_Oone__class_Oone(_1265405))), _1265409) = c_Groups_Oone__class_Oone(_1265405))], (1704 ^ _779999) ^ [_804407, _804409] : [-(class_Groups_Ocomm__monoid__mult(_804407)), _804409 = _804407, class_Groups_Ocomm__monoid__mult(_804409)], (38195 ^ _779999) ^ [_1509744, _1509746] : [c_Wellfounded_Owf(_1509744, _1509746), -(c_Wellfounded_Owf(tc_List_Olist(_1509744), c_List_Olex(_1509744, _1509746)))], (17880 ^ _779999) ^ [_1105489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105489)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1105489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4998 ^ _779999) ^ [_856326, _856328, _856330, _856332, _856334, _856336, _856338, _856340] : [-(c_Product__Type_Oscomp(_856340, _856336, _856332, _856328) = c_Product__Type_Oscomp(_856338, _856334, _856330, _856326)), _856340 = _856338, _856336 = _856334, _856332 = _856330, _856328 = _856326], (22389 ^ _779999) ^ [_1194159] : [-(c_Fun_Oinj__on(_1194159, tc_fun(_1194159, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1194159, tc_fun(_1194159, tc_HOL_Obool), tc_fun(_1194159, tc_HOL_Obool)), c_Set_Oinsert(_1194159)), c_Orderings_Obot__class_Obot(tc_fun(_1194159, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1194159, tc_HOL_Obool))))], (37921 ^ _779999) ^ [_1503748, _1503750] : [-(c_Wellfounded_Owf(_1503748, hAPP(c_Wellfounded_Omeasure(_1503748), _1503750)))], (22101 ^ _779999) ^ [_1188483, _1188485] : [-(hBOOL(hAPP(hAPP(c_member(_1188483), _1188485), c_Orderings_Otop__class_Otop(tc_fun(_1188483, tc_HOL_Obool)))))], (35366 ^ _779999) ^ [_1445487, _1445489, _1445491] : [class_Rings_Osemiring__1(_1445487), hBOOL(hAPP(hAPP(c_member(_1445487), _1445489), c_Nat_Osemiring__1__class_ONats(_1445487))), hBOOL(hAPP(hAPP(c_member(_1445487), _1445491), c_Nat_Osemiring__1__class_ONats(_1445487))), -(hBOOL(hAPP(hAPP(c_member(_1445487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1445487), _1445489), _1445491)), c_Nat_Osemiring__1__class_ONats(_1445487))))], (1514 ^ _779999) ^ [_802032, _802034] : [-(class_Orderings_Obot(_802032)), _802034 = _802032, class_Orderings_Obot(_802034)], (7779 ^ _779999) ^ [_911069, _911071, _911073, _911075, _911077, _911079] : [-(hBOOL(hAPP(hAPP(c_member(_911069), _911071), _911073))), -(hAPP(c_Fun_Ooverride__on(_911069, _911075, _911077, _911079, _911073), _911071) = hAPP(_911077, _911071))], (6877 ^ _779999) ^ [_892792, _892794, _892796, _892798] : [-(hAPP(hAPP(c_Set_Oinsert(_892792), _892794), hAPP(hAPP(c_Set_Oinsert(_892792), _892796), _892798)) = hAPP(hAPP(c_Set_Oinsert(_892792), _892796), hAPP(hAPP(c_Set_Oinsert(_892792), _892794), _892798)))], (17613 ^ _779999) ^ [_1099878, _1099880, _1099882, _1099884, _1099886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1099878), _1099880)), 17616 ^ _779999 : [(17623 ^ _779999) ^ [] : [_1099884 = 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), _1099880), _1099878)), _1099882)), _1099886), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1099878), _1099882)), _1099884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1099880), _1099882)), _1099886))], (17617 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1099878), _1099882)), _1099884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1099880), _1099882)), _1099886), -(_1099884 = 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), _1099880), _1099878)), _1099882)), _1099886))]]], (50700 ^ _779999) ^ [_1805143, _1805145, _1805147, _1805149] : [class_Complete__Lattice_Ocomplete__lattice(_1805143), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1805145, _1805143), _1805147), _1805149) = c_Complete__Lattice_OSup__class_OSup(_1805143, hAPP(c_Set_OCollect(_1805143), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool), tc_HOL_Obool, _1805143), c_HOL_OEx(tc_fun(_1805145, _1805143))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool), tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool), _1805143), hAPP(c_COMBS(tc_fun(_1805145, _1805143), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1805145, _1805143)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1805145, _1805143), tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1805145, _1805143))), _1805147)))), hAPP(hAPP(c_COMBC(_1805143, tc_fun(tc_fun(_1805145, _1805143), _1805143), tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1805143, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1805145, _1805143), _1805143), tc_fun(tc_fun(_1805145, _1805143), tc_HOL_Obool)), _1805143), c_COMBB(_1805143, tc_HOL_Obool, tc_fun(_1805145, _1805143))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1805145, _1805143), _1805145, _1805143), c_COMBI(tc_fun(_1805145, _1805143))), _1805149)))))))], (22259 ^ _779999) ^ [_1191801, _1191803] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1191801, _1191803)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1191801, _1191803), tc_HOL_Obool)))), 22262 ^ _779999 : [(22265 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1191803), c_Orderings_Otop__class_Otop(tc_fun(_1191803, tc_HOL_Obool)))))], (22263 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1191801), c_Orderings_Otop__class_Otop(tc_fun(_1191801, tc_HOL_Obool)))))]]], (18225 ^ _779999) ^ [_1111692, _1111694, _1111696] : [class_Rings_Osemiring__1(_1111692), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111692), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111694), _1111696)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111692), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111692), _1111694)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111692), _1111696)))], (21064 ^ _779999) ^ [_1162730, _1162732, _1162734] : [class_Orderings_Oorder(_1162730), 21067 ^ _779999 : [(21074 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162730), _1162732), _1162734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1162730, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1162730), _1162732)), hAPP(c_SetInterval_Oord__class_OatMost(_1162730), _1162734))))], (21068 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1162730, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1162730), _1162732)), hAPP(c_SetInterval_Oord__class_OatMost(_1162730), _1162734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162730), _1162732), _1162734)))]]], (4842 ^ _779999) ^ [_853818, _853820, _853822, _853824, _853826, _853828, _853830, _853832, _853834, _853836] : [-(c_Nitpick_Opair__box_Opair__box__rec(_853836, _853832, _853828, _853824, _853820) = c_Nitpick_Opair__box_Opair__box__rec(_853834, _853830, _853826, _853822, _853818)), _853836 = _853834, _853832 = _853830, _853828 = _853826, _853824 = _853822, _853820 = _853818], (8688 ^ _779999) ^ [_928656, _928658, _928660, _928662, _928664, _928666] : [hBOOL(hAPP(hAPP(c_member(_928656), _928658), _928660)), -(hAPP(c_Set_Oimage(_928656, _928662, c_Fun_Ofun__upd(_928656, _928662, _928664, _928658, _928666)), _928660) = hAPP(hAPP(c_Set_Oinsert(_928662), _928666), hAPP(c_Set_Oimage(_928656, _928662, _928664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928656, tc_HOL_Obool)), _928660), hAPP(hAPP(c_Set_Oinsert(_928656), _928658), c_Orderings_Obot__class_Obot(tc_fun(_928656, tc_HOL_Obool)))))))], (21680 ^ _779999) ^ [_1174895, _1174897, _1174899] : [hBOOL(hAPP(hAPP(c_member(_1174895), _1174897), hAPP(c_Set_OCollect(_1174895), _1174899))), -(hBOOL(hAPP(_1174899, _1174897)))], (35149 ^ _779999) ^ [_1437042, _1437044, _1437046, _1437048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool)), _1437046), _1437048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437042, tc_fun(_1437044, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1437042, tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_fun(_1437044, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437044, tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_fun(_1437044, tc_HOL_Obool)), _1437042), c_COMBC(_1437044, tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437044, tc_prod(_1437042, _1437044)), tc_fun(_1437044, tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), _1437042), hAPP(c_COMBB(tc_prod(_1437042, _1437044), tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool), _1437044), c_member(tc_prod(_1437042, _1437044)))), c_Product__Type_OPair(_1437042, _1437044)))), _1437046)), hAPP(hAPP(c_COMBC(_1437042, tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_fun(_1437044, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437044, tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_fun(_1437044, tc_HOL_Obool)), _1437042), c_COMBC(_1437044, tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437044, tc_prod(_1437042, _1437044)), tc_fun(_1437044, tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool)), _1437042), hAPP(c_COMBB(tc_prod(_1437042, _1437044), tc_fun(tc_fun(tc_prod(_1437042, _1437044), tc_HOL_Obool), tc_HOL_Obool), _1437044), c_member(tc_prod(_1437042, _1437044)))), c_Product__Type_OPair(_1437042, _1437044)))), _1437048))))], (9949 ^ _779999) ^ [_951284, _951286, _951288, _951290, _951292, _951294] : [class_Groups_Ocomm__monoid__add(_951284), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951286, _951284), hAPP(hAPP(c_COMBC(_951286, tc_fun(_951288, tc_HOL_Obool), _951284), hAPP(hAPP(c_COMBB(tc_fun(_951288, _951284), tc_fun(tc_fun(_951288, tc_HOL_Obool), _951284), _951286), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951288, _951284)), _951290)), _951292)), _951294) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951288, _951284), hAPP(hAPP(c_COMBC(_951288, tc_fun(_951286, tc_HOL_Obool), _951284), hAPP(hAPP(c_COMBB(tc_fun(_951286, _951284), tc_fun(tc_fun(_951286, tc_HOL_Obool), _951284), _951288), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951286, _951284)), hAPP(c_COMBC(_951286, _951288, _951284), _951290))), _951294)), _951292))], (9714 ^ _779999) ^ [_945163, _945165] : [class_Complete__Lattice_Ocomplete__lattice(_945163), c_Orderings_Oorder__class_Omono(_945163, _945163, _945165), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945163), c_Inductive_Ocomplete__lattice__class_Ogfp(_945163, _945165)), hAPP(_945165, c_Inductive_Ocomplete__lattice__class_Ogfp(_945163, _945165)))))], (37284 ^ _779999) ^ [_1486512, _1486514, _1486516, _1486518, _1486520, _1486522, _1486524] : [-(hAPP(c_Product__Type_Oapfst(_1486512, _1486514, _1486516, _1486518), hAPP(c_Product__Type_Oapsnd(_1486520, _1486516, _1486512, _1486522), _1486524)) = hAPP(hAPP(c_Product__Type_OPair(_1486514, _1486516), hAPP(_1486518, hAPP(c_Product__Type_Ofst(_1486512, _1486520), _1486524))), hAPP(_1486522, hAPP(c_Product__Type_Osnd(_1486512, _1486520), _1486524))))], (13093 ^ _779999) ^ [_1012911, _1012913, _1012915, _1012917] : [class_Groups_Oab__semigroup__add(_1012911), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012911), _1012913), _1012915)), _1012917) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012911), _1012913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012911), _1012915), _1012917)))], (5402 ^ _779999) ^ [_862628, _862630, _862632, _862634] : [-(c_Quickcheck_Obeyond(_862634, _862630) = c_Quickcheck_Obeyond(_862632, _862628)), _862634 = _862632, _862630 = _862628], (11813 ^ _779999) ^ [_987603, _987605, _987607, _987609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987603, tc_HOL_Obool)), _987605), hAPP(hAPP(c_Set_Oinsert(_987603), _987607), _987609)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987603, tc_HOL_Obool)), _987605), _987609))))], (37962 ^ _779999) ^ [_1504471, _1504473, _1504475, _1504477, _1504479, _1504481, _1504483] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1504471, _1504473, _1504475, _1504477, _1504479), _1504481), _1504483))), 37963 ^ _779999 : [(37964 ^ _779999) ^ [_1504542] : [hBOOL(hAPP(hAPP(_1504477, _1504481), _1504542)), hBOOL(hAPP(hAPP(_1504479, _1504542), _1504483))]]], (50245 ^ _779999) ^ [_1794466, _1794468, _1794470] : [-(c_List_Olist__ex1(_1794466, _1794468, _1794470)), 50246 ^ _779999 : [(50247 ^ _779999) ^ [_1794560] : [hBOOL(hAPP(hAPP(c_member(_1794466), _1794560), hAPP(c_List_Oset(_1794466), _1794470))), hBOOL(hAPP(_1794468, _1794560)), 50255 ^ _779999 : [(50260 ^ _779999) ^ [] : [50254 ^ [_1794466, _1794468, _1794470, _1794560] = _1794560], (50258 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1794468, 50254 ^ [_1794466, _1794468, _1794470, _1794560])))], (50256 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794466), 50254 ^ [_1794466, _1794468, _1794470, _1794560]), hAPP(c_List_Oset(_1794466), _1794470))))]]]]], (15071 ^ _779999) ^ [_1050543, _1050545, _1050547, _1050549, _1050551, _1050553] : [-(hBOOL(hAPP(hAPP(c_member(_1050543), _1050545), c_SetInterval_Oord_OgreaterThanAtMost(_1050543, _1050547, _1050549, _1050551, _1050553)))), hBOOL(hAPP(hAPP(_1050549, _1050551), _1050545)), hBOOL(hAPP(hAPP(_1050547, _1050545), _1050553))], (6550 ^ _779999) ^ [_885904, _885906, _885908, _885910, _885912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885904, tc_HOL_Obool)), _885906), hAPP(c_Set_Oimage(_885908, _885904, _885910), _885912))), 6554 ^ _779999 : [(6557 ^ _779999) ^ [] : [-(_885906 = hAPP(c_Set_Oimage(_885908, _885904, _885910), 6553 ^ [_885904, _885906, _885908, _885910, _885912]))], (6555 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885908, tc_HOL_Obool)), 6553 ^ [_885904, _885906, _885908, _885910, _885912]), _885912)))]]], (24256 ^ _779999) ^ [_1234300, _1234302, _1234304, _1234306] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1234300), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234300), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234300), _1234302), _1234304)), _1234306) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234300), _1234302), _1234306)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234300), _1234304), _1234306)))], (52292 ^ _779999) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (11342 ^ _779999) ^ [_976877, _976879, _976881, _976883] : [hBOOL(hAPP(hAPP(c_member(_976877), _976879), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976877, tc_HOL_Obool)), _976881), _976883))), -(hBOOL(hAPP(hAPP(c_member(_976877), _976879), _976881)))], (49880 ^ _779999) ^ [_1787323, _1787325, _1787327] : [-(_1787323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1787325, c_List_Oreplicate(_1787325, _1787323, _1787327)) = _1787327)], (37866 ^ _779999) ^ [_1502739, _1502741, _1502743, _1502745] : [-(c_Wellfounded_Omax__extp(_1502739, _1502741, _1502743, _1502745)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502739), _1502743)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502739), _1502745)), -(_1502745 = c_Orderings_Obot__class_Obot(tc_fun(_1502739, tc_HOL_Obool))), 37880 ^ _779999 : [(37883 ^ _779999) ^ [_1503084] : [hBOOL(hAPP(hAPP(c_member(_1502739), _1503084), _1502745)), hBOOL(hAPP(hAPP(_1502741, 37879 ^ [_1502739, _1502741, _1502743, _1502745]), _1503084))], (37881 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502739), 37879 ^ [_1502739, _1502741, _1502743, _1502745]), _1502743)))]]], (17671 ^ _779999) ^ [_1101298, _1101300, _1101302] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101298), _1101300) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101298), _1101302), -(_1101298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1101300 = _1101302)], (11456 ^ _779999) ^ [_979796, _979798, _979800, _979802] : [hBOOL(hAPP(hAPP(c_member(_979796), _979802), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979796, tc_HOL_Obool)), _979798), _979800))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979796, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_979796, tc_fun(_979796, tc_HOL_Obool), tc_HOL_Obool), c_member(_979796)), _979798)), hAPP(hAPP(c_COMBC(_979796, tc_fun(_979796, tc_HOL_Obool), tc_HOL_Obool), c_member(_979796)), _979800)), _979802)))], (2504 ^ _779999) ^ [_816935, _816937, _816939, _816941] : [-(c_Divides_Opdivmod(_816941, _816937) = c_Divides_Opdivmod(_816939, _816935)), _816941 = _816939, _816937 = _816935], (33807 ^ _779999) ^ [_1412556, _1412558, _1412560] : [class_Int_Onumber__ring(_1412556), 33810 ^ _779999 : [(33817 ^ _779999) ^ [] : [c_Int_Oiszero(_1412556, hAPP(c_Int_Onumber__class_Onumber__of(_1412556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1412558), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412560)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412556), _1412558) = hAPP(c_Int_Onumber__class_Onumber__of(_1412556), _1412560))], (33811 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412556), _1412558) = hAPP(c_Int_Onumber__class_Onumber__of(_1412556), _1412560), -(c_Int_Oiszero(_1412556, hAPP(c_Int_Onumber__class_Onumber__of(_1412556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1412558), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412560)))))]]], (7326 ^ _779999) ^ [_901505, _901507, _901509, _901511] : [_901511 = c_Orderings_Obot__class_Obot(tc_fun(_901505, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_901505, _901507, _901509), _901511) = c_Orderings_Obot__class_Obot(tc_fun(_901507, tc_HOL_Obool)))], (47563 ^ _779999) ^ [_1736806, _1736808] : [-(c_List_Oconcat(tc_List_Olist(_1736806), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736806), tc_List_Olist(tc_List_Olist(_1736806))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1736806)), _1736806, c_List_Olist_ONil(tc_List_Olist(_1736806)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1736806), tc_List_Olist(tc_List_Olist(_1736806))), _1736806), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736806), tc_List_Olist(tc_List_Olist(_1736806)), tc_List_Olist(tc_List_Olist(_1736806))), c_List_Olist_OCons(tc_List_Olist(_1736806))), c_List_Olist_ONil(tc_List_Olist(_1736806)))))), _1736808)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736806), tc_List_Olist(_1736806)), c_List_Otl(_1736806)), hAPP(c_List_Ofilter(tc_List_Olist(_1736806), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1736806)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736806), tc_List_Olist(_1736806), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1736806)))), _1736808)))], (32465 ^ _779999) ^ [_1388947, _1388949, _1388951, _1388953] : [class_Fields_Olinordered__field__inverse__zero(_1388947), class_Int_Onumber(_1388947), 32472 ^ _779999 : [(32473 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388947), _1388949), _1388951)), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953))), 32476 ^ _779999 : [(32483 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), _1388951))), 32486 ^ _779999 : [(32493 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), _1388951), c_Groups_Ozero__class_Ozero(_1388947)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953))))], (32487 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), _1388951), c_Groups_Ozero__class_Ozero(_1388947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388947), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)), _1388951)), _1388949)))]]], (32477 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), _1388951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), _1388949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388947), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)), _1388951))))]]], (32499 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388947), _1388949), _1388951)), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)))), 32502 ^ _779999 : [(32505 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), _1388949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388947), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)), _1388951)))], (32503 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), _1388951)))]], 32506 ^ _779999 : [(32509 ^ _779999) ^ [] : [32510 ^ _779999 : [(32513 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388947), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)), _1388951)), _1388949))], (32511 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), _1388951), c_Groups_Ozero__class_Ozero(_1388947))))]], 32514 ^ _779999 : [(32517 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), hAPP(c_Int_Onumber__class_Onumber__of(_1388947), _1388953)))], (32515 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), _1388951), c_Groups_Ozero__class_Ozero(_1388947)))]]], (32507 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388947), c_Groups_Ozero__class_Ozero(_1388947)), _1388951))]]]]], (36711 ^ _779999) ^ [_1472646, _1472648, _1472650, _1472652] : [c_Equiv__Relations_Oequiv(_1472646, _1472648, _1472650), hBOOL(hAPP(hAPP(c_member(_1472646), _1472652), _1472648)), -(hBOOL(hAPP(hAPP(c_member(_1472646), _1472652), hAPP(c_Relation_OImage(_1472646, _1472646, _1472650), hAPP(hAPP(c_Set_Oinsert(_1472646), _1472652), c_Orderings_Obot__class_Obot(tc_fun(_1472646, tc_HOL_Obool)))))))], (22267 ^ _779999) ^ [_1191966, _1191968] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1191966, _1191968)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1191966, _1191968), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191966), c_Orderings_Otop__class_Otop(tc_fun(_1191966, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191968), c_Orderings_Otop__class_Otop(tc_fun(_1191968, tc_HOL_Obool))))], (35854 ^ _779999) ^ [_1455408, _1455410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455410)), -(c_Divides_OposDivAlg(_1455408, _1455410) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1455408), _1455410)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1455408, _1455410)))], (12295 ^ _779999) ^ [_997441, _997443, _997445, _997447, _997449] : [class_Groups_Ocomm__monoid__add(_997441), hBOOL(hAPP(c_Finite__Set_Ofinite(_997443), _997445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997443, tc_HOL_Obool)), _997447), _997445)), 12309 ^ _779999 : [(12312 ^ _779999) ^ [] : [hAPP(_997449, 12308 ^ [_997441, _997443, _997445, _997447, _997449]) = c_Groups_Ozero__class_Ozero(_997441)], (12310 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997443), 12308 ^ [_997441, _997443, _997445, _997447, _997449]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997443, tc_HOL_Obool)), _997445), _997447))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_997443, _997441), _997449), _997445) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_997443, _997441), _997449), _997447))], (19577 ^ _779999) ^ [_1136833, _1136835, _1136837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136833)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1136835), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1136837)), 19584 ^ _779999 : [(19585 ^ _779999) ^ [_1137041] : [19587 ^ _779999 : [(19593 ^ _779999) ^ [] : [-(_1137041 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19589 ^ [_1136833, _1136835, _1136837, _1137041]), 19586 ^ [_1136833, _1136835, _1136837, _1137041]))], (19591 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19589 ^ [_1136833, _1136835, _1136837, _1137041]), _1136837)))], (19588 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19586 ^ [_1136833, _1136835, _1136837, _1137041]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1136833))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137041), _1136835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1137041), _1136833)), _1136835)))]]], (38732 ^ _779999) ^ [_1525987, _1525989] : [-(hAPP(c_Fun_Oid(_1525987), _1525989) = _1525989)], (5136 ^ _779999) ^ [_858541, _858543, _858545, _858547] : [-(c_Product__Type_Ofst(_858547, _858543) = c_Product__Type_Ofst(_858545, _858541)), _858547 = _858545, _858543 = _858541], (3518 ^ _779999) ^ [_832720, _832722, _832724, _832726, _832728, _832730, _832732, _832734] : [-(c_Nitpick_Osetsum_H(_832734, _832730, _832726, _832722) = c_Nitpick_Osetsum_H(_832732, _832728, _832724, _832720)), _832734 = _832732, _832730 = _832728, _832726 = _832724, _832722 = _832720], (35705 ^ _779999) ^ [_1452887, _1452889] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1452887, _1452889) = 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), _1452887), _1452889)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1452887, _1452889)))], (41053 ^ _779999) ^ [_1581915, _1581917, _1581919] : [c_Relation_Osingle__valued(_1581915, _1581915, _1581917), -(c_Relation_Osingle__valued(_1581915, _1581915, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581915, _1581915), tc_HOL_Obool), _1581919), _1581917)))], (4892 ^ _779999) ^ [_854657, _854659, _854661, _854663, _854665, _854667] : [-(c_FunDef_OTHE__default(_854667, _854663, _854659) = c_FunDef_OTHE__default(_854665, _854661, _854657)), _854667 = _854665, _854663 = _854661, _854659 = _854657], (19157 ^ _779999) ^ [_1129200, _1129202, _1129204, _1129206] : [_1129204 = _1129206, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1129200, _1129202, hAPP(hAPP(c_Set_Oinsert(_1129200), _1129204), c_Orderings_Obot__class_Obot(tc_fun(_1129200, tc_HOL_Obool)))), _1129206)))], (46312 ^ _779999) ^ [_1707876, _1707878] : [-(hAPP(hAPP(c_List_Ozip(_1707876, _1707876), _1707878), _1707878) = hAPP(hAPP(c_List_Omap(_1707876, tc_prod(_1707876, _1707876)), hAPP(hAPP(c_COMBS(_1707876, _1707876, tc_prod(_1707876, _1707876)), c_Product__Type_OPair(_1707876, _1707876)), c_COMBI(_1707876))), _1707878))], (34877 ^ _779999) ^ [_1432153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1432153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1432153)))], (10385 ^ _779999) ^ [_958743, _958745, _958747] : [class_Complete__Lattice_Ocomplete__lattice(_958743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958743), hAPP(_958745, _958747)), _958747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958743), c_Inductive_Ocomplete__lattice__class_Olfp(_958743, _958745)), _958747)))], (35592 ^ _779999) ^ [_1450228, _1450230, _1450232, _1450234, _1450236, _1450238] : [hBOOL(hAPP(hAPP(_1450228, _1450230), _1450232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450234, tc_fun(_1450236, tc_HOL_Obool))), _1450228), _1450238)), -(hBOOL(hAPP(hAPP(_1450238, _1450230), _1450232)))], (27494 ^ _779999) ^ [_1297160] : [-(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, _1297160))))))], (44782 ^ _779999) ^ [_1673580, _1673582, _1673584] : [-(_1673580 = c_List_Olist_ONil(_1673582)), -(hBOOL(hAPP(hAPP(c_member(_1673582), hAPP(c_Product__Type_Ofst(_1673582, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1673582, _1673580), _1673584))), hAPP(c_List_Oset(_1673582), _1673580))))], (34611 ^ _779999) ^ [_1427083, _1427085] : [class_Rings_Oring__1(_1427083), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427083), hAPP(c_Groups_Ouminus__class_Ouminus(_1427083), c_Groups_Oone__class_Oone(_1427083))), 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)))), _1427085)) = c_Groups_Oone__class_Oone(_1427083))], (8296 ^ _779999) ^ [_920986, _920988, _920990, _920992] : [c_Com_Ocom_OSemi(_920986, _920988) = c_Com_Ocom_OWhile(_920990, _920992)], (37660 ^ _779999) ^ [_1496479, _1496481, _1496483, _1496485, _1496487, _1496489, _1496491] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496479, _1496481, _1496483), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496485, tc_fun(tc_prod(_1496479, _1496481), tc_HOL_Obool)), _1496487), _1496489)), _1496491) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496485, tc_fun(tc_prod(_1496479, _1496483), tc_HOL_Obool)), _1496487), hAPP(hAPP(c_COMBC(_1496485, tc_fun(tc_prod(_1496481, _1496483), tc_HOL_Obool), tc_fun(tc_prod(_1496479, _1496483), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1496479, _1496481), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1496481, _1496483), tc_HOL_Obool), tc_fun(tc_prod(_1496479, _1496483), tc_HOL_Obool)), _1496485), c_Relation_Orel__comp(_1496479, _1496481, _1496483)), _1496489)), _1496491)))], (27478 ^ _779999) ^ [_1296951] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296951))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28044 ^ _779999) ^ [_1307160, _1307162, _1307164] : [class_Rings_Olinordered__idom(_1307160), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307160), c_Groups_Ozero__class_Ozero(_1307160)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307160), hAPP(c_Groups_Oabs__class_Oabs(_1307160), _1307162)), _1307164))))], (30104 ^ _779999) ^ [_1344185, _1344187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344185)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344185), _1344187)), _1344185) = _1344187)], (34899 ^ _779999) ^ [_1432432] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1432432), c_Int_OMin) = c_Int_Opred(_1432432))], (34623 ^ _779999) ^ [_1427344, _1427346] : [-(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), _1427344)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1427346))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427344))) = 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), _1427346)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427344)))], (7037 ^ _779999) ^ [_895674, _895676, _895678, _895680] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895674), _895676), _895678)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895674), _895676), _895680)), -(_895680 = _895678)], (14990 ^ _779999) ^ [_1048964, _1048966, _1048968, _1048970, _1048972, _1048974, _1048976] : [c_Big__Operators_Ocomm__monoid__big(_1048964, _1048966, _1048968, _1048970, _1048972), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048966), _1048974))), -(hAPP(hAPP(_1048972, _1048976), _1048974) = _1048970)], (12954 ^ _779999) ^ [_1010034, _1010036, _1010038, _1010040] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010034), _1010036)), hBOOL(hAPP(hAPP(c_member(_1010034), _1010038), _1010036)), hBOOL(hAPP(hAPP(c_member(_1010034), _1010040), _1010036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1010034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010034, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010034, tc_HOL_Obool)), _1010036), hAPP(hAPP(c_Set_Oinsert(_1010034), _1010038), c_Orderings_Obot__class_Obot(tc_fun(_1010034, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1010034), _1010040), c_Orderings_Obot__class_Obot(tc_fun(_1010034, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1010034), _1010036))))], (52024 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (19029 ^ _779999) ^ [_1126892] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126892) = _1126892)], (35582 ^ _779999) ^ [_1450037, _1450039, _1450041, _1450043, _1450045, _1450047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450037, tc_fun(_1450039, tc_HOL_Obool))), _1450041), _1450043)), hBOOL(hAPP(hAPP(_1450041, _1450045), _1450047)), -(hBOOL(hAPP(hAPP(_1450043, _1450045), _1450047)))], (27186 ^ _779999) ^ [_1291771, _1291773, _1291775, _1291777] : [class_Rings_Odivision__ring(_1291771), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291771), _1291773), _1291775)), _1291777) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291771), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291771), _1291773), _1291777)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291771), _1291775), _1291777)))], (51880 ^ _779999) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (31337 ^ _779999) ^ [_1366949, _1366951] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1366949), _1366951)), _1366951) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366949), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366949, _1366951)))], (9398 ^ _779999) ^ [_939952, _939954, _939956] : [class_Orderings_Opreorder(_939952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939952), _939954), _939956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939952), _939954), _939956)))], (49239 ^ _779999) ^ [_1772861, _1772863, _1772865, _1772867, _1772869] : [hAPP(c_List_Ofilter(_1772861, _1772863), _1772865) = hAPP(hAPP(c_List_Olist_OCons(_1772861), _1772867), _1772869), 49244 ^ _779999 : [(49253 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1772863, _1772867)))], (49255 ^ _779999) ^ [] : [-(_1772869 = hAPP(c_List_Ofilter(_1772861, _1772863), 49243 ^ [_1772861, _1772863, _1772865, _1772867, _1772869]))], (49247 ^ _779999) ^ [_1773175] : [hBOOL(hAPP(hAPP(c_member(_1772861), _1773175), hAPP(c_List_Oset(_1772861), 49242 ^ [_1772861, _1772863, _1772865, _1772867, _1772869]))), hBOOL(hAPP(_1772863, _1773175))], (49245 ^ _779999) ^ [] : [-(_1772865 = hAPP(hAPP(c_List_Oappend(_1772861), 49242 ^ [_1772861, _1772863, _1772865, _1772867, _1772869]), hAPP(hAPP(c_List_Olist_OCons(_1772861), _1772867), 49243 ^ [_1772861, _1772863, _1772865, _1772867, _1772869])))]]], (4032 ^ _779999) ^ [_840699, _840701, _840703, _840705, _840707, _840709, _840711, _840713] : [-(c_List_Ofoldl(_840713, _840709, _840705, _840701) = c_List_Ofoldl(_840711, _840707, _840703, _840699)), _840713 = _840711, _840709 = _840707, _840705 = _840703, _840701 = _840699], (21207 ^ _779999) ^ [_1166066, _1166068, _1166070] : [class_Orderings_Olinorder(_1166066), 21210 ^ _779999 : [(21217 ^ _779999) ^ [] : [_1166068 = _1166070, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1166066), _1166068) = hAPP(c_SetInterval_Oord__class_OatLeast(_1166066), _1166070))], (21211 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1166066), _1166068) = hAPP(c_SetInterval_Oord__class_OatLeast(_1166066), _1166070), -(_1166068 = _1166070)]]], (18665 ^ _779999) ^ [_1120319, _1120321, _1120323] : [class_Orderings_Oorder(_1120319), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120319, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1120319), _1120321)), c_SetInterval_Oord__class_OatLeastAtMost(_1120319, _1120321, _1120323)) = c_Orderings_Obot__class_Obot(tc_fun(_1120319, tc_HOL_Obool)))], (40505 ^ _779999) ^ [] : [-(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))))], (462 ^ _779999) ^ [_787112, _787114, _787116, _787118] : [-(c_Relation_Oirrefl(_787116, _787112)), c_Relation_Oirrefl(_787118, _787114), _787118 = _787116, _787114 = _787112], (38224 ^ _779999) ^ [_1510250, _1510252, _1510254] : [-(hAPP(c_Relation_ORange(_1510250, _1510252), hAPP(c_Set_OCollect(tc_prod(_1510250, _1510252)), hAPP(c_Product__Type_Oprod_Oprod__case(_1510250, _1510252, tc_HOL_Obool), _1510254))) = hAPP(c_Set_OCollect(_1510252), hAPP(hAPP(c_COMBB(tc_fun(_1510250, tc_HOL_Obool), tc_HOL_Obool, _1510252), c_HOL_OEx(_1510250)), hAPP(c_COMBC(_1510250, _1510252, tc_HOL_Obool), _1510254))))], (4748 ^ _779999) ^ [_852309, _852311] : [_852311 = _852309, -(c_Lazy__Sequence_Oyieldn(_852311) = c_Lazy__Sequence_Oyieldn(_852309))], (52282 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (45664 ^ _779999) ^ [_1694473, _1694475, _1694477] : [-(hAPP(c_List_Orotate1(_1694473), hAPP(c_List_Orotate(_1694473, _1694475), _1694477)) = hAPP(c_List_Orotate(_1694473, _1694475), hAPP(c_List_Orotate1(_1694473), _1694477)))], (25628 ^ _779999) ^ [_1260618, _1260620, _1260622, _1260624, _1260626, _1260628] : [c_Com_Ocom_OCond(_1260618, _1260620, _1260622) = c_Com_Ocom_OCond(_1260624, _1260626, _1260628), 25631 ^ _779999 : [(25636 ^ _779999) ^ [] : [-(_1260622 = _1260628)], (25634 ^ _779999) ^ [] : [-(_1260620 = _1260626)], (25632 ^ _779999) ^ [] : [-(_1260618 = _1260624)]]], (48739 ^ _779999) ^ [_1761177, _1761179, _1761181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761177)), c_List_OdropWhile(_1761177, _1761179, _1761181))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761177)), _1761181))))], (20564 ^ _779999) ^ [_1153628, _1153630] : [c_Nat__Transfer_Ois__nat(_1153628), c_Nat__Transfer_Ois__nat(_1153630), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1153628, _1153630)))], (51606 ^ _779999) ^ [_1824548, _1824550, _1824552, _1824554, _1824556, _1824558] : [c_Fun_Obij__betw(_1824548, _1824550, _1824552, _1824554, _1824556), hBOOL(hAPP(hAPP(c_member(_1824548), _1824558), _1824554)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1824550, _1824548, _1824556, c_Hilbert__Choice_Oinv__into(_1824548, _1824550, _1824554, _1824552)), _1824558) = hAPP(_1824552, _1824558))], (50454 ^ _779999) ^ [_1799349, _1799351, _1799353, _1799355, _1799357, _1799359, _1799361] : [hBOOL(hAPP(hAPP(_1799349, hAPP(c_Product__Type_Osnd(_1799351, _1799353), _1799355)), hAPP(c_Product__Type_Ofst(_1799351, _1799353), _1799355))), 50461 ^ _779999 : [(50464 ^ _779999) ^ [] : [hBOOL(hAPP(_1799357, hAPP(hAPP(_1799359, 50459 ^ [_1799349, _1799351, _1799353, _1799355, _1799357, _1799359, _1799361]), 50460 ^ [_1799349, _1799351, _1799353, _1799355, _1799357, _1799359, _1799361])))], (50462 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1799349, 50460 ^ [_1799349, _1799351, _1799353, _1799355, _1799357, _1799359, _1799361]), 50459 ^ [_1799349, _1799351, _1799353, _1799355, _1799357, _1799359, _1799361])))]], -(hBOOL(hAPP(_1799357, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1799351, _1799353, _1799361), _1799359), _1799355))))], (31531 ^ _779999) ^ [_1370472, _1370474, _1370476, _1370478, _1370480, _1370482] : [class_Groups_Oab__semigroup__mult(_1370472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370474), _1370476)), 31541 ^ _779999 : [(31544 ^ _779999) ^ [] : [hAPP(_1370478, 31540 ^ [_1370472, _1370474, _1370476, _1370478, _1370480, _1370482]) = hAPP(_1370480, 31540 ^ [_1370472, _1370474, _1370476, _1370478, _1370480, _1370482])], (31542 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370474), 31540 ^ [_1370472, _1370474, _1370476, _1370478, _1370480, _1370482]), _1370476)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1370472, _1370474, c_Groups_Otimes__class_Otimes(_1370472)), _1370478), _1370482), _1370476) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1370472, _1370474, c_Groups_Otimes__class_Otimes(_1370472)), _1370480), _1370482), _1370476))], (29470 ^ _779999) ^ [_1333248, _1333250, _1333252, _1333254] : [class_Divides_Osemiring__div(_1333248), -(_1333250 = c_Groups_Ozero__class_Ozero(_1333248)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1333248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333248), _1333250), _1333252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333248), _1333250), _1333254)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1333248), _1333252), _1333254))], (3934 ^ _779999) ^ [_839190, _839192] : [_839192 = _839190, -(c_List_Oembed__list(_839192) = c_List_Oembed__list(_839190))], (10677 ^ _779999) ^ [_963847, _963849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _963847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963847), hAPP(c_Nat_OSuc, _963849))), _963847)))], (34319 ^ _779999) ^ [] : [-(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)))))], (5881 ^ _779999) ^ [_873521, _873523, _873525, _873527, _873529] : [-(hAPP(c_Set_Oimage(_873521, _873523, _873525), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873521, tc_HOL_Obool)), _873527), _873529)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873523, tc_HOL_Obool)), hAPP(c_Set_Oimage(_873521, _873523, _873525), _873527)), hAPP(c_Set_Oimage(_873521, _873523, _873525), _873529)))], (46759 ^ _779999) ^ [_1717838, _1717840, _1717842, _1717844, _1717846] : [c_List_Opartition(_1717838, _1717840, _1717842) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1717838), tc_List_Olist(_1717838)), _1717844), _1717846), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1717838, tc_HOL_Obool)), hAPP(c_List_Oset(_1717838), _1717844)), hAPP(c_List_Oset(_1717838), _1717846)) = hAPP(c_List_Oset(_1717838), _1717842))], (34839 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (23391 ^ _779999) ^ [_1216464, _1216466, _1216468, _1216470, _1216472] : [hBOOL(hAPP(hAPP(c_member(_1216464), _1216466), hAPP(c_Set_Ovimage(_1216464, _1216468, _1216470), _1216472))), -(hBOOL(hAPP(hAPP(c_member(_1216468), hAPP(_1216470, _1216466)), _1216472)))], (26440 ^ _779999) ^ [_1275355, _1275357] : [class_Groups_Oordered__ab__group__add__abs(_1275355), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275355), hAPP(c_Groups_Ouminus__class_Ouminus(_1275355), _1275357)), hAPP(c_Groups_Oabs__class_Oabs(_1275355), _1275357))))], (17784 ^ _779999) ^ [_1103659, _1103661] : [class_Rings_Ocomm__semiring__1(_1103659), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103659), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103659), c_Groups_Oone__class_Oone(_1103659)), c_Groups_Oone__class_Oone(_1103659))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1103659), c_Nat_Osemiring__1__class_Oof__nat(_1103659)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1103661))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103659), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103659), _1103661)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103659), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103659), _1103661)), c_Groups_Oone__class_Oone(_1103659))))], (42153 ^ _779999) ^ [_1608657, _1608659, _1608661, _1608663, _1608665] : [_1608657 = c_Orderings_Obot__class_Obot(tc_fun(_1608659, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608661, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608659, tc_fun(_1608661, tc_HOL_Obool)), _1608657), _1608663)), _1608665) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608661, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1608661, tc_HOL_Obool))), _1608665))], (7649 ^ _779999) ^ [_908531, _908533] : [hAPP(c_Nat_OSuc, _908531) = hAPP(c_Nat_OSuc, _908533), -(_908531 = _908533)], (5472 ^ _779999) ^ [_863727, _863729, _863731, _863733, _863735, _863737, _863739, _863741] : [-(c_Hilbert__Choice_Oinv__into(_863741, _863737, _863733, _863729) = c_Hilbert__Choice_Oinv__into(_863739, _863735, _863731, _863727)), _863741 = _863739, _863737 = _863735, _863733 = _863731, _863729 = _863727], (40281 ^ _779999) ^ [_1563347, _1563349, _1563351] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563347, _1563347)), hAPP(hAPP(c_Product__Type_OPair(_1563347, _1563347), _1563349), _1563349)), c_Transitive__Closure_Ortrancl(_1563347, _1563351))))], (47717 ^ _779999) ^ [_1740841, _1740843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740841)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740843))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740841), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740843)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740841)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740841)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740843))))], (45931 ^ _779999) ^ [_1700322, _1700324, _1700326, _1700328, _1700330] : [class_Orderings_Olinorder(_1700322), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700324)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700324, _1700322, _1700326), _1700328), _1700330)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700324)), _1700330)))], (14101 ^ _779999) ^ [_1031586, _1031588, _1031590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031586), _1031588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1031586, tc_HOL_Obool)), _1031590), _1031588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1031586), _1031590)), hAPP(c_Finite__Set_Ocard(_1031586), _1031588))))], (52014 ^ _779999) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (20060 ^ _779999) ^ [_1145652, _1145654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1145652)), hAPP(c_Int_Onat, _1145654))), 20063 ^ _779999 : [(20066 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145652), _1145654)))], (20064 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145654)))]]], (40157 ^ _779999) ^ [_1559603, _1559605, _1559607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559603, _1559603), tc_HOL_Obool)), _1559605), _1559607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559603, _1559603), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1559603, _1559603, _1559603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1559603, _1559603), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559603, _1559605)), _1559607)), _1559605)), _1559607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559603, _1559603), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559603, _1559605)), _1559607)))], (49396 ^ _779999) ^ [_1776342, _1776344, _1776346, _1776348] : [c_List_Olist__ex(_1776342, _1776344, hAPP(hAPP(c_List_Oappend(_1776342), _1776346), _1776348)), -(c_List_Olist__ex(_1776342, _1776344, _1776346)), -(c_List_Olist__ex(_1776342, _1776344, _1776348))], (41083 ^ _779999) ^ [_1582411, _1582413, _1582415, _1582417, _1582419, _1582421] : [c_Relation_Osingle__valued(_1582411, _1582413, _1582415), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582411, _1582413)), hAPP(hAPP(c_Product__Type_OPair(_1582411, _1582413), _1582417), _1582419)), _1582415)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582411, _1582413)), hAPP(hAPP(c_Product__Type_OPair(_1582411, _1582413), _1582417), _1582421)), _1582415)), -(_1582419 = _1582421)], (19489 ^ _779999) ^ [_1135306, _1135308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135308)), -(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), _1135306), _1135308))))], (49558 ^ _779999) ^ [_1779656, _1779658] : [-(c_List_Olist__all(_1779656, _1779658, c_List_Olist_ONil(_1779656)))], (44744 ^ _779999) ^ [_1672872, _1672874, _1672876, _1672878] : [-(_1672872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1672874), _1672872), hAPP(hAPP(c_List_Olist_OCons(_1672874), _1672876), _1672878)) = hAPP(hAPP(c_List_Olist_OCons(_1672874), _1672876), hAPP(hAPP(c_List_Otake(_1672874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1672872), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1672878)))], (10508 ^ _779999) ^ [_960880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960880)), -(_960880 = hAPP(c_Nat_OSuc, 10511 ^ [_960880]))], (35801 ^ _779999) ^ [_1454583, _1454585] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454583, _1454583)), hAPP(hAPP(c_Product__Type_OPair(_1454583, _1454583), 35802 ^ [_1454583, _1454585]), 35802 ^ [_1454583, _1454585])), _1454585)), -(c_Nitpick_Orefl_H(_1454583, _1454585))], (24156 ^ _779999) ^ [_1231314, _1231316] : [class_Orderings_Olinorder(_1231314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1231314), _1231316)), -(_1231316 = c_Orderings_Obot__class_Obot(tc_fun(_1231314, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1231314), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1231314), 24169 ^ [_1231314, _1231316]), 24170 ^ [_1231314, _1231316])), hAPP(hAPP(c_Set_Oinsert(_1231314), 24169 ^ [_1231314, _1231316]), hAPP(hAPP(c_Set_Oinsert(_1231314), 24170 ^ [_1231314, _1231316]), c_Orderings_Obot__class_Obot(tc_fun(_1231314, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1231314), c_Big__Operators_Olattice_OInf__fin(_1231314, c_Orderings_Oord__class_Omin(_1231314), _1231316)), _1231316)))], (23867 ^ _779999) ^ [_1225713, _1225715, _1225717] : [class_Orderings_Olinorder(_1225713), hBOOL(hAPP(c_Finite__Set_Ofinite(_1225713), _1225715)), -(_1225715 = c_Orderings_Obot__class_Obot(tc_fun(_1225713, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1225713), _1225717)), -(_1225717 = c_Orderings_Obot__class_Obot(tc_fun(_1225713, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1225713, tc_HOL_Obool)), _1225715), _1225717) = c_Orderings_Obot__class_Obot(tc_fun(_1225713, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1225713, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1225713, tc_HOL_Obool)), _1225715), _1225717)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225713), c_Big__Operators_Olinorder__class_OMin(_1225713, _1225715)), c_Big__Operators_Olinorder__class_OMin(_1225713, _1225717)))], (29580 ^ _779999) ^ [_1335039, _1335041, _1335043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335041), _1335043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1335039), _1335043)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1335039), _1335041))))], (46290 ^ _779999) ^ [_1707424, _1707426, _1707428, _1707430, _1707432] : [c_Fun_Oinj__on(_1707424, _1707426, _1707428, c_Orderings_Otop__class_Otop(tc_fun(_1707424, tc_HOL_Obool))), 46293 ^ _779999 : [(46300 ^ _779999) ^ [] : [_1707430 = _1707432, -(hAPP(hAPP(c_List_Omap(_1707424, _1707426), _1707428), _1707430) = hAPP(hAPP(c_List_Omap(_1707424, _1707426), _1707428), _1707432))], (46294 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Omap(_1707424, _1707426), _1707428), _1707430) = hAPP(hAPP(c_List_Omap(_1707424, _1707426), _1707428), _1707432), -(_1707430 = _1707432)]]], (36989 ^ _779999) ^ [_1478843, _1478845, _1478847, _1478849, _1478851, _1478853] : [c_Equiv__Relations_Ocongruent(_1478843, _1478845, _1478847, _1478849), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478843, _1478843)), hAPP(hAPP(c_Product__Type_OPair(_1478843, _1478843), _1478851), _1478853)), _1478847)), -(hAPP(_1478849, _1478851) = hAPP(_1478849, _1478853))], (48103 ^ _779999) ^ [_1747819, _1747821, _1747823] : [class_Orderings_Olinorder(_1747819), 48106 ^ _779999 : [(48125 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747819, hAPP(hAPP(c_List_Oappend(_1747819), _1747821), _1747823))), c_List_Olinorder__class_Osorted(_1747819, _1747821), c_List_Olinorder__class_Osorted(_1747819, _1747823), 48135 ^ _779999 : [(48141 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747819), 48134 ^ [_1747819, _1747821, _1747823]), 48137 ^ [_1747819, _1747821, _1747823]))], (48139 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747819), 48137 ^ [_1747819, _1747821, _1747823]), hAPP(c_List_Oset(_1747819), _1747823))))], (48136 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747819), 48134 ^ [_1747819, _1747821, _1747823]), hAPP(c_List_Oset(_1747819), _1747821))))]]], (48107 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1747819, hAPP(hAPP(c_List_Oappend(_1747819), _1747821), _1747823)), 48110 ^ _779999 : [(48115 ^ _779999) ^ [_1748055] : [hBOOL(hAPP(hAPP(c_member(_1747819), _1748055), hAPP(c_List_Oset(_1747819), _1747821))), 48118 ^ _779999 : [(48119 ^ _779999) ^ [_1748165] : [hBOOL(hAPP(hAPP(c_member(_1747819), _1748165), hAPP(c_List_Oset(_1747819), _1747823))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747819), _1748055), _1748165)))]]], (48113 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747819, _1747823))], (48111 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747819, _1747821))]]]]], (26947 ^ _779999) ^ [_1286478, _1286480, _1286482, _1286484, _1286486] : [class_Groups_Ocomm__monoid__mult(_1286478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286480), _1286482)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286480, _1286478), _1286484), hAPP(hAPP(c_Set_Oinsert(_1286480), _1286486), _1286482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286478), hAPP(_1286484, _1286486)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286480, _1286478), _1286484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286480, tc_HOL_Obool)), _1286482), hAPP(hAPP(c_Set_Oinsert(_1286480), _1286486), c_Orderings_Obot__class_Obot(tc_fun(_1286480, tc_HOL_Obool)))))))], (47105 ^ _779999) ^ [_1726167, _1726169, _1726171, _1726173, _1726175, _1726177] : [c_List_Olist__all2(_1726167, _1726169, _1726171, _1726173, _1726175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726177), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726169)), _1726175))), -(hBOOL(hAPP(hAPP(_1726171, hAPP(hAPP(c_List_Onth(_1726167), _1726173), _1726177)), hAPP(hAPP(c_List_Onth(_1726169), _1726175), _1726177))))], (29272 ^ _779999) ^ [_1329842, _1329844, _1329846, _1329848] : [class_Fields_Olinordered__field(_1329842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329842), c_Groups_Ozero__class_Ozero(_1329842)), _1329844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329842), _1329846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329842), _1329848), _1329844))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329842), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329842), _1329846), _1329844)), _1329848)))], (19025 ^ _779999) ^ [_1126835] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126835), _1126835)))], (2412 ^ _779999) ^ [_815541, _815543, _815545, _815547, _815549, _815551] : [-(c_Nat_Onat_Onat__rec(_815551, _815547, _815543) = c_Nat_Onat_Onat__rec(_815549, _815545, _815541)), _815551 = _815549, _815547 = _815545, _815543 = _815541], (20212 ^ _779999) ^ [_1148106, _1148108] : [hAPP(c_Int_Onat, _1148106) = _1148108, 20215 ^ _779999 : [(20222 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148106))), -(_1148108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20216 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148106)), -(_1148106 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148108))]]], (43537 ^ _779999) ^ [_1644117, _1644119, _1644121] : [c_Relation_Orefl__on(_1644117, _1644119, _1644121), -(c_Relation_Orefl__on(tc_List_Olist(_1644117), c_List_Olists(_1644117, _1644119), c_List_Olistrel(_1644117, _1644121)))], (27466 ^ _779999) ^ [_1296758, _1296760] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296758)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296760))))), _1296758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1296760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40297 ^ _779999) ^ [_1563740, _1563742] : [-(c_Transitive__Closure_Otrancl(_1563740, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563740, _1563740), tc_HOL_Obool)), _1563742), c_Relation_OId(_1563740))) = c_Transitive__Closure_Ortrancl(_1563740, _1563742))], (21736 ^ _779999) ^ [_1176296, _1176298, _1176300] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1176296, tc_HOL_Obool)), _1176298), _1176300) = hAPP(c_Set_OCollect(_1176296), hAPP(hAPP(c_COMBS(_1176296, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1176296), c_fconj), hAPP(hAPP(c_COMBC(_1176296, tc_fun(_1176296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176296)), _1176298))), hAPP(hAPP(c_COMBC(_1176296, tc_fun(_1176296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176296)), _1176300))))], (18117 ^ _779999) ^ [] : [-(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))], (20429 ^ _779999) ^ [_1151724, _1151726] : [-(c_Int_Onat__aux(_1151724, _1151726) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1151724)), _1151726))], (15369 ^ _779999) ^ [_1056331] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1056331)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16765 ^ _779999) ^ [_1083389, _1083391, _1083393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1083391), _1083393)), -(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, _1083389)), _1083391)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1083389)), _1083393))))], (26236 ^ _779999) ^ [_1271811, _1271813] : [class_Groups_Oordered__ab__group__add(_1271811), 26239 ^ _779999 : [(26246 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271811), c_Groups_Ozero__class_Ozero(_1271811)), _1271813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271811), hAPP(c_Groups_Ouminus__class_Ouminus(_1271811), _1271813)), c_Groups_Ozero__class_Ozero(_1271811))))], (26240 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271811), hAPP(c_Groups_Ouminus__class_Ouminus(_1271811), _1271813)), c_Groups_Ozero__class_Ozero(_1271811))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271811), c_Groups_Ozero__class_Ozero(_1271811)), _1271813)))]]], (22349 ^ _779999) ^ [_1193431, _1193433] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1193431, tc_HOL_Obool)), _1193433), c_Orderings_Otop__class_Otop(tc_fun(_1193431, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1193431, tc_HOL_Obool)))], (33715 ^ _779999) ^ [_1410878, _1410880, _1410882, _1410884, _1410886] : [-(c_Nat_Onat_Onat__case(_1410878, _1410880, _1410882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410884)), _1410886)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1410878), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1410884))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1410878, _1410878), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1410878, tc_fun(_1410878, _1410878)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410878, tc_fun(_1410878, _1410878)), tc_Int_Oint), c_If(_1410878)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1410878, _1410880, _1410882, _1410886))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1410878, tc_Int_Oint), _1410882), 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)), _1410886)))))], (45368 ^ _779999) ^ [_1687909, _1687911] : [-(hAPP(hAPP(c_List_Odrop(_1687909), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1687911) = _1687911)], (37978 ^ _779999) ^ [_1504798, _1504800, _1504802] : [c_Wellfounded_Owf(_1504798, _1504800), -(c_Wellfounded_Owf(_1504798, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1504798, _1504798), tc_HOL_Obool)), _1504802), _1504800)))], (44166 ^ _779999) ^ [_1661271, _1661273, _1661275, _1661277, _1661279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661271, tc_HOL_Obool)), hAPP(c_List_Oset(_1661271), _1661273)), _1661275)), hBOOL(hAPP(hAPP(c_member(_1661271), _1661277), _1661275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661271, tc_HOL_Obool)), hAPP(c_List_Oset(_1661271), hAPP(hAPP(c_List_Olist__update(_1661271, _1661273), _1661279), _1661277))), _1661275)))], (2376 ^ _779999) ^ [_815009, _815011, _815013, _815015] : [-(c_SMT_Oz3div(_815015, _815011) = c_SMT_Oz3div(_815013, _815009)), _815015 = _815013, _815011 = _815009], (628 ^ _779999) ^ [_789673, _789675, _789677, _789679, _789681, _789683] : [-(c_Nitpick_Oless__eq__frac(_789681, _789677, _789673)), c_Nitpick_Oless__eq__frac(_789683, _789679, _789675), _789683 = _789681, _789679 = _789677, _789675 = _789673], (20453 ^ _779999) ^ [_1152105, _1152107] : [c_Nat__Transfer_Onat__set(_1152105), c_Nat__Transfer_Onat__set(_1152107), 20460 ^ _779999 : [(20467 ^ _779999) ^ [] : [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), _1152105)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1152107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1152105), _1152107)))], (20461 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1152105), _1152107)), -(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), _1152105)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1152107))))]]], (21724 ^ _779999) ^ [_1175802, _1175804, _1175806] : [-(hAPP(hAPP(c_Set_Oinsert(_1175802), _1175804), hAPP(c_Set_OCollect(_1175802), _1175806)) = hAPP(c_Set_OCollect(_1175802), hAPP(hAPP(c_COMBS(_1175802, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175802), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1175802), c_fNot), hAPP(hAPP(c_COMBC(_1175802, _1175802, tc_HOL_Obool), c_fequal), _1175804)))), _1175806)))], (39867 ^ _779999) ^ [_1552783, _1552785, _1552787, _1552789, _1552791, _1552793] : [c_Finite__Set_Ofolding__idem(_1552783, _1552785, _1552787, _1552789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552783), _1552791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552783, tc_HOL_Obool)), _1552793), _1552791)), -(hAPP(c_Fun_Ocomp(_1552785, _1552785, _1552785, hAPP(_1552789, _1552791)), hAPP(_1552789, _1552793)) = hAPP(_1552789, _1552791))], (42956 ^ _779999) ^ [_1627041, _1627043, _1627045, _1627047, _1627049, _1627051, _1627053, _1627055] : [c_Finite__Set_Ofolding__image__simple__idem(_1627041, _1627043, _1627045, _1627047, _1627049, _1627051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627043), _1627053)), hBOOL(hAPP(hAPP(c_member(_1627043), _1627055), _1627053)), -(hAPP(hAPP(_1627045, hAPP(_1627049, _1627055)), hAPP(_1627051, _1627053)) = hAPP(_1627051, _1627053))], (38544 ^ _779999) ^ [_1519722, _1519724, _1519726, _1519728] : [38545 ^ _779999 : [(38546 ^ _779999) ^ [_1519776] : [hBOOL(hAPP(hAPP(_1519726, _1519728), _1519776))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1519722, _1519724, _1519726), _1519728)))], (3196 ^ _779999) ^ [_827679, _827681] : [_827681 = _827679, -(c_Nitpick_Odenom(_827681) = c_Nitpick_Odenom(_827679))], (52270 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (38117 ^ _779999) ^ [_1507604, _1507606] : [c_FunDef_Oreduction__pair(_1507604, _1507606), 38120 ^ _779999 : [(38123 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507604, _1507604, _1507604), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool), tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool)), _1507606)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool), tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool)), _1507606))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool), tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool)), _1507606))))], (38121 ^ _779999) ^ [] : [-(c_Wellfounded_Owf(_1507604, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool), tc_fun(tc_prod(_1507604, _1507604), tc_HOL_Obool)), _1507606)))]]], (30703 ^ _779999) ^ [_1355574, _1355576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355574), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355574), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355576, _1355574))))], (39344 ^ _779999) ^ [_1540716, _1540718, _1540720] : [-(c_Hilbert__Choice_OEps(tc_prod(_1540716, _1540718), hAPP(c_Product__Type_Oprod_Oprod__case(_1540716, _1540718, tc_HOL_Obool), _1540720)) = c_Hilbert__Choice_OEps(tc_prod(_1540716, _1540718), hAPP(hAPP(c_COMBS(tc_prod(_1540716, _1540718), _1540718, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1540716, tc_fun(_1540718, tc_HOL_Obool), tc_prod(_1540716, _1540718)), _1540720), c_Product__Type_Ofst(_1540716, _1540718))), c_Product__Type_Osnd(_1540716, _1540718))))], (40919 ^ _779999) ^ [_1578394, _1578396, _1578398] : [c_Wellfounded_Owf(_1578394, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578394, _1578394), tc_HOL_Obool), _1578396), _1578398)), -(c_Wellfounded_Owf(_1578394, _1578398))], (29440 ^ _779999) ^ [_1332830, _1332832, _1332834] : [class_Divides_Osemiring__div(_1332830), -(_1332832 = c_Groups_Ozero__class_Ozero(_1332830)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1332830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332830), _1332834), _1332832)), _1332832) = _1332834)], (27250 ^ _779999) ^ [_1293001, _1293003, _1293005, _1293007] : [class_Rings_Odivision__ring(_1293001), -(_1293003 = c_Groups_Ozero__class_Ozero(_1293001)), 27257 ^ _779999 : [(27264 ^ _779999) ^ [] : [_1293005 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293001), _1293007), _1293003), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293001), _1293005), _1293003) = _1293007)], (27258 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293001), _1293005), _1293003) = _1293007, -(_1293005 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293001), _1293007), _1293003))]]], (25456 ^ _779999) ^ [_1257729, _1257731, _1257733] : [class_Groups_Oordered__ab__group__add(_1257729), 25459 ^ _779999 : [(25466 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257729), hAPP(c_Groups_Ouminus__class_Ouminus(_1257729), _1257733)), _1257731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257729), hAPP(c_Groups_Ouminus__class_Ouminus(_1257729), _1257731)), _1257733)))], (25460 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257729), hAPP(c_Groups_Ouminus__class_Ouminus(_1257729), _1257731)), _1257733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257729), hAPP(c_Groups_Ouminus__class_Ouminus(_1257729), _1257733)), _1257731)))]]], (49996 ^ _779999) ^ [_1789369, _1789371] : [-(c_List_Oreplicate(_1789369, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1789371) = c_List_Olist_ONil(_1789369))], (34913 ^ _779999) ^ [_1432611] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1432611), c_Int_OMin) = c_Int_Osucc(_1432611))], (26691 ^ _779999) ^ [_1280362, _1280364] : [class_Groups_Oabs__if(_1280362), 26694 ^ _779999 : [(26701 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280362), _1280364), c_Groups_Ozero__class_Ozero(_1280362)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1280362), _1280364) = _1280364)], (26695 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280362), _1280364), c_Groups_Ozero__class_Ozero(_1280362))), -(hAPP(c_Groups_Oabs__class_Oabs(_1280362), _1280364) = hAPP(c_Groups_Ouminus__class_Ouminus(_1280362), _1280364))]]], (18141 ^ _779999) ^ [_1110224, _1110226] : [class_Rings_Olinordered__semidom(_1110224), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110224), c_Groups_Ozero__class_Ozero(_1110224)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110224), _1110226))))], (45392 ^ _779999) ^ [_1688513, _1688515] : [-(hAPP(hAPP(c_List_Odrop(_1688513), _1688515), c_List_Olist_ONil(_1688513)) = c_List_Olist_ONil(_1688513))], (18319 ^ _779999) ^ [_1113321, _1113323, _1113325, _1113327] : [class_Groups_Ocomm__monoid__add(_1113321), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113321), _1113323), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1113325)), hAPP(c_Nat_OSuc, _1113327))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113321), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1113321, tc_Nat_Onat), _1113323), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1113325), _1113327)))], (37588 ^ _779999) ^ [] : [-(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))))))], (5338 ^ _779999) ^ [_861684, _861686] : [_861686 = _861684, -(c_HOL_OEx(_861686) = c_HOL_OEx(_861684))], (8202 ^ _779999) ^ [_918960] : [-(hAPP(c_Set_OPow(_918960), c_Orderings_Obot__class_Obot(tc_fun(_918960, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_918960, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_918960, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_918960, tc_HOL_Obool), tc_HOL_Obool))))], (38335 ^ _779999) ^ [_1513234, _1513236, _1513238, _1513240, _1513242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513234, _1513236)), hAPP(hAPP(c_Product__Type_OPair(_1513234, _1513236), _1513238), _1513240)), _1513242)), -(hBOOL(hAPP(hAPP(c_member(_1513234), _1513238), hAPP(c_Relation_ODomain(_1513234, _1513236), _1513242))))], (26931 ^ _779999) ^ [_1285973, _1285975, _1285977, _1285979, _1285981, _1285983] : [-(hBOOL(hAPP(hAPP(c_member(_1285973), _1285975), _1285977))), 26934 ^ _779999 : [(26941 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285973), _1285979), _1285977))), -(hAPP(c_Set_Ovimage(_1285981, _1285973, hAPP(hAPP(c_COMBC(_1285981, _1285973, _1285973), hAPP(hAPP(c_COMBC(_1285981, _1285973, tc_fun(_1285973, _1285973)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1285973, tc_fun(_1285973, _1285973)), _1285981), c_If(_1285973)), hAPP(hAPP(c_COMBC(_1285981, tc_fun(_1285981, tc_HOL_Obool), tc_HOL_Obool), c_member(_1285981)), _1285983))), _1285975)), _1285979)), _1285977) = c_Orderings_Obot__class_Obot(tc_fun(_1285981, tc_HOL_Obool)))], (26935 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1285973), _1285979), _1285977)), -(hAPP(c_Set_Ovimage(_1285981, _1285973, hAPP(hAPP(c_COMBC(_1285981, _1285973, _1285973), hAPP(hAPP(c_COMBC(_1285981, _1285973, tc_fun(_1285973, _1285973)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1285973, tc_fun(_1285973, _1285973)), _1285981), c_If(_1285973)), hAPP(hAPP(c_COMBC(_1285981, tc_fun(_1285981, tc_HOL_Obool), tc_HOL_Obool), c_member(_1285981)), _1285983))), _1285975)), _1285979)), _1285977) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285981, tc_HOL_Obool)), _1285983))]]], (27178 ^ _779999) ^ [_1291585, _1291587] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291585)), _1291587) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1291585), _1291587)))], (31703 ^ _779999) ^ [_1374659, _1374661] : [class_Int_Onumber__ring(_1374659), -(hAPP(c_Int_Onumber__class_Onumber__of(_1374659), _1374661) = hAPP(c_Int_Oring__1__class_Oof__int(_1374659), _1374661))], (26070 ^ _779999) ^ [_1269034, _1269036, _1269038, _1269040] : [class_Rings_Ocomm__semiring__1(_1269034), class_Rings_Ono__zero__divisors(_1269034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269036), _1269038)), 26081 ^ _779999 : [(26091 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269036, _1269034), _1269040), _1269038) = c_Groups_Ozero__class_Ozero(_1269034)), 26092 ^ _779999 : [(26093 ^ _779999) ^ [_1269412] : [hBOOL(hAPP(hAPP(c_member(_1269036), _1269412), _1269038)), hAPP(_1269040, _1269412) = c_Groups_Ozero__class_Ozero(_1269034)]]], (26082 ^ _779999) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269036, _1269034), _1269040), _1269038) = c_Groups_Ozero__class_Ozero(_1269034), 26086 ^ _779999 : [(26089 ^ _779999) ^ [] : [-(hAPP(_1269040, 26085 ^ [_1269034, _1269036, _1269038, _1269040]) = c_Groups_Ozero__class_Ozero(_1269034))], (26087 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1269036), 26085 ^ [_1269034, _1269036, _1269038, _1269040]), _1269038)))]]]]], (38742 ^ _779999) ^ [_1526143, _1526145] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1526143, _1526145, tc_prod(_1526143, _1526145)), c_Product__Type_OPair(_1526143, _1526145)) = c_Fun_Oid(tc_prod(_1526143, _1526145)))], (6079 ^ _779999) ^ [_876730, _876732, _876734] : [class_Orderings_Olinorder(_876730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876730), _876732), _876734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876730), _876734), _876732)))], (39360 ^ _779999) ^ [_1541129, _1541131] : [39361 ^ _779999 : [(39362 ^ _779999) ^ [_1541175] : [hBOOL(hAPP(_1541129, _1541175))]], -(hBOOL(hAPP(_1541129, c_Hilbert__Choice_OEps(_1541131, _1541129))))], (20974 ^ _779999) ^ [_1160856, _1160858, _1160860] : [class_Groups_Oordered__ab__group__add__abs(_1160856), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160856), hAPP(c_Groups_Oabs__class_Oabs(_1160856), _1160858)), hAPP(c_Groups_Oabs__class_Oabs(_1160856), _1160860))), hAPP(c_Groups_Oabs__class_Oabs(_1160856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160856), _1160860), _1160858)))))], (43163 ^ _779999) ^ [_1632252, _1632254] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1632252))), c_Enum_Osublists(_1632252, _1632254)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632252)), _1632254)))], (3356 ^ _779999) ^ [_830159, _830161, _830163, _830165] : [-(c_List_Olistrel1(_830165, _830161) = c_List_Olistrel1(_830163, _830159)), _830165 = _830163, _830161 = _830159], (46810 ^ _779999) ^ [_1719052, _1719054, _1719056, _1719058] : [-(hBOOL(hAPP(c_List_Olistsp(_1719052, hAPP(hAPP(c_COMBS(_1719052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1719052), c_fconj), _1719054)), _1719056)), _1719058))), hBOOL(hAPP(c_List_Olistsp(_1719052, _1719054), _1719058)), hBOOL(hAPP(c_List_Olistsp(_1719052, _1719056), _1719058))], (1334 ^ _779999) ^ [_799782, _799784] : [-(class_Int_Oring__char__0(_799782)), _799784 = _799782, class_Int_Oring__char__0(_799784)], (17971 ^ _779999) ^ [_1107162, _1107164, _1107166, _1107168, _1107170] : [class_Orderings_Olinorder(_1107162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107162), _1107164), _1107166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107162), _1107168), _1107170)), 17982 ^ _779999 : [(17991 ^ _779999) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107162, _1107164), _1107166) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107162, _1107168), _1107170)), _1107164 = _1107168, _1107166 = _1107170], (17983 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107162, _1107164), _1107166) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107162, _1107168), _1107170), 17986 ^ _779999 : [(17989 ^ _779999) ^ [] : [-(_1107166 = _1107170)], (17987 ^ _779999) ^ [] : [-(_1107164 = _1107168)]]]]], (48372 ^ _779999) ^ [_1753420, _1753422] : [hBOOL(hAPP(c_List_Odistinct(_1753420), hAPP(c_List_Orev(_1753420), _1753422))), -(hBOOL(hAPP(c_List_Odistinct(_1753420), _1753422)))], (39050 ^ _779999) ^ [_1533733, _1533735] : [c_Predicate_Oreflp(_1533733, _1533735), -(c_Relation_Orefl__on(_1533733, c_Orderings_Otop__class_Otop(tc_fun(_1533733, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1533733, _1533733)), hAPP(c_Product__Type_Oprod_Oprod__case(_1533733, _1533733, tc_HOL_Obool), _1533735))))], (48404 ^ _779999) ^ [_1754132, _1754134, _1754136] : [hAPP(c_List_Orev(_1754132), _1754134) = hAPP(c_List_Orev(_1754132), _1754136), -(_1754134 = _1754136)], (40411 ^ _779999) ^ [_1566539, _1566541, _1566543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566539, _1566539)), hAPP(hAPP(c_Product__Type_OPair(_1566539, _1566539), _1566541), _1566543)), c_Relation_OId(_1566539))), -(_1566541 = _1566543)], (50670 ^ _779999) ^ [_1804431, _1804433, _1804435] : [c_List_Olist__ex(_1804431, _1804435, _1804433), 50674 ^ _779999 : [(50677 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1804435, 50673 ^ [_1804431, _1804433, _1804435])))], (50675 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804431), 50673 ^ [_1804431, _1804433, _1804435]), hAPP(c_List_Oset(_1804431), _1804433))))]]], (46211 ^ _779999) ^ [_1705233, _1705235, _1705237, _1705239] : [_1705239 = c_List_Olist_ONil(_1705235), -(c_List_Olist_ONil(_1705233) = hAPP(hAPP(c_List_Omap(_1705235, _1705233), _1705237), _1705239))], (31126 ^ _779999) ^ [_1363415, _1363417] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1363415), _1363417) = 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), _1363415)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363417)))))], (27174 ^ _779999) ^ [_1291499, _1291501] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1291499), _1291501)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291499)), _1291501))], (36124 ^ _779999) ^ [_1460094, _1460096] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1460094, _1460096), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1460094), _1460096)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1460094, _1460096)))))], (10874 ^ _779999) ^ [_968120, _968122, _968124, _968126] : [hBOOL(hAPP(_968120, _968122)), hBOOL(hAPP(_968124, _968122)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968126, tc_HOL_Obool)), _968120), _968124), _968122)))], (28324 ^ _779999) ^ [_1312550, _1312552, _1312554, _1312556] : [class_Fields_Olinordered__field__inverse__zero(_1312550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312550), _1312552), _1312554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312550), _1312556), c_Groups_Ozero__class_Ozero(_1312550))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312550), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312550), _1312554), _1312556)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312550), _1312552), _1312556))))], (35649 ^ _779999) ^ [_1451464, _1451466, _1451468, _1451470, _1451472, _1451474] : [-(hAPP(hAPP(c_Product__Type_OPair(_1451464, _1451466), _1451468), _1451470) = hAPP(hAPP(c_Product__Type_OPair(_1451464, _1451466), _1451472), _1451474)), _1451468 = _1451472, _1451470 = _1451474], (52314 ^ _779999) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (11098 ^ _779999) ^ [_972273, _972275, _972277] : [-(hAPP(c_Set_OPow(_972273), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972273, tc_HOL_Obool)), _972275), _972277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_972273, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_972273), _972275)), hAPP(c_Set_OPow(_972273), _972277)))], (44660 ^ _779999) ^ [_1671166] : [-(c_List_Obutlast(_1671166, c_List_Olist_ONil(_1671166)) = c_List_Olist_ONil(_1671166))], (17587 ^ _779999) ^ [_1099368, _1099370] : [17589 ^ _779999 : [(17592 ^ _779999) ^ [] : [hBOOL(hAPP(_1099370, 17588 ^ [_1099368, _1099370]))], (17590 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17588 ^ [_1099368, _1099370]), _1099368)))]], 17593 ^ _779999 : [(17594 ^ _779999) ^ [_1099519] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1099519), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1099368))), -(hBOOL(hAPP(_1099370, _1099519)))]]], (41142 ^ _779999) ^ [_1583846, _1583848, _1583850, _1583852, _1583854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), _1583848), _1583850)), c_Transitive__Closure_Ortrancl(_1583846, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583846, _1583846), tc_HOL_Obool)), _1583852), _1583854)))), 41148 ^ _779999 : [(41154 ^ _779999) ^ [] : [41150 ^ [_1583846, _1583848, _1583850, _1583852, _1583854] = 41147 ^ [_1583846, _1583848, _1583850, _1583852, _1583854]], (41152 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), 41150 ^ [_1583846, _1583848, _1583850, _1583852, _1583854]), 41147 ^ [_1583846, _1583848, _1583850, _1583852, _1583854])), _1583854)))], (41149 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), 41147 ^ [_1583846, _1583848, _1583850, _1583852, _1583854]), _1583850)), c_Transitive__Closure_Ortrancl(_1583846, _1583852))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), _1583848), _1583850)), c_Transitive__Closure_Ortrancl(_1583846, _1583852))))], (39553 ^ _779999) ^ [_1545334, _1545336, _1545338] : [-(c_Hilbert__Choice_OEps(tc_prod(_1545334, _1545336), _1545338) = c_Hilbert__Choice_OEps(tc_prod(_1545334, _1545336), hAPP(c_Product__Type_Oprod_Oprod__case(_1545334, _1545336, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1545336, tc_prod(_1545334, _1545336)), tc_fun(_1545336, tc_HOL_Obool), _1545334), hAPP(c_COMBB(tc_prod(_1545334, _1545336), tc_HOL_Obool, _1545336), _1545338)), c_Product__Type_OPair(_1545334, _1545336)))))], (37469 ^ _779999) ^ [_1490438, _1490440] : [-(c_Relation_OId__on(_1490438, _1490440) = hAPP(c_Product__Type_Oprod_Oprod__case(_1490438, _1490438, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1490438, tc_HOL_Obool, tc_fun(_1490438, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490438, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1490438, tc_HOL_Obool)), _1490438), c_COMBC(_1490438, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490438, tc_HOL_Obool), tc_fun(_1490438, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1490438), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490438), c_fconj)), c_fequal))), _1490440)))], (33225 ^ _779999) ^ [] : [-(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))))], (4948 ^ _779999) ^ [_855565, _855567, _855569, _855571, _855573, _855575] : [-(c_Lazy__Sequence_Oappend(_855575, _855571, _855567) = c_Lazy__Sequence_Oappend(_855573, _855569, _855565)), _855575 = _855573, _855571 = _855569, _855567 = _855565], (17377 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38491 ^ _779999) ^ [_1517880, _1517882, _1517884, _1517886, _1517888] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517880, _1517882), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517880, tc_HOL_Obool)), _1517884), _1517886)), hAPP(c_COMBK(tc_fun(_1517882, tc_HOL_Obool), _1517880), _1517888)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517880, _1517882), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517880, _1517882), _1517884), hAPP(c_COMBK(tc_fun(_1517882, tc_HOL_Obool), _1517880), _1517888))), hAPP(hAPP(c_Product__Type_OSigma(_1517880, _1517882), _1517886), hAPP(c_COMBK(tc_fun(_1517882, tc_HOL_Obool), _1517880), _1517888))))], (40501 ^ _779999) ^ [_1568702] : [-(hAPP(c_Relation_ORange(_1568702, _1568702), c_Relation_OId(_1568702)) = c_Orderings_Otop__class_Otop(tc_fun(_1568702, tc_HOL_Obool)))], (2732 ^ _779999) ^ [_820469, _820471, _820473, _820475, _820477, _820479, _820481, _820483] : [-(c_Recdef_Osame__fst(_820483, _820479, _820475, _820471) = c_Recdef_Osame__fst(_820481, _820477, _820473, _820469)), _820483 = _820481, _820479 = _820477, _820475 = _820473, _820471 = _820469], (15561 ^ _779999) ^ [_1060642, _1060644, _1060646] : [class_Lattices_Oab__semigroup__idem__mult(_1060642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060642), _1060644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060642), _1060644), _1060646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060642), _1060644), _1060646))], (7900 ^ _779999) ^ [_913370, _913372, _913374, _913376, _913378, _913380] : [c_Natural_Oevaln(_913370, _913372, _913374, _913376), c_Natural_Oevaln(_913378, _913376, _913374, _913380), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_913370, _913378), _913372, _913374, _913380))], (47850 ^ _779999) ^ [_1743629, _1743631, _1743633] : [class_Orderings_Olinorder(_1743629), 47853 ^ _779999 : [(47860 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1743629, _1743633), -(c_List_Olinorder__class_Osorted(_1743629, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1743629, _1743629, c_COMBI(_1743629)), _1743631), _1743633)))], (47854 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1743629, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1743629, _1743629, c_COMBI(_1743629)), _1743631), _1743633)), -(c_List_Olinorder__class_Osorted(_1743629, _1743633))]]], (14357 ^ _779999) ^ [_1036424, _1036426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1036424), _1036426))), 14360 ^ _779999 : [(14363 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1036424), _1036426)))], (14361 ^ _779999) ^ [] : [_1036426 = c_Orderings_Obot__class_Obot(tc_fun(_1036424, tc_HOL_Obool))]]], (44584 ^ _779999) ^ [_1669892, _1669894, _1669896] : [44585 ^ _779999 : [(44588 ^ _779999) ^ [] : [_1669896 = c_List_Olist_ONil(_1669892)], (44586 ^ _779999) ^ [] : [_1669894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1669892), _1669894), _1669896) = c_List_Olist_ONil(_1669892))], (52434 ^ _779999) ^ [_1835218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs))), _1835218)), -(c_Hoare__Mirabelle_Ohoare__derivs(t_a, _1835218, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), 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))), v_Q)), v_Procs)))], (22643 ^ _779999) ^ [_1199048, _1199050, _1199052, _1199054] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1199048, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199050, tc_fun(tc_fun(_1199048, tc_HOL_Obool), tc_HOL_Obool)), _1199052), hAPP(hAPP(c_COMBB(tc_fun(_1199048, tc_HOL_Obool), tc_fun(tc_fun(_1199048, tc_HOL_Obool), tc_HOL_Obool), _1199050), c_Set_OPow(_1199048)), _1199054))), hAPP(c_Set_OPow(_1199048), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199050, tc_fun(_1199048, tc_HOL_Obool)), _1199052), _1199054)))))], (52002 ^ _779999) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (32577 ^ _779999) ^ [_1391085, _1391087, _1391089, _1391091] : [class_Fields_Olinordered__field__inverse__zero(_1391085), class_Int_Onumber(_1391085), 32584 ^ _779999 : [(32585 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391087), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391085), _1391089), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)))), 32588 ^ _779999 : [(32595 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), c_Groups_Ozero__class_Ozero(_1391085)), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)))), 32598 ^ _779999 : [(32605 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)), c_Groups_Ozero__class_Ozero(_1391085)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391087), c_Groups_Ozero__class_Ozero(_1391085))))], (32599 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)), c_Groups_Ozero__class_Ozero(_1391085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391085), _1391087), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)))))]]], (32589 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), c_Groups_Ozero__class_Ozero(_1391085)), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391085), _1391087), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))), _1391089)))]]], (32611 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391087), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391085), _1391089), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))))), 32614 ^ _779999 : [(32617 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391085), _1391087), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))), _1391089))], (32615 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), c_Groups_Ozero__class_Ozero(_1391085)), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))))]], 32618 ^ _779999 : [(32621 ^ _779999) ^ [] : [32622 ^ _779999 : [(32625 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391085), _1391087), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091))))], (32623 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)), c_Groups_Ozero__class_Ozero(_1391085))))]], 32626 ^ _779999 : [(32629 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391085), _1391087), c_Groups_Ozero__class_Ozero(_1391085)))], (32627 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)), c_Groups_Ozero__class_Ozero(_1391085)))]]], (32619 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391085), c_Groups_Ozero__class_Ozero(_1391085)), hAPP(c_Int_Onumber__class_Onumber__of(_1391085), _1391091)))]]]]], (52388 ^ _779999) ^ [_1834666, _1834668] : [hBOOL(_1834666), -(hBOOL(hAPP(hAPP(c_fdisj, _1834666), _1834668)))], (11927 ^ _779999) ^ [_989723, _989725, _989727, _989729, _989731] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_989723), _989725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989727, tc_HOL_Obool)), _989729), hAPP(c_Set_Oimage(_989723, _989727, _989731), _989725))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_989727), _989729)))], (44794 ^ _779999) ^ [_1673976, _1673978, _1673980, _1673982] : [-(hAPP(c_List_Olist_Olist__case(_1673976, _1673978, _1673980, _1673982), c_List_Olist_ONil(_1673978)) = _1673980)], (8702 ^ _779999) ^ [_928957, _928959] : [-(c_HOL_OThe(_928957, hAPP(hAPP(c_COMBC(_928957, _928957, tc_HOL_Obool), c_fequal), _928959)) = _928959)], (43651 ^ _779999) ^ [_1647175, _1647177, _1647179, _1647181] : [_1647175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1647177), hAPP(hAPP(c_List_Olist_OCons(_1647177), _1647179), _1647181)), _1647175) = _1647179)], (46504 ^ _779999) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50264 ^ _779999) ^ [_1794922, _1794924, _1794926, _1794928, _1794930, _1794932] : [c_Nitpick_Opair__box_OPairBox(_1794922, _1794924, _1794926, _1794928) = c_Nitpick_Opair__box_OPairBox(_1794922, _1794924, _1794930, _1794932), 50267 ^ _779999 : [(50270 ^ _779999) ^ [] : [-(_1794928 = _1794932)], (50268 ^ _779999) ^ [] : [-(_1794926 = _1794930)]]], (38664 ^ _779999) ^ [_1522786, _1522788, _1522790, _1522792] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522786), _1522788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522786, _1522786), tc_HOL_Obool)), _1522790), hAPP(hAPP(c_Product__Type_OSigma(_1522786, _1522786), _1522788), hAPP(c_COMBK(tc_fun(_1522786, tc_HOL_Obool), _1522786), _1522788)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1522786, tc_HOL_Obool)), _1522792), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1522786), _1522788), _1522790))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522786), _1522792)))], (24314 ^ _779999) ^ [_1235407, _1235409, _1235411, _1235413] : [class_Orderings_Olinorder(_1235407), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235407), _1235409), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235407), _1235411), _1235413)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235407), _1235411), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235407), _1235409), _1235413)))], (43967 ^ _779999) ^ [_1656436, _1656438, _1656440, _1656442, _1656444, _1656446] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656436, _1656438)), hAPP(hAPP(c_Product__Type_OPair(_1656436, _1656438), _1656440), _1656442)), hAPP(c_List_Oset(tc_prod(_1656436, _1656438)), hAPP(hAPP(c_List_Ozip(_1656436, _1656438), _1656444), _1656446)))), -(hBOOL(hAPP(hAPP(c_member(_1656438), _1656442), hAPP(c_List_Oset(_1656438), _1656446))))], (35763 ^ _779999) ^ [_1453836, _1453838] : [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), _1453836))), 35766 ^ _779999 : [(35773 ^ _779999) ^ [] : [-(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), _1453838)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453838), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453838), 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), _1453836)))))], (35767 ^ _779999) ^ [] : [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), _1453838)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453838), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836)) = 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), _1453838)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453836))))]]], (35085 ^ _779999) ^ [] : [-(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)))], (47350 ^ _779999) ^ [_1731123, _1731125] : [class_Orderings_Olinorder(_1731123), -(c_List_Olinorder__class_Osort__key(_1731123, _1731123, c_COMBI(_1731123), _1731125) = hAPP(c_List_Ofoldl(tc_List_Olist(_1731123), _1731123, hAPP(c_COMBC(_1731123, tc_List_Olist(_1731123), tc_List_Olist(_1731123)), c_List_Olinorder__class_Oinsort__key(_1731123, _1731123, c_COMBI(_1731123))), c_List_Olist_ONil(_1731123)), _1731125))], (18349 ^ _779999) ^ [_1113982, _1113984, _1113986, _1113988, _1113990] : [class_Groups_Ocomm__monoid__add(_1113982), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113982), _1113984), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113986), _1113988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113990), _1113988))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113982), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1113982, tc_Nat_Onat), _1113984), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1113988))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1113986), _1113990)))], (35986 ^ _779999) ^ [_1457701, _1457703, _1457705] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1457701), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1457703)), _1457705)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457701, _1457703), hAPP(c_Divides_OnegateSnd, _1457705))))], (34729 ^ _779999) ^ [_1429370, _1429372] : [class_Rings_Oring__1(_1429370), 34732 ^ _779999 : [(34739 ^ _779999) ^ [] : [-(_1429372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34742 ^ _779999 : [(34749 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429372), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1429370), _1429372) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1429370), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1429370, _1429370)), tc_fun(tc_Int_Oint, _1429370)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1429370, _1429370), _1429370), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1429370, _1429370)), tc_fun(tc_Int_Oint, _1429370)), tc_Int_Oint), c_COMBB(tc_fun(_1429370, _1429370), _1429370, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1429370, tc_fun(tc_fun(_1429370, _1429370), _1429370), tc_Int_Oint), c_HOL_OLet(_1429370, _1429370)), c_Int_Oring__1__class_Oof__int(_1429370)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1429370, _1429370), tc_fun(_1429370, _1429370)), hAPP(hAPP(c_COMBB(tc_fun(_1429370, tc_fun(_1429370, _1429370)), tc_fun(tc_fun(_1429370, _1429370), tc_fun(_1429370, _1429370)), tc_Int_Oint), c_COMBS(_1429370, _1429370, _1429370)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1429370, _1429370), tc_fun(_1429370, tc_fun(_1429370, _1429370))), hAPP(hAPP(c_COMBB(tc_fun(_1429370, tc_fun(_1429370, _1429370)), tc_fun(tc_fun(_1429370, _1429370), tc_fun(_1429370, tc_fun(_1429370, _1429370))), tc_Int_Oint), c_COMBB(_1429370, tc_fun(_1429370, _1429370), _1429370)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1429370, tc_fun(_1429370, _1429370)), tc_Int_Oint), c_If(_1429370)), 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(_1429370, _1429370, _1429370), c_Groups_Oplus__class_Oplus(_1429370)), c_COMBI(_1429370))))), hAPP(hAPP(c_COMBC(_1429370, _1429370, _1429370), hAPP(hAPP(c_COMBB(_1429370, tc_fun(_1429370, _1429370), _1429370), c_Groups_Oplus__class_Oplus(_1429370)), hAPP(hAPP(c_COMBS(_1429370, _1429370, _1429370), c_Groups_Oplus__class_Oplus(_1429370)), c_COMBI(_1429370)))), c_Groups_Oone__class_Oone(_1429370))))), c_Divides_Odivmod__int(_1429372, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34743 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429372), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1429370), _1429372) = hAPP(c_Groups_Ouminus__class_Ouminus(_1429370), hAPP(c_Int_Oring__1__class_Oof__int(_1429370), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1429372))))]]], (34733 ^ _779999) ^ [] : [_1429372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1429370), _1429372) = c_Groups_Ozero__class_Ozero(_1429370))]]], (43525 ^ _779999) ^ [_1643883, _1643885, _1643887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643883, tc_HOL_Obool)), _1643885), _1643887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1643883), tc_HOL_Obool)), c_List_Olists(_1643883, _1643885)), c_List_Olists(_1643883, _1643887))))], (31518 ^ _779999) ^ [_1370272, _1370274] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370272), _1370274)), 31524 ^ _779999 : [(31527 ^ _779999) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31525 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370272), 31523 ^ [_1370272, _1370274]), _1370274)))]], -(hAPP(c_Finite__Set_Ocard(_1370272), _1370274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29128 ^ _779999) ^ [_1327037, _1327039, _1327041, _1327043] : [class_Fields_Ofield(_1327037), -(_1327039 = c_Groups_Ozero__class_Ozero(_1327037)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1327037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327037), _1327041), _1327039)), _1327043) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327037), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1327037), _1327041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327037), _1327039), _1327043))), _1327039))], (11068 ^ _779999) ^ [_971680, _971682, _971684, _971686] : [class_Lattices_Osemilattice__inf(_971680), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971680), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971680), _971682), _971684)), _971686) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971680), _971682), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971680), _971684), _971686)))], (45295 ^ _779999) ^ [_1685959, _1685961, _1685963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685959), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685961)), _1685963))), -(hAPP(hAPP(c_List_Otake(_1685961), hAPP(c_Nat_OSuc, _1685959)), _1685963) = hAPP(hAPP(c_List_Oappend(_1685961), hAPP(hAPP(c_List_Otake(_1685961), _1685959), _1685963)), hAPP(hAPP(c_List_Olist_OCons(_1685961), hAPP(hAPP(c_List_Onth(_1685961), _1685963), _1685959)), c_List_Olist_ONil(_1685961))))], (44658 ^ _779999) ^ [_1671134] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671134)), c_List_Olist_ONil(_1671134)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (570 ^ _779999) ^ [_788734, _788736, _788738, _788740, _788742, _788744, _788746, _788748, _788750, _788752, _788754, _788756] : [-(c_Finite__Set_Ofolding__image__simple__idem(_788754, _788750, _788746, _788742, _788738, _788734)), c_Finite__Set_Ofolding__image__simple__idem(_788756, _788752, _788748, _788744, _788740, _788736), _788756 = _788754, _788752 = _788750, _788748 = _788746, _788744 = _788742, _788740 = _788738, _788736 = _788734], (48358 ^ _779999) ^ [_1753091, _1753093, _1753095] : [hAPP(c_List_Orev(_1753091), _1753093) = hAPP(hAPP(c_List_Olist_OCons(_1753091), _1753095), c_List_Olist_ONil(_1753091)), -(_1753093 = hAPP(hAPP(c_List_Olist_OCons(_1753091), _1753095), c_List_Olist_ONil(_1753091)))], (34203 ^ _779999) ^ [_1419605, _1419607] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1419605)), c_Int_OBit1(_1419607)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419605), c_Int_Osucc(_1419607))))], (51472 ^ _779999) ^ [_1821405, _1821407, _1821409, _1821411, _1821413, _1821415, _1821417] : [c_Fun_Oinj__on(_1821405, _1821407, _1821409, hAPP(c_Set_Oimage(_1821411, _1821405, _1821413), _1821415)), c_Fun_Oinj__on(_1821411, _1821405, _1821413, _1821415), hBOOL(hAPP(hAPP(c_member(_1821407), _1821417), hAPP(c_Set_Oimage(_1821405, _1821407, _1821409), hAPP(c_Set_Oimage(_1821411, _1821405, _1821413), _1821415)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1821411, _1821407, _1821415, hAPP(c_Fun_Ocomp(_1821405, _1821407, _1821411, _1821409), _1821413)), _1821417) = hAPP(hAPP(c_Fun_Ocomp(_1821405, _1821411, _1821407, c_Hilbert__Choice_Oinv__into(_1821411, _1821405, _1821415, _1821413)), c_Hilbert__Choice_Oinv__into(_1821405, _1821407, hAPP(c_Set_Oimage(_1821411, _1821405, _1821413), _1821415), _1821409)), _1821417))], (52080 ^ _779999) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (5378 ^ _779999) ^ [_862288, _862290] : [_862290 = _862288, -(c_Groups_Otimes__class_Otimes(_862290) = c_Groups_Otimes__class_Otimes(_862288))], (27654 ^ _779999) ^ [_1299990, _1299992] : [27655 ^ _779999 : [(27658 ^ _779999) ^ [] : [_1299990 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27656 ^ _779999) ^ [] : [_1299992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1299990), _1299992) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48955 ^ _779999) ^ [_1765787, _1765789, _1765791, _1765793] : [-(hAPP(c_List_OremoveAll(_1765787, _1765789), hAPP(hAPP(c_List_Oappend(_1765787), _1765791), _1765793)) = hAPP(hAPP(c_List_Oappend(_1765787), hAPP(c_List_OremoveAll(_1765787, _1765789), _1765791)), hAPP(c_List_OremoveAll(_1765787, _1765789), _1765793)))], (678 ^ _779999) ^ [_790420, _790422] : [-(class_Lattices_Oab__semigroup__idem__mult(_790420)), _790422 = _790420, class_Lattices_Oab__semigroup__idem__mult(_790422)], (17935 ^ _779999) ^ [_1106445, _1106447] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106445)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106447)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1106445), _1106447)))], (27412 ^ _779999) ^ [_1295684, _1295686] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295684)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295686)), _1295684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295686 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33823 ^ _779999) ^ [_1412839, _1412841] : [class_Int_Onumber__ring(_1412839), 33826 ^ _779999 : [(33833 ^ _779999) ^ [] : [c_Int_Oiszero(_1412839, hAPP(c_Int_Onumber__class_Onumber__of(_1412839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412841)))), -(c_Groups_Ozero__class_Ozero(_1412839) = hAPP(c_Int_Onumber__class_Onumber__of(_1412839), _1412841))], (33827 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_1412839) = hAPP(c_Int_Onumber__class_Onumber__of(_1412839), _1412841), -(c_Int_Oiszero(_1412839, hAPP(c_Int_Onumber__class_Onumber__of(_1412839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412841)))))]]], (16167 ^ _779999) ^ [_1071946, _1071948, _1071950, _1071952, _1071954] : [class_Rings_Oordered__semiring(_1071946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071946), _1071948), _1071950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071946), _1071952), _1071954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071946), c_Groups_Ozero__class_Ozero(_1071946)), _1071948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071946), c_Groups_Ozero__class_Ozero(_1071946)), _1071952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071946), _1071948), _1071952)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071946), _1071950), _1071954))))], (6869 ^ _779999) ^ [_892620, _892622, _892624] : [_892622 = _892624, -(hBOOL(hAPP(hAPP(c_member(_892620), _892622), hAPP(hAPP(c_Set_Oinsert(_892620), _892624), c_Orderings_Obot__class_Obot(tc_fun(_892620, tc_HOL_Obool))))))], (1614 ^ _779999) ^ [_803282, _803284] : [-(class_Groups_Oordered__ab__semigroup__add(_803282)), _803284 = _803282, class_Groups_Oordered__ab__semigroup__add(_803284)], (43169 ^ _779999) ^ [_1632677, _1632679, _1632681, _1632683] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632677), tc_List_Olist(_1632677))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632677), tc_List_Olist(_1632677)), _1632679), _1632681)), c_List_Olex(_1632677, _1632683))), 43172 ^ _779999 : [(43175 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632677)), _1632679) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632677)), _1632681))], (43173 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632677), tc_List_Olist(_1632677))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632677), tc_List_Olist(_1632677)), _1632679), _1632681)), c_List_Olexord(_1632677, _1632683))))]]], (34915 ^ _779999) ^ [_1432642, _1432644] : [class_Int_Onumber__ring(_1432642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432642), hAPP(c_Int_Onumber__class_Onumber__of(_1432642), c_Int_OMin)), _1432644) = hAPP(c_Groups_Ouminus__class_Ouminus(_1432642), _1432644))], (48881 ^ _779999) ^ [_1764250, _1764252, _1764254, _1764256] : [48883 ^ _779999 : [(48886 ^ _779999) ^ [] : [hBOOL(hAPP(_1764252, hAPP(hAPP(c_List_Onth(_1764254), _1764256), 48882 ^ [_1764250, _1764252, _1764254, _1764256])))], (48884 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48882 ^ [_1764250, _1764252, _1764254, _1764256]), _1764250)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764250), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764254)), _1764256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764250), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764254)), c_List_OtakeWhile(_1764254, _1764252, _1764256)))))], (30296 ^ _779999) ^ [_1347569, _1347571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1347569), _1347571)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1347571), _1347569) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1347571), _1347569)), _1347569)))], (11216 ^ _779999) ^ [_974333, _974335, _974337, _974339] : [class_Lattices_Osemilattice__inf(_974333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974333), _974335), _974337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974333), _974335), _974339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974333), _974335), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974333), _974337), _974339))))], (5184 ^ _779999) ^ [_859297, _859299, _859301, _859303] : [-(c_List_Olexord(_859303, _859299) = c_List_Olexord(_859301, _859297)), _859303 = _859301, _859299 = _859297], (24448 ^ _779999) ^ [_1237900, _1237902, _1237904, _1237906] : [class_Orderings_Olinorder(_1237900), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237900), _1237902), _1237904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237900), _1237906), _1237904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237900), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237900), _1237902), _1237906)), _1237904)))], (48494 ^ _779999) ^ [_1755954, _1755956, _1755958] : [-(hAPP(c_List_Orotate(_1755954, _1755956), hAPP(c_List_Orev(_1755954), _1755958)) = hAPP(c_List_Orev(_1755954), hAPP(c_List_Orotate(_1755954, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755954)), _1755958)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1755956, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755954)), _1755958)))), _1755958)))], (19151 ^ _779999) ^ [_1129085, _1129087, _1129089, _1129091] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1129085, _1129087, hAPP(hAPP(c_Set_Oinsert(_1129085), _1129089), c_Orderings_Obot__class_Obot(tc_fun(_1129085, tc_HOL_Obool)))), _1129091)), -(_1129089 = _1129091)], (42468 ^ _779999) ^ [_1615668, _1615670] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615668, tc_HOL_Obool), hAPP(c_Set_OPow(_1615668), _1615670)) = _1615670)], (19345 ^ _779999) ^ [_1132754, _1132756] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1132754, _1132756))))], (45682 ^ _779999) ^ [_1694831, _1694833, _1694835] : [-(hAPP(c_List_Otl(_1694831), hAPP(hAPP(c_List_Oappend(_1694831), _1694833), _1694835)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1694831), _1694831, hAPP(c_List_Otl(_1694831), _1694835), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1694831), tc_List_Olist(_1694831)), _1694831), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694831), tc_List_Olist(_1694831), tc_List_Olist(_1694831)), c_List_Oappend(_1694831)), _1694835))), _1694833))], (31584 ^ _779999) ^ [_1371906, _1371908, _1371910] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371906), _1371908), _1371910) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1371906, tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool)), _1371908), hAPP(hAPP(c_COMBC(_1371906, tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1371906, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool)), _1371906), c_Set_Oinsert(tc_fun(_1371906, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371906, tc_HOL_Obool), tc_fun(_1371906, tc_HOL_Obool), _1371906), c_Relation_OImage(_1371906, _1371906, _1371910)), hAPP(hAPP(c_COMBC(_1371906, tc_fun(_1371906, tc_HOL_Obool), tc_fun(_1371906, tc_HOL_Obool)), c_Set_Oinsert(_1371906)), c_Orderings_Obot__class_Obot(tc_fun(_1371906, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1371906, tc_HOL_Obool), tc_HOL_Obool)))))], (27224 ^ _779999) ^ [_1292490, _1292492, _1292494, _1292496, _1292498] : [class_Fields_Ofield(_1292490), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292490), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292492, _1292490), _1292494), _1292496)), _1292498) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292492, _1292490), hAPP(hAPP(c_COMBC(_1292492, _1292490, _1292490), hAPP(hAPP(c_COMBB(_1292490, tc_fun(_1292490, _1292490), _1292492), c_Rings_Oinverse__class_Odivide(_1292490)), _1292494)), _1292498)), _1292496))], (45919 ^ _779999) ^ [_1700094] : [class_Orderings_Olinorder(_1700094), -(c_Finite__Set_Ofun__left__comm(_1700094, tc_List_Olist(_1700094), c_List_Olinorder__class_Oinsort__key(_1700094, _1700094, c_COMBI(_1700094))))], (28684 ^ _779999) ^ [_1318767, _1318769, _1318771] : [class_Fields_Olinordered__field(_1318767), -(_1318769 = c_Groups_Ozero__class_Ozero(_1318767)), -(hAPP(c_Groups_Oabs__class_Oabs(_1318767), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318767), _1318771), _1318769)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318767), hAPP(c_Groups_Oabs__class_Oabs(_1318767), _1318771)), hAPP(c_Groups_Oabs__class_Oabs(_1318767), _1318769)))], (41702 ^ _779999) ^ [_1595932, _1595934, _1595936, _1595938, _1595940, _1595942] : [c_Finite__Set_Ofun__left__comm(_1595932, _1595934, _1595936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595932), _1595938)), -(hBOOL(hAPP(hAPP(c_member(_1595932), _1595940), _1595938))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595932, _1595934, _1595936), _1595942), hAPP(hAPP(c_Set_Oinsert(_1595932), _1595940), _1595938)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595932, _1595934, _1595936), hAPP(hAPP(_1595936, _1595940), _1595942)), _1595938))], (13886 ^ _779999) ^ [_1027540, _1027542] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027540), _1027542)), 13887 ^ _779999 : [(13894 ^ _779999) ^ [] : [_1027540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1027542 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13888 ^ _779999) ^ [] : [_1027540 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45620 ^ _779999) ^ [_1693625, _1693627, _1693629] : [-(hAPP(c_List_Otl(_1693625), hAPP(hAPP(c_List_Olist_OCons(_1693625), _1693627), _1693629)) = _1693629)], (3062 ^ _779999) ^ [_825606, _825608] : [_825608 = _825606, -(c_Equiv__Relations_Oquotient(_825608) = c_Equiv__Relations_Oquotient(_825606))], (29868 ^ _779999) ^ [_1340029, _1340031] : [class_Rings_Oring__1(_1340029), 29871 ^ _779999 : [(29878 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340031), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1340029), _1340031) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1340029), hAPP(c_Int_Onat, _1340031)))], (29872 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340031), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1340029), _1340031) = hAPP(c_Groups_Ouminus__class_Ouminus(_1340029), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1340029), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1340031)))))]]], (5805 ^ _779999) ^ [_871787, _871789, _871791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_871787), tc_HOL_Obool)), _871789), _871791)), -(c_Hoare__Mirabelle_Ohoare__derivs(_871787, _871791, _871789))], (24734 ^ _779999) ^ [_1243472, _1243474, _1243476] : [class_Orderings_Olinorder(_1243472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1243472), _1243474)), -(_1243474 = c_Orderings_Obot__class_Obot(tc_fun(_1243472, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1243472, hAPP(hAPP(c_Set_Oinsert(_1243472), _1243476), _1243474)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243472), _1243476), c_Big__Operators_Olinorder__class_OMax(_1243472, _1243474)))], (32787 ^ _779999) ^ [_1395022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395022), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1395022)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34859 ^ _779999) ^ [_1431832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431832), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431832)), c_Int_OMin)))], (44194 ^ _779999) ^ [_1661866, _1661868, _1661870, _1661872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661866), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661868)), _1661870))), 44197 ^ _779999 : [(44204 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Onth(_1661868), _1661870), _1661866) = _1661872, -(hAPP(hAPP(c_List_Olist__update(_1661868, _1661870), _1661866), _1661872) = _1661870)], (44198 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1661868, _1661870), _1661866), _1661872) = _1661870, -(hAPP(hAPP(c_List_Onth(_1661868), _1661870), _1661866) = _1661872)]]], (44756 ^ _779999) ^ [_1673120, _1673122] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1673120)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1673122)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1673120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1673122)) = c_List_Olist_ONil(tc_Int_Oint))], (28960 ^ _779999) ^ [_1323882, _1323884, _1323886, _1323888] : [class_Fields_Olinordered__field(_1323882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323882), c_Groups_Ozero__class_Ozero(_1323882)), _1323884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323882), _1323886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323882), _1323888), _1323884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323882), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323882), _1323886), _1323884)), _1323888)))], (43121 ^ _779999) ^ [_1630802, _1630804, _1630806, _1630808] : [class_Rings_Olinordered__semidom(_1630802), 43127 ^ _779999 : [(43130 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630802), c_Groups_Ozero__class_Ozero(_1630802)), hAPP(_1630808, 43126 ^ [_1630802, _1630804, _1630806, _1630808])))], (43128 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630804), 43126 ^ [_1630802, _1630804, _1630806, _1630808]), _1630806)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630802), c_Groups_Ozero__class_Ozero(_1630802)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1630804, _1630802), _1630808), _1630806))))], (10591 ^ _779999) ^ [_962278, _962280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962280), _962278)), _962280)))], (16373 ^ _779999) ^ [_1075757, _1075759, _1075761] : [class_Rings_Olinordered__semiring__strict(_1075757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075757), c_Groups_Ozero__class_Ozero(_1075757)), _1075759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075757), _1075761), c_Groups_Ozero__class_Ozero(_1075757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075757), _1075761), _1075759)), c_Groups_Ozero__class_Ozero(_1075757))))], (38321 ^ _779999) ^ [_1512963, _1512965, _1512967] : [c_Wellfounded_Owf(_1512963, _1512965), c_Wellfounded_Owf(_1512963, _1512967), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512963, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1512963, _1512963), _1512965)), hAPP(c_Relation_ORange(_1512963, _1512963), _1512967)) = c_Orderings_Obot__class_Obot(tc_fun(_1512963, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1512963, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512963, _1512963), tc_HOL_Obool)), _1512965), _1512967)))], (45418 ^ _779999) ^ [_1689057, _1689059, _1689061] : [hAPP(hAPP(c_List_Odrop(_1689057), _1689059), _1689061) = c_List_Olist_ONil(_1689057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689057)), _1689061)), _1689059)))], (19097 ^ _779999) ^ [_1128011, _1128013, _1128015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128011), _1128013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1128015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128015), _1128011)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128015), _1128013))))], (10173 ^ _779999) ^ [_955345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _955345)), _955345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46382 ^ _779999) ^ [_1710001] : [-(hAPP(c_List_Omap(_1710001, _1710001), c_Fun_Oid(_1710001)) = c_Fun_Oid(tc_List_Olist(_1710001)))], (42568 ^ _779999) ^ [_1618165, _1618167] : [class_Complete__Lattice_Ocomplete__lattice(_1618165), -(c_Complete__Lattice_OSup__class_OSup(_1618165, hAPP(hAPP(c_Set_Oinsert(_1618165), _1618167), c_Orderings_Obot__class_Obot(tc_fun(_1618165, tc_HOL_Obool)))) = _1618167)], (6879 ^ _779999) ^ [_892874, _892876, _892878, _892880] : [hBOOL(hAPP(hAPP(c_member(_892874), _892876), hAPP(hAPP(c_Set_Oinsert(_892874), _892878), _892880))), -(_892876 = _892878), -(hBOOL(hAPP(hAPP(c_member(_892874), _892876), _892880)))], (49656 ^ _779999) ^ [_1781531, _1781533, _1781535] : [c_List_Olist__ex1(_1781531, _1781533, _1781535), 49660 ^ _779999 : [(49665 ^ _779999) ^ [_1781777] : [-(_1781777 = 49659 ^ [_1781531, _1781533, _1781535]), hBOOL(hAPP(hAPP(c_member(_1781531), _1781777), hAPP(c_List_Oset(_1781531), _1781535))), hBOOL(hAPP(_1781533, _1781777))], (49663 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1781533, 49659 ^ [_1781531, _1781533, _1781535])))], (49661 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781531), 49659 ^ [_1781531, _1781533, _1781535]), hAPP(c_List_Oset(_1781531), _1781535))))]]], (52316 ^ _779999) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (34117 ^ _779999) ^ [_1418068, _1418070] : [class_Int_Onumber__ring(_1418068), class_Int_Oring__char__0(_1418068), 34124 ^ _779999 : [(34131 ^ _779999) ^ [] : [c_Int_Oiszero(_1418068, hAPP(c_Int_Onumber__class_Onumber__of(_1418068), _1418070)), -(c_Int_Oiszero(_1418068, hAPP(c_Int_Onumber__class_Onumber__of(_1418068), c_Int_OBit0(_1418070))))], (34125 ^ _779999) ^ [] : [c_Int_Oiszero(_1418068, hAPP(c_Int_Onumber__class_Onumber__of(_1418068), c_Int_OBit0(_1418070))), -(c_Int_Oiszero(_1418068, hAPP(c_Int_Onumber__class_Onumber__of(_1418068), _1418070)))]]], (38032 ^ _779999) ^ [_1505791] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1505791)))], (17900 ^ _779999) ^ [_1105776] : [_1105776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105776) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2236 ^ _779999) ^ [_812829, _812831, _812833, _812835, _812837, _812839] : [-(c_SetInterval_Oord_OatMost(_812839, _812835, _812831) = c_SetInterval_Oord_OatMost(_812837, _812833, _812829)), _812839 = _812837, _812835 = _812833, _812831 = _812829], (44474 ^ _779999) ^ [_1667852, _1667854, _1667856] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667852, tc_HOL_Obool)), hAPP(c_List_Oset(_1667852), c_List_Oremove1(_1667852, _1667854, _1667856))), hAPP(c_List_Oset(_1667852), _1667856))))], (15895 ^ _779999) ^ [_1066590, _1066592] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066590), _1066592), 15898 ^ _779999 : [(15901 ^ _779999) ^ [] : [-(_1066592 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15899 ^ _779999) ^ [] : [-(_1066590 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (40351 ^ _779999) ^ [_1565101, _1565103] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565101, _1565101), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565101, _1565103)), c_Relation_OId(_1565101)) = c_Transitive__Closure_Ortrancl(_1565101, _1565103))], (12441 ^ _779999) ^ [_1000196, _1000198, _1000200] : [class_Lattices_Olattice(_1000196), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000196), _1000198)), -(_1000198 = c_Orderings_Obot__class_Obot(tc_fun(_1000196, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1000196, hAPP(hAPP(c_Set_Oinsert(_1000196), _1000200), _1000198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1000196), _1000200), c_Big__Operators_Olattice__class_OSup__fin(_1000196, _1000198)))], (30064 ^ _779999) ^ [_1343429, _1343431] : [class_Rings_Oring__1(_1343429), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343429), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343431)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343429), hAPP(c_Int_Oring__1__class_Oof__int(_1343429), _1343431)))], (3662 ^ _779999) ^ [_834918, _834920, _834922, _834924, _834926, _834928] : [-(c_List_Opartition(_834928, _834924, _834920) = c_List_Opartition(_834926, _834922, _834918)), _834928 = _834926, _834924 = _834922, _834920 = _834918], (48364 ^ _779999) ^ [_1753216, _1753218, _1753220] : [_1753218 = hAPP(hAPP(c_List_Olist_OCons(_1753216), _1753220), c_List_Olist_ONil(_1753216)), -(hAPP(c_List_Orev(_1753216), _1753218) = hAPP(hAPP(c_List_Olist_OCons(_1753216), _1753220), c_List_Olist_ONil(_1753216)))], (44764 ^ _779999) ^ [_1673255, _1673257] : [-(c_List_Oset__Cons(_1673255, _1673257, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1673255)), c_List_Olist_ONil(_1673255)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1673255), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1673255, tc_List_Olist(_1673255), hAPP(hAPP(c_COMBC(_1673255, tc_List_Olist(_1673255), tc_List_Olist(_1673255)), c_List_Olist_OCons(_1673255)), c_List_Olist_ONil(_1673255))), _1673257))], (49702 ^ _779999) ^ [_1782526, _1782528, _1782530, _1782532, _1782534] : [-(_1782526 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1782528, _1782530, _1782532, _1782534), _1782526) = c_Lazy__Sequence_Ohb__bind(_1782528, _1782530, hAPP(_1782532, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1782526), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1782528, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1782530))), _1782534), _1782526)))], (18859 ^ _779999) ^ [_1124168, _1124170] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124168), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1124170) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1124168, _1124170))], (45666 ^ _779999) ^ [_1694522, _1694524] : [-(c_List_Orotate(_1694522, _1694524) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1694522), tc_List_Olist(_1694522)), _1694524), c_List_Orotate1(_1694522)))], (5302 ^ _779999) ^ [_861152, _861154, _861156, _861158] : [-(c_Transitive__Closure_Otrancl(_861158, _861154) = c_Transitive__Closure_Otrancl(_861156, _861152)), _861158 = _861156, _861154 = _861152], (20136 ^ _779999) ^ [_1146805, _1146807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146805), hAPP(c_Int_Onat, _1146807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146805)), _1146807)))], (46942 ^ _779999) ^ [_1722538, _1722540, _1722542, _1722544, _1722546, _1722548, _1722550] : [c_List_Olist__all2(_1722538, _1722540, _1722542, hAPP(hAPP(c_List_Omap(_1722544, _1722538), _1722546), _1722548), _1722550), -(c_List_Olist__all2(_1722544, _1722540, hAPP(hAPP(c_COMBB(_1722538, tc_fun(_1722540, tc_HOL_Obool), _1722544), _1722542), _1722546), _1722548, _1722550))], (28650 ^ _779999) ^ [_1318273, _1318275, _1318277, _1318279] : [class_Fields_Ofield__inverse__zero(_1318273), 28653 ^ _779999 : [(28654 ^ _779999) ^ [] : [_1318275 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318273), _1318277), _1318279), 28657 ^ _779999 : [(28664 ^ _779999) ^ [] : [_1318279 = c_Groups_Ozero__class_Ozero(_1318273), -(_1318275 = c_Groups_Ozero__class_Ozero(_1318273))], (28658 ^ _779999) ^ [] : [-(_1318279 = c_Groups_Ozero__class_Ozero(_1318273)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318273), _1318275), _1318279) = _1318277)]]], (28670 ^ _779999) ^ [] : [-(_1318275 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318273), _1318277), _1318279)), 28673 ^ _779999 : [(28676 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318273), _1318275), _1318279) = _1318277], (28674 ^ _779999) ^ [] : [_1318279 = c_Groups_Ozero__class_Ozero(_1318273)]], 28677 ^ _779999 : [(28680 ^ _779999) ^ [] : [_1318275 = c_Groups_Ozero__class_Ozero(_1318273)], (28678 ^ _779999) ^ [] : [-(_1318279 = c_Groups_Ozero__class_Ozero(_1318273))]]]]], (40507 ^ _779999) ^ [_1568786, _1568788, _1568790, _1568792] : [-(hBOOL(hAPP(hAPP(c_member(_1568786), _1568788), hAPP(c_Relation_ODomain(_1568786, _1568786), _1568790)))), 40510 ^ _779999 : [(40517 ^ _779999) ^ [] : [_1568788 = _1568792, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568786, _1568786)), hAPP(hAPP(c_Product__Type_OPair(_1568786, _1568786), _1568788), _1568792)), c_Transitive__Closure_Ortrancl(_1568786, _1568790))))], (40511 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568786, _1568786)), hAPP(hAPP(c_Product__Type_OPair(_1568786, _1568786), _1568788), _1568792)), c_Transitive__Closure_Ortrancl(_1568786, _1568790))), -(_1568788 = _1568792)]]], (15159 ^ _779999) ^ [_1052340, _1052342, _1052344, _1052346] : [hBOOL(hAPP(hAPP(c_member(_1052340), _1052342), c_SetInterval_Oord_OatLeast(_1052340, _1052344, _1052346))), -(hBOOL(hAPP(hAPP(_1052344, _1052346), _1052342)))], (51990 ^ _779999) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (38798 ^ _779999) ^ [_1527526, _1527528, _1527530, _1527532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527526), _1527528)), 38804 ^ _779999 : [(38807 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527530), hAPP(_1527532, 38803 ^ [_1527526, _1527528, _1527530, _1527532])))], (38805 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527526), 38803 ^ [_1527526, _1527528, _1527530, _1527532]), _1527528)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1527526, _1527530)), hAPP(hAPP(c_Product__Type_OSigma(_1527526, _1527530), _1527528), _1527532)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527526, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1527530, tc_HOL_Obool), tc_Nat_Onat, _1527526), c_Finite__Set_Ocard(_1527530)), _1527532)), _1527528))], (42682 ^ _779999) ^ [_1620462, _1620464, _1620466, _1620468, _1620470, _1620472, _1620474, _1620476] : [c_Fun_Oinj__on(_1620462, _1620464, _1620466, _1620468), 42688 ^ _779999 : [(42691 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620462, tc_HOL_Obool)), hAPP(_1620474, 42687 ^ [_1620462, _1620464, _1620466, _1620468, _1620470, _1620472, _1620474, _1620476])), _1620468))], (42689 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620470), 42687 ^ [_1620462, _1620464, _1620466, _1620468, _1620470, _1620472, _1620474, _1620476]), _1620472)))]], hBOOL(hAPP(hAPP(c_member(_1620470), _1620476), _1620472)), -(hAPP(c_Set_Oimage(_1620462, _1620464, _1620466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620470, tc_fun(_1620462, tc_HOL_Obool)), _1620472), _1620474)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620470, tc_fun(_1620464, tc_HOL_Obool)), _1620472), hAPP(hAPP(c_COMBB(tc_fun(_1620462, tc_HOL_Obool), tc_fun(_1620464, tc_HOL_Obool), _1620470), c_Set_Oimage(_1620462, _1620464, _1620466)), _1620474)))], (41945 ^ _779999) ^ [_1602624, _1602626, _1602628, _1602630] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602624, tc_fun(_1602626, tc_HOL_Obool)), _1602628), _1602630) = c_Orderings_Otop__class_Otop(tc_fun(_1602626, tc_HOL_Obool)), 41948 ^ _779999 : [(41949 ^ _779999) ^ [_1602740] : [hBOOL(hAPP(hAPP(c_member(_1602624), _1602740), _1602628)), -(hAPP(_1602630, _1602740) = c_Orderings_Otop__class_Otop(tc_fun(_1602626, tc_HOL_Obool)))]]], (47906 ^ _779999) ^ [_1744429, _1744431] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1744429, _1744431)))], (35191 ^ _779999) ^ [_1441489, _1441491, _1441493, _1441495] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1441489, tc_fun(_1441491, tc_HOL_Obool))), _1441493), _1441495)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1441489, _1441491)), hAPP(hAPP(c_Product__Type_OPair(_1441489, _1441491), _1441493), _1441495)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1441489, _1441491), tc_HOL_Obool)))))], (8346 ^ _779999) ^ [_922189, _922191, _922193, _922195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922189, tc_HOL_Obool)), _922191), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922189, tc_HOL_Obool)), _922193), _922195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922189, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922189, tc_HOL_Obool)), _922191), _922193)), _922195)))], (12713 ^ _779999) ^ [_1005002, _1005004] : [class_Lattices_Olattice(_1005002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005002), _1005004)), -(_1005004 = c_Orderings_Obot__class_Obot(tc_fun(_1005002, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1005002), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005002), 12726 ^ [_1005002, _1005004]), 12727 ^ [_1005002, _1005004])), hAPP(hAPP(c_Set_Oinsert(_1005002), 12726 ^ [_1005002, _1005004]), hAPP(hAPP(c_Set_Oinsert(_1005002), 12727 ^ [_1005002, _1005004]), c_Orderings_Obot__class_Obot(tc_fun(_1005002, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1005002), c_Big__Operators_Olattice__class_OInf__fin(_1005002, _1005004)), _1005004)))], (18261 ^ _779999) ^ [_1112423, _1112425, _1112427] : [class_Orderings_Oorder(_1112423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112423), _1112425), _1112427)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1112423, _1112427), _1112425) = c_Orderings_Obot__class_Obot(tc_fun(_1112423, tc_HOL_Obool)))], (46314 ^ _779999) ^ [_1707940, _1707942, _1707944, _1707946, _1707948, _1707950, _1707952, _1707954] : [-(hAPP(hAPP(c_List_Ozip(_1707940, _1707942), hAPP(hAPP(c_List_Omap(_1707944, _1707940), _1707946), _1707948)), hAPP(hAPP(c_List_Omap(_1707950, _1707942), _1707952), _1707954)) = hAPP(hAPP(c_List_Omap(tc_prod(_1707944, _1707950), tc_prod(_1707940, _1707942)), hAPP(c_Product__Type_Oprod_Oprod__case(_1707944, _1707950, tc_prod(_1707940, _1707942)), hAPP(hAPP(c_COMBC(_1707944, tc_fun(_1707950, _1707942), tc_fun(_1707950, tc_prod(_1707940, _1707942))), hAPP(hAPP(c_COMBB(tc_fun(_1707942, tc_prod(_1707940, _1707942)), tc_fun(tc_fun(_1707950, _1707942), tc_fun(_1707950, tc_prod(_1707940, _1707942))), _1707944), c_COMBB(_1707942, tc_prod(_1707940, _1707942), _1707950)), hAPP(hAPP(c_COMBB(_1707940, tc_fun(_1707942, tc_prod(_1707940, _1707942)), _1707944), c_Product__Type_OPair(_1707940, _1707942)), _1707946))), _1707952))), hAPP(hAPP(c_List_Ozip(_1707944, _1707950), _1707948), _1707954)))], (35842 ^ _779999) ^ [_1455229] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1455229) = 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)))], (49416 ^ _779999) ^ [_1776655, _1776657, _1776659] : [hBOOL(hAPP(hAPP(c_member(_1776655), _1776657), hAPP(c_List_Oset(_1776655), _1776659))), -(_1776659 = hAPP(hAPP(c_List_Oappend(_1776655), 49419 ^ [_1776655, _1776657, _1776659]), hAPP(hAPP(c_List_Olist_OCons(_1776655), _1776657), 49420 ^ [_1776655, _1776657, _1776659])))], (49414 ^ _779999) ^ [_1776609, _1776611] : [c_List_Olist__ex(_1776609, _1776611, c_List_Olist_ONil(_1776609))], (48729 ^ _779999) ^ [_1761038, _1761040, _1761042] : [class_Orderings_Olinorder(_1761038), c_List_Olinorder__class_Osorted(_1761038, _1761040), -(c_List_Olinorder__class_Osorted(_1761038, c_List_OdropWhile(_1761038, _1761042, _1761040)))], (17800 ^ _779999) ^ [_1104069, _1104071, _1104073, _1104075] : [class_Groups_Ocomm__monoid__add(_1104069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104071), _1104073)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1104069), _1104075), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1104071, _1104073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104069), hAPP(_1104075, _1104071)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1104069), _1104075), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1104071, _1104073))))], (15147 ^ _779999) ^ [_1052095, _1052097, _1052099, _1052101] : [hBOOL(hAPP(hAPP(c_member(_1052095), _1052097), c_SetInterval_Oord_OlessThan(_1052095, _1052099, _1052101))), -(hBOOL(hAPP(hAPP(_1052099, _1052097), _1052101)))], (5646 ^ _779999) ^ [_866412, _866414] : [_866414 = _866412, -(c_COMBI(_866414) = c_COMBI(_866412))], (17171 ^ _779999) ^ [_1090731, _1090733, _1090735] : [class_Rings_Olinordered__idom(_1090731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090731), c_Groups_Ozero__class_Ozero(_1090731)), _1090733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090731), c_Groups_Ozero__class_Ozero(_1090731)), _1090735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090731), _1090735), c_Groups_Oone__class_Oone(_1090731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090731), _1090733), _1090735)), _1090733)))], (44150 ^ _779999) ^ [_1660801, _1660803, _1660805, _1660807] : [-(hAPP(hAPP(c_List_Olist__update(_1660801, hAPP(hAPP(c_List_Olist_OCons(_1660801), _1660803), _1660805)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1660807) = hAPP(hAPP(c_List_Olist_OCons(_1660801), _1660807), _1660805))], (20106 ^ _779999) ^ [_1146378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146378))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1146378)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33751 ^ _779999) ^ [_1411666, _1411668, _1411670, _1411672] : [-(hAPP(c_Nat_Onat_Onat__rec(_1411666, _1411668, _1411670), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411672)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1411666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411672))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411666, _1411666), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1411666, tc_fun(_1411666, _1411666)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1411666, tc_fun(_1411666, _1411666)), tc_Int_Oint), c_If(_1411666)), c_Nat__Numeral_Oneg)), _1411668)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411666, _1411666), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1411666, _1411666), tc_Int_Oint), _1411670), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411666, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1411666, _1411668, _1411670)), c_Int_Onat)))))], (34089 ^ _779999) ^ [_1417542, _1417544] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1417542)), c_Int_OBit1(_1417544)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417542), _1417544)))], (20627 ^ _779999) ^ [_1154559] : [-(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)), _1154559)))], (31206 ^ _779999) ^ [_1364710, _1364712, _1364714] : [class_Rings_Olinordered__idom(_1364710), -(c_Groups_Osgn__class_Osgn(_1364710, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364710), _1364712), _1364714)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364710), c_Groups_Osgn__class_Osgn(_1364710, _1364712)), c_Groups_Osgn__class_Osgn(_1364710, _1364714)))], (21421 ^ _779999) ^ [_1170028, _1170030, _1170032] : [class_Orderings_Olinorder(_1170028), 21424 ^ _779999 : [(21431 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170028), _1170032), _1170030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170028, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1170028), _1170030)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1170028), _1170032))))], (21425 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170028, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1170028), _1170030)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1170028), _1170032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170028), _1170032), _1170030)))]]], (33601 ^ _779999) ^ [_1408235, _1408237] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408235))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408237)) = 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)))), _1408235), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408237)))], (29152 ^ _779999) ^ [_1327462, _1327464, _1327466] : [class_Fields_Olinordered__field(_1327462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327462), _1327464), _1327466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327462), _1327464), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327462), _1327464), _1327466)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327462), c_Groups_Oone__class_Oone(_1327462)), c_Groups_Oone__class_Oone(_1327462))))))], (38061 ^ _779999) ^ [_1506321, _1506323, _1506325] : [c_Wellfounded_Owf(_1506321, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506321, _1506321), tc_HOL_Obool)), _1506323), _1506325)), -(c_Wellfounded_Owf(_1506321, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506321, _1506321), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506321, _1506321), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1506321, _1506321, _1506321), _1506323), _1506323)), hAPP(hAPP(c_Relation_Orel__comp(_1506321, _1506321, _1506321), _1506325), _1506323))), _1506325)))], (35394 ^ _779999) ^ [_1445997] : [class_Rings_Osemiring__1(_1445997), -(hBOOL(hAPP(hAPP(c_member(_1445997), c_Groups_Oone__class_Oone(_1445997)), c_Nat_Osemiring__1__class_ONats(_1445997))))], (6341 ^ _779999) ^ [_882040, _882042] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_882040, tc_HOL_Obool)), _882042), _882042) = _882042)], (47623 ^ _779999) ^ [_1739063, _1739065, _1739067, _1739069] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1739063, tc_Nat_Onat), _1739063), c_Product__Type_Ofst(_1739063, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1739063, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1739063, 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(_1739063, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1739063, tc_Nat_Onat))), _1739065)), hAPP(hAPP(c_List_Ozip(_1739063, tc_Nat_Onat), _1739067), c_List_Oupt(_1739069, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1739069), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739063)), _1739067)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1739063, tc_Nat_Onat), _1739063), c_Product__Type_Ofst(_1739063, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1739063, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1739063, 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(_1739063, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1739063, 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(_1739063, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1739063, tc_Nat_Onat))), _1739069))), _1739065)), hAPP(hAPP(c_List_Ozip(_1739063, tc_Nat_Onat), _1739067), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739063)), _1739067))))))], (13610 ^ _779999) ^ [_1022894] : [-(hAPP(c_Finite__Set_Ocard(_1022894), c_Orderings_Obot__class_Obot(tc_fun(_1022894, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46692 ^ _779999) ^ [_1716585] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716585)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (27400 ^ _779999) ^ [_1295463, _1295465, _1295467] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1295463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295465), _1295467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1295463), _1295465)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1295463), _1295467)))], (31568 ^ _779999) ^ [_1371316, _1371318, _1371320] : [_1371318 = c_Orderings_Obot__class_Obot(tc_fun(_1371316, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371316), _1371318), _1371320) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1371316, tc_HOL_Obool), tc_HOL_Obool)))], (45546 ^ _779999) ^ [_1692205, _1692207, _1692209, _1692211, _1692213] : [-(hAPP(hAPP(c_List_Ozip(_1692205, _1692207), _1692209), hAPP(hAPP(c_List_Oappend(_1692207), _1692211), _1692213)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1692205, _1692207)), hAPP(hAPP(c_List_Ozip(_1692205, _1692207), hAPP(hAPP(c_List_Otake(_1692205), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692207)), _1692211)), _1692209)), _1692211)), hAPP(hAPP(c_List_Ozip(_1692205, _1692207), hAPP(hAPP(c_List_Odrop(_1692205), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692207)), _1692211)), _1692209)), _1692213)))], (43427 ^ _779999) ^ [_1640702, _1640704, _1640706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1640702, _1640702), tc_HOL_Obool)), _1640704), _1640706)), c_Relation_Orefl__on(_1640702, c_Orderings_Otop__class_Otop(tc_fun(_1640702, tc_HOL_Obool)), _1640706), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1640702), tc_List_Olist(_1640702)), tc_HOL_Obool)), c_List_Olistrel1(_1640702, _1640704)), c_List_Olistrel(_1640702, _1640706))))], (18505 ^ _779999) ^ [_1116998, _1117000] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1116998, _1117000)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117000), _1116998))], (29362 ^ _779999) ^ [_1331569, _1331571] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331569), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331571)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331569)), _1331571))], (47402 ^ _779999) ^ [_1733071, _1733073] : [-(c_List_Oconcat(_1733071, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733071), tc_List_Olist(_1733071)), c_List_Olist_Olist__case(tc_List_Olist(_1733071), _1733071, c_List_Olist_ONil(_1733071), hAPP(hAPP(c_COMBB(tc_List_Olist(_1733071), tc_fun(tc_List_Olist(_1733071), tc_List_Olist(_1733071)), _1733071), c_COMBK(tc_List_Olist(_1733071), tc_List_Olist(_1733071))), hAPP(hAPP(c_COMBC(_1733071, tc_List_Olist(_1733071), tc_List_Olist(_1733071)), c_List_Olist_OCons(_1733071)), c_List_Olist_ONil(_1733071))))), _1733073)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733071), _1733071), c_List_Ohd(_1733071)), hAPP(c_List_Ofilter(tc_List_Olist(_1733071), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1733071)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1733071), tc_List_Olist(_1733071), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1733071)))), _1733073)))], (9937 ^ _779999) ^ [_951082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951082), hAPP(c_Nat_OSuc, _951082))))], (39897 ^ _779999) ^ [_1553418, _1553420, _1553422, _1553424, _1553426] : [c_Finite__Set_Ofolding__idem(_1553418, _1553420, _1553422, _1553424), -(hAPP(c_Fun_Ocomp(_1553420, _1553420, _1553420, hAPP(_1553422, _1553426)), hAPP(_1553422, _1553426)) = hAPP(_1553422, _1553426))], (38000 ^ _779999) ^ [_1505127, _1505129, _1505131] : [c_Wellfounded_Owf(_1505127, _1505129), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505127, _1505127)), hAPP(hAPP(c_Product__Type_OPair(_1505127, _1505127), _1505131), _1505131)), _1505129))], (7229 ^ _779999) ^ [_899485, _899487, _899489, _899491, _899493] : [hBOOL(hAPP(hAPP(c_member(_899485), _899487), hAPP(c_Set_Oimage(_899489, _899485, _899491), _899493))), 7233 ^ _779999 : [(7236 ^ _779999) ^ [] : [-(_899487 = hAPP(_899491, 7232 ^ [_899485, _899487, _899489, _899491, _899493]))], (7234 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899489), 7232 ^ [_899485, _899487, _899489, _899491, _899493]), _899493)))]]], (33943 ^ _779999) ^ [_1415096, _1415098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1415096)), c_Int_OBit0(_1415098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415096), _1415098)))], (50543 ^ _779999) ^ [_1801711, _1801713] : [c_Relation_Otrans(_1801711, _1801713), -(c_Relation_Otrans(_1801711, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1801711, _1801711), tc_HOL_Obool)), _1801713), c_Relation_OId(_1801711))))], (22872 ^ _779999) ^ [_1204867, _1204869, _1204871, _1204873, _1204875, _1204877] : [-(hAPP(c_Set_Oimage(_1204867, _1204869, _1204871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204873, tc_fun(_1204867, tc_HOL_Obool)), _1204875), _1204877)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204873, tc_fun(_1204869, tc_HOL_Obool)), _1204875), hAPP(hAPP(c_COMBB(tc_fun(_1204867, tc_HOL_Obool), tc_fun(_1204869, tc_HOL_Obool), _1204873), c_Set_Oimage(_1204867, _1204869, _1204871)), _1204877)))], (29648 ^ _779999) ^ [_1336112, _1336114] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336112), _1336114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1336114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29657 ^ _779999 : [(29660 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336112), _1336114)))], (29658 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336112)))]], 29661 ^ _779999 : [(29664 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336114), _1336112)))], (29662 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1336112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (39917 ^ _779999) ^ [_1553804, _1553806, _1553808, _1553810, _1553812, _1553814, _1553816, _1553818] : [class_Groups_Ocomm__monoid__mult(_1553804), c_Fun_Oinj__on(_1553806, _1553808, _1553810, _1553812), _1553814 = hAPP(c_Set_Oimage(_1553806, _1553808, _1553810), _1553812), 39931 ^ _779999 : [(39934 ^ _779999) ^ [] : [hAPP(_1553816, 39930 ^ [_1553804, _1553806, _1553808, _1553810, _1553812, _1553814, _1553816, _1553818]) = hAPP(hAPP(c_Fun_Ocomp(_1553808, _1553804, _1553806, _1553818), _1553810), 39930 ^ [_1553804, _1553806, _1553808, _1553810, _1553812, _1553814, _1553816, _1553818])], (39932 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553806), 39930 ^ [_1553804, _1553806, _1553808, _1553810, _1553812, _1553814, _1553816, _1553818]), _1553812)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1553808, _1553804), _1553818), _1553814) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1553806, _1553804), _1553816), _1553812))], (218 ^ _779999) ^ [_783394, _783396, _783398, _783400] : [-(c_Int_Oiszero(_783398, _783394)), c_Int_Oiszero(_783400, _783396), _783400 = _783398, _783396 = _783394], (22279 ^ _779999) ^ [_1192187] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1192187, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1192187), hAPP(c_COMBK(tc_HOL_Obool, _1192187), c_fTrue)))], (49980 ^ _779999) ^ [_1789098, _1789100, _1789102, _1789104] : [-(c_List_Oreplicate(_1789098, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1789100), _1789102), _1789104) = hAPP(hAPP(c_List_Oappend(_1789098), c_List_Oreplicate(_1789098, _1789100, _1789104)), c_List_Oreplicate(_1789098, _1789102, _1789104)))], (3500 ^ _779999) ^ [_832419, _832421, _832423, _832425, _832427, _832429, _832431, _832433] : [-(c_Enum_Oproduct(_832433, _832429, _832425, _832421) = c_Enum_Oproduct(_832431, _832427, _832423, _832419)), _832433 = _832431, _832429 = _832427, _832425 = _832423, _832421 = _832419], (18971 ^ _779999) ^ [_1126132, _1126134] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126132), _1126134))), -(_1126132 = _1126134), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126134), _1126132)))], (50086 ^ _779999) ^ [_1790913, _1790915] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1790913), _1790915))), 50089 ^ _779999 : [(50096 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1790913), _1790915))), -(c_Lazy__Sequence_Osmall__lazy_H(_1790913, _1790915) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1790915), c_Lazy__Sequence_Osmall__lazy_H(_1790913, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1790915), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50090 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1790913), _1790915)), -(c_Lazy__Sequence_Osmall__lazy_H(_1790913, _1790915) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (13335 ^ _779999) ^ [_1017457, _1017459] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017457), _1017459) = _1017457, -(_1017459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14810 ^ _779999) ^ [_1045864] : [class_Rings_Olinordered__semidom(_1045864), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045864), c_Groups_Ozero__class_Ozero(_1045864)), c_Groups_Oone__class_Oone(_1045864))))], (18857 ^ _779999) ^ [_1124137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124137)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (49730 ^ _779999) ^ [_1783138, _1783140, _1783142, _1783144, _1783146, _1783148, _1783150] : [-(c_New__Random__Sequence_Opos__decr__bind(_1783138, _1783140, _1783142, _1783144, _1783146, _1783148, _1783150) = c_New__DSequence_Opos__decr__bind(_1783138, _1783140, hAPP(hAPP(hAPP(_1783142, _1783146), _1783148), _1783150), hAPP(hAPP(c_COMBC(_1783138, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1783140))), hAPP(hAPP(c_COMBC(_1783138, 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(_1783140)))), hAPP(hAPP(c_COMBC(_1783138, 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(_1783140))))), _1783144), _1783146)), _1783148)), _1783150)))], (45903 ^ _779999) ^ [_1699729, _1699731, _1699733, _1699735, _1699737, _1699739] : [class_Orderings_Olinorder(_1699729), -(hAPP(_1699731, _1699733) = hAPP(_1699731, _1699735)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699737, _1699729, _1699731), _1699735), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699737, _1699729, _1699731), _1699733), _1699739)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699737, _1699729, _1699731), _1699733), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699737, _1699729, _1699731), _1699735), _1699739)))], (14061 ^ _779999) ^ [_1030843, _1030845, _1030847, _1030849, _1030851, _1030853, _1030855] : [c_Finite__Set_Ofolding__image__simple(_1030843, _1030845, _1030847, _1030849, _1030851, _1030853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030845), _1030855)), -(hAPP(_1030853, _1030855) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030843, _1030845, _1030847), _1030851), _1030849), _1030855))], (5460 ^ _779999) ^ [_863557, _863559] : [_863559 = _863557, -(c_Fun_Oid(_863559) = c_Fun_Oid(_863557))], (14365 ^ _779999) ^ [_1036565, _1036567] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1036565), _1036567)))), -(_1036567 = c_Orderings_Obot__class_Obot(tc_fun(_1036565, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036565), _1036567))], (38267 ^ _779999) ^ [_1511291, _1511293, _1511295, _1511297] : [38268 ^ _779999 : [(38269 ^ _779999) ^ [_1511366] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1511295, _1511291)), hAPP(hAPP(c_Product__Type_OPair(_1511295, _1511291), _1511366), _1511293)), _1511297))]], -(hBOOL(hAPP(hAPP(c_member(_1511291), _1511293), hAPP(c_Relation_ORange(_1511295, _1511291), _1511297))))], (11623 ^ _779999) ^ [_983680, _983682, _983684, _983686, _983688, _983690] : [c_Fun_Oinj__on(_983680, _983682, _983684, _983686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983680, tc_HOL_Obool)), _983688), _983686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983680, tc_HOL_Obool)), _983690), _983686)), -(hAPP(c_Set_Oimage(_983680, _983682, _983684), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983680, tc_HOL_Obool)), _983688), _983690)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983682, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983680, _983682, _983684), _983688)), hAPP(c_Set_Oimage(_983680, _983682, _983684), _983690)))], (37403 ^ _779999) ^ [_1488997, _1488999, _1489001, _1489003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1488997), _1488999)), -(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), _1488997), _1489001)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488999), _1489003))), c_FunDef_Opair__leq)))], (29376 ^ _779999) ^ [_1331808, _1331810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331808), 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)), _1331810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331808), _1331810)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29138 ^ _779999) ^ [_1327215, _1327217, _1327219, _1327221, _1327223] : [class_Fields_Ofield(_1327215), -(_1327217 = c_Groups_Ozero__class_Ozero(_1327215)), -(_1327219 = c_Groups_Ozero__class_Ozero(_1327215)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1327215), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327215), _1327221), _1327217)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327215), _1327223), _1327219)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1327215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327215), _1327221), _1327219)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327215), _1327223), _1327217))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327215), _1327217), _1327219)))], (17844 ^ _779999) ^ [_1104937] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1104937) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1104937))], (13526 ^ _779999) ^ [_1021036, _1021038] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1021036), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021036), _1021038))))], (41841 ^ _779999) ^ [_1599241, _1599243, _1599245, _1599247, _1599249] : [_1599241 = c_Orderings_Obot__class_Obot(tc_fun(_1599243, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599245, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599243, tc_fun(_1599245, tc_HOL_Obool)), _1599241), _1599247)), _1599249) = _1599249)], (33025 ^ _779999) ^ [_1399158, _1399160] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399158)), hAPP(c_Nat_OSuc, _1399160)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1399158))), 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)), _1399160)))))], (47785 ^ _779999) ^ [_1742145, _1742147, _1742149, _1742151] : [class_Groups_Ocomm__monoid__add(_1742145), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1742145), _1742147), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1742149, _1742151))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1742145), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1742145), _1742147), c_List_Oupt(_1742149, _1742151))))], (45315 ^ _779999) ^ [_1686557, _1686559, _1686561, _1686563, _1686565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686557), tc_List_Olist(_1686557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686557), tc_List_Olist(_1686557)), hAPP(hAPP(c_List_Oappend(_1686557), _1686559), _1686561)), hAPP(hAPP(c_List_Oappend(_1686557), _1686559), _1686563))), c_List_Olexord(_1686557, _1686565))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1686557, _1686557)), hAPP(hAPP(c_Product__Type_OPair(_1686557, _1686557), 45320 ^ [_1686557, _1686559, _1686561, _1686563, _1686565]), 45320 ^ [_1686557, _1686559, _1686561, _1686563, _1686565])), _1686565))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686557), tc_List_Olist(_1686557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686557), tc_List_Olist(_1686557)), _1686561), _1686563)), c_List_Olexord(_1686557, _1686565))))], (4108 ^ _779999) ^ [_841913, _841915, _841917, _841919, _841921, _841923] : [-(c_List_Olinorder__class_Oinsort__key(_841923, _841919, _841915) = c_List_Olinorder__class_Oinsort__key(_841921, _841917, _841913)), _841923 = _841921, _841919 = _841917, _841915 = _841913], (49108 ^ _779999) ^ [_1769257, _1769259, _1769261, _1769263, _1769265, _1769267, _1769269, _1769271] : [49110 ^ _779999 : [(49113 ^ _779999) ^ [] : [hAPP(c_Fun_Ocomp(_1769261, _1769261, _1769263, hAPP(_1769265, 49109 ^ [_1769257, _1769259, _1769261, _1769263, _1769265, _1769267, _1769269, _1769271])), _1769267) = hAPP(c_Fun_Ocomp(_1769263, _1769261, _1769263, _1769267), hAPP(_1769269, 49109 ^ [_1769257, _1769259, _1769261, _1769263, _1769265, _1769267, _1769269, _1769271]))], (49111 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769257), 49109 ^ [_1769257, _1769259, _1769261, _1769263, _1769265, _1769267, _1769269, _1769271]), hAPP(c_List_Oset(_1769257), _1769259))))]], -(hAPP(c_List_Ofoldl(_1769261, _1769257, hAPP(c_COMBC(_1769257, _1769261, _1769261), _1769265), hAPP(_1769267, _1769271)), _1769259) = hAPP(_1769267, hAPP(c_List_Ofoldl(_1769263, _1769257, hAPP(c_COMBC(_1769257, _1769263, _1769263), _1769269), _1769271), _1769259)))], (13856 ^ _779999) ^ [_1027115, _1027117] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027115), _1027117) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 13857 ^ _779999 : [(13864 ^ _779999) ^ [] : [_1027115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1027117 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13858 ^ _779999) ^ [] : [_1027115 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (42530 ^ _779999) ^ [_1617385, _1617387, _1617389] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617385, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1617385, tc_HOL_Obool), tc_HOL_Obool)), _1617387), _1617389)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1617385, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617385, tc_HOL_Obool), _1617387)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617385, tc_HOL_Obool), _1617389)))], (36637 ^ _779999) ^ [_1470180] : [-(hAPP(c_Int_Onat, _1470180) = 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, _1470180)), 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)))))))], (12125 ^ _779999) ^ [_994006, _994008, _994010, _994012, _994014, _994016, _994018, _994020] : [c_Finite__Set_Ofolding__image__simple(_994006, _994008, _994010, _994012, _994014, _994016), hBOOL(hAPP(c_Finite__Set_Ofinite(_994008), _994018)), -(hBOOL(hAPP(hAPP(c_member(_994008), _994020), _994018))), -(hAPP(_994016, hAPP(hAPP(c_Set_Oinsert(_994008), _994020), _994018)) = hAPP(hAPP(_994010, hAPP(_994014, _994020)), hAPP(_994016, _994018)))], (45119 ^ _779999) ^ [_1681716, _1681718, _1681720] : [hAPP(hAPP(c_List_Oappend(_1681716), _1681718), _1681720) = c_List_Olist_ONil(_1681716), 45122 ^ _779999 : [(45125 ^ _779999) ^ [] : [-(_1681720 = c_List_Olist_ONil(_1681716))], (45123 ^ _779999) ^ [] : [-(_1681718 = c_List_Olist_ONil(_1681716))]]], (16519 ^ _779999) ^ [_1078489, _1078491, _1078493, _1078495] : [class_Rings_Olinordered__ring__strict(_1078489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078489), _1078491), _1078493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078489), _1078495), c_Groups_Ozero__class_Ozero(_1078489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078489), _1078495), _1078493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078489), _1078495), _1078491))))], (45261 ^ _779999) ^ [_1684980, _1684982, _1684984, _1684986, _1684988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684980), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684982)), _1684984))), -(hAPP(hAPP(c_List_Olist__update(_1684982, hAPP(hAPP(c_List_Oappend(_1684982), _1684984), _1684986)), _1684980), _1684988) = hAPP(hAPP(c_List_Oappend(_1684982), hAPP(hAPP(c_List_Olist__update(_1684982, _1684984), _1684980), _1684988)), _1684986))], (43401 ^ _779999) ^ [_1639895, _1639897] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1639895), tc_List_Olist(_1639895)), tc_HOL_Obool)), c_List_Olistrel(_1639895, _1639897)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1639895), c_List_Olistrel1(_1639895, _1639897)))))], (4068 ^ _779999) ^ [_841301, _841303] : [_841303 = _841301, -(c_New__DSequence_Opos__not__seq(_841303) = c_New__DSequence_Opos__not__seq(_841301))], (16865 ^ _779999) ^ [_1084987, _1084989] : [class_Orderings_Oorder(_1084987), -(c_SetInterval_Oord__class_OatLeastAtMost(_1084987, _1084989, _1084989) = hAPP(hAPP(c_Set_Oinsert(_1084987), _1084989), c_Orderings_Obot__class_Obot(tc_fun(_1084987, tc_HOL_Obool))))], (11637 ^ _779999) ^ [_984015, _984017, _984019] : [class_Complete__Lattice_Ocomplete__lattice(_984015), c_Orderings_Oorder__class_Omono(_984015, _984015, _984017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984015), hAPP(_984017, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_984015), c_Inductive_Ocomplete__lattice__class_Olfp(_984015, _984017)), _984019))), _984019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984015), c_Inductive_Ocomplete__lattice__class_Olfp(_984015, _984017)), _984019)))], (38260 ^ _779999) ^ [_1511134, _1511136, _1511138, _1511140] : [hBOOL(hAPP(hAPP(c_member(_1511134), _1511136), hAPP(c_Relation_ORange(_1511138, _1511134), _1511140))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1511138, _1511134)), hAPP(hAPP(c_Product__Type_OPair(_1511138, _1511134), 38263 ^ [_1511134, _1511136, _1511138, _1511140]), _1511136)), _1511140)))], (19059 ^ _779999) ^ [_1127503, _1127505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127503), _1127505)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1127505, _1127503) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (44234 ^ _779999) ^ [_1662692, _1662694, _1662696, _1662698] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662692), tc_List_Olist(_1662692))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662692), tc_List_Olist(_1662692)), _1662694), _1662696)), c_List_Olistrel1(_1662692, _1662698))), 44239 ^ _779999 : [(44244 ^ _779999) ^ [] : [-(_1662696 = hAPP(hAPP(c_List_Olist__update(_1662692, _1662694), 44238 ^ [_1662692, _1662694, _1662696, _1662698]), 44237 ^ [_1662692, _1662694, _1662696, _1662698]))], (44242 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44238 ^ [_1662692, _1662694, _1662696, _1662698]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662692)), _1662694))))], (44240 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662692, _1662692)), hAPP(hAPP(c_Product__Type_OPair(_1662692, _1662692), hAPP(hAPP(c_List_Onth(_1662692), _1662694), 44238 ^ [_1662692, _1662694, _1662696, _1662698])), 44237 ^ [_1662692, _1662694, _1662696, _1662698])), _1662698)))]]], (49972 ^ _779999) ^ [_1788922, _1788924, _1788926, _1788928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1788922), _1788924)), -(hAPP(hAPP(c_List_Onth(_1788926), c_List_Oreplicate(_1788926, _1788924, _1788928)), _1788922) = _1788928)], (52084 ^ _779999) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (38880 ^ _779999) ^ [_1529780, _1529782, _1529784, _1529786] : [c_Wellfounded_Owf(_1529780, _1529782), c_Fun_Oinj__on(_1529780, _1529784, _1529786, c_Orderings_Otop__class_Otop(tc_fun(_1529780, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1529784, hAPP(c_Set_Oimage(tc_prod(_1529780, _1529780), tc_prod(_1529784, _1529784), c_Product__Type_Omap__pair(_1529780, _1529784, _1529780, _1529784, _1529786, _1529786)), _1529782)))], (17207 ^ _779999) ^ [_1091377, _1091379, _1091381, _1091383, _1091385, _1091387] : [class_Rings_Oordered__ring(_1091377), 17210 ^ _779999 : [(17217 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091377), _1091383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1091377), _1091385), _1091379)), _1091381)), _1091387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), _1091379), _1091381)), _1091383)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), _1091385), _1091381)), _1091387))))], (17211 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), _1091379), _1091381)), _1091383)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), _1091385), _1091381)), _1091387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091377), _1091383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1091377), _1091385), _1091379)), _1091381)), _1091387))))]]], (22295 ^ _779999) ^ [_1192538, _1192540] : [class_Lattices_Obounded__lattice__top(_1192538), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1192538), c_Orderings_Otop__class_Otop(_1192538)), _1192540) = c_Orderings_Otop__class_Otop(_1192538))], (44646 ^ _779999) ^ [_1670946, _1670948] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670946)), _1670948) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1670948 = c_List_Olist_ONil(_1670946))], (47593 ^ _779999) ^ [_1738312, _1738314, _1738316, _1738318] : [-(c_List_Ofoldr(_1738312, _1738314, _1738316, c_List_Olist_ONil(_1738312), _1738318) = _1738318)], (28766 ^ _779999) ^ [_1320281, _1320283, _1320285, _1320287, _1320289] : [class_Fields_Olinordered__field(_1320281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320281), c_Groups_Ozero__class_Ozero(_1320281)), _1320283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320281), _1320283), _1320285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320281), c_Groups_Ozero__class_Ozero(_1320281)), _1320287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320281), _1320287), _1320289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320281), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320281), _1320283), _1320289)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320281), _1320285), _1320287))))], (36118 ^ _779999) ^ [_1459979, _1459981, _1459983, _1459985] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459979, _1459981), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1459983), _1459985))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1459979), _1459981) = _1459983)], (13562 ^ _779999) ^ [_1021898, _1021900, _1021902, _1021904] : [class_Groups_Ocomm__monoid__add(_1021898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021900), _1021902)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1021900, _1021898), _1021904), _1021902) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1021898, _1021900, c_Groups_Oplus__class_Oplus(_1021898)), _1021904), c_Groups_Ozero__class_Ozero(_1021898)), _1021902))], (9630 ^ _779999) ^ [_943735, _943737, _943739, _943741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943735, tc_HOL_Obool)), _943737), _943739)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943735, tc_HOL_Obool)), _943739), _943741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943735, tc_HOL_Obool)), _943737), _943741)))], (50611 ^ _779999) ^ [_1802832, _1802834] : [c_Relation_Otrans(_1802832, _1802834), -(c_Relation_Otrans(_1802832, hAPP(c_Relation_Oconverse(_1802832, _1802832), _1802834)))], (47480 ^ _779999) ^ [_1734730, _1734732, _1734734, _1734736] : [-(hAPP(c_List_Ofilter(_1734730, _1734732), c_List_Oremove1(_1734730, _1734734, _1734736)) = c_List_Oremove1(_1734730, _1734734, hAPP(c_List_Ofilter(_1734730, _1734732), _1734736)))], (43026 ^ _779999) ^ [_1628537, _1628539, _1628541] : [hBOOL(hAPP(hAPP(c_member(_1628537), _1628539), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628537, tc_HOL_Obool), _1628541))), 43030 ^ _779999 : [(43033 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628537, tc_HOL_Obool)), 43029 ^ [_1628537, _1628539, _1628541]), _1628541)))], (43031 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628537), _1628539), 43029 ^ [_1628537, _1628539, _1628541])))]]], (34201 ^ _779999) ^ [_1419560, _1419562] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1419560)), c_Int_OBit1(_1419562)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1419560)), _1419562)))], (26675 ^ _779999) ^ [_1280084, _1280086] : [class_Groups_Oordered__ab__group__add__abs(_1280084), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280084), hAPP(c_Groups_Ouminus__class_Ouminus(_1280084), hAPP(c_Groups_Oabs__class_Oabs(_1280084), _1280086))), c_Groups_Ozero__class_Ozero(_1280084))))], (49638 ^ _779999) ^ [_1781202] : [class_Nat_Osize(_1781202), -(c_FunDef_Ois__measure(_1781202, c_Nat_Osize__class_Osize(_1781202)))], (41596 ^ _779999) ^ [_1593810, _1593812, _1593814] : [class_Orderings_Olinorder(_1593810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593810), _1593812)), -(hBOOL(hAPP(hAPP(c_member(_1593810), _1593814), _1593812))), -(c_Big__Operators_Olattice_OInf__fin(_1593810, c_Orderings_Oord__class_Omin(_1593810), hAPP(hAPP(c_Set_Oinsert(_1593810), _1593814), _1593812)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593810, _1593810, c_Orderings_Oord__class_Omin(_1593810)), _1593814), _1593812))], (29700 ^ _779999) ^ [_1336928, _1336930, _1336932, _1336934] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1336928, _1336930, _1336932), _1336934), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1336930)], (34695 ^ _779999) ^ [_1428760, _1428762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428760)), -(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)))), _1428762)), 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)))), _1428760)) = 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, _1428762, _1428760))))], (23461 ^ _779999) ^ [_1217942, _1217944, _1217946, _1217948] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1217942, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1217944, _1217942, _1217946), hAPP(c_Set_Ovimage(_1217944, _1217942, _1217946), _1217948))), _1217948)))], (49491 ^ _779999) ^ [_1778467, _1778469, _1778471, _1778473] : [c_List_Olist__all(_1778467, _1778469, hAPP(hAPP(c_List_Olist_OCons(_1778467), _1778471), _1778473)), 49494 ^ _779999 : [(49497 ^ _779999) ^ [] : [-(c_List_Olist__all(_1778467, _1778469, _1778473))], (49495 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1778469, _1778471)))]]], (15265 ^ _779999) ^ [_1054253, _1054255, _1054257, _1054259] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054253), _1054255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054257), _1054259)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1054253, _1054257)), c_Sum__Type_OPlus(_1054253, _1054257, _1054255, _1054259))))], (48216 ^ _779999) ^ [_1749944, _1749946] : [class_Orderings_Olinorder(_1749944), 48219 ^ _779999 : [(48220 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1749944, _1749946), 48223 ^ _779999 : [(48224 ^ _779999) ^ [_1750115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750115), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749944)), _1749946))), 48227 ^ _779999 : [(48228 ^ _779999) ^ [_1750232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1750232), _1750115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1749944), hAPP(hAPP(c_List_Onth(_1749944), _1749946), _1750232)), hAPP(hAPP(c_List_Onth(_1749944), _1749946), _1750115))))]]]]], (48234 ^ _779999) ^ [] : [48236 ^ _779999 : [(48242 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1749944), hAPP(hAPP(c_List_Onth(_1749944), _1749946), 48238 ^ [_1749944, _1749946])), hAPP(hAPP(c_List_Onth(_1749944), _1749946), 48235 ^ [_1749944, _1749946])))], (48240 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48238 ^ [_1749944, _1749946]), 48235 ^ [_1749944, _1749946])))], (48237 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48235 ^ [_1749944, _1749946]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749944)), _1749946))))]], -(c_List_Olinorder__class_Osorted(_1749944, _1749946))]]], (26334 ^ _779999) ^ [_1273458, _1273460, _1273462] : [class_Groups_Ogroup__add(_1273458), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273458), _1273460), hAPP(c_Groups_Ouminus__class_Ouminus(_1273458), _1273462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273458), _1273460), _1273462))], (23277 ^ _779999) ^ [_1214281, _1214283, _1214285, _1214287, _1214289] : [class_Orderings_Olinorder(_1214281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214281), _1214283), _1214285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214281), _1214287), _1214289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214281), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214281), _1214283), _1214287)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214281), _1214285), _1214289))))], (51908 ^ _779999) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (3940 ^ _779999) ^ [_839275, _839277] : [_839277 = _839275, -(c_List_Omonoid__add__class_Olistsum(_839277) = c_List_Omonoid__add__class_Olistsum(_839275))], (52118 ^ _779999) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (39081 ^ _779999) ^ [_1534423, _1534425] : [c_Wellfounded_Owf(_1534423, _1534425), -(c_Wellfounded_Oacyclic(_1534423, _1534425))], (39463 ^ _779999) ^ [_1543251, _1543253, _1543255, _1543257, _1543259, _1543261] : [-(hAPP(c_Set_Oimage(_1543251, _1543253, hAPP(c_Fun_Ocomp(_1543255, _1543253, _1543251, _1543257), _1543259)), _1543261) = hAPP(c_Set_Oimage(_1543255, _1543253, _1543257), hAPP(c_Set_Oimage(_1543251, _1543255, _1543259), _1543261)))], (37329 ^ _779999) ^ [_1487682] : [-(c_Wellfounded_Omeasure(_1487682) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1487682), c_Wellfounded_Oless__than))], (31046 ^ _779999) ^ [_1361987, _1361989] : [-(_1361987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31049 ^ _779999 : [(31056 ^ _779999) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361989, _1361987) = 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), _1361989)), _1361987) = 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), _1361989), _1361987))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31050 ^ _779999) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361989, _1361987) = 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), _1361989)), _1361987) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1361989), _1361987)))]]], (21116 ^ _779999) ^ [_1163795, _1163797] : [-(c_Nitpick_Oint__lcm(_1163795, _1163797) = 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), _1163795)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1163797)))))], (33887 ^ _779999) ^ [_1414086, _1414088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1414086)), c_Int_OBit0(_1414088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414086), _1414088)))], (414 ^ _779999) ^ [_786314, _786316, _786318, _786320, _786322, _786324, _786326, _786328, _786330, _786332] : [-(c_Finite__Set_Ofolding__image(_786330, _786326, _786322, _786318, _786314)), c_Finite__Set_Ofolding__image(_786332, _786328, _786324, _786320, _786316), _786332 = _786330, _786328 = _786326, _786324 = _786322, _786320 = _786318, _786316 = _786314], (35938 ^ _779999) ^ [_1456748, _1456750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1456748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1456748), _1456750)), -(c_Divides_Odivmod__nat(_1456750, _1456748) = 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), _1456750), _1456748)), _1456748))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1456750), _1456748), _1456748)))], (31839 ^ _779999) ^ [_1377048, _1377050, _1377052, _1377054] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377048), hAPP(c_Int_Onumber__class_Onumber__of(_1377048), _1377050)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377048), _1377052), _1377054)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377048), hAPP(c_Int_Onumber__class_Onumber__of(_1377048), _1377050)), _1377052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377048), hAPP(c_Int_Onumber__class_Onumber__of(_1377048), _1377050)), _1377054))), class_Int_Onumber(_1377048), class_Rings_Oring(_1377048)], (9660 ^ _779999) ^ [_944259, _944261, _944263] : [class_Complete__Lattice_Ocomplete__lattice(_944259), _944261 = c_Inductive_Ocomplete__lattice__class_Ogfp(_944259, _944263), c_Orderings_Oorder__class_Omono(_944259, _944259, _944263), -(_944261 = hAPP(_944263, _944261))], (29064 ^ _779999) ^ [_1325900, _1325902, _1325904, _1325906, _1325908] : [class_Fields_Ofield(_1325900), -(_1325902 = c_Groups_Ozero__class_Ozero(_1325900)), -(_1325904 = c_Groups_Ozero__class_Ozero(_1325900)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325900), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325900), _1325906), _1325902)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325900), _1325908), _1325904)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325900), _1325906), _1325904)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325900), _1325908), _1325902))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325900), _1325902), _1325904)))], (13431 ^ _779999) ^ [_1019186, _1019188, _1019190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1019188), _1019190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019186), _1019188)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019186), _1019190))))], (14485 ^ _779999) ^ [_1039112, _1039114, _1039116] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039112), _1039114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1039112), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039112, tc_HOL_Obool)), _1039114), hAPP(hAPP(c_Set_Oinsert(_1039112), _1039116), c_Orderings_Obot__class_Obot(tc_fun(_1039112, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1039112), _1039114))))], (30477 ^ _779999) ^ [_1351141, _1351143, _1351145, _1351147] : [class_Divides_Oring__div(_1351141), -(c_Divides_Odiv__class_Omod(_1351141, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351141), _1351143), _1351145), _1351147) = c_Divides_Odiv__class_Omod(_1351141, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351141), _1351143), c_Divides_Odiv__class_Omod(_1351141, _1351145, _1351147)), _1351147))], (50852 ^ _779999) ^ [_1809093, _1809095, _1809097, _1809099] : [-(c_Wellfounded_Omax__extp(_1809093, _1809095, _1809097, _1809099)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1809093), _1809097)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1809093), _1809099)), -(_1809099 = c_Orderings_Obot__class_Obot(tc_fun(_1809093, tc_HOL_Obool))), 50866 ^ _779999 : [(50869 ^ _779999) ^ [_1809438] : [hBOOL(hAPP(hAPP(c_member(_1809093), _1809438), _1809099)), hBOOL(hAPP(hAPP(_1809095, 50865 ^ [_1809093, _1809095, _1809097, _1809099]), _1809438))], (50867 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1809093), 50865 ^ [_1809093, _1809095, _1809097, _1809099]), _1809097)))]]], (28816 ^ _779999) ^ [_1321214, _1321216, _1321218, _1321220] : [class_Fields_Olinordered__field__inverse__zero(_1321214), 28819 ^ _779999 : [(28820 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321216), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321214), _1321218), _1321220))), 28823 ^ _779999 : [(28830 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), c_Groups_Ozero__class_Ozero(_1321214)), _1321220))), 28833 ^ _779999 : [(28840 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321220), c_Groups_Ozero__class_Ozero(_1321214)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321216), c_Groups_Ozero__class_Ozero(_1321214))))], (28834 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321220), c_Groups_Ozero__class_Ozero(_1321214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321214), _1321216), _1321220))))]]], (28824 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), c_Groups_Ozero__class_Ozero(_1321214)), _1321220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321214), _1321216), _1321220)), _1321218)))]]], (28846 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321216), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321214), _1321218), _1321220)))), 28849 ^ _779999 : [(28852 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321214), _1321216), _1321220)), _1321218))], (28850 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), c_Groups_Ozero__class_Ozero(_1321214)), _1321220)))]], 28853 ^ _779999 : [(28856 ^ _779999) ^ [] : [28857 ^ _779999 : [(28860 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321214), _1321216), _1321220)))], (28858 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321220), c_Groups_Ozero__class_Ozero(_1321214))))]], 28861 ^ _779999 : [(28864 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321216), c_Groups_Ozero__class_Ozero(_1321214)))], (28862 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), _1321220), c_Groups_Ozero__class_Ozero(_1321214)))]]], (28854 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321214), c_Groups_Ozero__class_Ozero(_1321214)), _1321220))]]]]], (31983 ^ _779999) ^ [_1379972, _1379974] : [class_Int_Onumber__ring(_1379972), -(hBOOL(hAPP(hAPP(c_member(_1379972), hAPP(c_Int_Onumber__class_Onumber__of(_1379972), _1379974)), c_Int_Oring__1__class_OInts(_1379972))))], (30611 ^ _779999) ^ [_1353896, _1353898, _1353900] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353896), _1353898), _1353900) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353896), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1353898, _1353900)), _1353900))], (34191 ^ _779999) ^ [_1419388, _1419390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419388), _1419390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1419388)), c_Int_OBit0(_1419390))))], (44724 ^ _779999) ^ [_1672513, _1672515, _1672517] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1672513)), -(c_List_Osublist(_1672515, hAPP(hAPP(c_List_Olist_OCons(_1672515), _1672517), c_List_Olist_ONil(_1672515)), _1672513) = hAPP(hAPP(c_List_Olist_OCons(_1672515), _1672517), c_List_Olist_ONil(_1672515)))], (6839 ^ _779999) ^ [_892081, _892083, _892085] : [hBOOL(hAPP(hAPP(c_member(_892081), _892083), _892085)), -(hBOOL(hAPP(_892085, _892083)))], (41476 ^ _779999) ^ [_1591644, _1591646, _1591648] : [class_Orderings_Olinorder(_1591644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591644), _1591646)), -(c_Big__Operators_Olattice_OInf__fin(_1591644, c_Orderings_Oord__class_Omin(_1591644), hAPP(hAPP(c_Set_Oinsert(_1591644), _1591648), _1591646)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591644, _1591644, c_Orderings_Oord__class_Omin(_1591644)), _1591648), _1591646))], (51810 ^ _779999) ^ [_1828546, _1828548] : [class_Orderings_Opreorder(_1828546), -(class_Orderings_Opreorder(tc_fun(_1828548, _1828546)))], (3980 ^ _779999) ^ [_839879, _839881, _839883, _839885, _839887, _839889] : [-(c_List_Oinsert(_839889, _839885, _839881) = c_List_Oinsert(_839887, _839883, _839879)), _839889 = _839887, _839885 = _839883, _839881 = _839879], (33839 ^ _779999) ^ [_1413098, _1413100] : [class_Int_Onumber__ring(_1413098), 33842 ^ _779999 : [(33849 ^ _779999) ^ [] : [c_Int_Oiszero(_1413098, hAPP(c_Int_Onumber__class_Onumber__of(_1413098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413100), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413098), _1413100) = c_Groups_Ozero__class_Ozero(_1413098))], (33843 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413098), _1413100) = c_Groups_Ozero__class_Ozero(_1413098), -(c_Int_Oiszero(_1413098, hAPP(c_Int_Onumber__class_Onumber__of(_1413098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413100), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (35699 ^ _779999) ^ [_1452746, _1452748, _1452750, _1452752, _1452754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452746, _1452748)), hAPP(hAPP(c_Product__Type_OPair(_1452746, _1452748), _1452752), _1452754)), _1452750)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1452746, _1452748, _1452750), _1452752), _1452754)))], (22361 ^ _779999) ^ [_1193664, _1193666, _1193668, _1193670, _1193672] : [c_Fun_Oinj__on(_1193664, _1193666, _1193668, c_Orderings_Otop__class_Otop(tc_fun(_1193664, tc_HOL_Obool))), 22364 ^ _779999 : [(22371 ^ _779999) ^ [] : [_1193670 = _1193672, -(hAPP(c_Set_Oimage(_1193664, _1193666, _1193668), _1193670) = hAPP(c_Set_Oimage(_1193664, _1193666, _1193668), _1193672))], (22365 ^ _779999) ^ [] : [hAPP(c_Set_Oimage(_1193664, _1193666, _1193668), _1193670) = hAPP(c_Set_Oimage(_1193664, _1193666, _1193668), _1193672), -(_1193670 = _1193672)]]], (18135 ^ _779999) ^ [_1110133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110133)), -(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), _1110133))))], (41158 ^ _779999) ^ [_1584405, _1584407, _1584409, _1584411, _1584413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584405, _1584405)), hAPP(hAPP(c_Product__Type_OPair(_1584405, _1584405), _1584407), _1584409)), c_Transitive__Closure_Ortrancl(_1584405, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584405, _1584405), tc_HOL_Obool)), _1584411), _1584413)))), 41164 ^ _779999 : [(41170 ^ _779999) ^ [] : [41163 ^ [_1584405, _1584407, _1584409, _1584411, _1584413] = 41166 ^ [_1584405, _1584407, _1584409, _1584411, _1584413]], (41168 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584405, _1584405)), hAPP(hAPP(c_Product__Type_OPair(_1584405, _1584405), 41163 ^ [_1584405, _1584407, _1584409, _1584411, _1584413]), 41166 ^ [_1584405, _1584407, _1584409, _1584411, _1584413])), _1584413)))], (41165 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584405, _1584405)), hAPP(hAPP(c_Product__Type_OPair(_1584405, _1584405), _1584407), 41163 ^ [_1584405, _1584407, _1584409, _1584411, _1584413])), c_Transitive__Closure_Ortrancl(_1584405, _1584411))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584405, _1584405)), hAPP(hAPP(c_Product__Type_OPair(_1584405, _1584405), _1584407), _1584409)), c_Transitive__Closure_Ortrancl(_1584405, _1584411))))], (30575 ^ _779999) ^ [_1353294, _1353296, _1353298, _1353300, _1353302, _1353304] : [class_Divides_Osemiring__div(_1353294), c_Divides_Odiv__class_Omod(_1353294, _1353296, _1353298) = c_Divides_Odiv__class_Omod(_1353294, _1353300, _1353298), c_Divides_Odiv__class_Omod(_1353294, _1353302, _1353298) = c_Divides_Odiv__class_Omod(_1353294, _1353304, _1353298), -(c_Divides_Odiv__class_Omod(_1353294, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353294), _1353296), _1353302), _1353298) = c_Divides_Odiv__class_Omod(_1353294, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353294), _1353300), _1353304), _1353298))], (50385 ^ _779999) ^ [_1797774, _1797776, _1797778] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1797774, _1797776, _1797778) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797774)], (46998 ^ _779999) ^ [_1723873, _1723875, _1723877, _1723879, _1723881, _1723883] : [c_List_Olist__all2(_1723873, _1723875, _1723877, _1723879, _1723881), -(c_List_Olist__all2(_1723873, _1723875, _1723877, hAPP(hAPP(c_List_Odrop(_1723873), _1723883), _1723879), hAPP(hAPP(c_List_Odrop(_1723875), _1723883), _1723881)))], (41210 ^ _779999) ^ [_1586156, _1586158, _1586160, _1586162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586156, _1586156)), hAPP(hAPP(c_Product__Type_OPair(_1586156, _1586156), _1586158), _1586160)), c_Transitive__Closure_Otrancl(_1586156, _1586162))), 41214 ^ _779999 : [(41217 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586156, _1586156)), hAPP(hAPP(c_Product__Type_OPair(_1586156, _1586156), 41213 ^ [_1586156, _1586158, _1586160, _1586162]), _1586160)), c_Transitive__Closure_Ortrancl(_1586156, _1586162))))], (41215 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586156, _1586156)), hAPP(hAPP(c_Product__Type_OPair(_1586156, _1586156), _1586158), 41213 ^ [_1586156, _1586158, _1586160, _1586162])), _1586162)))]]], (24610 ^ _779999) ^ [_1240882, _1240884, _1240886, _1240888, _1240890] : [class_Orderings_Olinorder(_1240882), class_Orderings_Olinorder(_1240884), c_Orderings_Oorder__class_Omono(_1240884, _1240882, _1240886), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240882), hAPP(_1240886, _1240888)), hAPP(_1240886, _1240890)) = hAPP(_1240886, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240884), _1240888), _1240890)))], (1534 ^ _779999) ^ [_802282, _802284] : [-(class_Lazy__Sequence_Osmall__lazy(_802282)), _802284 = _802282, class_Lazy__Sequence_Osmall__lazy(_802284)], (48894 ^ _779999) ^ [_1764558, _1764560] : [class_Orderings_Olinorder(_1764558), 48897 ^ _779999 : [(48918 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1764558, _1764560)), 48919 ^ _779999 : [(48922 ^ _779999) ^ [_1765118, _1765120] : [_1764560 = hAPP(hAPP(c_List_Olist_OCons(_1764558), _1765118), _1765120), 48928 ^ _779999 : [(48931 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1764558), _1765118), 48927 ^ [_1764558, _1764560, _1765118, _1765120]))], (48929 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764558), 48927 ^ [_1764558, _1764560, _1765118, _1765120]), hAPP(c_List_Oset(_1764558), _1765120))))]], c_List_Olinorder__class_Osorted(_1764558, _1765120)], (48920 ^ _779999) ^ [] : [_1764560 = c_List_Olist_ONil(_1764558)]]], (48898 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1764558, _1764560), -(_1764560 = c_List_Olist_ONil(_1764558)), 48907 ^ _779999 : [(48910 ^ _779999) ^ [_1764892] : [hBOOL(hAPP(hAPP(c_member(_1764558), _1764892), hAPP(c_List_Oset(_1764558), 48905 ^ [_1764558, _1764560]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1764558), 48906 ^ [_1764558, _1764560]), _1764892)))], (48916 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1764558, 48905 ^ [_1764558, _1764560]))], (48908 ^ _779999) ^ [] : [-(_1764560 = hAPP(hAPP(c_List_Olist_OCons(_1764558), 48906 ^ [_1764558, _1764560]), 48905 ^ [_1764558, _1764560]))]]]]], (46790 ^ _779999) ^ [_1718609, _1718611, _1718613] : [-(c_List_Olistsp(_1718609, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1718609, tc_HOL_Obool)), _1718611), _1718613)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1718609), tc_HOL_Obool)), c_List_Olistsp(_1718609, _1718611)), c_List_Olistsp(_1718609, _1718613)))], (35896 ^ _779999) ^ [_1456150, _1456152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456150)), 35899 ^ _779999 : [(35906 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456152))), 35909 ^ _779999 : [(35916 ^ _779999) ^ [] : [-(_1456150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1456150, _1456152) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456152))))], (35910 ^ _779999) ^ [] : [_1456150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1456150, _1456152) = 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)))]]], (35900 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456152)), -(c_Divides_Odivmod__int(_1456150, _1456152) = c_Divides_OposDivAlg(_1456150, _1456152))]]], (9955 ^ _779999) ^ [_951578, _951580, _951582, _951584] : [c_Fun_Oinj__on(_951578, _951580, _951582, _951584), 9958 ^ _779999 : [(9959 ^ _779999) ^ [_951686] : [hBOOL(hAPP(hAPP(c_member(_951578), _951686), _951584)), 9962 ^ _779999 : [(9963 ^ _779999) ^ [_951788] : [hBOOL(hAPP(hAPP(c_member(_951578), _951788), _951584)), hAPP(_951582, _951686) = hAPP(_951582, _951788), -(_951686 = _951788)]]]]], (8177 ^ _779999) ^ [_918502] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _918502)], (14019 ^ _779999) ^ [_1029913, _1029915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029913), _1029915)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029915), _1029913)) = _1029915)], (48772 ^ _779999) ^ [_1761860, _1761862, _1761864, _1761866] : [hBOOL(hAPP(_1761860, _1761862)), -(c_List_OdropWhile(_1761864, _1761860, hAPP(hAPP(c_List_Olist_OCons(_1761864), _1761862), _1761866)) = c_List_OdropWhile(_1761864, _1761860, _1761866))], (43815 ^ _779999) ^ [_1651455, _1651457, _1651459, _1651461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651455), _1651457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651459, tc_HOL_Obool)), hAPP(c_List_Oset(_1651459), hAPP(hAPP(c_List_Otake(_1651459), _1651455), _1651461))), hAPP(c_List_Oset(_1651459), hAPP(hAPP(c_List_Otake(_1651459), _1651457), _1651461)))))], (50423 ^ _779999) ^ [_1798388, _1798390, _1798392] : [50425 ^ _779999 : [(50428 ^ _779999) ^ [] : [hBOOL(hAPP(_1798388, 50424 ^ [_1798388, _1798390, _1798392]))], (50426 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 50424 ^ [_1798388, _1798390, _1798392]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1798390, _1798392))))]], -(c_List_Oall__interval__int(_1798388, _1798390, _1798392))], (50448 ^ _779999) ^ [_1799168, _1799170, _1799172] : [-(c_Random__Sequence_Oempty(_1799168, _1799170, _1799172) = 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(_1799168)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1799168)))], (12225 ^ _779999) ^ [_995937, _995939, _995941, _995943] : [c_Finite__Set_Ofolding__one(_995937, _995939, _995941), hBOOL(hAPP(c_Finite__Set_Ofinite(_995937), _995943)), -(_995943 = c_Orderings_Obot__class_Obot(tc_fun(_995937, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_995937), hAPP(hAPP(_995939, 12238 ^ [_995937, _995939, _995941, _995943]), 12239 ^ [_995937, _995939, _995941, _995943])), hAPP(hAPP(c_Set_Oinsert(_995937), 12238 ^ [_995937, _995939, _995941, _995943]), hAPP(hAPP(c_Set_Oinsert(_995937), 12239 ^ [_995937, _995939, _995941, _995943]), c_Orderings_Obot__class_Obot(tc_fun(_995937, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_995937), hAPP(_995941, _995943)), _995943)))], (43421 ^ _779999) ^ [_1640495, _1640497, _1640499, _1640501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640495), tc_List_Olist(_1640495))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640495), tc_List_Olist(_1640495)), _1640497), _1640499)), c_List_Olistrel1(_1640495, _1640501))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640495), tc_List_Olist(_1640495))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640495), tc_List_Olist(_1640495)), _1640497), _1640499)), c_List_Olistrel(_1640495, c_Transitive__Closure_Ortrancl(_1640495, _1640501)))))], (11140 ^ _779999) ^ [_973024, _973026, _973028, _973030] : [class_Lattices_Osemilattice__inf(_973024), 11143 ^ _779999 : [(11152 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973024), _973028), _973030)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), _973028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), _973030))], (11144 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973024), _973028), _973030))), 11147 ^ _779999 : [(11150 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), _973030)))], (11148 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973024), _973026), _973028)))]]]]], (38073 ^ _779999) ^ [_1506740, _1506742] : [c_Wellfounded_Owf(_1506740, _1506742), 38077 ^ _779999 : [(38078 ^ _779999) ^ [_1506876] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1506740, _1506740)), hAPP(hAPP(c_Product__Type_OPair(_1506740, _1506740), hAPP(_1506876, hAPP(c_Nat_OSuc, 38076 ^ [_1506740, _1506742, _1506876]))), hAPP(_1506876, 38076 ^ [_1506740, _1506742, _1506876]))), _1506742))]]], (44718 ^ _779999) ^ [_1672455, _1672457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1672455), _1672457))), -(c_List_Oupto(_1672455, _1672457) = c_List_Olist_ONil(tc_Int_Oint))], (18209 ^ _779999) ^ [_1111415, _1111417, _1111419] : [class_Rings_Olinordered__semidom(_1111415), 18212 ^ _779999 : [(18219 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111417), _1111419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111415), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111415), _1111417)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111415), _1111419))))], (18213 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111415), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111415), _1111417)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111415), _1111419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111417), _1111419)))]]], (30858 ^ _779999) ^ [_1358450, _1358452] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358450), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1358452), _1358450)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358452), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358452, _1358450)))], (44798 ^ _779999) ^ [_1674063, _1674065, _1674067, _1674069, _1674071] : [-(hAPP(hAPP(c_List_Ozip(_1674063, _1674065), hAPP(hAPP(c_List_Olist_OCons(_1674063), _1674067), _1674069)), _1674071) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1674063, _1674065)), _1674065, c_List_Olist_ONil(tc_prod(_1674063, _1674065)), hAPP(hAPP(c_COMBC(_1674065, tc_fun(tc_List_Olist(_1674065), tc_List_Olist(tc_prod(_1674063, _1674065))), tc_fun(tc_List_Olist(_1674065), tc_List_Olist(tc_prod(_1674063, _1674065)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1674063, _1674065)), tc_List_Olist(tc_prod(_1674063, _1674065))), tc_fun(tc_fun(tc_List_Olist(_1674065), tc_List_Olist(tc_prod(_1674063, _1674065))), tc_fun(tc_List_Olist(_1674065), tc_List_Olist(tc_prod(_1674063, _1674065)))), _1674065), c_COMBB(tc_List_Olist(tc_prod(_1674063, _1674065)), tc_List_Olist(tc_prod(_1674063, _1674065)), tc_List_Olist(_1674065))), hAPP(hAPP(c_COMBB(tc_prod(_1674063, _1674065), tc_fun(tc_List_Olist(tc_prod(_1674063, _1674065)), tc_List_Olist(tc_prod(_1674063, _1674065))), _1674065), c_List_Olist_OCons(tc_prod(_1674063, _1674065))), hAPP(c_Product__Type_OPair(_1674063, _1674065), _1674067)))), hAPP(c_List_Ozip(_1674063, _1674065), _1674069))), _1674071))], (48623 ^ _779999) ^ [_1758790, _1758792, _1758794, _1758796, _1758798] : [-(c_List_OtakeWhile(_1758790, _1758792, hAPP(hAPP(c_List_Omap(_1758794, _1758790), _1758796), _1758798)) = hAPP(hAPP(c_List_Omap(_1758794, _1758790), _1758796), c_List_OtakeWhile(_1758794, hAPP(c_Fun_Ocomp(_1758790, tc_HOL_Obool, _1758794, _1758792), _1758796), _1758798)))], (34895 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (49874 ^ _779999) ^ [_1787172, _1787174, _1787176, _1787178] : [-(hAPP(hAPP(c_List_Oappend(_1787172), c_List_Oreplicate(_1787172, _1787174, _1787176)), hAPP(hAPP(c_List_Olist_OCons(_1787172), _1787176), _1787178)) = hAPP(hAPP(c_List_Olist_OCons(_1787172), _1787176), hAPP(hAPP(c_List_Oappend(_1787172), c_List_Oreplicate(_1787172, _1787174, _1787176)), _1787178)))], (896 ^ _779999) ^ [_793693, _793695, _793697, _793699, _793701, _793703] : [-(c_List_Oall__interval__int(_793701, _793697, _793693)), c_List_Oall__interval__int(_793703, _793699, _793695), _793703 = _793701, _793699 = _793697, _793695 = _793693], (26392 ^ _779999) ^ [_1274461, _1274463] : [class_Lattices_Oboolean__algebra(_1274461), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1274461), _1274463), hAPP(c_Groups_Ouminus__class_Ouminus(_1274461), _1274463)) = c_Orderings_Obot__class_Obot(_1274461))], (9134 ^ _779999) ^ [_936057, _936059, _936061, _936063, _936065] : [hAPP(_936061, _936063) = _936065, -(c_Fun_Ofun__upd(_936057, _936059, _936061, _936063, _936065) = _936061)], (23165 ^ _779999) ^ [_1212374, _1212376, _1212378, _1212380] : [class_Orderings_Olinorder(_1212374), 23168 ^ _779999 : [(23177 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212374), _1212378), _1212380)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), _1212378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), _1212380))], (23169 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212374), _1212378), _1212380))), 23172 ^ _779999 : [(23175 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), _1212380)))], (23173 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212374), _1212376), _1212378)))]]]]], (36835 ^ _779999) ^ [_1475213, _1475215, _1475217, _1475219, _1475221] : [c_Equiv__Relations_Oequiv(_1475213, _1475215, _1475217), hBOOL(hAPP(hAPP(c_member(_1475213), _1475219), _1475215)), hBOOL(hAPP(hAPP(c_member(_1475213), _1475221), _1475215)), 36846 ^ _779999 : [(36853 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1475213, _1475213)), hAPP(hAPP(c_Product__Type_OPair(_1475213, _1475213), _1475219), _1475221)), _1475217)), -(hAPP(c_Relation_OImage(_1475213, _1475213, _1475217), hAPP(hAPP(c_Set_Oinsert(_1475213), _1475219), c_Orderings_Obot__class_Obot(tc_fun(_1475213, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475213, _1475213, _1475217), hAPP(hAPP(c_Set_Oinsert(_1475213), _1475221), c_Orderings_Obot__class_Obot(tc_fun(_1475213, tc_HOL_Obool)))))], (36847 ^ _779999) ^ [] : [hAPP(c_Relation_OImage(_1475213, _1475213, _1475217), hAPP(hAPP(c_Set_Oinsert(_1475213), _1475219), c_Orderings_Obot__class_Obot(tc_fun(_1475213, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475213, _1475213, _1475217), hAPP(hAPP(c_Set_Oinsert(_1475213), _1475221), c_Orderings_Obot__class_Obot(tc_fun(_1475213, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475213, _1475213)), hAPP(hAPP(c_Product__Type_OPair(_1475213, _1475213), _1475219), _1475221)), _1475217)))]]], (7274 ^ _779999) ^ [_900386, _900388, _900390, _900392] : [7275 ^ _779999 : [(7278 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900386), _900388), _900392))], (7276 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900386), _900388), _900390))]], -(hBOOL(hAPP(hAPP(c_member(_900386), _900388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900386, tc_HOL_Obool)), _900390), _900392))))], (27482 ^ _779999) ^ [_1297025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1297025), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1297025) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1297025))], (44848 ^ _779999) ^ [_1675714, _1675716, _1675718, _1675720, _1675722, _1675724] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675714), tc_List_Olist(_1675714))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675714), tc_List_Olist(_1675714)), hAPP(hAPP(c_List_Oappend(_1675714), _1675716), hAPP(hAPP(c_List_Olist_OCons(_1675714), _1675718), c_List_Olist_ONil(_1675714)))), hAPP(hAPP(c_List_Oappend(_1675714), _1675720), hAPP(hAPP(c_List_Olist_OCons(_1675714), _1675722), c_List_Olist_ONil(_1675714))))), c_List_Olistrel1(_1675714, _1675724)))), 44849 ^ _779999 : [(44856 ^ _779999) ^ [] : [_1675716 = _1675720, hBOOL(hAPP(hAPP(c_member(tc_prod(_1675714, _1675714)), hAPP(hAPP(c_Product__Type_OPair(_1675714, _1675714), _1675718), _1675722)), _1675724))], (44850 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675714), tc_List_Olist(_1675714))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675714), tc_List_Olist(_1675714)), _1675716), _1675720)), c_List_Olistrel1(_1675714, _1675724))), _1675718 = _1675722]]], (45073 ^ _779999) ^ [_1680890, _1680892] : [-(hAPP(hAPP(c_List_Oappend(_1680890), c_List_Olist_ONil(_1680890)), _1680892) = _1680892)], (3400 ^ _779999) ^ [_830843, _830845, _830847, _830849] : [-(c_Finite__Set_Ofold1(_830849, _830845) = c_Finite__Set_Ofold1(_830847, _830843)), _830849 = _830847, _830845 = _830843], (27848 ^ _779999) ^ [_1303430, _1303432, _1303434] : [class_Groups_Omonoid__mult(_1303430), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303430), _1303432), hAPP(c_Nat_OSuc, _1303434)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303430), hAPP(hAPP(c_Power_Opower__class_Opower(_1303430), _1303432), _1303434)), _1303432))], (20162 ^ _779999) ^ [_1147286, _1147288] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1147286), _1147288)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1147288), _1147286)))], (38258 ^ _779999) ^ [_1511067, _1511069, _1511071] : [-(hAPP(c_Set_Oimage(tc_prod(_1511067, _1511069), _1511069, c_Product__Type_Osnd(_1511067, _1511069)), _1511071) = hAPP(c_Relation_ORange(_1511067, _1511069), _1511071))], (38864 ^ _779999) ^ [_1529272, _1529274, _1529276, _1529278] : [-(c_Product__Type_Oapfst(_1529272, _1529274, _1529276, _1529278) = c_Product__Type_Omap__pair(_1529272, _1529274, _1529276, _1529276, _1529278, c_Fun_Oid(_1529276)))], (38533 ^ _779999) ^ [_1519361, _1519363, _1519365, _1519367, _1519369] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519361, _1519363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519361, tc_HOL_Obool)), _1519365), _1519367)), hAPP(c_COMBK(tc_fun(_1519363, tc_HOL_Obool), _1519361), _1519369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1519361, _1519363), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519361, _1519363), _1519365), hAPP(c_COMBK(tc_fun(_1519363, tc_HOL_Obool), _1519361), _1519369))), hAPP(hAPP(c_Product__Type_OSigma(_1519361, _1519363), _1519367), hAPP(c_COMBK(tc_fun(_1519363, tc_HOL_Obool), _1519361), _1519369))))], (36299 ^ _779999) ^ [_1463608, _1463610, _1463612] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1463608, _1463610), _1463612)), 36302 ^ _779999 : [(36303 ^ _779999) ^ [_1463693] : [hBOOL(hAPP(hAPP(_1463610, _1463693), _1463612)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1463608, _1463610), _1463693)))]]], (41853 ^ _779999) ^ [_1599519, _1599521, _1599523, _1599525, _1599527] : [_1599519 = c_Orderings_Obot__class_Obot(tc_fun(_1599521, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599523, tc_HOL_Obool)), _1599525), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599521, tc_fun(_1599523, tc_HOL_Obool)), _1599519), _1599527)) = _1599525)], (34889 ^ _779999) ^ [] : [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)], (40167 ^ _779999) ^ [_1559874, _1559876, _1559878] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559874, _1559874)), _1559876), _1559878)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559874, _1559874)), _1559876), c_Transitive__Closure_Otrancl(_1559874, _1559878))))], (5418 ^ _779999) ^ [_862862, _862864, _862866, _862868, _862870, _862872] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_862872, _862868, _862864) = c_Lazy__Sequence_Olazy__sequence_OInsert(_862870, _862866, _862862)), _862872 = _862870, _862868 = _862866, _862864 = _862862], (1102 ^ _779999) ^ [_796666, _796668, _796670, _796672] : [-(c_Equiv__Relations_Opart__equivp(_796670, _796666)), c_Equiv__Relations_Opart__equivp(_796672, _796668), _796672 = _796670, _796668 = _796666], (17761 ^ _779999) ^ [_1103035, _1103037, _1103039] : [-(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), _1103035)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1103037))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1103039))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103035), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103039), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1103037)))))], (33151 ^ _779999) ^ [_1401035] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1401035)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1401035))))], (6511 ^ _779999) ^ [_885061, _885063, _885065, _885067, _885069] : [class_Orderings_Oord(_885061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885063, _885061)), _885065), _885067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885061), hAPP(_885065, _885069)), hAPP(_885067, _885069))))], (8175 ^ _779999) ^ [_918467] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _918467)], (13634 ^ _779999) ^ [_1023251, _1023253] : [class_Groups_Olinordered__ab__group__add(_1023251), 13637 ^ _779999 : [(13644 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023251), _1023253), c_Groups_Ozero__class_Ozero(_1023251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023251), _1023253), _1023253)), c_Groups_Ozero__class_Ozero(_1023251))))], (13638 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023251), _1023253), _1023253)), c_Groups_Ozero__class_Ozero(_1023251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023251), _1023253), c_Groups_Ozero__class_Ozero(_1023251))))]]], (32817 ^ _779999) ^ [_1395516, _1395518, _1395520] : [class_Int_Onumber__ring(_1395516), 32820 ^ _779999 : [(32827 ^ _779999) ^ [] : [-(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), _1395518)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1395516), _1395520), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1395518))) = c_Groups_Oone__class_Oone(_1395516))], (32821 ^ _779999) ^ [] : [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), _1395518))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1395516), _1395520), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1395518))) = hAPP(hAPP(c_HOL_OLet(_1395516, _1395516), hAPP(hAPP(c_Power_Opower__class_Opower(_1395516), _1395520), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395518))), hAPP(hAPP(c_COMBS(_1395516, _1395516, _1395516), hAPP(hAPP(c_COMBB(_1395516, tc_fun(_1395516, _1395516), _1395516), c_Groups_Otimes__class_Otimes(_1395516)), hAPP(c_Groups_Otimes__class_Otimes(_1395516), _1395520))), c_COMBI(_1395516))))]]], (22115 ^ _779999) ^ [] : [-(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)))], (32749 ^ _779999) ^ [_1394353, _1394355] : [_1394353 = _1394355, -(c_Int_OBit1(_1394353) = c_Int_OBit1(_1394355))], (45075 ^ _779999) ^ [_1680943, _1680945, _1680947] : [c_List_Olist_ONil(_1680943) = hAPP(hAPP(c_List_Oappend(_1680943), _1680945), _1680947), 45078 ^ _779999 : [(45081 ^ _779999) ^ [] : [-(_1680947 = c_List_Olist_ONil(_1680943))], (45079 ^ _779999) ^ [] : [-(_1680945 = c_List_Olist_ONil(_1680943))]]], (18551 ^ _779999) ^ [_1117832, _1117834, _1117836, _1117838] : [class_Rings_Ocomm__semiring__1(_1117832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117832), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117832), c_Groups_Oone__class_Oone(_1117832)), c_Groups_Oone__class_Oone(_1117832))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1117832), hAPP(hAPP(c_COMBB(_1117832, _1117832, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1117832), _1117834)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1117832, _1117832), hAPP(hAPP(c_COMBB(_1117832, tc_fun(_1117832, _1117832), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1117832)), c_Nat_Osemiring__1__class_Oof__nat(_1117832))), _1117836))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1117838))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117832), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117832), _1117838)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117832), _1117834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117832), _1117834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117832), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117832), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117838), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1117836)))))], (52022 ^ _779999) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (39044 ^ _779999) ^ [_1533403, _1533405] : [c_Wellfounded_Owf(_1533403, _1533405), -(c_Wellfounded_OwfP(_1533403, hAPP(hAPP(c_COMBC(_1533403, tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_fun(_1533403, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533403, tc_fun(tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_fun(_1533403, tc_HOL_Obool)), _1533403), c_COMBC(_1533403, tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533403, tc_prod(_1533403, _1533403)), tc_fun(_1533403, tc_fun(tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_HOL_Obool)), _1533403), hAPP(c_COMBB(tc_prod(_1533403, _1533403), tc_fun(tc_fun(tc_prod(_1533403, _1533403), tc_HOL_Obool), tc_HOL_Obool), _1533403), c_member(tc_prod(_1533403, _1533403)))), c_Product__Type_OPair(_1533403, _1533403)))), _1533405)))], (48546 ^ _779999) ^ [_1757054, _1757056] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1757054), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1757054))), _1757056))), 48549 ^ _779999 : [(48556 ^ _779999) ^ [] : [-(_1757056 = c_List_Olist_ONil(tc_List_Olist(_1757054))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757054))), c_List_Otranspose(_1757054, _1757056)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757054)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1757054)), _1757056), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48550 ^ _779999) ^ [] : [_1757056 = c_List_Olist_ONil(tc_List_Olist(_1757054)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757054))), c_List_Otranspose(_1757054, _1757056)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (38453 ^ _779999) ^ [_1516689, _1516691, _1516693, _1516695, _1516697, _1516699] : [class_Groups_Ocomm__monoid__add(_1516689), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516691, _1516689), hAPP(hAPP(c_COMBC(_1516691, tc_fun(_1516693, tc_HOL_Obool), _1516689), hAPP(hAPP(c_COMBB(tc_fun(_1516693, _1516689), tc_fun(tc_fun(_1516693, tc_HOL_Obool), _1516689), _1516691), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516693, _1516689)), _1516695)), _1516697)), _1516699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1516691, _1516693), _1516689), hAPP(c_Product__Type_Oprod_Oprod__case(_1516691, _1516693, _1516689), _1516695)), hAPP(hAPP(c_Product__Type_OSigma(_1516691, _1516693), _1516699), hAPP(c_COMBK(tc_fun(_1516693, tc_HOL_Obool), _1516691), _1516697))))], (42211 ^ _779999) ^ [_1609938, _1609940, _1609942, _1609944, _1609946] : [class_Complete__Lattice_Ocomplete__lattice(_1609938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609940), _1609942)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1609938), _1609944), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609940, _1609938), _1609942), _1609946)) = hAPP(hAPP(c_Finite__Set_Ofold(_1609940, _1609938, hAPP(hAPP(c_COMBB(_1609938, tc_fun(_1609938, _1609938), _1609940), c_Lattices_Osemilattice__inf__class_Oinf(_1609938)), _1609946)), _1609944), _1609942))], (46380 ^ _779999) ^ [_1709933, _1709935, _1709937, _1709939, _1709941, _1709943] : [-(hAPP(hAPP(c_List_Omap(_1709933, _1709935), _1709937), hAPP(hAPP(c_List_Omap(_1709939, _1709933), _1709941), _1709943)) = hAPP(hAPP(c_List_Omap(_1709939, _1709935), hAPP(c_Fun_Ocomp(_1709933, _1709935, _1709939, _1709937), _1709941)), _1709943))], (44524 ^ _779999) ^ [_1668897] : [-(hBOOL(hAPP(c_List_Odistinct(_1668897), c_List_Olist_ONil(_1668897))))], (47777 ^ _779999) ^ [_1741953, _1741955] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1741953), hAPP(c_List_Onth(_1741953), _1741955)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741953)), _1741955))) = _1741955)], (4864 ^ _779999) ^ [_854207, _854209, _854211, _854213, _854215, _854217, _854219, _854221] : [-(c_Nitpick_Opair__box_OPairBox(_854221, _854217, _854213, _854209) = c_Nitpick_Opair__box_OPairBox(_854219, _854215, _854211, _854207)), _854221 = _854219, _854217 = _854215, _854213 = _854211, _854209 = _854207], (6927 ^ _779999) ^ [_893796, _893798, _893800, _893802] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_893796), _893798), _893800), _893802)), -(_893798 = _893802), -(hBOOL(hAPP(_893800, _893802)))], (10496 ^ _779999) ^ [_960700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960700), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_960700 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9360 ^ _779999) ^ [_939360, _939362, _939364] : [class_Orderings_Oorder(_939360), -(_939362 = _939364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939360), _939362), _939364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939360), _939362), _939364)))], (11402 ^ _779999) ^ [_978137, _978139, _978141, _978143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978137, tc_HOL_Obool)), _978139), _978141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978137, tc_HOL_Obool)), _978139), _978143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978137, tc_HOL_Obool)), _978139), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978137, tc_HOL_Obool)), _978141), _978143))))], (814 ^ _779999) ^ [_792484, _792486, _792488, _792490] : [-(c_FunDef_Ois__measure(_792488, _792484)), c_FunDef_Ois__measure(_792490, _792486), _792490 = _792488, _792486 = _792484], (4978 ^ _779999) ^ [_856020, _856022, _856024, _856026, _856028, _856030] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_856030, _856026, _856022) = c_SetInterval_Oord__class_OatLeastAtMost(_856028, _856024, _856020)), _856030 = _856028, _856026 = _856024, _856022 = _856020], (21504 ^ _779999) ^ [_1171489, _1171491, _1171493] : [class_Lattices_Oab__semigroup__idem__mult(_1171489), -(_1171491 = c_Orderings_Obot__class_Obot(tc_fun(_1171489, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171489), _1171491)), -(hAPP(c_Finite__Set_Ofold1(_1171489, c_Groups_Otimes__class_Otimes(_1171489)), hAPP(hAPP(c_Set_Oinsert(_1171489), _1171493), _1171491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171489), _1171493), hAPP(c_Finite__Set_Ofold1(_1171489, c_Groups_Otimes__class_Otimes(_1171489)), _1171491)))], (16903 ^ _779999) ^ [_1085605, _1085607, _1085609, _1085611] : [class_Rings_Olinordered__ring__strict(_1085605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085605), c_Groups_Ozero__class_Ozero(_1085605)), _1085607)), 16910 ^ _779999 : [(16917 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085605), _1085609), _1085611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085605), _1085607), _1085609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085605), _1085607), _1085611))))], (16911 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085605), _1085607), _1085609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085605), _1085607), _1085611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085605), _1085609), _1085611)))]]], (48973 ^ _779999) ^ [_1766043, _1766045, _1766047] : [hBOOL(hAPP(c_List_Odistinct(_1766043), _1766045)), -(hBOOL(hAPP(c_List_Odistinct(_1766043), c_List_Oinsert(_1766043, _1766047, _1766045))))], (34329 ^ _779999) ^ [_1421938, _1421940] : [class_Rings_Olinordered__idom(_1421938), -(hAPP(c_Groups_Oabs__class_Oabs(_1421938), hAPP(hAPP(c_Power_Opower__class_Opower(_1421938), _1421940), 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(_1421938), _1421940), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25700 ^ _779999) ^ [_1261837, _1261839, _1261841] : [class_Groups_Ogroup__add(_1261837), 25703 ^ _779999 : [(25710 ^ _779999) ^ [] : [_1261839 = _1261841, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1261837), _1261839) = hAPP(c_Groups_Ouminus__class_Ouminus(_1261837), _1261841))], (25704 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1261837), _1261839) = hAPP(c_Groups_Ouminus__class_Ouminus(_1261837), _1261841), -(_1261839 = _1261841)]]], (1664 ^ _779999) ^ [_803907, _803909] : [-(class_Groups_Ocancel__semigroup__add(_803907)), _803909 = _803907, class_Groups_Ocancel__semigroup__add(_803909)], (10331 ^ _779999) ^ [_957696, _957698] : [10332 ^ _779999 : [(10335 ^ _779999) ^ [] : [_957696 = _957698], (10333 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957696), _957698))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957696), _957698)))], (38537 ^ _779999) ^ [_1519607, _1519609, _1519611, _1519613] : [hBOOL(hAPP(c_Predicate_ODomainP(_1519607, _1519609, _1519611), _1519613)), -(hBOOL(hAPP(hAPP(_1519611, _1519613), 38540 ^ [_1519607, _1519609, _1519611, _1519613])))], (43367 ^ _779999) ^ [_1638860, _1638862, _1638864, _1638866, _1638868, _1638870] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638860), tc_List_Olist(_1638860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638860), tc_List_Olist(_1638860)), hAPP(hAPP(c_List_Olist_OCons(_1638860), _1638862), _1638864)), hAPP(hAPP(c_List_Olist_OCons(_1638860), _1638866), _1638868))), c_List_Olistrel1(_1638860, _1638870)))), 43368 ^ _779999 : [(43375 ^ _779999) ^ [] : [_1638862 = _1638866, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638860), tc_List_Olist(_1638860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638860), tc_List_Olist(_1638860)), _1638864), _1638868)), c_List_Olistrel1(_1638860, _1638870)))], (43369 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638860, _1638860)), hAPP(hAPP(c_Product__Type_OPair(_1638860, _1638860), _1638862), _1638866)), _1638870)), _1638864 = _1638868]]], (38854 ^ _779999) ^ [_1529027, _1529029, _1529031] : [-(hAPP(c_Product__Type_Omap__pair(_1529027, _1529027, _1529029, _1529029, c_COMBI(_1529027), c_COMBI(_1529029)), _1529031) = _1529031)], (43932 ^ _779999) ^ [_1655471, _1655473, _1655475, _1655477, _1655479, _1655481] : [-(hAPP(hAPP(c_List_Ozip(_1655471, _1655473), hAPP(hAPP(c_List_Olist_OCons(_1655471), _1655475), _1655477)), hAPP(hAPP(c_List_Olist_OCons(_1655473), _1655479), _1655481)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1655471, _1655473)), hAPP(hAPP(c_Product__Type_OPair(_1655471, _1655473), _1655475), _1655479)), hAPP(hAPP(c_List_Ozip(_1655471, _1655473), _1655477), _1655481)))], (42012 ^ _779999) ^ [_1604554, _1604556, _1604558, _1604560, _1604562] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604554, tc_fun(_1604556, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1604554, tc_HOL_Obool)), _1604558), _1604560)), _1604562) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1604556, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604554, tc_fun(_1604556, tc_HOL_Obool)), _1604558), _1604562)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604554, tc_fun(_1604556, tc_HOL_Obool)), _1604560), _1604562)))], (33713 ^ _779999) ^ [_1410812, _1410814] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410812)), hAPP(c_Nat_OSuc, _1410814)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1410812))), 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, _1410814))), 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)), _1410814)))))], (9526 ^ _779999) ^ [_941819, _941821, _941823, _941825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941819, tc_HOL_Obool)), _941821), _941823)), hBOOL(hAPP(hAPP(c_member(_941819), _941825), _941821)), -(hBOOL(hAPP(hAPP(c_member(_941819), _941825), _941823)))], (6538 ^ _779999) ^ [_885592, _885594, _885596, _885598, _885600] : [class_Lattices_Olattice(_885592), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_885594, _885592)), _885596), _885598), _885600) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_885592), hAPP(_885596, _885600)), hAPP(_885598, _885600)))], (39555 ^ _779999) ^ [_1545412, _1545414, _1545416, _1545418, _1545420] : [class_Groups_Ocomm__monoid__add(_1545412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545414), _1545416)), c_Fun_Oinj__on(_1545414, _1545414, _1545418, _1545416), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545414, _1545412), _1545420), hAPP(c_Set_Oimage(_1545414, _1545414, _1545418), _1545416)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545414, _1545412), hAPP(c_Fun_Ocomp(_1545414, _1545412, _1545414, _1545420), _1545418)), _1545416))], (18798 ^ _779999) ^ [_1123022, _1123024, _1123026] : [class_Orderings_Olinorder(_1123022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123022), _1123024), _1123026)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123022, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1123022, _1123024, _1123026)), hAPP(hAPP(c_Set_Oinsert(_1123022), _1123026), c_Orderings_Obot__class_Obot(tc_fun(_1123022, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1123022, _1123024, _1123026))], (26993 ^ _779999) ^ [_1287537, _1287539] : [class_Groups_Olinordered__ab__group__add(_1287537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287537), _1287539)), -(_1287539 = c_Orderings_Obot__class_Obot(tc_fun(_1287537, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1287537), c_Big__Operators_Olinorder__class_OMin(_1287537, _1287539)) = c_Big__Operators_Olinorder__class_OMax(_1287537, hAPP(c_Set_Oimage(_1287537, _1287537, c_Groups_Ouminus__class_Ouminus(_1287537)), _1287539)))], (45113 ^ _779999) ^ [_1681597, _1681599, _1681601] : [_1681601 = c_List_Olist_ONil(_1681599), -(_1681597 = hAPP(hAPP(c_List_Oappend(_1681599), _1681601), _1681597))], (46642 ^ _779999) ^ [_1715687, _1715689] : [-(c_Random_Oselect(_1715687, _1715689) = 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(_1715687, 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(_1715687)), _1715689)))), hAPP(hAPP(c_COMBB(_1715687, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1715687, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1715687, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1715687, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1715687), _1715689)), c_Code__Numeral_Onat__of))))], (34511 ^ _779999) ^ [_1424977, _1424979, _1424981] : [class_Rings_Oring__1(_1424977), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424977), hAPP(c_Groups_Ouminus__class_Ouminus(_1424977), _1424979)), 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)))), _1424981)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1424977), _1424979), 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)))), _1424981)))], (18959 ^ _779999) ^ [_1125920, _1125922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125920), _1125922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1125920), _1125922)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10543 ^ _779999) ^ [_961415, _961417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961415), _961417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961415)), _961417)))], (34411 ^ _779999) ^ [_1423402, _1423404] : [class_Rings_Olinordered__idom(_1423402), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423402), c_Groups_Ozero__class_Ozero(_1423402)), hAPP(hAPP(c_Power_Opower__class_Opower(_1423402), _1423404), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (5837 ^ _779999) ^ [_872721, _872723, _872725, _872727] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_872721, tc_HOL_Obool)), _872723), _872725), _872727)), -(hBOOL(hAPP(_872723, _872727))), -(hBOOL(hAPP(_872725, _872727)))], (47046 ^ _779999) ^ [_1724853, _1724855, _1724857, _1724859] : [c_List_Olist__all2(_1724853, _1724855, _1724857, c_List_Olist_ONil(_1724853), _1724859), -(_1724859 = c_List_Olist_ONil(_1724855))], (46340 ^ _779999) ^ [_1708956, _1708958, _1708960, _1708962, _1708964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708956), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708958)), _1708960))), -(hAPP(hAPP(c_List_Onth(_1708962), hAPP(hAPP(c_List_Omap(_1708958, _1708962), _1708964), _1708960)), _1708956) = hAPP(_1708964, hAPP(hAPP(c_List_Onth(_1708958), _1708960), _1708956)))], (16139 ^ _779999) ^ [_1071408, _1071410, _1071412, _1071414] : [class_Rings_Oordered__ring(_1071408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071408), _1071410), _1071412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071408), _1071414), c_Groups_Ozero__class_Ozero(_1071408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071408), _1071412), _1071414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071408), _1071410), _1071414))))], (30557 ^ _779999) ^ [_1352881, _1352883, _1352885, _1352887] : [class_Divides_Osemiring__div(_1352881), -(c_Divides_Odiv__class_Omod(_1352881, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352881), _1352883), _1352885), _1352887) = c_Divides_Odiv__class_Omod(_1352881, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352881), c_Divides_Odiv__class_Omod(_1352881, _1352883, _1352887)), c_Divides_Odiv__class_Omod(_1352881, _1352885, _1352887)), _1352887))], (43011 ^ _779999) ^ [_1628137, _1628139, _1628141, _1628143, _1628145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628137, tc_HOL_Obool)), _1628139), _1628141)), 43017 ^ _779999 : [(43022 ^ _779999) ^ [] : [hBOOL(hAPP(_1628145, 43016 ^ [_1628137, _1628139, _1628141, _1628143, _1628145]))], (43020 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1628143, 43016 ^ [_1628137, _1628139, _1628141, _1628143, _1628145])))], (43018 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628137), 43016 ^ [_1628137, _1628139, _1628141, _1628143, _1628145]), _1628139)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628137, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628137, tc_HOL_Obool)), _1628139), hAPP(c_Set_OCollect(_1628137), _1628143))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628137, tc_HOL_Obool)), _1628141), hAPP(c_Set_OCollect(_1628137), _1628145)))))], (48492 ^ _779999) ^ [_1755888, _1755890, _1755892] : [-(hAPP(c_List_Orev(_1755888), hAPP(hAPP(c_List_Otake(_1755888), _1755890), _1755892)) = hAPP(hAPP(c_List_Odrop(_1755888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755888)), _1755892)), _1755890)), hAPP(c_List_Orev(_1755888), _1755892)))], (18419 ^ _779999) ^ [_1115265, _1115267, _1115269] : [-(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)), _1115265)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1115267), _1115269)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115267), _1115265)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115269), _1115265)))], (31040 ^ _779999) ^ [_1361833, _1361835, _1361837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361833)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361835, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361837), _1361833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361837), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1361835), _1361837), _1361833))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361835, _1361837)))], (31588 ^ _779999) ^ [_1372149, _1372151, _1372153, _1372155] : [hBOOL(hAPP(hAPP(c_member(_1372149), _1372151), _1372153)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1372149, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1372149, _1372149, _1372155), hAPP(hAPP(c_Set_Oinsert(_1372149), _1372151), c_Orderings_Obot__class_Obot(tc_fun(_1372149, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372149), _1372153), _1372155))))], (15799 ^ _779999) ^ [_1064852, _1064854, _1064856] : [15800 ^ _779999 : [(15803 ^ _779999) ^ [] : [_1064852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15801 ^ _779999) ^ [] : [_1064854 = _1064856]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064852), _1064854) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064852), _1064856))], (44592 ^ _779999) ^ [_1670035, _1670037] : [-(hAPP(hAPP(c_List_Otake(_1670035), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1670037) = c_List_Olist_ONil(_1670035))], (36739 ^ _779999) ^ [_1473171, _1473173, _1473175, _1473177, _1473179] : [c_Equiv__Relations_Oequiv(_1473171, _1473173, _1473175), hBOOL(hAPP(hAPP(c_member(tc_prod(_1473171, _1473171)), hAPP(hAPP(c_Product__Type_OPair(_1473171, _1473171), _1473177), _1473179)), _1473175)), -(hAPP(c_Relation_OImage(_1473171, _1473171, _1473175), hAPP(hAPP(c_Set_Oinsert(_1473171), _1473177), c_Orderings_Obot__class_Obot(tc_fun(_1473171, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1473171, _1473171, _1473175), hAPP(hAPP(c_Set_Oinsert(_1473171), _1473179), c_Orderings_Obot__class_Obot(tc_fun(_1473171, tc_HOL_Obool)))))], (20242 ^ _779999) ^ [_1148537, _1148539] : [_1148537 = hAPP(c_Int_Onat, _1148539), 20245 ^ _779999 : [(20252 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148539))), -(_1148537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20246 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148539)), -(_1148539 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148537))]]], (30018 ^ _779999) ^ [_1342559, _1342561, _1342563] : [class_Rings_Olinordered__idom(_1342559), 30021 ^ _779999 : [(30028 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342561), _1342563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342559), hAPP(c_Int_Oring__1__class_Oof__int(_1342559), _1342561)), hAPP(c_Int_Oring__1__class_Oof__int(_1342559), _1342563))))], (30022 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342559), hAPP(c_Int_Oring__1__class_Oof__int(_1342559), _1342561)), hAPP(c_Int_Oring__1__class_Oof__int(_1342559), _1342563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342561), _1342563)))]]], (52284 ^ _779999) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (48428 ^ _779999) ^ [_1754542, _1754544] : [-(hAPP(c_List_Orev(_1754542), hAPP(c_List_Orev(_1754542), _1754544)) = _1754544)], (13181 ^ _779999) ^ [_1014646, _1014648, _1014650, _1014652] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1014646), 13184 ^ _779999 : [(13191 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014646), _1014648), _1014652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014646), _1014648), _1014650)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014646), _1014652), _1014650))))], (13185 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014646), _1014648), _1014650)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014646), _1014652), _1014650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014646), _1014648), _1014652)))]]], (52332 ^ _779999) ^ [_1833863, _1833865, _1833867, _1833869, _1833871, _1833873] : [-(hAPP(hAPP(hAPP(c_COMBB(_1833863, _1833865, _1833867), _1833869), _1833871), _1833873) = hAPP(_1833869, hAPP(_1833871, _1833873)))], (38644 ^ _779999) ^ [_1522305, _1522307, _1522309, _1522311] : [-(_1522305 = c_Orderings_Obot__class_Obot(tc_fun(_1522307, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1522309, _1522307), _1522309, c_Product__Type_Ofst(_1522309, _1522307)), hAPP(hAPP(c_Product__Type_OSigma(_1522309, _1522307), _1522311), hAPP(c_COMBK(tc_fun(_1522307, tc_HOL_Obool), _1522309), _1522305))) = _1522311)], (20022 ^ _779999) ^ [_1145031, _1145033] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1145031), _1145033) = 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)), _1145031)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1145033))))], (33931 ^ _779999) ^ [_1414873, _1414875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1414873)), c_Int_OBit0(_1414875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414873), _1414875)))], (49317 ^ _779999) ^ [_1774695, _1774697, _1774699] : [-(c_List_Olist__ex(_1774695, _1774697, _1774699)), 49318 ^ _779999 : [(49319 ^ _779999) ^ [_1774760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774695)), _1774699))), hBOOL(hAPP(_1774697, hAPP(hAPP(c_List_Onth(_1774695), _1774699), _1774760)))]]], (9768 ^ _779999) ^ [_946210, _946212, _946214, _946216] : [c_Orderings_Oorder__class_Omono(tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool), _946212), hBOOL(hAPP(hAPP(c_member(_946210), _946214), _946216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946210, tc_HOL_Obool)), _946216), hAPP(_946212, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_946210, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_946210, tc_HOL_Obool), tc_fun(tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool)), tc_fun(_946210, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946210, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_946210, tc_HOL_Obool), tc_fun(tc_fun(_946210, tc_HOL_Obool), tc_fun(_946210, tc_HOL_Obool)), tc_fun(_946210, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946210, tc_HOL_Obool))), _946212)), _946216))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_946210, tc_HOL_Obool), _946212)))))), -(hBOOL(hAPP(hAPP(c_member(_946210), _946214), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_946210, tc_HOL_Obool), _946212))))], (40130 ^ _779999) ^ [_1559028, _1559030, _1559032, _1559034] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1559028, _1559030, _1559032, tc_prod(_1559030, _1559032)), _1559034), c_Product__Type_OPair(_1559030, _1559032)) = _1559034)], (7556 ^ _779999) ^ [_906909, _906911] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _906909), _906911)), -(_906911 = _906909)], (21704 ^ _779999) ^ [_1175321] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1175321, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1175321), hAPP(c_COMBK(tc_HOL_Obool, _1175321), c_fFalse)))], (9442 ^ _779999) ^ [_940539, _940541, _940543] : [class_Orderings_Oorder(_940539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940539), _940541), _940543)), -(_940541 = _940543), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940539), _940541), _940543)))], (28462 ^ _779999) ^ [_1315061, _1315063, _1315065] : [class_Fields_Olinordered__field(_1315061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315061), _1315063), c_Groups_Ozero__class_Ozero(_1315061))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315061), c_Groups_Ozero__class_Ozero(_1315061)), _1315065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315061), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315061), _1315063), _1315065)), c_Groups_Ozero__class_Ozero(_1315061))))], (42588 ^ _779999) ^ [_1618615, _1618617] : [class_Complete__Lattice_Ocomplete__lattice(_1618615), -(c_Complete__Lattice_OInf__class_OInf(_1618615, hAPP(hAPP(c_Set_Oinsert(_1618615), _1618617), c_Orderings_Obot__class_Obot(tc_fun(_1618615, tc_HOL_Obool)))) = _1618617)], (25430 ^ _779999) ^ [_1257267, _1257269, _1257271] : [class_Lattices_Oboolean__algebra(_1257267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257267), _1257269), _1257271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257267), hAPP(c_Groups_Ouminus__class_Ouminus(_1257267), _1257271)), hAPP(c_Groups_Ouminus__class_Ouminus(_1257267), _1257269))))], (43273 ^ _779999) ^ [_1636000, _1636002, _1636004, _1636006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1636000), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1636002), _1636004))), -(hAPP(c_Random_Opick(_1636002, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1636002)), _1636004), _1636006)), _1636000) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1636002), _1636004))], (33275 ^ _779999) ^ [_1403012, _1403014] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1403012), _1403014), hAPP(c_Int_Onumber__class_Onumber__of(_1403012), c_Int_OBit1(c_Int_OPls))) = _1403014), class_Fields_Ofield(_1403012), class_Int_Onumber__ring(_1403012)], (9882 ^ _779999) ^ [_949866, _949868, _949870, _949872] : [-(hBOOL(hAPP(hAPP(c_member(_949866), _949868), _949870))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_949866, tc_Nat_Onat), _949872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949866, tc_HOL_Obool)), _949870), hAPP(hAPP(c_Set_Oinsert(_949866), _949868), c_Orderings_Obot__class_Obot(tc_fun(_949866, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_949866, tc_Nat_Onat), _949872), _949870))], (45366 ^ _779999) ^ [_1687850, _1687852, _1687854, _1687856] : [-(hAPP(hAPP(c_List_Odrop(_1687850), _1687852), hAPP(hAPP(c_List_Odrop(_1687850), _1687854), _1687856)) = hAPP(hAPP(c_List_Odrop(_1687850), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1687852), _1687854)), _1687856))], (51498 ^ _779999) ^ [_1822090, _1822092, _1822094, _1822096, _1822098] : [c_Fun_Oinj__on(_1822090, _1822092, _1822094, c_Orderings_Otop__class_Otop(tc_fun(_1822090, tc_HOL_Obool))), 51504 ^ _779999 : [(51507 ^ _779999) ^ [] : [hBOOL(hAPP(_1822096, hAPP(c_Hilbert__Choice_Oinv__into(_1822090, _1822092, c_Orderings_Otop__class_Otop(tc_fun(_1822090, tc_HOL_Obool)), _1822094), 51503 ^ [_1822090, _1822092, _1822094, _1822096, _1822098])))], (51505 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822092), 51503 ^ [_1822090, _1822092, _1822094, _1822096, _1822098]), hAPP(c_Set_Oimage(_1822090, _1822092, _1822094), c_Orderings_Otop__class_Otop(tc_fun(_1822090, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1822096, _1822098)))], (20691 ^ _779999) ^ [_1155529] : [c_Nat__Transfer_Onat__set(_1155529), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1155529) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155529)))], (26915 ^ _779999) ^ [_1285482, _1285484, _1285486, _1285488, _1285490, _1285492] : [hBOOL(hAPP(hAPP(c_member(_1285482), _1285484), _1285486)), 26918 ^ _779999 : [(26925 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285482), _1285488), _1285486))), -(hAPP(c_Set_Ovimage(_1285490, _1285482, hAPP(hAPP(c_COMBC(_1285490, _1285482, _1285482), hAPP(hAPP(c_COMBC(_1285490, _1285482, tc_fun(_1285482, _1285482)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1285482, tc_fun(_1285482, _1285482)), _1285490), c_If(_1285482)), hAPP(hAPP(c_COMBC(_1285490, tc_fun(_1285490, tc_HOL_Obool), tc_HOL_Obool), c_member(_1285490)), _1285492))), _1285484)), _1285488)), _1285486) = _1285492)], (26919 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1285482), _1285488), _1285486)), -(hAPP(c_Set_Ovimage(_1285490, _1285482, hAPP(hAPP(c_COMBC(_1285490, _1285482, _1285482), hAPP(hAPP(c_COMBC(_1285490, _1285482, tc_fun(_1285482, _1285482)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1285482, tc_fun(_1285482, _1285482)), _1285490), c_If(_1285482)), hAPP(hAPP(c_COMBC(_1285490, tc_fun(_1285490, tc_HOL_Obool), tc_HOL_Obool), c_member(_1285490)), _1285492))), _1285484)), _1285488)), _1285486) = c_Orderings_Otop__class_Otop(tc_fun(_1285490, tc_HOL_Obool)))]]], (4332 ^ _779999) ^ [_845759, _845761, _845763, _845765, _845767, _845769, _845771, _845773] : [-(c_New__Random__Sequence_Oneg__bind(_845773, _845769, _845765, _845761) = c_New__Random__Sequence_Oneg__bind(_845771, _845767, _845763, _845759)), _845773 = _845771, _845769 = _845767, _845765 = _845763, _845761 = _845759], (36661 ^ _779999) ^ [_1470896, _1470898] : [hAPP(c_Int_ORep__Integ, _1470896) = hAPP(c_Int_ORep__Integ, _1470898), -(_1470896 = _1470898)], (31634 ^ _779999) ^ [_1373364, _1373366, _1373368, _1373370, _1373372] : [-(hAPP(c_Relation_OImage(_1373364, _1373366, _1373368), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1373364, tc_HOL_Obool)), _1373370), _1373372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1373366, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1373364, _1373366, _1373368), _1373370)), hAPP(c_Relation_OImage(_1373364, _1373366, _1373368), _1373372)))], (25398 ^ _779999) ^ [_1256658, _1256660, _1256662, _1256664, _1256666] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1256658, _1256660, _1256662)), _1256664), _1256666)), 25403 ^ _779999 : [(25406 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1256660), _1256664), _1256666)))], (25404 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1256658, _1256664)))]], 25407 ^ _779999 : [(25410 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1256662), _1256664), _1256666)))], (25408 ^ _779999) ^ [] : [hBOOL(hAPP(_1256658, _1256664))]]], (49762 ^ _779999) ^ [_1784033, _1784035, _1784037, _1784039] : [-(c_Lazy__Sequence_Oproduct(_1784033, _1784035, _1784037, _1784039) = hAPP(c_Lazy__Sequence_Obind(_1784033, tc_prod(_1784033, _1784035), _1784037), hAPP(hAPP(c_COMBB(tc_fun(_1784035, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1784033, _1784035))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1784033, _1784035)), _1784033), c_Lazy__Sequence_Obind(_1784035, tc_prod(_1784033, _1784035), _1784039)), hAPP(hAPP(c_COMBB(tc_fun(_1784035, tc_prod(_1784033, _1784035)), tc_fun(_1784035, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1784033, _1784035))), _1784033), hAPP(c_COMBB(tc_prod(_1784033, _1784035), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1784033, _1784035)), _1784035), c_Lazy__Sequence_Osingle(tc_prod(_1784033, _1784035)))), c_Product__Type_OPair(_1784033, _1784035)))))], (33095 ^ _779999) ^ [_1400166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400166)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400166), c_Int_OPls)))], (9180 ^ _779999) ^ [_936764, _936766, _936768, _936770, _936772, _936774] : [-(_936764 = _936766), -(hAPP(c_Fun_Ofun__upd(_936768, _936770, _936772, _936766, _936774), _936764) = hAPP(_936772, _936764))], (52184 ^ _779999) ^ [_1832304] : [class_Finite__Set_Ofinite(_1832304), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1832304)))], (49187 ^ _779999) ^ [_1771450, _1771452, _1771454, _1771456, _1771458] : [class_Orderings_Olinorder(_1771450), 49193 ^ _779999 : [(49196 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1771450), hAPP(_1771456, _1771458)), hAPP(_1771456, 49192 ^ [_1771450, _1771452, _1771454, _1771456, _1771458])))], (49194 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771452), 49192 ^ [_1771450, _1771452, _1771454, _1771456, _1771458]), hAPP(c_List_Oset(_1771452), _1771454))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1771452, _1771450, _1771456), _1771458), _1771454) = hAPP(hAPP(c_List_Olist_OCons(_1771452), _1771458), _1771454))], (49858 ^ _779999) ^ [_1786860, _1786862, _1786864] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1786860, _1786862), _1786864) = c_Lazy__Sequence_Oproduct(_1786860, _1786862, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786860, _1786864), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786862, _1786864))), class_Lazy__Sequence_Osmall__lazy(_1786860), class_Lazy__Sequence_Osmall__lazy(_1786862)], (38125 ^ _779999) ^ [_1507893, _1507895] : [-(c_FunDef_Oreduction__pair(_1507893, _1507895)), c_Wellfounded_Owf(_1507893, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool), tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool)), _1507895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507893, _1507893, _1507893), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool), tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool)), _1507895)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool), tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool)), _1507895))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool), tc_fun(tc_prod(_1507893, _1507893), tc_HOL_Obool)), _1507895)))], (13933 ^ _779999) ^ [_1028280, _1028282] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028280), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028282), _1028280)))))], (45851 ^ _779999) ^ [_1698491, _1698493, _1698495] : [class_Orderings_Olinorder(_1698491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1698491), _1698493)), -(c_List_Olinorder__class_Osorted__list__of__set(_1698491, hAPP(hAPP(c_Set_Oinsert(_1698491), _1698495), _1698493)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698491, _1698491, c_COMBI(_1698491)), _1698495), c_List_Olinorder__class_Osorted__list__of__set(_1698491, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698491, tc_HOL_Obool)), _1698493), hAPP(hAPP(c_Set_Oinsert(_1698491), _1698495), c_Orderings_Obot__class_Obot(tc_fun(_1698491, tc_HOL_Obool)))))))], (4780 ^ _779999) ^ [_852785, _852787] : [_852787 = _852785, -(c_List_Olist_OCons(_852787) = c_List_Olist_OCons(_852785))], (20341 ^ _779999) ^ [_1150153, _1150155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150153)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1150153), _1150155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1150153)), hAPP(c_Int_Onat, _1150155)))], (43323 ^ _779999) ^ [_1637395, _1637397, _1637399, _1637401, _1637403] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637395), tc_List_Olist(_1637395))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637395), tc_List_Olist(_1637395)), _1637397), _1637399)), c_List_Olistrel1(_1637395, _1637401))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637395), tc_List_Olist(_1637395))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637395), tc_List_Olist(_1637395)), hAPP(hAPP(c_List_Olist_OCons(_1637395), _1637403), _1637397)), hAPP(hAPP(c_List_Olist_OCons(_1637395), _1637403), _1637399))), c_List_Olistrel1(_1637395, _1637401))))], (37893 ^ _779999) ^ [_1503270, _1503272, _1503274, _1503276, _1503278, _1503280, _1503282, _1503284] : [hBOOL(hAPP(hAPP(_1503270, _1503272), _1503274)), hBOOL(hAPP(hAPP(_1503276, _1503274), _1503278)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1503280, _1503282, _1503284, _1503270, _1503276), _1503272), _1503278)))], (44115 ^ _779999) ^ [_1660034, _1660036, _1660038, _1660040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660036)), _1660038))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660036)), _1660040))), 44125 ^ _779999 : [(44128 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Onth(_1660036), _1660038), 44124 ^ [_1660034, _1660036, _1660038, _1660040]) = hAPP(hAPP(c_List_Onth(_1660036), _1660040), 44124 ^ [_1660034, _1660036, _1660038, _1660040])], (44126 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44124 ^ [_1660034, _1660036, _1660038, _1660040]), _1660034)))]], -(hAPP(hAPP(c_List_Otake(_1660036), _1660034), _1660038) = hAPP(hAPP(c_List_Otake(_1660036), _1660034), _1660040))], (46792 ^ _779999) ^ [_1718669, _1718671, _1718673, _1718675] : [hBOOL(hAPP(c_List_Olistsp(_1718669, _1718671), _1718673)), hBOOL(hAPP(c_List_Olistsp(_1718669, _1718675), _1718673)), -(hBOOL(hAPP(c_List_Olistsp(_1718669, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1718669, tc_HOL_Obool)), _1718671), _1718675)), _1718673)))], (40984 ^ _779999) ^ [_1580177, _1580179, _1580181, _1580183] : [-(hAPP(hAPP(c_Nat_Ocompow(_1580177, _1580177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1580179), _1580181)), _1580183) = hAPP(c_Fun_Ocomp(_1580177, _1580177, _1580177, hAPP(hAPP(c_Nat_Ocompow(_1580177, _1580177), _1580179), _1580183)), hAPP(hAPP(c_Nat_Ocompow(_1580177, _1580177), _1580181), _1580183)))], (25732 ^ _779999) ^ [_1262319, _1262321, _1262323] : [class_Groups_Ogroup__add(_1262319), 25735 ^ _779999 : [(25742 ^ _779999) ^ [] : [_1262323 = hAPP(c_Groups_Ouminus__class_Ouminus(_1262319), _1262321), -(_1262321 = hAPP(c_Groups_Ouminus__class_Ouminus(_1262319), _1262323))], (25736 ^ _779999) ^ [] : [_1262321 = hAPP(c_Groups_Ouminus__class_Ouminus(_1262319), _1262323), -(_1262323 = hAPP(c_Groups_Ouminus__class_Ouminus(_1262319), _1262321))]]], (26632 ^ _779999) ^ [_1279234, _1279236] : [class_Orderings_Olinorder(_1279234), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279234, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1279234), _1279236)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1279234), _1279236))], (30052 ^ _779999) ^ [_1343193, _1343195, _1343197] : [class_Rings_Oring__1(_1343193), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343193), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1343195), _1343197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1343193), hAPP(c_Int_Oring__1__class_Oof__int(_1343193), _1343195)), hAPP(c_Int_Oring__1__class_Oof__int(_1343193), _1343197)))], (16669 ^ _779999) ^ [_1081507, _1081509, _1081511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1081507), _1081509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1081511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081511), _1081507)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081511), _1081509))))], (52062 ^ _779999) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (47964 ^ _779999) ^ [_1745382, _1745384, _1745386] : [class_Orderings_Olinorder(_1745382), c_List_Olinorder__class_Osorted(_1745382, _1745384), -(c_List_Olinorder__class_Osorted(_1745382, c_List_Olinorder__class_Oinsort__insert__key(_1745382, _1745382, c_COMBI(_1745382), _1745386, _1745384)))], (18253 ^ _779999) ^ [_1112274, _1112276] : [class_Rings_Oring__1(_1112274), -(hBOOL(hAPP(hAPP(c_member(_1112274), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1112274), _1112276)), c_Int_Oring__1__class_OInts(_1112274))))], (49910 ^ _779999) ^ [_1787848, _1787850, _1787852, _1787854] : [49918 ^ _779999 : [(49921 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1787854, 49917 ^ [_1787848, _1787850, _1787852, _1787854])))], (49919 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787848), 49917 ^ [_1787848, _1787850, _1787852, _1787854]), hAPP(c_List_Oset(_1787848), c_List_Oreplicate(_1787848, _1787850, _1787852)))))]], hBOOL(hAPP(_1787854, _1787852)), -(_1787850 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40856 ^ _779999) ^ [_1576758, _1576760, _1576762] : [c_Relation_Ototal__on(_1576758, _1576760, _1576762), -(c_Relation_Ototal__on(_1576758, _1576760, hAPP(c_Relation_Oconverse(_1576758, _1576758), _1576762)))], (46318 ^ _779999) ^ [_1708215, _1708217, _1708219, _1708221, _1708223, _1708225, _1708227, _1708229] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1708215, _1708217), _1708219), _1708221), hAPP(hAPP(c_List_Ozip(_1708215, _1708217), hAPP(hAPP(c_List_Omap(_1708223, _1708215), _1708225), _1708227)), _1708229)) = hAPP(hAPP(c_List_Omap(tc_prod(_1708223, _1708217), _1708219), hAPP(c_Product__Type_Oprod_Oprod__case(_1708223, _1708217, _1708219), hAPP(hAPP(c_COMBB(tc_fun(_1708217, tc_prod(_1708215, _1708217)), tc_fun(_1708217, _1708219), _1708223), hAPP(c_COMBB(tc_prod(_1708215, _1708217), _1708219, _1708217), _1708221)), hAPP(hAPP(c_COMBB(_1708215, tc_fun(_1708217, tc_prod(_1708215, _1708217)), _1708223), c_Product__Type_OPair(_1708215, _1708217)), _1708225)))), hAPP(hAPP(c_List_Ozip(_1708223, _1708217), _1708227), _1708229)))], (31889 ^ _779999) ^ [_1377953, _1377955, _1377957] : [class_Int_Onumber(_1377953), class_Orderings_Oord(_1377953), 31896 ^ _779999 : [(31903 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377953), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377955)), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377957)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1377953), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377955)), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377957)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377957))], (31897 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377953), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377955)), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377957))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1377953), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377955)), hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377957)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377953), _1377955))]]], (30657 ^ _779999) ^ [_1354771, _1354773, _1354775] : [class_Divides_Osemiring__div(_1354771), -(c_Divides_Odiv__class_Omod(_1354771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354771), _1354773), _1354775), _1354773) = c_Groups_Ozero__class_Ozero(_1354771))], (33607 ^ _779999) ^ [_1408376, _1408378] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408376)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408378)) = 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)))), _1408376)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408378)))], (30850 ^ _779999) ^ [_1358208, _1358210] : [-(_1358208 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358210), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1358208), _1358210))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358208, _1358210)))], (25249 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (46043 ^ _779999) ^ [_1702302, _1702304, _1702306] : [_1702302 = c_List_Olist_ONil(_1702304), -(c_List_Olast(_1702304, hAPP(hAPP(c_List_Oappend(_1702304), _1702306), _1702302)) = c_List_Olast(_1702304, _1702306))], (9104 ^ _779999) ^ [_935641, _935643, _935645] : [class_Orderings_Opreorder(_935641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935641), _935643), _935645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935641), _935645), _935643))], (46608 ^ _779999) ^ [_1714944, _1714946, _1714948] : [-(c_List_Olist_Olist__size(_1714944, _1714946, _1714948) = 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(_1714944, tc_Nat_Onat), _1714946), _1714948))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714944)), _1714948)))], (3556 ^ _779999) ^ [_833319, _833321, _833323, _833325, _833327, _833329] : [-(c_List_Olist_Olist__size(_833329, _833325, _833321) = c_List_Olist_Olist__size(_833327, _833323, _833319)), _833329 = _833327, _833325 = _833323, _833321 = _833319], (50016 ^ _779999) ^ [_1789703, _1789705, _1789707] : [_1789705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1789703, _1789705, _1789707) = c_List_Olist_ONil(_1789703))], (21714 ^ _779999) ^ [_1175573, _1175575, _1175577] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1175573), hAPP(c_Set_OCollect(_1175573), hAPP(hAPP(c_COMBS(_1175573, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175573), c_fdisj), _1175575)), _1175577))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175573), hAPP(c_Set_OCollect(_1175573), _1175575))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175573), hAPP(c_Set_OCollect(_1175573), _1175577)))], (5877 ^ _779999) ^ [_873405, _873407, _873409, _873411, _873413, _873415] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_873405, _873407, _873409, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873405), _873411), _873413), _873415)) = hAPP(hAPP(hAPP(_873409, _873411), _873413), _873415))], (12427 ^ _779999) ^ [_999967, _999969, _999971] : [class_Lattices_Olattice(_999967), hBOOL(hAPP(c_Finite__Set_Ofinite(_999967), _999969)), hBOOL(hAPP(hAPP(c_member(_999967), _999971), _999969)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_999967), _999971), c_Big__Operators_Olattice__class_OSup__fin(_999967, _999969)) = _999971)], (30551 ^ _779999) ^ [_1352746, _1352748, _1352750, _1352752] : [class_Divides_Osemiring__div(_1352746), -(c_Divides_Odiv__class_Omod(_1352746, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352746), _1352748), _1352750), _1352752) = c_Divides_Odiv__class_Omod(_1352746, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352746), c_Divides_Odiv__class_Omod(_1352746, _1352748, _1352752)), _1352750), _1352752))], (39342 ^ _779999) ^ [_1540602, _1540604, _1540606, _1540608, _1540610, _1540612] : [-(hAPP(c_Set_Ovimage(_1540602, tc_prod(_1540604, _1540606), _1540608), hAPP(hAPP(c_Product__Type_OSigma(_1540604, _1540606), _1540610), hAPP(c_COMBK(tc_fun(_1540606, tc_HOL_Obool), _1540604), _1540612))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1540602, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1540602, _1540604, hAPP(c_Fun_Ocomp(tc_prod(_1540604, _1540606), _1540604, _1540602, c_Product__Type_Ofst(_1540604, _1540606)), _1540608)), _1540610)), hAPP(c_Set_Ovimage(_1540602, _1540606, hAPP(c_Fun_Ocomp(tc_prod(_1540604, _1540606), _1540606, _1540602, c_Product__Type_Osnd(_1540604, _1540606)), _1540608)), _1540612)))], (51196 ^ _779999) ^ [_1815349, _1815351, _1815353, _1815355, _1815357] : [c_Equiv__Relations_Opart__equivp(_1815349, _1815351), hBOOL(hAPP(hAPP(_1815351, _1815353), _1815355)), hBOOL(hAPP(hAPP(_1815351, _1815355), _1815357)), -(hBOOL(hAPP(hAPP(_1815351, _1815353), _1815357)))], (34311 ^ _779999) ^ [_1421622] : [-(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)))), _1421622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1421622), _1421622))], (12585 ^ _779999) ^ [_1002412, _1002414, _1002416] : [class_Lattices_Olattice(_1002412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002412), _1002414)), 12592 ^ _779999 : [(12599 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002412, tc_HOL_Obool)), _1002414), hAPP(hAPP(c_Set_Oinsert(_1002412), _1002416), c_Orderings_Obot__class_Obot(tc_fun(_1002412, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1002412, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1002412, hAPP(hAPP(c_Set_Oinsert(_1002412), _1002416), _1002414)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002412), _1002416), c_Big__Operators_Olattice__class_OSup__fin(_1002412, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002412, tc_HOL_Obool)), _1002414), hAPP(hAPP(c_Set_Oinsert(_1002412), _1002416), c_Orderings_Obot__class_Obot(tc_fun(_1002412, tc_HOL_Obool)))))))], (12593 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002412, tc_HOL_Obool)), _1002414), hAPP(hAPP(c_Set_Oinsert(_1002412), _1002416), c_Orderings_Obot__class_Obot(tc_fun(_1002412, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1002412, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1002412, hAPP(hAPP(c_Set_Oinsert(_1002412), _1002416), _1002414)) = _1002416)]]], (9484 ^ _779999) ^ [_941120, _941122, _941124, _941126] : [class_Orderings_Oorder(_941120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941120), _941122), _941124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941120), _941126), _941122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941120), _941126), _941124)))], (15431 ^ _779999) ^ [_1057440, _1057442] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1057440, _1057442)) = 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), _1057440)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1057442))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (946 ^ _779999) ^ [_794424, _794426, _794428, _794430, _794432, _794434, _794436, _794438] : [-(c_Wellfounded_Omax__extp(_794436, _794432, _794428, _794424)), c_Wellfounded_Omax__extp(_794438, _794434, _794430, _794426), _794438 = _794436, _794434 = _794432, _794430 = _794428, _794426 = _794424], (11757 ^ _779999) ^ [_986568, _986570, _986572] : [11758 ^ _779999 : [(11761 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986568), _986572))], (11759 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986568), _986570))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_986568), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_986568, tc_HOL_Obool)), _986570), _986572))))], (21540 ^ _779999) ^ [_1172138, _1172140, _1172142] : [class_Orderings_Oorder(_1172138), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1172138, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1172138, _1172140, _1172142)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1172138), _1172142)) = c_Orderings_Obot__class_Obot(tc_fun(_1172138, tc_HOL_Obool)))], (6149 ^ _779999) ^ [_878190, _878192, _878194] : [class_Lattices_Olattice(_878190), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878190), _878192), _878194) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878190), _878194), _878192))], (48398 ^ _779999) ^ [_1754009, _1754011] : [class_Groups_Ocomm__monoid__add(_1754009), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1754009), hAPP(c_List_Orev(_1754009), _1754011)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1754009), _1754011))], (13367 ^ _779999) ^ [_1017956, _1017958] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1017956)), _1017958) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017956), hAPP(c_Nat_OSuc, _1017958)))], (4670 ^ _779999) ^ [_851082, _851084, _851086, _851088, _851090, _851092] : [-(c_New__DSequence_Opos__union(_851092, _851088, _851084) = c_New__DSequence_Opos__union(_851090, _851086, _851082)), _851092 = _851090, _851088 = _851086, _851084 = _851082], (18193 ^ _779999) ^ [_1111138, _1111140, _1111142] : [class_Rings_Olinordered__semidom(_1111138), 18196 ^ _779999 : [(18203 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111140), _1111142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111138), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111138), _1111140)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111138), _1111142))))], (18197 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111138), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111138), _1111140)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111138), _1111142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111140), _1111142)))]]], (6207 ^ _779999) ^ [_879200, _879202, _879204] : [_879200 = _879202, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879204, tc_HOL_Obool)), _879200), _879202)))], (25692 ^ _779999) ^ [_1261679, _1261681] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261679, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261679, tc_HOL_Obool)), _1261681)) = _1261681)], (8108 ^ _779999) ^ [_917041, _917043] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917041, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_917041, tc_HOL_Obool))), _917043) = c_Orderings_Obot__class_Obot(tc_fun(_917041, tc_HOL_Obool)))], (25263 ^ _779999) ^ [_1254146] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254146), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50591 ^ _779999) ^ [_1802511] : [-(c_Relation_Otrans(tc_fun(_1802511, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1802511)))], (51804 ^ _779999) ^ [_1828467, _1828469] : [class_Lattices_Oboolean__algebra(_1828467), -(class_Lattices_Oboolean__algebra(tc_fun(_1828469, _1828467)))], (36475 ^ _779999) ^ [_1466938, _1466940, _1466942, _1466944] : [-(hAPP(c_Product__Type_Ofst(_1466938, _1466940), hAPP(hAPP(c_Product__Type_OPair(_1466938, _1466940), _1466942), _1466944)) = _1466942)], (51321 ^ _779999) ^ [_1817972, _1817974, _1817976, _1817978, _1817980] : [hBOOL(hAPP(hAPP(c_member(_1817972), _1817974), hAPP(c_Set_Oimage(_1817976, _1817972, _1817978), _1817980))), -(hAPP(_1817978, hAPP(c_Hilbert__Choice_Oinv__into(_1817976, _1817972, _1817980, _1817978), _1817974)) = _1817974)], (51561 ^ _779999) ^ [_1823689] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51557 ^ [_1823689]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45101 ^ _779999) ^ [_1681383, _1681385, _1681387] : [_1681387 = c_List_Olist_ONil(_1681385), -(_1681383 = hAPP(hAPP(c_List_Oappend(_1681385), _1681383), _1681387))], (44282 ^ _779999) ^ [_1663919, _1663921, _1663923, _1663925] : [hBOOL(hAPP(c_List_Odistinct(_1663919), _1663921)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1663923, _1663919)), hAPP(hAPP(c_List_Ozip(_1663923, _1663919), _1663925), _1663921))))], (35328 ^ _779999) ^ [_1444976, _1444978, _1444980] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444976, _1444976), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1444978), _1444980))), -(_1444976 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1444978 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11550 ^ _779999) ^ [_982075, _982077, _982079] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982075, tc_HOL_Obool)), _982077), _982079) = c_Orderings_Obot__class_Obot(tc_fun(_982075, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982075, tc_HOL_Obool)), _982077), _982079) = _982077)], (27522 ^ _779999) ^ [_1297642, _1297644] : [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), _1297642)), _1297644))), _1297642 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1297644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34587 ^ _779999) ^ [_1426429, _1426431, _1426433] : [class_Int_Onumber__ring(_1426429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426429), _1426431), _1426433)), 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(_1426429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426429), hAPP(hAPP(c_Power_Opower__class_Opower(_1426429), _1426431), 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(_1426429), _1426433), 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(_1426429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426429), hAPP(c_Int_Onumber__class_Onumber__of(_1426429), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1426431)), _1426433)))], (46960 ^ _779999) ^ [_1723049, _1723051, _1723053, _1723055, _1723057, _1723059, _1723061] : [c_List_Olist__all2(_1723049, _1723057, hAPP(hAPP(c_COMBC(_1723049, tc_fun(_1723057, _1723051), tc_fun(_1723057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1723051, tc_HOL_Obool), tc_fun(tc_fun(_1723057, _1723051), tc_fun(_1723057, tc_HOL_Obool)), _1723049), c_COMBB(_1723051, tc_HOL_Obool, _1723057)), _1723053)), _1723059), _1723055, _1723061), -(c_List_Olist__all2(_1723049, _1723051, _1723053, _1723055, hAPP(hAPP(c_List_Omap(_1723057, _1723051), _1723059), _1723061)))], (50985 ^ _779999) ^ [_1811845, _1811847, _1811849, _1811851] : [c_Relation_Osym(_1811845, _1811847), hBOOL(hAPP(hAPP(c_member(tc_prod(_1811845, _1811845)), hAPP(hAPP(c_Product__Type_OPair(_1811845, _1811845), _1811849), _1811851)), _1811847)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811845, _1811845)), hAPP(hAPP(c_Product__Type_OPair(_1811845, _1811845), _1811851), _1811849)), _1811847)))], (45937 ^ _779999) ^ [_1700457, _1700459, _1700461, _1700463, _1700465] : [class_Orderings_Olinorder(_1700457), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700459, _1700457, _1700461), _1700463), _1700465) = c_List_Olist_ONil(_1700459)], (14764 ^ _779999) ^ [_1045194, _1045196] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045194), _1045196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045196), _1045194))], (33577 ^ _779999) ^ [_1407838, _1407840, _1407842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407838), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407840)), _1407842)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13447 ^ _779999) ^ [_1019518, _1019520, _1019522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019518), _1019520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019522), _1019520))))], (12793 ^ _779999) ^ [_1006696, _1006698, _1006700, _1006702, _1006704] : [c_Finite__Set_Ofolding__one__idem(_1006696, _1006698, _1006700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006696), _1006702)), -(_1006702 = c_Orderings_Obot__class_Obot(tc_fun(_1006696, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006696), _1006704)), -(_1006704 = c_Orderings_Obot__class_Obot(tc_fun(_1006696, tc_HOL_Obool))), -(hAPP(_1006700, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006696, tc_HOL_Obool)), _1006702), _1006704)) = hAPP(hAPP(_1006698, hAPP(_1006700, _1006702)), hAPP(_1006700, _1006704)))], (38764 ^ _779999) ^ [_1526572, _1526574, _1526576, _1526578, _1526580, _1526582] : [class_Groups_Ocomm__monoid__mult(_1526572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526574), _1526576)), 38774 ^ _779999 : [(38777 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526578), hAPP(_1526580, 38773 ^ [_1526572, _1526574, _1526576, _1526578, _1526580, _1526582])))], (38775 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526574), 38773 ^ [_1526572, _1526574, _1526576, _1526578, _1526580, _1526582]), _1526576)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526574, _1526572), hAPP(hAPP(c_COMBS(_1526574, tc_fun(_1526578, tc_HOL_Obool), _1526572), hAPP(hAPP(c_COMBB(tc_fun(_1526578, _1526572), tc_fun(tc_fun(_1526578, tc_HOL_Obool), _1526572), _1526574), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526578, _1526572)), _1526582)), _1526580)), _1526576) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1526574, _1526578), _1526572), hAPP(c_Product__Type_Oprod_Oprod__case(_1526574, _1526578, _1526572), _1526582)), hAPP(hAPP(c_Product__Type_OSigma(_1526574, _1526578), _1526576), _1526580)))], (21265 ^ _779999) ^ [_1167066, _1167068, _1167070] : [class_Orderings_Oorder(_1167066), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1167066, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1167066, _1167068), _1167070)), hAPP(c_SetInterval_Oord__class_OatLeast(_1167066), _1167070)) = c_Orderings_Obot__class_Obot(tc_fun(_1167066, tc_HOL_Obool)))], (51974 ^ _779999) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (2278 ^ _779999) ^ [_813500, _813502, _813504, _813506] : [-(c_Nat__Transfer_Otsub(_813506, _813502) = c_Nat__Transfer_Otsub(_813504, _813500)), _813506 = _813504, _813502 = _813500], (52366 ^ _779999) ^ [_1834353, _1834355] : [hBOOL(_1834353), hBOOL(_1834355), -(hBOOL(hAPP(hAPP(c_fconj, _1834353), _1834355)))], (7031 ^ _779999) ^ [_895543, _895545, _895547] : [hAPP(hAPP(c_Set_Oinsert(_895543), _895545), c_Orderings_Obot__class_Obot(tc_fun(_895543, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_895543), _895547), c_Orderings_Obot__class_Obot(tc_fun(_895543, tc_HOL_Obool))), -(_895545 = _895547)], (50284 ^ _779999) ^ [_1795258, _1795260, _1795262, _1795264, _1795266, _1795268] : [-(c_Nitpick_Opair__box_Opair__box__case(_1795258, _1795260, _1795262, _1795264, c_Nitpick_Opair__box_OPairBox(_1795258, _1795260, _1795266, _1795268)) = hAPP(hAPP(_1795264, _1795266), _1795268))], (44482 ^ _779999) ^ [_1668060, _1668062, _1668064] : [-(hBOOL(hAPP(hAPP(c_member(_1668060), _1668062), hAPP(c_List_Oset(_1668060), _1668064)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668060)), c_List_Oremove1(_1668060, _1668062, _1668064)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668060)), _1668064))], (30519 ^ _779999) ^ [_1352110, _1352112, _1352114, _1352116, _1352118, _1352120] : [class_Divides_Osemiring__div(_1352110), c_Divides_Odiv__class_Omod(_1352110, _1352112, _1352114) = c_Divides_Odiv__class_Omod(_1352110, _1352116, _1352114), c_Divides_Odiv__class_Omod(_1352110, _1352118, _1352114) = c_Divides_Odiv__class_Omod(_1352110, _1352120, _1352114), -(c_Divides_Odiv__class_Omod(_1352110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352110), _1352112), _1352118), _1352114) = c_Divides_Odiv__class_Omod(_1352110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352110), _1352116), _1352120), _1352114))], (19499 ^ _779999) ^ [_1135459] : [-(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), _1135459))))], (27128 ^ _779999) ^ [_1290531, _1290533] : [-(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), _1290531))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1290533))))], (43893 ^ _779999) ^ [_1653265, _1653267] : [-(hAPP(c_List_Oset(_1653265), _1653267) = hAPP(c_Set_OCollect(_1653265), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1653265), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1653265, 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)), _1653265), 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)), _1653265), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1653265, tc_fun(tc_Nat_Onat, _1653265), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1653265, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1653265), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1653265), c_COMBB(_1653265, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1653265), _1653267))))), 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(_1653265)), _1653267))))))], (50432 ^ _779999) ^ [_1798564, _1798566, _1798568, _1798570] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1798564, _1798566, _1798568, c_Code__Numeral_OSuc__code__numeral(_1798570)) = hAPP(hAPP(_1798568, _1798570), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1798564, _1798566, _1798568, _1798570)))], (30740 ^ _779999) ^ [_1356188] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1356188), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43353 ^ _779999) ^ [_1638490, _1638492, _1638494, _1638496, _1638498, _1638500] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638490), tc_List_Olist(_1638490))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638490), tc_List_Olist(_1638490)), hAPP(hAPP(c_List_Olist_OCons(_1638490), _1638492), _1638494)), hAPP(hAPP(c_List_Olist_OCons(_1638490), _1638496), _1638498))), c_List_Olistrel1(_1638490, _1638500))), 43358 ^ _779999 : [(43361 ^ _779999) ^ [] : [-(_1638494 = _1638498)], (43359 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638490, _1638490)), hAPP(hAPP(c_Product__Type_OPair(_1638490, _1638490), _1638492), _1638496)), _1638500)))]], 43362 ^ _779999 : [(43365 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638490), tc_List_Olist(_1638490))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638490), tc_List_Olist(_1638490)), _1638494), _1638498)), c_List_Olistrel1(_1638490, _1638500))))], (43363 ^ _779999) ^ [] : [-(_1638492 = _1638496)]]], (22902 ^ _779999) ^ [_1206298, _1206300, _1206302, _1206304, _1206306] : [class_Complete__Lattice_Ocomplete__lattice(_1206298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1206300, tc_HOL_Obool)), _1206302), _1206304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206298), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206300, _1206298), _1206302), _1206306)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206300, _1206298), _1206304), _1206306))))], (2796 ^ _779999) ^ [_821459, _821461, _821463, _821465] : [-(c_Predicate_OPowp(_821465, _821461) = c_Predicate_OPowp(_821463, _821459)), _821465 = _821463, _821461 = _821459], (34173 ^ _779999) ^ [_1419064, _1419066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1419064)), c_Int_OBit0(_1419066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419064), _1419066)))], (51952 ^ _779999) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (1354 ^ _779999) ^ [_800032, _800034] : [-(class_Groups_Osgn__if(_800032)), _800034 = _800032, class_Groups_Osgn__if(_800034)], (7288 ^ _779999) ^ [_900702, _900704, _900706, _900708] : [hBOOL(hAPP(hAPP(c_member(_900702), _900704), _900706)), -(hBOOL(hAPP(hAPP(c_member(_900702), _900704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900702, tc_HOL_Obool)), _900708), _900706))))], (51986 ^ _779999) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (21175 ^ _779999) ^ [_1165223, _1165225, _1165227, _1165229, _1165231] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1165223, _1165225, hAPP(hAPP(c_Set_Oinsert(_1165223), _1165227), _1165229)), _1165231)), 21180 ^ _779999 : [(21185 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1165223), 21178 ^ [_1165223, _1165225, _1165227, _1165229, _1165231]), 21179 ^ [_1165223, _1165225, _1165227, _1165229, _1165231]))], (21183 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1165223, _1165223, _1165225, 21178 ^ [_1165223, _1165225, _1165227, _1165229, _1165231], 21179 ^ [_1165223, _1165225, _1165227, _1165229, _1165231]), _1165231)))], (21181 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1165223), _1165227), _1165229) = hAPP(hAPP(c_Set_Oinsert(_1165223), 21178 ^ [_1165223, _1165225, _1165227, _1165229, _1165231]), 21179 ^ [_1165223, _1165225, _1165227, _1165229, _1165231]))]]], (33603 ^ _779999) ^ [_1408286, _1408288] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408286))), _1408288) = 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)))), _1408286), _1408288))], (49035 ^ _779999) ^ [_1767216, _1767218, _1767220, _1767222, _1767224] : [-(c_List_Omaps(_1767216, _1767218, _1767220, hAPP(hAPP(c_List_Olist_OCons(_1767216), _1767222), _1767224)) = hAPP(hAPP(c_List_Oappend(_1767218), hAPP(_1767220, _1767222)), c_List_Omaps(_1767216, _1767218, _1767220, _1767224)))], (28616 ^ _779999) ^ [_1317779, _1317781, _1317783, _1317785] : [class_Fields_Ofield__inverse__zero(_1317779), 28619 ^ _779999 : [(28620 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317779), _1317781), _1317783) = _1317785, 28623 ^ _779999 : [(28630 ^ _779999) ^ [] : [_1317783 = c_Groups_Ozero__class_Ozero(_1317779), -(_1317785 = c_Groups_Ozero__class_Ozero(_1317779))], (28624 ^ _779999) ^ [] : [-(_1317783 = c_Groups_Ozero__class_Ozero(_1317779)), -(_1317781 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317779), _1317785), _1317783))]]], (28636 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317779), _1317781), _1317783) = _1317785), 28639 ^ _779999 : [(28642 ^ _779999) ^ [] : [_1317781 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317779), _1317785), _1317783)], (28640 ^ _779999) ^ [] : [_1317783 = c_Groups_Ozero__class_Ozero(_1317779)]], 28643 ^ _779999 : [(28646 ^ _779999) ^ [] : [_1317785 = c_Groups_Ozero__class_Ozero(_1317779)], (28644 ^ _779999) ^ [] : [-(_1317783 = c_Groups_Ozero__class_Ozero(_1317779))]]]]], (48631 ^ _779999) ^ [_1758954, _1758956, _1758958, _1758960, _1758962] : [-(hBOOL(hAPP(_1758954, _1758956))), -(c_List_OtakeWhile(_1758958, _1758954, hAPP(hAPP(c_List_Oappend(_1758958), _1758960), hAPP(hAPP(c_List_Olist_OCons(_1758958), _1758956), _1758962))) = c_List_OtakeWhile(_1758958, _1758954, _1758960))], (13453 ^ _779999) ^ [_1019629, _1019631, _1019633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019629), _1019631)), _1019633)), 13456 ^ _779999 : [(13459 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019631), _1019633)))], (13457 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019629), _1019633)))]]], (31257 ^ _779999) ^ [_1365513, _1365515] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1365513), _1365515))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365513, _1365515) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1365513), _1365515), _1365515))], (1374 ^ _779999) ^ [_800282, _800284] : [-(class_Rings_Oring__1(_800282)), _800284 = _800282, class_Rings_Oring__1(_800284)], (3228 ^ _779999) ^ [_828155, _828157, _828159, _828161] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_828161, _828157) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_828159, _828155)), _828161 = _828159, _828157 = _828155], (29218 ^ _779999) ^ [_1328811, _1328813, _1328815, _1328817] : [class_Fields_Olinordered__field(_1328811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328811), _1328813), c_Groups_Ozero__class_Ozero(_1328811))), 29225 ^ _779999 : [(29232 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328811), _1328817), _1328813)), _1328815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328811), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328811), _1328815), _1328813)), _1328817)))], (29226 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328811), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328811), _1328815), _1328813)), _1328817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328811), _1328817), _1328813)), _1328815)))]]], (36242 ^ _779999) ^ [_1462297, _1462299, _1462301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462297, tc_fun(_1462297, tc_HOL_Obool))), _1462299), _1462301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462297, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1462297, _1462301)), c_Wellfounded_Oaccp(_1462297, _1462299))))], (5354 ^ _779999) ^ [_861918, _861920, _861922, _861924] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861924, _861920) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861922, _861918)), _861924 = _861922, _861920 = _861918], (52328 ^ _779999) ^ [_1833795, _1833797] : [-(hAPP(c_COMBI(_1833795), _1833797) = _1833797)], (33955 ^ _779999) ^ [_1415316] : [c_Int_OBit0(_1415316) = c_Int_OPls, -(_1415316 = c_Int_OPls)], (50650 ^ _779999) ^ [_1803788, _1803790] : [c_Relation_Otrans(_1803788, _1803790), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1803788, _1803788), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1803788, _1803788, _1803788), _1803790), _1803790)), _1803790)))], (48145 ^ _779999) ^ [_1748667, _1748669, _1748671, _1748673, _1748675, _1748677] : [class_Orderings_Olinorder(_1748667), c_List_Olinorder__class_Osorted(_1748667, hAPP(hAPP(c_List_Omap(_1748669, _1748667), _1748671), _1748673)), hBOOL(hAPP(_1748675, _1748677)), -(hAPP(c_List_Ofilter(_1748669, _1748675), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1748669, _1748667, _1748671), _1748677), _1748673)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1748669, _1748667, _1748671), _1748677), hAPP(c_List_Ofilter(_1748669, _1748675), _1748673)))], (47599 ^ _779999) ^ [_1738467, _1738469, _1738471] : [class_Groups_Oab__semigroup__add(_1738467), -(c_List_Ofoldr(_1738467, _1738467, c_Groups_Oplus__class_Oplus(_1738467), _1738469, _1738471) = hAPP(c_List_Ofoldl(_1738467, _1738467, c_Groups_Oplus__class_Oplus(_1738467), _1738471), _1738469))], (7047 ^ _779999) ^ [_895839, _895841, _895843] : [c_Hoare__Mirabelle_Otriple__valid(_895839, hAPP(c_Nat_OSuc, _895841), _895843), -(c_Hoare__Mirabelle_Otriple__valid(_895839, _895841, _895843))], (20 ^ _779999) ^ [_780259, _780261, _780263, _780265, _780267, _780269, _780271, _780273, _780275, _780277, _780279, _780281] : [-(c_Nitpick_Ofold__graph_H(_780279, _780275, _780271, _780267, _780263, _780259)), c_Nitpick_Ofold__graph_H(_780281, _780277, _780273, _780269, _780265, _780261), _780281 = _780279, _780277 = _780275, _780273 = _780271, _780269 = _780267, _780265 = _780263, _780261 = _780259], (41767 ^ _779999) ^ [_1597232, _1597234, _1597236, _1597238, _1597240, _1597242] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597232, tc_fun(_1597234, tc_HOL_Obool)), _1597236), _1597238), _1597240)), -(hBOOL(hAPP(hAPP(_1597238, _1597242), _1597240))), hBOOL(hAPP(hAPP(c_member(_1597232), _1597242), _1597236))], (7994 ^ _779999) ^ [_914895, _914897, _914899, _914901] : [-(c_Com_Ocom_OWhile(_914895, _914897) = c_Com_Ocom_OWhile(_914899, _914901)), _914895 = _914899, _914897 = _914901], (23783 ^ _779999) ^ [_1224109, _1224111, _1224113, _1224115, _1224117] : [c_Fun_Oinj__on(_1224109, _1224111, _1224113, c_Orderings_Otop__class_Otop(tc_fun(_1224109, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1224111, tc_HOL_Obool)), _1224115), hAPP(c_Set_Oimage(_1224109, _1224111, _1224113), _1224117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1224109, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1224109, _1224111, _1224113), _1224115)), _1224117)))], (1464 ^ _779999) ^ [_801407, _801409] : [-(class_Lattices_Osemilattice__inf(_801407)), _801409 = _801407, class_Lattices_Osemilattice__inf(_801409)], (13842 ^ _779999) ^ [_1026931, _1026933] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026931), _1026933) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13847 ^ _779999 : [(13850 ^ _779999) ^ [] : [-(_1026933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13848 ^ _779999) ^ [] : [-(_1026931 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13851 ^ _779999 : [(13854 ^ _779999) ^ [] : [-(_1026933 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13852 ^ _779999) ^ [] : [-(_1026931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5318 ^ _779999) ^ [_861386, _861388, _861390, _861392] : [-(c_List_Olistrel(_861392, _861388) = c_List_Olistrel(_861390, _861386)), _861392 = _861390, _861388 = _861386], (34095 ^ _779999) ^ [_1417661, _1417663] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1417661)), c_Int_OBit0(_1417663)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417661), _1417663)))], (7584 ^ _779999) ^ [_907363, _907365] : [class_Orderings_Owellorder(_907363), 7589 ^ _779999 : [(7590 ^ _779999) ^ [_907457] : [hBOOL(hAPP(_907365, _907457))]], -(hBOOL(hAPP(_907365, c_Orderings_Oord__class_OLeast(_907363, _907365))))], (48619 ^ _779999) ^ [_1758642, _1758644, _1758646, _1758648, _1758650] : [-(hAPP(hAPP(c_List_Ozip(_1758642, _1758644), c_List_OtakeWhile(_1758642, _1758646, _1758648)), _1758650) = c_List_OtakeWhile(tc_prod(_1758642, _1758644), hAPP(c_Fun_Ocomp(_1758642, tc_HOL_Obool, tc_prod(_1758642, _1758644), _1758646), c_Product__Type_Ofst(_1758642, _1758644)), hAPP(hAPP(c_List_Ozip(_1758642, _1758644), _1758648), _1758650)))], (1834 ^ _779999) ^ [_806032, _806034] : [-(class_Groups_Omonoid__mult(_806032)), _806034 = _806032, class_Groups_Omonoid__mult(_806034)], (43585 ^ _779999) ^ [_1645350, _1645352, _1645354, _1645356] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645350), tc_List_Olist(_1645350))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645350), tc_List_Olist(_1645350)), _1645352), _1645354)), c_List_Olistrel(_1645350, _1645356)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645350)), _1645352) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645350)), _1645354), 43591 ^ _779999 : [(43594 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645350, _1645350)), hAPP(hAPP(c_Product__Type_OPair(_1645350, _1645350), hAPP(hAPP(c_List_Onth(_1645350), _1645352), 43590 ^ [_1645350, _1645352, _1645354, _1645356])), hAPP(hAPP(c_List_Onth(_1645350), _1645354), 43590 ^ [_1645350, _1645352, _1645354, _1645356]))), _1645356))], (43592 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43590 ^ [_1645350, _1645352, _1645354, _1645356]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645350)), _1645352))))]]], (6721 ^ _779999) ^ [_889963, _889965] : [hBOOL(hAPP(hAPP(c_member(_889963), _889965), c_Orderings_Obot__class_Obot(tc_fun(_889963, tc_HOL_Obool))))], (10127 ^ _779999) ^ [_954673, _954675, _954677, _954679, _954681] : [c_Fun_Oinj__on(_954673, _954675, _954677, _954679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954673, tc_HOL_Obool)), _954681), _954679)), -(c_Fun_Oinj__on(_954673, _954675, _954677, _954681))], (21652 ^ _779999) ^ [_1174487, _1174489] : [c_Orderings_Obot__class_Obot(tc_fun(_1174487, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1174487), _1174489), 21655 ^ _779999 : [(21656 ^ _779999) ^ [_1174572] : [hBOOL(hAPP(_1174489, _1174572))]]], (25287 ^ _779999) ^ [_1254445, _1254447, _1254449, _1254451, _1254453, _1254455] : [class_Groups_Ocomm__monoid__add(_1254445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254447), _1254449)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1254447, _1254445), hAPP(hAPP(c_COMBS(_1254447, _1254445, _1254445), hAPP(hAPP(c_COMBS(_1254447, _1254445, tc_fun(_1254445, _1254445)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1254445, tc_fun(_1254445, _1254445)), _1254447), c_If(_1254445)), _1254451)), _1254453)), _1254455)), _1254449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1254447, _1254445), _1254453), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1254447, tc_HOL_Obool)), _1254449), hAPP(c_Set_OCollect(_1254447), _1254451)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1254447, _1254445), _1254455), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1254447, tc_HOL_Obool)), _1254449), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1254447, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1254447), _1254451))))))], (24434 ^ _779999) ^ [_1237651, _1237653, _1237655, _1237657] : [class_Orderings_Olinorder(_1237651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237651), _1237653), _1237655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237651), _1237657), _1237655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237651), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237651), _1237653), _1237657)), _1237655)))], (48344 ^ _779999) ^ [_1752767] : [-(hAPP(c_List_Orev(_1752767), c_List_Olist_ONil(_1752767)) = c_List_Olist_ONil(_1752767))], (35832 ^ _779999) ^ [_1455160, _1455162] : [-(c_Divides_OposDivAlg(_1455160, _1455162) = hAPP(c_Divides_Oadjust(_1455162), c_Divides_OposDivAlg(_1455160, 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)))), _1455162)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1455160), _1455162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1455162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14672 ^ _779999) ^ [_1043209, _1043211, _1043213] : [hAPP(c_Finite__Set_Ocard(_1043209), _1043211) = hAPP(c_Nat_OSuc, _1043213), 14677 ^ _779999 : [(14680 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1043209), 14675 ^ [_1043209, _1043211, _1043213]), 14676 ^ [_1043209, _1043211, _1043213]))], (14682 ^ _779999) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1043209), 14676 ^ [_1043209, _1043211, _1043213]) = _1043213)], (14684 ^ _779999) ^ [] : [_1043213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(14676 ^ [_1043209, _1043211, _1043213] = c_Orderings_Obot__class_Obot(tc_fun(_1043209, tc_HOL_Obool)))], (14678 ^ _779999) ^ [] : [-(_1043211 = hAPP(hAPP(c_Set_Oinsert(_1043209), 14675 ^ [_1043209, _1043211, _1043213]), 14676 ^ [_1043209, _1043211, _1043213]))]]], (13397 ^ _779999) ^ [_1018513, _1018515, _1018517, _1018519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018513), _1018515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018517), _1018519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018513), _1018517)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018515), _1018519))))], (29424 ^ _779999) ^ [_1332524, _1332526, _1332528, _1332530] : [class_Divides_Osemiring__div(_1332524), 29427 ^ _779999 : [(29434 ^ _779999) ^ [] : [-(_1332526 = c_Groups_Ozero__class_Ozero(_1332524)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1332524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332524), _1332526), _1332528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332524), _1332526), _1332530)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1332524), _1332528), _1332530))], (29428 ^ _779999) ^ [] : [_1332526 = c_Groups_Ozero__class_Ozero(_1332524), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1332524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332524), _1332526), _1332528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332524), _1332526), _1332530)) = c_Groups_Ozero__class_Ozero(_1332524))]]], (18597 ^ _779999) ^ [_1118940, _1118942, _1118944] : [class_Groups_Ocomm__monoid__add(_1118940), hAPP(_1118942, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1118940), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1118940), _1118942), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1118944)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1118940), _1118942), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1118944)))], (8385 ^ _779999) ^ [_923222, _923224, _923226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923222, tc_HOL_Obool)), _923224), _923226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_923222, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_923222), _923224)), hAPP(c_Set_OPow(_923222), _923226))))], (2902 ^ _779999) ^ [_823174, _823176, _823178, _823180] : [-(c_Wellfounded_Omax__ext(_823180, _823176) = c_Wellfounded_Omax__ext(_823178, _823174)), _823180 = _823178, _823176 = _823174], (6249 ^ _779999) ^ [_879944, _879946, _879948, _879950] : [hBOOL(hAPP(_879944, _879946)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879948, tc_HOL_Obool)), _879944), _879950), _879946)))], (7388 ^ _779999) ^ [_902820, _902822, _902824, _902826] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902820, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_902820, tc_fun(_902820, tc_HOL_Obool), tc_HOL_Obool), c_member(_902820)), _902822)), hAPP(hAPP(c_COMBC(_902820, tc_fun(_902820, tc_HOL_Obool), tc_HOL_Obool), c_member(_902820)), _902824)), _902826)), -(hBOOL(hAPP(hAPP(c_member(_902820), _902826), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902820, tc_HOL_Obool)), _902822), _902824))))], (43437 ^ _779999) ^ [_1640919, _1640921, _1640923, _1640925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640919), tc_List_Olist(_1640919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640919), tc_List_Olist(_1640919)), _1640921), _1640923)), c_List_Olistrel(_1640919, _1640925))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640919), tc_List_Olist(_1640919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640919), tc_List_Olist(_1640919)), _1640921), _1640923)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1640919), c_List_Olistrel1(_1640919, _1640925)))))], (4906 ^ _779999) ^ [_854878, _854880, _854882, _854884] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854884, _854880) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854882, _854878)), _854884 = _854882, _854880 = _854878], (7195 ^ _779999) ^ [_898772, _898774, _898776, _898778] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898772, tc_HOL_Obool)), _898774), hAPP(hAPP(c_Set_Oinsert(_898772), _898776), _898778)) = hAPP(hAPP(c_Set_Oinsert(_898772), _898776), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898772, tc_HOL_Obool)), _898774), _898778)))], (25600 ^ _779999) ^ [_1260047, _1260049, _1260051] : [class_Groups_Oordered__ab__group__add(_1260047), 25603 ^ _779999 : [(25610 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260047), _1260051), _1260049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260047), hAPP(c_Groups_Ouminus__class_Ouminus(_1260047), _1260049)), hAPP(c_Groups_Ouminus__class_Ouminus(_1260047), _1260051))))], (25604 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260047), hAPP(c_Groups_Ouminus__class_Ouminus(_1260047), _1260049)), hAPP(c_Groups_Ouminus__class_Ouminus(_1260047), _1260051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260047), _1260051), _1260049)))]]], (11839 ^ _779999) ^ [_988131, _988133, _988135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988131), hAPP(hAPP(c_Set_Oinsert(_988131), _988133), _988135))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988131), _988135)))], (2690 ^ _779999) ^ [_819844, _819846] : [_819846 = _819844, -(c_Wellfounded_Omeasure(_819846) = c_Wellfounded_Omeasure(_819844))], (15753 ^ _779999) ^ [_1064164, _1064166] : [class_Groups_Omonoid__mult(_1064164), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064164), c_Groups_Oone__class_Oone(_1064164)), _1064166) = _1064166)], (38836 ^ _779999) ^ [_1528452, _1528454, _1528456, _1528458, _1528460, _1528462] : [hAPP(c_Set_Oimage(_1528452, _1528454, _1528456), c_Orderings_Otop__class_Otop(tc_fun(_1528452, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528454, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528458, _1528460, _1528462), c_Orderings_Otop__class_Otop(tc_fun(_1528458, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528460, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1528452, _1528458), tc_prod(_1528454, _1528460), c_Product__Type_Omap__pair(_1528452, _1528454, _1528458, _1528460, _1528456, _1528462)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1528452, _1528458), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1528454, _1528460), tc_HOL_Obool)))], (25269 ^ _779999) ^ [_1254231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254231), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254231)))], (52042 ^ _779999) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (16609 ^ _779999) ^ [_1080246, _1080248, _1080250, _1080252, _1080254, _1080256] : [class_Rings_Oring(_1080246), 16612 ^ _779999 : [(16619 ^ _779999) ^ [] : [_1080252 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080246), _1080254), _1080248)), _1080250)), _1080256), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), _1080248), _1080250)), _1080252) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), _1080254), _1080250)), _1080256))], (16613 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), _1080248), _1080250)), _1080252) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), _1080254), _1080250)), _1080256), -(_1080252 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080246), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080246), _1080254), _1080248)), _1080250)), _1080256))]]], (24296 ^ _779999) ^ [_1235048, _1235050, _1235052] : [class_Orderings_Olinorder(_1235048), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235048), _1235050), _1235052) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235048), _1235052), _1235050))], (14584 ^ _779999) ^ [_1041397, _1041399] : [class_Rings_Olinordered__idom(_1041397), 14587 ^ _779999 : [(14594 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041397), _1041399), c_Groups_Ozero__class_Ozero(_1041397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041397), _1041399), _1041399)), c_Groups_Ozero__class_Ozero(_1041397))))], (14588 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041397), _1041399), _1041399)), c_Groups_Ozero__class_Ozero(_1041397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041397), _1041399), c_Groups_Ozero__class_Ozero(_1041397))))]]], (26975 ^ _779999) ^ [_1287142, _1287144, _1287146, _1287148, _1287150] : [class_Groups_Ocomm__monoid__mult(_1287142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287144), _1287146)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287144), _1287148)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287144, tc_HOL_Obool)), _1287146), _1287148) = c_Orderings_Obot__class_Obot(tc_fun(_1287144, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287144, _1287142), _1287150), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287144, tc_HOL_Obool)), _1287146), _1287148)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287142), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287144, _1287142), _1287150), _1287146)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287144, _1287142), _1287150), _1287148)))], (10615 ^ _779999) ^ [_962695, _962697, _962699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962695), _962697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962695), _962699)), 10622 ^ _779999 : [(10629 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962697), _962699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962697), _962695)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962699), _962695))))], (10623 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962697), _962695)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962699), _962695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962697), _962699)))]]], (7918 ^ _779999) ^ [_913655, _913657] : [hAPP(c_Set_OPow(_913655), _913657) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_913655, tc_HOL_Obool), tc_HOL_Obool))], (8154 ^ _779999) ^ [_918099, _918101, _918103] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_918099), _918101), _918103)), -(c_Natural_Oevaln(_918099, _918101, 8157 ^ [_918099, _918101, _918103], _918103))], (15351 ^ _779999) ^ [_1055936, _1055938, _1055940, _1055942] : [class_Rings_Ocomm__semiring__1(_1055936), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055936), _1055938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055936), _1055940), _1055942)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055936), _1055938), _1055940)), _1055942))], (4074 ^ _779999) ^ [_841386, _841388, _841390, _841392, _841394, _841396] : [-(c_List_OdropWhile(_841396, _841392, _841388) = c_List_OdropWhile(_841394, _841390, _841386)), _841396 = _841394, _841392 = _841390, _841388 = _841386], (40972 ^ _779999) ^ [_1579808, _1579810, _1579812, _1579814, _1579816, _1579818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579808, _1579808)), hAPP(hAPP(c_Product__Type_OPair(_1579808, _1579808), _1579810), _1579812)), _1579814)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1579808, _1579808)), hAPP(hAPP(c_Product__Type_OPair(_1579808, _1579808), _1579812), _1579816)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579808, _1579808), tc_HOL_Obool), _1579818), _1579814))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579808, _1579808)), hAPP(hAPP(c_Product__Type_OPair(_1579808, _1579808), _1579810), _1579816)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579808, _1579808), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1579818)), _1579814))))], (34775 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (29360 ^ _779999) ^ [_1331543] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331543) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40685 ^ _779999) ^ [_1572337, _1572339, _1572341, _1572343, _1572345] : [-(hAPP(c_Relation_Oconverse(_1572337, _1572339), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1572341, tc_fun(tc_prod(_1572337, _1572339), tc_HOL_Obool)), _1572343), _1572345)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1572341, tc_fun(tc_prod(_1572339, _1572337), tc_HOL_Obool)), _1572343), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1572337, _1572339), tc_HOL_Obool), tc_fun(tc_prod(_1572339, _1572337), tc_HOL_Obool), _1572341), c_Relation_Oconverse(_1572337, _1572339)), _1572345)))], (24766 ^ _779999) ^ [_1243994, _1243996, _1243998] : [class_Orderings_Olinorder(_1243994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1243994), _1243996)), hBOOL(hAPP(hAPP(c_member(_1243994), _1243998), _1243996)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243994), _1243998), c_Big__Operators_Olattice_OInf__fin(_1243994, c_Orderings_Oord__class_Omin(_1243994), _1243996)) = _1243998)], (706 ^ _779999) ^ [_790814, _790816, _790818, _790820, _790822, _790824, _790826, _790828, _790830, _790832] : [-(c_Typedef_Otype__definition(_790830, _790826, _790822, _790818, _790814)), c_Typedef_Otype__definition(_790832, _790828, _790824, _790820, _790816), _790832 = _790830, _790828 = _790826, _790824 = _790822, _790820 = _790818, _790816 = _790814], (18001 ^ _779999) ^ [_1107643, _1107645, _1107647, _1107649, _1107651] : [class_Orderings_Olinorder(_1107643), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107643, _1107645), _1107647) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107643, _1107649), _1107651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107643), _1107645), _1107647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107643), _1107649), _1107651)), -(_1107645 = _1107649)], (14858 ^ _779999) ^ [_1046691, _1046693] : [-(hAPP(c_Finite__Set_Ocard(_1046691), _1046693) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046691, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1046691), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1046693))], (19027 ^ _779999) ^ [_1126863] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126863), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1126863)], (9906 ^ _779999) ^ [_950452, _950454, _950456, _950458] : [hBOOL(hAPP(_950452, _950454)), hBOOL(hAPP(_950456, _950458)), -(hBOOL(hAPP(_950452, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _950452) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _950456))), 9922 ^ _779999 : [(9925 ^ _779999) ^ [] : [hBOOL(hAPP(_950456, 9919 ^ [_950452, _950454, _950456, _950458]))], (9923 ^ _779999) ^ [] : [-(hBOOL(hAPP(_950452, hAPP(c_Nat_OSuc, 9919 ^ [_950452, _950454, _950456, _950458]))))]], 9926 ^ _779999 : [(9929 ^ _779999) ^ [] : [hBOOL(hAPP(_950452, hAPP(c_Nat_OSuc, 9919 ^ [_950452, _950454, _950456, _950458])))], (9927 ^ _779999) ^ [] : [-(hBOOL(hAPP(_950456, 9919 ^ [_950452, _950454, _950456, _950458])))]]], (42538 ^ _779999) ^ [_1617630, _1617632, _1617634] : [class_Complete__Lattice_Ocomplete__lattice(_1617630), hBOOL(hAPP(hAPP(c_member(_1617630), _1617632), _1617634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1617630), _1617632), c_Complete__Lattice_OSup__class_OSup(_1617630, _1617634))))], (10930 ^ _779999) ^ [_969041, _969043] : [-(_969041 = _969043), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969041), _969043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969043), _969041)))], (15125 ^ _779999) ^ [_1051642, _1051644, _1051646, _1051648, _1051650] : [-(hBOOL(hAPP(hAPP(c_member(_1051642), _1051644), c_SetInterval_Oord_OatLeastAtMost(_1051642, _1051646, _1051648, _1051650)))), hBOOL(hAPP(hAPP(_1051646, _1051648), _1051644)), hBOOL(hAPP(hAPP(_1051646, _1051644), _1051650))], (49834 ^ _779999) ^ [_1785674, _1785676, _1785678, _1785680, _1785682] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1785674, _1785676, hAPP(hAPP(c_COMBC(_1785674, tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_fun(_1785676, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1785676, tc_fun(tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_fun(_1785676, tc_HOL_Obool)), _1785674), c_COMBC(_1785676, tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1785676, tc_prod(_1785674, _1785676)), tc_fun(_1785676, tc_fun(tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_HOL_Obool)), _1785674), hAPP(c_COMBB(tc_prod(_1785674, _1785676), tc_fun(tc_fun(tc_prod(_1785674, _1785676), tc_HOL_Obool), tc_HOL_Obool), _1785676), c_member(tc_prod(_1785674, _1785676)))), c_Product__Type_OPair(_1785674, _1785676)))), _1785678)), _1785680), _1785682)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785676, _1785674)), hAPP(hAPP(c_Product__Type_OPair(_1785676, _1785674), _1785680), _1785682)), hAPP(c_Relation_Oconverse(_1785674, _1785676), _1785678))))], (50314 ^ _779999) ^ [_1795889, _1795891, _1795893, _1795895] : [class_Groups_Ocomm__monoid__add(_1795889), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1795891, tc_HOL_Obool)), _1795893)), 50324 ^ _779999 : [(50327 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795891), 50323 ^ [_1795889, _1795891, _1795893, _1795895]))], (50325 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1795891, tc_HOL_Obool)), 50323 ^ [_1795889, _1795891, _1795893, _1795895]), _1795893)))]], 50331 ^ _779999 : [(50335 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1795891, tc_HOL_Obool)), 50333 ^ [_1795889, _1795891, _1795893, _1795895]), _1795893)))], (50332 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1795891, tc_HOL_Obool)), 50330 ^ [_1795889, _1795891, _1795893, _1795895]), _1795893)))], (50344 ^ _779999) ^ [] : [hAPP(_1795895, 50338 ^ [_1795889, _1795891, _1795893, _1795895]) = c_Groups_Ozero__class_Ozero(_1795889)], (50340 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795891), 50338 ^ [_1795889, _1795891, _1795893, _1795895]), 50330 ^ [_1795889, _1795891, _1795893, _1795895])))], (50342 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795891), 50338 ^ [_1795889, _1795891, _1795893, _1795895]), 50333 ^ [_1795889, _1795891, _1795893, _1795895])))], (50337 ^ _779999) ^ [] : [50330 ^ [_1795889, _1795891, _1795893, _1795895] = 50333 ^ [_1795889, _1795891, _1795893, _1795895]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1795891, _1795889), _1795895), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1795891, tc_HOL_Obool), _1795893)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1795891, tc_HOL_Obool), _1795889), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1795891, _1795889), _1795895)), _1795893))], (27878 ^ _779999) ^ [_1304039, _1304041, _1304043, _1304045] : [class_Fields_Ofield(_1304039), -(_1304041 = c_Groups_Ozero__class_Ozero(_1304039)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1304039), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304039), _1304043), _1304041)), _1304045) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304039), hAPP(hAPP(c_Power_Opower__class_Opower(_1304039), _1304043), _1304045)), hAPP(hAPP(c_Power_Opower__class_Opower(_1304039), _1304041), _1304045)))], (52086 ^ _779999) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (10083 ^ _779999) ^ [_953938, _953940, _953942, _953944, _953946, _953948] : [c_Fun_Oinj__on(_953938, _953940, _953942, _953944), hBOOL(hAPP(hAPP(c_member(_953938), _953946), _953944)), hBOOL(hAPP(hAPP(c_member(_953938), _953948), _953944)), 10094 ^ _779999 : [(10101 ^ _779999) ^ [] : [_953946 = _953948, -(hAPP(_953942, _953946) = hAPP(_953942, _953948))], (10095 ^ _779999) ^ [] : [hAPP(_953942, _953946) = hAPP(_953942, _953948), -(_953946 = _953948)]]], (13145 ^ _779999) ^ [_1013949, _1013951, _1013953, _1013955] : [class_Groups_Oordered__ab__semigroup__add(_1013949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013949), _1013951), _1013953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013949), _1013955), _1013951)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013949), _1013955), _1013953))))], (44306 ^ _779999) ^ [_1664350, _1664352, _1664354] : [hBOOL(hAPP(c_List_Odistinct(_1664350), _1664352)), -(hBOOL(hAPP(c_List_Odistinct(_1664350), hAPP(hAPP(c_List_Otake(_1664350), _1664354), _1664352))))], (51372 ^ _779999) ^ [_1819217, _1819219, _1819221, _1819223, _1819225, _1819227] : [hAPP(c_Set_Oimage(_1819217, _1819219, _1819221), _1819223) = _1819225, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1819219, tc_HOL_Obool)), _1819227), _1819225)), -(hAPP(c_Set_Oimage(_1819217, _1819219, _1819221), hAPP(c_Set_Oimage(_1819219, _1819217, c_Hilbert__Choice_Oinv__into(_1819217, _1819219, _1819223, _1819221)), _1819227)) = _1819227)], (37539 ^ _779999) ^ [_1492569, _1492571] : [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)), _1492569), 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)), _1492571), 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)), _1492569), _1492571)), c_Int_Ointrel)))], (45754 ^ _779999) ^ [_1696442, _1696444] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1696442), _1696444) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45757 ^ _779999 : [(45760 ^ _779999) ^ [_1696556] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1696556), hAPP(c_List_Oset(tc_Nat_Onat), _1696444))), -(_1696556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45758 ^ _779999) ^ [] : [-(_1696442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (48687 ^ _779999) ^ [_1760008, _1760010, _1760012, _1760014, _1760016] : [class_Orderings_Olinorder(_1760008), c_List_Olinorder__class_Osorted(_1760008, hAPP(c_List_Orev(_1760008), hAPP(hAPP(c_List_Omap(_1760010, _1760008), _1760012), _1760014))), -(hAPP(c_List_Ofilter(_1760010, hAPP(hAPP(c_COMBB(_1760008, tc_HOL_Obool, _1760010), hAPP(c_Orderings_Oord__class_Oless(_1760008), _1760016)), _1760012)), _1760014) = c_List_OtakeWhile(_1760010, hAPP(hAPP(c_COMBB(_1760008, tc_HOL_Obool, _1760010), hAPP(c_Orderings_Oord__class_Oless(_1760008), _1760016)), _1760012), _1760014))], (8700 ^ _779999) ^ [_928926, _928928] : [-(c_HOL_OThe(_928926, hAPP(c_fequal, _928928)) = _928928)], (51616 ^ _779999) ^ [_1824745, _1824747, _1824749, _1824751, _1824753] : [c_Fun_Obij__betw(_1824745, _1824747, _1824749, _1824751, _1824753), -(c_Fun_Obij__betw(_1824747, _1824745, c_Hilbert__Choice_Oinv__into(_1824745, _1824747, _1824751, _1824749), _1824753, _1824751))], (46696 ^ _779999) ^ [] : [-(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))], (31773 ^ _779999) ^ [_1375752, _1375754] : [class_Int_Onumber__ring(_1375752), 31776 ^ _779999 : [(31783 ^ _779999) ^ [] : [-(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), _1375754)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1375752), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375754)) = c_Groups_Ozero__class_Ozero(_1375752))], (31777 ^ _779999) ^ [] : [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), _1375754))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1375752), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375754)) = hAPP(c_Int_Onumber__class_Onumber__of(_1375752), _1375754))]]], (26909 ^ _779999) ^ [_1285286, _1285288, _1285290, _1285292] : [c_Fun_Oinj__on(_1285286, _1285288, _1285290, c_Orderings_Otop__class_Otop(tc_fun(_1285286, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285288, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1285286, _1285288, _1285290), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285286, tc_HOL_Obool)), _1285292))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285288, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1285286, _1285288, _1285290), _1285292)))))], (37953 ^ _779999) ^ [_1504281, _1504283, _1504285, _1504287, _1504289, _1504291, _1504293] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1504281, _1504283, _1504285, _1504287, _1504289), _1504291), _1504293)), 37957 ^ _779999 : [(37960 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1504289, 37956 ^ [_1504281, _1504283, _1504285, _1504287, _1504289, _1504291, _1504293]), _1504293)))], (37958 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1504287, _1504291), 37956 ^ [_1504281, _1504283, _1504285, _1504287, _1504289, _1504291, _1504293])))]]], (14822 ^ _779999) ^ [_1046055, _1046057] : [class_Rings_Olinordered__semidom(_1046055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046055), _1046057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046055), _1046057), c_Groups_Oone__class_Oone(_1046055)))))], (52008 ^ _779999) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (31636 ^ _779999) ^ [_1373438, _1373440, _1373442] : [31638 ^ _779999 : [(31643 ^ _779999) ^ [] : [hBOOL(hAPP(_1373440, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31637 ^ [_1373438, _1373440, _1373442]), _1373438)))], (31641 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1373440, 31637 ^ [_1373438, _1373440, _1373442])))], (31639 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31637 ^ [_1373438, _1373440, _1373442]), _1373438)))]], hBOOL(hAPP(_1373440, _1373442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373442), _1373438)), -(hBOOL(hAPP(_1373440, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46856 ^ _779999) ^ [_1719959, _1719961, _1719963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1719959, tc_HOL_Obool)), _1719961), _1719963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1719959), tc_HOL_Obool)), c_List_Olistsp(_1719959, _1719961)), c_List_Olistsp(_1719959, _1719963))))], (10693 ^ _779999) ^ [_964117, _964119] : [class_Complete__Lattice_Ocomplete__lattice(_964117), c_Orderings_Oorder__class_Omono(_964117, _964117, _964119), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964117), c_Inductive_Ocomplete__lattice__class_Olfp(_964117, _964119)), hAPP(_964119, c_Inductive_Ocomplete__lattice__class_Olfp(_964117, _964119)))))], (1744 ^ _779999) ^ [_804907, _804909] : [-(class_Groups_Ocomm__monoid__add(_804907)), _804909 = _804907, class_Groups_Ocomm__monoid__add(_804909)], (44826 ^ _779999) ^ [_1674896, _1674898, _1674900, _1674902, _1674904] : [-(_1674896 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1674898, _1674900, _1674902), _1674896), _1674904) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1674900), _1674898), tc_prod(_1674900, _1674898), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1674900), _1674898), c_List_Olist_ONil(_1674900)), _1674904), hAPP(c_Product__Type_Oprod_Oprod__case(_1674900, _1674898, tc_prod(tc_List_Olist(_1674900), _1674898)), hAPP(hAPP(c_COMBC(_1674900, tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898)), tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1674900), _1674898), tc_prod(tc_List_Olist(_1674900), _1674898)), tc_fun(tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898)), tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898))), _1674900), c_COMBB(tc_prod(tc_List_Olist(_1674900), _1674898), tc_prod(tc_List_Olist(_1674900), _1674898), _1674898)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1674900), tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898))), tc_fun(tc_prod(tc_List_Olist(_1674900), _1674898), tc_prod(tc_List_Olist(_1674900), _1674898)), _1674900), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1674900), _1674898, tc_prod(tc_List_Olist(_1674900), _1674898))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1674900), tc_List_Olist(_1674900)), tc_fun(tc_List_Olist(_1674900), tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898))), _1674900), hAPP(c_COMBB(tc_List_Olist(_1674900), tc_fun(_1674898, tc_prod(tc_List_Olist(_1674900), _1674898)), tc_List_Olist(_1674900)), c_Product__Type_OPair(tc_List_Olist(_1674900), _1674898))), c_List_Olist_OCons(_1674900))))), hAPP(c_Lazy__Sequence_Oanamorph(_1674898, _1674900, _1674902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1674896), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1674902, _1674904)))], (27532 ^ _779999) ^ [_1297791, _1297793] : [27533 ^ _779999 : [(27536 ^ _779999) ^ [] : [_1297793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27534 ^ _779999) ^ [] : [-(_1297791 = 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), _1297791)), _1297793))))], (7795 ^ _779999) ^ [_911410, _911412, _911414, _911416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911410, tc_HOL_Obool)), _911412), hAPP(hAPP(c_Set_Oinsert(_911410), _911414), _911416))), 7798 ^ _779999 : [(7805 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911410), _911414), _911412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911410, tc_HOL_Obool)), _911412), _911416)))], (7799 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_911410), _911414), _911412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911410, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911410, tc_HOL_Obool)), _911412), hAPP(hAPP(c_Set_Oinsert(_911410), _911414), c_Orderings_Obot__class_Obot(tc_fun(_911410, tc_HOL_Obool))))), _911416)))]]], (32839 ^ _779999) ^ [_1396040, _1396042] : [-(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), _1396040)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1396042), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1396040))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (42776 ^ _779999) ^ [_1622947, _1622949, _1622951] : [42778 ^ _779999 : [(42781 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622947, tc_HOL_Obool)), 42777 ^ [_1622947, _1622949, _1622951]), _1622951))], (42779 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1622947, tc_HOL_Obool)), 42777 ^ [_1622947, _1622949, _1622951]), _1622949)))]], -(_1622949 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1622947, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622947, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1622947, tc_HOL_Obool), _1622949)), _1622951)))], (31078 ^ _779999) ^ [_1362534, _1362536, _1362538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362534), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31081 ^ _779999 : [(31082 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1362536, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1362538), _1362534)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362538, _1362534))), 31085 ^ _779999 : [(31086 ^ _779999) ^ [_1362744, _1362746] : [-(hBOOL(hAPP(hAPP(_1362536, _1362746), _1362744))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362534), _1362744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362744), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1362538 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362534), _1362746)), _1362744)]]], (31100 ^ _779999) ^ [] : [31103 ^ _779999 : [(31106 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31102 ^ [_1362534, _1362536, _1362538]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31108 ^ _779999) ^ [] : [-(_1362538 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362534), 31101 ^ [_1362534, _1362536, _1362538])), 31102 ^ [_1362534, _1362536, _1362538]))], (31110 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1362536, 31101 ^ [_1362534, _1362536, _1362538]), 31102 ^ [_1362534, _1362536, _1362538]))], (31104 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362534), 31102 ^ [_1362534, _1362536, _1362538])))]], -(hBOOL(hAPP(hAPP(_1362536, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1362538), _1362534)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362538, _1362534))))]]], (39669 ^ _779999) ^ [_1547919, _1547921, _1547923, _1547925, _1547927, _1547929, _1547931, _1547933] : [c_Finite__Set_Ofolding(_1547919, _1547921, _1547923, _1547925), -(hAPP(c_Fun_Ocomp(_1547921, _1547921, _1547927, hAPP(_1547923, _1547929)), hAPP(c_Fun_Ocomp(_1547921, _1547921, _1547927, hAPP(_1547923, _1547931)), _1547933)) = hAPP(c_Fun_Ocomp(_1547921, _1547921, _1547927, hAPP(_1547923, _1547931)), hAPP(c_Fun_Ocomp(_1547921, _1547921, _1547927, hAPP(_1547923, _1547929)), _1547933)))], (50064 ^ _779999) ^ [_1790526, _1790528, _1790530] : [-(hAPP(c_List_Oset(_1790526), c_List_Oreplicate(_1790526, hAPP(c_Nat_OSuc, _1790528), _1790530)) = hAPP(hAPP(c_Set_Oinsert(_1790526), _1790530), c_Orderings_Obot__class_Obot(tc_fun(_1790526, tc_HOL_Obool))))], (38402 ^ _779999) ^ [_1515157, _1515159, _1515161, _1515163] : [hBOOL(hAPP(hAPP(c_member(_1515157), _1515163), hAPP(c_Relation_ODomain(_1515157, _1515159), _1515161))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1515157, _1515159, hAPP(hAPP(c_COMBC(_1515157, tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_fun(_1515159, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515159, tc_fun(tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_fun(_1515159, tc_HOL_Obool)), _1515157), c_COMBC(_1515159, tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515159, tc_prod(_1515157, _1515159)), tc_fun(_1515159, tc_fun(tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_HOL_Obool)), _1515157), hAPP(c_COMBB(tc_prod(_1515157, _1515159), tc_fun(tc_fun(tc_prod(_1515157, _1515159), tc_HOL_Obool), tc_HOL_Obool), _1515159), c_member(tc_prod(_1515157, _1515159)))), c_Product__Type_OPair(_1515157, _1515159)))), _1515161)), _1515163)))], (23459 ^ _779999) ^ [_1217858, _1217860, _1217862, _1217864, _1217866, _1217868] : [-(hAPP(c_Set_Ovimage(_1217858, _1217860, _1217862), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1217864, tc_fun(_1217860, tc_HOL_Obool)), _1217866), _1217868)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1217864, tc_fun(_1217858, tc_HOL_Obool)), _1217866), hAPP(hAPP(c_COMBB(tc_fun(_1217860, tc_HOL_Obool), tc_fun(_1217858, tc_HOL_Obool), _1217864), c_Set_Ovimage(_1217858, _1217860, _1217862)), _1217868)))], (35043 ^ _779999) ^ [_1434570, _1434572] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434570), hAPP(c_Int_Onumber__class_Onumber__of(_1434570), c_Int_OMin)), _1434572) = hAPP(c_Groups_Ouminus__class_Ouminus(_1434570), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434570), c_Groups_Oone__class_Oone(_1434570)), _1434572))), class_Fields_Ofield__inverse__zero(_1434570), class_Int_Onumber__ring(_1434570)], (50470 ^ _779999) ^ [_1799872, _1799874, _1799876, _1799878, _1799880] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799872), tc_List_Olist(_1799872))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799872), tc_List_Olist(_1799872)), _1799874), _1799876)), c_List_Olexord(_1799872, _1799878))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799872), tc_List_Olist(_1799872))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799872), tc_List_Olist(_1799872)), _1799876), _1799880)), c_List_Olexord(_1799872, _1799878))), c_Relation_Otrans(_1799872, _1799878), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799872), tc_List_Olist(_1799872))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799872), tc_List_Olist(_1799872)), _1799874), _1799880)), c_List_Olexord(_1799872, _1799878))))], (26252 ^ _779999) ^ [_1272085, _1272087] : [class_Groups_Olinordered__ab__group__add(_1272085), 26255 ^ _779999 : [(26262 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272085), c_Groups_Ozero__class_Ozero(_1272085)), _1272087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272085), hAPP(c_Groups_Ouminus__class_Ouminus(_1272085), _1272087)), _1272087)))], (26256 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272085), hAPP(c_Groups_Ouminus__class_Ouminus(_1272085), _1272087)), _1272087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272085), c_Groups_Ozero__class_Ozero(_1272085)), _1272087)))]]], (36102 ^ _779999) ^ [_1459706, _1459708, _1459710] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459706, _1459708), _1459710)), -(c_Divides_Odivmod__nat(_1459706, _1459708) = _1459710)], (29891 ^ _779999) ^ [_1340404, _1340406, _1340408, _1340410, _1340412] : [class_Groups_Ocomm__monoid__mult(_1340404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340406), _1340408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1340406, tc_HOL_Obool)), _1340410), _1340408)), 29905 ^ _779999 : [(29908 ^ _779999) ^ [] : [hAPP(_1340412, 29904 ^ [_1340404, _1340406, _1340408, _1340410, _1340412]) = c_Groups_Oone__class_Oone(_1340404)], (29906 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340406), 29904 ^ [_1340404, _1340406, _1340408, _1340410, _1340412]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340406, tc_HOL_Obool)), _1340408), _1340410))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340406, _1340404), _1340412), _1340410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340406, _1340404), _1340412), _1340408))], (22139 ^ _779999) ^ [_1189425] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1189425)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1189425), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1189425), c_Orderings_Otop__class_Otop(tc_fun(_1189425, tc_HOL_Obool)))))], (20864 ^ _779999) ^ [_1158781, _1158783] : [class_Rings_Olinordered__idom(_1158781), -(hAPP(c_Groups_Oabs__class_Oabs(_1158781), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1158781), _1158783)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1158781), _1158783))], (41496 ^ _779999) ^ [_1592026, _1592028, _1592030] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1592026), _1592028)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1592026, tc_HOL_Obool)), _1592030), _1592028) = hAPP(hAPP(c_Finite__Set_Ofold(_1592026, tc_fun(_1592026, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1592026, tc_HOL_Obool), tc_fun(tc_fun(_1592026, tc_HOL_Obool), tc_fun(_1592026, tc_HOL_Obool)), _1592026), hAPP(c_COMBC(tc_fun(_1592026, tc_HOL_Obool), tc_fun(_1592026, tc_HOL_Obool), tc_fun(_1592026, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1592026, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1592026, tc_fun(_1592026, tc_HOL_Obool), tc_fun(_1592026, tc_HOL_Obool)), c_Set_Oinsert(_1592026)), c_Orderings_Obot__class_Obot(tc_fun(_1592026, tc_HOL_Obool))))), _1592030), _1592028))], (39569 ^ _779999) ^ [_1545687, _1545689, _1545691, _1545693, _1545695] : [class_Groups_Ocomm__monoid__mult(_1545687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545689), _1545691)), c_Fun_Oinj__on(_1545689, _1545689, _1545693, _1545691), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1545689, _1545687), _1545695), hAPP(c_Set_Oimage(_1545689, _1545689, _1545693), _1545691)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1545689, _1545687), hAPP(c_Fun_Ocomp(_1545689, _1545687, _1545689, _1545695), _1545693)), _1545691))], (44698 ^ _779999) ^ [_1671826, _1671828, _1671830] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671826), tc_List_Olist(_1671826))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671826), tc_List_Olist(_1671826)), _1671828), c_List_Olist_ONil(_1671826))), c_List_Olistrel1(_1671826, _1671830)))], (39611 ^ _779999) ^ [_1546636, _1546638, _1546640, _1546642, _1546644, _1546646] : [c_Finite__Set_Ofolding(_1546636, _1546638, _1546640, _1546642), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546636), _1546644)), hBOOL(hAPP(hAPP(c_member(_1546636), _1546646), _1546644)), -(hAPP(_1546642, _1546644) = hAPP(c_Fun_Ocomp(_1546638, _1546638, _1546638, hAPP(_1546642, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1546636, tc_HOL_Obool)), _1546644), hAPP(hAPP(c_Set_Oinsert(_1546636), _1546646), c_Orderings_Obot__class_Obot(tc_fun(_1546636, tc_HOL_Obool)))))), hAPP(_1546640, _1546646)))], (47220 ^ _779999) ^ [_1728511, _1728513] : [c_List_Oremdups(_1728511, _1728513) = _1728513, -(hBOOL(hAPP(c_List_Odistinct(_1728511), _1728513)))], (52262 ^ _779999) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (40029 ^ _779999) ^ [_1556725, _1556727, _1556729] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1556725, _1556727, _1556729)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1556729)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41466 ^ _779999) ^ [_1591459, _1591461, _1591463] : [class_Orderings_Olinorder(_1591459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591459), _1591461)), -(c_Big__Operators_Olinorder__class_OMax(_1591459, hAPP(hAPP(c_Set_Oinsert(_1591459), _1591463), _1591461)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591459, _1591459, c_Orderings_Oord__class_Omax(_1591459)), _1591463), _1591461))], (32639 ^ _779999) ^ [_1392298] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392298)))), -(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), _1392298)) = 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), _1392298))))], (26841 ^ _779999) ^ [_1283862, _1283864, _1283866, _1283868, _1283870] : [class_Groups_Ocomm__monoid__mult(_1283862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283864), _1283866)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283864), _1283868)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283862), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283864, _1283862), _1283870), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283864, tc_HOL_Obool)), _1283866), _1283868))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283864, _1283862), _1283870), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1283864, tc_HOL_Obool)), _1283866), _1283868))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283862), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283864, _1283862), _1283870), _1283866)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283864, _1283862), _1283870), _1283868)))], (15679 ^ _779999) ^ [_1062731, _1062733, _1062735, _1062737, _1062739] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1062731), 15682 ^ _779999 : [(15683 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062733), _1062737)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062735), _1062739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062733), _1062739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062735), _1062737)), -(_1062733 = _1062735), -(_1062737 = _1062739)], (15693 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062733), _1062737)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062735), _1062739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062733), _1062739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062731), _1062735), _1062737))), 15696 ^ _779999 : [(15699 ^ _779999) ^ [] : [_1062737 = _1062739], (15697 ^ _779999) ^ [] : [_1062733 = _1062735]]]]], (29344 ^ _779999) ^ [_1331313, _1331315] : [class_Divides_Osemiring__div(_1331313), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1331313), _1331315), c_Groups_Oone__class_Oone(_1331313)) = _1331315)], (21459 ^ _779999) ^ [_1170674, _1170676, _1170678] : [class_Lattices_Osemilattice__inf(_1170674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170674), _1170676)), hBOOL(hAPP(hAPP(c_member(_1170674), _1170678), _1170676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170674), hAPP(c_Finite__Set_Ofold1(_1170674, c_Lattices_Osemilattice__inf__class_Oinf(_1170674)), _1170676)), _1170678)))], (11851 ^ _779999) ^ [_988351, _988353, _988355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_988351, tc_HOL_Obool)), _988353), _988355)), hBOOL(hAPP(c_Finite__Set_Ofinite(_988351), _988355)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988351), _988353)))], (29172 ^ _779999) ^ [_1327892, _1327894, _1327896] : [class_Fields_Olinordered__field__inverse__zero(_1327892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327892), c_Groups_Ozero__class_Ozero(_1327892)), _1327894)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327892), hAPP(c_Groups_Oabs__class_Oabs(_1327892), _1327896)), _1327894) = hAPP(c_Groups_Oabs__class_Oabs(_1327892), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327892), _1327896), _1327894)))], (46416 ^ _779999) ^ [_1710754, _1710756, _1710758] : [c_Fun_Oinj__on(tc_List_Olist(_1710754), tc_List_Olist(_1710756), hAPP(c_List_Omap(_1710754, _1710756), _1710758), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1710754), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1710754, _1710756, _1710758, c_Orderings_Otop__class_Otop(tc_fun(_1710754, tc_HOL_Obool))))], (22884 ^ _779999) ^ [_1205437, _1205439, _1205441, _1205443, _1205445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205437, tc_HOL_Obool)), _1205439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205441, tc_fun(_1205437, tc_HOL_Obool)), _1205443), _1205445)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205441, tc_fun(_1205437, tc_HOL_Obool)), _1205443), hAPP(hAPP(c_COMBB(tc_fun(_1205437, tc_HOL_Obool), tc_fun(_1205437, tc_HOL_Obool), _1205441), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205437, tc_HOL_Obool)), _1205439)), _1205445)))], (15089 ^ _779999) ^ [_1050916, _1050918, _1050920, _1050922, _1050924, _1050926] : [-(hBOOL(hAPP(hAPP(c_member(_1050916), _1050918), c_SetInterval_Oord_OatLeastLessThan(_1050916, _1050920, _1050922, _1050924, _1050926)))), hBOOL(hAPP(hAPP(_1050920, _1050924), _1050918)), hBOOL(hAPP(hAPP(_1050922, _1050918), _1050926))], (24598 ^ _779999) ^ [_1240564, _1240566, _1240568, _1240570] : [class_Orderings_Olinorder(_1240564), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240564), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240564), _1240566), _1240568)), _1240570) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240564), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240564), _1240566), _1240570)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240564), _1240568), _1240570)))], (15403 ^ _779999) ^ [_1056899, _1056901] : [class_Int_Oring__char__0(_1056899), hBOOL(hAPP(hAPP(c_member(_1056899), _1056901), c_Int_Oring__1__class_OInts(_1056899))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056899), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056899), c_Groups_Oone__class_Oone(_1056899)), _1056901)), _1056901) = c_Groups_Ozero__class_Ozero(_1056899)], (18671 ^ _779999) ^ [_1120446, _1120448, _1120450, _1120452, _1120454, _1120456, _1120458] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1120446, _1120448, _1120450, _1120452, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1120446, tc_HOL_Obool)), _1120454), hAPP(hAPP(c_Set_Oinsert(_1120446), _1120456), c_Orderings_Obot__class_Obot(tc_fun(_1120446, tc_HOL_Obool))))), _1120458)), hBOOL(hAPP(hAPP(c_member(_1120446), _1120456), _1120454)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1120446, _1120448, _1120450, _1120452, _1120454), hAPP(hAPP(_1120450, _1120456), _1120458))))], (10187 ^ _779999) ^ [_955518, _955520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955520), hAPP(c_Nat_OSuc, _955518))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955518), _955520))], (45008 ^ _779999) ^ [_1679358, _1679360, _1679362, _1679364, _1679366] : [hAPP(hAPP(c_List_Oappend(_1679358), _1679360), _1679362) = hAPP(hAPP(c_List_Oappend(_1679358), _1679364), _1679366), 45014 ^ _779999 : [(45017 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1679358), 45011 ^ [_1679358, _1679360, _1679362, _1679364, _1679366]), _1679362) = _1679366)], (45015 ^ _779999) ^ [] : [-(_1679360 = hAPP(hAPP(c_List_Oappend(_1679358), _1679364), 45011 ^ [_1679358, _1679360, _1679362, _1679364, _1679366]))]], 45018 ^ _779999 : [(45021 ^ _779999) ^ [] : [-(_1679362 = hAPP(hAPP(c_List_Oappend(_1679358), 45011 ^ [_1679358, _1679360, _1679362, _1679364, _1679366]), _1679366))], (45019 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1679358), _1679360), 45011 ^ [_1679358, _1679360, _1679362, _1679364, _1679366]) = _1679364)]]], (47713 ^ _779999) ^ [_1740769] : [-(c_List_Oupt(_1740769, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (31622 ^ _779999) ^ [_1373048, _1373050, _1373052, _1373054, _1373056, _1373058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1373048, _1373050), tc_HOL_Obool)), _1373052), _1373054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373048, tc_HOL_Obool)), _1373056), _1373058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373050, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1373048, _1373050, _1373052), _1373056)), hAPP(c_Relation_OImage(_1373048, _1373050, _1373054), _1373058))))], (16401 ^ _779999) ^ [_1076267, _1076269, _1076271] : [class_Rings_Olinordered__semiring__strict(_1076267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076267), c_Groups_Ozero__class_Ozero(_1076267)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076267), _1076269), _1076271))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076267), c_Groups_Ozero__class_Ozero(_1076267)), _1076271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076267), c_Groups_Ozero__class_Ozero(_1076267)), _1076269)))], (46061 ^ _779999) ^ [_1702580, _1702582, _1702584] : [-(_1702580 = c_List_Olist_ONil(_1702582)), -(c_List_Olast(_1702582, hAPP(hAPP(c_List_Oappend(_1702582), _1702584), _1702580)) = c_List_Olast(_1702582, _1702580))], (2526 ^ _779999) ^ [_817254, _817256, _817258, _817260] : [-(c_Nitpick_Onat__gcd(_817260, _817256) = c_Nitpick_Onat__gcd(_817258, _817254)), _817260 = _817258, _817256 = _817254], (40347 ^ _779999) ^ [_1564987, _1564989] : [-(c_Transitive__Closure_Ortrancl(_1564987, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564987, _1564987), tc_HOL_Obool)), _1564989), c_Relation_OId(_1564987))) = c_Transitive__Closure_Ortrancl(_1564987, _1564989))], (49832 ^ _779999) ^ [_1785581, _1785583, _1785585, _1785587] : [-(c_Predicate_Oconversep(_1785581, _1785583, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785581, tc_fun(_1785583, tc_HOL_Obool))), _1785585), _1785587)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785583, tc_fun(_1785581, tc_HOL_Obool))), c_Predicate_Oconversep(_1785581, _1785583, _1785585)), c_Predicate_Oconversep(_1785581, _1785583, _1785587)))], (22671 ^ _779999) ^ [] : [-(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))], (38935 ^ _779999) ^ [_1531230, _1531232] : [c_Wellfounded_OwfP(_1531230, _1531232), -(c_Wellfounded_Owf(_1531230, hAPP(c_Set_OCollect(tc_prod(_1531230, _1531230)), hAPP(c_Product__Type_Oprod_Oprod__case(_1531230, _1531230, tc_HOL_Obool), _1531232))))], (24624 ^ _779999) ^ [_1241131] : [class_Orderings_Olinorder(_1241131), -(c_Finite__Set_Ofun__left__comm__idem(_1241131, _1241131, c_Orderings_Oord__class_Omax(_1241131)))], (24020 ^ _779999) ^ [_1228791, _1228793, _1228795] : [class_Orderings_Olinorder(_1228791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1228791), _1228793)), -(_1228793 = c_Orderings_Obot__class_Obot(tc_fun(_1228791, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1228791, c_Orderings_Oord__class_Omin(_1228791), hAPP(hAPP(c_Set_Oinsert(_1228791), _1228795), _1228793)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1228791), _1228795), c_Big__Operators_Olattice_OInf__fin(_1228791, c_Orderings_Oord__class_Omin(_1228791), _1228793)))], (12177 ^ _779999) ^ [_994925, _994927, _994929] : [class_Lattices_Olattice(_994925), hBOOL(hAPP(c_Finite__Set_Ofinite(_994925), _994927)), hBOOL(hAPP(hAPP(c_member(_994925), _994929), _994927)), 12188 ^ _779999 : [(12195 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_994925, tc_HOL_Obool)), _994927), hAPP(hAPP(c_Set_Oinsert(_994925), _994929), c_Orderings_Obot__class_Obot(tc_fun(_994925, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_994925, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_994925, _994927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994925), _994929), c_Big__Operators_Olattice__class_OInf__fin(_994925, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_994925, tc_HOL_Obool)), _994927), hAPP(hAPP(c_Set_Oinsert(_994925), _994929), c_Orderings_Obot__class_Obot(tc_fun(_994925, tc_HOL_Obool)))))))], (12189 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_994925, tc_HOL_Obool)), _994927), hAPP(hAPP(c_Set_Oinsert(_994925), _994929), c_Orderings_Obot__class_Obot(tc_fun(_994925, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_994925, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_994925, _994927) = _994929)]]], (52028 ^ _779999) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (35167 ^ _779999) ^ [_1439017, _1439019, _1439021, _1439023] : [hAPP(hAPP(c_COMBC(_1439017, tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_fun(_1439019, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439019, tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_fun(_1439019, tc_HOL_Obool)), _1439017), c_COMBC(_1439019, tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439019, tc_prod(_1439017, _1439019)), tc_fun(_1439019, tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), _1439017), hAPP(c_COMBB(tc_prod(_1439017, _1439019), tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool), _1439019), c_member(tc_prod(_1439017, _1439019)))), c_Product__Type_OPair(_1439017, _1439019)))), _1439021) = hAPP(hAPP(c_COMBC(_1439017, tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_fun(_1439019, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439019, tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_fun(_1439019, tc_HOL_Obool)), _1439017), c_COMBC(_1439019, tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439019, tc_prod(_1439017, _1439019)), tc_fun(_1439019, tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool)), _1439017), hAPP(c_COMBB(tc_prod(_1439017, _1439019), tc_fun(tc_fun(tc_prod(_1439017, _1439019), tc_HOL_Obool), tc_HOL_Obool), _1439019), c_member(tc_prod(_1439017, _1439019)))), c_Product__Type_OPair(_1439017, _1439019)))), _1439023), -(_1439021 = _1439023)], (10948 ^ _779999) ^ [_969219, _969221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969219), _969221)), _969219 = _969221], (10922 ^ _779999) ^ [_968907, _968909] : [10923 ^ _779999 : [(10926 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968909), _968907))], (10924 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968907), _968909))]], _968907 = _968909], (31959 ^ _779999) ^ [_1379446, _1379448, _1379450, _1379452] : [class_Int_Onumber__ring(_1379446), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379446), hAPP(c_Int_Onumber__class_Onumber__of(_1379446), _1379448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379446), hAPP(c_Int_Onumber__class_Onumber__of(_1379446), _1379450)), _1379452)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379446), hAPP(c_Int_Onumber__class_Onumber__of(_1379446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1379448), _1379450))), _1379452))], (41111 ^ _779999) ^ [_1583086, _1583088, _1583090] : [41114 ^ _779999 : [(41120 ^ _779999) ^ [] : [41113 ^ [_1583086, _1583088, _1583090] = 41116 ^ [_1583086, _1583088, _1583090]], (41118 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583086, _1583088)), hAPP(hAPP(c_Product__Type_OPair(_1583086, _1583088), 41112 ^ [_1583086, _1583088, _1583090]), 41116 ^ [_1583086, _1583088, _1583090])), _1583090)))], (41115 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583086, _1583088)), hAPP(hAPP(c_Product__Type_OPair(_1583086, _1583088), 41112 ^ [_1583086, _1583088, _1583090]), 41113 ^ [_1583086, _1583088, _1583090])), _1583090)))]], -(c_Relation_Osingle__valued(_1583086, _1583088, _1583090))], (31154 ^ _779999) ^ [_1363861, _1363863] : [class_Rings_Olinordered__idom(_1363861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363861), _1363863), c_Groups_Ozero__class_Ozero(_1363861))), -(c_Groups_Osgn__class_Osgn(_1363861, _1363863) = hAPP(c_Groups_Ouminus__class_Ouminus(_1363861), c_Groups_Oone__class_Oone(_1363861)))], (40435 ^ _779999) ^ [_1567058, _1567060, _1567062, _1567064] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567058, _1567058)), hAPP(hAPP(c_Product__Type_OPair(_1567058, _1567058), _1567060), _1567062)), c_Transitive__Closure_Ortrancl(_1567058, _1567064)))), 40436 ^ _779999 : [(40439 ^ _779999) ^ [] : [-(_1567060 = _1567062), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567058, _1567058)), hAPP(hAPP(c_Product__Type_OPair(_1567058, _1567058), _1567060), _1567062)), c_Transitive__Closure_Otrancl(_1567058, _1567064)))], (40437 ^ _779999) ^ [] : [_1567060 = _1567062]]], (17906 ^ _779999) ^ [_1105859] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1105859)) = 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), _1105859)))], (20473 ^ _779999) ^ [_1152408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152408)), 20477 ^ _779999 : [(20480 ^ _779999) ^ [] : [-(_1152408 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20476 ^ [_1152408]))], (20478 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20476 ^ [_1152408])))]]], (51190 ^ _779999) ^ [_1815272, _1815274] : [c_Equiv__Relations_Oequivp(_1815272, _1815274), -(c_Equiv__Relations_Opart__equivp(_1815272, _1815274))], (28064 ^ _779999) ^ [_1307546, _1307548, _1307550] : [class_Rings_Oring__1(_1307546), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307546), hAPP(c_Groups_Ouminus__class_Ouminus(_1307546), _1307548)), _1307550) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307546), hAPP(hAPP(c_Power_Opower__class_Opower(_1307546), hAPP(c_Groups_Ouminus__class_Ouminus(_1307546), c_Groups_Oone__class_Oone(_1307546))), _1307550)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307546), _1307548), _1307550)))], (35143 ^ _779999) ^ [_1436441, _1436443, _1436445, _1436447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1436441, tc_fun(_1436443, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1436441, tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_fun(_1436443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1436443, tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_fun(_1436443, tc_HOL_Obool)), _1436441), c_COMBC(_1436443, tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1436443, tc_prod(_1436441, _1436443)), tc_fun(_1436443, tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), _1436441), hAPP(c_COMBB(tc_prod(_1436441, _1436443), tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool), _1436443), c_member(tc_prod(_1436441, _1436443)))), c_Product__Type_OPair(_1436441, _1436443)))), _1436445)), hAPP(hAPP(c_COMBC(_1436441, tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_fun(_1436443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1436443, tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_fun(_1436443, tc_HOL_Obool)), _1436441), c_COMBC(_1436443, tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1436443, tc_prod(_1436441, _1436443)), tc_fun(_1436443, tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool)), _1436441), hAPP(c_COMBB(tc_prod(_1436441, _1436443), tc_fun(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool), tc_HOL_Obool), _1436443), c_member(tc_prod(_1436441, _1436443)))), c_Product__Type_OPair(_1436441, _1436443)))), _1436447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1436441, _1436443), tc_HOL_Obool)), _1436445), _1436447)))], (49710 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46422 ^ _779999) ^ [_1710881, _1710883, _1710885] : [c_Fun_Oinj__on(_1710881, _1710883, _1710885, c_Orderings_Otop__class_Otop(tc_fun(_1710881, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1710881), tc_List_Olist(_1710883), hAPP(c_List_Omap(_1710881, _1710883), _1710885), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1710881), tc_HOL_Obool))))], (40619 ^ _779999) ^ [_1571274, _1571276] : [-(c_Random_Olog(_1571274, _1571276) = 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(_1571274, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1571276), _1571274)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1571274), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571276), _1571274)))], (47210 ^ _779999) ^ [_1728333, _1728335] : [-(hAPP(c_List_Oset(_1728333), c_List_Oremdups(_1728333, _1728335)) = hAPP(c_List_Oset(_1728333), _1728335))], (42502 ^ _779999) ^ [_1616694, _1616696, _1616698] : [c_Equiv__Relations_Oequiv(_1616694, _1616696, _1616698), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616694, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1616694), _1616696), _1616698)) = _1616696)], (8096 ^ _779999) ^ [_916778, _916780, _916782, _916784] : [hBOOL(hAPP(hAPP(c_member(_916778), _916780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916778, tc_HOL_Obool)), _916782), _916784))), -(hBOOL(hAPP(hAPP(c_member(_916778), _916780), _916782)))], (49357 ^ _779999) ^ [_1775606, _1775608, _1775610, _1775612] : [49358 ^ _779999 : [(49361 ^ _779999) ^ [] : [c_List_Olist__ex(_1775606, _1775608, _1775612)], (49359 ^ _779999) ^ [] : [hBOOL(hAPP(_1775608, _1775610))]], -(c_List_Olist__ex(_1775606, _1775608, hAPP(hAPP(c_List_Olist_OCons(_1775606), _1775610), _1775612)))], (38067 ^ _779999) ^ [_1506520, _1506522, _1506524] : [c_Wellfounded_Owf(_1506520, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506520, _1506520), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506520, _1506520), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1506520, _1506520, _1506520), _1506522), _1506522)), hAPP(hAPP(c_Relation_Orel__comp(_1506520, _1506520, _1506520), _1506524), _1506522))), _1506524)), -(c_Wellfounded_Owf(_1506520, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506520, _1506520), tc_HOL_Obool)), _1506522), _1506524)))], (48991 ^ _779999) ^ [_1766383, _1766385, _1766387, _1766389] : [-(_1766383 = _1766385), -(hAPP(c_List_OremoveAll(_1766387, _1766383), hAPP(hAPP(c_List_Olist_OCons(_1766387), _1766385), _1766389)) = hAPP(hAPP(c_List_Olist_OCons(_1766387), _1766385), hAPP(c_List_OremoveAll(_1766387, _1766383), _1766389)))], (5126 ^ _779999) ^ [_858392, _858394, _858396, _858398] : [-(c_Product__Type_Osnd(_858398, _858394) = c_Product__Type_Osnd(_858396, _858392)), _858398 = _858396, _858394 = _858392], (21030 ^ _779999) ^ [_1162142] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1162142)) = hAPP(c_Nat_OSuc, _1162142))], (20554 ^ _779999) ^ [_1153493, _1153495] : [c_Nat__Transfer_Ois__nat(_1153493), c_Nat__Transfer_Ois__nat(_1153495), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1153493), _1153495)))], (23117 ^ _779999) ^ [_1211559, _1211561, _1211563, _1211565, _1211567] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1211559, _1211561, _1211563), _1211565), _1211567)), -(hBOOL(hAPP(_1211565, hAPP(_1211563, _1211567))))], (42616 ^ _779999) ^ [_1619232, _1619234, _1619236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619232, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619232, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1619232, tc_HOL_Obool), tc_HOL_Obool)), _1619234), _1619236))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619232, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619232, tc_HOL_Obool), _1619234)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619232, tc_HOL_Obool), _1619236)))))], (51382 ^ _779999) ^ [_1819434, _1819436, _1819438, _1819440, _1819442] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1819434, _1819436, _1819438, _1819440), _1819442) = c_Hilbert__Choice_OEps(_1819434, hAPP(hAPP(c_COMBS(_1819434, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1819434), c_fconj), hAPP(hAPP(c_COMBC(_1819434, tc_fun(_1819434, tc_HOL_Obool), tc_HOL_Obool), c_member(_1819434)), _1819438))), hAPP(hAPP(c_COMBC(_1819434, _1819436, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1819436, tc_fun(_1819436, tc_HOL_Obool), _1819434), c_fequal), _1819440)), _1819442))))], (46726 ^ _779999) ^ [_1717186, _1717188] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1717186), _1717188) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1717186)), hAPP(c_Code__Numeral_Onat__of, _1717188))))], (2468 ^ _779999) ^ [_816403, _816405] : [_816405 = _816403, -(c_Nat_Osemiring__1__class_ONats(_816405) = c_Nat_Osemiring__1__class_ONats(_816403))], (45652 ^ _779999) ^ [_1694277, _1694279, _1694281] : [hAPP(c_List_Orotate(_1694277, _1694279), _1694281) = c_List_Olist_ONil(_1694277), -(_1694281 = c_List_Olist_ONil(_1694277))], (47812 ^ _779999) ^ [_1742961, _1742963, _1742965, _1742967, _1742969] : [class_Orderings_Olinorder(_1742961), hBOOL(hAPP(hAPP(c_member(_1742963), _1742965), hAPP(c_List_Oset(_1742963), _1742967))), c_List_Olinorder__class_Osorted(_1742961, hAPP(hAPP(c_List_Omap(_1742963, _1742961), _1742969), _1742967)), hAPP(c_List_Ohd(_1742963), hAPP(c_List_Ofilter(_1742963, hAPP(hAPP(c_COMBB(_1742961, tc_HOL_Obool, _1742963), hAPP(c_fequal, hAPP(_1742969, _1742965))), _1742969)), _1742967)) = _1742965, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742963, _1742961, _1742969), _1742965), c_List_Oremove1(_1742963, _1742965, _1742967)) = _1742967)], (22922 ^ _779999) ^ [_1206698, _1206700, _1206702, _1206704, _1206706, _1206708] : [hBOOL(hAPP(hAPP(c_member(_1206698), _1206700), _1206702)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206698, tc_fun(_1206704, tc_HOL_Obool)), _1206702), hAPP(hAPP(c_COMBB(tc_fun(_1206704, tc_HOL_Obool), tc_fun(_1206704, tc_HOL_Obool), _1206698), hAPP(c_Set_Oinsert(_1206704), _1206706)), _1206708)) = hAPP(hAPP(c_Set_Oinsert(_1206704), _1206706), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206698, tc_fun(_1206704, tc_HOL_Obool)), _1206702), _1206708)))], (28120 ^ _779999) ^ [_1308630, _1308632, _1308634, _1308636] : [class_Rings_Olinordered__semidom(_1308630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1308632), _1308634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308630), c_Groups_Ozero__class_Ozero(_1308630)), _1308636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308630), _1308636), c_Groups_Oone__class_Oone(_1308630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308630), hAPP(hAPP(c_Power_Opower__class_Opower(_1308630), _1308636), _1308634)), hAPP(hAPP(c_Power_Opower__class_Opower(_1308630), _1308636), _1308632))))], (14736 ^ _779999) ^ [_1044666, _1044668, _1044670] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044666), _1044668) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044670), _1044668), -(_1044666 = _1044670)], (27402 ^ _779999) ^ [_1295520] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1295520)), _1295520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25530 ^ _779999) ^ [_1258932, _1258934] : [class_Groups_Olinordered__ab__group__add(_1258932), 25533 ^ _779999 : [(25540 ^ _779999) ^ [] : [_1258934 = c_Groups_Ozero__class_Ozero(_1258932), -(_1258934 = hAPP(c_Groups_Ouminus__class_Ouminus(_1258932), _1258934))], (25534 ^ _779999) ^ [] : [_1258934 = hAPP(c_Groups_Ouminus__class_Ouminus(_1258932), _1258934), -(_1258934 = c_Groups_Ozero__class_Ozero(_1258932))]]], (15953 ^ _779999) ^ [_1068037, _1068039] : [class_Rings_Olinordered__ring(_1068037), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068037), c_Groups_Ozero__class_Ozero(_1068037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068037), _1068039), _1068039))))], (31757 ^ _779999) ^ [_1375512, _1375514] : [class_Int_Onumber__ring(_1375512), 31760 ^ _779999 : [(31767 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375514)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1375512), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375514)) = hAPP(c_Int_Onumber__class_Onumber__of(_1375512), _1375514))], (31761 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375514))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1375512), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375514)) = c_Groups_Ozero__class_Ozero(_1375512))]]], (30254 ^ _779999) ^ [_1346897, _1346899] : [class_Rings_Olinordered__idom(_1346897), 30257 ^ _779999 : [(30264 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346897), hAPP(c_Int_Oring__1__class_Oof__int(_1346897), _1346899)), c_Groups_Ozero__class_Ozero(_1346897))))], (30258 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346897), hAPP(c_Int_Oring__1__class_Oof__int(_1346897), _1346899)), c_Groups_Ozero__class_Ozero(_1346897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26805 ^ _779999) ^ [_1282959, _1282961] : [class_Groups_Oordered__ab__group__add(_1282959), -(hAPP(c_Set_Oimage(_1282959, _1282959, c_Groups_Ouminus__class_Ouminus(_1282959)), hAPP(c_SetInterval_Oord__class_OatLeast(_1282959), _1282961)) = hAPP(c_SetInterval_Oord__class_OatMost(_1282959), hAPP(c_Groups_Ouminus__class_Ouminus(_1282959), _1282961)))], (49136 ^ _779999) ^ [_1770301, _1770303, _1770305, _1770307, _1770309] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770301)), _1770303) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770305)), _1770307), 49142 ^ _779999 : [(49145 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1770309, hAPP(hAPP(c_List_Onth(_1770301), _1770303), 49141 ^ [_1770301, _1770303, _1770305, _1770307, _1770309])), hAPP(hAPP(c_List_Onth(_1770305), _1770307), 49141 ^ [_1770301, _1770303, _1770305, _1770307, _1770309])))], (49143 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49141 ^ [_1770301, _1770303, _1770305, _1770307, _1770309]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770301)), _1770303))))]], -(c_List_Olist__all2(_1770301, _1770305, _1770309, _1770303, _1770307))], (6811 ^ _779999) ^ [_891666, _891668] : [-(hBOOL(hAPP(hAPP(c_member(_891666), 6812 ^ [_891666, _891668]), _891668))), -(_891668 = c_Orderings_Obot__class_Obot(tc_fun(_891666, tc_HOL_Obool)))], (50157 ^ _779999) ^ [_1792299, _1792301, _1792303, _1792305] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1792299, _1792301), c_Lazy__Sequence_Olazy__sequence_OInsert(_1792299, _1792303, _1792305)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1792301, _1792303)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1792299, _1792301), _1792305))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44574 ^ _779999) ^ [_1669780, _1669782, _1669784] : [hAPP(hAPP(c_List_Otake(_1669780), _1669782), _1669784) = c_List_Olist_ONil(_1669780), -(_1669782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1669784 = c_List_Olist_ONil(_1669780))], (6337 ^ _779999) ^ [_881931, _881933, _881935] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881931, tc_HOL_Obool)), _881933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881931, tc_HOL_Obool)), _881933), _881935)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881931, tc_HOL_Obool)), _881933), _881935))], (15567 ^ _779999) ^ [_1060767, _1060769] : [class_Lattices_Oab__semigroup__idem__mult(_1060767), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060767), _1060769), _1060769) = _1060769)], (46916 ^ _779999) ^ [_1721871, _1721873, _1721875, _1721877, _1721879] : [-(c_List_Olist__all2(_1721871, _1721873, _1721875, _1721877, _1721879)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721871)), _1721877) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721873)), _1721879), 46922 ^ _779999 : [(46925 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1721871, _1721873, tc_HOL_Obool), _1721875), 46921 ^ [_1721871, _1721873, _1721875, _1721877, _1721879]))], (46923 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1721871, _1721873)), 46921 ^ [_1721871, _1721873, _1721875, _1721877, _1721879]), hAPP(c_List_Oset(tc_prod(_1721871, _1721873)), hAPP(hAPP(c_List_Ozip(_1721871, _1721873), _1721877), _1721879)))))]]], (50155 ^ _779999) ^ [_1792254, _1792256, _1792258, _1792260] : [-(c_Lazy__Sequence_Oappend(_1792254, c_Lazy__Sequence_Olazy__sequence_OInsert(_1792254, _1792256, _1792258), _1792260) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1792254, _1792256, c_Lazy__Sequence_Oappend(_1792254, _1792258, _1792260)))], (51884 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (49149 ^ _779999) ^ [_1770659, _1770661] : [class_Orderings_Olinorder(_1770659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1770659), _1770661)), 49157 ^ _779999 : [(49160 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1770659, 49156 ^ [_1770659, _1770661]))], (49162 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1770659), 49156 ^ [_1770659, _1770661])))], (49164 ^ _779999) ^ [_1770985] : [-(_1770985 = 49156 ^ [_1770659, _1770661]), hAPP(c_List_Oset(_1770659), _1770985) = _1770661, c_List_Olinorder__class_Osorted(_1770659, _1770985), hBOOL(hAPP(c_List_Odistinct(_1770659), _1770985))], (49158 ^ _779999) ^ [] : [-(hAPP(c_List_Oset(_1770659), 49156 ^ [_1770659, _1770661]) = _1770661)]]], (19699 ^ _779999) ^ [_1139166, _1139168, _1139170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139166)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1139168), _1139170)), 19706 ^ _779999 : [(19707 ^ _779999) ^ [_1139356] : [19709 ^ _779999 : [(19715 ^ _779999) ^ [] : [-(_1139356 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19711 ^ [_1139166, _1139168, _1139170, _1139356]), 19708 ^ [_1139166, _1139168, _1139170, _1139356]))], (19713 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19711 ^ [_1139166, _1139168, _1139170, _1139356]), _1139170)))], (19710 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19708 ^ [_1139166, _1139168, _1139170, _1139356]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1139166))))]], -(_1139356 = _1139168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1139356), _1139166) = _1139168]]], (2268 ^ _779999) ^ [_813351, _813353, _813355, _813357] : [-(c_Int_Onat__aux(_813357, _813353) = c_Int_Onat__aux(_813355, _813351)), _813357 = _813355, _813353 = _813351], (47214 ^ _779999) ^ [_1728405, _1728407] : [hBOOL(hAPP(c_List_Odistinct(_1728405), _1728407)), -(c_List_Oremdups(_1728405, _1728407) = _1728407)], (21020 ^ _779999) ^ [_1161859, _1161861, _1161863, _1161865, _1161867] : [class_Groups_Oordered__ab__group__add__abs(_1161859), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161859), hAPP(c_Groups_Oabs__class_Oabs(_1161859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161859), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161859), _1161861), _1161863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161859), _1161865), _1161867)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161859), hAPP(c_Groups_Oabs__class_Oabs(_1161859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161859), _1161861), _1161865))), hAPP(c_Groups_Oabs__class_Oabs(_1161859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161859), _1161863), _1161867))))))], (21277 ^ _779999) ^ [_1167324] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167324)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1167324)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1167324), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (11831 ^ _779999) ^ [_987998, _988000] : [class_Finite__Set_Ofinite(_987998), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987998), _988000)))], (42047 ^ _779999) ^ [_1605758, _1605760, _1605762, _1605764, _1605766] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605758, tc_HOL_Obool)), _1605760), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605762, tc_fun(_1605758, tc_HOL_Obool)), _1605764), _1605766)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605762, tc_fun(_1605758, tc_HOL_Obool)), _1605764), hAPP(hAPP(c_COMBB(tc_fun(_1605758, tc_HOL_Obool), tc_fun(_1605758, tc_HOL_Obool), _1605762), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605758, tc_HOL_Obool)), _1605760)), _1605766)))], (35446 ^ _779999) ^ [_1447260, _1447262, _1447264, _1447266] : [_1447260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1447262), _1447264)), _1447266), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1447260, _1447262), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1447264), _1447266)))), 35453 ^ _779999 : [(35456 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447266), _1447262))], (35454 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447262)))]], 35461 ^ _779999 : [(35464 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447262), _1447266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1447266), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35462 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447262))]]], (42123 ^ _779999) ^ [_1607827, _1607829, _1607831, _1607833, _1607835] : [-(_1607827 = c_Orderings_Obot__class_Obot(tc_fun(_1607829, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607829, tc_fun(_1607831, tc_HOL_Obool)), _1607827), hAPP(hAPP(c_COMBB(tc_fun(_1607831, tc_HOL_Obool), tc_fun(_1607831, tc_HOL_Obool), _1607829), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607831, tc_HOL_Obool)), _1607833)), _1607835)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607831, tc_HOL_Obool)), _1607833), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607829, tc_fun(_1607831, tc_HOL_Obool)), _1607827), _1607835)))], (48665 ^ _779999) ^ [_1759491, _1759493, _1759495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759491)), c_List_OtakeWhile(_1759491, _1759493, _1759495))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759491)), _1759495))), hBOOL(hAPP(_1759493, hAPP(hAPP(c_List_Onth(_1759491), _1759495), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759491)), c_List_OtakeWhile(_1759491, _1759493, _1759495)))))], (45618 ^ _779999) ^ [_1693572, _1693574, _1693576] : [-(hAPP(c_List_Otl(_1693572), hAPP(hAPP(c_List_Odrop(_1693572), _1693574), _1693576)) = hAPP(hAPP(c_List_Odrop(_1693572), _1693574), hAPP(c_List_Otl(_1693572), _1693576)))], (40884 ^ _779999) ^ [_1577362, _1577364, _1577366] : [40886 ^ _779999 : [(40887 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577362), 40885 ^ [_1577362, _1577364, _1577366]), _1577364)))], (40892 ^ _779999) ^ [] : [40885 ^ [_1577362, _1577364, _1577366] = 40888 ^ [_1577362, _1577364, _1577366]], (40896 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577362, _1577362)), hAPP(hAPP(c_Product__Type_OPair(_1577362, _1577362), 40888 ^ [_1577362, _1577364, _1577366]), 40885 ^ [_1577362, _1577364, _1577366])), _1577366))], (40894 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577362, _1577362)), hAPP(hAPP(c_Product__Type_OPair(_1577362, _1577362), 40885 ^ [_1577362, _1577364, _1577366]), 40888 ^ [_1577362, _1577364, _1577366])), _1577366))], (40890 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577362), 40888 ^ [_1577362, _1577364, _1577366]), _1577364)))]], -(c_Relation_Ototal__on(_1577362, _1577364, _1577366))], (12625 ^ _779999) ^ [_1003352, _1003354, _1003356] : [class_Lattices_Olattice(_1003352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003352), _1003354)), -(_1003354 = c_Orderings_Obot__class_Obot(tc_fun(_1003352, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003352), _1003356)), -(_1003356 = c_Orderings_Obot__class_Obot(tc_fun(_1003352, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1003352, tc_HOL_Obool)), _1003354), _1003356) = c_Orderings_Obot__class_Obot(tc_fun(_1003352, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1003352, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003352, tc_HOL_Obool)), _1003354), _1003356)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1003352), c_Big__Operators_Olattice__class_OSup__fin(_1003352, _1003354)), c_Big__Operators_Olattice__class_OSup__fin(_1003352, _1003356)))], (21594 ^ _779999) ^ [_1173253, _1173255, _1173257] : [class_Lattices_Oab__semigroup__idem__mult(_1173253), hAPP(_1173255, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173253), 21599 ^ [_1173253, _1173255, _1173257]), 21600 ^ [_1173253, _1173255, _1173257])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173253), hAPP(_1173255, 21599 ^ [_1173253, _1173255, _1173257])), hAPP(_1173255, 21600 ^ [_1173253, _1173255, _1173257])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173253), _1173257)), -(_1173257 = c_Orderings_Obot__class_Obot(tc_fun(_1173253, tc_HOL_Obool))), -(hAPP(_1173255, hAPP(c_Finite__Set_Ofold1(_1173253, c_Groups_Otimes__class_Otimes(_1173253)), _1173257)) = hAPP(c_Finite__Set_Ofold1(_1173253, c_Groups_Otimes__class_Otimes(_1173253)), hAPP(c_Set_Oimage(_1173253, _1173253, _1173255), _1173257)))], (19139 ^ _779999) ^ [_1128866, _1128868, _1128870] : [class_Rings_Osemiring__1(_1128866), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1128866, _1128868, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1128870) = _1128870)], (40913 ^ _779999) ^ [_1578223, _1578225] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578223, _1578223), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1578225) = _1578225)], (21473 ^ _779999) ^ [_1170911, _1170913, _1170915] : [class_Lattices_Osemilattice__inf(_1170911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170911), _1170913)), -(_1170913 = c_Orderings_Obot__class_Obot(tc_fun(_1170911, tc_HOL_Obool))), 21484 ^ _779999 : [(21485 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170911), _1170915), hAPP(c_Finite__Set_Ofold1(_1170911, c_Lattices_Osemilattice__inf__class_Oinf(_1170911)), _1170913))), 21488 ^ _779999 : [(21489 ^ _779999) ^ [_1171204] : [hBOOL(hAPP(hAPP(c_member(_1170911), _1171204), _1170913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170911), _1170915), _1171204)))]]], (21495 ^ _779999) ^ [] : [21497 ^ _779999 : [(21500 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170911), _1170915), 21496 ^ [_1170911, _1170913, _1170915]))], (21498 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170911), 21496 ^ [_1170911, _1170913, _1170915]), _1170913)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170911), _1170915), hAPP(c_Finite__Set_Ofold1(_1170911, c_Lattices_Osemilattice__inf__class_Oinf(_1170911)), _1170913))))]]], (13077 ^ _779999) ^ [_1012646, _1012648, _1012650, _1012652] : [class_Groups_Ocancel__semigroup__add(_1012646), 13080 ^ _779999 : [(13087 ^ _779999) ^ [] : [_1012650 = _1012652, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012646), _1012648), _1012650) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012646), _1012648), _1012652))], (13081 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012646), _1012648), _1012650) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012646), _1012648), _1012652), -(_1012650 = _1012652)]]], (33855 ^ _779999) ^ [_1413357, _1413359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413357), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1413359)), 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)))), _1413357)) = 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), _1413359), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1413357))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15861 ^ _779999) ^ [_1065966, _1065968, _1065970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1065966), _1065968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065966), _1065970)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065968), _1065970))))], (51948 ^ _779999) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (43749 ^ _779999) ^ [_1649924, _1649926, _1649928] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649924, tc_HOL_Obool)), hAPP(c_List_Oset(_1649924), hAPP(hAPP(c_List_Otake(_1649924), _1649926), _1649928))), hAPP(c_List_Oset(_1649924), _1649928))))], (11048 ^ _779999) ^ [_971178, _971180, _971182, _971184] : [class_Lattices_Osemilattice__inf(_971178), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971178), _971180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971178), _971182), _971184)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971178), _971182), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971178), _971180), _971184)))], (45644 ^ _779999) ^ [_1694107] : [-(c_List_Orotate(_1694107, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1694107)))], (15472 ^ _779999) ^ [_1058361, _1058363] : [15474 ^ _779999 : [(15477 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058363), 15473 ^ [_1058361, _1058363]))], (15475 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 15473 ^ [_1058361, _1058363]), _1058361)))]], -(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)), _1058363), _1058361))], (26492 ^ _779999) ^ [_1276268, _1276270, _1276272] : [class_Rings_Olinordered__idom(_1276268), 26495 ^ _779999 : [(26504 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), hAPP(c_Groups_Oabs__class_Oabs(_1276268), _1276270)), _1276272))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), _1276270), _1276272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), hAPP(c_Groups_Ouminus__class_Ouminus(_1276268), _1276270)), _1276272))], (26496 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), hAPP(c_Groups_Oabs__class_Oabs(_1276268), _1276270)), _1276272)), 26499 ^ _779999 : [(26502 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), hAPP(c_Groups_Ouminus__class_Ouminus(_1276268), _1276270)), _1276272)))], (26500 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276268), _1276270), _1276272)))]]]]], (33113 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (13594 ^ _779999) ^ [_1022566, _1022568, _1022570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022566), _1022568)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022566), _1022570)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1022566, tc_HOL_Obool)), _1022568), _1022570) = c_Orderings_Obot__class_Obot(tc_fun(_1022566, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1022566), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022566, tc_HOL_Obool)), _1022568), _1022570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1022566), _1022568)), hAPP(c_Finite__Set_Ocard(_1022566), _1022570)))], (13419 ^ _779999) ^ [_1018938, _1018940, _1018942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018938), _1018940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018940), _1018942))))], (18727 ^ _779999) ^ [_1121647, _1121649, _1121651] : [hBOOL(hAPP(_1121647, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121649), _1121651)))), 18730 ^ _779999 : [(18737 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121649), _1121651)), -(hBOOL(hAPP(_1121647, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18731 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121651), _1121649)), -(hBOOL(hAPP(_1121647, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121649)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121651)))))]]], (50724 ^ _779999) ^ [_1806915, _1806917, _1806919, _1806921] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806915), _1806917)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1806915), _1806919)), -(_1806919 = c_Orderings_Obot__class_Obot(tc_fun(_1806915, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1806915, _1806921, _1806917, _1806919)), 50738 ^ _779999 : [(50741 ^ _779999) ^ [_1807260] : [hBOOL(hAPP(hAPP(c_member(_1806915), _1807260), _1806919)), hBOOL(hAPP(hAPP(_1806921, 50737 ^ [_1806915, _1806917, _1806919, _1806921]), _1807260))], (50739 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806915), 50737 ^ [_1806915, _1806917, _1806919, _1806921]), _1806917)))]]], (12988 ^ _779999) ^ [_1010851, _1010853, _1010855, _1010857, _1010859] : [c_Finite__Set_Ofolding__one__idem(_1010851, _1010853, _1010855), hAPP(_1010857, hAPP(hAPP(_1010853, 12993 ^ [_1010851, _1010853, _1010855, _1010857, _1010859]), 12994 ^ [_1010851, _1010853, _1010855, _1010857, _1010859])) = hAPP(hAPP(_1010853, hAPP(_1010857, 12993 ^ [_1010851, _1010853, _1010855, _1010857, _1010859])), hAPP(_1010857, 12994 ^ [_1010851, _1010853, _1010855, _1010857, _1010859])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010851), _1010859)), -(_1010859 = c_Orderings_Obot__class_Obot(tc_fun(_1010851, tc_HOL_Obool))), -(hAPP(_1010857, hAPP(_1010855, _1010859)) = hAPP(_1010855, hAPP(c_Set_Oimage(_1010851, _1010851, _1010857), _1010859)))], (21439 ^ _779999) ^ [_1170360, _1170362] : [class_Lattices_Olattice(_1170360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170360), _1170362)), -(c_Big__Operators_Olattice__class_OSup__fin(_1170360, _1170362) = hAPP(c_Finite__Set_Ofold1(_1170360, c_Lattices_Osemilattice__sup__class_Osup(_1170360)), _1170362))], (21978 ^ _779999) ^ [_1183877] : [-(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)))), _1183877)) = 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), _1183877), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (50549 ^ _779999) ^ [_1801820] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1801820, tc_HOL_Obool) = c_Set_OBex(_1801820))], (9818 ^ _779999) ^ [_947715, _947717, _947719, _947721, _947723, _947725, _947727] : [-(c_Nitpick_Ofold__graph_H(_947715, _947717, _947719, _947721, _947723, hAPP(hAPP(_947719, _947725), _947727))), 9819 ^ _779999 : [(9826 ^ _779999) ^ [_947944, _947946] : [hAPP(hAPP(_947719, _947725), _947727) = hAPP(hAPP(_947719, _947946), _947944), hBOOL(hAPP(hAPP(c_member(_947715), _947946), _947723)), c_Nitpick_Ofold__graph_H(_947715, _947717, _947719, _947721, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947715, tc_HOL_Obool)), _947723), hAPP(hAPP(c_Set_Oinsert(_947715), _947946), c_Orderings_Obot__class_Obot(tc_fun(_947715, tc_HOL_Obool)))), _947944)], (9820 ^ _779999) ^ [] : [_947723 = c_Orderings_Obot__class_Obot(tc_fun(_947715, tc_HOL_Obool)), hAPP(hAPP(_947719, _947725), _947727) = _947721]]], (42271 ^ _779999) ^ [_1611109, _1611111, _1611113, _1611115] : [hBOOL(hAPP(hAPP(c_member(_1611109), _1611111), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1611109, tc_HOL_Obool), _1611113))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1611109, tc_HOL_Obool)), _1611115), _1611113)), -(hBOOL(hAPP(hAPP(c_member(_1611109), _1611111), _1611115)))], (5078 ^ _779999) ^ [_857620, _857622] : [_857622 = _857620, -(c_DSequence_Osingle(_857622) = c_DSequence_Osingle(_857620))], (38408 ^ _779999) ^ [_1515514, _1515516, _1515518, _1515520] : [hBOOL(hAPP(hAPP(c_member(_1515514), _1515516), hAPP(c_Relation_ODomain(_1515514, _1515518), _1515520))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515514, _1515518)), hAPP(hAPP(c_Product__Type_OPair(_1515514, _1515518), _1515516), 38411 ^ [_1515514, _1515516, _1515518, _1515520])), _1515520)))], (39447 ^ _779999) ^ [_1542943, _1542945, _1542947, _1542949, _1542951] : [c_Fun_Oinj__on(_1542943, _1542945, _1542947, c_Orderings_Otop__class_Otop(tc_fun(_1542943, tc_HOL_Obool))), c_Fun_Oinj__on(_1542949, _1542943, _1542951, c_Orderings_Otop__class_Otop(tc_fun(_1542949, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1542949, _1542945, hAPP(c_Fun_Ocomp(_1542943, _1542945, _1542949, _1542947), _1542951), c_Orderings_Otop__class_Otop(tc_fun(_1542949, tc_HOL_Obool))))], (44432 ^ _779999) ^ [_1667150, _1667152, _1667154] : [-(hBOOL(hAPP(hAPP(c_member(_1667150), _1667152), hAPP(c_List_Oset(_1667150), _1667154)))), -(c_List_Oremove1(_1667150, _1667152, _1667154) = _1667154)], (23209 ^ _779999) ^ [_1213103, _1213105, _1213107, _1213109] : [class_Orderings_Olinorder(_1213103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213103), _1213105), _1213107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213103), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213103), _1213105), _1213109)), _1213107)))], (22054 ^ _779999) ^ [_1187129, _1187131, _1187133] : [class_Groups_Olinordered__ab__semigroup__add(_1187129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187129), _1187131)), -(_1187131 = c_Orderings_Obot__class_Obot(tc_fun(_1187129, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187129), _1187133), c_Big__Operators_Olinorder__class_OMax(_1187129, _1187131)) = c_Big__Operators_Olinorder__class_OMax(_1187129, hAPP(c_Set_OCollect(_1187129), hAPP(hAPP(c_COMBB(tc_fun(_1187129, tc_HOL_Obool), tc_HOL_Obool, _1187129), c_HOL_OEx(_1187129)), hAPP(hAPP(c_COMBC(_1187129, tc_fun(_1187129, tc_HOL_Obool), tc_fun(_1187129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1187129, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1187129, tc_HOL_Obool), tc_fun(_1187129, tc_HOL_Obool)), _1187129), c_COMBS(_1187129, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1187129, tc_HOL_Obool), tc_fun(_1187129, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1187129), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1187129), c_fconj)), hAPP(hAPP(c_COMBC(_1187129, tc_fun(_1187129, _1187129), tc_fun(_1187129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1187129, tc_HOL_Obool), tc_fun(tc_fun(_1187129, _1187129), tc_fun(_1187129, tc_HOL_Obool)), _1187129), c_COMBB(_1187129, tc_HOL_Obool, _1187129)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1187129), _1187133))))), hAPP(hAPP(c_COMBC(_1187129, tc_fun(_1187129, tc_HOL_Obool), tc_HOL_Obool), c_member(_1187129)), _1187131))))))], (22613 ^ _779999) ^ [_1198435, _1198437, _1198439] : [class_Orderings_Olinorder(_1198435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198435, tc_HOL_Obool)), _1198437), _1198439)), -(_1198437 = c_Orderings_Obot__class_Obot(tc_fun(_1198435, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198435), _1198439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198435), c_Big__Operators_Olinorder__class_OMin(_1198435, _1198439)), c_Big__Operators_Olinorder__class_OMin(_1198435, _1198437))))], (45137 ^ _779999) ^ [_1682026, _1682028, _1682030] : [hAPP(hAPP(c_List_Oappend(_1682026), _1682028), _1682030) = _1682028, -(_1682030 = c_List_Olist_ONil(_1682026))], (33929 ^ _779999) ^ [_1414815, _1414817] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1414815)), c_Int_OBit0(_1414817)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1414815), _1414817)))], (31562 ^ _779999) ^ [_1371199, _1371201, _1371203] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371199), _1371201), _1371203) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1371199, tc_HOL_Obool), tc_HOL_Obool)), -(_1371201 = c_Orderings_Obot__class_Obot(tc_fun(_1371199, tc_HOL_Obool)))], (20796 ^ _779999) ^ [_1157545, _1157547, _1157549] : [class_Groups_Oordered__ab__group__add__abs(_1157545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157545), hAPP(c_Groups_Oabs__class_Oabs(_1157545), _1157547)), _1157549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157545), _1157547), _1157549)))], (38846 ^ _779999) ^ [_1528737, _1528739, _1528741, _1528743, _1528745, _1528747, _1528749, _1528751, _1528753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528737, _1528739)), hAPP(hAPP(c_Product__Type_OPair(_1528737, _1528739), _1528741), _1528743)), _1528745)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528747, _1528749)), hAPP(hAPP(c_Product__Type_OPair(_1528747, _1528749), hAPP(_1528751, _1528741)), hAPP(_1528753, _1528743))), hAPP(c_Set_Oimage(tc_prod(_1528737, _1528739), tc_prod(_1528747, _1528749), c_Product__Type_Omap__pair(_1528737, _1528747, _1528739, _1528749, _1528751, _1528753)), _1528745))))], (31120 ^ _779999) ^ [_1363365, _1363367] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363365))), -(c_SMT_Oz3mod(_1363367, _1363365) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363367, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1363365)))], (26188 ^ _779999) ^ [_1270995, _1270997] : [class_Groups_Oordered__ab__group__add(_1270995), 26191 ^ _779999 : [(26198 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270995), c_Groups_Ozero__class_Ozero(_1270995)), _1270997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270995), hAPP(c_Groups_Ouminus__class_Ouminus(_1270995), _1270997)), c_Groups_Ozero__class_Ozero(_1270995))))], (26192 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270995), hAPP(c_Groups_Ouminus__class_Ouminus(_1270995), _1270997)), c_Groups_Ozero__class_Ozero(_1270995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270995), c_Groups_Ozero__class_Ozero(_1270995)), _1270997)))]]], (42994 ^ _779999) ^ [_1627816, _1627818] : [-(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)))), _1627816)) = 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)))), _1627818))), 42996 ^ _779999 : [(42999 ^ _779999) ^ [] : [43000 ^ _779999 : [(43003 ^ _779999) ^ [] : [hBOOL(hAPP(_1627818, 42995 ^ [_1627816, _1627818]))], (43001 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1627816, 42995 ^ [_1627816, _1627818])))]], 43004 ^ _779999 : [(43007 ^ _779999) ^ [] : [hBOOL(hAPP(_1627816, 42995 ^ [_1627816, _1627818]))], (43005 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1627818, 42995 ^ [_1627816, _1627818])))]]], (42997 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42995 ^ [_1627816, _1627818])))]]], (16757 ^ _779999) ^ [_1083194, _1083196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1083194)), _1083196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1083194), _1083196)))], (40447 ^ _779999) ^ [_1567324, _1567326, _1567328, _1567330, _1567332] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567324, _1567324)), hAPP(hAPP(c_Product__Type_OPair(_1567324, _1567324), _1567326), _1567328)), _1567330)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567324, _1567324)), hAPP(hAPP(c_Product__Type_OPair(_1567324, _1567324), _1567328), _1567332)), c_Transitive__Closure_Ortrancl(_1567324, _1567330))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567324, _1567324)), hAPP(hAPP(c_Product__Type_OPair(_1567324, _1567324), _1567326), _1567332)), c_Transitive__Closure_Otrancl(_1567324, _1567330))))], (23761 ^ _779999) ^ [_1223760, _1223762, _1223764] : [class_Orderings_Olinorder(_1223760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223760), _1223762)), -(_1223762 = c_Orderings_Obot__class_Obot(tc_fun(_1223760, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223760), _1223764)), -(_1223764 = c_Orderings_Obot__class_Obot(tc_fun(_1223760, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1223760, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1223760, tc_HOL_Obool)), _1223762), _1223764)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1223760), c_Big__Operators_Olinorder__class_OMin(_1223760, _1223762)), c_Big__Operators_Olinorder__class_OMin(_1223760, _1223764)))], (16643 ^ _779999) ^ [_1081066, _1081068] : [class_Rings_Ocomm__semiring__1(_1081066), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081066), _1081068), _1081068) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081066), c_Groups_Oone__class_Oone(_1081066)), c_Groups_Oone__class_Oone(_1081066))), _1081068))], (31431 ^ _779999) ^ [_1368724, _1368726] : [class_Rings_Olinordered__idom(_1368724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368724), c_Groups_Ozero__class_Ozero(_1368724)), _1368726)), -(c_Groups_Osgn__class_Osgn(_1368724, _1368726) = c_Groups_Oone__class_Oone(_1368724))], (11230 ^ _779999) ^ [_974582, _974584, _974586, _974588, _974590] : [class_Lattices_Osemilattice__inf(_974582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974582), _974584), _974586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974582), _974588), _974590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974582), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974582), _974584), _974588)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974582), _974586), _974590))))], (27192 ^ _779999) ^ [_1291930, _1291932] : [class_Rings_Odivision__ring__inverse__zero(_1291930), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291930), _1291932), c_Groups_Ozero__class_Ozero(_1291930)) = c_Groups_Ozero__class_Ozero(_1291930))], (23105 ^ _779999) ^ [_1211249, _1211251, _1211253, _1211255] : [class_Orderings_Olinorder(_1211249), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211249), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211249), _1211251), _1211253)), _1211255) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211249), _1211251), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211249), _1211253), _1211255)))], (33547 ^ _779999) ^ [_1407277, _1407279] : [class_Int_Onumber__ring(_1407277), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407277), hAPP(c_Int_Onumber__class_Onumber__of(_1407277), _1407279)), c_Groups_Oone__class_Oone(_1407277)) = hAPP(c_Int_Onumber__class_Onumber__of(_1407277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1407279), c_Int_OBit1(c_Int_OPls))))], (35338 ^ _779999) ^ [_1445092, _1445094, _1445096, _1445098] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445092, _1445094), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445096), _1445098))), -(_1445094 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1445092, _1445094) = _1445098)], (33403 ^ _779999) ^ [_1404973] : [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), _1404973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1404973)))], (45340 ^ _779999) ^ [_1687313, _1687315, _1687317, _1687319, _1687321] : [hAPP(hAPP(c_List_Odrop(_1687313), _1687315), _1687317) = hAPP(hAPP(c_List_Olist_OCons(_1687313), _1687319), _1687321), -(hAPP(hAPP(c_List_Onth(_1687313), _1687317), _1687315) = _1687319)], (45897 ^ _779999) ^ [_1699620, _1699622, _1699624] : [class_Orderings_Olinorder(_1699620), -(c_List_Oremove1(_1699620, _1699622, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699620, _1699620, c_COMBI(_1699620)), _1699622), _1699624)) = _1699624)], (16725 ^ _779999) ^ [_1082584, _1082586] : [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), _1082584), _1082586))), 16728 ^ _779999 : [(16731 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082586)))], (16729 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082584)))]]], (19379 ^ _779999) ^ [] : [-(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))))], (33219 ^ _779999) ^ [_1402081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1402081), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51954 ^ _779999) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (35069 ^ _779999) ^ [_1435001, _1435003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1435001), _1435003)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435001), _1435003) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (20661 ^ _779999) ^ [_1155064, _1155066, _1155068] : [class_Groups_Ocomm__monoid__add(_1155064), class_Groups_Ocomm__monoid__mult(_1155064), c_Nat__Transfer_Onat__set(_1155066), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1155064), _1155068), _1155066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1155064), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1155064, tc_Nat_Onat), _1155068), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155066)))], (39891 ^ _779999) ^ [_1553261, _1553263, _1553265, _1553267, _1553269, _1553271, _1553273] : [c_Finite__Set_Ofolding__idem(_1553261, _1553263, _1553265, _1553267), -(hAPP(c_Fun_Ocomp(_1553263, _1553263, _1553269, hAPP(_1553265, _1553271)), hAPP(c_Fun_Ocomp(_1553263, _1553263, _1553269, hAPP(_1553265, _1553271)), _1553273)) = hAPP(c_Fun_Ocomp(_1553263, _1553263, _1553269, hAPP(_1553265, _1553271)), _1553273))], (49716 ^ _779999) ^ [_1782820, _1782822, _1782824, _1782826, _1782828, _1782830, _1782832] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1782820, _1782822, _1782824, _1782826), _1782828), _1782830), _1782832) = c_New__DSequence_Oneg__bind(_1782820, _1782822, hAPP(hAPP(hAPP(_1782824, _1782828), _1782830), _1782832), hAPP(hAPP(c_COMBC(_1782820, 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(_1782822)))), hAPP(hAPP(c_COMBC(_1782820, 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(_1782822))))), hAPP(hAPP(c_COMBC(_1782820, 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(_1782822)))))), _1782826), _1782828)), _1782830)), _1782832)))], (17255 ^ _779999) ^ [_1092694, _1092696, _1092698, _1092700, _1092702, _1092704] : [class_Rings_Oordered__ring(_1092694), 17258 ^ _779999 : [(17265 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092694), _1092696), _1092702)), _1092698)), _1092700)), _1092704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), _1092696), _1092698)), _1092700)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), _1092702), _1092698)), _1092704))))], (17259 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), _1092696), _1092698)), _1092700)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), _1092702), _1092698)), _1092704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092694), _1092696), _1092702)), _1092698)), _1092700)), _1092704)))]]], (5762 ^ _779999) ^ [_868168, _868170] : [_868170 = _868168, -(tc_Hoare__Mirabelle_Otriple(_868170) = tc_Hoare__Mirabelle_Otriple(_868168))], (48757 ^ _779999) ^ [_1761550, _1761552, _1761554] : [48759 ^ _779999 : [(48762 ^ _779999) ^ [] : [hBOOL(hAPP(_1761552, 48758 ^ [_1761550, _1761552, _1761554]))], (48760 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761550), 48758 ^ [_1761550, _1761552, _1761554]), hAPP(c_List_Oset(_1761550), _1761554))))]], -(c_List_OdropWhile(_1761550, _1761552, _1761554) = c_List_Olist_ONil(_1761550))], (13991 ^ _779999) ^ [_1029376, _1029378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029376), _1029378)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029378), _1029376)), _1029376) = _1029378)], (44670 ^ _779999) ^ [_1671327, _1671329, _1671331] : [-(hAPP(hAPP(c_List_Olist__update(_1671327, c_List_Olist_ONil(_1671327)), _1671329), _1671331) = c_List_Olist_ONil(_1671327))], (20635 ^ _779999) ^ [_1154671, _1154673] : [c_Nat__Transfer_Onat__set(_1154671), c_Nat__Transfer_Onat__set(_1154673), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1154671), _1154673) = 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), _1154671)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1154673))))], (26763 ^ _779999) ^ [_1281976, _1281978, _1281980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281976, tc_HOL_Obool)), _1281978), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1281976, tc_HOL_Obool)), _1281980))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281976, tc_HOL_Obool)), _1281978), _1281980) = c_Orderings_Obot__class_Obot(tc_fun(_1281976, tc_HOL_Obool)))], (49589 ^ _779999) ^ [_1780282, _1780284, _1780286] : [49591 ^ _779999 : [(49594 ^ _779999) ^ [] : [hBOOL(hAPP(_1780284, 49590 ^ [_1780282, _1780284, _1780286]))], (49592 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780282), 49590 ^ [_1780282, _1780284, _1780286]), hAPP(c_List_Oset(_1780282), _1780286))))]], -(c_List_Olist__all(_1780282, _1780284, _1780286))], (13010 ^ _779999) ^ [_1011379, _1011381, _1011383, _1011385, _1011387, _1011389, _1011391, _1011393] : [c_Finite__Set_Ofolding__image__simple(_1011379, _1011381, _1011383, _1011385, _1011387, _1011389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011381), _1011391)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011381), _1011393)), 13024 ^ _779999 : [(13027 ^ _779999) ^ [] : [hAPP(_1011387, 13023 ^ [_1011379, _1011381, _1011383, _1011385, _1011387, _1011389, _1011391, _1011393]) = _1011385], (13025 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1011381), 13023 ^ [_1011379, _1011381, _1011383, _1011385, _1011387, _1011389, _1011391, _1011393]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011381, tc_HOL_Obool)), _1011391), _1011393))))]], -(hAPP(_1011389, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011381, tc_HOL_Obool)), _1011391), _1011393)) = hAPP(hAPP(_1011383, hAPP(_1011389, _1011391)), hAPP(_1011389, _1011393)))], (22984 ^ _779999) ^ [_1208268, _1208270, _1208272, _1208274, _1208276] : [-(_1208268 = c_Orderings_Obot__class_Obot(tc_fun(_1208270, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1208272, tc_HOL_Obool)), _1208274), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1208270, tc_fun(_1208272, tc_HOL_Obool)), _1208268), _1208276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1208270, tc_fun(_1208272, tc_HOL_Obool)), _1208268), hAPP(hAPP(c_COMBB(tc_fun(_1208272, tc_HOL_Obool), tc_fun(_1208272, tc_HOL_Obool), _1208270), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1208272, tc_HOL_Obool)), _1208274)), _1208276)))], (40759 ^ _779999) ^ [_1574135, _1574137, _1574139] : [-(hAPP(c_Relation_ORange(_1574135, _1574137), hAPP(c_Relation_Oconverse(_1574137, _1574135), _1574139)) = hAPP(c_Relation_ODomain(_1574137, _1574135), _1574139))], (13694 ^ _779999) ^ [_1024260, _1024262, _1024264, _1024266] : [class_Groups_Oordered__comm__monoid__add(_1024260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024260), c_Groups_Ozero__class_Ozero(_1024260)), _1024262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024260), _1024264), _1024266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024260), _1024264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024260), _1024262), _1024266))))], (42321 ^ _779999) ^ [_1612398, _1612400, _1612402, _1612404] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1612398, tc_HOL_Obool), tc_fun(_1612400, tc_HOL_Obool)), _1612402), hAPP(hAPP(c_COMBC(tc_fun(_1612398, tc_HOL_Obool), tc_fun(_1612398, tc_fun(_1612400, tc_HOL_Obool)), tc_fun(_1612400, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612398, tc_fun(_1612400, tc_HOL_Obool))), _1612404)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612398, tc_fun(_1612400, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1612398, tc_HOL_Obool), _1612402)), _1612404))], (39978 ^ _779999) ^ [_1555385, _1555387, _1555389, _1555391] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1555385, tc_HOL_Obool), tc_fun(_1555385, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1555385, tc_HOL_Obool), tc_fun(_1555385, tc_HOL_Obool)), _1555387), _1555389)), c_Wellfounded_Omax__ext(_1555385, _1555391))), 39981 ^ _779999 : [(39984 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555385), _1555389)))], (39986 ^ _779999) ^ [] : [_1555389 = c_Orderings_Obot__class_Obot(tc_fun(_1555385, tc_HOL_Obool))], (39988 ^ _779999) ^ [_1555679] : [hBOOL(hAPP(hAPP(c_member(_1555385), _1555679), _1555387)), 39992 ^ _779999 : [(39995 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555385, _1555385)), hAPP(hAPP(c_Product__Type_OPair(_1555385, _1555385), _1555679), 39991 ^ [_1555385, _1555387, _1555389, _1555391, _1555679])), _1555391)))], (39993 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555385), 39991 ^ [_1555385, _1555387, _1555389, _1555391, _1555679]), _1555389)))]]], (39982 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555385), _1555387)))]]], (25078 ^ _779999) ^ [_1250586, _1250588, _1250590] : [class_Orderings_Olinorder(_1250586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250586), _1250588)), -(hBOOL(hAPP(hAPP(c_member(_1250586), _1250590), _1250588))), -(_1250588 = c_Orderings_Obot__class_Obot(tc_fun(_1250586, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1250586, c_Orderings_Oord__class_Omax(_1250586), hAPP(hAPP(c_Set_Oinsert(_1250586), _1250590), _1250588)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250586), _1250590), c_Big__Operators_Olattice_OSup__fin(_1250586, c_Orderings_Oord__class_Omax(_1250586), _1250588)))], (13927 ^ _779999) ^ [_1028160, _1028162] : [13928 ^ _779999 : [(13929 ^ _779999) ^ [_1028213] : [_1028162 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028160), _1028213))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028160), _1028162)))], (35302 ^ _779999) ^ [_1443773, _1443775, _1443777, _1443779, _1443781, _1443783] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443773, _1443775), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443777), _1443779))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443773, _1443775), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443781), _1443783))), -(_1443775 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443779 = _1443783)], (45779 ^ _779999) ^ [_1696879, _1696881, _1696883, _1696885, _1696887] : [c_Finite__Set_Ofun__left__comm__idem(_1696879, _1696881, _1696883), -(hAPP(hAPP(c_Finite__Set_Ofold(_1696879, _1696881, _1696883), _1696885), hAPP(c_List_Oset(_1696879), _1696887)) = hAPP(c_List_Ofoldl(_1696881, _1696879, hAPP(c_COMBC(_1696879, _1696881, _1696881), _1696883), _1696885), _1696887))], (23743 ^ _779999) ^ [_1223446, _1223448, _1223450] : [class_Orderings_Olinorder(_1223446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223446), _1223448)), -(_1223450 = c_Orderings_Obot__class_Obot(tc_fun(_1223446, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1223446, tc_HOL_Obool)), _1223450), _1223448)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1223446), c_Big__Operators_Olinorder__class_OMin(_1223446, _1223450)), c_Big__Operators_Olinorder__class_OMin(_1223446, _1223448)) = c_Big__Operators_Olinorder__class_OMin(_1223446, _1223448))], (29594 ^ _779999) ^ [_1335278, _1335280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335278)), 29597 ^ _779999 : [(29606 ^ _779999) ^ [] : [-(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), _1335278), _1335280)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335280), _1335278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335280))], (29598 ^ _779999) ^ [] : [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), _1335278), _1335280))), 29601 ^ _779999 : [(29604 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335280)))], (29602 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335280), _1335278)))]]]]], (13361 ^ _779999) ^ [_1017844] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1017844) = _1017844)], (11514 ^ _779999) ^ [_981255, _981257, _981259, _981261] : [-(hBOOL(hAPP(hAPP(c_member(_981255), _981257), _981259))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981255, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_981255), _981257), _981261)), _981259) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981255, tc_HOL_Obool)), _981261), _981259))], (50161 ^ _779999) ^ [_1792455, _1792457, _1792459] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1792455, _1792457), _1792459) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1792455, tc_Lazy__Sequence_Olazy__sequence(_1792455)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1792455, tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1792455, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat)), _1792455), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1792455), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1792455)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1792455, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792455), tc_Nat_Onat)), _1792455), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1792455))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1792455), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1792457))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1792455, _1792457))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1792455), _1792459)))], (43217 ^ _779999) ^ [_1634102, _1634104, _1634106, _1634108, _1634110] : [hAPP(hAPP(c_List_Olist_OCons(_1634102), _1634104), _1634106) = hAPP(hAPP(c_List_Olist_OCons(_1634102), _1634108), _1634110), 43220 ^ _779999 : [(43223 ^ _779999) ^ [] : [-(_1634106 = _1634110)], (43221 ^ _779999) ^ [] : [-(_1634104 = _1634108)]]], (18039 ^ _779999) ^ [_1108275, _1108277, _1108279, _1108281] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1108275, _1108277, _1108279, _1108281, c_Orderings_Obot__class_Obot(tc_fun(_1108275, tc_HOL_Obool))), _1108281)))], (1894 ^ _779999) ^ [_806782, _806784] : [-(class_Rings_Osemiring(_806782)), _806784 = _806782, class_Rings_Osemiring(_806784)], (8326 ^ _779999) ^ [_921535, _921537, _921539, _921541] : [hBOOL(hAPP(hAPP(c_member(_921535), _921537), _921539)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921535, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_921535), _921537), _921541)), _921539) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921535, tc_HOL_Obool)), _921541), _921539))], (32721 ^ _779999) ^ [_1393846, _1393848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393846), _1393848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393846)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393848))))], (15046 ^ _779999) ^ [_1050019, _1050021, _1050023] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050019), _1050021)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050019), _1050023)), 15056 ^ _779999 : [(15059 ^ _779999) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15057 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1050019), 15055 ^ [_1050019, _1050021, _1050023]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1050019, tc_HOL_Obool)), _1050021), _1050023))))]], -(hAPP(c_Finite__Set_Ocard(_1050019), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1050019, tc_HOL_Obool)), _1050021), _1050023)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1050019), _1050021)), hAPP(c_Finite__Set_Ocard(_1050019), _1050023)))], (51444 ^ _779999) ^ [_1820775, _1820777, _1820779] : [hAPP(c_Set_Oimage(_1820775, _1820777, _1820779), c_Orderings_Otop__class_Otop(tc_fun(_1820775, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1820777, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1820777, _1820775, c_Hilbert__Choice_Oinv__into(_1820775, _1820777, c_Orderings_Otop__class_Otop(tc_fun(_1820775, tc_HOL_Obool)), _1820779), c_Orderings_Otop__class_Otop(tc_fun(_1820777, tc_HOL_Obool))))], (20407 ^ _779999) ^ [_1151335, _1151337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1151335, _1151337))))], (40665 ^ _779999) ^ [_1571952, _1571954] : [-(c_Transitive__Closure_Ortrancl(_1571952, hAPP(c_Relation_Oconverse(_1571952, _1571952), _1571954)) = hAPP(c_Relation_Oconverse(_1571952, _1571952), c_Transitive__Closure_Ortrancl(_1571952, _1571954)))], (41682 ^ _779999) ^ [_1595562, _1595564, _1595566, _1595568, _1595570, _1595572] : [c_Finite__Set_Ofun__left__comm(_1595562, _1595564, _1595566), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1595562, _1595564, _1595566, _1595568, _1595570), _1595572)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595562, _1595564, _1595566), _1595568), _1595570) = _1595572)], (30443 ^ _779999) ^ [_1350428, _1350430, _1350432] : [-(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, _1350428, _1350430)), _1350432), _1350430) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1350428), _1350432), _1350430))], (28802 ^ _779999) ^ [_1320959, _1320961, _1320963] : [class_Fields_Olinordered__field(_1320959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320959), c_Groups_Ozero__class_Ozero(_1320959)), _1320961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320959), c_Groups_Ozero__class_Ozero(_1320959)), _1320963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320959), c_Groups_Ozero__class_Ozero(_1320959)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320959), _1320961), _1320963))))], (14939 ^ _779999) ^ [_1048055] : [14941 ^ _779999 : [(14944 ^ _779999) ^ [_1048165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14940 ^ [_1048055, _1048165]), _1048165))], (14942 ^ _779999) ^ [_1048131] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14940 ^ [_1048055, _1048131]), _1048055)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1048055)))], (26578 ^ _779999) ^ [_1277991, _1277993, _1277995] : [class_Groups_Olinordered__ab__group__add(_1277991), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1277991), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277991), _1277993), _1277995)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277991), hAPP(c_Groups_Ouminus__class_Ouminus(_1277991), _1277993)), hAPP(c_Groups_Ouminus__class_Ouminus(_1277991), _1277995)))], (17953 ^ _779999) ^ [] : [-(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))], (45384 ^ _779999) ^ [_1688316, _1688318] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688316)), hAPP(c_List_Orotate1(_1688316), _1688318)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688316)), _1688318))], (15371 ^ _779999) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51319 ^ _779999) ^ [_1817935] : [-(c_Hilbert__Choice_Oinv__into(_1817935, _1817935, c_Orderings_Otop__class_Otop(tc_fun(_1817935, tc_HOL_Obool)), c_Fun_Oid(_1817935)) = c_Fun_Oid(_1817935))], (37825 ^ _779999) ^ [_1500821, _1500823, _1500825, _1500827, _1500829, _1500831, _1500833] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1500821, _1500823, _1500825, hAPP(hAPP(c_COMBC(_1500821, tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_fun(_1500823, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500823, tc_fun(tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_fun(_1500823, tc_HOL_Obool)), _1500821), c_COMBC(_1500823, tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500823, tc_prod(_1500821, _1500823)), tc_fun(_1500823, tc_fun(tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_HOL_Obool)), _1500821), hAPP(c_COMBB(tc_prod(_1500821, _1500823), tc_fun(tc_fun(tc_prod(_1500821, _1500823), tc_HOL_Obool), tc_HOL_Obool), _1500823), c_member(tc_prod(_1500821, _1500823)))), c_Product__Type_OPair(_1500821, _1500823)))), _1500827), hAPP(hAPP(c_COMBC(_1500823, tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_fun(_1500825, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500825, tc_fun(tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_fun(_1500825, tc_HOL_Obool)), _1500823), c_COMBC(_1500825, tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500825, tc_prod(_1500823, _1500825)), tc_fun(_1500825, tc_fun(tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_HOL_Obool)), _1500823), hAPP(c_COMBB(tc_prod(_1500823, _1500825), tc_fun(tc_fun(tc_prod(_1500823, _1500825), tc_HOL_Obool), tc_HOL_Obool), _1500825), c_member(tc_prod(_1500823, _1500825)))), c_Product__Type_OPair(_1500823, _1500825)))), _1500829)), _1500831), _1500833)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500821, _1500825)), hAPP(hAPP(c_Product__Type_OPair(_1500821, _1500825), _1500831), _1500833)), hAPP(hAPP(c_Relation_Orel__comp(_1500821, _1500823, _1500825), _1500827), _1500829))))], (37610 ^ _779999) ^ [_1494457, _1494459, _1494461, _1494463] : [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), _1494457), _1494459)), 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), _1494461), _1494463)), 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), _1494457), _1494463)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494461), _1494459))))], (49499 ^ _779999) ^ [_1778594, _1778596, _1778598, _1778600] : [-(c_List_Olist__all(_1778594, _1778596, hAPP(hAPP(c_List_Olist_OCons(_1778594), _1778598), _1778600))), hBOOL(hAPP(_1778596, _1778598)), c_List_Olist__all(_1778594, _1778596, _1778600)], (21562 ^ _779999) ^ [_1172587] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1172587)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1172587)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1172587)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (47974 ^ _779999) ^ [_1745529, _1745531] : [class_Orderings_Olinorder(_1745529), c_List_Olinorder__class_Osorted(_1745529, _1745531), -(c_List_Olinorder__class_Osorted(_1745529, c_List_Oremdups(_1745529, _1745531)))], (14854 ^ _779999) ^ [_1046613, _1046615] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046613), hAPP(c_Nat_OSuc, _1046615)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046613), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1046615))], (7354 ^ _779999) ^ [_902062, _902064] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_902062, _902064, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_902062), tc_HOL_Obool))))], (46374 ^ _779999) ^ [_1709723, _1709725, _1709727, _1709729, _1709731] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1709723), tc_List_Olist(_1709725), tc_List_Olist(_1709727), hAPP(c_List_Omap(_1709723, _1709725), _1709729)), hAPP(c_List_Omap(_1709727, _1709723), _1709731)) = hAPP(c_List_Omap(_1709727, _1709725), hAPP(c_Fun_Ocomp(_1709723, _1709725, _1709727, _1709729), _1709731)))], (24980 ^ _779999) ^ [_1248909, _1248911, _1248913] : [class_Orderings_Olinorder(_1248909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248909), _1248911)), hBOOL(hAPP(hAPP(c_member(_1248909), _1248913), _1248911)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1248909), _1248913), c_Big__Operators_Olattice_OSup__fin(_1248909, c_Orderings_Oord__class_Omax(_1248909), _1248911)) = c_Big__Operators_Olattice_OSup__fin(_1248909, c_Orderings_Oord__class_Omax(_1248909), _1248911))], (38153 ^ _779999) ^ [_1508615, _1508617] : [c_Wellfounded_Owf(_1508615, _1508617), -(c_Wellfounded_Owf(tc_List_Olist(_1508615), c_List_Olenlex(_1508615, _1508617)))], (7282 ^ _779999) ^ [_900571, _900573, _900575, _900577] : [hBOOL(hAPP(hAPP(c_member(_900571), _900573), _900575)), -(hBOOL(hAPP(hAPP(c_member(_900571), _900573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900571, tc_HOL_Obool)), _900575), _900577))))], (21650 ^ _779999) ^ [_1174442, _1174444] : [-(hAPP(c_Set_OCollect(_1174442), _1174444) = _1174444)], (15373 ^ _779999) ^ [_1056377, _1056379] : [class_Int_Oring__char__0(_1056377), hBOOL(hAPP(hAPP(c_member(_1056377), _1056379), c_Int_Oring__1__class_OInts(_1056377))), 15380 ^ _779999 : [(15387 ^ _779999) ^ [] : [_1056379 = c_Groups_Ozero__class_Ozero(_1056377), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056377), _1056379), _1056379) = c_Groups_Ozero__class_Ozero(_1056377))], (15381 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056377), _1056379), _1056379) = c_Groups_Ozero__class_Ozero(_1056377), -(_1056379 = c_Groups_Ozero__class_Ozero(_1056377))]]], (12316 ^ _779999) ^ [_997892, _997894, _997896, _997898, _997900] : [class_Groups_Ocomm__monoid__add(_997892), hBOOL(hAPP(c_Finite__Set_Ofinite(_997894), _997896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997894, tc_HOL_Obool)), _997898), _997896)), 12330 ^ _779999 : [(12333 ^ _779999) ^ [] : [hAPP(_997900, 12329 ^ [_997892, _997894, _997896, _997898, _997900]) = c_Groups_Ozero__class_Ozero(_997892)], (12331 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997894), 12329 ^ [_997892, _997894, _997896, _997898, _997900]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997894, tc_HOL_Obool)), _997896), _997898))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_997894, _997892), _997900), _997898) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_997894, _997892), _997900), _997896))], (27007 ^ _779999) ^ [_1287737, _1287739] : [class_Groups_Olinordered__ab__group__add(_1287737), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287737), _1287739)), -(_1287739 = c_Orderings_Obot__class_Obot(tc_fun(_1287737, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1287737), c_Big__Operators_Olinorder__class_OMax(_1287737, _1287739)) = c_Big__Operators_Olinorder__class_OMin(_1287737, hAPP(c_Set_Oimage(_1287737, _1287737, c_Groups_Ouminus__class_Ouminus(_1287737)), _1287739)))], (6779 ^ _779999) ^ [_891028, _891030] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891028, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_891028, tc_HOL_Obool))), _891030)))], (47472 ^ _779999) ^ [_1734609, _1734611, _1734613, _1734615] : [-(hAPP(c_List_Ofilter(_1734609, _1734611), hAPP(c_List_Ofilter(_1734609, _1734613), _1734615)) = hAPP(c_List_Ofilter(_1734609, hAPP(hAPP(c_COMBS(_1734609, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1734609), c_fconj), _1734613)), _1734611)), _1734615))], (4926 ^ _779999) ^ [_855176, _855178, _855180, _855182, _855184, _855186, _855188, _855190, _855192, _855194] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855194, _855190, _855186, _855182, _855178) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855192, _855188, _855184, _855180, _855176)), _855194 = _855192, _855190 = _855188, _855186 = _855184, _855182 = _855180, _855178 = _855176], (52236 ^ _779999) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (45187 ^ _779999) ^ [_1683159, _1683161, _1683163, _1683165] : [-(hBOOL(hAPP(hAPP(c_member(_1683159), _1683161), hAPP(c_List_Oset(_1683159), _1683163)))), -(c_List_Oremove1(_1683159, _1683161, hAPP(hAPP(c_List_Oappend(_1683159), _1683163), _1683165)) = hAPP(hAPP(c_List_Oappend(_1683159), _1683163), c_List_Oremove1(_1683159, _1683161, _1683165)))], (13271 ^ _779999) ^ [_1016235, _1016237, _1016239, _1016241] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1016235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016235), _1016237), _1016239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016235), _1016241), _1016237)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016235), _1016241), _1016239))))], (22313 ^ _779999) ^ [_1192831, _1192833] : [class_Lattices_Obounded__lattice__top(_1192831), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1192831), _1192833), c_Orderings_Otop__class_Otop(_1192831)) = _1192833)], (52336 ^ _779999) ^ [_1833967, _1833969, _1833971, _1833973, _1833975, _1833977] : [-(hAPP(hAPP(hAPP(c_COMBS(_1833967, _1833969, _1833971), _1833973), _1833975), _1833977) = hAPP(hAPP(_1833973, _1833977), hAPP(_1833975, _1833977)))], (16291 ^ _779999) ^ [_1074260, _1074262, _1074264, _1074266] : [class_Rings_Olinordered__ring__strict(_1074260), 16294 ^ _779999 : [(16309 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074260), _1074262), _1074264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074260), _1074262), _1074266)))), 16310 ^ _779999 : [(16317 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074262), c_Groups_Ozero__class_Ozero(_1074260))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074266), _1074264))], (16311 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), c_Groups_Ozero__class_Ozero(_1074260)), _1074262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074264), _1074266))]]], (16295 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074260), _1074262), _1074264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074260), _1074262), _1074266))), 16300 ^ _779999 : [(16303 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074264), _1074266)))], (16301 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), c_Groups_Ozero__class_Ozero(_1074260)), _1074262)))]], 16304 ^ _779999 : [(16307 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074266), _1074264)))], (16305 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074260), _1074262), c_Groups_Ozero__class_Ozero(_1074260))))]]]]], (50387 ^ _779999) ^ [_1797807] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1797807)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797807)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27986 ^ _779999) ^ [_1306066, _1306068, _1306070] : [class_Rings_Olinordered__semidom(_1306066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306066), c_Groups_Oone__class_Oone(_1306066)), _1306068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306066), c_Groups_Oone__class_Oone(_1306066)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306066), _1306068), hAPP(c_Nat_OSuc, _1306070)))))], (15903 ^ _779999) ^ [_1066701, _1066703] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066701), _1066703)), _1066701 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1066703 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (51792 ^ _779999) ^ [_1828309, _1828311] : [class_Lattices_Olattice(_1828309), -(class_Lattices_Osemilattice__inf(tc_fun(_1828311, _1828309)))], (2520 ^ _779999) ^ [_817169, _817171] : [_817171 = _817169, -(c_Int_OBit0(_817171) = c_Int_OBit0(_817169))], (39457 ^ _779999) ^ [_1543142, _1543144, _1543146, _1543148, _1543150, _1543152] : [c_Fun_Oinj__on(_1543142, _1543144, hAPP(c_Fun_Ocomp(_1543146, _1543144, _1543142, _1543148), _1543150), _1543152), -(c_Fun_Oinj__on(_1543142, _1543146, _1543150, _1543152))], (43074 ^ _779999) ^ [_1629801, _1629803] : [-(c_Nitpick_Ouminus__frac(_1629801, _1629803) = c_Nitpick_OAbs__Frac(_1629801, 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(_1629801), _1629803))), hAPP(c_Nitpick_Odenom(_1629801), _1629803))))], (21678 ^ _779999) ^ [_1174832, _1174834] : [-(hAPP(c_Set_OCollect(_1174832), hAPP(hAPP(c_COMBC(_1174832, tc_fun(_1174832, tc_HOL_Obool), tc_HOL_Obool), c_member(_1174832)), _1174834)) = _1174834)], (5883 ^ _779999) ^ [_873595, _873597, _873599] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873595, tc_HOL_Obool)), _873597), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873595, tc_HOL_Obool)), _873597), _873599))))], (9876 ^ _779999) ^ [_949675, _949677, _949679, _949681] : [hBOOL(hAPP(hAPP(c_member(_949675), _949677), _949679)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_949675, tc_Nat_Onat), _949681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949675, tc_HOL_Obool)), _949679), hAPP(hAPP(c_Set_Oinsert(_949675), _949677), c_Orderings_Obot__class_Obot(tc_fun(_949675, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_949675, tc_Nat_Onat), _949681), _949679)), hAPP(_949681, _949677)))], (14479 ^ _779999) ^ [_1038935, _1038937, _1038939] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038935), _1038937)), -(hAPP(c_Finite__Set_Ocard(_1038935), hAPP(hAPP(c_Set_Oinsert(_1038935), _1038939), _1038937)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1038935), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038935, tc_HOL_Obool)), _1038937), hAPP(hAPP(c_Set_Oinsert(_1038935), _1038939), c_Orderings_Obot__class_Obot(tc_fun(_1038935, tc_HOL_Obool)))))))], (46135 ^ _779999) ^ [_1703722, _1703724, _1703726] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1703722)), _1703724), c_List_Olists(_1703722, _1703726))), -(_1703724 = c_List_Olist_ONil(_1703722)), 46144 ^ _779999 : [(46149 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1703722)), 46143 ^ [_1703722, _1703724, _1703726]), c_List_Olists(_1703722, _1703726))))], (46147 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703722), 46142 ^ [_1703722, _1703724, _1703726]), _1703726)))], (46145 ^ _779999) ^ [] : [-(_1703724 = hAPP(hAPP(c_List_Olist_OCons(_1703722), 46142 ^ [_1703722, _1703724, _1703726]), 46143 ^ [_1703722, _1703724, _1703726]))]]], (44526 ^ _779999) ^ [_1668925, _1668927] : [-(_1668925 = c_List_Olist_ONil(_1668927)), hBOOL(hAPP(c_List_Odistinct(_1668927), _1668925)), -(hBOOL(hAPP(c_List_Odistinct(_1668927), c_List_Obutlast(_1668927, _1668925))))], (46520 ^ _779999) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (51091 ^ _779999) ^ [_1813818, _1813820, _1813822] : [c_Equiv__Relations_Oequiv(_1813818, _1813820, _1813822), 51094 ^ _779999 : [(51099 ^ _779999) ^ [] : [-(c_Relation_Otrans(_1813818, _1813822))], (51097 ^ _779999) ^ [] : [-(c_Relation_Osym(_1813818, _1813822))], (51095 ^ _779999) ^ [] : [-(c_Relation_Orefl__on(_1813818, _1813820, _1813822))]]], (10367 ^ _779999) ^ [_958316, _958318, _958320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958316), _958318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958316), _958320)), _958318)))], (44542 ^ _779999) ^ [_1669183, _1669185, _1669187] : [-(hAPP(hAPP(c_List_Ozip(_1669183, _1669185), _1669187), c_List_Olist_ONil(_1669185)) = c_List_Olist_ONil(tc_prod(_1669183, _1669185)))], (35677 ^ _779999) ^ [_1452087, _1452089, _1452091, _1452093, _1452095, _1452097] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1452087, _1452089, _1452091), _1452093), hAPP(hAPP(c_Product__Type_OPair(_1452087, _1452089), _1452095), _1452097)) = hAPP(hAPP(_1452093, _1452095), _1452097))], (52196 ^ _779999) ^ [_1832454] : [-(class_Nat_Osize(tc_Option_Ooption(_1832454)))], (28352 ^ _779999) ^ [_1313088, _1313090, _1313092] : [class_Fields_Olinordered__field__inverse__zero(_1313088), 28355 ^ _779999 : [(28370 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313088), _1313090), _1313092)), c_Groups_Ozero__class_Ozero(_1313088)))), 28371 ^ _779999 : [(28378 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), _1313090), c_Groups_Ozero__class_Ozero(_1313088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), c_Groups_Ozero__class_Ozero(_1313088)), _1313092))], (28372 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), c_Groups_Ozero__class_Ozero(_1313088)), _1313090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), _1313092), c_Groups_Ozero__class_Ozero(_1313088)))]]], (28356 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313088), _1313090), _1313092)), c_Groups_Ozero__class_Ozero(_1313088))), 28361 ^ _779999 : [(28364 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), _1313092), c_Groups_Ozero__class_Ozero(_1313088))))], (28362 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), c_Groups_Ozero__class_Ozero(_1313088)), _1313090)))]], 28365 ^ _779999 : [(28368 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), c_Groups_Ozero__class_Ozero(_1313088)), _1313092)))], (28366 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313088), _1313090), c_Groups_Ozero__class_Ozero(_1313088))))]]]]], (14886 ^ _779999) ^ [_1047022, _1047024, _1047026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047022), _1047024)), 14889 ^ _779999 : [(14909 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047022, tc_Nat_Onat), _1047026), _1047024) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 14910 ^ _779999 : [(14911 ^ _779999) ^ [_1047503] : [hBOOL(hAPP(hAPP(c_member(_1047022), _1047503), _1047024)), hAPP(_1047026, _1047503) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14919 ^ _779999 : [(14924 ^ _779999) ^ [] : [hAPP(_1047026, 14918 ^ [_1047022, _1047024, _1047026, _1047503]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14922 ^ _779999) ^ [] : [_1047503 = 14918 ^ [_1047022, _1047024, _1047026, _1047503]], (14920 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1047022), 14918 ^ [_1047022, _1047024, _1047026, _1047503]), _1047024)))]]]]], (14890 ^ _779999) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047022, tc_Nat_Onat), _1047026), _1047024) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14894 ^ _779999 : [(14899 ^ _779999) ^ [_1047342] : [hBOOL(hAPP(hAPP(c_member(_1047022), _1047342), _1047024)), -(14893 ^ [_1047022, _1047024, _1047026] = _1047342), -(hAPP(_1047026, _1047342) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14897 ^ _779999) ^ [] : [-(hAPP(_1047026, 14893 ^ [_1047022, _1047024, _1047026]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14895 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1047022), 14893 ^ [_1047022, _1047024, _1047026]), _1047024)))]]]]], (42159 ^ _779999) ^ [_1608822, _1608824, _1608826, _1608828, _1608830] : [-(_1608822 = c_Orderings_Obot__class_Obot(tc_fun(_1608824, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608826, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608824, tc_fun(_1608826, tc_HOL_Obool)), _1608822), _1608828)), _1608830) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608824, tc_fun(_1608826, tc_HOL_Obool)), _1608822), hAPP(hAPP(c_COMBC(_1608824, tc_fun(_1608826, tc_HOL_Obool), tc_fun(_1608826, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608826, tc_HOL_Obool), tc_fun(tc_fun(_1608826, tc_HOL_Obool), tc_fun(_1608826, tc_HOL_Obool)), _1608824), c_Groups_Ominus__class_Ominus(tc_fun(_1608826, tc_HOL_Obool))), _1608828)), _1608830)))], (22641 ^ _779999) ^ [_1198958, _1198960, _1198962, _1198964] : [-(hAPP(c_Set_Oimage(_1198958, _1198960, _1198962), _1198964) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1198958, tc_fun(_1198960, tc_HOL_Obool)), _1198964), hAPP(hAPP(c_COMBC(_1198958, tc_fun(_1198960, tc_HOL_Obool), tc_fun(_1198960, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1198960, tc_fun(tc_fun(_1198960, tc_HOL_Obool), tc_fun(_1198960, tc_HOL_Obool)), _1198958), c_Set_Oinsert(_1198960)), _1198962)), c_Orderings_Obot__class_Obot(tc_fun(_1198960, tc_HOL_Obool)))))], (18037 ^ _779999) ^ [] : [-(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)))], (38306 ^ _779999) ^ [_1512639, _1512641, _1512643, _1512645] : [38307 ^ _779999 : [(38308 ^ _779999) ^ [_1512693] : [hBOOL(hAPP(hAPP(_1512643, _1512693), _1512645))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1512639, _1512641, _1512643), _1512645)))], (46005 ^ _779999) ^ [_1701631, _1701633, _1701635] : [class_Orderings_Olinorder(_1701631), -(hAPP(c_List_Oset(_1701631), c_List_Olinorder__class_Oinsort__insert__key(_1701631, _1701631, c_COMBI(_1701631), _1701633, _1701635)) = hAPP(hAPP(c_Set_Oinsert(_1701631), _1701633), hAPP(c_List_Oset(_1701631), _1701635)))], (25488 ^ _779999) ^ [_1258295, _1258297, _1258299] : [class_Groups_Oordered__ab__group__add(_1258295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258295), _1258297), _1258299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258295), hAPP(c_Groups_Ouminus__class_Ouminus(_1258295), _1258299)), hAPP(c_Groups_Ouminus__class_Ouminus(_1258295), _1258297))))], (8950 ^ _779999) ^ [_933170, _933172, _933174] : [class_Orderings_Opreorder(_933170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933170), _933172), _933174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933170), _933174), _933172))], (42488 ^ _779999) ^ [_1616372, _1616374, _1616376] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1616372, tc_HOL_Obool)), _1616374), _1616376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616372, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1616372, tc_HOL_Obool), _1616376)), _1616374)))], (47172 ^ _779999) ^ [_1727681, _1727683] : [c_List_Oremdups(_1727681, _1727683) = c_List_Olist_ONil(_1727681), -(_1727683 = c_List_Olist_ONil(_1727681))], (43692 ^ _779999) ^ [_1648130, _1648132, _1648134, _1648136] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648130), tc_List_Olist(_1648130))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648130), tc_List_Olist(_1648130)), _1648132), _1648134)), c_List_Olexord(_1648130, _1648136)))), 43693 ^ _779999 : [(43700 ^ _779999) ^ [_1648437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1648437), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648130)), _1648132)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648130)), _1648134)))), hAPP(hAPP(c_List_Otake(_1648130), _1648437), _1648132) = hAPP(hAPP(c_List_Otake(_1648130), _1648437), _1648134), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648130, _1648130)), hAPP(hAPP(c_Product__Type_OPair(_1648130, _1648130), hAPP(hAPP(c_List_Onth(_1648130), _1648132), _1648437)), hAPP(hAPP(c_List_Onth(_1648130), _1648134), _1648437))), _1648136))], (43694 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648130)), _1648132)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648130)), _1648134))), hAPP(hAPP(c_List_Otake(_1648130), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648130)), _1648132)), _1648134) = _1648132]]], (40673 ^ _779999) ^ [_1572161, _1572163] : [c_Wellfounded_Oacyclic(_1572161, hAPP(c_Relation_Oconverse(_1572161, _1572161), _1572163)), -(c_Wellfounded_Oacyclic(_1572161, _1572163))], (44294 ^ _779999) ^ [_1664143, _1664145, _1664147, _1664149] : [hBOOL(hAPP(c_List_Odistinct(_1664143), _1664145)), hBOOL(hAPP(c_List_Odistinct(_1664147), _1664149)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1664143, _1664147)), c_Enum_Oproduct(_1664143, _1664147, _1664145, _1664149))))], (20423 ^ _779999) ^ [_1151587, _1151589] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1151587), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1151589)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1151587), _1151589)))], (16651 ^ _779999) ^ [_1081253, _1081255] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081253), _1081255) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16654 ^ _779999 : [(16657 ^ _779999) ^ [] : [-(_1081255 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16655 ^ _779999) ^ [] : [-(_1081253 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (51313 ^ _779999) ^ [_1817800, _1817802, _1817804] : [hAPP(c_Fun_Ocomp(_1817802, _1817800, _1817800, c_Hilbert__Choice_Oinv__into(_1817800, _1817802, c_Orderings_Otop__class_Otop(tc_fun(_1817800, tc_HOL_Obool)), _1817804)), _1817804) = c_Fun_Oid(_1817800), -(c_Fun_Oinj__on(_1817800, _1817802, _1817804, c_Orderings_Otop__class_Otop(tc_fun(_1817800, tc_HOL_Obool))))], (15513 ^ _779999) ^ [_1059430, _1059432, _1059434, _1059436, _1059438] : [class_Rings_Ocomm__semiring__1(_1059430), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), _1059432), _1059434)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), _1059436), _1059438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), _1059432), _1059436)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059430), _1059434), _1059438)))], (44552 ^ _779999) ^ [_1669350, _1669352] : [-(c_List_Osublist(_1669350, c_List_Olist_ONil(_1669350), _1669352) = c_List_Olist_ONil(_1669350))], (45338 ^ _779999) ^ [_1687270, _1687272, _1687274] : [-(hAPP(hAPP(c_List_Odrop(_1687270), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1687270), _1687272), _1687274)) = _1687274)], (10555 ^ _779999) ^ [_961636, _961638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961636)), _961638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961636), _961638)))], (21756 ^ _779999) ^ [_1176780, _1176782] : [-(hAPP(c_Set_OCollect(_1176780), hAPP(c_fequal, _1176782)) = hAPP(hAPP(c_Set_Oinsert(_1176780), _1176782), c_Orderings_Obot__class_Obot(tc_fun(_1176780, tc_HOL_Obool))))], (13532 ^ _779999) ^ [_1021159, _1021161, _1021163] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021159), _1021161)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021159), _1021163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1021161), _1021163))], (49033 ^ _779999) ^ [_1767180, _1767182, _1767184] : [-(c_List_Omaps(_1767180, _1767182, _1767184, c_List_Olist_ONil(_1767180)) = c_List_Olist_ONil(_1767182))], (18681 ^ _779999) ^ [_1120701, _1120703, _1120705, _1120707] : [class_Groups_Ocomm__monoid__add(_1120701), 18684 ^ _779999 : [(18691 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120703), _1120705))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1120701), _1120707), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1120705), hAPP(c_Nat_OSuc, _1120703))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120701), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1120701), _1120707), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1120705), _1120703))), hAPP(_1120707, _1120703)))], (18685 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120703), _1120705)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1120701), _1120707), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1120705), hAPP(c_Nat_OSuc, _1120703))) = c_Groups_Ozero__class_Ozero(_1120701))]]], (33077 ^ _779999) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (26204 ^ _779999) ^ [_1271269, _1271271] : [class_Groups_Olinordered__ab__group__add(_1271269), 26207 ^ _779999 : [(26214 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271269), c_Groups_Ozero__class_Ozero(_1271269)), _1271271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271269), hAPP(c_Groups_Ouminus__class_Ouminus(_1271269), _1271271)), _1271271)))], (26208 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271269), hAPP(c_Groups_Ouminus__class_Ouminus(_1271269), _1271271)), _1271271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271269), c_Groups_Ozero__class_Ozero(_1271269)), _1271271)))]]], (32871 ^ _779999) ^ [_1396562, _1396564] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1396562) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1396564), 32874 ^ _779999 : [(32881 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396562)))), 32884 ^ _779999 : [(32891 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396564)))), -(_1396562 = _1396564)], (32885 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396564))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396562) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (32875 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396564)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (35667 ^ _779999) ^ [_1451798, _1451800, _1451802, _1451804, _1451806, _1451808] : [_1451798 = _1451800, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1451802, _1451804, _1451806), _1451808), _1451798) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1451802, _1451804, _1451806), _1451808), _1451800))], (14726 ^ _779999) ^ [_1044413, _1044415, _1044417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044413), _1044415)), hBOOL(hAPP(hAPP(c_member(_1044413), _1044417), _1044415)), -(hAPP(c_Finite__Set_Ocard(_1044413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044413, tc_HOL_Obool)), _1044415), hAPP(hAPP(c_Set_Oinsert(_1044413), _1044417), c_Orderings_Obot__class_Obot(tc_fun(_1044413, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044413), _1044415)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (19351 ^ _779999) ^ [_1132849, _1132851] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1132849, _1132851))))], (34939 ^ _779999) ^ [_1433058] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1433058), hAPP(c_Int_Onumber__class_Onumber__of(_1433058), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1433058)), class_Int_Onumber__ring(_1433058), class_Rings_Olinordered__idom(_1433058)], (44087 ^ _779999) ^ [_1659349, _1659351, _1659353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659349), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659351)), _1659353))), -(c_List_Obutlast(_1659351, hAPP(hAPP(c_List_Otake(_1659351), _1659349), _1659353)) = hAPP(hAPP(c_List_Otake(_1659351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1659349), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1659353))], (24718 ^ _779999) ^ [_1243214, _1243216] : [class_Orderings_Olinorder(_1243214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1243214), _1243216)), -(c_Big__Operators_Olinorder__class_OMax(_1243214, _1243216) = hAPP(c_Finite__Set_Ofold1(_1243214, c_Orderings_Oord__class_Omax(_1243214)), _1243216))], (8620 ^ _779999) ^ [_927513, _927515, _927517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927513), _927515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927517), _927515)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927517), _927513))))], (45869 ^ _779999) ^ [_1698931, _1698933, _1698935] : [45870 ^ _779999 : [(45871 ^ _779999) ^ [_1699020, _1699022] : [_1698933 = hAPP(hAPP(c_List_Olist_OCons(_1698931), _1699022), _1699020)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1698931), tc_List_Olist(_1698931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1698931), tc_List_Olist(_1698931)), c_List_Olist_ONil(_1698931)), _1698933)), c_List_Olexord(_1698931, _1698935))))], (44330 ^ _779999) ^ [_1664840, _1664842] : [hAPP(c_Finite__Set_Ocard(_1664840), hAPP(c_List_Oset(_1664840), _1664842)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664840)), _1664842), -(hBOOL(hAPP(c_List_Odistinct(_1664840), _1664842)))], (21614 ^ _779999) ^ [_1173672, _1173674] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173672))), -(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)), _1173672))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1173674)))) = 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)), _1173672))), 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, _1173674))))))], (15016 ^ _779999) ^ [_1049498, _1049500, _1049502, _1049504] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049498), _1049500)), hBOOL(hAPP(hAPP(c_member(_1049498), _1049502), _1049500)), -(hBOOL(hAPP(hAPP(c_member(_1049498), _1049502), _1049504))), -(hAPP(c_Finite__Set_Ocard(_1049498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049498, tc_HOL_Obool)), _1049500), hAPP(hAPP(c_Set_Oinsert(_1049498), _1049502), _1049504))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1049498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049498, tc_HOL_Obool)), _1049500), _1049504))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13155 ^ _779999) ^ [_1014144, _1014146, _1014148, _1014150] : [class_Groups_Oordered__ab__semigroup__add(_1014144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014144), _1014146), _1014148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014144), _1014146), _1014150)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014144), _1014148), _1014150))))], (52360 ^ _779999) ^ [_1834318] : [-(hBOOL(_1834318)), -(hBOOL(hAPP(c_fNot, _1834318)))], (34893 ^ _779999) ^ [_1432367] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1432367) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1432367))], (45201 ^ _779999) ^ [_1683462, _1683464, _1683466] : [-(c_List_Obutlast(_1683462, hAPP(hAPP(c_List_Oappend(_1683462), _1683464), hAPP(hAPP(c_List_Olist_OCons(_1683462), _1683466), c_List_Olist_ONil(_1683462)))) = _1683464)], (50640 ^ _779999) ^ [_1803627, _1803629, _1803631] : [c_Relation_Otrans(_1803627, _1803629), c_Relation_Otrans(_1803627, _1803631), -(c_Relation_Otrans(_1803627, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1803627, _1803627), tc_HOL_Obool)), _1803629), _1803631)))], (49696 ^ _779999) ^ [_1782429, _1782431, _1782433, _1782435, _1782437] : [_1782429 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1782431, _1782433, _1782435, _1782437), _1782429) = c_Lazy__Sequence_Ohit__bound(_1782433))], (15667 ^ _779999) ^ [_1062413, _1062415, _1062417, _1062419] : [class_Rings_Ocomm__semiring(_1062413), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062413), _1062415), _1062417)), _1062419) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062413), _1062415), _1062419)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062413), _1062417), _1062419)))], (24112 ^ _779999) ^ [_1230447, _1230449, _1230451] : [class_Orderings_Olinorder(_1230447), hBOOL(hAPP(c_Finite__Set_Ofinite(_1230447), _1230449)), -(_1230449 = c_Orderings_Obot__class_Obot(tc_fun(_1230447, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1230447), _1230451)), -(_1230451 = c_Orderings_Obot__class_Obot(tc_fun(_1230447, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1230447, tc_HOL_Obool)), _1230449), _1230451) = c_Orderings_Obot__class_Obot(tc_fun(_1230447, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1230447, c_Orderings_Oord__class_Omin(_1230447), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230447, tc_HOL_Obool)), _1230449), _1230451)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1230447), c_Big__Operators_Olattice_OInf__fin(_1230447, c_Orderings_Oord__class_Omin(_1230447), _1230449)), c_Big__Operators_Olattice_OInf__fin(_1230447, c_Orderings_Oord__class_Omin(_1230447), _1230451)))], (7701 ^ _779999) ^ [_909372, _909374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909372), hAPP(c_Nat_OSuc, _909374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909372), _909374))), -(_909372 = hAPP(c_Nat_OSuc, _909374))], (45179 ^ _779999) ^ [_1682918, _1682920, _1682922, _1682924, _1682926] : [-(hAPP(hAPP(c_List_Olist__update(_1682918, hAPP(hAPP(c_List_Oappend(_1682918), _1682920), hAPP(hAPP(c_List_Olist_OCons(_1682918), _1682922), _1682924))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682918)), _1682920)), _1682926) = hAPP(hAPP(c_List_Oappend(_1682918), _1682920), hAPP(hAPP(c_List_Olist_OCons(_1682918), _1682926), _1682924)))], (49982 ^ _779999) ^ [_1789168, _1789170, _1789172, _1789174] : [hBOOL(hAPP(_1789168, _1789170)), -(hAPP(c_List_Ofilter(_1789172, _1789168), c_List_Oreplicate(_1789172, _1789174, _1789170)) = c_List_Oreplicate(_1789172, _1789174, _1789170))], (4534 ^ _779999) ^ [_848902, _848904, _848906, _848908] : [-(c_List_Ozip(_848908, _848904) = c_List_Ozip(_848906, _848902)), _848908 = _848906, _848904 = _848902], (47373 ^ _779999) ^ [_1731911, _1731913, _1731915] : [47375 ^ _779999 : [(47378 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1731911), tc_List_Olist(_1731911), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731911), tc_fun(tc_List_Olist(_1731911), tc_Nat_Onat), tc_fun(tc_List_Olist(_1731911), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1731911), tc_Nat_Onat), tc_fun(tc_List_Olist(_1731911), tc_HOL_Obool)), tc_List_Olist(_1731911)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731911))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1731911)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1731911))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1731911)))), 47374 ^ [_1731911, _1731913, _1731915]))], (47376 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731911), tc_List_Olist(_1731911))), 47374 ^ [_1731911, _1731913, _1731915]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1731911), tc_List_Olist(_1731911))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1731911), tc_List_Olist(_1731911)), _1731913), _1731915)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731911))), _1731913) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731911))), _1731915), 47383 ^ _779999 : [(47390 ^ _779999) ^ [] : [_1731913 = _1731915, -(c_List_Oconcat(_1731911, _1731913) = c_List_Oconcat(_1731911, _1731915))], (47384 ^ _779999) ^ [] : [c_List_Oconcat(_1731911, _1731913) = c_List_Oconcat(_1731911, _1731915), -(_1731913 = _1731915)]]], (50348 ^ _779999) ^ [_1796886, _1796888, _1796890, _1796892, _1796894, _1796896, _1796898] : [50350 ^ _779999 : [(50353 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1796890, 50349 ^ [_1796886, _1796888, _1796890, _1796892, _1796894, _1796896, _1796898]), _1796892), _1796894))], (50351 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796886), 50349 ^ [_1796886, _1796888, _1796890, _1796892, _1796894, _1796896, _1796898]), _1796888)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1796886, tc_fun(_1796896, tc_fun(_1796898, tc_HOL_Obool))), _1796888), _1796890), _1796892), _1796894)))], (48396 ^ _779999) ^ [_1753969, _1753971] : [-(hAPP(c_List_Oset(_1753969), hAPP(c_List_Orev(_1753969), _1753971)) = hAPP(c_List_Oset(_1753969), _1753971))], (35079 ^ _779999) ^ [_1435168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435168)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1435168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1435168), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38495 ^ _779999) ^ [_1518105, _1518107, _1518109, _1518111, _1518113, _1518115, _1518117, _1518119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518105, _1518107), tc_HOL_Obool)), _1518109), hAPP(hAPP(c_Product__Type_OSigma(_1518105, _1518107), _1518111), hAPP(c_COMBK(tc_fun(_1518107, tc_HOL_Obool), _1518105), _1518113)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518107, _1518115), tc_HOL_Obool)), _1518117), hAPP(hAPP(c_Product__Type_OSigma(_1518107, _1518115), _1518113), hAPP(c_COMBK(tc_fun(_1518115, tc_HOL_Obool), _1518107), _1518119)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518105, _1518115), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518105, _1518107, _1518115), _1518109), _1518117)), hAPP(hAPP(c_Product__Type_OSigma(_1518105, _1518115), _1518111), hAPP(c_COMBK(tc_fun(_1518115, tc_HOL_Obool), _1518105), _1518119)))))], (37636 ^ _779999) ^ [_1495056, _1495058, _1495060] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1495056, hAPP(hAPP(c_COMBC(_1495056, tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_fun(_1495056, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495056, tc_fun(tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_fun(_1495056, tc_HOL_Obool)), _1495056), c_COMBC(_1495056, tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495056, tc_prod(_1495056, _1495056)), tc_fun(_1495056, tc_fun(tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_HOL_Obool)), _1495056), hAPP(c_COMBB(tc_prod(_1495056, _1495056), tc_fun(tc_fun(tc_prod(_1495056, _1495056), tc_HOL_Obool), tc_HOL_Obool), _1495056), c_member(tc_prod(_1495056, _1495056)))), c_Product__Type_OPair(_1495056, _1495056)))), _1495058)), _1495060)), -(hBOOL(hAPP(hAPP(c_member(_1495056), _1495060), c_Wellfounded_Oacc(_1495056, _1495058))))], (6137 ^ _779999) ^ [_877956, _877958, _877960] : [class_Lattices_Osemilattice__sup(_877956), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877956), _877958), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877956), _877958), _877960)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877956), _877958), _877960))], (29386 ^ _779999) ^ [_1331973, _1331975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331973), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29389 ^ _779999 : [(29396 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331975), _1331973)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29390 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331975), _1331973)), 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)), _1331975)))]]], (23087 ^ _779999) ^ [_1210838, _1210840, _1210842] : [class_Orderings_Olinorder(_1210838), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210838), _1210840), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210838), _1210840), _1210842)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210838), _1210840), _1210842))], (25898 ^ _779999) ^ [_1265669, _1265671, _1265673, _1265675] : [class_Groups_Oab__group__add(_1265669), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1265671, _1265669), hAPP(hAPP(c_COMBB(_1265669, _1265669, _1265671), c_Groups_Ouminus__class_Ouminus(_1265669)), _1265673)), _1265675) = hAPP(c_Groups_Ouminus__class_Ouminus(_1265669), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1265671, _1265669), _1265673), _1265675)))], (22830 ^ _779999) ^ [_1203707, _1203709, _1203711] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203707, tc_fun(_1203709, tc_HOL_Obool)), _1203711), hAPP(c_COMBK(tc_fun(_1203709, tc_HOL_Obool), _1203707), c_Orderings_Obot__class_Obot(tc_fun(_1203709, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1203709, tc_HOL_Obool)))], (11546 ^ _779999) ^ [_981937, _981939, _981941, _981943, _981945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981937, tc_HOL_Obool)), hAPP(c_Set_Oimage(_981939, _981937, _981941), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981939, tc_HOL_Obool)), _981943), _981945))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981937, tc_HOL_Obool)), hAPP(c_Set_Oimage(_981939, _981937, _981941), _981943)), hAPP(c_Set_Oimage(_981939, _981937, _981941), _981945)))))], (34635 ^ _779999) ^ [_1427524] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1427524, 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, _1427524, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (44700 ^ _779999) ^ [_1671900, _1671902, _1671904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671900), tc_List_Olist(_1671900))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671900), tc_List_Olist(_1671900)), c_List_Olist_ONil(_1671900)), _1671902)), c_List_Olistrel1(_1671900, _1671904)))], (35426 ^ _779999) ^ [_1446723, _1446725, _1446727, _1446729, _1446731, _1446733, _1446735] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446723, _1446725), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1446727), _1446729))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446731, _1446725), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1446733), _1446735))), -(_1446725 = 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), _1446723), _1446731), _1446725), 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), _1446727), _1446733)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446729), _1446735)), _1446725))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446729), _1446735), _1446725)))))], (46724 ^ _779999) ^ [_1717140, _1717142] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1717140), _1717142) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1717140)), hAPP(c_Code__Numeral_Onat__of, _1717142))))], (45678 ^ _779999) ^ [_1694733, _1694735, _1694737] : [-(hAPP(hAPP(c_List_Odrop(_1694733), hAPP(c_Nat_OSuc, _1694735)), _1694737) = hAPP(hAPP(c_List_Odrop(_1694733), _1694735), hAPP(c_List_Otl(_1694733), _1694737)))], (25778 ^ _779999) ^ [_1263096, _1263098, _1263100] : [hBOOL(hAPP(hAPP(c_member(_1263096), _1263098), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1263096, tc_HOL_Obool)), _1263100))), hBOOL(hAPP(hAPP(c_member(_1263096), _1263098), _1263100))], (39113 ^ _779999) ^ [_1534891, _1534893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1534891, _1534891)), _1534893)), 39116 ^ _779999 : [(39123 ^ _779999) ^ [] : [c_Wellfounded_Oacyclic(_1534891, _1534893), -(c_Wellfounded_Owf(_1534891, _1534893))], (39117 ^ _779999) ^ [] : [c_Wellfounded_Owf(_1534891, _1534893), -(c_Wellfounded_Oacyclic(_1534891, _1534893))]]], (43946 ^ _779999) ^ [_1655887, _1655889, _1655891] : [-(_1655887 = _1655889), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655891)), _1655887) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655891)), _1655889), 43952 ^ _779999 : [(43955 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1655891, _1655891, tc_HOL_Obool), c_fequal), 43951 ^ [_1655887, _1655889, _1655891]))], (43953 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655891, _1655891)), 43951 ^ [_1655887, _1655889, _1655891]), hAPP(c_List_Oset(tc_prod(_1655891, _1655891)), hAPP(hAPP(c_List_Ozip(_1655891, _1655891), _1655887), _1655889)))))]]], (35992 ^ _779999) ^ [_1457827, _1457829] : [35993 ^ _779999 : [(35996 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457829), _1457827))], (35994 ^ _779999) ^ [] : [_1457827 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1457829, _1457827) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457829))], (47317 ^ _779999) ^ [_1730363, _1730365] : [c_List_Olist_ONil(_1730363) = c_List_Oconcat(_1730363, _1730365), 47320 ^ _779999 : [(47321 ^ _779999) ^ [_1730454] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730363)), _1730454), hAPP(c_List_Oset(tc_List_Olist(_1730363)), _1730365))), -(_1730454 = c_List_Olist_ONil(_1730363))]]], (9734 ^ _779999) ^ [_945485, _945487, _945489, _945491, _945493, _945495] : [hBOOL(hAPP(hAPP(c_member(_945485), _945487), _945489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945491, tc_HOL_Obool)), hAPP(c_Set_Oimage(_945485, _945491, _945493), _945489)), hAPP(_945495, hAPP(c_Set_Oimage(_945485, _945491, _945493), _945489)))), -(hBOOL(hAPP(hAPP(c_member(_945491), hAPP(_945493, _945487)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_945491, tc_HOL_Obool), _945495))))], (32993 ^ _779999) ^ [_1398652, _1398654] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398652)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398652)), _1398654) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398652)), _1398654)))], (38740 ^ _779999) ^ [_1526101] : [-(hAPP(c_Set_Oimage(_1526101, _1526101, c_Fun_Oid(_1526101)), c_Orderings_Otop__class_Otop(tc_fun(_1526101, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1526101, tc_HOL_Obool)))], (52198 ^ _779999) ^ [_1832478, _1832480] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1832478, _1832480)))], (45726 ^ _779999) ^ [_1695801, _1695803, _1695805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1695801), _1695803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1695801), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1695803), _1695805))))], (51850 ^ _779999) ^ [_1829070, _1829072] : [class_Orderings_Obot(_1829070), -(class_Orderings_Obot(tc_fun(_1829072, _1829070)))], (11502 ^ _779999) ^ [_981107, _981109, _981111, _981113] : [-(hBOOL(hAPP(hAPP(c_member(_981107), _981109), _981111))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981107, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_981107), _981109), _981113)), _981111) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981107, tc_HOL_Obool)), _981113), _981111))], (34581 ^ _779999) ^ [_1426285, _1426287, _1426289] : [class_Rings_Olinordered__idom(_1426285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1426285), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426285), hAPP(hAPP(c_Power_Opower__class_Opower(_1426285), _1426287), 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(_1426285), _1426289), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1426285)))], (50169 ^ _779999) ^ [_1792792, _1792794, _1792796, _1792798, _1792800] : [50171 ^ _779999 : [(50174 ^ _779999) ^ [] : [c_Relation_Orefl__on(_1792796, hAPP(_1792798, 50170 ^ [_1792792, _1792794, _1792796, _1792798, _1792800]), hAPP(_1792800, 50170 ^ [_1792792, _1792794, _1792796, _1792798, _1792800]))], (50172 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792792), 50170 ^ [_1792792, _1792794, _1792796, _1792798, _1792800]), _1792794)))]], -(c_Relation_Orefl__on(_1792796, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1792792, tc_fun(_1792796, tc_HOL_Obool)), _1792794), _1792798), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1792792, tc_fun(tc_prod(_1792796, _1792796), tc_HOL_Obool)), _1792794), _1792800)))], (36943 ^ _779999) ^ [_1477831, _1477833, _1477835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1477831, tc_HOL_Obool), tc_fun(_1477831, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1477831, tc_HOL_Obool), tc_fun(_1477831, tc_HOL_Obool)), _1477833), _1477835)), c_Wellfounded_Ofinite__psubset(_1477831))), 36946 ^ _779999 : [(36949 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1477831), _1477835)))], (36947 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1477831, tc_HOL_Obool)), _1477833), _1477835)))]]], (45219 ^ _779999) ^ [_1683958, _1683960, _1683962, _1683964, _1683966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683958), tc_List_Olist(_1683958))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683958), tc_List_Olist(_1683958)), _1683960), _1683962)), c_List_Olexord(_1683958, _1683964))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683958), tc_List_Olist(_1683958))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683958), tc_List_Olist(_1683958)), hAPP(hAPP(c_List_Oappend(_1683958), _1683966), _1683960)), hAPP(hAPP(c_List_Oappend(_1683958), _1683966), _1683962))), c_List_Olexord(_1683958, _1683964))))], (15735 ^ _779999) ^ [_1063879, _1063881] : [class_Groups_Ocomm__monoid__mult(_1063879), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063879), _1063881), c_Groups_Oone__class_Oone(_1063879)) = _1063881)], (51115 ^ _779999) ^ [_1814140, _1814142, _1814144] : [c_Relation_Orefl__on(_1814140, _1814142, _1814144), c_Relation_Osym(_1814140, _1814144), c_Relation_Otrans(_1814140, _1814144), -(c_Equiv__Relations_Oequiv(_1814140, _1814142, _1814144))], (10910 ^ _779999) ^ [_968821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968821), _968821))], (30619 ^ _779999) ^ [_1354100, _1354102] : [c_Nat__Transfer_Ois__nat(_1354100), c_Nat__Transfer_Ois__nat(_1354102), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354100, _1354102)))], (11777 ^ _779999) ^ [_986953] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_986953), c_Orderings_Obot__class_Obot(tc_fun(_986953, tc_HOL_Obool)))))], (33559 ^ _779999) ^ [_1407525, _1407527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1407525)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1407527)), _1407525) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1407527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1407525), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (16359 ^ _779999) ^ [_1075502, _1075504, _1075506] : [class_Rings_Olinordered__semiring__strict(_1075502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075502), c_Groups_Ozero__class_Ozero(_1075502)), _1075504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075502), _1075506), c_Groups_Ozero__class_Ozero(_1075502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075502), _1075504), _1075506)), c_Groups_Ozero__class_Ozero(_1075502))))], (37590 ^ _779999) ^ [_1493788] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1493788) = 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), _1493788), 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))))))], (46179 ^ _779999) ^ [_1704556, _1704558, _1704560, _1704562] : [-(_1704556 = c_List_Olist_ONil(_1704558)), -(c_List_Olast(_1704560, hAPP(hAPP(c_List_Omap(_1704558, _1704560), _1704562), _1704556)) = hAPP(_1704562, c_List_Olast(_1704558, _1704556)))], (25275 ^ _779999) ^ [_1254322] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254322)), -(hAPP(c_Int_Onat, _1254322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9640 ^ _779999) ^ [_943932, _943934, _943936] : [class_Complete__Lattice_Ocomplete__lattice(_943932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943932), _943934), hAPP(_943936, _943934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943932), _943934), c_Inductive_Ocomplete__lattice__class_Ogfp(_943932, _943936))))], (46121 ^ _779999) ^ [_1703454, _1703456, _1703458, _1703460] : [-(hAPP(hAPP(c_List_Oappend(_1703454), _1703456), hAPP(hAPP(c_List_Olist_OCons(_1703454), _1703458), c_List_Olist_ONil(_1703454))) = _1703460), -(_1703460 = c_List_Olist_ONil(_1703454)), c_List_Obutlast(_1703454, _1703460) = _1703456, c_List_Olast(_1703454, _1703460) = _1703458], (7912 ^ _779999) ^ [_913560, _913562, _913564] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _913560, _913562, _913564), -(_913564 = _913560)], (45512 ^ _779999) ^ [_1691386, _1691388, _1691390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691386), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691388)), _1691390))), -(hAPP(hAPP(c_List_Olist_OCons(_1691388), hAPP(hAPP(c_List_Onth(_1691388), _1691390), _1691386)), hAPP(hAPP(c_List_Odrop(_1691388), hAPP(c_Nat_OSuc, _1691386)), _1691390)) = hAPP(hAPP(c_List_Odrop(_1691388), _1691386), _1691390))], (22832 ^ _779999) ^ [_1203786, _1203788, _1203790, _1203792] : [c_Orderings_Obot__class_Obot(tc_fun(_1203786, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203788, tc_fun(_1203786, tc_HOL_Obool)), _1203790), _1203792), 22835 ^ _779999 : [(22836 ^ _779999) ^ [_1203902] : [hBOOL(hAPP(hAPP(c_member(_1203788), _1203902), _1203790)), -(hAPP(_1203792, _1203902) = c_Orderings_Obot__class_Obot(tc_fun(_1203786, tc_HOL_Obool)))]]], (14804 ^ _779999) ^ [_1045768] : [class_Rings_Olinordered__semidom(_1045768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045768), c_Groups_Oone__class_Oone(_1045768)), c_Groups_Ozero__class_Ozero(_1045768)))], (20645 ^ _779999) ^ [_1154838] : [c_Nat__Transfer_Onat__set(_1154838), -(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), _1154838)) = _1154838)], (2696 ^ _779999) ^ [_819929, _819931, _819933, _819935] : [-(c_Wellfounded_Omin__ext(_819935, _819931) = c_Wellfounded_Omin__ext(_819933, _819929)), _819935 = _819933, _819931 = _819929], (7151 ^ _779999) ^ [_897826, _897828, _897830] : [_897828 = _897830, -(hAPP(hAPP(c_COMBC(_897826, tc_fun(_897826, tc_HOL_Obool), tc_HOL_Obool), c_member(_897826)), _897828) = hAPP(hAPP(c_COMBC(_897826, tc_fun(_897826, tc_HOL_Obool), tc_HOL_Obool), c_member(_897826)), _897830))], (41986 ^ _779999) ^ [_1603891, _1603893, _1603895, _1603897, _1603899, _1603901] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603891, tc_fun(_1603893, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1603895, _1603891, _1603897), _1603899)), _1603901) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603895, tc_fun(_1603893, tc_HOL_Obool)), _1603899), hAPP(hAPP(c_COMBB(_1603891, tc_fun(_1603893, tc_HOL_Obool), _1603895), _1603901), _1603897)))], (35288 ^ _779999) ^ [_1443569, _1443571, _1443573, _1443575, _1443577, _1443579] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443569, _1443571), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443573), _1443575))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443569, _1443571), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443577), _1443579))), -(_1443571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443573 = _1443577)], (51982 ^ _779999) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (20726 ^ _779999) ^ [_1156153] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1156153) = 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), _1156153))))], (10297 ^ _779999) ^ [_957231, _957233] : [10298 ^ _779999 : [(10301 ^ _779999) ^ [] : [_957231 = _957233], (10299 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957231), _957233))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957231), _957233)))], (30862 ^ _779999) ^ [_1358544, _1358546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358544), _1358546)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358544, _1358546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358544), _1358546))], (13507 ^ _779999) ^ [_1020675, _1020677, _1020679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020677), _1020679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020675), _1020677)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020675), _1020679))))], (30513 ^ _779999) ^ [_1351975, _1351977, _1351979, _1351981] : [class_Divides_Osemiring__div(_1351975), -(c_Divides_Odiv__class_Omod(_1351975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351975), c_Divides_Odiv__class_Omod(_1351975, _1351977, _1351979)), _1351981), _1351979) = c_Divides_Odiv__class_Omod(_1351975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351975), _1351977), _1351981), _1351979))], (31676 ^ _779999) ^ [_1374172, _1374174, _1374176] : [class_Orderings_Olinorder(_1374172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374172), _1374174)), 31686 ^ _779999 : [(31689 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374172), _1374176), 31685 ^ [_1374172, _1374174, _1374176]))], (31687 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374172), 31685 ^ [_1374172, _1374174, _1374176]), _1374174)))]], hBOOL(hAPP(hAPP(c_member(_1374172), _1374176), _1374174)), -(c_Big__Operators_Olinorder__class_OMin(_1374172, _1374174) = _1374176)], (44708 ^ _779999) ^ [_1672181, _1672183, _1672185] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672181), tc_List_Olist(_1672181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672181), tc_List_Olist(_1672181)), _1672183), c_List_Olist_ONil(_1672181))), c_List_Olex(_1672181, _1672185)))], (24354 ^ _779999) ^ [_1236249, _1236251, _1236253, _1236255] : [class_Orderings_Olinorder(_1236249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236249), _1236251), _1236253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236249), _1236251), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236249), _1236253), _1236255))))], (26570 ^ _779999) ^ [_1277779, _1277781, _1277783] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277779, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277779, tc_HOL_Obool)), _1277781), _1277783)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277779, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277779, tc_HOL_Obool)), _1277781)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277779, tc_HOL_Obool)), _1277783)))], (3300 ^ _779999) ^ [_829321, _829323] : [_829323 = _829321, -(c_Set_OPow(_829323) = c_Set_OPow(_829321))], (47508 ^ _779999) ^ [_1735310, _1735312] : [-(c_List_Otranspose(_1735310, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1735310)), c_List_Olist_ONil(_1735310)), _1735312)) = c_List_Otranspose(_1735310, _1735312))], (37582 ^ _779999) ^ [_1493552, _1493554, _1493556, _1493558] : [-(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), _1493552), _1493554)), 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), _1493556), _1493558)), 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), _1493552), _1493556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1493554), _1493558))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1493552), _1493558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1493554), _1493556)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45628 ^ _779999) ^ [_1693786, _1693788, _1693790] : [hBOOL(hAPP(c_List_Odistinct(_1693786), hAPP(c_List_Orotate(_1693786, _1693788), _1693790))), -(hBOOL(hAPP(c_List_Odistinct(_1693786), _1693790)))], (32645 ^ _779999) ^ [_1392356] : [-(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), _1392356)) = 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), _1392356))))], (27162 ^ _779999) ^ [_1291245, _1291247, _1291249, _1291251] : [class_Rings_Ocomm__semiring__1(_1291245), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1291245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291245), _1291247), _1291249)), _1291251) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291245), hAPP(hAPP(c_Power_Opower__class_Opower(_1291245), _1291247), _1291251)), hAPP(hAPP(c_Power_Opower__class_Opower(_1291245), _1291249), _1291251)))], (11202 ^ _779999) ^ [_974084, _974086, _974088, _974090] : [class_Lattices_Osemilattice__inf(_974084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974084), _974086), _974088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974084), _974086), _974090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974084), _974086), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974084), _974088), _974090))))], (17739 ^ _779999) ^ [_1102443, _1102445, _1102447, _1102449, _1102451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102443), _1102445)), 17742 ^ _779999 : [(17749 ^ _779999) ^ [] : [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), _1102445), _1102443)), _1102447)), _1102449)), _1102451)), -(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), _1102445), _1102447)), _1102449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102443), _1102447)), _1102451))))], (17743 ^ _779999) ^ [] : [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), _1102445), _1102447)), _1102449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102443), _1102447)), _1102451))), -(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), _1102445), _1102443)), _1102447)), _1102449)), _1102451)))]]], (24920 ^ _779999) ^ [_1247725, _1247727] : [class_Orderings_Olinorder(_1247725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247725), _1247727)), -(_1247727 = c_Orderings_Obot__class_Obot(tc_fun(_1247725, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1247725), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1247725), 24933 ^ [_1247725, _1247727]), 24934 ^ [_1247725, _1247727])), hAPP(hAPP(c_Set_Oinsert(_1247725), 24933 ^ [_1247725, _1247727]), hAPP(hAPP(c_Set_Oinsert(_1247725), 24934 ^ [_1247725, _1247727]), c_Orderings_Obot__class_Obot(tc_fun(_1247725, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1247725), c_Big__Operators_Olinorder__class_OMax(_1247725, _1247727)), _1247727)))], (30637 ^ _779999) ^ [_1354394, _1354396] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354394), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354396)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354394, _1354396)))], (8169 ^ _779999) ^ [_918362] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _918362)], (40305 ^ _779999) ^ [_1563889, _1563891] : [-(c_Transitive__Closure_Ortrancl(_1563889, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1563889, _1563889), tc_HOL_Obool)), _1563891), c_Relation_OId(_1563889))) = c_Transitive__Closure_Ortrancl(_1563889, _1563891))], (13231 ^ _779999) ^ [_1015479, _1015481] : [class_Groups_Ocomm__monoid__add(_1015479), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015479), _1015481), c_Groups_Ozero__class_Ozero(_1015479)) = _1015481)], (47773 ^ _779999) ^ [_1741880, _1741882] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1741880, _1741882) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1741880), _1741882)))], (50159 ^ _779999) ^ [_1792359, _1792361] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1792359)), _1792361) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1792359, tc_Lazy__Sequence_Olazy__sequence(_1792359)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1792359, tc_Lazy__Sequence_Olazy__sequence(_1792359), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1792359), tc_Nat_Onat), _1792359), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1792359), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1792359)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1792359)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1792359), _1792361)))], (35097 ^ _779999) ^ [_1435652, _1435654] : [_1435652 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1435652, _1435654) = _1435654)], (9838 ^ _779999) ^ [_948236, _948238, _948240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948236, tc_HOL_Obool)), _948238), hAPP(_948240, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_948236, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), _948240)), _948238))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_948236, tc_HOL_Obool), _948240)))))), c_Orderings_Oorder__class_Omono(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), _948240), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948236, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_948236, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), _948240)), _948238))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_948236, tc_HOL_Obool), _948240)))), hAPP(_948240, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_948236, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_948236, tc_HOL_Obool), tc_fun(tc_fun(_948236, tc_HOL_Obool), tc_fun(_948236, tc_HOL_Obool)), tc_fun(_948236, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948236, tc_HOL_Obool))), _948240)), _948238))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_948236, tc_HOL_Obool), _948240)))))))], (208 ^ _779999) ^ [_783269, _783271] : [-(class_Fields_Olinordered__field__inverse__zero(_783269)), _783271 = _783269, class_Fields_Olinordered__field__inverse__zero(_783271)], (47028 ^ _779999) ^ [_1724499, _1724501, _1724503] : [c_List_Olist__all2(_1724503, _1724503, c_fequal, _1724499, _1724501), -(_1724499 = _1724501)], (43241 ^ _779999) ^ [_1634596, _1634598, _1634600, _1634602, _1634604, _1634606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634596), tc_List_Olist(_1634596))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634596), tc_List_Olist(_1634596)), hAPP(hAPP(c_List_Olist_OCons(_1634596), _1634598), _1634600)), hAPP(hAPP(c_List_Olist_OCons(_1634596), _1634602), _1634604))), c_List_Olex(_1634596, _1634606))), 43246 ^ _779999 : [(43249 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634596)), _1634600) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634596)), _1634604))], (43247 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634596, _1634596)), hAPP(hAPP(c_Product__Type_OPair(_1634596, _1634596), _1634598), _1634602)), _1634606)))]], 43250 ^ _779999 : [(43253 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634596), tc_List_Olist(_1634596))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634596), tc_List_Olist(_1634596)), _1634600), _1634604)), c_List_Olex(_1634596, _1634606))))], (43251 ^ _779999) ^ [] : [-(_1634598 = _1634602)]]], (29350 ^ _779999) ^ [_1331408, _1331410] : [c_Nat__Transfer_Ois__nat(_1331408), c_Nat__Transfer_Ois__nat(_1331410), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331408), _1331410)))], (46434 ^ _779999) ^ [_1711145, _1711147, _1711149, _1711151] : [class_Groups_Ocomm__monoid__add(_1711145), hBOOL(hAPP(c_List_Odistinct(_1711147), _1711149)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711145), hAPP(hAPP(c_List_Omap(_1711147, _1711145), _1711151), _1711149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1711147, _1711145), _1711151), hAPP(c_List_Oset(_1711147), _1711149)))], (2756 ^ _779999) ^ [_820855, _820857] : [_820857 = _820855, -(c_Nitpick_Oone__frac(_820857) = c_Nitpick_Oone__frac(_820855))], (40353 ^ _779999) ^ [_1565148, _1565150, _1565152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565148, _1565148), tc_HOL_Obool)), _1565150), c_Transitive__Closure_Ortrancl(_1565148, _1565152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565148, _1565148), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565148, _1565150)), c_Transitive__Closure_Ortrancl(_1565148, _1565152))))], (50593 ^ _779999) ^ [_1802539, _1802541, _1802543] : [hBOOL(hAPP(hAPP(c_member(_1802541), _1802539), c_Orderings_Obot__class_Obot(tc_fun(_1802541, tc_HOL_Obool)))), hBOOL(hAPP(_1802543, _1802539))], (48456 ^ _779999) ^ [_1755125, _1755127, _1755129, _1755131, _1755133] : [-(hAPP(c_List_Ofoldl(_1755125, _1755127, _1755129, _1755131), _1755133) = c_List_Ofoldr(_1755127, _1755125, hAPP(c_COMBC(_1755125, _1755127, _1755125), _1755129), hAPP(c_List_Orev(_1755127), _1755133), _1755131))], (35033 ^ _779999) ^ [_1434427] : [class_Int_Onumber__ring(_1434427), -(hAPP(c_Int_Oring__1__class_Oof__int(_1434427), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434427), c_Int_OMin))], (23905 ^ _779999) ^ [_1226378, _1226380] : [class_Orderings_Olinorder(_1226378), hBOOL(hAPP(c_Finite__Set_Ofinite(_1226378), _1226380)), -(_1226380 = c_Orderings_Obot__class_Obot(tc_fun(_1226378, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1226378), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1226378), 23918 ^ [_1226378, _1226380]), 23919 ^ [_1226378, _1226380])), hAPP(hAPP(c_Set_Oinsert(_1226378), 23918 ^ [_1226378, _1226380]), hAPP(hAPP(c_Set_Oinsert(_1226378), 23919 ^ [_1226378, _1226380]), c_Orderings_Obot__class_Obot(tc_fun(_1226378, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1226378), c_Big__Operators_Olinorder__class_OMin(_1226378, _1226380)), _1226380)))], (43649 ^ _779999) ^ [_1647105, _1647107, _1647109, _1647111] : [-(hAPP(hAPP(c_List_Onth(_1647105), hAPP(hAPP(c_List_Olist_OCons(_1647105), _1647107), _1647109)), _1647111) = c_Nat_Onat_Onat__case(_1647105, _1647107, hAPP(c_List_Onth(_1647105), _1647109), _1647111))], (46386 ^ _779999) ^ [_1710092, _1710094, _1710096, _1710098] : [hBOOL(hAPP(c_List_Odistinct(_1710092), hAPP(hAPP(c_List_Omap(_1710094, _1710092), _1710096), _1710098))), 46389 ^ _779999 : [(46392 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_1710094, _1710092, _1710096, hAPP(c_List_Oset(_1710094), _1710098)))], (46390 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1710094), _1710098)))]]], (23698 ^ _779999) ^ [_1222688, _1222690, _1222692] : [class_Orderings_Olinorder(_1222688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222688), _1222690)), -(_1222690 = c_Orderings_Obot__class_Obot(tc_fun(_1222688, tc_HOL_Obool))), 23709 ^ _779999 : [(23719 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222688), hAPP(c_Finite__Set_Ofold1(_1222688, c_Orderings_Oord__class_Omin(_1222688)), _1222690)), _1222692))), 23720 ^ _779999 : [(23721 ^ _779999) ^ [_1223077] : [hBOOL(hAPP(hAPP(c_member(_1222688), _1223077), _1222690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222688), _1223077), _1222692))]]], (23710 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222688), hAPP(c_Finite__Set_Ofold1(_1222688, c_Orderings_Oord__class_Omin(_1222688)), _1222690)), _1222692)), 23714 ^ _779999 : [(23717 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222688), 23713 ^ [_1222688, _1222690, _1222692]), _1222692)))], (23715 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222688), 23713 ^ [_1222688, _1222690, _1222692]), _1222690)))]]]]], (47542 ^ _779999) ^ [_1736321, _1736323] : [c_List_Otranspose(_1736321, _1736323) = c_List_Olist_ONil(tc_List_Olist(_1736321)), 47545 ^ _779999 : [(47546 ^ _779999) ^ [_1736416] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1736321)), _1736416), hAPP(c_List_Oset(tc_List_Olist(_1736321)), _1736323))), -(_1736416 = c_List_Olist_ONil(_1736321))]]], (4224 ^ _779999) ^ [_843881, _843883, _843885, _843887, _843889, _843891, _843893, _843895, _843897, _843899, _843901, _843903, _843905, _843907] : [-(c_New__Random__Sequence_Opos__decr__bind(_843907, _843903, _843899, _843895, _843891, _843887, _843883) = c_New__Random__Sequence_Opos__decr__bind(_843905, _843901, _843897, _843893, _843889, _843885, _843881)), _843907 = _843905, _843903 = _843901, _843899 = _843897, _843895 = _843893, _843891 = _843889, _843887 = _843885, _843883 = _843881], (10982 ^ _779999) ^ [_969780, _969782] : [class_Lattices_Osemilattice__inf(_969780), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969780), _969782), _969782) = _969782)], (35544 ^ _779999) ^ [_1449136, _1449138, _1449140, _1449142, _1449144, _1449146] : [hBOOL(hAPP(hAPP(_1449136, _1449138), _1449140)), hBOOL(hAPP(hAPP(_1449142, _1449138), _1449140)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449144, tc_fun(_1449146, tc_HOL_Obool))), _1449136), _1449142), _1449138), _1449140)))], (32727 ^ _779999) ^ [_1393969] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1393969)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393969))))], (49327 ^ _779999) ^ [_1774933, _1774935, _1774937] : [hBOOL(hAPP(hAPP(c_member(_1774933), _1774935), hAPP(c_List_Oset(_1774933), _1774937))), 49332 ^ _779999 : [(49335 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1774933), _1774935), hAPP(c_List_Oset(_1774933), 49330 ^ [_1774933, _1774935, _1774937])))], (49333 ^ _779999) ^ [] : [-(_1774937 = hAPP(hAPP(c_List_Oappend(_1774933), 49330 ^ [_1774933, _1774935, _1774937]), hAPP(hAPP(c_List_Olist_OCons(_1774933), _1774935), 49331 ^ [_1774933, _1774935, _1774937])))]]], (49756 ^ _779999) ^ [_1783922, _1783924] : [-(c_List_Osplice(_1783922, c_List_Olist_ONil(_1783922), _1783924) = _1783924)], (37634 ^ _779999) ^ [] : [-(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))], (3008 ^ _779999) ^ [_824819, _824821, _824823, _824825] : [-(c_Random_Oinc__shift(_824825, _824821) = c_Random_Oinc__shift(_824823, _824819)), _824825 = _824823, _824821 = _824819], (23431 ^ _779999) ^ [_1217252, _1217254, _1217256, _1217258, _1217260] : [-(hAPP(c_Set_Ovimage(_1217252, _1217254, _1217256), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1217254, tc_HOL_Obool)), _1217258), _1217260)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1217252, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1217252, _1217254, _1217256), _1217258)), hAPP(c_Set_Ovimage(_1217252, _1217254, _1217256), _1217260)))], (45616 ^ _779999) ^ [_1693519, _1693521, _1693523] : [-(hAPP(hAPP(c_List_Odrop(_1693519), _1693521), hAPP(c_List_Otl(_1693519), _1693523)) = hAPP(c_List_Otl(_1693519), hAPP(hAPP(c_List_Odrop(_1693519), _1693521), _1693523)))], (37461 ^ _779999) ^ [_1490244] : [-(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)), _1490244), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (38982 ^ _779999) ^ [_1532019, _1532021, _1532023, _1532025, _1532027] : [c_Relation_Orefl__on(_1532019, _1532021, _1532023), c_Relation_Orefl__on(_1532019, _1532025, _1532027), -(c_Relation_Orefl__on(_1532019, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1532019, tc_HOL_Obool)), _1532021), _1532025), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1532019, _1532019), tc_HOL_Obool)), _1532023), _1532027)))], (25848 ^ _779999) ^ [_1264452, _1264454, _1264456] : [class_Groups_Ogroup__add(_1264452), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264452), hAPP(c_Groups_Ouminus__class_Ouminus(_1264452), _1264454)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264452), _1264454), _1264456)) = _1264456)], (34219 ^ _779999) ^ [_1420011] : [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), _1420011))), 34222 ^ _779999 : [(34225 ^ _779999) ^ [] : [-(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(_1420011)))))], (34223 ^ _779999) ^ [] : [-(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(_1420011)))))]]], (16631 ^ _779999) ^ [_1080776, _1080778, _1080780] : [class_Rings_Ocomm__semiring__1(_1080776), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080776), _1080778), _1080780)), _1080780) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080776), _1080778), c_Groups_Oone__class_Oone(_1080776))), _1080780))], (440 ^ _779999) ^ [_786759, _786761, _786763, _786765, _786767, _786769, _786771, _786773] : [-(c_Finite__Set_Ofolding__idem(_786771, _786767, _786763, _786759)), c_Finite__Set_Ofolding__idem(_786773, _786769, _786765, _786761), _786773 = _786771, _786769 = _786767, _786765 = _786763, _786761 = _786759], (19967 ^ _779999) ^ [_1144157] : [-(hBOOL(hAPP(_1144157, 19974 ^ [_1144157]))), 19968 ^ _779999 : [(19969 ^ _779999) ^ [_1144209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144209)), hBOOL(hAPP(_1144157, hAPP(c_Int_Onat, _1144209)))]]], (7580 ^ _779999) ^ [_907295, _907297] : [c_Com_Ocom_OSemi(_907295, _907297) = c_Com_Ocom_OSKIP], (45881 ^ _779999) ^ [_1699238, _1699240, _1699242, _1699244, _1699246, _1699248] : [class_Orderings_Olinorder(_1699238), 45884 ^ _779999 : [(45891 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699238), hAPP(_1699240, _1699242)), hAPP(_1699240, _1699244)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699246, _1699238, _1699240), _1699242), hAPP(hAPP(c_List_Olist_OCons(_1699246), _1699244), _1699248)) = hAPP(hAPP(c_List_Olist_OCons(_1699246), _1699244), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699246, _1699238, _1699240), _1699242), _1699248)))], (45885 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699238), hAPP(_1699240, _1699242)), hAPP(_1699240, _1699244))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699246, _1699238, _1699240), _1699242), hAPP(hAPP(c_List_Olist_OCons(_1699246), _1699244), _1699248)) = hAPP(hAPP(c_List_Olist_OCons(_1699246), _1699242), hAPP(hAPP(c_List_Olist_OCons(_1699246), _1699244), _1699248)))]]], (51914 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (39153 ^ _779999) ^ [_1535424, _1535426] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1535424), c_Int_OInteg)), hBOOL(hAPP(_1535426, hAPP(c_Int_ORep__Integ, 39158 ^ [_1535424, _1535426]))), -(hBOOL(hAPP(_1535426, _1535424)))], (42524 ^ _779999) ^ [_1617173] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617173, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1617173, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1617173, tc_HOL_Obool)))], (44964 ^ _779999) ^ [_1678408, _1678410, _1678412, _1678414] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678408)), hAPP(hAPP(c_List_Oappend(_1678408), _1678410), _1678412)), c_List_Olists(_1678408, _1678414)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678408)), _1678410), c_List_Olists(_1678408, _1678414))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678408)), _1678412), c_List_Olists(_1678408, _1678414)))], (43785 ^ _779999) ^ [_1650709, _1650711, _1650713] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1650709, tc_HOL_Obool)), hAPP(c_List_Oset(_1650709), c_List_Osublist(_1650709, _1650711, _1650713))), hAPP(c_List_Oset(_1650709), _1650711))))], (27854 ^ _779999) ^ [_1303561, _1303563, _1303565] : [class_Power_Opower(_1303561), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303561), _1303563), hAPP(c_Nat_OSuc, _1303565)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303561), _1303563), hAPP(hAPP(c_Power_Opower__class_Opower(_1303561), _1303563), _1303565)))], (16759 ^ _779999) ^ [_1083258, _1083260, _1083262] : [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, _1083258)), _1083260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1083258)), _1083262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1083260), _1083262)))], (12103 ^ _779999) ^ [_993519, _993521, _993523, _993525, _993527, _993529, _993531, _993533] : [c_Finite__Set_Ofolding__image__simple(_993519, _993521, _993523, _993525, _993527, _993529), hBOOL(hAPP(c_Finite__Set_Ofinite(_993521), _993531)), -(hAPP(_993529, hAPP(hAPP(c_Set_Oinsert(_993521), _993533), _993531)) = hAPP(hAPP(_993523, hAPP(_993527, _993533)), hAPP(_993529, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993521, tc_HOL_Obool)), _993531), hAPP(hAPP(c_Set_Oinsert(_993521), _993533), c_Orderings_Obot__class_Obot(tc_fun(_993521, tc_HOL_Obool)))))))], (20379 ^ _779999) ^ [_1150882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1150882)), -(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, _1150882))))], (43934 ^ _779999) ^ [_1655576, _1655578, _1655580] : [_1655576 = _1655578, 43937 ^ _779999 : [(43940 ^ _779999) ^ [_1655732] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1655580, _1655580)), _1655732), hAPP(c_List_Oset(tc_prod(_1655580, _1655580)), hAPP(hAPP(c_List_Ozip(_1655580, _1655580), _1655576), _1655578)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1655580, _1655580, tc_HOL_Obool), c_fequal), _1655732)))], (43938 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655580)), _1655576) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655580)), _1655578))]]], (52268 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (33637 ^ _779999) ^ [_1409065, _1409067] : [hAPP(c_Nat_OSuc, _1409065) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409067), -(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(_1409067))), 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)), _1409065))))))], (22221 ^ _779999) ^ [_1191130, _1191132] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1191130, tc_HOL_Obool)), _1191132), c_Orderings_Otop__class_Otop(tc_fun(_1191130, tc_HOL_Obool)))))], (41867 ^ _779999) ^ [_1599837, _1599839, _1599841, _1599843] : [class_Complete__Lattice_Ocomplete__lattice(_1599837), -(_1599839 = c_Orderings_Obot__class_Obot(tc_fun(_1599841, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599841, _1599837), _1599839), hAPP(c_COMBK(_1599837, _1599841), _1599843)) = _1599843)], (5714 ^ _779999) ^ [_867428, _867430, _867432, _867434, _867436, _867438] : [-(c_COMBS(_867438, _867434, _867430) = c_COMBS(_867436, _867432, _867428)), _867438 = _867436, _867434 = _867432, _867430 = _867428], (14748 ^ _779999) ^ [_1044888, _1044890, _1044892] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044888), _1044890) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044888), _1044892), -(_1044890 = _1044892)], (44216 ^ _779999) ^ [_1662299, _1662301, _1662303, _1662305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662299), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662301)), _1662303))), -(hBOOL(hAPP(hAPP(c_member(_1662301), _1662305), hAPP(c_List_Oset(_1662301), hAPP(hAPP(c_List_Olist__update(_1662301, _1662303), _1662299), _1662305)))))], (8694 ^ _779999) ^ [_928853, _928855, _928857, _928859, _928861, _928863] : [-(hBOOL(hAPP(hAPP(c_member(_928853), _928855), _928857))), -(hAPP(c_Set_Oimage(_928853, _928859, c_Fun_Ofun__upd(_928853, _928859, _928861, _928855, _928863)), _928857) = hAPP(c_Set_Oimage(_928853, _928859, _928861), _928857))], (11889 ^ _779999) ^ [_989033, _989035, _989037] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_989033), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989033, tc_HOL_Obool)), _989035), _989037)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_989033), _989035)), hBOOL(hAPP(c_Finite__Set_Ofinite(_989033), _989037))], (36873 ^ _779999) ^ [_1476094, _1476096, _1476098, _1476100, _1476102] : [c_Equiv__Relations_Oequiv(_1476094, _1476096, _1476098), hBOOL(hAPP(hAPP(c_member(tc_prod(_1476094, _1476094)), hAPP(hAPP(c_Product__Type_OPair(_1476094, _1476094), _1476100), _1476102)), _1476098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476094, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1476094, _1476094, _1476098), hAPP(hAPP(c_Set_Oinsert(_1476094), _1476100), c_Orderings_Obot__class_Obot(tc_fun(_1476094, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1476094, _1476094, _1476098), hAPP(hAPP(c_Set_Oinsert(_1476094), _1476102), c_Orderings_Obot__class_Obot(tc_fun(_1476094, tc_HOL_Obool)))))))], (28084 ^ _779999) ^ [_1307994, _1307996, _1307998, _1308000] : [class_Rings_Olinordered__semidom(_1307994), hAPP(hAPP(c_Power_Opower__class_Opower(_1307994), _1307996), _1307998) = hAPP(hAPP(c_Power_Opower__class_Opower(_1307994), _1308000), _1307998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307994), c_Groups_Ozero__class_Ozero(_1307994)), _1307996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307994), c_Groups_Ozero__class_Ozero(_1307994)), _1308000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1307998)), -(_1307996 = _1308000)], (31174 ^ _779999) ^ [_1364198, _1364200, _1364202] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364198), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364200, _1364202)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364198), _1364200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364198), _1364202)))], (50044 ^ _779999) ^ [_1790246, _1790248, _1790250] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1790246), hAPP(c_COMBK(_1790246, tc_Nat_Onat), _1790248)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1790250)) = c_List_Oreplicate(_1790246, _1790250, _1790248))], (40917 ^ _779999) ^ [_1578331, _1578333, _1578335, _1578337] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1578331, _1578333), tc_fun(_1578331, _1578333)), _1578335), c_Fun_Ocomp(_1578333, _1578333, _1578331, _1578337)) = c_Fun_Ocomp(_1578333, _1578333, _1578331, hAPP(hAPP(c_Nat_Ocompow(_1578333, _1578333), _1578335), _1578337)))], (33005 ^ _779999) ^ [_1398836, _1398838] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398836)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398836)), _1398838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1398836))), _1398838))], (40925 ^ _779999) ^ [_1578497, _1578499, _1578501, _1578503] : [-(hAPP(_1578497, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1578499, _1578499), _1578501), _1578497), _1578503)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1578499, _1578499), _1578501), _1578497), hAPP(_1578497, _1578503)))], (7773 ^ _779999) ^ [_910952, _910954, _910956, _910958, _910960, _910962] : [hBOOL(hAPP(hAPP(c_member(_910952), _910954), _910956)), -(hAPP(c_Fun_Ooverride__on(_910952, _910958, _910960, _910962, _910956), _910954) = hAPP(_910962, _910954))], (47412 ^ _779999) ^ [_1733394, _1733396, _1733398, _1733400, _1733402] : [-(hAPP(c_List_Ofilter(_1733394, _1733396), hAPP(hAPP(c_List_Omap(_1733398, _1733394), _1733400), _1733402)) = hAPP(hAPP(c_List_Omap(_1733398, _1733394), _1733400), hAPP(c_List_Ofilter(_1733398, hAPP(c_Fun_Ocomp(_1733394, tc_HOL_Obool, _1733398, _1733396), _1733400)), _1733402)))], (35252 ^ _779999) ^ [_1442927, _1442929, _1442931, _1442933, _1442935] : [-(hBOOL(hAPP(hAPP(c_member(_1442927), _1442929), hAPP(c_Relation_OImage(_1442931, _1442927, _1442933), _1442935)))), 35253 ^ _779999 : [(35254 ^ _779999) ^ [_1443013] : [hBOOL(hAPP(hAPP(c_member(_1442931), _1443013), _1442935)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1442931, _1442927)), hAPP(hAPP(c_Product__Type_OPair(_1442931, _1442927), _1443013), _1442929)), _1442933))]]], (21271 ^ _779999) ^ [_1167197, _1167199, _1167201] : [class_Orderings_Oorder(_1167197), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1167197, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1167197, _1167199, _1167201)), hAPP(c_SetInterval_Oord__class_OatLeast(_1167197), _1167201)) = c_Orderings_Obot__class_Obot(tc_fun(_1167197, tc_HOL_Obool)))], (1844 ^ _779999) ^ [_806157, _806159] : [-(class_Groups_Omonoid__add(_806157)), _806159 = _806157, class_Groups_Omonoid__add(_806159)], (31329 ^ _779999) ^ [_1366719, _1366721, _1366723] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366721), _1366723)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366721), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1366719), _1366721), _1366723))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366719, _1366721)))], (51890 ^ _779999) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (16659 ^ _779999) ^ [_1081364, _1081366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081364), _1081366) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1081364 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1081366 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46562 ^ _779999) ^ [_1713952, _1713954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1713952)), hAPP(c_Code__Numeral_Oof__nat, _1713954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713952), _1713954)))], (3052 ^ _779999) ^ [_825457, _825459, _825461, _825463] : [-(c_Relation_ORange(_825463, _825459) = c_Relation_ORange(_825461, _825457)), _825463 = _825461, _825459 = _825457], (51896 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (49424 ^ _779999) ^ [_1776814, _1776816, _1776818] : [49425 ^ _779999 : [(49426 ^ _779999) ^ [_1776891, _1776893] : [_1776818 = hAPP(hAPP(c_List_Oappend(_1776814), _1776893), hAPP(hAPP(c_List_Olist_OCons(_1776814), _1776816), _1776891))]], -(hBOOL(hAPP(hAPP(c_member(_1776814), _1776816), hAPP(c_List_Oset(_1776814), _1776818))))], (39639 ^ _779999) ^ [_1547238, _1547240, _1547242, _1547244, _1547246, _1547248] : [c_Finite__Set_Ofolding(_1547238, _1547240, _1547242, _1547244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547238), _1547246)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547238), _1547248)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1547238, tc_HOL_Obool)), _1547246), _1547248) = c_Orderings_Obot__class_Obot(tc_fun(_1547238, tc_HOL_Obool)), -(hAPP(_1547244, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547238, tc_HOL_Obool)), _1547246), _1547248)) = hAPP(c_Fun_Ocomp(_1547240, _1547240, _1547240, hAPP(_1547244, _1547246)), hAPP(_1547244, _1547248)))], (40149 ^ _779999) ^ [_1559371, _1559373, _1559375, _1559377] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559371, _1559371)), hAPP(hAPP(c_Product__Type_OPair(_1559371, _1559371), _1559373), _1559375)), _1559377)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559371, _1559371)), hAPP(hAPP(c_Product__Type_OPair(_1559371, _1559371), _1559373), _1559375)), c_Transitive__Closure_Otrancl(_1559371, _1559377))))], (39242 ^ _779999) ^ [_1537728, _1537730, _1537732, _1537734] : [c_Equiv__Relations_Ocongruent(_1537728, _1537730, _1537732, _1537734), 39245 ^ _779999 : [(39246 ^ _779999) ^ [_1537873] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537728, _1537728)), _1537873), _1537732)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1537728, _1537728, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1537728, tc_fun(_1537728, _1537730), tc_fun(_1537728, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537730, tc_HOL_Obool), tc_fun(tc_fun(_1537728, _1537730), tc_fun(_1537728, tc_HOL_Obool)), _1537728), c_COMBB(_1537730, tc_HOL_Obool, _1537728)), hAPP(hAPP(c_COMBB(_1537730, tc_fun(_1537730, tc_HOL_Obool), _1537728), c_fequal), _1537734))), _1537734)), _1537873)))]]], (49386 ^ _779999) ^ [_1776125, _1776127, _1776129] : [-(c_List_Olist__ex(_1776125, _1776127, _1776129)), 49387 ^ _779999 : [(49388 ^ _779999) ^ [_1776182] : [hBOOL(hAPP(hAPP(c_member(_1776125), _1776182), hAPP(c_List_Oset(_1776125), _1776129))), hBOOL(hAPP(_1776127, _1776182))]]], (5985 ^ _779999) ^ [_875301, _875303, _875305, _875307] : [class_Orderings_Oord(_875301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875301), _875303), _875305)), _875305 = _875307, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875301), _875303), _875307)))], (16965 ^ _779999) ^ [_1086790, _1086792, _1086794, _1086796, _1086798] : [class_Rings_Olinordered__semiring__strict(_1086790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), _1086792), _1086794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), _1086796), _1086798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086790), c_Groups_Ozero__class_Ozero(_1086790)), _1086792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086790), c_Groups_Ozero__class_Ozero(_1086790)), _1086796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086790), _1086792), _1086796)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086790), _1086794), _1086798))))], (43787 ^ _779999) ^ [_1650760, _1650762] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1650760), hAPP(c_List_Oset(_1650760), _1650762))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650760)), _1650762))))], (42482 ^ _779999) ^ [_1616160, _1616162, _1616164, _1616166] : [-(hAPP(c_Set_Oimage(_1616160, _1616162, _1616164), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616160, tc_HOL_Obool), _1616166)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1616160, tc_HOL_Obool), tc_fun(_1616162, tc_HOL_Obool)), _1616166), c_Set_Oimage(_1616160, _1616162, _1616164)))], (19855 ^ _779999) ^ [_1142174, _1142176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142174), _1142176)), -(c_Nat__Transfer_Otsub(_1142176, _1142174) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142176), _1142174))], (14304 ^ _779999) ^ [_1035374, _1035376, _1035378] : [-(hBOOL(hAPP(_1035374, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035376), _1035378)))), 14307 ^ _779999 : [(14310 ^ _779999) ^ [] : [hBOOL(hAPP(_1035374, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14308 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035376), _1035378)))]], 14312 ^ _779999 : [(14315 ^ _779999) ^ [] : [hBOOL(hAPP(_1035374, 14311 ^ [_1035374, _1035376, _1035378]))], (14313 ^ _779999) ^ [] : [-(_1035376 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035378), 14311 ^ [_1035374, _1035376, _1035378]))]]], (13528 ^ _779999) ^ [_1021072, _1021074] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1021072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021074), _1021072))))], (46767 ^ _779999) ^ [_1718139, _1718141] : [-(hBOOL(hAPP(c_List_Olistsp(_1718139, _1718141), c_List_Olist_ONil(_1718139))))], (51898 ^ _779999) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (13750 ^ _779999) ^ [_1025292, _1025294, _1025296, _1025298, _1025300] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1025292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025292), _1025294), _1025296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025292), _1025298), _1025300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025292), _1025294), _1025298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025292), _1025296), _1025300))))], (42614 ^ _779999) ^ [_1619103, _1619105, _1619107, _1619109, _1619111] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619103, tc_fun(_1619105, tc_HOL_Obool)), _1619107), hAPP(hAPP(c_COMBS(_1619103, tc_fun(_1619105, tc_HOL_Obool), tc_fun(_1619105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619105, tc_HOL_Obool), tc_fun(tc_fun(_1619105, tc_HOL_Obool), tc_fun(_1619105, tc_HOL_Obool)), _1619103), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619105, tc_HOL_Obool))), _1619109)), _1619111)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619105, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619105, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619103, tc_fun(_1619105, tc_HOL_Obool), _1619109), _1619107))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619105, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619103, tc_fun(_1619105, tc_HOL_Obool), _1619111), _1619107))))], (41516 ^ _779999) ^ [_1592515, _1592517, _1592519, _1592521] : [class_Complete__Lattice_Ocomplete__lattice(_1592515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592517), _1592519)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1592517, _1592515), _1592519), _1592521) = hAPP(hAPP(c_Finite__Set_Ofold(_1592517, _1592515, hAPP(hAPP(c_COMBB(_1592515, tc_fun(_1592515, _1592515), _1592517), c_Lattices_Osemilattice__sup__class_Osup(_1592515)), _1592521)), c_Orderings_Obot__class_Obot(_1592515)), _1592519))], (46740 ^ _779999) ^ [_1717376, _1717378, _1717380, _1717382, _1717384] : [class_Groups_Omonoid__add(_1717376), class_Groups_Oordered__ab__semigroup__add(_1717376), 46750 ^ _779999 : [(46753 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717376), hAPP(_1717382, 46749 ^ [_1717376, _1717378, _1717380, _1717382, _1717384])), hAPP(_1717384, 46749 ^ [_1717376, _1717378, _1717380, _1717382, _1717384])))], (46751 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1717378), 46749 ^ [_1717376, _1717378, _1717380, _1717382, _1717384]), hAPP(c_List_Oset(_1717378), _1717380))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717376), hAPP(c_List_Omonoid__add__class_Olistsum(_1717376), hAPP(hAPP(c_List_Omap(_1717378, _1717376), _1717382), _1717380))), hAPP(c_List_Omonoid__add__class_Olistsum(_1717376), hAPP(hAPP(c_List_Omap(_1717378, _1717376), _1717384), _1717380)))))], (5676 ^ _779999) ^ [_866867, _866869] : [_866869 = _866867, -(c_Lattices_Osemilattice__sup__class_Osup(_866869) = c_Lattices_Osemilattice__sup__class_Osup(_866867))], (35155 ^ _779999) ^ [_1437676, _1437678, _1437680, _1437682, _1437684, _1437686] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437676, tc_fun(_1437678, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1437676, tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_fun(_1437678, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437678, tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_fun(_1437678, tc_HOL_Obool)), _1437676), c_COMBC(_1437678, tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437678, tc_prod(_1437676, _1437678)), tc_fun(_1437678, tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), _1437676), hAPP(c_COMBB(tc_prod(_1437676, _1437678), tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool), _1437678), c_member(tc_prod(_1437676, _1437678)))), c_Product__Type_OPair(_1437676, _1437678)))), _1437680)), hAPP(hAPP(c_COMBC(_1437676, tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_fun(_1437678, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437678, tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_fun(_1437678, tc_HOL_Obool)), _1437676), c_COMBC(_1437678, tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437678, tc_prod(_1437676, _1437678)), tc_fun(_1437678, tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool)), _1437676), hAPP(c_COMBB(tc_prod(_1437676, _1437678), tc_fun(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool), tc_HOL_Obool), _1437678), c_member(tc_prod(_1437676, _1437678)))), c_Product__Type_OPair(_1437676, _1437678)))), _1437682)), _1437684), _1437686)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1437676, _1437678)), hAPP(hAPP(c_Product__Type_OPair(_1437676, _1437678), _1437684), _1437686)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1437676, _1437678), tc_HOL_Obool)), _1437680), _1437682))))], (38207 ^ _779999) ^ [_1509926, _1509928] : [-(c_List_Olex(_1509926, _1509928) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1509926), tc_List_Olist(_1509926)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1509926, _1509928)))], (33893 ^ _779999) ^ [_1414187, _1414189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414187), _1414189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1414187)), c_Int_OBit0(_1414189))))], (1204 ^ _779999) ^ [_798157, _798159] : [-(class_Rings_Oring__1__no__zero__divisors(_798157)), _798159 = _798157, class_Rings_Oring__1__no__zero__divisors(_798159)], (36254 ^ _779999) ^ [_1462569, _1462571, _1462573, _1462575] : [-(hAPP(c_Product__Type_Osnd(_1462569, _1462571), hAPP(hAPP(c_Product__Type_OPair(_1462569, _1462571), _1462573), _1462575)) = _1462575)], (51307 ^ _779999) ^ [_1817671, _1817673, _1817675] : [c_Fun_Oinj__on(_1817671, _1817673, _1817675, c_Orderings_Otop__class_Otop(tc_fun(_1817671, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1817673, _1817671, _1817671, c_Hilbert__Choice_Oinv__into(_1817671, _1817673, c_Orderings_Otop__class_Otop(tc_fun(_1817671, tc_HOL_Obool)), _1817675)), _1817675) = c_Fun_Oid(_1817671))], (47631 ^ _779999) ^ [_1739372, _1739374, _1739376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1739372), _1739374)), -(c_List_Oupt(_1739372, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1739374), _1739376)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1739372, _1739374)), c_List_Oupt(_1739374, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1739374), _1739376))))], (39213 ^ _779999) ^ [_1537156] : [-(_1537156 = hAPP(c_Int_OAbs__Integ, 39211 ^ [_1537156]))], (4754 ^ _779999) ^ [_852394, _852396, _852398, _852400, _852402, _852404] : [-(c_Lazy__Sequence_Oanamorph(_852404, _852400, _852396) = c_Lazy__Sequence_Oanamorph(_852402, _852398, _852394)), _852404 = _852402, _852400 = _852398, _852396 = _852394], (46203 ^ _779999) ^ [_1705069, _1705071, _1705073] : [-(hAPP(hAPP(c_List_Omap(_1705069, _1705071), _1705073), c_List_Olist_ONil(_1705069)) = c_List_Olist_ONil(_1705071))], (11276 ^ _779999) ^ [_975434, _975436] : [class_Lattices_Obounded__lattice__bot(_975434), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975434), c_Orderings_Obot__class_Obot(_975434)), _975436) = c_Orderings_Obot__class_Obot(_975434))], (23423 ^ _779999) ^ [_1217057, _1217059, _1217061, _1217063, _1217065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1217057, tc_HOL_Obool)), _1217059), _1217061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1217063, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1217063, _1217057, _1217065), _1217059)), hAPP(c_Set_Ovimage(_1217063, _1217057, _1217065), _1217061))))], (50178 ^ _779999) ^ [_1793078, _1793080, _1793082] : [hBOOL(hAPP(hAPP(c_member(_1793078), _1793080), hAPP(c_List_Oset(_1793078), _1793082))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1793078), _1793082), _1793080)))], (19241 ^ _779999) ^ [_1130850, _1130852, _1130854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130850)), _1130850 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1130850), _1130854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130854), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38026 ^ _779999) ^ [_1505673, _1505675, _1505677] : [c_Wellfounded_Owf(_1505673, _1505675), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505673, _1505673)), hAPP(hAPP(c_Product__Type_OPair(_1505673, _1505673), _1505677), _1505677)), _1505675))], (16211 ^ _779999) ^ [_1072792, _1072794, _1072796] : [class_Rings_Oordered__ring(_1072792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072792), c_Groups_Ozero__class_Ozero(_1072792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072792), _1072794), _1072796)))), 16216 ^ _779999 : [(16223 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072792), _1072794), c_Groups_Ozero__class_Ozero(_1072792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072792), _1072796), c_Groups_Ozero__class_Ozero(_1072792)))], (16217 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072792), c_Groups_Ozero__class_Ozero(_1072792)), _1072794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072792), c_Groups_Ozero__class_Ozero(_1072792)), _1072796))]]], (44796 ^ _779999) ^ [_1674015, _1674017, _1674019] : [-(c_List_Olistset(_1674015, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1674015, tc_HOL_Obool)), _1674017), _1674019)) = c_List_Oset__Cons(_1674015, _1674017, c_List_Olistset(_1674015, _1674019)))], (39853 ^ _779999) ^ [_1552502, _1552504, _1552506, _1552508, _1552510, _1552512] : [c_Finite__Set_Ofolding__idem(_1552502, _1552504, _1552506, _1552508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552502), _1552510)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552502), _1552512)), -(hAPP(_1552508, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552502, tc_HOL_Obool)), _1552510), _1552512)) = hAPP(c_Fun_Ocomp(_1552504, _1552504, _1552504, hAPP(_1552508, _1552510)), hAPP(_1552508, _1552512)))], (46769 ^ _779999) ^ [_1718171, _1718173] : [-(hBOOL(hAPP(c_List_Olistsp(_1718171, _1718173), c_List_Olist_ONil(_1718171))))], (52304 ^ _779999) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (5282 ^ _779999) ^ [_860854, _860856, _860858, _860860] : [-(c_Transitive__Closure_Ortrancl(_860860, _860856) = c_Transitive__Closure_Ortrancl(_860858, _860854)), _860860 = _860858, _860856 = _860854], (27270 ^ _779999) ^ [_1293329, _1293331, _1293333, _1293335] : [class_Rings_Odivision__ring(_1293329), -(_1293331 = c_Groups_Ozero__class_Ozero(_1293329)), _1293333 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293329), _1293335), _1293331), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293329), _1293333), _1293331) = _1293335)], (29108 ^ _779999) ^ [_1326681, _1326683, _1326685, _1326687] : [class_Fields_Ofield__inverse__zero(_1326681), -(_1326683 = c_Groups_Ozero__class_Ozero(_1326681)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326681), _1326685), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326681), _1326687), _1326683)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326681), _1326687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326681), _1326685), _1326683))), _1326683))], (11412 ^ _779999) ^ [_978356, _978358, _978360, _978362, _978364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978356, tc_HOL_Obool)), _978358), _978360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978356, tc_HOL_Obool)), _978362), _978364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978356, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978356, tc_HOL_Obool)), _978358), _978362)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978356, tc_HOL_Obool)), _978360), _978364))))], (30778 ^ _779999) ^ [_1357094, _1357096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357096), _1357094)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357094, _1357096) = _1357094)], (52116 ^ _779999) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (37616 ^ _779999) ^ [_1494650, _1494652, _1494654, _1494656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494650), _1494656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494654), _1494652))), -(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), _1494650), _1494652)), 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), _1494654), _1494656)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (7187 ^ _779999) ^ [_898555, _898557, _898559, _898561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898555, tc_HOL_Obool)), _898557), _898559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898555, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_898555), _898561), _898557)), hAPP(hAPP(c_Set_Oinsert(_898555), _898561), _898559))))], (52020 ^ _779999) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (20812 ^ _779999) ^ [_1157813] : [class_Groups_Oordered__ab__group__add__abs(_1157813), -(hAPP(c_Groups_Oabs__class_Oabs(_1157813), c_Groups_Ozero__class_Ozero(_1157813)) = c_Groups_Ozero__class_Ozero(_1157813))], (37891 ^ _779999) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (44260 ^ _779999) ^ [_1663473, _1663475, _1663477, _1663479] : [hBOOL(hAPP(c_List_Odistinct(_1663473), _1663475)), -(hBOOL(hAPP(hAPP(c_member(_1663473), _1663477), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1663473, tc_HOL_Obool)), hAPP(c_List_Oset(_1663473), _1663475)), hAPP(hAPP(c_Set_Oinsert(_1663473), hAPP(hAPP(c_List_Onth(_1663473), _1663475), _1663479)), c_Orderings_Obot__class_Obot(tc_fun(_1663473, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1663473), hAPP(hAPP(c_List_Olist__update(_1663473, _1663475), _1663479), _1663477))))], (24278 ^ _779999) ^ [_1234747] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1234747), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1234747)], (38862 ^ _779999) ^ [_1529229, _1529231, _1529233, _1529235] : [-(c_Product__Type_Oapsnd(_1529229, _1529231, _1529233, _1529235) = c_Product__Type_Omap__pair(_1529233, _1529233, _1529229, _1529231, c_Fun_Oid(_1529233), _1529235))], (48943 ^ _779999) ^ [_1765618, _1765620, _1765622] : [hBOOL(hAPP(hAPP(c_member(_1765618), _1765620), hAPP(c_List_Oset(_1765618), _1765622))), -(c_List_Oinsert(_1765618, _1765620, _1765622) = _1765622)], (17651 ^ _779999) ^ [_1100831, _1100833, _1100835, _1100837, _1100839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100831), _1100833)), 17654 ^ _779999 : [(17661 ^ _779999) ^ [] : [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), _1100833), _1100831)), _1100835)), _1100837) = _1100839, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100833), _1100835)), _1100837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100831), _1100835)), _1100839))], (17655 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100833), _1100835)), _1100837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100831), _1100835)), _1100839), -(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), _1100833), _1100831)), _1100835)), _1100837) = _1100839)]]], (9470 ^ _779999) ^ [_940887, _940889, _940891, _940893] : [class_Orderings_Opreorder(_940887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940887), _940889), _940891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940887), _940891), _940893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940887), _940889), _940893)))], (33415 ^ _779999) ^ [] : [-(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)))], (33043 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (2038 ^ _779999) ^ [_809572, _809574] : [_809574 = _809572, -(c_Hoare__Mirabelle_OMGT(_809574) = c_Hoare__Mirabelle_OMGT(_809572))], (22004 ^ _779999) ^ [_1185058, _1185060, _1185062] : [class_Lattices_Odistrib__lattice(_1185058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1185058), _1185060)), -(_1185060 = c_Orderings_Obot__class_Obot(tc_fun(_1185058, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1185058), _1185062), c_Big__Operators_Olattice__class_OInf__fin(_1185058, _1185060)) = c_Big__Operators_Olattice__class_OInf__fin(_1185058, hAPP(c_Set_OCollect(_1185058), hAPP(hAPP(c_COMBB(tc_fun(_1185058, tc_HOL_Obool), tc_HOL_Obool, _1185058), c_HOL_OEx(_1185058)), hAPP(hAPP(c_COMBC(_1185058, tc_fun(_1185058, tc_HOL_Obool), tc_fun(_1185058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1185058, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1185058, tc_HOL_Obool), tc_fun(_1185058, tc_HOL_Obool)), _1185058), c_COMBS(_1185058, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1185058, tc_HOL_Obool), tc_fun(_1185058, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1185058), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1185058), c_fconj)), hAPP(hAPP(c_COMBC(_1185058, tc_fun(_1185058, _1185058), tc_fun(_1185058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1185058, tc_HOL_Obool), tc_fun(tc_fun(_1185058, _1185058), tc_fun(_1185058, tc_HOL_Obool)), _1185058), c_COMBB(_1185058, tc_HOL_Obool, _1185058)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1185058), _1185062))))), hAPP(hAPP(c_COMBC(_1185058, tc_fun(_1185058, tc_HOL_Obool), tc_HOL_Obool), c_member(_1185058)), _1185060))))))], (22347 ^ _779999) ^ [_1193380, _1193382, _1193384, _1193386] : [-(hBOOL(hAPP(hAPP(c_member(_1193380), hAPP(_1193382, _1193384)), hAPP(c_Set_Oimage(_1193386, _1193380, _1193382), c_Orderings_Otop__class_Otop(tc_fun(_1193386, tc_HOL_Obool))))))], (42329 ^ _779999) ^ [_1612669, _1612671] : [class_Complete__Lattice_Ocomplete__lattice(_1612669), -(c_Complete__Lattice_OSup__class_OSup(_1612669, _1612671) = c_Complete__Lattice_OInf__class_OInf(_1612669, hAPP(c_Set_OCollect(_1612669), hAPP(hAPP(c_COMBB(tc_fun(_1612669, tc_HOL_Obool), tc_HOL_Obool, _1612669), c_HOL_OAll(_1612669)), hAPP(hAPP(c_COMBB(tc_fun(_1612669, tc_HOL_Obool), tc_fun(_1612669, tc_HOL_Obool), _1612669), hAPP(c_COMBS(_1612669, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1612669), c_fimplies), hAPP(hAPP(c_COMBC(_1612669, tc_fun(_1612669, tc_HOL_Obool), tc_HOL_Obool), c_member(_1612669)), _1612671)))), hAPP(c_COMBC(_1612669, _1612669, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1612669)))))))], (22257 ^ _779999) ^ [] : [-(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))))], (34065 ^ _779999) ^ [_1417111, _1417113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1417111)), c_Int_OBit0(_1417113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417111), _1417113)))], (22708 ^ _779999) ^ [_1200814, _1200816, _1200818, _1200820, _1200822, _1200824] : [class_Complete__Lattice_Ocomplete__lattice(_1200814), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1200816, _1200814), _1200818), hAPP(hAPP(c_COMBB(tc_fun(_1200820, _1200814), _1200814, _1200816), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1200820, _1200814), _1200822)), _1200824)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1200820, _1200814), _1200822), hAPP(hAPP(c_COMBB(tc_fun(_1200816, _1200814), _1200814, _1200820), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1200816, _1200814), _1200818)), hAPP(c_COMBC(_1200816, _1200820, _1200814), _1200824))))], (19471 ^ _779999) ^ [] : [-(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))))], (52110 ^ _779999) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (11669 ^ _779999) ^ [_984569, _984571, _984573] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_984569), _984571)), 11672 ^ _779999 : [(11692 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_984569, tc_Nat_Onat), _984573), _984571) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 11693 ^ _779999 : [(11694 ^ _779999) ^ [_985050] : [hBOOL(hAPP(hAPP(c_member(_984569), _985050), _984571)), hAPP(_984573, _985050) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11702 ^ _779999 : [(11707 ^ _779999) ^ [] : [hAPP(_984573, 11701 ^ [_984569, _984571, _984573, _985050]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11705 ^ _779999) ^ [] : [_985050 = 11701 ^ [_984569, _984571, _984573, _985050]], (11703 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_984569), 11701 ^ [_984569, _984571, _984573, _985050]), _984571)))]]]]], (11673 ^ _779999) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_984569, tc_Nat_Onat), _984573), _984571) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11677 ^ _779999 : [(11682 ^ _779999) ^ [_984889] : [hBOOL(hAPP(hAPP(c_member(_984569), _984889), _984571)), -(11676 ^ [_984569, _984571, _984573] = _984889), -(hAPP(_984573, _984889) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11680 ^ _779999) ^ [] : [-(hAPP(_984573, 11676 ^ [_984569, _984571, _984573]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11678 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_984569), 11676 ^ [_984569, _984571, _984573]), _984571)))]]]]], (3280 ^ _779999) ^ [_829023, _829025, _829027, _829029] : [-(c_List_Olexn(_829029, _829025) = c_List_Olexn(_829027, _829023)), _829029 = _829027, _829025 = _829023], (41847 ^ _779999) ^ [_1599374, _1599376, _1599378, _1599380, _1599382] : [-(_1599374 = c_Orderings_Obot__class_Obot(tc_fun(_1599376, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599378, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599376, tc_fun(_1599378, tc_HOL_Obool)), _1599374), _1599380)), _1599382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599376, tc_fun(_1599378, tc_HOL_Obool)), _1599374), hAPP(hAPP(c_COMBC(_1599376, tc_fun(_1599378, tc_HOL_Obool), tc_fun(_1599378, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599378, tc_HOL_Obool), tc_fun(tc_fun(_1599378, tc_HOL_Obool), tc_fun(_1599378, tc_HOL_Obool)), _1599376), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599378, tc_HOL_Obool))), _1599380)), _1599382)))], (34321 ^ _779999) ^ [] : [-(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)))))], (45388 ^ _779999) ^ [_1688415, _1688417, _1688419] : [-(c_List_Obutlast(_1688415, hAPP(hAPP(c_List_Odrop(_1688415), _1688417), _1688419)) = hAPP(hAPP(c_List_Odrop(_1688415), _1688417), c_List_Obutlast(_1688415, _1688419)))], (49784 ^ _779999) ^ [_1784668, _1784670, _1784672] : [-(_1784670 = _1784672), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1784668, _1784668, hAPP(hAPP(c_COMBB(tc_fun(_1784668, tc_HOL_Obool), tc_fun(_1784668, tc_HOL_Obool), _1784668), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1784668), c_fNot)), c_fequal)), _1784670), _1784672)))], (18437 ^ _779999) ^ [_1115629, _1115631, _1115633, _1115635] : [class_Orderings_Oorder(_1115629), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1115629, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1115629, _1115631, _1115633)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1115629, _1115633, _1115635)) = c_Orderings_Obot__class_Obot(tc_fun(_1115629, tc_HOL_Obool)))], (1924 ^ _779999) ^ [_807157, _807159] : [-(class_Power_Opower(_807157)), _807159 = _807157, class_Power_Opower(_807159)], (32701 ^ _779999) ^ [_1393492, _1393494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1393492)), c_Int_OBit1(_1393494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393492), _1393494)))], (46666 ^ _779999) ^ [_1716160, _1716162] : [hAPP(c_Code__Numeral_Onat__of, _1716160) = hAPP(c_Code__Numeral_Onat__of, _1716162), -(_1716160 = _1716162)], (40385 ^ _779999) ^ [_1565918, _1565920] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1565918, _1565918, _1565918), c_Transitive__Closure_Ortrancl(_1565918, _1565920)), c_Transitive__Closure_Ortrancl(_1565918, _1565920)) = c_Transitive__Closure_Ortrancl(_1565918, _1565920))], (20738 ^ _779999) ^ [_1156384, _1156386, _1156388] : [class_Orderings_Olinorder(_1156384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156384), _1156386), _1156388)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1156384, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1156384), _1156386)), c_SetInterval_Oord__class_OatLeastAtMost(_1156384, _1156386, _1156388)) = hAPP(c_SetInterval_Oord__class_OatMost(_1156384), _1156388))], (31277 ^ _779999) ^ [_1365906, _1365908] : [_1365906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1365908, _1365906) = _1365908)], (32669 ^ _779999) ^ [_1392918, _1392920] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392918)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392920)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392920))))], (22153 ^ _779999) ^ [_1189709] : [-(hAPP(c_Set_OPow(_1189709), c_Orderings_Otop__class_Otop(tc_fun(_1189709, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1189709, tc_HOL_Obool), tc_HOL_Obool)))], (33675 ^ _779999) ^ [_1410020, _1410022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410020)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410022))), -(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(_1410022))), 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), _1410020)), c_Int_Onat))))))], (23063 ^ _779999) ^ [_1210404, _1210406] : [class_Orderings_Olinorder(_1210404), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210404), _1210406), _1210406) = _1210406)], (31971 ^ _779999) ^ [_1379750, _1379752] : [class_Int_Onumber__ring(_1379750), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1379750), hAPP(c_Int_Onumber__class_Onumber__of(_1379750), _1379752)) = hAPP(c_Int_Onumber__class_Onumber__of(_1379750), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1379752)))], (19075 ^ _779999) ^ [_1127710, _1127712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127710)), 19078 ^ _779999 : [(19087 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1127710), _1127712) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1127710 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1127712 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (19079 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1127710), _1127712) = c_Groups_Oone__class_Oone(tc_Int_Oint), 19082 ^ _779999 : [(19085 ^ _779999) ^ [] : [-(_1127712 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19083 ^ _779999) ^ [] : [-(_1127710 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (42508 ^ _779999) ^ [_1616803, _1616805, _1616807] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616803, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1616803, tc_HOL_Obool)), _1616805), _1616807)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616803, tc_HOL_Obool)), _1616805), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616803, tc_HOL_Obool), _1616807)))], (33609 ^ _779999) ^ [_1408431, _1408433] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1408431)))), _1408433) = 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)))), _1408431)), _1408433))], (27632 ^ _779999) ^ [_1299689] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1299689)) = _1299689)], (25766 ^ _779999) ^ [_1262910, _1262912, _1262914] : [-(hBOOL(hAPP(hAPP(c_member(_1262910), _1262912), _1262914))), -(hBOOL(hAPP(hAPP(c_member(_1262910), _1262912), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262910, tc_HOL_Obool)), _1262914))))], (41877 ^ _779999) ^ [_1599971, _1599973, _1599975, _1599977, _1599979] : [hBOOL(hAPP(hAPP(c_member(_1599971), _1599973), _1599975)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599977, tc_HOL_Obool)), hAPP(_1599979, _1599973)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599971, tc_fun(_1599977, tc_HOL_Obool)), _1599975), _1599979)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599971, tc_fun(_1599977, tc_HOL_Obool)), _1599975), _1599979))], (11871 ^ _779999) ^ [_988689, _988691, _988693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988689), _988691)), hBOOL(hAPP(c_Finite__Set_Ofinite(_988689), _988693)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988689), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988689, tc_HOL_Obool)), _988691), _988693))))], (45458 ^ _779999) ^ [_1690012, _1690014, _1690016, _1690018] : [-(_1690012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1690014), _1690012), hAPP(hAPP(c_List_Olist_OCons(_1690014), _1690016), _1690018)) = hAPP(hAPP(c_List_Odrop(_1690014), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1690012), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1690018))], (36571 ^ _779999) ^ [_1469035, _1469037, _1469039] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1469035, _1469037), _1469039)), 36574 ^ _779999 : [(36583 ^ _779999) ^ [] : [-(_1469037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36586 ^ _779999 : [(36595 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469037))), 36598 ^ _779999 : [(36601 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469039)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36599 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1469037), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469039))))]]], (36587 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469037)), 36590 ^ _779999 : [(36593 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469039)), _1469037)))], (36591 ^ _779999) ^ [] : [-(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), _1469039))))]]]]], (36577 ^ _779999) ^ [] : [_1469037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1469039) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36575 ^ _779999) ^ [] : [-(_1469035 = 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), _1469039)), _1469037)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1469039)))]]], (42612 ^ _779999) ^ [_1619029, _1619031, _1619033] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619029, tc_HOL_Obool)), _1619031), _1619033) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619029, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619029, tc_HOL_Obool)), _1619031), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619029, tc_HOL_Obool)), _1619033), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619029, tc_HOL_Obool), tc_HOL_Obool))))))], (44750 ^ _779999) ^ [_1672961, _1672963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672961)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672963))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672961), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672963)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672961)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672961)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1672963))))], (27424 ^ _779999) ^ [_1295884, _1295886] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1295884), _1295886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1295884), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1295886)))], (26568 ^ _779999) ^ [_1277706, _1277708, _1277710] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277706, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277706, tc_HOL_Obool)), _1277708), _1277710)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277706, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277706, tc_HOL_Obool)), _1277708)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277706, tc_HOL_Obool)), _1277710)))], (30445 ^ _779999) ^ [_1350479, _1350481, _1350483] : [class_Divides_Osemiring__div(_1350479), -(c_Divides_Odiv__class_Omod(_1350479, c_Divides_Odiv__class_Omod(_1350479, _1350481, _1350483), _1350483) = c_Divides_Odiv__class_Omod(_1350479, _1350481, _1350483))], (47449 ^ _779999) ^ [_1734070, _1734072, _1734074] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734070)), hAPP(c_List_Ofilter(_1734070, _1734072), _1734074))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734070)), hAPP(c_List_Ofilter(_1734070, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1734070), c_fNot), _1734072)), _1734074))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734070)), _1734074))], (8173 ^ _779999) ^ [_918432] : [hAPP(c_Nat_OSuc, _918432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34359 ^ _779999) ^ [_1422482, _1422484] : [class_Fields_Olinordered__field__inverse__zero(_1422482), class_Int_Onumber__ring(_1422482), 34366 ^ _779999 : [(34373 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422482), c_Groups_Ozero__class_Ozero(_1422482)), _1422484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422482), c_Groups_Ozero__class_Ozero(_1422482)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422482), _1422484), hAPP(c_Int_Onumber__class_Onumber__of(_1422482), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34367 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422482), c_Groups_Ozero__class_Ozero(_1422482)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422482), _1422484), hAPP(c_Int_Onumber__class_Onumber__of(_1422482), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422482), c_Groups_Ozero__class_Ozero(_1422482)), _1422484)))]]], (19553 ^ _779999) ^ [_1136349, _1136351, _1136353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136349)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1136351), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1136353)), 19560 ^ _779999 : [(19561 ^ _779999) ^ [_1136557] : [19563 ^ _779999 : [(19569 ^ _779999) ^ [] : [-(_1136557 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19565 ^ [_1136349, _1136351, _1136353, _1136557]), 19562 ^ [_1136349, _1136351, _1136353, _1136557]))], (19567 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19565 ^ [_1136349, _1136351, _1136353, _1136557]), _1136353)))], (19564 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19562 ^ [_1136349, _1136351, _1136353, _1136557]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1136349))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136351), _1136557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1136557), _1136349))))]]], (36529 ^ _779999) ^ [_1468127, _1468129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468127), _1468129) = 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), _1468127), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468129)))))], (32847 ^ _779999) ^ [_1396143] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396143))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1396143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37604 ^ _779999) ^ [_1494237, _1494239, _1494241, _1494243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494237), _1494243)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494241), _1494239))), -(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), _1494237), _1494239)), 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), _1494241), _1494243)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (52352 ^ _779999) ^ [] : [-(hBOOL(c_fTrue))], (44512 ^ _779999) ^ [_1668603, _1668605, _1668607] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668603), tc_List_Olist(_1668603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668603), tc_List_Olist(_1668603)), c_List_Olist_ONil(_1668603)), _1668605)), c_List_Olistrel(_1668603, _1668607))), -(_1668605 = c_List_Olist_ONil(_1668603))], (17379 ^ _779999) ^ [_1095198, _1095200, _1095202, _1095204, _1095206] : [class_Orderings_Oorder(_1095198), 17382 ^ _779999 : [(17403 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1095198, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1095198, _1095200, _1095202)), c_SetInterval_Oord__class_OatLeastAtMost(_1095198, _1095204, _1095206)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095204), _1095206)), 17406 ^ _779999 : [(17409 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095204), _1095200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095202), _1095206)), 17416 ^ _779999 : [(17419 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095198), _1095202), _1095206))], (17417 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095198), _1095204), _1095200))]]], (17407 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095200), _1095202)))]]], (17383 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1095198, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1095198, _1095200, _1095202)), c_SetInterval_Oord__class_OatLeastAtMost(_1095198, _1095204, _1095206))), 17386 ^ _779999 : [(17387 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095200), _1095202)), 17390 ^ _779999 : [(17395 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095198), _1095204), _1095200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095198), _1095202), _1095206)))], (17393 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095202), _1095206)))], (17391 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095204), _1095200)))]]], (17401 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095198), _1095204), _1095206)))]]]]], (10239 ^ _779999) ^ [_956357, _956359] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956357), _956359))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956357), hAPP(c_Nat_OSuc, _956359))), -(_956359 = _956357)], (35179 ^ _779999) ^ [_1440148, _1440150, _1440152, _1440154, _1440156, _1440158] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440148, tc_fun(_1440150, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1440148, tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_fun(_1440150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440150, tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_fun(_1440150, tc_HOL_Obool)), _1440148), c_COMBC(_1440150, tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440150, tc_prod(_1440148, _1440150)), tc_fun(_1440150, tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), _1440148), hAPP(c_COMBB(tc_prod(_1440148, _1440150), tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool), _1440150), c_member(tc_prod(_1440148, _1440150)))), c_Product__Type_OPair(_1440148, _1440150)))), _1440152)), hAPP(hAPP(c_COMBC(_1440148, tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_fun(_1440150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440150, tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_fun(_1440150, tc_HOL_Obool)), _1440148), c_COMBC(_1440150, tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440150, tc_prod(_1440148, _1440150)), tc_fun(_1440150, tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool)), _1440148), hAPP(c_COMBB(tc_prod(_1440148, _1440150), tc_fun(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool), tc_HOL_Obool), _1440150), c_member(tc_prod(_1440148, _1440150)))), c_Product__Type_OPair(_1440148, _1440150)))), _1440154)), _1440156), _1440158)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440148, _1440150)), hAPP(hAPP(c_Product__Type_OPair(_1440148, _1440150), _1440156), _1440158)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1440148, _1440150), tc_HOL_Obool)), _1440152), _1440154))))], (33949 ^ _779999) ^ [_1415197, _1415199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415197), _1415199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1415197)), c_Int_OBit0(_1415199))))], (2536 ^ _779999) ^ [_817403, _817405] : [_817405 = _817403, -(c_Nat_Onat_Onat__size(_817405) = c_Nat_Onat_Onat__size(_817403))], (6429 ^ _779999) ^ [_883633, _883635, _883637, _883639] : [class_Lattices_Osemilattice__sup(_883633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883633), _883635), _883637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883633), _883635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883633), _883637), _883639))))], (36318 ^ _779999) ^ [_1463980, _1463982, _1463984, _1463986] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1463980, _1463982), _1463984)), hBOOL(hAPP(hAPP(_1463982, _1463986), _1463984)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1463980, _1463982), _1463986)))], (39417 ^ _779999) ^ [_1542385, _1542387, _1542389] : [hBOOL(hAPP(_1542385, _1542387)), -(hBOOL(hAPP(_1542385, c_Hilbert__Choice_OEps(_1542389, _1542385))))], (32383 ^ _779999) ^ [_1387306, _1387308] : [class_Int_Onumber__ring(_1387306), class_Rings_Olinordered__idom(_1387306), 32390 ^ _779999 : [(32397 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387306), hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308)), c_Groups_Ozero__class_Ozero(_1387306)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1387306), hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308)) = hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308))], (32391 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387306), hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308)), c_Groups_Ozero__class_Ozero(_1387306))), -(hAPP(c_Groups_Oabs__class_Oabs(_1387306), hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1387306), hAPP(c_Int_Onumber__class_Onumber__of(_1387306), _1387308)))]]], (34517 ^ _779999) ^ [_1425108, _1425110, _1425112] : [class_Rings_Olinordered__semidom(_1425108), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425108), hAPP(hAPP(c_Power_Opower__class_Opower(_1425108), _1425110), 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(_1425108), _1425112), 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(_1425108), c_Groups_Ozero__class_Ozero(_1425108)), _1425112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425108), _1425110), _1425112)))], (1564 ^ _779999) ^ [_802657, _802659] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_802657)), _802659 = _802657, class_Groups_Oordered__cancel__ab__semigroup__add(_802659)], (5728 ^ _779999) ^ [_867649, _867651, _867653, _867655] : [-(hAPP(_867655, _867651) = hAPP(_867653, _867649)), _867655 = _867653, _867651 = _867649], (46610 ^ _779999) ^ [_1715006] : [-(_1715006 = 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)), _1715006)))], (46522 ^ _779999) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36112 ^ _779999) ^ [_1459868, _1459870, _1459872, _1459874] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459868, _1459870), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1459872), _1459874))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1459868, _1459870) = _1459874)], (6495 ^ _779999) ^ [_884769, _884771, _884773] : [class_Lattices_Olattice(_884769), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884769), _884771), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884769), _884771), _884773))))], (42536 ^ _779999) ^ [_1617573, _1617575, _1617577, _1617579] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617573, tc_HOL_Obool), hAPP(c_Set_Oimage(_1617575, tc_fun(_1617573, tc_HOL_Obool), _1617577), _1617579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617575, tc_fun(_1617573, tc_HOL_Obool)), _1617579), _1617577))], (46644 ^ _779999) ^ [_1715775, _1715777] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1715775)), hAPP(c_Code__Numeral_Oof__nat, _1715777)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1715775), _1715777)))], (35976 ^ _779999) ^ [_1457515, _1457517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457515), _1457517)), -(c_Divides_Odivmod__nat(_1457515, _1457517) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457515))], (43060 ^ _779999) ^ [_1629491, _1629493, _1629495] : [-(c_Nitpick_Otimes__frac(_1629491, _1629493, _1629495) = hAPP(hAPP(c_Nitpick_Ofrac(_1629491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1629491), _1629493)), hAPP(c_Nitpick_Onum(_1629491), _1629495))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1629491), _1629493)), hAPP(c_Nitpick_Odenom(_1629491), _1629495))))], (3880 ^ _779999) ^ [_838333, _838335, _838337, _838339, _838341, _838343, _838345, _838347, _838349, _838351] : [-(c_List_Ofoldr(_838351, _838347, _838343, _838339, _838335) = c_List_Ofoldr(_838349, _838345, _838341, _838337, _838333)), _838351 = _838349, _838347 = _838345, _838343 = _838341, _838339 = _838337, _838335 = _838333], (37439 ^ _779999) ^ [_1489787] : [-(hAPP(c_Relation_OField(_1489787), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489787, _1489787), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1489787, tc_HOL_Obool)))], (27684 ^ _779999) ^ [_1300447, _1300449] : [27685 ^ _779999 : [(27688 ^ _779999) ^ [] : [_1300449 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27686 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1300447))]], -(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), _1300447), _1300449))))], (5915 ^ _779999) ^ [_874190, _874192, _874194, _874196] : [class_Orderings_Oorder(_874190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874190), _874192), _874194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874190), _874196), _874192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874190), _874196), _874194)))], (7053 ^ _779999) ^ [_895928, _895930] : [class_Enum_Oenum(_895928), 7056 ^ _779999 : [(7064 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_895928), _895930)), 7067 ^ _779999 : [(7068 ^ _779999) ^ [_896146] : [-(hBOOL(hAPP(_895930, _896146)))]]], (7057 ^ _779999) ^ [] : [hBOOL(hAPP(_895930, 7058 ^ [_895928, _895930])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_895928), _895930)))]]], (42802 ^ _779999) ^ [_1623500, _1623502, _1623504, _1623506, _1623508, _1623510, _1623512] : [c_Finite__Set_Ofun__left__comm(_1623500, _1623502, _1623504), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1623500, _1623502, _1623504, _1623506, hAPP(hAPP(c_Set_Oinsert(_1623500), _1623508), _1623510)), _1623512)), -(hBOOL(hAPP(hAPP(c_member(_1623500), _1623508), _1623510))), 42814 ^ _779999 : [(42817 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1623500, _1623502, _1623504, _1623506, _1623510), 42813 ^ [_1623500, _1623502, _1623504, _1623506, _1623508, _1623510, _1623512])))], (42815 ^ _779999) ^ [] : [-(_1623512 = hAPP(hAPP(_1623504, _1623508), 42813 ^ [_1623500, _1623502, _1623504, _1623506, _1623508, _1623510, _1623512]))]]], (35844 ^ _779999) ^ [_1455255, _1455257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455257)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1455255, _1455257), c_Divides_OposDivAlg(_1455255, _1455257))))], (50658 ^ _779999) ^ [_1804039, _1804041, _1804043, _1804045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1804039, tc_fun(_1804041, tc_HOL_Obool)), _1804043), _1804045) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1804041, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1804041, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1804039, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1804041, tc_HOL_Obool)), c_HOL_OEx(_1804039)), hAPP(hAPP(c_COMBB(tc_fun(_1804039, tc_HOL_Obool), tc_fun(_1804039, tc_HOL_Obool), tc_fun(_1804041, tc_HOL_Obool)), hAPP(c_COMBS(_1804039, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1804039), c_fconj), hAPP(hAPP(c_COMBC(_1804039, tc_fun(_1804039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1804039)), _1804043)))), hAPP(hAPP(c_COMBC(tc_fun(_1804041, tc_HOL_Obool), tc_fun(_1804039, tc_fun(_1804041, tc_HOL_Obool)), tc_fun(_1804039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1804041, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1804039, tc_fun(_1804041, tc_HOL_Obool)), tc_fun(_1804039, tc_HOL_Obool)), tc_fun(_1804041, tc_HOL_Obool)), c_COMBB(tc_fun(_1804041, tc_HOL_Obool), tc_HOL_Obool, _1804039)), c_fequal)), _1804045))))))], (47723 ^ _779999) ^ [_1740994, _1740996] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740996)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1740996)) = c_List_Olist_ONil(tc_Nat_Onat))], (28596 ^ _779999) ^ [_1317455, _1317457, _1317459, _1317461] : [class_Fields_Ofield__inverse__zero(_1317455), -(_1317457 = c_Groups_Ozero__class_Ozero(_1317455)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317455), _1317457), _1317459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317455), _1317457), _1317461)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317455), _1317459), _1317461))], (18837 ^ _779999) ^ [_1123789, _1123791] : [18838 ^ _779999 : [(18839 ^ _779999) ^ [_1123842] : [_1123791 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123789), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123842))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123789), _1123791)))], (43035 ^ _779999) ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628729, _1628731)), _1628733), hAPP(hAPP(c_Relation_Orel__comp(_1628729, _1628735, _1628731), _1628737), _1628739))), 43041 ^ _779999 : [(43046 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628735, _1628731)), hAPP(hAPP(c_Product__Type_OPair(_1628735, _1628731), 43039 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739]), 43040 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739])), _1628739)))], (43044 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628729, _1628735)), hAPP(hAPP(c_Product__Type_OPair(_1628729, _1628735), 43038 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739]), 43039 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739])), _1628737)))], (43042 ^ _779999) ^ [] : [-(_1628733 = hAPP(hAPP(c_Product__Type_OPair(_1628729, _1628731), 43038 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739]), 43040 ^ [_1628729, _1628731, _1628733, _1628735, _1628737, _1628739]))]]], (20347 ^ _779999) ^ [_1150276, _1150278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150278)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1150276)), hAPP(c_Int_Onat, _1150278)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1150276), _1150278)))], (39062 ^ _779999) ^ [_1533969, _1533971, _1533973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533969, _1533969), tc_HOL_Obool)), _1533971), hAPP(hAPP(c_Product__Type_OSigma(_1533969, _1533969), _1533973), hAPP(c_COMBK(tc_fun(_1533969, tc_HOL_Obool), _1533969), _1533973)))), 39068 ^ _779999 : [(39071 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533969, _1533969)), hAPP(hAPP(c_Product__Type_OPair(_1533969, _1533969), 39067 ^ [_1533969, _1533971, _1533973]), 39067 ^ [_1533969, _1533971, _1533973])), _1533971))], (39069 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533969), 39067 ^ [_1533969, _1533971, _1533973]), _1533973)))]], -(c_Relation_Orefl__on(_1533969, _1533973, _1533971))], (41360 ^ _779999) ^ [_1589448, _1589450, _1589452, _1589454, _1589456] : [c_Finite__Set_Ofolding__one__idem(_1589448, _1589450, _1589452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589448), _1589454)), -(hAPP(_1589452, hAPP(hAPP(c_Set_Oinsert(_1589448), _1589456), _1589454)) = hAPP(hAPP(c_Finite__Set_Ofold(_1589448, _1589448, _1589450), _1589456), _1589454))], (4122 ^ _779999) ^ [_842134, _842136] : [_842136 = _842134, -(c_Groups_Oabs__class_Oabs(_842136) = c_Groups_Oabs__class_Oabs(_842134))], (8796 ^ _779999) ^ [_930975, _930977, _930979, _930981, _930983, _930985, _930987] : [hBOOL(hAPP(hAPP(c_member(_930975), _930977), _930979)), c_Nitpick_Ofold__graph_H(_930975, _930981, _930983, _930985, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930975, tc_HOL_Obool)), _930979), hAPP(hAPP(c_Set_Oinsert(_930975), _930977), c_Orderings_Obot__class_Obot(tc_fun(_930975, tc_HOL_Obool)))), _930987), -(c_Nitpick_Ofold__graph_H(_930975, _930981, _930983, _930985, _930979, hAPP(hAPP(_930983, _930977), _930987)))], (1904 ^ _779999) ^ [_806907, _806909] : [-(class_Orderings_Oord(_806907)), _806909 = _806907, class_Orderings_Oord(_806909)], (34865 ^ _779999) ^ [_1431945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1431945)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431945), c_Int_OMin)))], (10143 ^ _779999) ^ [_954955, _954957, _954959, _954961, _954963] : [c_Fun_Oinj__on(_954955, _954957, _954959, _954961), hBOOL(hAPP(hAPP(c_member(_954957), _954963), hAPP(c_Set_Oimage(_954955, _954957, _954959), _954961))), -(hAPP(_954959, hAPP(c_Fun_Othe__inv__into(_954955, _954957, _954961, _954959), _954963)) = _954963)], (21620 ^ _779999) ^ [_1173755, _1173757] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173755)), 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)), _1173755))), 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, _1173757))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17892 ^ _779999) ^ [] : [-(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))], (41777 ^ _779999) ^ [_1597433, _1597435, _1597437, _1597439, _1597441, _1597443] : [hBOOL(hAPP(hAPP(c_member(_1597433), _1597435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597437, tc_fun(_1597433, tc_HOL_Obool)), _1597439), _1597441))), -(hBOOL(hAPP(hAPP(c_member(_1597433), _1597435), hAPP(_1597441, _1597443)))), hBOOL(hAPP(hAPP(c_member(_1597437), _1597443), _1597439))], (31333 ^ _779999) ^ [_1366855, _1366857] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366855, _1366857) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1366855), _1366857)), _1366857)))], (14215 ^ _779999) ^ [_1033681, _1033683, _1033685, _1033687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1033681), _1033683)), hAPP(c_Finite__Set_Ocard(_1033685), hAPP(c_Set_Oimage(_1033681, _1033685, _1033687), _1033683)) = hAPP(c_Finite__Set_Ocard(_1033681), _1033683), -(c_Fun_Oinj__on(_1033681, _1033685, _1033687, _1033683))], (35516 ^ _779999) ^ [_1448542, _1448544, _1448546] : [-(hAPP(c_Divides_Oadjust(_1448542), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1448544), _1448546)) = 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), _1448546), _1448542)), 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)))), _1448544)), 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)))), _1448544)), _1448546))))], (21772 ^ _779999) ^ [_1177137, _1177139, _1177141] : [hBOOL(hAPP(_1177137, _1177139)), -(hAPP(c_Set_OCollect(_1177141), hAPP(hAPP(c_COMBS(_1177141, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177141), c_fconj), hAPP(hAPP(c_COMBC(_1177141, _1177141, tc_HOL_Obool), c_fequal), _1177139))), _1177137)) = hAPP(hAPP(c_Set_Oinsert(_1177141), _1177139), c_Orderings_Obot__class_Obot(tc_fun(_1177141, tc_HOL_Obool))))], (7785 ^ _779999) ^ [_911134, _911136, _911138, _911140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911134, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911134, tc_HOL_Obool)), _911136), hAPP(hAPP(c_Set_Oinsert(_911134), _911138), c_Orderings_Obot__class_Obot(tc_fun(_911134, tc_HOL_Obool))))), _911140)), hBOOL(hAPP(hAPP(c_member(_911134), _911138), _911136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911134, tc_HOL_Obool)), _911136), hAPP(hAPP(c_Set_Oinsert(_911134), _911138), _911140))))], (16251 ^ _779999) ^ [_1073544, _1073546] : [class_Rings_Olinordered__ring(_1073544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073544), _1073546), _1073546)), c_Groups_Ozero__class_Ozero(_1073544)))], (38636 ^ _779999) ^ [_1522008, _1522010, _1522012, _1522014] : [-(hAPP(c_Set_OCollect(tc_prod(_1522008, _1522010)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522008, _1522010, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1522008, tc_fun(_1522010, tc_HOL_Obool), tc_fun(_1522010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1522010, tc_HOL_Obool), tc_fun(_1522010, tc_HOL_Obool)), _1522008), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1522010)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522008), c_fconj), _1522012))), _1522014))) = hAPP(hAPP(c_Product__Type_OSigma(_1522008, _1522010), hAPP(c_Set_OCollect(_1522008), _1522012)), hAPP(hAPP(c_COMBB(tc_fun(_1522010, tc_HOL_Obool), tc_fun(_1522010, tc_HOL_Obool), _1522008), c_Set_OCollect(_1522010)), _1522014)))], (37745 ^ _779999) ^ [_1499129, _1499131, _1499133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499129, _1499129), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1499129, _1499129, _1499129), _1499131), _1499133)), _1499131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1499129, _1499131)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1499129, _1499133)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1499129, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1499129, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1499129, tc_HOL_Obool), tc_fun(_1499129, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1499129, _1499131))))], (35316 ^ _779999) ^ [_1444004, _1444006, _1444008, _1444010, _1444012, _1444014] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1444004, tc_fun(_1444006, tc_fun(_1444008, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1444004, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_fun(_1444006, tc_fun(_1444008, tc_HOL_Obool)), _1444004), hAPP(c_COMBC(_1444006, tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_fun(_1444008, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444008, tc_fun(tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_fun(_1444008, tc_HOL_Obool)), _1444006), c_COMBC(_1444008, tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444008, tc_prod(_1444006, _1444008)), tc_fun(_1444008, tc_fun(tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_HOL_Obool)), _1444006), hAPP(c_COMBB(tc_prod(_1444006, _1444008), tc_fun(tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool), tc_HOL_Obool), _1444008), c_member(tc_prod(_1444006, _1444008)))), c_Product__Type_OPair(_1444006, _1444008))))), _1444010)), _1444012), _1444014)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1444006, _1444008)), hAPP(hAPP(c_Product__Type_OPair(_1444006, _1444008), _1444012), _1444014)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1444004, tc_fun(tc_prod(_1444006, _1444008), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1444004, tc_HOL_Obool))), _1444010))))], (45155 ^ _779999) ^ [_1682335, _1682337, _1682339] : [_1682337 = c_List_Olist_ONil(_1682335), -(hAPP(hAPP(c_List_Oappend(_1682335), _1682337), _1682339) = _1682339)], (3208 ^ _779999) ^ [_827849, _827851] : [_827851 = _827849, -(c_Nitpick_ORep__Frac(_827851) = c_Nitpick_ORep__Frac(_827849))], (39429 ^ _779999) ^ [_1542599, _1542601, _1542603, _1542605] : [c_Finite__Set_Ofun__left__comm__idem(_1542599, _1542601, _1542603), -(hAPP(c_Fun_Ocomp(_1542601, _1542601, _1542601, hAPP(_1542603, _1542605)), hAPP(_1542603, _1542605)) = hAPP(_1542603, _1542605))], (51984 ^ _779999) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (23123 ^ _779999) ^ [_1211666, _1211668, _1211670, _1211672, _1211674] : [hBOOL(hAPP(_1211672, hAPP(_1211670, _1211674))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1211666, _1211668, _1211670), _1211672), _1211674)))], (17574 ^ _779999) ^ [_1099113, _1099115] : [17582 ^ _779999 : [(17585 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1099115, 17581 ^ [_1099113, _1099115])))], (17583 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17581 ^ [_1099113, _1099115]), _1099113)))]], 17575 ^ _779999 : [(17576 ^ _779999) ^ [_1099182] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1099182), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1099113))), hBOOL(hAPP(_1099115, _1099182))]]], (2888 ^ _779999) ^ [_822953, _822955, _822957, _822959, _822961, _822963] : [-(c_Hoare__Mirabelle_Opeek__and(_822963, _822959, _822955) = c_Hoare__Mirabelle_Opeek__and(_822961, _822957, _822953)), _822963 = _822961, _822959 = _822957, _822955 = _822953], (39093 ^ _779999) ^ [_1534589, _1534591, _1534593] : [c_Wellfounded_Oacyclic(_1534589, _1534591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534589, _1534589), tc_HOL_Obool)), _1534593), _1534591)), -(c_Wellfounded_Oacyclic(_1534589, _1534593))], (23019 ^ _779999) ^ [_1209482, _1209484, _1209486] : [class_Orderings_Olinorder(_1209482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209482), _1209484)), hBOOL(hAPP(hAPP(c_member(_1209482), _1209486), _1209484)), 23030 ^ _779999 : [(23037 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1209482, tc_HOL_Obool)), _1209484), hAPP(hAPP(c_Set_Oinsert(_1209482), _1209486), c_Orderings_Obot__class_Obot(tc_fun(_1209482, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1209482, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1209482, _1209484) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209482), _1209486), c_Big__Operators_Olinorder__class_OMin(_1209482, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1209482, tc_HOL_Obool)), _1209484), hAPP(hAPP(c_Set_Oinsert(_1209482), _1209486), c_Orderings_Obot__class_Obot(tc_fun(_1209482, tc_HOL_Obool)))))))], (23031 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1209482, tc_HOL_Obool)), _1209484), hAPP(hAPP(c_Set_Oinsert(_1209482), _1209486), c_Orderings_Obot__class_Obot(tc_fun(_1209482, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1209482, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1209482, _1209484) = _1209486)]]], (29702 ^ _779999) ^ [_1336967, _1336969, _1336971, _1336973, _1336975] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1336967, _1336969, _1336971), _1336973), hAPP(c_Nat_OSuc, _1336975)) = hAPP(hAPP(_1336971, _1336973), hAPP(hAPP(c_Power_Opower_Opower(_1336967, _1336969, _1336971), _1336973), _1336975)))], (27488 ^ _779999) ^ [_1297116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1297116), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1297116) = _1297116)], (23573 ^ _779999) ^ [_1220372, _1220374, _1220376, _1220378] : [hBOOL(hAPP(hAPP(c_member(_1220372), _1220374), _1220376)), -(hAPP(c_Set_Ovimage(_1220378, _1220372, hAPP(c_COMBK(_1220372, _1220378), _1220374)), _1220376) = c_Orderings_Otop__class_Otop(tc_fun(_1220378, tc_HOL_Obool)))], (31283 ^ _779999) ^ [_1365983, _1365985] : [-(_1365983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1365985, _1365983) = c_Nitpick_Onat__gcd(_1365983, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365985, _1365983)))], (38529 ^ _779999) ^ [_1519219, _1519221] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519219, _1519219), tc_HOL_Obool)), c_Relation_OId__on(_1519219, _1519221)), hAPP(hAPP(c_Product__Type_OSigma(_1519219, _1519219), _1519221), hAPP(c_COMBK(tc_fun(_1519219, tc_HOL_Obool), _1519219), _1519221)))))], (14856 ^ _779999) ^ [_1046659] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046659)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1046659)], (12527 ^ _779999) ^ [_1001589, _1001591, _1001593] : [class_Lattices_Olattice(_1001589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001589), _1001591)), -(_1001591 = c_Orderings_Obot__class_Obot(tc_fun(_1001589, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001589), _1001593)), -(_1001593 = c_Orderings_Obot__class_Obot(tc_fun(_1001589, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1001589, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001589, tc_HOL_Obool)), _1001591), _1001593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1001589), c_Big__Operators_Olattice__class_OInf__fin(_1001589, _1001591)), c_Big__Operators_Olattice__class_OInf__fin(_1001589, _1001593)))], (37282 ^ _779999) ^ [_1486434, _1486436, _1486438, _1486440, _1486442, _1486444, _1486446] : [-(hAPP(c_Product__Type_Oapsnd(_1486434, _1486436, _1486438, _1486440), hAPP(c_Product__Type_Oapfst(_1486442, _1486438, _1486434, _1486444), _1486446)) = hAPP(hAPP(c_Product__Type_OPair(_1486438, _1486436), hAPP(_1486444, hAPP(c_Product__Type_Ofst(_1486442, _1486434), _1486446))), hAPP(_1486440, hAPP(c_Product__Type_Osnd(_1486442, _1486434), _1486446))))], (33245 ^ _779999) ^ [_1402483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402483), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1402483)), c_Int_OPls)))], (42014 ^ _779999) ^ [_1604643, _1604645, _1604647, _1604649] : [-(hAPP(c_Set_OCollect(_1604643), hAPP(hAPP(c_COMBB(tc_fun(_1604645, tc_HOL_Obool), tc_HOL_Obool, _1604643), c_HOL_OAll(_1604645)), hAPP(hAPP(c_COMBB(tc_fun(_1604645, tc_HOL_Obool), tc_fun(_1604645, tc_HOL_Obool), _1604643), hAPP(c_COMBS(_1604645, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1604645), c_fimplies), hAPP(hAPP(c_COMBC(_1604645, tc_fun(_1604645, tc_HOL_Obool), tc_HOL_Obool), c_member(_1604645)), _1604647)))), _1604649))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604645, tc_fun(_1604643, tc_HOL_Obool)), _1604647), hAPP(hAPP(c_COMBB(tc_fun(_1604643, tc_HOL_Obool), tc_fun(_1604643, tc_HOL_Obool), _1604645), c_Set_OCollect(_1604643)), hAPP(c_COMBC(_1604643, _1604645, tc_HOL_Obool), _1604649))))], (20878 ^ _779999) ^ [_1159091, _1159093] : [class_Groups_Oordered__ab__group__add__abs(_1159091), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159091), c_Groups_Ozero__class_Ozero(_1159091)), hAPP(c_Groups_Oabs__class_Oabs(_1159091), _1159093))))], (4684 ^ _779999) ^ [_851303, _851305, _851307, _851309] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_851309, _851305) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_851307, _851303)), _851309 = _851307, _851305 = _851303], (850 ^ _779999) ^ [_793030, _793032] : [-(class_Fields_Olinordered__field(_793030)), _793032 = _793030, class_Fields_Olinordered__field(_793032)], (45748 ^ _779999) ^ [_1696332] : [class_Groups_Omonoid__add(_1696332), -(c_List_Omonoid__add__class_Olistsum(_1696332) = c_List_Ofoldl(_1696332, _1696332, c_Groups_Oplus__class_Oplus(_1696332), c_Groups_Ozero__class_Ozero(_1696332)))], (4418 ^ _779999) ^ [_847130, _847132, _847134, _847136] : [-(c_New__DSequence_Opos__single(_847136, _847132) = c_New__DSequence_Opos__single(_847134, _847130)), _847136 = _847134, _847132 = _847130], (29744 ^ _779999) ^ [_1337711, _1337713, _1337715, _1337717] : [_1337711 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337713), _1337715)), _1337717), -(_1337713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1337711), _1337713) = _1337715), 29751 ^ _779999 : [(29754 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337717), _1337713))], (29752 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337713)))]], 29759 ^ _779999 : [(29762 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337713), _1337717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337717), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29760 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337713))]]], (33527 ^ _779999) ^ [_1406972, _1406974] : [class_Int_Onumber__ring(_1406972), class_Rings_Olinordered__idom(_1406972), 33534 ^ _779999 : [(33541 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1406974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406972), c_Groups_Oone__class_Oone(_1406972)), hAPP(c_Int_Onumber__class_Onumber__of(_1406972), _1406974))))], (33535 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406972), c_Groups_Oone__class_Oone(_1406972)), hAPP(c_Int_Onumber__class_Onumber__of(_1406972), _1406974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1406974)))]]], (18822 ^ _779999) ^ [_1123500, _1123502] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1123500, _1123502))))], (17937 ^ _779999) ^ [_1106506, _1106508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106506)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106506), _1106508)))], (50973 ^ _779999) ^ [_1811445, _1811447, _1811449, _1811451, _1811453, _1811455] : [-(c_Partial__Function_Ofun__lub(_1811445, _1811447, _1811449, _1811451, _1811453, _1811455) = hAPP(_1811451, hAPP(c_Set_OCollect(_1811445), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool), tc_HOL_Obool, _1811445), c_HOL_OEx(tc_fun(_1811449, _1811445))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool), tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool), _1811445), hAPP(c_COMBS(tc_fun(_1811449, _1811445), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1811449, _1811445)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1811449, _1811445), tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1811449, _1811445))), _1811453)))), hAPP(hAPP(c_COMBC(_1811445, tc_fun(tc_fun(_1811449, _1811445), _1811445), tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1811445, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1811449, _1811445), _1811445), tc_fun(tc_fun(_1811449, _1811445), tc_HOL_Obool)), _1811445), c_COMBB(_1811445, tc_HOL_Obool, tc_fun(_1811449, _1811445))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1811449, _1811445), _1811449, _1811445), c_COMBI(tc_fun(_1811449, _1811445))), _1811455)))))))], (19073 ^ _779999) ^ [_1127684] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1127684) = _1127684)], (10357 ^ _779999) ^ [_958129, _958131, _958133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958129), _958131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958129), _958133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958133), _958131)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958133), _958129))))], (42141 ^ _779999) ^ [_1608305, _1608307, _1608309, _1608311, _1608313] : [_1608305 = c_Orderings_Obot__class_Obot(tc_fun(_1608307, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608307, tc_fun(_1608309, tc_HOL_Obool)), _1608305), hAPP(hAPP(c_COMBC(_1608307, tc_fun(_1608309, tc_HOL_Obool), tc_fun(_1608309, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608309, tc_HOL_Obool), tc_fun(tc_fun(_1608309, tc_HOL_Obool), tc_fun(_1608309, tc_HOL_Obool)), _1608307), c_Groups_Ominus__class_Ominus(tc_fun(_1608309, tc_HOL_Obool))), _1608311)), _1608313)) = c_Orderings_Otop__class_Otop(tc_fun(_1608309, tc_HOL_Obool)))], (4992 ^ _779999) ^ [_856241, _856243] : [_856243 = _856241, -(c_Code__Numeral_OSuc__code__numeral(_856243) = c_Code__Numeral_OSuc__code__numeral(_856241))], (6603 ^ _779999) ^ [_887072, _887074] : [_887072 = _887074, -(hAPP(c_Com_Ocom_OBODY, _887072) = hAPP(c_Com_Ocom_OBODY, _887074))], (37630 ^ _779999) ^ [_1494957] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1494957)), c_Int_OInteg)))], (25802 ^ _779999) ^ [_1263607, _1263609, _1263611] : [class_Rings_Oring(_1263607), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263607), hAPP(c_Groups_Ouminus__class_Ouminus(_1263607), _1263609)), hAPP(c_Groups_Ouminus__class_Ouminus(_1263607), _1263611)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263607), _1263609), _1263611))], (33409 ^ _779999) ^ [_1405058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1405058)), -(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), _1405058))))], (656 ^ _779999) ^ [_790067, _790069, _790071, _790073, _790075, _790077, _790079, _790081] : [-(c_List_Olistrelp(_790079, _790075, _790071, _790067)), c_List_Olistrelp(_790081, _790077, _790073, _790069), _790081 = _790079, _790077 = _790075, _790073 = _790071, _790069 = _790067], (41654 ^ _779999) ^ [_1595016] : [class_Groups_Oab__semigroup__mult(_1595016), -(c_Finite__Set_Ofun__left__comm(_1595016, _1595016, c_Groups_Otimes__class_Otimes(_1595016)))], (18939 ^ _779999) ^ [_1125571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1125571)))], (44566 ^ _779999) ^ [_1669592, _1669594, _1669596] : [c_List_Olist_ONil(_1669592) = hAPP(hAPP(c_List_Olist_OCons(_1669592), _1669594), _1669596)], (37254 ^ _779999) ^ [_1485777, _1485779] : [-(c_Equiv__Relations_Oequivp(_1485777, _1485779)), 37259 ^ _779999 : [(37262 ^ _779999) ^ [] : [hAPP(_1485779, 37255 ^ [_1485777, _1485779]) = hAPP(_1485779, 37256 ^ [_1485777, _1485779])], (37260 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1485779, 37255 ^ [_1485777, _1485779]), 37256 ^ [_1485777, _1485779])))]], 37263 ^ _779999 : [(37266 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1485779, 37255 ^ [_1485777, _1485779]), 37256 ^ [_1485777, _1485779]))], (37264 ^ _779999) ^ [] : [-(hAPP(_1485779, 37255 ^ [_1485777, _1485779]) = hAPP(_1485779, 37256 ^ [_1485777, _1485779]))]]], (33173 ^ _779999) ^ [_1401360, _1401362] : [class_Int_Onumber__ring(_1401360), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401360), hAPP(c_Int_Onumber__class_Onumber__of(_1401360), c_Int_OBit1(c_Int_OPls))), _1401362) = _1401362)], (46384 ^ _779999) ^ [_1710036] : [-(hAPP(c_List_Omap(_1710036, _1710036), c_COMBI(_1710036)) = c_Fun_Oid(tc_List_Olist(_1710036)))], (52056 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (45680 ^ _779999) ^ [_1694784, _1694786, _1694788] : [-(hAPP(c_List_Orotate(_1694784, hAPP(c_Nat_OSuc, _1694786)), _1694788) = hAPP(c_List_Orotate1(_1694784), hAPP(c_List_Orotate(_1694784, _1694786), _1694788)))], (11915 ^ _779999) ^ [_989507, _989509] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_989507, tc_HOL_Obool)), hAPP(c_Set_OPow(_989507), _989509))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_989507), _989509)))], (44107 ^ _779999) ^ [_1659824, _1659826] : [-(c_List_Obutlast(_1659824, _1659826) = hAPP(hAPP(c_List_Otake(_1659824), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659824)), _1659826)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1659826))], (46650 ^ _779999) ^ [_1715879] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1715879)) = _1715879)], (45875 ^ _779999) ^ [_1699115, _1699117, _1699119, _1699121] : [class_Orderings_Olinorder(_1699115), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699117, _1699115, _1699119), _1699121), c_List_Olist_ONil(_1699117)) = hAPP(hAPP(c_List_Olist_OCons(_1699117), _1699121), c_List_Olist_ONil(_1699117)))], (37763 ^ _779999) ^ [_1499726, _1499728, _1499730, _1499732, _1499734, _1499736, _1499738] : [c_Typedef_Otype__definition(_1499726, _1499728, _1499730, _1499732, _1499734), hBOOL(hAPP(hAPP(c_member(_1499728), _1499736), _1499734)), hBOOL(hAPP(hAPP(c_member(_1499728), _1499738), _1499734)), 37774 ^ _779999 : [(37781 ^ _779999) ^ [] : [_1499736 = _1499738, -(hAPP(_1499732, _1499736) = hAPP(_1499732, _1499738))], (37775 ^ _779999) ^ [] : [hAPP(_1499732, _1499736) = hAPP(_1499732, _1499738), -(_1499736 = _1499738)]]], (17669 ^ _779999) ^ [_1101243, _1101245] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101243), _1101245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101245), _1101243))], (5855 ^ _779999) ^ [_873006, _873008, _873010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873006, tc_HOL_Obool)), _873008), _873010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873006, tc_HOL_Obool)), _873010), _873008)), -(_873008 = _873010)], (33081 ^ _779999) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (26839 ^ _779999) ^ [_1283582, _1283584] : [-(hAPP(c_Set_OPow(_1283582), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283582, tc_HOL_Obool)), _1283584)) = hAPP(c_Set_OCollect(tc_fun(_1283582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1283582, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1283582, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1283582, tc_HOL_Obool), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1283582, tc_HOL_Obool)), c_COMBS(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1283582, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1283582, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1283582, tc_HOL_Obool), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_fun(_1283582, tc_HOL_Obool)), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_fun(_1283582, tc_HOL_Obool)), tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1283582, tc_HOL_Obool)), c_COMBB(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1283582, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1283582, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1283582, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1283582, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1283582, tc_HOL_Obool)), _1283584)), c_Set_OPow(_1283582))))))], (11056 ^ _779999) ^ [_971394, _971396, _971398, _971400] : [class_Lattices_Osemilattice__inf(_971394), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971394), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971394), _971396), _971398)), _971400) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971394), _971396), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971394), _971398), _971400)))], (18891 ^ _779999) ^ [_1124695, _1124697] : [18892 ^ _779999 : [(18895 ^ _779999) ^ [] : [_1124695 = _1124697], (18893 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124695), _1124697))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124697), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33717 ^ _779999) ^ [_1410996, _1410998, _1411000, _1411002, _1411004] : [-(hAPP(c_Nat_Onat_Onat__rec(_1410996, _1410998, _1411000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411002)), _1411004)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1410996), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411002))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1410996, _1410996), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1410996, tc_fun(_1410996, _1410996)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410996, tc_fun(_1410996, _1410996)), tc_Int_Oint), c_If(_1410996)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1410996, _1410998, _1411000), _1411004))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1410996, _1410996), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1410996, _1410996), tc_Int_Oint), _1411000), 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)), _1411004))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1410996, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1410996, _1410998, _1411000)), 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)), _1411004))))))], (7117 ^ _779999) ^ [_897084, _897086, _897088, _897090] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897084, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897084), _897086), _897088)), _897090))), hBOOL(hAPP(hAPP(c_member(_897084), _897086), _897090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897084, tc_HOL_Obool)), _897088), _897090))], (9710 ^ _779999) ^ [_945091, _945093, _945095] : [-(c_Nat_Onat_Onat__case(_945091, _945093, _945095, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _945093)], (23811 ^ _779999) ^ [_1224569, _1224571, _1224573] : [class_Orderings_Olinorder(_1224569), -(_1224571 = c_Orderings_Obot__class_Obot(tc_fun(_1224569, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1224569, tc_HOL_Obool)), _1224571), _1224573)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224569), _1224573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224569), hAPP(c_Finite__Set_Ofold1(_1224569, c_Orderings_Oord__class_Omin(_1224569)), _1224573)), hAPP(c_Finite__Set_Ofold1(_1224569, c_Orderings_Oord__class_Omin(_1224569)), _1224571))))], (15959 ^ _779999) ^ [_1068146, _1068148, _1068150] : [class_Rings_Olinordered__ring__strict(_1068146), 15962 ^ _779999 : [(15977 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068146), _1068148), _1068150)))), 15978 ^ _779999 : [(15985 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), _1068148), c_Groups_Ozero__class_Ozero(_1068146))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), _1068150), c_Groups_Ozero__class_Ozero(_1068146)))], (15979 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), _1068148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), _1068150))]]], (15963 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068146), _1068148), _1068150))), 15968 ^ _779999 : [(15971 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), _1068150)))], (15969 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), c_Groups_Ozero__class_Ozero(_1068146)), _1068148)))]], 15972 ^ _779999 : [(15975 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), _1068150), c_Groups_Ozero__class_Ozero(_1068146))))], (15973 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068146), _1068148), c_Groups_Ozero__class_Ozero(_1068146))))]]]]], (51920 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (49898 ^ _779999) ^ [_1787606, _1787608, _1787610, _1787612] : [49905 ^ _779999 : [(49908 ^ _779999) ^ [] : [_1787608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49906 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1787612, _1787610)))]], 49899 ^ _779999 : [(49900 ^ _779999) ^ [_1787678] : [hBOOL(hAPP(hAPP(c_member(_1787606), _1787678), hAPP(c_List_Oset(_1787606), c_List_Oreplicate(_1787606, _1787608, _1787610)))), hBOOL(hAPP(_1787612, _1787678))]]], (52112 ^ _779999) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (38638 ^ _779999) ^ [_1522148, _1522150, _1522152, _1522154] : [_1522148 = c_Orderings_Obot__class_Obot(tc_fun(_1522150, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1522152, _1522150), _1522152, c_Product__Type_Ofst(_1522152, _1522150)), hAPP(hAPP(c_Product__Type_OSigma(_1522152, _1522150), _1522154), hAPP(c_COMBK(tc_fun(_1522150, tc_HOL_Obool), _1522152), _1522148))) = c_Orderings_Obot__class_Obot(tc_fun(_1522152, tc_HOL_Obool)))], (8336 ^ _779999) ^ [_921856, _921858, _921860] : [-(hAPP(hAPP(c_Set_Oinsert(_921856), _921858), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921856, tc_HOL_Obool)), _921860), hAPP(hAPP(c_Set_Oinsert(_921856), _921858), c_Orderings_Obot__class_Obot(tc_fun(_921856, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_921856), _921858), _921860))], (37343 ^ _779999) ^ [_1487944, _1487946, _1487948, _1487950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1487944), _1487946)), -(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), _1487944), _1487948)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1487946), _1487950))), c_FunDef_Opair__less)))], (41827 ^ _779999) ^ [_1598549, _1598551, _1598553, _1598555] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598549, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598551, tc_fun(_1598549, tc_HOL_Obool)), _1598553), _1598555)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598551, tc_fun(_1598549, tc_HOL_Obool)), _1598553), hAPP(hAPP(c_COMBB(tc_fun(_1598549, tc_HOL_Obool), tc_fun(_1598549, tc_HOL_Obool), _1598551), c_Groups_Ouminus__class_Ouminus(tc_fun(_1598549, tc_HOL_Obool))), _1598555)))], (30854 ^ _779999) ^ [_1358328, _1358330, _1358332] : [-(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), _1358328), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1358330), _1358328))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358330, _1358328))), _1358332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358330), _1358332))], (1324 ^ _779999) ^ [_799657, _799659] : [-(class_Divides_Oring__div(_799657)), _799659 = _799657, class_Divides_Oring__div(_799659)], (38314 ^ _779999) ^ [_1512798, _1512800, _1512802, _1512804] : [hBOOL(hAPP(hAPP(c_member(_1512798), _1512800), hAPP(c_Relation_ORange(_1512802, _1512798), _1512804))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1512802, _1512798)), hAPP(hAPP(c_Product__Type_OPair(_1512802, _1512798), 38317 ^ [_1512798, _1512800, _1512802, _1512804]), _1512800)), _1512804)))], (19815 ^ _779999) ^ [_1141349, _1141351, _1141353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141349)), 19818 ^ _779999 : [(19819 ^ _779999) ^ [_1141483] : [19821 ^ _779999 : [(19827 ^ _779999) ^ [] : [-(_1141483 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19823 ^ [_1141349, _1141351, _1141353, _1141483]), 19820 ^ [_1141349, _1141351, _1141353, _1141483]))], (19825 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19823 ^ [_1141349, _1141351, _1141353, _1141483]), _1141351)))], (19822 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19820 ^ [_1141349, _1141351, _1141353, _1141483]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1141349))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141353), _1141483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141353), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141483), _1141349))))]]], (20910 ^ _779999) ^ [_1159602, _1159604] : [class_Groups_Oordered__ab__group__add__abs(_1159602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159602), hAPP(c_Groups_Oabs__class_Oabs(_1159602), _1159604)), c_Groups_Ozero__class_Ozero(_1159602)))], (29954 ^ _779999) ^ [_1341587, _1341589, _1341591] : [-(_1341587 = 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), _1341587), _1341589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1341587), _1341591)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341589), _1341591))], (28572 ^ _779999) ^ [_1317006, _1317008, _1317010, _1317012, _1317014] : [class_Fields_Ofield(_1317006), -(_1317008 = c_Groups_Ozero__class_Ozero(_1317006)), -(_1317010 = c_Groups_Ozero__class_Ozero(_1317006)), 28583 ^ _779999 : [(28590 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317006), _1317012), _1317010) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317006), _1317014), _1317008), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317006), _1317012), _1317008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317006), _1317014), _1317010))], (28584 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317006), _1317012), _1317008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317006), _1317014), _1317010), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317006), _1317012), _1317010) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317006), _1317014), _1317008))]]], (52144 ^ _779999) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (9945 ^ _779999) ^ [_951222] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _951222))))], (52410 ^ _779999) ^ [_1834934, _1834936] : [-(hBOOL(_1834934)), -(hBOOL(hAPP(hAPP(c_fimplies, _1834934), _1834936)))], (51712 ^ _779999) ^ [_1826783, _1826785, _1826787, _1826789, _1826791, _1826793] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1826783, _1826785, _1826787, _1826789), _1826791), _1826793) = hAPP(_1826789, hAPP(hAPP(c_Product__Type_OPair(_1826783, _1826785), _1826791), _1826793)))], (27900 ^ _779999) ^ [_1304505, _1304507, _1304509, _1304511] : [class_Rings_Olinordered__semidom(_1304505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304505), hAPP(hAPP(c_Power_Opower__class_Opower(_1304505), _1304507), _1304509)), hAPP(hAPP(c_Power_Opower__class_Opower(_1304505), _1304511), _1304509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304505), c_Groups_Ozero__class_Ozero(_1304505)), _1304511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304505), _1304507), _1304511)))], (7765 ^ _779999) ^ [_910690, _910692, _910694, _910696] : [-(c_Hoare__Mirabelle_Otriple__valid(_910690, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910690), _910692), hAPP(c_Com_Ocom_OBODY, _910694)), _910696)))], (3750 ^ _779999) ^ [_836278, _836280] : [_836280 = _836278, -(c_Int_Onumber__class_Onumber__of(_836280) = c_Int_Onumber__class_Onumber__of(_836278))], (13489 ^ _779999) ^ [_1020316, _1020318, _1020320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020316), _1020318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020316), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020320), _1020318))))], (52258 ^ _779999) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50887 ^ _779999) ^ [_1809782, _1809784] : [c_Relation_Oantisym(_1809782, hAPP(c_Relation_Oconverse(_1809782, _1809782), _1809784)), -(c_Relation_Oantisym(_1809782, _1809784))], (22870 ^ _779999) ^ [_1204790, _1204792, _1204794, _1204796, _1204798, _1204800] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204790, tc_fun(_1204792, tc_HOL_Obool)), _1204794), hAPP(hAPP(c_COMBB(_1204796, tc_fun(_1204792, tc_HOL_Obool), _1204790), _1204798), _1204800)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204796, tc_fun(_1204792, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1204790, _1204796, _1204800), _1204794)), _1204798))], (51886 ^ _779999) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (20078 ^ _779999) ^ [_1145954, _1145956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145956)), 20085 ^ _779999 : [(20092 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145954), _1145956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1145954)), hAPP(c_Int_Onat, _1145956))))], (20086 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1145954)), hAPP(c_Int_Onat, _1145956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145954), _1145956)))]]], (5200 ^ _779999) ^ [_859531, _859533] : [_859533 = _859531, -(c_List_Oset(_859533) = c_List_Oset(_859531))], (46954 ^ _779999) ^ [_1722852, _1722854, _1722856, _1722858, _1722860, _1722862, _1722864] : [c_List_Olist__all2(_1722852, _1722854, _1722856, _1722858, hAPP(hAPP(c_List_Omap(_1722860, _1722854), _1722862), _1722864)), -(c_List_Olist__all2(_1722852, _1722860, hAPP(hAPP(c_COMBC(_1722852, tc_fun(_1722860, _1722854), tc_fun(_1722860, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1722854, tc_HOL_Obool), tc_fun(tc_fun(_1722860, _1722854), tc_fun(_1722860, tc_HOL_Obool)), _1722852), c_COMBB(_1722854, tc_HOL_Obool, _1722860)), _1722856)), _1722862), _1722858, _1722864))], (14049 ^ _779999) ^ [_1030546, _1030548] : [-(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)), _1030546), _1030548))], (23239 ^ _779999) ^ [_1213622, _1213624, _1213626] : [class_Orderings_Olinorder(_1213622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213622), _1213624), _1213626)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213622), _1213626), _1213624) = _1213624)], (1264 ^ _779999) ^ [_798907, _798909] : [-(class_Rings_Olinordered__ring(_798907)), _798909 = _798907, class_Rings_Olinordered__ring(_798909)], (47070 ^ _779999) ^ [_1725274, _1725276, _1725278, _1725280, _1725282] : [c_List_Olist__all2(_1725274, _1725276, _1725278, _1725280, _1725282), 47073 ^ _779999 : [(47076 ^ _779999) ^ [_1725437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725274)), _1725280))), -(hBOOL(hAPP(hAPP(_1725278, hAPP(hAPP(c_List_Onth(_1725274), _1725280), _1725437)), hAPP(hAPP(c_List_Onth(_1725276), _1725282), _1725437))))], (47074 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725274)), _1725280) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725276)), _1725282))]]], (33383 ^ _779999) ^ [_1404647, _1404649] : [class_Int_Onumber__ring(_1404647), class_Rings_Olinordered__idom(_1404647), 33390 ^ _779999 : [(33397 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404649), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404647), hAPP(c_Int_Onumber__class_Onumber__of(_1404647), _1404649)), c_Groups_Ozero__class_Ozero(_1404647))))], (33391 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404647), hAPP(c_Int_Onumber__class_Onumber__of(_1404647), _1404649)), c_Groups_Ozero__class_Ozero(_1404647))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404649), c_Int_OPls)))]]], (31495 ^ _779999) ^ [_1369662, _1369664, _1369666] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369662), _1369664)), 31501 ^ _779999 : [(31504 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1369666, 31500 ^ [_1369662, _1369664, _1369666])))], (31502 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369662), 31500 ^ [_1369662, _1369664, _1369666]), _1369664)))]], -(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(_1369662, tc_Nat_Onat), _1369666), _1369664))))], (21223 ^ _779999) ^ [_1166307, _1166309, _1166311] : [class_Orderings_Oord(_1166307), 21226 ^ _779999 : [(21233 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166307), _1166311), _1166309)), -(hBOOL(hAPP(hAPP(c_member(_1166307), _1166309), hAPP(c_SetInterval_Oord__class_OatLeast(_1166307), _1166311))))], (21227 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1166307), _1166309), hAPP(c_SetInterval_Oord__class_OatLeast(_1166307), _1166311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166307), _1166311), _1166309)))]]], (48068 ^ _779999) ^ [_1747179, _1747181, _1747183] : [class_Orderings_Olinorder(_1747179), -(c_List_Olinorder__class_Osorted(_1747179, hAPP(c_List_Ofilter(_1747179, hAPP(hAPP(c_COMBC(_1747179, _1747179, tc_HOL_Obool), c_fequal), hAPP(_1747181, _1747183))), _1747183)))], (30641 ^ _779999) ^ [_1354479, _1354481, _1354483, _1354485] : [class_Divides_Oring__div(_1354479), c_Divides_Odiv__class_Omod(_1354479, _1354481, _1354483) = c_Divides_Odiv__class_Omod(_1354479, _1354485, _1354483), -(c_Divides_Odiv__class_Omod(_1354479, hAPP(c_Groups_Ouminus__class_Ouminus(_1354479), _1354481), _1354483) = c_Divides_Odiv__class_Omod(_1354479, hAPP(c_Groups_Ouminus__class_Ouminus(_1354479), _1354485), _1354483))], (5905 ^ _779999) ^ [_874070, _874072, _874074] : [class_Orderings_Olinorder(_874070), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874070), _874072), _874074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874070), _874074), _874072)))], (46187 ^ _779999) ^ [_1704718, _1704720, _1704722, _1704724, _1704726] : [-(hAPP(c_List_Orotate(_1704718, _1704720), hAPP(hAPP(c_List_Omap(_1704722, _1704718), _1704724), _1704726)) = hAPP(hAPP(c_List_Omap(_1704722, _1704718), _1704724), hAPP(c_List_Orotate(_1704722, _1704720), _1704726)))], (43100 ^ _779999) ^ [_1630343] : [-(c_Nitpick_Odenom(_1630343) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1630343, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1630343)))], (22525 ^ _779999) ^ [_1196933, _1196935, _1196937, _1196939, _1196941] : [c_Fun_Oinj__on(_1196933, _1196935, _1196937, c_Orderings_Otop__class_Otop(tc_fun(_1196933, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1196933, _1196935, _1196937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1196933, tc_HOL_Obool)), _1196939), _1196941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1196935, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1196933, _1196935, _1196937), _1196939)), hAPP(c_Set_Oimage(_1196933, _1196935, _1196937), _1196941)))], (33101 ^ _779999) ^ [_1400261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400261), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400261)), c_Int_OPls)))], (36485 ^ _779999) ^ [_1467141, _1467143, _1467145, _1467147, _1467149] : [-(hAPP(c_Product__Type_Ofst(_1467141, _1467143), hAPP(c_Product__Type_Oapsnd(_1467145, _1467143, _1467141, _1467147), _1467149)) = hAPP(c_Product__Type_Ofst(_1467141, _1467145), _1467149))], (47518 ^ _779999) ^ [_1735669, _1735671, _1735673] : [-(hAPP(c_List_Oset(_1735669), hAPP(c_List_Ofilter(_1735669, _1735671), _1735673)) = hAPP(c_Set_OCollect(_1735669), hAPP(hAPP(c_COMBS(_1735669, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1735669), c_fconj), hAPP(hAPP(c_COMBC(_1735669, tc_fun(_1735669, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735669)), hAPP(c_List_Oset(_1735669), _1735673)))), _1735671)))], (22878 ^ _779999) ^ [_1205149, _1205151, _1205153, _1205155, _1205157] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205149, tc_fun(_1205151, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1205149, tc_HOL_Obool)), _1205153), _1205155)), _1205157) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1205151, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205149, tc_fun(_1205151, tc_HOL_Obool)), _1205153), _1205157)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205149, tc_fun(_1205151, tc_HOL_Obool)), _1205155), _1205157)))], (34965 ^ _779999) ^ [_1433471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433471), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433471)), c_Int_OMin)))], (11312 ^ _779999) ^ [_976168, _976170, _976172, _976174] : [class_Lattices_Odistrib__lattice(_976168), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976168), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976168), _976170), _976172)), _976174) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976168), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976168), _976170), _976174)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976168), _976172), _976174)))], (12413 ^ _779999) ^ [_999732, _999734, _999736] : [class_Lattices_Olattice(_999732), hBOOL(hAPP(c_Finite__Set_Ofinite(_999732), _999734)), hBOOL(hAPP(hAPP(c_member(_999732), _999736), _999734)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_999732), _999736), c_Big__Operators_Olattice__class_OInf__fin(_999732, _999734)) = c_Big__Operators_Olattice__class_OInf__fin(_999732, _999734))], (19453 ^ _779999) ^ [_1134705, _1134707] : [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)), _1134705)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1134705), _1134707)))], (43517 ^ _779999) ^ [_1643600, _1643602, _1643604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1643600, _1643600), tc_HOL_Obool)), _1643602), hAPP(hAPP(c_Product__Type_OSigma(_1643600, _1643600), _1643604), hAPP(c_COMBK(tc_fun(_1643600, tc_HOL_Obool), _1643600), _1643604)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1643600), tc_List_Olist(_1643600)), tc_HOL_Obool)), c_List_Olistrel(_1643600, _1643602)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1643600), tc_List_Olist(_1643600)), c_List_Olists(_1643600, _1643604)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1643600), tc_HOL_Obool), tc_List_Olist(_1643600)), c_List_Olists(_1643600, _1643604))))))], (31479 ^ _779999) ^ [_1369400, _1369402] : [class_Rings_Olinordered__idom(_1369400), 31482 ^ _779999 : [(31489 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369400), _1369402), c_Groups_Ozero__class_Ozero(_1369400))), -(c_Groups_Osgn__class_Osgn(_1369400, _1369402) = hAPP(c_Groups_Ouminus__class_Ouminus(_1369400), c_Groups_Oone__class_Oone(_1369400)))], (31483 ^ _779999) ^ [] : [c_Groups_Osgn__class_Osgn(_1369400, _1369402) = hAPP(c_Groups_Ouminus__class_Ouminus(_1369400), c_Groups_Oone__class_Oone(_1369400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369400), _1369402), c_Groups_Ozero__class_Ozero(_1369400))))]]], (35494 ^ _779999) ^ [_1448244, _1448246] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448244), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35497 ^ _779999 : [(35506 ^ _779999) ^ [] : [-(c_Nitpick_Onorm__frac(_1448246, _1448244) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1448246), _1448244)), 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), _1448246))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1448244)))), -(_1448246 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1448244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35498 ^ _779999) ^ [] : [35499 ^ _779999 : [(35502 ^ _779999) ^ [] : [_1448244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35500 ^ _779999) ^ [] : [_1448246 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1448246, _1448244) = 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)))]]], (16871 ^ _779999) ^ [_1085096, _1085098, _1085100, _1085102] : [class_Orderings_Oorder(_1085096), 16874 ^ _779999 : [(16883 ^ _779999) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1085096, _1085098, _1085100) = hAPP(hAPP(c_Set_Oinsert(_1085096), _1085102), c_Orderings_Obot__class_Obot(tc_fun(_1085096, tc_HOL_Obool)))), _1085098 = _1085100, _1085100 = _1085102], (16875 ^ _779999) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1085096, _1085098, _1085100) = hAPP(hAPP(c_Set_Oinsert(_1085096), _1085102), c_Orderings_Obot__class_Obot(tc_fun(_1085096, tc_HOL_Obool))), 16878 ^ _779999 : [(16881 ^ _779999) ^ [] : [-(_1085100 = _1085102)], (16879 ^ _779999) ^ [] : [-(_1085098 = _1085100)]]]]], (38417 ^ _779999) ^ [_1515876, _1515878, _1515880, _1515882, _1515884] : [hBOOL(hAPP(hAPP(_1515876, _1515878), _1515880)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1515882, _1515884, _1515876), _1515878)))], (12065 ^ _779999) ^ [_992648, _992650, _992652, _992654, _992656, _992658, _992660, _992662] : [c_Finite__Set_Ofolding__image__simple(_992648, _992650, _992652, _992654, _992656, _992658), hBOOL(hAPP(c_Finite__Set_Ofinite(_992650), _992660)), hBOOL(hAPP(c_Finite__Set_Ofinite(_992650), _992662)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_992650, tc_HOL_Obool)), _992660), _992662) = c_Orderings_Obot__class_Obot(tc_fun(_992650, tc_HOL_Obool)), -(hAPP(_992658, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992650, tc_HOL_Obool)), _992660), _992662)) = hAPP(hAPP(_992652, hAPP(_992658, _992660)), hAPP(_992658, _992662)))], (27448 ^ _779999) ^ [_1296414, _1296416, _1296418] : [class_Fields_Ofield(_1296414), -(_1296416 = c_Groups_Oone__class_Oone(_1296414)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1296414), hAPP(c_Power_Opower__class_Opower(_1296414), _1296416)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1296418)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1296414), hAPP(hAPP(c_Power_Opower__class_Opower(_1296414), _1296416), _1296418)), c_Groups_Oone__class_Oone(_1296414))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1296414), _1296416), c_Groups_Oone__class_Oone(_1296414))))], (40499 ^ _779999) ^ [_1568666] : [-(hAPP(c_Relation_ODomain(_1568666, _1568666), c_Relation_OId(_1568666)) = c_Orderings_Otop__class_Otop(tc_fun(_1568666, tc_HOL_Obool)))], (27404 ^ _779999) ^ [_1295567, _1295569] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295567)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295569), 27407 ^ _779999 : [(27410 ^ _779999) ^ [] : [-(_1295569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27408 ^ _779999) ^ [] : [-(_1295567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16231 ^ _779999) ^ [_1073168, _1073170, _1073172] : [class_Rings_Oordered__cancel__semiring(_1073168), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073168), _1073170), _1073172)), c_Groups_Ozero__class_Ozero(_1073168)))), 16236 ^ _779999 : [(16243 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073168), _1073170), c_Groups_Ozero__class_Ozero(_1073168))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073168), c_Groups_Ozero__class_Ozero(_1073168)), _1073172))], (16237 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073168), c_Groups_Ozero__class_Ozero(_1073168)), _1073170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073168), _1073172), c_Groups_Ozero__class_Ozero(_1073168)))]]], (39533 ^ _779999) ^ [_1544879, _1544881, _1544883, _1544885, _1544887, _1544889, _1544891, _1544893] : [class_Groups_Ocomm__monoid__mult(_1544879), c_Fun_Oinj__on(_1544881, _1544883, _1544885, _1544887), _1544889 = hAPP(c_Set_Oimage(_1544881, _1544883, _1544885), _1544887), _1544891 = hAPP(c_Fun_Ocomp(_1544883, _1544879, _1544881, _1544893), _1544885), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544883, _1544879), _1544893), _1544889) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544881, _1544879), _1544891), _1544887))], (19487 ^ _779999) ^ [] : [-(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)))], (13363 ^ _779999) ^ [_1017870, _1017872] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017870), hAPP(c_Nat_OSuc, _1017872)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017870), _1017872)))], (24994 ^ _779999) ^ [_1249156, _1249158] : [class_Orderings_Olinorder(_1249156), -(c_Big__Operators_Olattice_OSup__fin(_1249156, c_Orderings_Oord__class_Omax(_1249156), hAPP(hAPP(c_Set_Oinsert(_1249156), _1249158), c_Orderings_Obot__class_Obot(tc_fun(_1249156, tc_HOL_Obool)))) = _1249158)], (10291 ^ _779999) ^ [_957122, _957124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _957122)), hAPP(c_Nat_OSuc, _957124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957122), _957124)))], (51922 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (40126 ^ _779999) ^ [_1558850, _1558852, _1558854, _1558856, _1558858] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1558850, _1558852, _1558850, _1558854), hAPP(c_Product__Type_OPair(_1558852, _1558850), _1558856)), _1558858) = hAPP(_1558858, _1558856))], (41666 ^ _779999) ^ [_1595230, _1595232, _1595234, _1595236, _1595238] : [c_Finite__Set_Ofun__left__comm(_1595230, _1595232, _1595234), -(c_Finite__Set_Ofun__left__comm(_1595236, _1595232, hAPP(hAPP(c_COMBB(_1595230, tc_fun(_1595232, _1595232), _1595236), _1595234), _1595238)))], (26608 ^ _779999) ^ [_1278756, _1278758] : [class_Rings_Oring__1(_1278756), hBOOL(hAPP(hAPP(c_member(_1278756), _1278758), c_Int_Oring__1__class_OInts(_1278756))), -(hBOOL(hAPP(hAPP(c_member(_1278756), hAPP(c_Groups_Ouminus__class_Ouminus(_1278756), _1278758)), c_Int_Oring__1__class_OInts(_1278756))))], (15579 ^ _779999) ^ [_1060949, _1060951, _1060953, _1060955] : [class_Groups_Oab__semigroup__mult(_1060949), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060949), _1060951), _1060953)), _1060955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060949), _1060951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060949), _1060953), _1060955)))], (31550 ^ _779999) ^ [_1370941, _1370943, _1370945] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1370941, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1370941), _1370943), _1370945), -(_1370943 = c_Orderings_Obot__class_Obot(tc_fun(_1370941, tc_HOL_Obool)))], (35185 ^ _779999) ^ [_1440805, _1440807, _1440809, _1440811, _1440813, _1440815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1440805, _1440807)), hAPP(hAPP(c_Product__Type_OPair(_1440805, _1440807), _1440813), _1440815)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool)), _1440809), _1440811))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440805, tc_fun(_1440807, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1440805, tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_fun(_1440807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440807, tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_fun(_1440807, tc_HOL_Obool)), _1440805), c_COMBC(_1440807, tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440807, tc_prod(_1440805, _1440807)), tc_fun(_1440807, tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), _1440805), hAPP(c_COMBB(tc_prod(_1440805, _1440807), tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool), _1440807), c_member(tc_prod(_1440805, _1440807)))), c_Product__Type_OPair(_1440805, _1440807)))), _1440809)), hAPP(hAPP(c_COMBC(_1440805, tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_fun(_1440807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440807, tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_fun(_1440807, tc_HOL_Obool)), _1440805), c_COMBC(_1440807, tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440807, tc_prod(_1440805, _1440807)), tc_fun(_1440807, tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool)), _1440805), hAPP(c_COMBB(tc_prod(_1440805, _1440807), tc_fun(tc_fun(tc_prod(_1440805, _1440807), tc_HOL_Obool), tc_HOL_Obool), _1440807), c_member(tc_prod(_1440805, _1440807)))), c_Product__Type_OPair(_1440805, _1440807)))), _1440811)), _1440813), _1440815)))], (22225 ^ _779999) ^ [_1191216, _1191218] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1191216, tc_HOL_Obool)), _1191218), c_Orderings_Otop__class_Otop(tc_fun(_1191216, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1191216, tc_HOL_Obool)))], (1504 ^ _779999) ^ [_801907, _801909] : [-(class_Orderings_Otop(_801907)), _801909 = _801907, class_Orderings_Otop(_801909)], (45913 ^ _779999) ^ [_1699919, _1699921, _1699923, _1699925] : [class_Orderings_Olinorder(_1699919), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699919, _1699919, c_COMBI(_1699919)), _1699921), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699919, _1699919, c_COMBI(_1699919)), _1699923), _1699925)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699919, _1699919, c_COMBI(_1699919)), _1699923), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699919, _1699919, c_COMBI(_1699919)), _1699921), _1699925)))], (20018 ^ _779999) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40561 ^ _779999) ^ [_1569987, _1569989, _1569991, _1569993] : [c_Wellfounded_Oacyclic(_1569987, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1569987, _1569987)), hAPP(hAPP(c_Product__Type_OPair(_1569987, _1569987), _1569989), _1569991)), _1569993)), 40564 ^ _779999 : [(40567 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569987, _1569987)), hAPP(hAPP(c_Product__Type_OPair(_1569987, _1569987), _1569991), _1569989)), c_Transitive__Closure_Ortrancl(_1569987, _1569993)))], (40565 ^ _779999) ^ [] : [-(c_Wellfounded_Oacyclic(_1569987, _1569993))]]], (37138 ^ _779999) ^ [_1482771] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1482771)], (32845 ^ _779999) ^ [_1396094, _1396096] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396094)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396096)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1396094), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396096))))], (18923 ^ _779999) ^ [_1125306, _1125308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125306), _1125308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125306), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1125308)))], (45249 ^ _779999) ^ [_1684724, _1684726, _1684728, _1684730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684724), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684726)), _1684728))), -(hAPP(hAPP(c_List_Onth(_1684726), hAPP(hAPP(c_List_Oappend(_1684726), _1684728), _1684730)), _1684724) = hAPP(hAPP(c_List_Onth(_1684726), _1684728), _1684724))], (22789 ^ _779999) ^ [_1202873, _1202875, _1202877, _1202879] : [class_Complete__Lattice_Ocomplete__lattice(_1202873), -(_1202875 = c_Orderings_Obot__class_Obot(tc_fun(_1202877, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1202877, _1202873), _1202875), hAPP(c_COMBK(_1202873, _1202877), _1202879)) = _1202879)], (24502 ^ _779999) ^ [_1238829, _1238831, _1238833, _1238835] : [class_Orderings_Olinorder(_1238829), 24505 ^ _779999 : [(24514 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238829), _1238831), _1238833)), _1238835))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), _1238831), _1238835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), _1238833), _1238835))], (24506 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238829), _1238831), _1238833)), _1238835)), 24509 ^ _779999 : [(24512 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), _1238833), _1238835)))], (24510 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238829), _1238831), _1238835)))]]]]], (2330 ^ _779999) ^ [_814320, _814322, _814324, _814326] : [-(c_Orderings_Oord_Omax(_814326, _814322) = c_Orderings_Oord_Omax(_814324, _814320)), _814326 = _814324, _814322 = _814320], (50833 ^ _779999) ^ [_1808693, _1808695, _1808697, _1808699] : [c_Wellfounded_Omax__extp(_1808693, _1808695, _1808697, _1808699), 50836 ^ _779999 : [(50839 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1808693), _1808699)))], (50841 ^ _779999) ^ [] : [_1808699 = c_Orderings_Obot__class_Obot(tc_fun(_1808693, tc_HOL_Obool))], (50843 ^ _779999) ^ [_1808909] : [hBOOL(hAPP(hAPP(c_member(_1808693), _1808909), _1808697)), 50847 ^ _779999 : [(50850 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1808695, _1808909), 50846 ^ [_1808693, _1808695, _1808697, _1808699, _1808909])))], (50848 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808693), 50846 ^ [_1808693, _1808695, _1808697, _1808699, _1808909]), _1808699)))]]], (50837 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1808693), _1808697)))]]], (47453 ^ _779999) ^ [_1734217, _1734219, _1734221] : [hAPP(c_List_Ofilter(_1734217, _1734219), _1734221) = _1734221, 47456 ^ _779999 : [(47457 ^ _779999) ^ [_1734308] : [hBOOL(hAPP(hAPP(c_member(_1734217), _1734308), hAPP(c_List_Oset(_1734217), _1734221))), -(hBOOL(hAPP(_1734219, _1734308)))]]], (15393 ^ _779999) ^ [_1056688, _1056690, _1056692, _1056694] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056688), _1056690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056692), _1056694)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1056688, _1056692)), c_Sum__Type_OPlus(_1056688, _1056692, _1056690, _1056694)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056688), _1056690)), hAPP(c_Finite__Set_Ocard(_1056692), _1056694)))], (52122 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (25652 ^ _779999) ^ [_1260988, _1260990, _1260992] : [class_Lattices_Oboolean__algebra(_1260988), 25655 ^ _779999 : [(25662 ^ _779999) ^ [] : [_1260990 = _1260992, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1260988), _1260990) = hAPP(c_Groups_Ouminus__class_Ouminus(_1260988), _1260992))], (25656 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1260988), _1260990) = hAPP(c_Groups_Ouminus__class_Ouminus(_1260988), _1260992), -(_1260990 = _1260992)]]], (52220 ^ _779999) ^ [_1832763, _1832765] : [-(class_Enum_Oenum(tc_prod(_1832763, _1832765))), class_Enum_Oenum(_1832763), class_Enum_Oenum(_1832765)], (14533 ^ _779999) ^ [_1040216, _1040218, _1040220, _1040222, _1040224] : [class_Groups_Oab__group__add(_1040216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040218), _1040220)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040218), _1040222)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040218, _1040216), _1040224), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040218, tc_HOL_Obool)), _1040220), _1040222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040216), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040218, _1040216), _1040224), _1040220)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040218, _1040216), _1040224), _1040222))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040218, _1040216), _1040224), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040218, tc_HOL_Obool)), _1040220), _1040222))))], (37302 ^ _779999) ^ [_1487037, _1487039, _1487041, _1487043, _1487045] : [-(hAPP(c_Product__Type_Osnd(_1487037, _1487039), hAPP(c_Product__Type_Oapfst(_1487041, _1487037, _1487039, _1487043), _1487045)) = hAPP(c_Product__Type_Osnd(_1487041, _1487039), _1487045))], (19113 ^ _779999) ^ [_1128343, _1128345, _1128347] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128343), _1128345)), _1128347) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128345), _1128347)))], (47400 ^ _779999) ^ [_1732845, _1732847, _1732849, _1732851] : [-(c_List_Otranspose(_1732845, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1732845)), hAPP(hAPP(c_List_Olist_OCons(_1732845), _1732847), _1732849)), _1732851)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1732845)), hAPP(hAPP(c_List_Olist_OCons(_1732845), _1732847), c_List_Oconcat(_1732845, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732845), tc_List_Olist(_1732845)), c_List_Olist_Olist__case(tc_List_Olist(_1732845), _1732845, c_List_Olist_ONil(_1732845), hAPP(hAPP(c_COMBB(tc_List_Olist(_1732845), tc_fun(tc_List_Olist(_1732845), tc_List_Olist(_1732845)), _1732845), c_COMBK(tc_List_Olist(_1732845), tc_List_Olist(_1732845))), hAPP(hAPP(c_COMBC(_1732845, tc_List_Olist(_1732845), tc_List_Olist(_1732845)), c_List_Olist_OCons(_1732845)), c_List_Olist_ONil(_1732845))))), _1732851)))), c_List_Otranspose(_1732845, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1732845)), _1732849), c_List_Oconcat(tc_List_Olist(_1732845), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732845), tc_List_Olist(tc_List_Olist(_1732845))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1732845)), _1732845, c_List_Olist_ONil(tc_List_Olist(_1732845)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1732845), tc_List_Olist(tc_List_Olist(_1732845))), _1732845), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732845), tc_List_Olist(tc_List_Olist(_1732845)), tc_List_Olist(tc_List_Olist(_1732845))), c_List_Olist_OCons(tc_List_Olist(_1732845))), c_List_Olist_ONil(tc_List_Olist(_1732845)))))), _1732851))))))], (31947 ^ _779999) ^ [_1379176, _1379178, _1379180] : [class_Int_Onumber__ring(_1379176), -(hAPP(c_Int_Onumber__class_Onumber__of(_1379176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1379178), _1379180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379176), hAPP(c_Int_Onumber__class_Onumber__of(_1379176), _1379178)), hAPP(c_Int_Onumber__class_Onumber__of(_1379176), _1379180)))], (40112 ^ _779999) ^ [_1558594, _1558596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558594), _1558596)), -(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), _1558594), _1558596)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (45744 ^ _779999) ^ [_1696204, _1696206, _1696208, _1696210, _1696212, _1696214] : [-(hAPP(c_List_Ofoldl(_1696204, _1696206, _1696208, _1696210), hAPP(hAPP(c_List_Olist_OCons(_1696206), _1696212), _1696214)) = hAPP(c_List_Ofoldl(_1696204, _1696206, _1696208, hAPP(hAPP(_1696208, _1696210), _1696212)), _1696214))], (47663 ^ _779999) ^ [_1739978, _1739980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739978), _1739980)), -(c_List_Oupt(_1739978, _1739980) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1739978), c_List_Oupt(hAPP(c_Nat_OSuc, _1739978), _1739980)))], (33657 ^ _779999) ^ [_1409561, _1409563] : [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(_1409561))), 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)), _1409563)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409561)), hAPP(c_Nat_OSuc, _1409563))))], (33139 ^ _779999) ^ [_1400835, _1400837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400835), _1400837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1400835)), _1400837)))], (50286 ^ _779999) ^ [_1795308, _1795310, _1795312, _1795314, _1795316, _1795318] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1795308, _1795310, _1795312, _1795314, c_Nitpick_Opair__box_OPairBox(_1795308, _1795310, _1795316, _1795318)) = hAPP(hAPP(_1795314, _1795316), _1795318))], (33323 ^ _779999) ^ [_1403723, _1403725] : [class_Int_Onumber__ring(_1403723), class_Rings_Olinordered__idom(_1403723), 33330 ^ _779999 : [(33337 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1403725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403723), c_Groups_Ozero__class_Ozero(_1403723)), hAPP(c_Int_Onumber__class_Onumber__of(_1403723), _1403725))))], (33331 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403723), c_Groups_Ozero__class_Ozero(_1403723)), hAPP(c_Int_Onumber__class_Onumber__of(_1403723), _1403725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1403725)))]]], (41831 ^ _779999) ^ [_1598713, _1598715, _1598717, _1598719, _1598721] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598713, tc_fun(_1598715, tc_HOL_Obool)), _1598717), hAPP(hAPP(c_COMBB(tc_fun(_1598715, tc_HOL_Obool), tc_fun(_1598715, tc_HOL_Obool), _1598713), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598715, tc_HOL_Obool)), _1598719)), _1598721)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598715, tc_HOL_Obool)), _1598719), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598713, tc_fun(_1598715, tc_HOL_Obool)), _1598717), _1598721)))], (38281 ^ _779999) ^ [_1511690, _1511692, _1511694, _1511696] : [hBOOL(hAPP(c_Predicate_ORangeP(_1511690, _1511692, hAPP(hAPP(c_COMBC(_1511690, tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_fun(_1511692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511692, tc_fun(tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_fun(_1511692, tc_HOL_Obool)), _1511690), c_COMBC(_1511692, tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511692, tc_prod(_1511690, _1511692)), tc_fun(_1511692, tc_fun(tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_HOL_Obool)), _1511690), hAPP(c_COMBB(tc_prod(_1511690, _1511692), tc_fun(tc_fun(tc_prod(_1511690, _1511692), tc_HOL_Obool), tc_HOL_Obool), _1511692), c_member(tc_prod(_1511690, _1511692)))), c_Product__Type_OPair(_1511690, _1511692)))), _1511694)), _1511696)), -(hBOOL(hAPP(hAPP(c_member(_1511692), _1511696), hAPP(c_Relation_ORange(_1511690, _1511692), _1511694))))], (32853 ^ _779999) ^ [_1396249, _1396251] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1396249) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396251), 32856 ^ _779999 : [(32859 ^ _779999) ^ [] : [-(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), _1396251))))], (32857 ^ _779999) ^ [] : [-(_1396249 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396251)))]]], (33417 ^ _779999) ^ [] : [-(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)))))], (1074 ^ _779999) ^ [_796280, _796282, _796284, _796286] : [-(c_Predicate_Osymp(_796284, _796280)), c_Predicate_Osymp(_796286, _796282), _796286 = _796284, _796282 = _796280], (28338 ^ _779999) ^ [_1312819, _1312821, _1312823, _1312825] : [class_Fields_Olinordered__field__inverse__zero(_1312819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312819), _1312821), _1312823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312819), c_Groups_Ozero__class_Ozero(_1312819)), _1312825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312819), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312819), _1312821), _1312825)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312819), _1312823), _1312825))))], (31441 ^ _779999) ^ [_1368879, _1368881] : [class_Rings_Olinordered__idom(_1368879), 31444 ^ _779999 : [(31451 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368879), c_Groups_Ozero__class_Ozero(_1368879)), _1368881)), -(c_Groups_Osgn__class_Osgn(_1368879, _1368881) = c_Groups_Oone__class_Oone(_1368879))], (31445 ^ _779999) ^ [] : [c_Groups_Osgn__class_Osgn(_1368879, _1368881) = c_Groups_Oone__class_Oone(_1368879), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368879), c_Groups_Ozero__class_Ozero(_1368879)), _1368881)))]]], (13257 ^ _779999) ^ [_1015964, _1015966, _1015968, _1015970, _1015972] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1015964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015964), _1015966), _1015968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015964), _1015970), _1015972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015964), _1015966), _1015970)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015964), _1015968), _1015972))))], (19395 ^ _779999) ^ [_1133609, _1133611] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133609)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133611)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133609), _1133611)))], (33735 ^ _779999) ^ [_1411407, _1411409] : [class_Int_Onumber__ring(_1411407), 33738 ^ _779999 : [(33745 ^ _779999) ^ [] : [c_Int_Oiszero(_1411407, hAPP(c_Int_Onumber__class_Onumber__of(_1411407), 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), _1411409)))), -(c_Groups_Oone__class_Oone(_1411407) = hAPP(c_Int_Onumber__class_Onumber__of(_1411407), _1411409))], (33739 ^ _779999) ^ [] : [c_Groups_Oone__class_Oone(_1411407) = hAPP(c_Int_Onumber__class_Onumber__of(_1411407), _1411409), -(c_Int_Oiszero(_1411407, hAPP(c_Int_Onumber__class_Onumber__of(_1411407), 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), _1411409)))))]]], (45522 ^ _779999) ^ [_1691669, _1691671, _1691673, _1691675] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1691669) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1691671), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1691669)), hAPP(hAPP(c_List_Olist_OCons(_1691671), _1691673), _1691675)) = hAPP(hAPP(c_List_Olist_OCons(_1691671), _1691673), _1691675))], (52354 ^ _779999) ^ [_1834242] : [hBOOL(hAPP(c_fNot, _1834242)), hBOOL(_1834242)], (45107 ^ _779999) ^ [_1681502, _1681504, _1681506] : [_1681502 = hAPP(hAPP(c_List_Oappend(_1681504), _1681506), _1681502), -(_1681506 = c_List_Olist_ONil(_1681504))], (7087 ^ _779999) ^ [_896434, _896436, _896438, _896440, _896442] : [hBOOL(hAPP(hAPP(c_member(_896434), _896436), _896438)), -(hAPP(c_Set_Oimage(_896434, _896440, hAPP(c_COMBK(_896440, _896434), _896442)), _896438) = hAPP(hAPP(c_Set_Oinsert(_896440), _896442), c_Orderings_Obot__class_Obot(tc_fun(_896440, tc_HOL_Obool))))], (40741 ^ _779999) ^ [_1573742, _1573744, _1573746, _1573748, _1573750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573744, _1573742)), hAPP(hAPP(c_Product__Type_OPair(_1573744, _1573742), _1573748), _1573746)), _1573750)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573742, _1573744)), hAPP(hAPP(c_Product__Type_OPair(_1573742, _1573744), _1573746), _1573748)), hAPP(c_Relation_Oconverse(_1573744, _1573742), _1573750))))], (1934 ^ _779999) ^ [_807282, _807284] : [-(class_Groups_Ozero(_807282)), _807284 = _807282, class_Groups_Ozero(_807284)], (50799 ^ _779999) ^ [_1808194, _1808196, _1808198, _1808200] : [c_Predicate_Osymp(_1808194, _1808196), hBOOL(hAPP(hAPP(_1808196, _1808198), _1808200)), -(hBOOL(hAPP(hAPP(_1808196, _1808200), _1808198)))], (16771 ^ _779999) ^ [_1083526, _1083528] : [_1083526 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1083526), _1083528), -(_1083528 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1083526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22898 ^ _779999) ^ [_1206080, _1206082, _1206084, _1206086, _1206088] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206080, tc_fun(_1206082, tc_HOL_Obool)), _1206084), hAPP(hAPP(c_COMBC(_1206080, tc_fun(_1206082, tc_HOL_Obool), tc_fun(_1206082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1206082, tc_HOL_Obool), tc_fun(tc_fun(_1206082, tc_HOL_Obool), tc_fun(_1206082, tc_HOL_Obool)), _1206080), c_Groups_Ominus__class_Ominus(tc_fun(_1206082, tc_HOL_Obool))), _1206086)), _1206088)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206082, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206080, tc_fun(_1206082, tc_HOL_Obool)), _1206084), _1206086)), _1206088))], (30796 ^ _779999) ^ [_1357400, _1357402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357400), 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, _1357402, _1357400)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26957 ^ _779999) ^ [_1286747, _1286749, _1286751, _1286753, _1286755] : [class_Groups_Ocomm__monoid__mult(_1286747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286749), _1286751)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286749), _1286753)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1286749, tc_HOL_Obool)), _1286751), _1286753) = c_Orderings_Obot__class_Obot(tc_fun(_1286749, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286749, _1286747), _1286755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286749, tc_HOL_Obool)), _1286751), _1286753)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286747), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286749, _1286747), _1286755), _1286751)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286749, _1286747), _1286755), _1286753)))], (40695 ^ _779999) ^ [_1572633, _1572635, _1572637, _1572639] : [-(hAPP(c_Relation_Oconverse(_1572633, _1572635), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1572633, _1572635), tc_HOL_Obool)), _1572637), _1572639)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1572635, _1572633), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1572633, _1572635), _1572637)), hAPP(c_Relation_Oconverse(_1572633, _1572635), _1572639)))], (44023 ^ _779999) ^ [_1658097, _1658099] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1658097, _1658099)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1658097, _1658099))], (30382 ^ _779999) ^ [_1349250, _1349252, _1349254, _1349256, _1349258] : [class_Groups_Ocomm__monoid__add(_1349250), class_Groups_Ocomm__monoid__mult(_1349250), _1349252 = _1349254, c_Nat__Transfer_Onat__set(_1349254), 30400 ^ _779999 : [(30403 ^ _779999) ^ [] : [hAPP(_1349256, 30399 ^ [_1349250, _1349252, _1349254, _1349256, _1349258]) = hAPP(_1349258, 30399 ^ [_1349250, _1349252, _1349254, _1349256, _1349258])], (30401 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30399 ^ [_1349250, _1349252, _1349254, _1349256, _1349258])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1349250), _1349256), _1349252) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1349250), _1349258), _1349254))], (22277 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (44228 ^ _779999) ^ [_1662592, _1662594, _1662596, _1662598] : [-(_1662592 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662594)), _1662596)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1662594, hAPP(hAPP(c_List_Olist__update(_1662594, _1662596), _1662592), _1662598)) = hAPP(hAPP(c_List_Olist__update(_1662594, c_List_Obutlast(_1662594, _1662596)), _1662592), _1662598))], (37642 ^ _779999) ^ [_1495397, _1495399, _1495401] : [hBOOL(hAPP(hAPP(c_member(_1495397), _1495401), c_Wellfounded_Oacc(_1495397, _1495399))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1495397, hAPP(hAPP(c_COMBC(_1495397, tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_fun(_1495397, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495397, tc_fun(tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_fun(_1495397, tc_HOL_Obool)), _1495397), c_COMBC(_1495397, tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495397, tc_prod(_1495397, _1495397)), tc_fun(_1495397, tc_fun(tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_HOL_Obool)), _1495397), hAPP(c_COMBB(tc_prod(_1495397, _1495397), tc_fun(tc_fun(tc_prod(_1495397, _1495397), tc_HOL_Obool), tc_HOL_Obool), _1495397), c_member(tc_prod(_1495397, _1495397)))), c_Product__Type_OPair(_1495397, _1495397)))), _1495399)), _1495401)))], (34285 ^ _779999) ^ [_1421181, _1421183] : [class_Rings_Ocomm__semiring__1(_1421181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421181), _1421183), _1421183) = hAPP(hAPP(c_Power_Opower__class_Opower(_1421181), _1421183), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (47232 ^ _779999) ^ [_1728691, _1728693, _1728695, _1728697] : [-(c_List_Oremdups(_1728691, hAPP(hAPP(c_List_Omap(_1728693, _1728691), _1728695), c_List_Oremdups(_1728693, _1728697))) = c_List_Oremdups(_1728691, hAPP(hAPP(c_List_Omap(_1728693, _1728691), _1728695), _1728697)))], (23988 ^ _779999) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (20774 ^ _779999) ^ [_1157199, _1157201, _1157203] : [class_Orderings_Olinorder(_1157199), 20777 ^ _779999 : [(20784 ^ _779999) ^ [] : [_1157201 = _1157203, -(hAPP(c_SetInterval_Oord__class_OatMost(_1157199), _1157201) = hAPP(c_SetInterval_Oord__class_OatMost(_1157199), _1157203))], (20778 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1157199), _1157201) = hAPP(c_SetInterval_Oord__class_OatMost(_1157199), _1157203), -(_1157201 = _1157203)]]], (35243 ^ _779999) ^ [_1442711, _1442713, _1442715, _1442717, _1442719] : [hBOOL(hAPP(hAPP(c_member(_1442711), _1442713), hAPP(c_Relation_OImage(_1442715, _1442711, _1442717), _1442719))), 35247 ^ _779999 : [(35250 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442715, _1442711)), hAPP(hAPP(c_Product__Type_OPair(_1442715, _1442711), 35246 ^ [_1442711, _1442713, _1442715, _1442717, _1442719]), _1442713)), _1442717)))], (35248 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442715), 35246 ^ [_1442711, _1442713, _1442715, _1442717, _1442719]), _1442719)))]]], (17441 ^ _779999) ^ [_1096305, _1096307, _1096309, _1096311, _1096313, _1096315] : [class_Rings_Olinordered__semiring__1(_1096305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096305), _1096307), _1096309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096305), _1096311), _1096309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096305), c_Groups_Ozero__class_Ozero(_1096305)), _1096313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096305), c_Groups_Ozero__class_Ozero(_1096305)), _1096315)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096305), _1096313), _1096315) = c_Groups_Oone__class_Oone(_1096305), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096305), _1096313), _1096307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096305), _1096315), _1096311))), _1096309)))], (26737 ^ _779999) ^ [_1281305, _1281307, _1281309, _1281311, _1281313] : [class_Groups_Ocomm__monoid__mult(_1281305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281307), _1281309)), 26744 ^ _779999 : [(26751 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281307), _1281311), _1281309))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1281307, _1281305), hAPP(hAPP(c_COMBC(_1281307, _1281305, _1281305), hAPP(hAPP(c_COMBS(_1281307, _1281305, tc_fun(_1281305, _1281305)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1281305, tc_fun(_1281305, _1281305)), _1281307), c_If(_1281305)), hAPP(c_fequal, _1281311))), _1281313)), c_Groups_Oone__class_Oone(_1281305))), _1281309) = c_Groups_Oone__class_Oone(_1281305))], (26745 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1281307), _1281311), _1281309)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1281307, _1281305), hAPP(hAPP(c_COMBC(_1281307, _1281305, _1281305), hAPP(hAPP(c_COMBS(_1281307, _1281305, tc_fun(_1281305, _1281305)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1281305, tc_fun(_1281305, _1281305)), _1281307), c_If(_1281305)), hAPP(c_fequal, _1281311))), _1281313)), c_Groups_Oone__class_Oone(_1281305))), _1281309) = hAPP(_1281313, _1281311))]]], (48496 ^ _779999) ^ [_1756027, _1756029, _1756031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756027), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756029)), _1756031))), -(hAPP(hAPP(c_List_Onth(_1756029), hAPP(c_List_Orev(_1756029), _1756031)), _1756027) = hAPP(hAPP(c_List_Onth(_1756029), _1756031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756029)), _1756031)), hAPP(c_Nat_OSuc, _1756027))))], (24898 ^ _779999) ^ [_1246608, _1246610, _1246612] : [class_Orderings_Olinorder(_1246608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1246608), _1246610)), -(_1246610 = c_Orderings_Obot__class_Obot(tc_fun(_1246608, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1246608), _1246612)), -(_1246612 = c_Orderings_Obot__class_Obot(tc_fun(_1246608, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246608), c_Big__Operators_Olattice_OSup__fin(_1246608, c_Orderings_Oord__class_Omax(_1246608), _1246610)), c_Big__Operators_Olattice_OSup__fin(_1246608, c_Orderings_Oord__class_Omax(_1246608), _1246612)) = c_Big__Operators_Olattice_OSup__fin(_1246608, c_Orderings_Oord__class_Omax(_1246608), hAPP(c_Set_OCollect(_1246608), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_HOL_Obool), tc_HOL_Obool, _1246608), c_HOL_OEx(_1246608)), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool)), tc_fun(_1246608, tc_HOL_Obool), _1246608), hAPP(c_COMBB(tc_fun(_1246608, tc_HOL_Obool), tc_HOL_Obool, _1246608), c_HOL_OEx(_1246608))), hAPP(hAPP(c_COMBC(_1246608, tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool)), tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_fun(tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool))), tc_fun(tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool)), tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool))), _1246608), c_COMBS(_1246608, tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_fun(_1246608, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1246608, tc_fun(tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool))), _1246608), hAPP(c_COMBB(tc_fun(_1246608, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool)), _1246608), c_COMBS(_1246608, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool)), tc_fun(_1246608, tc_fun(_1246608, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1246608), hAPP(c_COMBB(tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1246608), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1246608), c_fconj))), hAPP(hAPP(c_COMBC(_1246608, tc_fun(_1246608, tc_fun(_1246608, _1246608)), tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1246608, _1246608), tc_fun(_1246608, tc_HOL_Obool)), tc_fun(tc_fun(_1246608, tc_fun(_1246608, _1246608)), tc_fun(_1246608, tc_fun(_1246608, tc_HOL_Obool))), _1246608), c_COMBB(tc_fun(_1246608, _1246608), tc_fun(_1246608, tc_HOL_Obool), _1246608)), hAPP(hAPP(c_COMBB(tc_fun(_1246608, tc_HOL_Obool), tc_fun(tc_fun(_1246608, _1246608), tc_fun(_1246608, tc_HOL_Obool)), _1246608), c_COMBB(_1246608, tc_HOL_Obool, _1246608)), c_fequal))), c_Orderings_Oord__class_Omin(_1246608)))))), hAPP(hAPP(c_COMBC(_1246608, tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1246608, tc_HOL_Obool), tc_fun(_1246608, tc_HOL_Obool)), _1246608), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1246608)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1246608), c_fconj), hAPP(hAPP(c_COMBC(_1246608, tc_fun(_1246608, tc_HOL_Obool), tc_HOL_Obool), c_member(_1246608)), _1246610)))), hAPP(hAPP(c_COMBC(_1246608, tc_fun(_1246608, tc_HOL_Obool), tc_HOL_Obool), c_member(_1246608)), _1246612))))))))], (41486 ^ _779999) ^ [_1591835, _1591837, _1591839] : [class_Orderings_Olinorder(_1591835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591835), _1591837)), -(c_Big__Operators_Olattice_OSup__fin(_1591835, c_Orderings_Oord__class_Omax(_1591835), hAPP(hAPP(c_Set_Oinsert(_1591835), _1591839), _1591837)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591835, _1591835, c_Orderings_Oord__class_Omax(_1591835)), _1591839), _1591837))], (42016 ^ _779999) ^ [_1604777, _1604779, _1604781, _1604783, _1604785] : [hBOOL(hAPP(hAPP(c_member(_1604777), _1604779), _1604781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604783, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604777, tc_fun(_1604783, tc_HOL_Obool)), _1604781), _1604785)), hAPP(_1604785, _1604779))))], (7743 ^ _779999) ^ [_910166, _910168, _910170, _910172] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910166)), _910168, _910170, _910172), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _910166), _910168, hAPP(c_Nat_OSuc, _910170), _910172))], (40063 ^ _779999) ^ [_1557549, _1557551, _1557553, _1557555, _1557557, _1557559] : [-(c_Com_Ocom_OLocal(_1557549, _1557551, _1557553) = c_Com_Ocom_OLocal(_1557555, _1557557, _1557559)), _1557549 = _1557555, _1557551 = _1557557, _1557553 = _1557559], (21086 ^ _779999) ^ [] : [-(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))))], (14984 ^ _779999) ^ [_1048867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1048867)), -(_1048867 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048867), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (38650 ^ _779999) ^ [_1522398, _1522400, _1522402, _1522404] : [_1522398 = c_Orderings_Obot__class_Obot(tc_fun(_1522400, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1522400, _1522402), _1522402, c_Product__Type_Osnd(_1522400, _1522402)), hAPP(hAPP(c_Product__Type_OSigma(_1522400, _1522402), _1522398), hAPP(c_COMBK(tc_fun(_1522402, tc_HOL_Obool), _1522400), _1522404))) = c_Orderings_Obot__class_Obot(tc_fun(_1522402, tc_HOL_Obool)))], (13291 ^ _779999) ^ [_1016625, _1016627, _1016629, _1016631] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1016625), 13294 ^ _779999 : [(13301 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016625), _1016629), _1016631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016625), _1016627), _1016629)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016625), _1016627), _1016631))))], (13295 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016625), _1016627), _1016629)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016625), _1016627), _1016631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016625), _1016629), _1016631)))]]], (42080 ^ _779999) ^ [_1606678, _1606680, _1606682, _1606684, _1606686] : [class_Complete__Lattice_Ocomplete__lattice(_1606678), 42083 ^ _779999 : [(42084 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1606678), _1606680), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606682, _1606678), _1606684), _1606686))), 42087 ^ _779999 : [(42088 ^ _779999) ^ [_1606859] : [hBOOL(hAPP(hAPP(c_member(_1606682), _1606859), _1606684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1606678), _1606680), hAPP(_1606686, _1606859))))]]], (42094 ^ _779999) ^ [] : [42096 ^ _779999 : [(42099 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1606678), _1606680), hAPP(_1606686, 42095 ^ [_1606678, _1606680, _1606682, _1606684, _1606686])))], (42097 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606682), 42095 ^ [_1606678, _1606680, _1606682, _1606684, _1606686]), _1606684)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1606678), _1606680), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606682, _1606678), _1606684), _1606686))))]]], (15063 ^ _779999) ^ [_1050390, _1050392, _1050394, _1050396, _1050398, _1050400] : [hBOOL(hAPP(hAPP(c_member(_1050390), _1050392), c_SetInterval_Oord_OgreaterThanAtMost(_1050390, _1050394, _1050396, _1050398, _1050400))), 15066 ^ _779999 : [(15069 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1050394, _1050392), _1050400)))], (15067 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1050396, _1050398), _1050392)))]]], (878 ^ _779999) ^ [_793424, _793426, _793428, _793430, _793432, _793434] : [-(c_List_Olist__all(_793432, _793428, _793424)), c_List_Olist__all(_793434, _793430, _793426), _793434 = _793432, _793430 = _793428, _793426 = _793424], (32773 ^ _779999) ^ [_1394779, _1394781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394779), _1394781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1394779)), c_Int_OBit1(_1394781))))], (27206 ^ _779999) ^ [_1292171, _1292173] : [c_Nat__Transfer_Ois__nat(_1292171), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1292171), _1292173)))], (16637 ^ _779999) ^ [_1080921, _1080923, _1080925] : [class_Rings_Ocomm__semiring__1(_1080921), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080921), _1080923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080921), _1080925), _1080923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080921), _1080925), c_Groups_Oone__class_Oone(_1080921))), _1080923))], (32159 ^ _779999) ^ [_1382940, _1382942, _1382944, _1382946] : [class_Fields_Olinordered__field__inverse__zero(_1382940), class_Int_Onumber(_1382940), 32166 ^ _779999 : [(32167 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382940), _1382942), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))), _1382946)), 32170 ^ _779999 : [(32177 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)))), 32180 ^ _779999 : [(32187 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)), c_Groups_Ozero__class_Ozero(_1382940)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), _1382946)))], (32181 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)), c_Groups_Ozero__class_Ozero(_1382940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382940), _1382946), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))), _1382942)))]]], (32171 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), _1382942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382940), _1382946), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)))))]]], (32193 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382940), _1382942), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))), _1382946))), 32196 ^ _779999 : [(32199 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), _1382942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382940), _1382946), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))))], (32197 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))))]], 32200 ^ _779999 : [(32203 ^ _779999) ^ [] : [32204 ^ _779999 : [(32207 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382940), _1382946), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944))), _1382942))], (32205 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)), c_Groups_Ozero__class_Ozero(_1382940))))]], 32208 ^ _779999 : [(32211 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), _1382946))], (32209 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)), c_Groups_Ozero__class_Ozero(_1382940)))]]], (32201 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382940), c_Groups_Ozero__class_Ozero(_1382940)), hAPP(c_Int_Onumber__class_Onumber__of(_1382940), _1382944)))]]]]], (5929 ^ _779999) ^ [_874423, _874425, _874427] : [class_Orderings_Oorder(_874423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874423), _874425), _874427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874423), _874427), _874425)), -(_874427 = _874425)], (40293 ^ _779999) ^ [_1563652, _1563654] : [-(c_Transitive__Closure_Otrancl(_1563652, _1563654) = hAPP(hAPP(c_Relation_Orel__comp(_1563652, _1563652, _1563652), c_Transitive__Closure_Ortrancl(_1563652, _1563654)), _1563654))], (43403 ^ _779999) ^ [_1639948, _1639950, _1639952, _1639954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639948), tc_List_Olist(_1639948))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639948), tc_List_Olist(_1639948)), _1639950), _1639952)), c_List_Olistrel(_1639948, _1639954))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639948)), _1639950) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639948)), _1639952))], (27204 ^ _779999) ^ [_1292128, _1292130] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1292128)), _1292130) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1292128), _1292130)))], (15867 ^ _779999) ^ [_1066089] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066089), _1066089)))))], (12337 ^ _779999) ^ [_998343, _998345, _998347] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_998343), _998345)), hBOOL(hAPP(_998347, _998345)), 12348 ^ _779999 : [(12351 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_998343), 12346 ^ [_998343, _998345, _998347]), 12347 ^ [_998343, _998345, _998347])))], (12353 ^ _779999) ^ [] : [-(hBOOL(hAPP(_998347, 12347 ^ [_998343, _998345, _998347])))], (12355 ^ _779999) ^ [] : [hBOOL(hAPP(_998347, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998343, tc_HOL_Obool)), 12347 ^ [_998343, _998345, _998347]), hAPP(hAPP(c_Set_Oinsert(_998343), 12346 ^ [_998343, _998345, _998347]), c_Orderings_Obot__class_Obot(tc_fun(_998343, tc_HOL_Obool))))))], (12349 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_998343), 12347 ^ [_998343, _998345, _998347])))]], -(hBOOL(hAPP(_998347, c_Orderings_Obot__class_Obot(tc_fun(_998343, tc_HOL_Obool)))))], (24472 ^ _779999) ^ [_1238310, _1238312, _1238314] : [class_Orderings_Olinorder(_1238310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238310), _1238312), _1238314)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238310), _1238312), _1238314) = _1238314)], (33987 ^ _779999) ^ [_1415765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415765), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1415765)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31335 ^ _779999) ^ [_1366902, _1366904] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366902), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1366904), _1366902)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366904), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366904, _1366902)))], (33885 ^ _779999) ^ [_1414038] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1414038)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1414038)))], (21449 ^ _779999) ^ [_1170517, _1170519] : [class_Lattices_Olattice(_1170517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170517), _1170519)), -(c_Big__Operators_Olattice__class_OInf__fin(_1170517, _1170519) = hAPP(c_Finite__Set_Ofold1(_1170517, c_Lattices_Osemilattice__inf__class_Oinf(_1170517)), _1170519))], (42526 ^ _779999) ^ [_1617215, _1617217] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617215, tc_HOL_Obool), _1617217) = hAPP(c_Set_OCollect(_1617215), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1617215, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1617215), c_HOL_OAll(tc_fun(_1617215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1617215, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1617215, tc_HOL_Obool), tc_HOL_Obool), _1617215), hAPP(c_COMBS(tc_fun(_1617215, 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(_1617215, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1617215, tc_HOL_Obool), tc_fun(tc_fun(_1617215, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1617215, tc_HOL_Obool))), _1617217)))), c_member(_1617215)))))], (17790 ^ _779999) ^ [_1103860, _1103862, _1103864] : [class_Orderings_Olinorder(_1103860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103860), _1103862), _1103864)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1103860, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1103860), _1103862), c_Orderings_Obot__class_Obot(tc_fun(_1103860, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1103860, _1103862, _1103864)) = c_SetInterval_Oord__class_OatLeastAtMost(_1103860, _1103862, _1103864))], (37387 ^ _779999) ^ [_1488842] : [-(_1488842 = 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)), _1488842), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (13165 ^ _779999) ^ [_1014339, _1014341, _1014343, _1014345] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1014339), 13168 ^ _779999 : [(13175 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014339), _1014343), _1014345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014339), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), _1014341), _1014343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), _1014341), _1014345))))], (13169 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014339), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), _1014341), _1014343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), _1014341), _1014345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014339), _1014343), _1014345)))]]], (21124 ^ _779999) ^ [_1163984, _1163986, _1163988, _1163990, _1163992] : [class_Groups_Ocomm__monoid__add(_1163984), class_Groups_Ocomm__monoid__mult(_1163984), _1163986 = _1163988, c_Nat__Transfer_Onat__set(_1163988), 21142 ^ _779999 : [(21145 ^ _779999) ^ [] : [hAPP(_1163990, 21141 ^ [_1163984, _1163986, _1163988, _1163990, _1163992]) = hAPP(_1163992, 21141 ^ [_1163984, _1163986, _1163988, _1163990, _1163992])], (21143 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21141 ^ [_1163984, _1163986, _1163988, _1163990, _1163992])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1163984), _1163990), _1163986) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1163984), _1163992), _1163988))], (25836 ^ _779999) ^ [_1264194, _1264196, _1264198] : [class_Groups_Ogroup__add(_1264194), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1264194), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264194), _1264196), _1264198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264194), hAPP(c_Groups_Ouminus__class_Ouminus(_1264194), _1264198)), hAPP(c_Groups_Ouminus__class_Ouminus(_1264194), _1264196)))], (25880 ^ _779999) ^ [_1265204, _1265206, _1265208, _1265210, _1265212] : [class_Groups_Ocomm__monoid__mult(_1265204), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265206, _1265204), hAPP(hAPP(c_COMBS(_1265206, _1265204, _1265204), hAPP(hAPP(c_COMBB(_1265204, tc_fun(_1265204, _1265204), _1265206), c_Groups_Otimes__class_Otimes(_1265204)), _1265208)), _1265210)), _1265212) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265204), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265206, _1265204), _1265208), _1265212)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265206, _1265204), _1265210), _1265212)))], (3134 ^ _779999) ^ [_826756, _826758] : [_826758 = _826756, -(c_Rings_Oinverse__class_Odivide(_826758) = c_Rings_Oinverse__class_Odivide(_826756))], (42478 ^ _779999) ^ [_1616007, _1616009, _1616011, _1616013] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1616007, tc_HOL_Obool), tc_fun(_1616009, tc_HOL_Obool)), _1616011), hAPP(hAPP(c_COMBC(tc_fun(_1616007, tc_HOL_Obool), tc_fun(_1616007, tc_fun(_1616009, tc_HOL_Obool)), tc_fun(_1616009, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1616007, tc_fun(_1616009, tc_HOL_Obool))), _1616013)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1616007, tc_fun(_1616009, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616007, tc_HOL_Obool), _1616011)), _1616013))], (42201 ^ _779999) ^ [_1609712, _1609714, _1609716, _1609718, _1609720, _1609722] : [c_Relation_Osingle__valued(_1609712, _1609714, hAPP(c_Relation_Oconverse(_1609714, _1609712), _1609716)), -(_1609718 = c_Orderings_Obot__class_Obot(tc_fun(_1609720, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1609714, _1609712, _1609716), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609720, tc_fun(_1609714, tc_HOL_Obool)), _1609718), _1609722)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609720, tc_fun(_1609712, tc_HOL_Obool)), _1609718), hAPP(hAPP(c_COMBB(tc_fun(_1609714, tc_HOL_Obool), tc_fun(_1609712, tc_HOL_Obool), _1609720), c_Relation_OImage(_1609714, _1609712, _1609716)), _1609722)))], (12861 ^ _779999) ^ [_1008056, _1008058, _1008060, _1008062, _1008064] : [class_Groups_Ocomm__monoid__add(_1008056), class_Groups_Oordered__cancel__ab__semigroup__add(_1008056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008058), _1008060)), -(_1008060 = c_Orderings_Obot__class_Obot(tc_fun(_1008058, tc_HOL_Obool))), 12879 ^ _779999 : [(12882 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008056), hAPP(_1008062, 12878 ^ [_1008056, _1008058, _1008060, _1008062, _1008064])), hAPP(_1008064, 12878 ^ [_1008056, _1008058, _1008060, _1008062, _1008064])))], (12880 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008058), 12878 ^ [_1008056, _1008058, _1008060, _1008062, _1008064]), _1008060)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008056), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008058, _1008056), _1008062), _1008060)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008058, _1008056), _1008064), _1008060))))], (10305 ^ _779999) ^ [_957366, _957368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957366), _957368)), -(_957366 = _957368), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957366), _957368)))], (6095 ^ _779999) ^ [_876991, _876993, _876995, _876997] : [class_Lattices_Olattice(_876991), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876991), _876993), _876995)), _876997) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876991), _876993), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876991), _876995), _876997)))], (9939 ^ _779999) ^ [_951113, _951115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951113), _951115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _951113)), hAPP(c_Nat_OSuc, _951115))))], (17073 ^ _779999) ^ [_1088866, _1088868, _1088870, _1088872] : [class_Rings_Olinordered__semiring__strict(_1088866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088866), _1088868), _1088870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088866), _1088868), _1088872))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088866), c_Groups_Ozero__class_Ozero(_1088866)), _1088868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088866), _1088870), _1088872)))], (30651 ^ _779999) ^ [_1354666, _1354668, _1354670] : [class_Divides_Osemiring__div(_1354666), -(c_Divides_Odiv__class_Omod(_1354666, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354666), _1354668), _1354670), _1354670) = c_Groups_Ozero__class_Ozero(_1354666))], (50562 ^ _779999) ^ [_1802063, _1802065] : [50563 ^ _779999 : [(50564 ^ _779999) ^ [_1802129] : [hBOOL(hAPP(_1802065, _1802129))]], 50566 ^ _779999 : [(50569 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1802065, 50565 ^ [_1802063, _1802065])))], (50567 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802063), 50565 ^ [_1802063, _1802065]), c_Orderings_Otop__class_Otop(tc_fun(_1802063, tc_HOL_Obool)))))]]], (50943 ^ _779999) ^ [_1810810, _1810812] : [50946 ^ _779999 : [(50951 ^ _779999) ^ [] : [50944 ^ [_1810810, _1810812] = 50945 ^ [_1810810, _1810812]], (50949 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1810810, _1810810)), hAPP(hAPP(c_Product__Type_OPair(_1810810, _1810810), 50945 ^ [_1810810, _1810812]), 50944 ^ [_1810810, _1810812])), _1810812)))], (50947 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1810810, _1810810)), hAPP(hAPP(c_Product__Type_OPair(_1810810, _1810810), 50944 ^ [_1810810, _1810812]), 50945 ^ [_1810810, _1810812])), _1810812)))]], -(c_Relation_Oantisym(_1810810, _1810812))], (48370 ^ _779999) ^ [_1753347, _1753349, _1753351] : [-(hAPP(c_List_Orev(_1753347), hAPP(hAPP(c_List_Oappend(_1753347), _1753349), _1753351)) = hAPP(hAPP(c_List_Oappend(_1753347), hAPP(c_List_Orev(_1753347), _1753351)), hAPP(c_List_Orev(_1753347), _1753349)))], (21034 ^ _779999) ^ [_1162215, _1162217, _1162219] : [class_Orderings_Oord(_1162215), 21037 ^ _779999 : [(21044 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162215), _1162217), _1162219)), -(hBOOL(hAPP(hAPP(c_member(_1162215), _1162217), hAPP(c_SetInterval_Oord__class_OatMost(_1162215), _1162219))))], (21038 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1162215), _1162217), hAPP(c_SetInterval_Oord__class_OatMost(_1162215), _1162219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162215), _1162217), _1162219)))]]], (50581 ^ _779999) ^ [_1802375, _1802377] : [c_Relation_Otrans(_1802375, _1802377), -(c_Transitive__Closure_Otrancl(_1802375, _1802377) = _1802377)], (43193 ^ _779999) ^ [_1633378, _1633380, _1633382, _1633384, _1633386, _1633388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633378), tc_List_Olist(_1633378))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633378), tc_List_Olist(_1633378)), hAPP(hAPP(c_List_Olist_OCons(_1633378), _1633380), _1633382)), hAPP(hAPP(c_List_Olist_OCons(_1633378), _1633384), _1633386))), c_List_Olexord(_1633378, _1633388))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633378, _1633378)), hAPP(hAPP(c_Product__Type_OPair(_1633378, _1633378), _1633380), _1633384)), _1633388))), 43200 ^ _779999 : [(43203 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633378), tc_List_Olist(_1633378))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633378), tc_List_Olist(_1633378)), _1633382), _1633386)), c_List_Olexord(_1633378, _1633388))))], (43201 ^ _779999) ^ [] : [-(_1633380 = _1633384)]]], (24302 ^ _779999) ^ [_1235157, _1235159, _1235161] : [class_Orderings_Olinorder(_1235157), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235157), _1235159), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235157), _1235159), _1235161)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235157), _1235159), _1235161))], (14948 ^ _779999) ^ [_1048246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1048246)), 14952 ^ _779999 : [(14953 ^ _779999) ^ [_1048326] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1048326), _1048246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048326), 14951 ^ [_1048246])))]]], (11568 ^ _779999) ^ [_982605, _982607, _982609] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982605, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982605, tc_HOL_Obool)), _982607), _982609)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982605, tc_HOL_Obool)), _982607), _982609)) = _982607)], (9076 ^ _779999) ^ [_935175, _935177, _935179, _935181] : [class_Orderings_Opreorder(_935175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935175), _935177), _935179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935175), _935179), _935181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935175), _935177), _935181)))], (20858 ^ _779999) ^ [_1158690] : [class_Rings_Olinordered__idom(_1158690), -(hAPP(c_Groups_Oabs__class_Oabs(_1158690), c_Groups_Oone__class_Oone(_1158690)) = c_Groups_Oone__class_Oone(_1158690))], (8892 ^ _779999) ^ [_932499, _932501, _932503] : [class_Orderings_Olinorder(_932499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932499), _932501), _932503))), -(_932501 = _932503), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932499), _932503), _932501)))], (50395 ^ _779999) ^ [_1797942, _1797944, _1797946] : [c_List_Oall__interval__int(_1797942, _1797944, _1797946), -(c_List_Olist__all(tc_Int_Oint, _1797942, c_List_Oupto(_1797944, _1797946)))], (21369 ^ _779999) ^ [_1169157, _1169159, _1169161] : [class_Orderings_Olinorder(_1169157), 21372 ^ _779999 : [(21379 ^ _779999) ^ [] : [_1169159 = _1169161, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169157), _1169159) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169157), _1169161))], (21373 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169157), _1169159) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1169157), _1169161), -(_1169159 = _1169161)]]], (22692 ^ _779999) ^ [_1200369, _1200371, _1200373, _1200375, _1200377] : [22694 ^ _779999 : [(22700 ^ _779999) ^ [] : [hBOOL(hAPP(_1200377, 22696 ^ [_1200369, _1200371, _1200373, _1200375, _1200377]))], (22698 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200369), 22696 ^ [_1200369, _1200371, _1200373, _1200375, _1200377]), hAPP(_1200375, 22693 ^ [_1200369, _1200371, _1200373, _1200375, _1200377]))))], (22695 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200371), 22693 ^ [_1200369, _1200371, _1200373, _1200375, _1200377]), _1200373)))]], 22701 ^ _779999 : [(22702 ^ _779999) ^ [_1200679] : [hBOOL(hAPP(hAPP(c_member(_1200369), _1200679), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1200371, tc_fun(_1200369, tc_HOL_Obool)), _1200373), _1200375))), -(hBOOL(hAPP(_1200377, _1200679)))]]], (2782 ^ _779999) ^ [_821238, _821240, _821242, _821244, _821246, _821248] : [-(c_FunDef_Oin__rel(_821248, _821244, _821240) = c_FunDef_Oin__rel(_821246, _821242, _821238)), _821248 = _821246, _821244 = _821242, _821240 = _821238], (8144 ^ _779999) ^ [_917838, _917840, _917842] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917838, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917838, tc_HOL_Obool)), _917840), _917842)), _917842) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917838, tc_HOL_Obool)), _917840), _917842))], (16505 ^ _779999) ^ [_1078220, _1078222, _1078224, _1078226] : [class_Rings_Olinordered__ring__strict(_1078220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078220), _1078222), _1078224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078220), _1078226), c_Groups_Ozero__class_Ozero(_1078220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078220), _1078224), _1078226)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078220), _1078222), _1078226))))], (23291 ^ _779999) ^ [_1214552, _1214554, _1214556, _1214558] : [class_Orderings_Olinorder(_1214552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214552), _1214554), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214552), _1214556), _1214558))), 23298 ^ _779999 : [(23301 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214552), _1214554), _1214558)))], (23299 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214552), _1214554), _1214556)))]]], (15413 ^ _779999) ^ [_1057106, _1057108, _1057110, _1057112] : [c_Sum__Type_OPlus(_1057106, _1057108, _1057110, _1057112) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1057106, _1057108), tc_HOL_Obool)), 15416 ^ _779999 : [(15419 ^ _779999) ^ [] : [-(_1057112 = c_Orderings_Obot__class_Obot(tc_fun(_1057108, tc_HOL_Obool)))], (15417 ^ _779999) ^ [] : [-(_1057110 = c_Orderings_Obot__class_Obot(tc_fun(_1057106, tc_HOL_Obool)))]]], (6181 ^ _779999) ^ [_878739, _878741, _878743, _878745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878739, tc_HOL_Obool)), _878741), _878743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878739, tc_HOL_Obool)), _878743), _878745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878739, tc_HOL_Obool)), _878741), _878745)))], (1060 ^ _779999) ^ [_796087, _796089, _796091, _796093] : [-(c_Equiv__Relations_Oequivp(_796091, _796087)), c_Equiv__Relations_Oequivp(_796093, _796089), _796093 = _796091, _796089 = _796087], (37331 ^ _779999) ^ [_1487728, _1487730] : [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), _1487728), _1487730)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1487728), _1487730)))], (51353 ^ _779999) ^ [_1818702, _1818704, _1818706, _1818708] : [hAPP(c_Set_Oimage(_1818702, _1818704, _1818706), c_Orderings_Otop__class_Otop(tc_fun(_1818702, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1818704, tc_HOL_Obool)), -(hAPP(_1818706, hAPP(c_Hilbert__Choice_Oinv__into(_1818702, _1818704, c_Orderings_Otop__class_Otop(tc_fun(_1818702, tc_HOL_Obool)), _1818706), _1818708)) = _1818708)], (14187 ^ _779999) ^ [_1033171, _1033173, _1033175] : [class_Groups_Oordered__comm__monoid__add(_1033171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033171), _1033173), c_Groups_Ozero__class_Ozero(_1033171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033171), _1033175), c_Groups_Ozero__class_Ozero(_1033171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033171), _1033173), _1033175)), c_Groups_Ozero__class_Ozero(_1033171))))], (27496 ^ _779999) ^ [_1297194, _1297196, _1297198, _1297200] : [class_Groups_Ocomm__monoid__mult(_1297194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297196), _1297198)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297196, _1297194), hAPP(c_COMBK(_1297194, _1297196), _1297200)), _1297198) = hAPP(hAPP(c_Power_Opower__class_Opower(_1297194), _1297200), hAPP(c_Finite__Set_Ocard(_1297196), _1297198)))], (10994 ^ _779999) ^ [_970008, _970010, _970012] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970008, tc_HOL_Obool)), _970010), _970012) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970008, tc_HOL_Obool)), _970012), _970010))], (28448 ^ _779999) ^ [_1314806, _1314808, _1314810] : [class_Fields_Olinordered__field(_1314806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314806), _1314808), c_Groups_Ozero__class_Ozero(_1314806))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314806), _1314810), c_Groups_Ozero__class_Ozero(_1314806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314806), c_Groups_Ozero__class_Ozero(_1314806)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314806), _1314808), _1314810))))], (18571 ^ _779999) ^ [_1118395, _1118397, _1118399, _1118401] : [class_Rings_Osemiring__1(_1118395), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1118397, _1118395), hAPP(c_COMBK(_1118395, _1118397), _1118399)), _1118401) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118395), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1118395), hAPP(c_Finite__Set_Ocard(_1118397), _1118401))), _1118399))], (25315 ^ _779999) ^ [_1255254, _1255256, _1255258, _1255260] : [class_Groups_Ocomm__monoid__mult(_1255254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1255256), _1255258)), 25325 ^ _779999 : [(25328 ^ _779999) ^ [] : [hAPP(_1255260, 25324 ^ [_1255254, _1255256, _1255258, _1255260]) = c_Groups_Oone__class_Oone(_1255254)], (25326 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1255256), 25324 ^ [_1255254, _1255256, _1255258, _1255260]), _1255258)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1255254, _1255256, c_Groups_Otimes__class_Otimes(_1255254)), _1255260), c_Groups_Oone__class_Oone(_1255254)), _1255258) = c_Groups_Oone__class_Oone(_1255254))], (23667 ^ _779999) ^ [_1222110, _1222112, _1222114] : [class_Orderings_Olinorder(_1222110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222110), _1222112)), -(_1222112 = c_Orderings_Obot__class_Obot(tc_fun(_1222110, tc_HOL_Obool))), 23678 ^ _779999 : [(23679 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222110), _1222114), hAPP(c_Finite__Set_Ofold1(_1222110, c_Orderings_Oord__class_Omin(_1222110)), _1222112))), 23682 ^ _779999 : [(23683 ^ _779999) ^ [_1222403] : [hBOOL(hAPP(hAPP(c_member(_1222110), _1222403), _1222112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222110), _1222114), _1222403)))]]], (23689 ^ _779999) ^ [] : [23691 ^ _779999 : [(23694 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222110), _1222114), 23690 ^ [_1222110, _1222112, _1222114]))], (23692 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222110), 23690 ^ [_1222110, _1222112, _1222114]), _1222112)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222110), _1222114), hAPP(c_Finite__Set_Ofold1(_1222110, c_Orderings_Oord__class_Omin(_1222110)), _1222112))))]]], (18259 ^ _779999) ^ [_1112377, _1112379] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1112377), _1112379)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1112377)), hAPP(c_Nat_OSuc, _1112379)))], (41007 ^ _779999) ^ [_1580749, _1580751] : [-(c_Transitive__Closure_Ortrancl(_1580749, _1580751) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1580749, _1580749), 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(_1580749, _1580749), tc_HOL_Obool), tc_fun(tc_prod(_1580749, _1580749), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1580749, _1580749), tc_HOL_Obool)), _1580751)))], (33319 ^ _779999) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (13323 ^ _779999) ^ [_1017239, _1017241, _1017243] : [class_Groups_Ogroup__add(_1017239), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1017239), _1017241), _1017243)), _1017243) = _1017241)], (47298 ^ _779999) ^ [_1729951, _1729953] : [c_List_Oconcat(_1729951, _1729953) = c_List_Olist_ONil(_1729951), 47301 ^ _779999 : [(47302 ^ _779999) ^ [_1730042] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729951)), _1730042), hAPP(c_List_Oset(tc_List_Olist(_1729951)), _1729953))), -(_1730042 = c_List_Olist_ONil(_1729951))]]], (7344 ^ _779999) ^ [_901875, _901877, _901879] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901875, tc_HOL_Obool)), _901877), _901879) = c_Orderings_Obot__class_Obot(tc_fun(_901875, tc_HOL_Obool))), _901877 = c_Orderings_Obot__class_Obot(tc_fun(_901875, tc_HOL_Obool)), _901879 = c_Orderings_Obot__class_Obot(tc_fun(_901875, tc_HOL_Obool))], (51780 ^ _779999) ^ [_1828151, _1828153] : [class_Lattices_Obounded__lattice(_1828151), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1828153, _1828151)))], (2340 ^ _779999) ^ [_814469, _814471, _814473, _814475] : [-(c_Orderings_Oord_Omin(_814475, _814471) = c_Orderings_Oord_Omin(_814473, _814469)), _814475 = _814473, _814471 = _814469], (40551 ^ _779999) ^ [_1569740, _1569742, _1569744, _1569746] : [-(c_Wellfounded_Owf(_1569740, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1569740, _1569740)), hAPP(hAPP(c_Product__Type_OPair(_1569740, _1569740), _1569742), _1569744)), _1569746))), c_Wellfounded_Owf(_1569740, _1569746), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569740, _1569740)), hAPP(hAPP(c_Product__Type_OPair(_1569740, _1569740), _1569744), _1569742)), c_Transitive__Closure_Ortrancl(_1569740, _1569746))))], (40407 ^ _779999) ^ [_1566448, _1566450, _1566452] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1566448, _1566448, _1566450), c_Relation_OId(_1566448)), _1566452) = _1566452)], (5072 ^ _779999) ^ [_857535, _857537] : [_857537 = _857535, -(c_DSequence_Oempty(_857537) = c_DSequence_Oempty(_857535))], (22483 ^ _779999) ^ [_1196019, _1196021] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1196019), c_Orderings_Otop__class_Otop(tc_fun(_1196019, tc_HOL_Obool)))), c_Fun_Oinj__on(_1196019, _1196019, _1196021, c_Orderings_Otop__class_Otop(tc_fun(_1196019, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1196019, _1196019, _1196021), c_Orderings_Otop__class_Otop(tc_fun(_1196019, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1196019, tc_HOL_Obool)))], (46249 ^ _779999) ^ [_1706387, _1706389, _1706391, _1706393] : [-(hAPP(hAPP(c_List_Omap(_1706387, _1706389), _1706391), c_List_Obutlast(_1706387, _1706393)) = c_List_Obutlast(_1706389, hAPP(hAPP(c_List_Omap(_1706387, _1706389), _1706391), _1706393)))], (19019 ^ _779999) ^ [_1126789, _1126791] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126789), _1126791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126791), _1126789)))], (47474 ^ _779999) ^ [_1734672, _1734674, _1734676, _1734678] : [-(hBOOL(hAPP(_1734672, _1734674))), -(c_List_Oremove1(_1734676, _1734674, hAPP(c_List_Ofilter(_1734676, _1734672), _1734678)) = hAPP(c_List_Ofilter(_1734676, _1734672), _1734678))], (27134 ^ _779999) ^ [_1290658, _1290660, _1290662] : [class_Rings_Odivision__ring(_1290658), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1290658), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290658), _1290660), _1290662)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290658), hAPP(c_Groups_Ouminus__class_Ouminus(_1290658), _1290660)), _1290662))], (40047 ^ _779999) ^ [_1557221, _1557223, _1557225, _1557227] : [hAPP(c_Com_Ocom_OBODY, _1557221) = c_Com_Ocom_OLocal(_1557223, _1557225, _1557227)], (40317 ^ _779999) ^ [_1564203, _1564205, _1564207, _1564209, _1564211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564203, _1564203)), hAPP(hAPP(c_Product__Type_OPair(_1564203, _1564203), _1564205), _1564207)), c_Transitive__Closure_Ortrancl(_1564203, _1564209))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564203, _1564203)), hAPP(hAPP(c_Product__Type_OPair(_1564203, _1564203), _1564207), _1564211)), _1564209)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564203, _1564203)), hAPP(hAPP(c_Product__Type_OPair(_1564203, _1564203), _1564205), _1564211)), c_Transitive__Closure_Ortrancl(_1564203, _1564209))))], (35203 ^ _779999) ^ [_1441809, _1441811, _1441813] : [class_Enum_Oenum(_1441809), class_Enum_Oenum(_1441811), 35210 ^ _779999 : [(35217 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1441811), hAPP(hAPP(c_COMBB(tc_fun(_1441809, tc_HOL_Obool), tc_HOL_Obool, _1441811), c_Enum_Oenum__class_Oenum__all(_1441809)), hAPP(hAPP(c_COMBB(tc_fun(_1441809, tc_prod(_1441811, _1441809)), tc_fun(_1441809, tc_HOL_Obool), _1441811), hAPP(c_COMBB(tc_prod(_1441811, _1441809), tc_HOL_Obool, _1441809), _1441813)), c_Product__Type_OPair(_1441811, _1441809))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1441811, _1441809)), _1441813)))], (35211 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1441811, _1441809)), _1441813)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1441811), hAPP(hAPP(c_COMBB(tc_fun(_1441809, tc_HOL_Obool), tc_HOL_Obool, _1441811), c_Enum_Oenum__class_Oenum__all(_1441809)), hAPP(hAPP(c_COMBB(tc_fun(_1441809, tc_prod(_1441811, _1441809)), tc_fun(_1441809, tc_HOL_Obool), _1441811), hAPP(c_COMBB(tc_prod(_1441811, _1441809), tc_HOL_Obool, _1441809), _1441813)), c_Product__Type_OPair(_1441811, _1441809))))))]]], (36338 ^ _779999) ^ [_1464310, _1464312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464312)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1464310, _1464312) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1464310, _1464312)))], (34341 ^ _779999) ^ [_1422154, _1422156] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1422154)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1422156))) = 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), _1422154), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422156))))], (39405 ^ _779999) ^ [_1542127, _1542129, _1542131, _1542133, _1542135, _1542137, _1542139, _1542141] : [hAPP(c_Fun_Ocomp(_1542127, _1542129, _1542131, _1542133), _1542135) = hAPP(c_Fun_Ocomp(_1542137, _1542129, _1542131, _1542139), _1542141), 39408 ^ _779999 : [(39409 ^ _779999) ^ [_1542242] : [-(hAPP(_1542133, hAPP(_1542135, _1542242)) = hAPP(_1542139, hAPP(_1542141, _1542242)))]]], (7520 ^ _779999) ^ [_905934, _905936, _905938, _905940, _905942, _905944] : [c_Hoare__Mirabelle_Ohoare__derivs(_905934, _905936, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905934)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905934), _905938), _905940), _905942)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905934), tc_HOL_Obool)))), 7527 ^ _779999 : [(7530 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_905938, 7525 ^ [_905934, _905936, _905938, _905940, _905942, _905944]), 7526 ^ [_905934, _905936, _905938, _905940, _905942, _905944]))], (7528 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_905944, 7525 ^ [_905934, _905936, _905938, _905940, _905942, _905944]), 7526 ^ [_905934, _905936, _905938, _905940, _905942, _905944])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_905934, _905936, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905934)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905934), _905944), _905940), _905942)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905934), tc_HOL_Obool)))))], (48052 ^ _779999) ^ [_1746829, _1746831, _1746833, _1746835, _1746837] : [class_Orderings_Olinorder(_1746829), -(c_List_Olinorder__class_Osorted(_1746829, hAPP(hAPP(c_List_Omap(_1746831, _1746829), _1746833), hAPP(c_List_Ofilter(_1746831, hAPP(hAPP(c_COMBC(_1746831, _1746829, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1746829, tc_fun(_1746829, tc_HOL_Obool), _1746831), c_fequal), _1746833)), hAPP(_1746835, _1746837))), _1746837))))], (14319 ^ _779999) ^ [_1035659, _1035661, _1035663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035659), _1035661)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035663), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035661), _1035659))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035663), _1035659)), hAPP(c_Nat_OSuc, _1035661)))], (11086 ^ _779999) ^ [_972071, _972073, _972075, _972077] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972071, tc_HOL_Obool)), _972073), _972075), _972077)), -(hBOOL(hAPP(_972075, _972077)))], (36398 ^ _779999) ^ [_1465374, _1465376, _1465378, _1465380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1465380, _1465376)), hAPP(_1465380, _1465378))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465374, _1465374)), hAPP(hAPP(c_Product__Type_OPair(_1465374, _1465374), _1465376), _1465378)), hAPP(c_Wellfounded_Omeasure(_1465374), _1465380))))], (40191 ^ _779999) ^ [_1560356, _1560358, _1560360, _1560362, _1560364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560356, _1560356)), hAPP(hAPP(c_Product__Type_OPair(_1560356, _1560356), _1560358), _1560360)), _1560362)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560356, _1560356)), hAPP(hAPP(c_Product__Type_OPair(_1560356, _1560356), _1560360), _1560364)), _1560362)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560356, _1560356)), hAPP(hAPP(c_Product__Type_OPair(_1560356, _1560356), _1560358), _1560364)), c_Transitive__Closure_Otrancl(_1560356, _1560362))))], (5652 ^ _779999) ^ [_866497, _866499, _866501, _866503] : [-(c_COMBK(_866503, _866499) = c_COMBK(_866501, _866497)), _866503 = _866501, _866499 = _866497], (39835 ^ _779999) ^ [_1552190, _1552192, _1552194, _1552196, _1552198] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1552190, _1552192, _1552194), _1552196), _1552198)), 39838 ^ _779999 : [(39841 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1552194, _1552198)))], (39839 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1552192, _1552196), _1552198)))]]], (14465 ^ _779999) ^ [_1038574, _1038576, _1038578, _1038580, _1038582] : [class_Groups_Ocomm__monoid__add(_1038574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038576), _1038578)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038576), _1038580)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038574), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038576, _1038574), _1038582), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038576, tc_HOL_Obool)), _1038578), _1038580))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038576, _1038574), _1038582), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038576, tc_HOL_Obool)), _1038578), _1038580))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038574), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038576, _1038574), _1038582), _1038578)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038576, _1038574), _1038582), _1038580)))], (3710 ^ _779999) ^ [_835674, _835676, _835678, _835680] : [-(c_Random_Opick(_835680, _835676) = c_Random_Opick(_835678, _835674)), _835680 = _835678, _835676 = _835674], (7382 ^ _779999) ^ [_902618, _902620, _902622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902618, tc_HOL_Obool)), _902620), _902622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902618, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_902618, tc_fun(_902618, tc_HOL_Obool), tc_HOL_Obool), c_member(_902618)), _902620)), hAPP(hAPP(c_COMBC(_902618, tc_fun(_902618, tc_HOL_Obool), tc_HOL_Obool), c_member(_902618)), _902622))))], (29008 ^ _779999) ^ [_1324801, _1324803, _1324805, _1324807] : [class_Fields_Olinordered__field(_1324801), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324801), _1324803), c_Groups_Ozero__class_Ozero(_1324801))), 29015 ^ _779999 : [(29022 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324801), _1324807), _1324803)), _1324805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324801), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324801), _1324805), _1324803)), _1324807)))], (29016 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324801), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324801), _1324805), _1324803)), _1324807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324801), _1324807), _1324803)), _1324805)))]]], (44738 ^ _779999) ^ [_1672761, _1672763, _1672765, _1672767] : [_1672761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1672763), _1672761), hAPP(hAPP(c_List_Olist_OCons(_1672763), _1672765), _1672767)) = c_List_Olist_ONil(_1672763))], (22888 ^ _779999) ^ [_1205617, _1205619, _1205621, _1205623, _1205625] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205617, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205619, tc_fun(_1205617, tc_HOL_Obool)), _1205621), _1205623)), _1205625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205619, tc_fun(_1205617, tc_HOL_Obool)), _1205621), hAPP(hAPP(c_COMBC(_1205619, tc_fun(_1205617, tc_HOL_Obool), tc_fun(_1205617, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205617, tc_HOL_Obool), tc_fun(tc_fun(_1205617, tc_HOL_Obool), tc_fun(_1205617, tc_HOL_Obool)), _1205619), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205617, tc_HOL_Obool))), _1205623)), _1205625)))], (3856 ^ _779999) ^ [_837963, _837965, _837967, _837969, _837971, _837973] : [-(c_Divides_Odiv__class_Omod(_837973, _837969, _837965) = c_Divides_Odiv__class_Omod(_837971, _837967, _837963)), _837973 = _837971, _837969 = _837967, _837965 = _837963], (18049 ^ _779999) ^ [_1108468, _1108470, _1108472, _1108474, _1108476, _1108478] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1108468, _1108470, _1108472, _1108474, _1108476), _1108478)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1108468), _1108476)))], (51918 ^ _779999) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (49178 ^ _779999) ^ [_1771216, _1771218, _1771220, _1771222] : [49180 ^ _779999 : [(49183 ^ _779999) ^ [] : [hBOOL(hAPP(_1771220, 49179 ^ [_1771216, _1771218, _1771220, _1771222]))], (49181 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771216), 49179 ^ [_1771216, _1771218, _1771220, _1771222]), hAPP(c_List_Oset(_1771216), _1771218))))]], -(c_List_OtakeWhile(_1771216, _1771220, hAPP(hAPP(c_List_Oappend(_1771216), _1771218), _1771222)) = hAPP(hAPP(c_List_Oappend(_1771216), _1771218), c_List_OtakeWhile(_1771216, _1771220, _1771222)))], (21239 ^ _779999) ^ [_1166575, _1166577, _1166579] : [class_Orderings_Oorder(_1166575), 21242 ^ _779999 : [(21249 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166575), _1166579), _1166577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166575, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1166575), _1166577)), hAPP(c_SetInterval_Oord__class_OatLeast(_1166575), _1166579))))], (21243 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166575, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1166575), _1166577)), hAPP(c_SetInterval_Oord__class_OatLeast(_1166575), _1166579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166575), _1166579), _1166577)))]]], (49460 ^ _779999) ^ [_1777751, _1777753, _1777755] : [49462 ^ _779999 : [(49465 ^ _779999) ^ [] : [hBOOL(hAPP(_1777753, hAPP(hAPP(c_List_Onth(_1777751), _1777755), 49461 ^ [_1777751, _1777753, _1777755])))], (49463 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49461 ^ [_1777751, _1777753, _1777755]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777751)), _1777755))))]], -(c_List_Olist__all(_1777751, _1777753, _1777755))], (36309 ^ _779999) ^ [_1463794, _1463796, _1463798] : [36311 ^ _779999 : [(36314 ^ _779999) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1463794, _1463796), 36310 ^ [_1463794, _1463796, _1463798]))], (36312 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1463796, 36310 ^ [_1463794, _1463796, _1463798]), _1463798)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1463794, _1463796), _1463798)))], (26446 ^ _779999) ^ [_1275464, _1275466, _1275468] : [class_Groups_Oordered__ab__group__add__abs(_1275464), 26449 ^ _779999 : [(26458 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), hAPP(c_Groups_Oabs__class_Oabs(_1275464), _1275466)), _1275468))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), _1275466), _1275468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), hAPP(c_Groups_Ouminus__class_Ouminus(_1275464), _1275466)), _1275468))], (26450 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), hAPP(c_Groups_Oabs__class_Oabs(_1275464), _1275466)), _1275468)), 26453 ^ _779999 : [(26456 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), hAPP(c_Groups_Ouminus__class_Ouminus(_1275464), _1275466)), _1275468)))], (26454 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275464), _1275466), _1275468)))]]]]], (24332 ^ _779999) ^ [_1235836, _1235838, _1235840, _1235842] : [class_Orderings_Olinorder(_1235836), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235836), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235836), _1235838), _1235840)), _1235842) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235836), _1235838), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235836), _1235840), _1235842)))], (26010 ^ _779999) ^ [_1267784, _1267786, _1267788, _1267790, _1267792] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1267784, _1267786, _1267788)), _1267790), _1267792))), 26011 ^ _779999 : [(26018 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1267784, _1267790))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267788), _1267790), _1267792))], (26012 ^ _779999) ^ [] : [hBOOL(hAPP(_1267784, _1267790)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267786), _1267790), _1267792))]]], (22391 ^ _779999) ^ [_1194215, _1194217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194215), hAPP(c_Set_OCollect(_1194215), _1194217))), 22394 ^ _779999 : [(22401 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194215), c_Orderings_Otop__class_Otop(tc_fun(_1194215, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1194215), hAPP(c_Set_OCollect(_1194215), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1194215), c_fNot), _1194217)))))], (22395 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194215), hAPP(c_Set_OCollect(_1194215), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1194215), c_fNot), _1194217)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1194215), c_Orderings_Otop__class_Otop(tc_fun(_1194215, tc_HOL_Obool)))))]]], (46225 ^ _779999) ^ [_1705645, _1705647, _1705649, _1705651, _1705653] : [class_Rings_Osemiring__0(_1705645), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705645), hAPP(hAPP(c_List_Omap(_1705647, _1705645), hAPP(hAPP(c_COMBC(_1705647, _1705645, _1705645), hAPP(hAPP(c_COMBB(_1705645, tc_fun(_1705645, _1705645), _1705647), c_Groups_Otimes__class_Otimes(_1705645)), _1705649)), _1705651)), _1705653)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1705645), hAPP(c_List_Omonoid__add__class_Olistsum(_1705645), hAPP(hAPP(c_List_Omap(_1705647, _1705645), _1705649), _1705653))), _1705651))], (18845 ^ _779999) ^ [_1123952, _1123954] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123952) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123954), -(_1123952 = _1123954)], (23004 ^ _779999) ^ [_1208986, _1208988, _1208990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208986, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208986, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23005 ^ [_1208986, _1208988, _1208990])), _1208988)), _1208990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208986, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208986, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1208988)), _1208990)))], (36659 ^ _779999) ^ [_1470640, _1470642, _1470644, _1470646] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1470640, _1470642), _1470644), _1470646) = hAPP(c_Set_OCollect(tc_prod(_1470642, _1470642)), hAPP(c_Product__Type_Oprod_Oprod__case(_1470642, _1470642, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1470642, tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_fun(_1470642, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470642, tc_fun(tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_fun(_1470642, tc_HOL_Obool)), _1470642), c_COMBC(_1470642, tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470642, tc_prod(_1470640, _1470640)), tc_fun(_1470642, tc_fun(tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_HOL_Obool)), _1470642), hAPP(c_COMBB(tc_prod(_1470640, _1470640), tc_fun(tc_fun(tc_prod(_1470640, _1470640), tc_HOL_Obool), tc_HOL_Obool), _1470642), c_member(tc_prod(_1470640, _1470640)))), hAPP(hAPP(c_COMBC(_1470642, tc_fun(_1470642, _1470640), tc_fun(_1470642, tc_prod(_1470640, _1470640))), hAPP(hAPP(c_COMBB(tc_fun(_1470640, tc_prod(_1470640, _1470640)), tc_fun(tc_fun(_1470642, _1470640), tc_fun(_1470642, tc_prod(_1470640, _1470640))), _1470642), c_COMBB(_1470640, tc_prod(_1470640, _1470640), _1470642)), hAPP(hAPP(c_COMBB(_1470640, tc_fun(_1470640, tc_prod(_1470640, _1470640)), _1470642), c_Product__Type_OPair(_1470640, _1470640)), _1470646))), _1470646)))), _1470644))))], (34841 ^ _779999) ^ [_1431553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1431553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1431553)))], (49744 ^ _779999) ^ [_1783608, _1783610, _1783612, _1783614] : [-(c_New__Random__Sequence_Opos__map(_1783608, _1783610, _1783612, _1783614) = c_New__Random__Sequence_Opos__bind(_1783608, _1783610, _1783614, hAPP(c_Fun_Ocomp(_1783610, 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(_1783610))))), _1783608, c_New__Random__Sequence_Opos__single(_1783610)), _1783612)))], (3146 ^ _779999) ^ [_826926, _826928, _826930, _826932] : [-(c_Nitpick_Oinverse__frac(_826932, _826928) = c_Nitpick_Oinverse__frac(_826930, _826926)), _826932 = _826930, _826928 = _826926], (10217 ^ _779999) ^ [_956014, _956016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956014), _956016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956014)), hAPP(c_Nat_OSuc, _956016))))], (7629 ^ _779999) ^ [_908212] : [hAPP(c_Com_Ocom_OBODY, _908212) = c_Com_Ocom_OSKIP], (34977 ^ _779999) ^ [_1433667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1433667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1433667))))], (10865 ^ _779999) ^ [_967938, _967940, _967942, _967944] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_967938, tc_Nat_Onat), _967940), _967942) = hAPP(c_Nat_OSuc, _967944), 10869 ^ _779999 : [(10872 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_967940, 10868 ^ [_967938, _967940, _967942, _967944]))))], (10870 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_967938), 10868 ^ [_967938, _967940, _967942, _967944]), _967942)))]]], (49894 ^ _779999) ^ [_1787462, _1787464, _1787466, _1787468] : [-(hAPP(hAPP(c_List_Odrop(_1787462), _1787464), c_List_Oreplicate(_1787462, _1787466, _1787468)) = c_List_Oreplicate(_1787462, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1787466), _1787464), _1787468))], (32805 ^ _779999) ^ [_1395316] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395316)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1395316)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395316)), 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)))))], (1138 ^ _779999) ^ [_797212, _797214, _797216, _797218, _797220, _797222, _797224, _797226, _797228, _797230] : [-(c_Fun_Obij__betw(_797228, _797224, _797220, _797216, _797212)), c_Fun_Obij__betw(_797230, _797226, _797222, _797218, _797214), _797230 = _797228, _797226 = _797224, _797222 = _797220, _797218 = _797216, _797214 = _797212], (18443 ^ _779999) ^ [_1115756, _1115758] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1115756), _1115758) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1115756, _1115758))], (15993 ^ _779999) ^ [_1068736, _1068738, _1068740] : [class_Rings_Olinordered__ring__strict(_1068736), 15996 ^ _779999 : [(16011 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068736), _1068738), _1068740)), c_Groups_Ozero__class_Ozero(_1068736)))), 16012 ^ _779999 : [(16019 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), _1068738), c_Groups_Ozero__class_Ozero(_1068736))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), c_Groups_Ozero__class_Ozero(_1068736)), _1068740))], (16013 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), c_Groups_Ozero__class_Ozero(_1068736)), _1068738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), _1068740), c_Groups_Ozero__class_Ozero(_1068736)))]]], (15997 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068736), _1068738), _1068740)), c_Groups_Ozero__class_Ozero(_1068736))), 16002 ^ _779999 : [(16005 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), _1068740), c_Groups_Ozero__class_Ozero(_1068736))))], (16003 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), c_Groups_Ozero__class_Ozero(_1068736)), _1068738)))]], 16006 ^ _779999 : [(16009 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), c_Groups_Ozero__class_Ozero(_1068736)), _1068740)))], (16007 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068736), _1068738), c_Groups_Ozero__class_Ozero(_1068736))))]]]]], (42006 ^ _779999) ^ [_1604486, _1604488, _1604490, _1604492] : [-(_1604486 = c_Orderings_Obot__class_Obot(tc_fun(_1604488, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604488, tc_fun(_1604490, tc_HOL_Obool)), _1604486), hAPP(c_COMBK(tc_fun(_1604490, tc_HOL_Obool), _1604488), _1604492)) = _1604492)], (4012 ^ _779999) ^ [_840401, _840403, _840405, _840407] : [-(c_List_Olex(_840407, _840403) = c_List_Olex(_840405, _840401)), _840407 = _840405, _840403 = _840401], (22018 ^ _779999) ^ [_1185544, _1185546, _1185548] : [class_Lattices_Odistrib__lattice(_1185544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1185544), _1185546)), -(_1185546 = c_Orderings_Obot__class_Obot(tc_fun(_1185544, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1185544), _1185548)), -(_1185548 = c_Orderings_Obot__class_Obot(tc_fun(_1185544, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1185544), c_Big__Operators_Olattice__class_OSup__fin(_1185544, _1185546)), c_Big__Operators_Olattice__class_OSup__fin(_1185544, _1185548)) = c_Big__Operators_Olattice__class_OSup__fin(_1185544, hAPP(c_Set_OCollect(_1185544), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_HOL_Obool), tc_HOL_Obool, _1185544), c_HOL_OEx(_1185544)), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool)), tc_fun(_1185544, tc_HOL_Obool), _1185544), hAPP(c_COMBB(tc_fun(_1185544, tc_HOL_Obool), tc_HOL_Obool, _1185544), c_HOL_OEx(_1185544))), hAPP(hAPP(c_COMBC(_1185544, tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool)), tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_fun(tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool))), tc_fun(tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool)), tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool))), _1185544), c_COMBS(_1185544, tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_fun(_1185544, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1185544, tc_fun(tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool))), _1185544), hAPP(c_COMBB(tc_fun(_1185544, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool)), _1185544), c_COMBS(_1185544, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool)), tc_fun(_1185544, tc_fun(_1185544, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1185544), hAPP(c_COMBB(tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1185544), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1185544), c_fconj))), hAPP(hAPP(c_COMBC(_1185544, tc_fun(_1185544, tc_fun(_1185544, _1185544)), tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1185544, _1185544), tc_fun(_1185544, tc_HOL_Obool)), tc_fun(tc_fun(_1185544, tc_fun(_1185544, _1185544)), tc_fun(_1185544, tc_fun(_1185544, tc_HOL_Obool))), _1185544), c_COMBB(tc_fun(_1185544, _1185544), tc_fun(_1185544, tc_HOL_Obool), _1185544)), hAPP(hAPP(c_COMBB(tc_fun(_1185544, tc_HOL_Obool), tc_fun(tc_fun(_1185544, _1185544), tc_fun(_1185544, tc_HOL_Obool)), _1185544), c_COMBB(_1185544, tc_HOL_Obool, _1185544)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1185544)))))), hAPP(hAPP(c_COMBC(_1185544, tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1185544, tc_HOL_Obool), tc_fun(_1185544, tc_HOL_Obool)), _1185544), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1185544)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1185544), c_fconj), hAPP(hAPP(c_COMBC(_1185544, tc_fun(_1185544, tc_HOL_Obool), tc_HOL_Obool), c_member(_1185544)), _1185546)))), hAPP(hAPP(c_COMBC(_1185544, tc_fun(_1185544, tc_HOL_Obool), tc_HOL_Obool), c_member(_1185544)), _1185548))))))))], (49632 ^ _779999) ^ [_1781127, _1781129] : [-(c_FunDef_Ois__measure(_1781127, _1781129))], (22589 ^ _779999) ^ [_1198012] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1198012), c_Orderings_Otop__class_Otop(tc_fun(_1198012, 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(_1198012), c_Orderings_Otop__class_Otop(tc_fun(_1198012, tc_HOL_Obool))))))], (25772 ^ _779999) ^ [_1262972, _1262974, _1262976] : [hBOOL(hAPP(hAPP(c_member(_1262972), _1262974), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262972, tc_HOL_Obool)), _1262976))), hBOOL(hAPP(hAPP(c_member(_1262972), _1262974), _1262976))], (9782 ^ _779999) ^ [_946703, _946705, _946707, _946709, _946711] : [_946703 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_946705, tc_HOL_Obool), _946707), c_Orderings_Oorder__class_Omono(tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool), _946707), hBOOL(hAPP(hAPP(c_member(_946705), _946709), _946711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946705, tc_HOL_Obool)), _946711), hAPP(_946707, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_946705, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_946705, tc_HOL_Obool), tc_fun(tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool)), tc_fun(_946705, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946705, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_946705, tc_HOL_Obool), tc_fun(tc_fun(_946705, tc_HOL_Obool), tc_fun(_946705, tc_HOL_Obool)), tc_fun(_946705, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946705, tc_HOL_Obool))), _946707)), _946711))), _946703))))), -(hBOOL(hAPP(hAPP(c_member(_946705), _946709), _946703)))], (48074 ^ _779999) ^ [_1747294, _1747296, _1747298] : [class_Orderings_Olinorder(_1747294), 48077 ^ _779999 : [(48090 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747294, hAPP(hAPP(c_List_Olist_OCons(_1747294), _1747296), _1747298))), c_List_Olinorder__class_Osorted(_1747294, _1747298), 48096 ^ _779999 : [(48099 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747294), _1747296), 48095 ^ [_1747294, _1747296, _1747298]))], (48097 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747294), 48095 ^ [_1747294, _1747296, _1747298]), hAPP(c_List_Oset(_1747294), _1747298))))]]], (48078 ^ _779999) ^ [] : [c_List_Olinorder__class_Osorted(_1747294, hAPP(hAPP(c_List_Olist_OCons(_1747294), _1747296), _1747298)), 48081 ^ _779999 : [(48084 ^ _779999) ^ [_1747480] : [hBOOL(hAPP(hAPP(c_member(_1747294), _1747480), hAPP(c_List_Oset(_1747294), _1747298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747294), _1747296), _1747480)))], (48082 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747294, _1747298))]]]]], (27198 ^ _779999) ^ [_1292029, _1292031] : [class_Rings_Odivision__ring(_1292029), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292029), c_Groups_Ozero__class_Ozero(_1292029)), _1292031) = c_Groups_Ozero__class_Ozero(_1292029))], (48949 ^ _779999) ^ [_1765723, _1765725, _1765727] : [-(hBOOL(hAPP(hAPP(c_member(_1765723), _1765725), hAPP(c_List_Oset(_1765723), _1765727)))), -(c_List_Oinsert(_1765723, _1765725, _1765727) = hAPP(hAPP(c_List_Olist_OCons(_1765723), _1765725), _1765727))], (1684 ^ _779999) ^ [_804157, _804159] : [-(class_Rings_Olinordered__semidom(_804157)), _804159 = _804157, class_Rings_Olinordered__semidom(_804159)], (13552 ^ _779999) ^ [_1021641, _1021643, _1021645] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1021641), _1021643)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021641), _1021645)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1021641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1021641, tc_HOL_Obool)), _1021643), _1021645))), hAPP(c_Finite__Set_Ocard(_1021641), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1021641, tc_HOL_Obool)), _1021643), _1021645))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1021641), _1021643)), hAPP(c_Finite__Set_Ocard(_1021641), _1021645)))], (26386 ^ _779999) ^ [_1274356, _1274358] : [class_Lattices_Oboolean__algebra(_1274356), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1274356), hAPP(c_Groups_Ouminus__class_Ouminus(_1274356), _1274358)), _1274358) = c_Orderings_Obot__class_Obot(_1274356))], (14257 ^ _779999) ^ [_1034487, _1034489, _1034491] : [hBOOL(hAPP(_1034487, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034489), _1034491))), 14260 ^ _779999 : [(14267 ^ _779999) ^ [_1034678] : [_1034489 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034491), _1034678), -(hBOOL(hAPP(_1034487, _1034678)))], (14261 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034489), _1034491)), -(hBOOL(hAPP(_1034487, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (20433 ^ _779999) ^ [_1151779, _1151781] : [c_Nat__Transfer_Ois__nat(_1151779), c_Nat__Transfer_Ois__nat(_1151781), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1151779, _1151781) = 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, _1151779), hAPP(c_Int_Onat, _1151781))))], (12549 ^ _779999) ^ [_1001938, _1001940, _1001942] : [class_Lattices_Olattice(_1001938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001938), _1001940)), -(hBOOL(hAPP(hAPP(c_member(_1001938), _1001942), _1001940))), -(_1001940 = c_Orderings_Obot__class_Obot(tc_fun(_1001938, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1001938, hAPP(hAPP(c_Set_Oinsert(_1001938), _1001942), _1001940)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1001938), _1001942), c_Big__Operators_Olattice__class_OSup__fin(_1001938, _1001940)))], (35089 ^ _779999) ^ [_1435303] : [-(c_Int_Oint__ge__less__than2(_1435303) = 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), _1435303)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (31295 ^ _779999) ^ [_1366130, _1366132, _1366134] : [-(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), _1366130), _1366132)), _1366134)), _1366132) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1366134), _1366132))], (13425 ^ _779999) ^ [_1019067, _1019069, _1019071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019067), _1019069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019067), _1019071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1019069), _1019071)))], (1032 ^ _779999) ^ [_795701, _795703, _795705, _795707] : [-(c_Relation_Otrans(_795705, _795701)), c_Relation_Otrans(_795707, _795703), _795707 = _795705, _795703 = _795701], (24290 ^ _779999) ^ [_1234939, _1234941, _1234943] : [class_Orderings_Olinorder(_1234939), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234939), _1234941), _1234943) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234939), _1234943), _1234941))], (49365 ^ _779999) ^ [_1775769, _1775771, _1775773] : [c_List_Olist__ex(_1775769, _1775771, hAPP(c_List_Orev(_1775769), _1775773)), -(c_List_Olist__ex(_1775769, _1775771, _1775773))], (49764 ^ _779999) ^ [_1784169, _1784171] : [c_Wellfounded_Oacyclic(_1784169, hAPP(c_Set_OCollect(tc_prod(_1784169, _1784169)), hAPP(c_Product__Type_Oprod_Oprod__case(_1784169, _1784169, tc_HOL_Obool), c_Predicate_Oconversep(_1784169, _1784169, _1784171)))), -(c_Wellfounded_Oacyclic(_1784169, hAPP(c_Set_OCollect(tc_prod(_1784169, _1784169)), hAPP(c_Product__Type_Oprod_Oprod__case(_1784169, _1784169, tc_HOL_Obool), _1784171))))], (46862 ^ _779999) ^ [_1720094, _1720096, _1720098, _1720100, _1720102] : [c_List_Opartition(_1720094, _1720096, _1720098) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720094), tc_List_Olist(_1720094)), _1720100), _1720102), 46865 ^ _779999 : [(46872 ^ _779999) ^ [_1720356] : [hBOOL(hAPP(hAPP(c_member(_1720094), _1720356), hAPP(c_List_Oset(_1720094), _1720102))), hBOOL(hAPP(_1720096, _1720356))], (46866 ^ _779999) ^ [_1720247] : [hBOOL(hAPP(hAPP(c_member(_1720094), _1720247), hAPP(c_List_Oset(_1720094), _1720100))), -(hBOOL(hAPP(_1720096, _1720247)))]]], (18917 ^ _779999) ^ [_1125195, _1125197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125195), _1125197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125195), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1125197)))], (52040 ^ _779999) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (33017 ^ _779999) ^ [_1399022, _1399024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399022), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399024)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399022)) = 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), _1399024), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399022)))), 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)))], (42594 ^ _779999) ^ [_1618722] : [class_Complete__Lattice_Ocomplete__lattice(_1618722), -(c_Complete__Lattice_OInf__class_OInf(_1618722, c_Orderings_Obot__class_Obot(tc_fun(_1618722, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1618722))], (9947 ^ _779999) ^ [_951250, _951252, _951254] : [-(c_Fun_Oinj__on(_951250, _951252, _951254, c_Orderings_Obot__class_Obot(tc_fun(_951250, tc_HOL_Obool))))], (48727 ^ _779999) ^ [_1760995, _1760997, _1760999] : [-(hAPP(hAPP(c_List_Oappend(_1760995), c_List_OtakeWhile(_1760995, _1760997, _1760999)), c_List_OdropWhile(_1760995, _1760997, _1760999)) = _1760999)], (3756 ^ _779999) ^ [_836363, _836365] : [_836365 = _836363, -(c_SetInterval_Oord__class_OlessThan(_836365) = c_SetInterval_Oord__class_OlessThan(_836363))], (25344 ^ _779999) ^ [_1255734, _1255736, _1255738, _1255740, _1255742, _1255744] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_1255734, _1255736, _1255738), _1255740, _1255742, _1255744), 25349 ^ _779999 : [(25352 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1255736, _1255740, _1255742, _1255744))], (25350 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1255734, _1255740)))]], 25353 ^ _779999 : [(25356 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_1255738, _1255740, _1255742, _1255744))], (25354 ^ _779999) ^ [] : [hBOOL(hAPP(_1255734, _1255740))]]], (50961 ^ _779999) ^ [_1811251, _1811253] : [c_Relation_Oantisym(_1811251, _1811253), -(c_Relation_Oantisym(_1811251, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1811251, _1811251), tc_HOL_Obool)), _1811253), c_Relation_OId(_1811251))))], (50617 ^ _779999) ^ [_1802923, _1802925, _1802927, _1802929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802923), _1802925)), 50620 ^ _779999 : [(50621 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802927), hAPP(c_Set_OCollect(_1802927), hAPP(hAPP(c_COMBB(tc_fun(_1802923, tc_HOL_Obool), tc_HOL_Obool, _1802927), c_HOL_OEx(_1802923)), hAPP(hAPP(c_COMBB(tc_fun(_1802923, tc_HOL_Obool), tc_fun(_1802923, tc_HOL_Obool), _1802927), hAPP(c_COMBS(_1802923, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1802923), c_fconj), hAPP(hAPP(c_COMBC(_1802923, tc_fun(_1802923, tc_HOL_Obool), tc_HOL_Obool), c_member(_1802923)), _1802925)))), _1802929))))), 50624 ^ _779999 : [(50625 ^ _779999) ^ [_1803231] : [hBOOL(hAPP(hAPP(c_member(_1802923), _1803231), _1802925)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802927), hAPP(c_Set_OCollect(_1802927), hAPP(hAPP(c_COMBC(_1802927, _1802923, tc_HOL_Obool), _1802929), _1803231)))))]]], (50631 ^ _779999) ^ [] : [50633 ^ _779999 : [(50636 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802927), hAPP(c_Set_OCollect(_1802927), hAPP(hAPP(c_COMBC(_1802927, _1802923, tc_HOL_Obool), _1802929), 50632 ^ [_1802923, _1802925, _1802927, _1802929]))))], (50634 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802923), 50632 ^ [_1802923, _1802925, _1802927, _1802929]), _1802925)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802927), hAPP(c_Set_OCollect(_1802927), hAPP(hAPP(c_COMBB(tc_fun(_1802923, tc_HOL_Obool), tc_HOL_Obool, _1802927), c_HOL_OEx(_1802923)), hAPP(hAPP(c_COMBB(tc_fun(_1802923, tc_HOL_Obool), tc_fun(_1802923, tc_HOL_Obool), _1802927), hAPP(c_COMBS(_1802923, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1802923), c_fconj), hAPP(hAPP(c_COMBC(_1802923, tc_fun(_1802923, tc_HOL_Obool), tc_HOL_Obool), c_member(_1802923)), _1802925)))), _1802929))))))]]], (51950 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (1974 ^ _779999) ^ [_807782, _807784] : [-(hBOOL(_807782)), _807784 = _807782, hBOOL(_807784)], (12113 ^ _779999) ^ [_993782, _993784, _993786, _993788, _993790, _993792] : [c_Finite__Set_Ofolding__image__simple(_993782, _993784, _993786, _993788, _993790, _993792), -(hAPP(_993792, c_Orderings_Obot__class_Obot(tc_fun(_993784, tc_HOL_Obool))) = _993788)], (5412 ^ _779999) ^ [_862777, _862779] : [_862779 = _862777, -(c_Groups_Ozero__class_Ozero(_862779) = c_Groups_Ozero__class_Ozero(_862777))], (39381 ^ _779999) ^ [_1541491, _1541493] : [-(c_Hilbert__Choice_OEps(_1541491, hAPP(c_fequal, _1541493)) = _1541493)], (34663 ^ _779999) ^ [_1428126, _1428128, _1428130] : [class_Rings_Olinordered__idom(_1428126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428126), _1428128), c_Groups_Ozero__class_Ozero(_1428126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428126), hAPP(hAPP(c_Power_Opower__class_Opower(_1428126), _1428128), 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)))), _1428130)))), c_Groups_Ozero__class_Ozero(_1428126))))], (1724 ^ _779999) ^ [_804657, _804659] : [-(class_Rings_Oordered__semiring(_804657)), _804659 = _804657, class_Rings_Oordered__semiring(_804659)], (4506 ^ _779999) ^ [_848498, _848500, _848502, _848504] : [-(c_List_Olast(_848504, _848500) = c_List_Olast(_848502, _848498)), _848504 = _848502, _848500 = _848498], (1654 ^ _779999) ^ [_803782, _803784] : [-(class_Rings_Oordered__comm__semiring(_803782)), _803784 = _803782, class_Rings_Oordered__comm__semiring(_803784)], (40956 ^ _779999) ^ [_1579352, _1579354, _1579356, _1579358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579352, _1579352)), hAPP(hAPP(c_Product__Type_OPair(_1579352, _1579352), _1579354), _1579356)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579352, _1579352), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1579358))), -(_1579354 = _1579356)], (28504 ^ _779999) ^ [_1315826, _1315828, _1315830] : [class_Fields_Olinordered__field__inverse__zero(_1315826), 28507 ^ _779999 : [(28522 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315826), _1315828), _1315830)), c_Groups_Ozero__class_Ozero(_1315826)))), 28523 ^ _779999 : [(28530 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), _1315828), c_Groups_Ozero__class_Ozero(_1315826))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), c_Groups_Ozero__class_Ozero(_1315826)), _1315830))], (28524 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), c_Groups_Ozero__class_Ozero(_1315826)), _1315828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), _1315830), c_Groups_Ozero__class_Ozero(_1315826)))]]], (28508 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315826), _1315828), _1315830)), c_Groups_Ozero__class_Ozero(_1315826))), 28513 ^ _779999 : [(28516 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), _1315830), c_Groups_Ozero__class_Ozero(_1315826))))], (28514 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), c_Groups_Ozero__class_Ozero(_1315826)), _1315828)))]], 28517 ^ _779999 : [(28520 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), c_Groups_Ozero__class_Ozero(_1315826)), _1315830)))], (28518 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315826), _1315828), c_Groups_Ozero__class_Ozero(_1315826))))]]]]], (38042 ^ _779999) ^ [_1505958, _1505960] : [hBOOL(hAPP(hAPP(c_member(_1505958), 38043 ^ [_1505958, _1505960]), c_Wellfounded_Oacc(_1505958, _1505960))), -(c_Wellfounded_Owf(_1505958, _1505960))], (38232 ^ _779999) ^ [_1510472, _1510474] : [-(hAPP(c_Relation_ORange(_1510472, _1510472), c_Relation_OId__on(_1510472, _1510474)) = _1510474)], (47579 ^ _779999) ^ [_1737793, _1737795] : [-(c_Random_Oselect__weight(_1737793, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1737793), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1737793, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1737793, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1737793)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1737795)) = c_Random_Oselect__weight(_1737793, _1737795))], (21686 ^ _779999) ^ [_1174998, _1175000, _1175002] : [hBOOL(hAPP(_1175002, _1175000)), -(hBOOL(hAPP(hAPP(c_member(_1174998), _1175000), hAPP(c_Set_OCollect(_1174998), _1175002))))], (51976 ^ _779999) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (7544 ^ _779999) ^ [_906692, _906694, _906696, _906698, _906700] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_906692), _906694), _906696)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_906698), _906696), _906700)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_906692, _906698)), _906694), _906700)))], (41300 ^ _779999) ^ [_1588102, _1588104, _1588106, _1588108] : [class_Lattices_Osemilattice__inf(_1588102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588102), _1588104)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1588102, _1588102, c_Lattices_Osemilattice__inf__class_Oinf(_1588102)), _1588106), hAPP(hAPP(c_Set_Oinsert(_1588102), _1588108), _1588104)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1588102), _1588108), hAPP(hAPP(c_Finite__Set_Ofold(_1588102, _1588102, c_Lattices_Osemilattice__inf__class_Oinf(_1588102)), _1588106), _1588104)))], (49708 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29332 ^ _779999) ^ [_1331115, _1331117] : [class_Divides_Osemiring__div(_1331115), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1331115), _1331117), c_Groups_Ozero__class_Ozero(_1331115)) = c_Groups_Ozero__class_Ozero(_1331115))], (18231 ^ _779999) ^ [_1111827, _1111829, _1111831] : [class_Rings_Osemiring__1(_1111827), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111829), _1111831)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111827), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111827), _1111829)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111827), _1111831)))], (37531 ^ _779999) ^ [] : [-(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)))], (28490 ^ _779999) ^ [_1315571, _1315573, _1315575] : [class_Fields_Olinordered__field(_1315571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315571), c_Groups_Ozero__class_Ozero(_1315571)), _1315573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315571), c_Groups_Ozero__class_Ozero(_1315571)), _1315575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315571), c_Groups_Ozero__class_Ozero(_1315571)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315571), _1315573), _1315575))))], (24688 ^ _779999) ^ [_1242439, _1242441, _1242443, _1242445, _1242447] : [class_Orderings_Olinorder(_1242439), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242439, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242439, _1242441), _1242443)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242439, _1242445), _1242447)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242439, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242439), _1242441), _1242445)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1242439), _1242443), _1242447)))], (4134 ^ _779999) ^ [_842304, _842306] : [_842306 = _842304, -(c_Lazy__Sequence_Ohit__bound(_842306) = c_Lazy__Sequence_Ohit__bound(_842304))], (17886 ^ _779999) ^ [_1105576] : [_1105576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105576)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10647 ^ _779999) ^ [_963267, _963269, _963271, _963273, _963275, _963277] : [c_Fun_Oinj__on(_963267, _963269, _963271, _963273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963267, tc_HOL_Obool)), _963275), _963273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963267, tc_HOL_Obool)), _963277), _963273)), -(hAPP(c_Set_Oimage(_963267, _963269, _963271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963267, tc_HOL_Obool)), _963275), _963277)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963269, tc_HOL_Obool)), hAPP(c_Set_Oimage(_963267, _963269, _963271), _963275)), hAPP(c_Set_Oimage(_963267, _963269, _963271), _963277)))], (43733 ^ _779999) ^ [_1649265, _1649267, _1649269, _1649271] : [-(hAPP(hAPP(c_List_Otake(_1649265), _1649267), hAPP(hAPP(c_List_Otake(_1649265), _1649269), _1649271)) = hAPP(hAPP(c_List_Otake(_1649265), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1649267), _1649269)), _1649271))], (33651 ^ _779999) ^ [_1409434, _1409436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409434)), hAPP(c_Nat_OSuc, _1409436))), -(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(_1409434))), 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)), _1409436)))))], (34701 ^ _779999) ^ [_1428887, _1428889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1428887), 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)))), _1428889))), 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)))), _1428887)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428889), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1428887))], (35743 ^ _779999) ^ [_1453561] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1453561) = 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), _1453561), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (42049 ^ _779999) ^ [_1605848, _1605850, _1605852, _1605854, _1605856] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605848, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605850, tc_fun(_1605848, tc_HOL_Obool)), _1605852), _1605854)), _1605856) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605850, tc_fun(_1605848, tc_HOL_Obool)), _1605852), hAPP(hAPP(c_COMBC(_1605850, tc_fun(_1605848, tc_HOL_Obool), tc_fun(_1605848, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605848, tc_HOL_Obool), tc_fun(tc_fun(_1605848, tc_HOL_Obool), tc_fun(_1605848, tc_HOL_Obool)), _1605850), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605848, tc_HOL_Obool))), _1605854)), _1605856)))], (18072 ^ _779999) ^ [_1108930, _1108932] : [18074 ^ _779999 : [(18077 ^ _779999) ^ [] : [hBOOL(hAPP(_1108932, 18073 ^ [_1108930, _1108932]))], (18075 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 18073 ^ [_1108930, _1108932]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108930))))]], 18078 ^ _779999 : [(18079 ^ _779999) ^ [_1109083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109083), _1108930)), -(hBOOL(hAPP(_1108932, _1109083)))]]], (50679 ^ _779999) ^ [_1804609, _1804611, _1804613] : [c_List_Olist__ex(_1804609, _1804611, _1804613), 50683 ^ _779999 : [(50686 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1804611, 50682 ^ [_1804609, _1804611, _1804613])))], (50684 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804609), 50682 ^ [_1804609, _1804611, _1804613]), hAPP(c_List_Oset(_1804609), _1804613))))]]], (39509 ^ _779999) ^ [_1544263, _1544265, _1544267, _1544269, _1544271, _1544273, _1544275, _1544277, _1544279, _1544281] : [-(c_Product__Type_Omap__pair(_1544263, _1544265, _1544267, _1544269, hAPP(c_Fun_Ocomp(_1544271, _1544265, _1544263, _1544273), _1544275), hAPP(c_Fun_Ocomp(_1544277, _1544269, _1544267, _1544279), _1544281)) = hAPP(c_Fun_Ocomp(tc_prod(_1544271, _1544277), tc_prod(_1544265, _1544269), tc_prod(_1544263, _1544267), c_Product__Type_Omap__pair(_1544271, _1544265, _1544277, _1544269, _1544273, _1544279)), c_Product__Type_Omap__pair(_1544263, _1544271, _1544267, _1544277, _1544275, _1544281)))], (6089 ^ _779999) ^ [_876848, _876850, _876852, _876854] : [class_Lattices_Osemilattice__sup(_876848), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876848), _876850), _876852)), _876854) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876848), _876850), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_876848), _876852), _876854)))], (47166 ^ _779999) ^ [_1727551, _1727553, _1727555] : [hBOOL(hAPP(c_List_Odistinct(_1727551), _1727553)), -(c_List_Oremove1(_1727551, _1727555, c_List_Oremdups(_1727551, _1727553)) = c_List_Oremdups(_1727551, c_List_Oremove1(_1727551, _1727555, _1727553)))], (44606 ^ _779999) ^ [_1670242, _1670244] : [-(c_Enum_On__lists(_1670242, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1670244) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1670242)), c_List_Olist_ONil(_1670242)), c_List_Olist_ONil(tc_List_Olist(_1670242))))], (18743 ^ _779999) ^ [_1121936, _1121938, _1121940] : [-(hBOOL(hAPP(_1121936, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121938), _1121940))))), 18746 ^ _779999 : [(18749 ^ _779999) ^ [] : [hBOOL(hAPP(_1121936, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121938)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121940))))], (18747 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121940), _1121938)))]], 18750 ^ _779999 : [(18753 ^ _779999) ^ [] : [hBOOL(hAPP(_1121936, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18751 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121938), _1121940)))]]], (41290 ^ _779999) ^ [_1587879, _1587881, _1587883, _1587885] : [class_Lattices_Osemilattice__sup(_1587879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587879), _1587881)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1587879, _1587879, c_Lattices_Osemilattice__sup__class_Osup(_1587879)), _1587883), hAPP(hAPP(c_Set_Oinsert(_1587879), _1587885), _1587881)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1587879), _1587885), hAPP(hAPP(c_Finite__Set_Ofold(_1587879, _1587879, c_Lattices_Osemilattice__sup__class_Osup(_1587879)), _1587883), _1587881)))], (14600 ^ _779999) ^ [_1041680, _1041682, _1041684, _1041686] : [class_Rings_Olinordered__semidom(_1041680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041680), c_Groups_Ozero__class_Ozero(_1041680)), _1041682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041680), _1041684), _1041686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041680), _1041684), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041680), _1041682), _1041686))))], (7667 ^ _779999) ^ [_908796, _908798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _908796)), _908798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _908796), _908798)))], (11556 ^ _779999) ^ [_982229, _982231, _982233, _982235] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982229, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982229, tc_HOL_Obool)), _982231), _982233)), _982235) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982229, tc_HOL_Obool)), _982231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982229, tc_HOL_Obool)), _982233), _982235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982229, tc_HOL_Obool)), _982235), _982231)))], (7944 ^ _779999) ^ [_914008, _914010] : [_914008 = _914010, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914008), _914010)))], (6569 ^ _779999) ^ [_886353, _886355, _886357, _886359, _886361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886353, tc_HOL_Obool)), _886355), _886357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886353, tc_HOL_Obool)), _886359), _886361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886353, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886353, tc_HOL_Obool)), _886355), _886359)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886353, tc_HOL_Obool)), _886357), _886361))))], (30076 ^ _779999) ^ [_1343643, _1343645, _1343647] : [class_Rings_Oring__1(_1343643), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343643), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1343645), _1343647)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1343643), hAPP(c_Int_Oring__1__class_Oof__int(_1343643), _1343645)), _1343647))], (7406 ^ _779999) ^ [_903317, _903319] : [class_Lattices_Obounded__lattice__bot(_903317), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903317), c_Orderings_Obot__class_Obot(_903317)), _903319) = _903319)], (43987 ^ _779999) ^ [_1657018, _1657020, _1657022, _1657024] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1657018, _1657018)), hAPP(hAPP(c_Product__Type_OPair(_1657018, _1657018), _1657020), _1657022)), hAPP(c_List_Oset(tc_prod(_1657018, _1657018)), hAPP(hAPP(c_List_Ozip(_1657018, _1657018), _1657024), _1657024))))), hBOOL(hAPP(hAPP(c_member(_1657018), _1657020), hAPP(c_List_Oset(_1657018), _1657024))), _1657020 = _1657022], (43393 ^ _779999) ^ [_1639684, _1639686, _1639688] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639684), tc_List_Olist(_1639684))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639684), tc_List_Olist(_1639684)), _1639686), _1639686)), c_List_Olistrel(_1639684, c_Transitive__Closure_Ortrancl(_1639684, _1639688)))))], (27866 ^ _779999) ^ [_1303789, _1303791] : [class_Power_Opower(_1303789), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303789), _1303791), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1303789))], (18767 ^ _779999) ^ [_1122367, _1122369, _1122371, _1122373, _1122375] : [class_Groups_Oordered__ab__semigroup__add(_1122367), class_Rings_Osemiring__1(_1122367), 18777 ^ _779999 : [(18780 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122367), hAPP(_1122373, 18776 ^ [_1122367, _1122369, _1122371, _1122373, _1122375])), _1122375))], (18778 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122369), 18776 ^ [_1122367, _1122369, _1122371, _1122373, _1122375]), _1122371)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122367), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122369, _1122367), _1122373), _1122371)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122367), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122367), hAPP(c_Finite__Set_Ocard(_1122369), _1122371))), _1122375))))], (13830 ^ _779999) ^ [_1026718] : [class_Lattices_Osemilattice__inf(_1026718), -(c_Finite__Set_Ofun__left__comm__idem(_1026718, _1026718, c_Lattices_Osemilattice__inf__class_Oinf(_1026718)))], (33687 ^ _779999) ^ [_1410331, _1410333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410331)), hAPP(c_Nat_OSuc, _1410333))), -(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(_1410331))), 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)), _1410333)))))], (40349 ^ _779999) ^ [_1565034, _1565036, _1565038] : [-(c_Transitive__Closure_Ortrancl(_1565034, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565034, _1565034), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565034, _1565036)), c_Transitive__Closure_Ortrancl(_1565034, _1565038))) = c_Transitive__Closure_Ortrancl(_1565034, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565034, _1565034), tc_HOL_Obool)), _1565036), _1565038)))], (50877 ^ _779999) ^ [_1809606, _1809608] : [c_Relation_Otrans(_1809606, _1809608), c_Relation_Oantisym(_1809606, _1809608), -(c_Relation_Otrans(_1809606, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1809606, _1809606), tc_HOL_Obool)), _1809608), c_Relation_OId(_1809606))))], (45346 ^ _779999) ^ [_1687444, _1687446, _1687448] : [hBOOL(hAPP(c_List_Odistinct(_1687444), _1687446)), -(hBOOL(hAPP(c_List_Odistinct(_1687444), hAPP(hAPP(c_List_Odrop(_1687444), _1687448), _1687446))))], (6339 ^ _779999) ^ [_881991, _881993, _881995] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881991, tc_HOL_Obool)), _881993), _881995) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881991, tc_HOL_Obool)), _881995), _881993))], (9933 ^ _779999) ^ [_950945, _950947, _950949, _950951, _950953] : [-(hAPP(c_Fun_Othe__inv__into(_950945, _950947, _950949, _950951), _950953) = c_HOL_OThe(_950945, hAPP(hAPP(c_COMBS(_950945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _950945), c_fconj), hAPP(hAPP(c_COMBC(_950945, tc_fun(_950945, tc_HOL_Obool), tc_HOL_Obool), c_member(_950945)), _950949))), hAPP(hAPP(c_COMBC(_950945, _950947, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_950947, tc_fun(_950947, tc_HOL_Obool), _950945), c_fequal), _950951)), _950953))))], (26268 ^ _779999) ^ [_1272353, _1272355] : [class_Rings_Olinordered__idom(_1272353), 26271 ^ _779999 : [(26278 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272353), _1272355), c_Groups_Ozero__class_Ozero(_1272353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272353), _1272355), hAPP(c_Groups_Ouminus__class_Ouminus(_1272353), _1272355))))], (26272 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272353), _1272355), hAPP(c_Groups_Ouminus__class_Ouminus(_1272353), _1272355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272353), _1272355), c_Groups_Ozero__class_Ozero(_1272353))))]]], (42447 ^ _779999) ^ [_1615074, _1615076, _1615078] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615074, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615074, tc_HOL_Obool), _1615076)), _1615078) = c_Orderings_Obot__class_Obot(tc_fun(_1615074, tc_HOL_Obool)), 42450 ^ _779999 : [(42451 ^ _779999) ^ [_1615209] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1615074, tc_HOL_Obool)), _1615209), _1615076)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615074, tc_HOL_Obool)), _1615209), _1615078) = c_Orderings_Obot__class_Obot(tc_fun(_1615074, tc_HOL_Obool)))]]], (26855 ^ _779999) ^ [_1284223, _1284225, _1284227, _1284229, _1284231] : [class_Groups_Ocomm__monoid__mult(_1284223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284225), _1284227)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284225), _1284229)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284223), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284225, _1284223), _1284231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284225, tc_HOL_Obool)), _1284227), _1284229))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284225, _1284223), _1284231), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284225, tc_HOL_Obool)), _1284227), _1284229))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284223), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284225, _1284223), _1284231), _1284227)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284225, _1284223), _1284231), _1284229)))], (23557 ^ _779999) ^ [_1220057, _1220059, _1220061, _1220063] : [class_Orderings_Olinorder(_1220057), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1220057, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1220057, _1220059, _1220061)), hAPP(c_SetInterval_Oord__class_OatMost(_1220057), _1220063)) = c_SetInterval_Oord__class_OatLeastAtMost(_1220057, _1220059, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1220057), _1220061), _1220063)))], (6615 ^ _779999) ^ [_887254, _887256, _887258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887254, tc_HOL_Obool)), _887256), _887258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887254, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_887254, _887256)), c_Predicate_OPowp(_887254, _887258))))], (7767 ^ _779999) ^ [_910734, _910736, _910738, _910740, _910742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910734, tc_HOL_Obool)), hAPP(c_Set_Oimage(_910736, _910734, _910738), _910740)), _910742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_910734, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_910736, tc_HOL_Obool), tc_fun(_910734, tc_HOL_Obool), c_Set_Oimage(_910736, _910734, _910738)), hAPP(c_Set_OPow(_910736), _910740))), hAPP(c_Set_OPow(_910734), _910742))))], (15893 ^ _779999) ^ [_1066546] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066546), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1066546)], (52046 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (39785 ^ _779999) ^ [_1550594, _1550596, _1550598, _1550600, _1550602, _1550604] : [c_Finite__Set_Ofolding(_1550594, _1550596, _1550598, _1550600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550594), _1550602)), -(hAPP(_1550600, hAPP(hAPP(c_Set_Oinsert(_1550594), _1550604), _1550602)) = hAPP(c_Fun_Ocomp(_1550596, _1550596, _1550596, hAPP(_1550600, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1550594, tc_HOL_Obool)), _1550602), hAPP(hAPP(c_Set_Oinsert(_1550594), _1550604), c_Orderings_Obot__class_Obot(tc_fun(_1550594, tc_HOL_Obool)))))), hAPP(_1550598, _1550604)))], (20834 ^ _779999) ^ [_1158136, _1158138, _1158140] : [class_Groups_Oordered__ab__group__add__abs(_1158136), -(hAPP(c_Groups_Oabs__class_Oabs(_1158136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158136), hAPP(c_Groups_Oabs__class_Oabs(_1158136), _1158138)), hAPP(c_Groups_Oabs__class_Oabs(_1158136), _1158140))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158136), hAPP(c_Groups_Oabs__class_Oabs(_1158136), _1158138)), hAPP(c_Groups_Oabs__class_Oabs(_1158136), _1158140)))], (21812 ^ _779999) ^ [_1178554, _1178556, _1178558, _1178560, _1178562] : [class_Groups_Ocomm__monoid__add(_1178554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178556), _1178558)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178556, _1178554), _1178560), hAPP(c_Set_OCollect(_1178556), hAPP(hAPP(c_COMBS(_1178556, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1178556), c_fconj), hAPP(hAPP(c_COMBC(_1178556, tc_fun(_1178556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1178556)), _1178558))), hAPP(hAPP(c_COMBC(_1178556, tc_fun(_1178556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1178556)), _1178562)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178556, _1178554), hAPP(hAPP(c_COMBC(_1178556, _1178554, _1178554), hAPP(hAPP(c_COMBS(_1178556, _1178554, tc_fun(_1178554, _1178554)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1178554, tc_fun(_1178554, _1178554)), _1178556), c_If(_1178554)), hAPP(hAPP(c_COMBC(_1178556, tc_fun(_1178556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1178556)), _1178562))), _1178560)), c_Groups_Ozero__class_Ozero(_1178554))), _1178558))], (45698 ^ _779999) ^ [_1695195, _1695197, _1695199] : [-(hAPP(c_List_Otl(_1695195), hAPP(hAPP(c_List_Otake(_1695195), _1695197), _1695199)) = hAPP(hAPP(c_List_Otake(_1695195), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1695197), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1695195), _1695199)))], (30629 ^ _779999) ^ [_1354231, _1354233] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354231, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354233)) = 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), _1354231), _1354233)))], (45374 ^ _779999) ^ [_1688076, _1688078, _1688080, _1688082] : [hBOOL(hAPP(hAPP(c_member(_1688076), _1688078), hAPP(c_List_Oset(_1688076), hAPP(hAPP(c_List_Odrop(_1688076), _1688080), _1688082)))), -(hBOOL(hAPP(hAPP(c_member(_1688076), _1688078), hAPP(c_List_Oset(_1688076), _1688082))))], (11008 ^ _779999) ^ [_970275, _970277, _970279] : [class_Lattices_Osemilattice__inf(_970275), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970275), _970277), _970279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970275), _970279), _970277))], (32987 ^ _779999) ^ [_1398547, _1398549] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398547))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398547)), _1398549) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1398549))], (51798 ^ _779999) ^ [_1828388, _1828390] : [class_Lattices_Odistrib__lattice(_1828388), -(class_Lattices_Odistrib__lattice(tc_fun(_1828390, _1828388)))], (21947 ^ _779999) ^ [_1182840, _1182842, _1182844, _1182846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182840), hAPP(c_Set_OCollect(_1182840), _1182842))), 21950 ^ _779999 : [(21951 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182844), hAPP(c_Set_OCollect(_1182844), hAPP(hAPP(c_COMBB(tc_fun(_1182840, tc_HOL_Obool), tc_HOL_Obool, _1182844), c_HOL_OEx(_1182840)), hAPP(hAPP(c_COMBB(tc_fun(_1182840, tc_HOL_Obool), tc_fun(_1182840, tc_HOL_Obool), _1182844), hAPP(c_COMBS(_1182840, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1182840), c_fconj), _1182842))), _1182846))))), 21954 ^ _779999 : [(21955 ^ _779999) ^ [_1183123] : [hBOOL(hAPP(_1182842, _1183123)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182844), hAPP(c_Set_OCollect(_1182844), hAPP(hAPP(c_COMBC(_1182844, _1182840, tc_HOL_Obool), _1182846), _1183123)))))]]], (21961 ^ _779999) ^ [] : [21963 ^ _779999 : [(21966 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182844), hAPP(c_Set_OCollect(_1182844), hAPP(hAPP(c_COMBC(_1182844, _1182840, tc_HOL_Obool), _1182846), 21962 ^ [_1182840, _1182842, _1182844, _1182846]))))], (21964 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1182842, 21962 ^ [_1182840, _1182842, _1182844, _1182846])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182844), hAPP(c_Set_OCollect(_1182844), hAPP(hAPP(c_COMBB(tc_fun(_1182840, tc_HOL_Obool), tc_HOL_Obool, _1182844), c_HOL_OEx(_1182840)), hAPP(hAPP(c_COMBB(tc_fun(_1182840, tc_HOL_Obool), tc_fun(_1182840, tc_HOL_Obool), _1182844), hAPP(c_COMBS(_1182840, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1182840), c_fconj), _1182842))), _1182846))))))]]], (41883 ^ _779999) ^ [_1600165, _1600167, _1600169, _1600171] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600165, tc_fun(_1600167, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1600165, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1600167, tc_HOL_Obool), tc_fun(_1600167, tc_HOL_Obool), _1600165), hAPP(c_COMBC(_1600167, tc_fun(_1600167, tc_HOL_Obool), tc_HOL_Obool), c_member(_1600167))), _1600169)), _1600171)), -(hBOOL(hAPP(hAPP(c_member(_1600167), _1600171), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600165, tc_fun(_1600167, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1600165, tc_HOL_Obool))), _1600169))))], (35418 ^ _779999) ^ [_1446563, _1446565] : [-(_1446563 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446565, _1446563), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1446565), _1446563)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1446565, _1446563)))))], (31463 ^ _779999) ^ [_1369208] : [-(_1369208 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31466 ^ _779999 : [(31473 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369208))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1369208) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31467 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369208)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1369208) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (38572 ^ _779999) ^ [_1520449, _1520451, _1520453, _1520455, _1520457, _1520459] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520449, _1520451)), hAPP(hAPP(c_Product__Type_OPair(_1520449, _1520451), _1520453), _1520455)), hAPP(hAPP(c_Product__Type_OSigma(_1520449, _1520451), _1520457), _1520459))), 38575 ^ _779999 : [(38578 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520451), _1520455), hAPP(_1520459, _1520453))))], (38576 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520449), _1520453), _1520457)))]]], (42548 ^ _779999) ^ [_1617795] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617795, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1617795, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1617795, tc_HOL_Obool)))], (6597 ^ _779999) ^ [_886987, _886989] : [hAPP(c_Com_Ocom_OBODY, _886987) = hAPP(c_Com_Ocom_OBODY, _886989), -(_886987 = _886989)], (5232 ^ _779999) ^ [_859999, _860001, _860003, _860005, _860007, _860009, _860011, _860013, _860015, _860017, _860019, _860021] : [-(c_Partial__Function_Ofun__lub(_860021, _860017, _860013, _860009, _860005, _860001) = c_Partial__Function_Ofun__lub(_860019, _860015, _860011, _860007, _860003, _859999)), _860021 = _860019, _860017 = _860015, _860013 = _860011, _860009 = _860007, _860005 = _860003, _860001 = _859999], (33681 ^ _779999) ^ [_1410165, _1410167] : [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(_1410167))), 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), _1410165)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410165)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410167))))], (19867 ^ _779999) ^ [_1142319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142319)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142319) = 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, _1142319))))], (52124 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (15227 ^ _779999) ^ [_1053574, _1053576] : [class_Rings_Ocomm__semiring__1(_1053574), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053574), c_Groups_Ozero__class_Ozero(_1053574)), _1053576) = _1053576)], (27618 ^ _779999) ^ [_1299424, _1299426, _1299428, _1299430] : [class_Rings_Olinordered__semidom(_1299424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299424), c_Groups_Oone__class_Oone(_1299424)), _1299426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299424), hAPP(hAPP(c_Power_Opower__class_Opower(_1299424), _1299426), _1299428)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299424), _1299426), _1299430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299428), _1299430)))], (23729 ^ _779999) ^ [_1223238, _1223240, _1223242] : [class_Orderings_Olinorder(_1223238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223238), _1223240)), -(_1223240 = c_Orderings_Obot__class_Obot(tc_fun(_1223238, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1223238, hAPP(hAPP(c_Set_Oinsert(_1223238), _1223242), _1223240)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1223238), _1223242), c_Big__Operators_Olinorder__class_OMin(_1223238, _1223240)))], (49469 ^ _779999) ^ [_1777959, _1777961, _1777963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1777959), _1777961)), hBOOL(hAPP(_1777963, c_Orderings_Obot__class_Obot(tc_fun(_1777959, tc_HOL_Obool)))), 49480 ^ _779999 : [(49483 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1777959), 49478 ^ [_1777959, _1777961, _1777963]), 49479 ^ [_1777959, _1777961, _1777963]))], (49485 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1777963, 49479 ^ [_1777959, _1777961, _1777963])))], (49487 ^ _779999) ^ [] : [hBOOL(hAPP(_1777963, hAPP(hAPP(c_Set_Oinsert(_1777959), 49478 ^ [_1777959, _1777961, _1777963]), 49479 ^ [_1777959, _1777961, _1777963])))], (49481 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777959), 49479 ^ [_1777959, _1777961, _1777963])))]], -(hBOOL(hAPP(_1777963, _1777961)))], (36499 ^ _779999) ^ [_1467544, _1467546, _1467548, _1467550, _1467552] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1467544, _1467546, _1467548), _1467550), _1467552) = hAPP(hAPP(_1467550, hAPP(c_Product__Type_Ofst(_1467544, _1467546), _1467552)), hAPP(c_Product__Type_Osnd(_1467544, _1467546), _1467552)))], (8652 ^ _779999) ^ [_928105, _928107] : [class_Groups_Ozero(_928105), 8655 ^ _779999 : [(8662 ^ _779999) ^ [] : [_928107 = c_Groups_Ozero__class_Ozero(_928105), -(c_Groups_Ozero__class_Ozero(_928105) = _928107)], (8656 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_928105) = _928107, -(_928107 = c_Groups_Ozero__class_Ozero(_928105))]]], (18929 ^ _779999) ^ [_1125424] : [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)), _1125424)), _1125424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (50440 ^ _779999) ^ [_1798757, _1798759, _1798761, _1798763] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1798757), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1798759, _1798761, _1798757, _1798763) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1798759, 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(_1798759)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1798761, _1798763)), 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(_1798759)))), 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(_1798759)))), 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(_1798759)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1798759, 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(_1798759)))), 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(_1798759)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1798759, _1798761, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1798757), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1798763))), 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(_1798759)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759)))), 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(_1798759)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1798759, 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(_1798759)))), 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(_1798759)))), 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(_1798759))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759)))), 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(_1798759)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759))))), tc_prod(_1798759, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1798759)), hAPP(hAPP(c_COMBB(_1798759, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1798759)))), tc_prod(_1798759, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1798759)), c_Product__Type_Ofst(_1798759, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (42936 ^ _779999) ^ [_1626641, _1626643, _1626645, _1626647, _1626649, _1626651, _1626653, _1626655] : [c_Finite__Set_Ofolding__image__simple__idem(_1626641, _1626643, _1626645, _1626647, _1626649, _1626651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626643), _1626653)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626643), _1626655)), -(hAPP(_1626651, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1626643, tc_HOL_Obool)), _1626653), _1626655)) = hAPP(hAPP(_1626645, hAPP(_1626651, _1626653)), hAPP(_1626651, _1626655)))], (3814 ^ _779999) ^ [_837276, _837278, _837280, _837282, _837284, _837286, _837288, _837290, _837292, _837294] : [-(c_List_Olinorder__class_Oinsort__insert__key(_837294, _837290, _837286, _837282, _837278) = c_List_Olinorder__class_Oinsort__insert__key(_837292, _837288, _837284, _837280, _837276)), _837294 = _837292, _837290 = _837288, _837286 = _837284, _837282 = _837280, _837278 = _837276], (46714 ^ _779999) ^ [_1716963] : [-(c_Code__Numeral_OSuc__code__numeral(_1716963) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1716963))))], (38055 ^ _779999) ^ [_1506190, _1506192] : [hAPP(hAPP(c_Relation_Orel__comp(_1506190, _1506190, _1506190), _1506192), _1506192) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506190, _1506190), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1506190, _1506192))], (38705 ^ _779999) ^ [_1525209, _1525211, _1525213, _1525215] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525211, _1525209), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1525209, tc_prod(_1525211, _1525209), 38701 ^ [_1525209, _1525211, _1525213, _1525215]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525211, tc_fun(_1525209, tc_HOL_Obool)), _1525213), _1525215))), hAPP(hAPP(c_Product__Type_OSigma(_1525211, _1525209), _1525213), _1525215))))], (41660 ^ _779999) ^ [_1595095, _1595097, _1595099, _1595101, _1595103, _1595105] : [c_Finite__Set_Ofun__left__comm(_1595095, _1595097, _1595099), -(hAPP(hAPP(_1595099, _1595101), hAPP(hAPP(_1595099, _1595103), _1595105)) = hAPP(hAPP(_1595099, _1595103), hAPP(hAPP(_1595099, _1595101), _1595105)))], (45169 ^ _779999) ^ [_1682595, _1682597, _1682599, _1682601] : [-(hAPP(hAPP(c_List_Onth(_1682595), hAPP(hAPP(c_List_Oappend(_1682595), _1682597), _1682599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682595)), _1682597)), _1682601)) = hAPP(hAPP(c_List_Onth(_1682595), _1682599), _1682601))], (43205 ^ _779999) ^ [_1633705, _1633707, _1633709, _1633711, _1633713, _1633715] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633705), tc_List_Olist(_1633705))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633705), tc_List_Olist(_1633705)), hAPP(hAPP(c_List_Olist_OCons(_1633705), _1633707), _1633709)), hAPP(hAPP(c_List_Olist_OCons(_1633705), _1633711), _1633713))), c_List_Olexord(_1633705, _1633715)))), 43206 ^ _779999 : [(43209 ^ _779999) ^ [] : [_1633707 = _1633711, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633705), tc_List_Olist(_1633705))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633705), tc_List_Olist(_1633705)), _1633709), _1633713)), c_List_Olexord(_1633705, _1633715)))], (43207 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633705, _1633705)), hAPP(hAPP(c_Product__Type_OPair(_1633705, _1633705), _1633707), _1633711)), _1633715))]]], (44019 ^ _779999) ^ [_1658015, _1658017] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1658015, _1658017) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1658015), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1658017), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33649 ^ _779999) ^ [_1409317, _1409319, _1409321, _1409323] : [-(c_Nat_Onat_Onat__case(_1409317, _1409319, _1409321, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409323)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1409317), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409323))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1409317, _1409317), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1409317, tc_fun(_1409317, _1409317)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409317, tc_fun(_1409317, _1409317)), tc_Int_Oint), c_If(_1409317)), c_Nat__Numeral_Oneg)), _1409319)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1409317, tc_Int_Oint), _1409321), c_Int_Onat))))], (38910 ^ _779999) ^ [_1530549, _1530551, _1530553] : [c_Relation_Orefl__on(_1530549, _1530551, _1530553), 38913 ^ _779999 : [(38916 ^ _779999) ^ [_1530731] : [hBOOL(hAPP(hAPP(c_member(_1530549), _1530731), _1530551)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530549, _1530549)), hAPP(hAPP(c_Product__Type_OPair(_1530549, _1530549), _1530731), _1530731)), _1530553)))], (38914 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530549, _1530549), tc_HOL_Obool)), _1530553), hAPP(hAPP(c_Product__Type_OSigma(_1530549, _1530549), _1530551), hAPP(c_COMBK(tc_fun(_1530549, tc_HOL_Obool), _1530549), _1530551)))))]]], (8112 ^ _779999) ^ [_917128, _917130] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917128, tc_HOL_Obool)), _917130), _917130) = c_Orderings_Obot__class_Obot(tc_fun(_917128, tc_HOL_Obool)))], (19065 ^ _779999) ^ [_1127592, _1127594] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127592), _1127594))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1127594, _1127592) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1127594), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127594), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1127592)))], (44025 ^ _779999) ^ [_1658132, _1658134] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1658132), _1658134) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1658132, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1658134), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51327 ^ _779999) ^ [_1818105, _1818107, _1818109, _1818111, _1818113] : [hBOOL(hAPP(hAPP(c_member(_1818105), _1818107), hAPP(c_Set_Oimage(_1818109, _1818105, _1818111), _1818113))), -(hBOOL(hAPP(hAPP(c_member(_1818109), hAPP(c_Hilbert__Choice_Oinv__into(_1818109, _1818105, _1818113, _1818111), _1818107)), _1818113)))], (7711 ^ _779999) ^ [_909490, _909492] : [7712 ^ _779999 : [(7715 ^ _779999) ^ [] : [_909490 = hAPP(c_Nat_OSuc, _909492)], (7713 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909490), _909492))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909490), hAPP(c_Nat_OSuc, _909492))))], (29714 ^ _779999) ^ [_1337205, _1337207, _1337209, _1337211] : [class_Divides_Osemiring__div(_1337205), -(_1337207 = c_Groups_Ozero__class_Ozero(_1337205)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337205), _1337209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337205), _1337207), _1337211))), _1337207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337205), _1337211), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337205), _1337209), _1337207)))], (36024 ^ _779999) ^ [_1458236, _1458238] : [_1458236 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1458236, _1458238) = 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)))], (18423 ^ _779999) ^ [_1115364, _1115366, _1115368, _1115370] : [class_Orderings_Olinorder(_1115364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115364), _1115366), _1115368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115364), _1115368), _1115370)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1115364, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1115364, _1115366, _1115368)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1115364, _1115368, _1115370)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1115364, _1115366, _1115370))], (11548 ^ _779999) ^ [_982021, _982023, _982025] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982021, tc_HOL_Obool)), _982023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982021, tc_HOL_Obool)), _982025), _982023)) = c_Orderings_Obot__class_Obot(tc_fun(_982021, tc_HOL_Obool)))], (22665 ^ _779999) ^ [_1199740, _1199742, _1199744, _1199746, _1199748] : [-(_1199740 = c_Orderings_Obot__class_Obot(tc_fun(_1199742, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199742, tc_fun(_1199744, tc_HOL_Obool)), _1199740), hAPP(hAPP(c_COMBC(_1199742, tc_fun(_1199744, tc_HOL_Obool), tc_fun(_1199744, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199744, tc_HOL_Obool), tc_fun(tc_fun(_1199744, tc_HOL_Obool), tc_fun(_1199744, tc_HOL_Obool)), _1199742), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199744, tc_HOL_Obool))), _1199746)), _1199748)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1199744, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1199742, tc_fun(_1199744, tc_HOL_Obool)), _1199740), _1199746)), _1199748))], (23451 ^ _779999) ^ [_1217723] : [class_Orderings_Olinorder(_1217723), -(c_Finite__Set_Ofun__left__comm__idem(_1217723, _1217723, c_Orderings_Oord__class_Omin(_1217723)))], (32767 ^ _779999) ^ [_1394678, _1394680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1394678)), c_Int_OBit1(_1394680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394678), _1394680)))], (40783 ^ _779999) ^ [_1574825, _1574827, _1574829, _1574831] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574825, _1574825)), hAPP(hAPP(c_Product__Type_OPair(_1574825, _1574825), _1574827), _1574829)), hAPP(c_Relation_Oconverse(_1574825, _1574825), c_Transitive__Closure_Otrancl(_1574825, _1574831)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574825, _1574825)), hAPP(hAPP(c_Product__Type_OPair(_1574825, _1574825), _1574827), _1574829)), c_Transitive__Closure_Otrancl(_1574825, hAPP(c_Relation_Oconverse(_1574825, _1574825), _1574831)))))], (19327 ^ _779999) ^ [_1132399, _1132401, _1132403, _1132405, _1132407] : [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), _1132399), _1132401)), _1132403)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132399), _1132405)), _1132407))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132407), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132399), _1132407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132399), _1132403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132405), _1132401)))], (30563 ^ _779999) ^ [_1353024, _1353026, _1353028, _1353030] : [class_Divides_Osemiring__div(_1353024), -(c_Divides_Odiv__class_Omod(_1353024, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353024), _1353026), c_Divides_Odiv__class_Omod(_1353024, _1353028, _1353030)), _1353030) = c_Divides_Odiv__class_Omod(_1353024, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353024), _1353026), _1353028), _1353030))], (8198 ^ _779999) ^ [_918888, _918890] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _918888, _918890, _918888))], (42466 ^ _779999) ^ [_1615605, _1615607] : [-(hAPP(c_Relation_OField(_1615605), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1615605, _1615605), tc_HOL_Obool), _1615607)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615605, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1615605, _1615605), tc_HOL_Obool), tc_fun(_1615605, tc_HOL_Obool), c_Relation_OField(_1615605)), _1615607)))], (37393 ^ _779999) ^ [_1488887] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1488887)), -(_1488887 = 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))), _1488887)), c_FunDef_Omax__strict)))], (22718 ^ _779999) ^ [_1201261, _1201263, _1201265, _1201267, _1201269, _1201271] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201261, tc_fun(_1201263, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201265, tc_fun(_1201261, tc_HOL_Obool)), _1201267), _1201269)), _1201271) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201265, tc_fun(_1201263, tc_HOL_Obool)), _1201267), hAPP(hAPP(c_COMBC(_1201265, tc_fun(_1201261, tc_fun(_1201263, tc_HOL_Obool)), tc_fun(_1201263, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1201261, tc_HOL_Obool), tc_fun(tc_fun(_1201261, tc_fun(_1201263, tc_HOL_Obool)), tc_fun(_1201263, tc_HOL_Obool)), _1201265), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201261, tc_fun(_1201263, tc_HOL_Obool))), _1201269)), _1201271)))], (47866 ^ _779999) ^ [_1743876, _1743878] : [class_Orderings_Olinorder(_1743876), c_List_Olinorder__class_Osorted(_1743876, _1743878), -(c_List_Olinorder__class_Osorted(_1743876, hAPP(c_List_Otl(_1743876), _1743878)))], (35733 ^ _779999) ^ [_1453380, _1453382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453380), 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)), _1453382)), -(c_Divides_OnegDivAlg(_1453380, _1453382) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1453380), _1453382)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1453380, _1453382)))], (11711 ^ _779999) ^ [_985403, _985405, _985407, _985409, _985411] : [class_Groups_Ocomm__monoid__add(_985403), hBOOL(hAPP(c_Finite__Set_Ofinite(_985405), _985407)), 11718 ^ _779999 : [(11725 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985405), _985409), _985407))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985405, _985403), hAPP(hAPP(c_COMBC(_985405, _985403, _985403), hAPP(hAPP(c_COMBS(_985405, _985403, tc_fun(_985403, _985403)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_985403, tc_fun(_985403, _985403)), _985405), c_If(_985403)), hAPP(hAPP(c_COMBC(_985405, _985405, tc_HOL_Obool), c_fequal), _985409))), _985411)), c_Groups_Ozero__class_Ozero(_985403))), _985407) = c_Groups_Ozero__class_Ozero(_985403))], (11719 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_985405), _985409), _985407)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985405, _985403), hAPP(hAPP(c_COMBC(_985405, _985403, _985403), hAPP(hAPP(c_COMBS(_985405, _985403, tc_fun(_985403, _985403)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_985403, tc_fun(_985403, _985403)), _985405), c_If(_985403)), hAPP(hAPP(c_COMBC(_985405, _985405, tc_HOL_Obool), c_fequal), _985409))), _985411)), c_Groups_Ozero__class_Ozero(_985403))), _985407) = hAPP(_985411, _985409))]]], (3596 ^ _779999) ^ [_833923, _833925] : [_833925 = _833923, -(c_Divides_Odiv__class_Odiv(_833925) = c_Divides_Odiv__class_Odiv(_833923))], (15283 ^ _779999) ^ [_1054594, _1054596, _1054598, _1054600] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1054594, _1054596)), c_Sum__Type_OPlus(_1054594, _1054596, _1054598, _1054600)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054594), _1054598)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054596), _1054600))], (51432 ^ _779999) ^ [_1820489, _1820491, _1820493, _1820495] : [c_Fun_Oinj__on(_1820489, _1820491, _1820493, c_Orderings_Otop__class_Otop(tc_fun(_1820489, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1820491, _1820489, c_Hilbert__Choice_Oinv__into(_1820489, _1820491, c_Orderings_Otop__class_Otop(tc_fun(_1820489, tc_HOL_Obool)), _1820493)), hAPP(c_Set_Oimage(_1820489, _1820491, _1820493), _1820495)) = _1820495)], (8554 ^ _779999) ^ [_926302, _926304] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _926302)), hAPP(c_Nat_OSuc, _926304)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926302), _926304))], (23385 ^ _779999) ^ [_1216331, _1216333, _1216335, _1216337, _1216339] : [hBOOL(hAPP(hAPP(c_member(_1216335), hAPP(_1216337, _1216333)), _1216339)), -(hBOOL(hAPP(hAPP(c_member(_1216331), _1216333), hAPP(c_Set_Ovimage(_1216331, _1216335, _1216337), _1216339))))], (38852 ^ _779999) ^ [_1528956, _1528958, _1528960, _1528962, _1528964, _1528966, _1528968, _1528970] : [-(hAPP(c_Product__Type_Omap__pair(_1528956, _1528958, _1528960, _1528962, _1528964, _1528966), hAPP(hAPP(c_Product__Type_OPair(_1528956, _1528960), _1528968), _1528970)) = hAPP(hAPP(c_Product__Type_OPair(_1528958, _1528962), hAPP(_1528964, _1528968)), hAPP(_1528966, _1528970)))], (44652 ^ _779999) ^ [_1671037, _1671039] : [_1671039 = c_List_Olist_ONil(_1671037), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671037)), _1671039) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34091 ^ _779999) ^ [_1417585, _1417587] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1417585)), c_Int_OBit0(_1417587)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417585), _1417587)))], (11124 ^ _779999) ^ [_972768, _972770, _972772] : [class_Lattices_Osemilattice__inf(_972768), 11127 ^ _779999 : [(11134 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972768), _972770), _972772) = _972770, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972768), _972770), _972772)))], (11128 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972768), _972770), _972772)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972768), _972770), _972772) = _972770)]]], (46310 ^ _779999) ^ [_1707808, _1707810, _1707812, _1707814, _1707816] : [-(hAPP(hAPP(c_List_Omap(_1707808, _1707810), _1707812), hAPP(hAPP(c_List_Olist_OCons(_1707808), _1707814), _1707816)) = hAPP(hAPP(c_List_Olist_OCons(_1707810), hAPP(_1707812, _1707814)), hAPP(hAPP(c_List_Omap(_1707808, _1707810), _1707812), _1707816)))], (39969 ^ _779999) ^ [_1555137, _1555139, _1555141] : [-(hBOOL(hAPP(hAPP(c_member(_1555137), _1555139), c_Wellfounded_Oacc(_1555137, _1555141)))), 39973 ^ _779999 : [(39976 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1555137), 39972 ^ [_1555137, _1555139, _1555141]), c_Wellfounded_Oacc(_1555137, _1555141)))], (39974 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555137, _1555137)), hAPP(hAPP(c_Product__Type_OPair(_1555137, _1555137), 39972 ^ [_1555137, _1555139, _1555141]), _1555139)), _1555141)))]]], (44152 ^ _779999) ^ [_1660855, _1660857, _1660859, _1660861, _1660863] : [-(hAPP(hAPP(c_List_Olist__update(_1660855, hAPP(hAPP(c_List_Olist_OCons(_1660855), _1660857), _1660859)), _1660861), _1660863) = c_Nat_Onat_Onat__case(tc_List_Olist(_1660855), hAPP(hAPP(c_List_Olist_OCons(_1660855), _1660863), _1660859), hAPP(hAPP(c_COMBB(tc_List_Olist(_1660855), tc_List_Olist(_1660855), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1660855), _1660857)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1660855, tc_List_Olist(_1660855)), c_List_Olist__update(_1660855, _1660859)), _1660863)), _1660861))], (6357 ^ _779999) ^ [_882363, _882365, _882367, _882369, _882371] : [class_Lattices_Osemilattice__sup(_882363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882363), _882365), _882367)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882363), _882369), _882371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882363), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_882363), _882365), _882369)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_882363), _882367), _882371))))], (3614 ^ _779999) ^ [_834178, _834180, _834182, _834184] : [-(c_List_Olists(_834184, _834180) = c_List_Olists(_834182, _834178)), _834184 = _834182, _834180 = _834178], (9754 ^ _779999) ^ [_945961, _945963, _945965] : [class_Complete__Lattice_Ocomplete__lattice(_945961), c_Orderings_Oorder__class_Omono(_945961, _945961, _945963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945961), _945965), hAPP(_945963, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_945961), _945965), c_Inductive_Ocomplete__lattice__class_Ogfp(_945961, _945963))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945961), _945965), c_Inductive_Ocomplete__lattice__class_Ogfp(_945961, _945963))))], (30270 ^ _779999) ^ [_1347159, _1347161] : [class_Rings_Olinordered__idom(_1347159), 30273 ^ _779999 : [(30280 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347159), c_Groups_Ozero__class_Ozero(_1347159)), hAPP(c_Int_Oring__1__class_Oof__int(_1347159), _1347161))))], (30274 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347159), c_Groups_Ozero__class_Ozero(_1347159)), hAPP(c_Int_Oring__1__class_Oof__int(_1347159), _1347161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347161)))]]], (52134 ^ _779999) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (16593 ^ _779999) ^ [_1079849, _1079851, _1079853, _1079855, _1079857, _1079859] : [class_Rings_Oring(_1079849), 16596 ^ _779999 : [(16603 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079849), _1079851), _1079857)), _1079853)), _1079855) = _1079859, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), _1079851), _1079853)), _1079855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), _1079857), _1079853)), _1079859))], (16597 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), _1079851), _1079853)), _1079855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), _1079857), _1079853)), _1079859), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079849), _1079851), _1079857)), _1079853)), _1079855) = _1079859)]]], (33967 ^ _779999) ^ [_1415484] : [c_Int_OPls = c_Int_OBit0(_1415484), -(c_Int_OPls = _1415484)], (22211 ^ _779999) ^ [_1190901, _1190903] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1190901, 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(_1190901, tc_HOL_Obool)), tc_fun(_1190901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1190901, tc_HOL_Obool)), tc_fun(_1190901, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1190901, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1190903)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1190901, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1190903))], (23357 ^ _779999) ^ [_1215683, _1215685, _1215687, _1215689] : [class_Orderings_Olinorder(_1215683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215683), _1215685), _1215687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215683), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215683), _1215689), _1215685)), _1215687)))], (6241 ^ _779999) ^ [_879798, _879800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879798, tc_HOL_Obool)), _879800), _879800)))], (35019 ^ _779999) ^ [_1434259, _1434261] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434259), _1434261) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1434259 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1434259 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (52152 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (44426 ^ _779999) ^ [_1667051, _1667053, _1667055] : [hBOOL(hAPP(c_List_Odistinct(_1667051), _1667053)), -(hBOOL(hAPP(c_List_Odistinct(_1667051), c_List_Oremove1(_1667051, _1667055, _1667053))))], (42634 ^ _779999) ^ [_1619748, _1619750, _1619752] : [class_Complete__Lattice_Ocomplete__lattice(_1619748), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619748), _1619750)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1619748), _1619752), c_Complete__Lattice_OSup__class_OSup(_1619748, _1619750)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619748, _1619748, c_Lattices_Osemilattice__sup__class_Osup(_1619748)), _1619752), _1619750))], (45143 ^ _779999) ^ [_1682121, _1682123, _1682125] : [_1682125 = c_List_Olist_ONil(_1682121), -(hAPP(hAPP(c_List_Oappend(_1682121), _1682123), _1682125) = _1682123)], (47591 ^ _779999) ^ [_1738143, _1738145, _1738147, _1738149] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738143)), _1738145))), c_List_Ofoldr(tc_List_Olist(_1738147), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1738147)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1738147))), _1738149, 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(_1738143)), _1738145)), c_List_Ofoldr(tc_List_Olist(_1738147), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1738147)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738147), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1738147)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1738147)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1738147), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1738147)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738147), tc_List_Olist(_1738147), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1738147)))), _1738149), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (49031 ^ _779999) ^ [_1767132, _1767134, _1767136, _1767138] : [-(c_List_Oconcat(_1767132, hAPP(hAPP(c_List_Omap(_1767134, tc_List_Olist(_1767132)), _1767136), _1767138)) = c_List_Omaps(_1767134, _1767132, _1767136, _1767138))], (21325 ^ _779999) ^ [_1168351, _1168353, _1168355] : [class_Groups_Oab__semigroup__mult(_1168351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168351), _1168353)), -(_1168353 = c_Orderings_Obot__class_Obot(tc_fun(_1168351, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168351), _1168355)), -(_1168355 = c_Orderings_Obot__class_Obot(tc_fun(_1168351, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1168351, tc_HOL_Obool)), _1168353), _1168355) = c_Orderings_Obot__class_Obot(tc_fun(_1168351, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1168351, c_Groups_Otimes__class_Otimes(_1168351)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1168351, tc_HOL_Obool)), _1168353), _1168355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168351), hAPP(c_Finite__Set_Ofold1(_1168351, c_Groups_Otimes__class_Otimes(_1168351)), _1168353)), hAPP(c_Finite__Set_Ofold1(_1168351, c_Groups_Otimes__class_Otimes(_1168351)), _1168355)))], (8578 ^ _779999) ^ [_926755, _926757, _926759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926755), _926757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926755), _926759)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926757), _926755)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926759), _926755)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926757), _926759))], (34077 ^ _779999) ^ [_1417334, _1417336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1417334)), c_Int_OBit0(_1417336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417334), _1417336)))], (8940 ^ _779999) ^ [_933024, _933026, _933028] : [class_Orderings_Oorder(_933024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933024), _933026), _933028)), _933026 = _933028], (21014 ^ _779999) ^ [_1161706, _1161708, _1161710] : [class_Groups_Oordered__ab__group__add__abs(_1161706), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161706), hAPP(c_Groups_Oabs__class_Oabs(_1161706), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161706), _1161708), _1161710))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161706), hAPP(c_Groups_Oabs__class_Oabs(_1161706), _1161708)), hAPP(c_Groups_Oabs__class_Oabs(_1161706), _1161710)))))], (5466 ^ _779999) ^ [_863642, _863644] : [_863644 = _863642, -(c_member(_863644) = c_member(_863642))], (30545 ^ _779999) ^ [_1352611, _1352613, _1352615, _1352617] : [class_Divides_Osemiring__div(_1352611), -(c_Divides_Odiv__class_Omod(_1352611, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352611), _1352613), _1352615), _1352617) = c_Divides_Odiv__class_Omod(_1352611, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352611), _1352613), c_Divides_Odiv__class_Omod(_1352611, _1352615, _1352617)), _1352617))], (38193 ^ _779999) ^ [] : [-(c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_fequal)), c_Nat_OSuc))))], (17367 ^ _779999) ^ [_1094865, _1094867, _1094869, _1094871, _1094873] : [class_Groups_Ocomm__monoid__mult(_1094865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094867), _1094869)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1094865, _1094867, c_Groups_Otimes__class_Otimes(_1094865)), hAPP(hAPP(c_COMBS(_1094867, _1094865, _1094865), hAPP(hAPP(c_COMBB(_1094865, tc_fun(_1094865, _1094865), _1094867), c_Groups_Otimes__class_Otimes(_1094865)), _1094871)), _1094873)), c_Groups_Oone__class_Oone(_1094865)), _1094869) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094865), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1094865, _1094867, c_Groups_Otimes__class_Otimes(_1094865)), _1094871), c_Groups_Oone__class_Oone(_1094865)), _1094869)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1094865, _1094867, c_Groups_Otimes__class_Otimes(_1094865)), _1094873), c_Groups_Oone__class_Oone(_1094865)), _1094869)))], (6125 ^ _779999) ^ [_877706, _877708, _877710] : [class_Lattices_Osemilattice__sup(_877706), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877706), _877708), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877706), _877708), _877710)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877706), _877708), _877710))], (13513 ^ _779999) ^ [_1020815, _1020817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020815), _1020817)), -(_1020817 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020815), 13516 ^ [_1020815, _1020817]))], (8004 ^ _779999) ^ [_915067, _915069, _915071, _915073] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_915067, _915069), _915071, _915073, _915071), hBOOL(hAPP(_915067, _915071)), 8012 ^ _779999 : [(8015 ^ _779999) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_915067, _915069), 8011 ^ [_915067, _915069, _915071, _915073], _915073, _915071))], (8013 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_915069, _915071, _915073, 8011 ^ [_915067, _915069, _915071, _915073]))]]], (35348 ^ _779999) ^ [_1445218, _1445220, _1445222, _1445224] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445218, _1445220), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445222), _1445224))), -(_1445220 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1445218), _1445220) = _1445222)], (9144 ^ _779999) ^ [_936272, _936274, _936276, _936278, _936280, _936282] : [_936272 = _936274, -(hAPP(c_Fun_Ofun__upd(_936276, _936278, _936280, _936274, _936282), _936272) = _936282)], (47246 ^ _779999) ^ [_1728958, _1728960] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728958)), c_List_Oremdups(_1728958, _1728960)) = hAPP(c_Finite__Set_Ocard(_1728958), hAPP(c_List_Oset(_1728958), _1728960)))], (52034 ^ _779999) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (40128 ^ _779999) ^ [_1558901, _1558903, _1558905, _1558907, _1558909, _1558911, _1558913, _1558915, _1558917] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1558901, _1558903, _1558905, _1558907), hAPP(hAPP(c_Product__Type_Oscomp(_1558901, _1558909, _1558911, tc_prod(_1558903, _1558905)), _1558913), _1558915)), _1558917) = hAPP(hAPP(c_Product__Type_Oscomp(_1558901, _1558909, _1558911, _1558907), _1558913), hAPP(hAPP(c_COMBC(_1558909, tc_fun(_1558903, tc_fun(_1558905, _1558907)), tc_fun(_1558911, _1558907)), hAPP(hAPP(c_COMBB(tc_fun(_1558911, tc_prod(_1558903, _1558905)), tc_fun(tc_fun(_1558903, tc_fun(_1558905, _1558907)), tc_fun(_1558911, _1558907)), _1558909), c_Product__Type_Oscomp(_1558911, _1558903, _1558905, _1558907)), _1558915)), _1558917)))], (46346 ^ _779999) ^ [_1709119, _1709121, _1709123, _1709125, _1709127] : [hAPP(hAPP(c_List_Omap(_1709119, _1709121), _1709123), _1709125) = hAPP(hAPP(c_List_Omap(_1709119, _1709121), _1709123), _1709127), c_Fun_Oinj__on(_1709119, _1709121, _1709123, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1709119, tc_HOL_Obool)), hAPP(c_List_Oset(_1709119), _1709125)), hAPP(c_List_Oset(_1709119), _1709127))), -(_1709125 = _1709127)], (52100 ^ _779999) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (41859 ^ _779999) ^ [_1599652, _1599654, _1599656, _1599658, _1599660] : [-(_1599652 = c_Orderings_Obot__class_Obot(tc_fun(_1599654, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599656, tc_HOL_Obool)), _1599658), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599654, tc_fun(_1599656, tc_HOL_Obool)), _1599652), _1599660)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599654, tc_fun(_1599656, tc_HOL_Obool)), _1599652), hAPP(hAPP(c_COMBB(tc_fun(_1599656, tc_HOL_Obool), tc_fun(_1599656, tc_HOL_Obool), _1599654), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599656, tc_HOL_Obool)), _1599658)), _1599660)))], (42241 ^ _779999) ^ [_1610507, _1610509] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610507), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1610507, tc_HOL_Obool), _1610509)))), 42242 ^ _779999 : [(42243 ^ _779999) ^ [_1610571] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1610507, tc_HOL_Obool)), _1610571), _1610509)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610507), _1610571))]]], (34205 ^ _779999) ^ [_1419650, _1419652, _1419654] : [class_Int_Onumber__ring(_1419650), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419650), _1419652), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1419654))) = hAPP(hAPP(c_HOL_OLet(_1419650, _1419650), hAPP(hAPP(c_Power_Opower__class_Opower(_1419650), _1419652), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419654))), hAPP(hAPP(c_COMBS(_1419650, _1419650, _1419650), c_Groups_Otimes__class_Otimes(_1419650)), c_COMBI(_1419650))))], (8462 ^ _779999) ^ [_924802, _924804, _924806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_924802, tc_HOL_Obool)), _924804), hAPP(hAPP(c_Set_Oinsert(_924802), _924806), c_Orderings_Obot__class_Obot(tc_fun(_924802, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_924802, _924806, _924804) = _924806)], (46097 ^ _779999) ^ [_1703007, _1703009, _1703011] : [-(c_List_Olast(_1703007, hAPP(hAPP(c_List_Oappend(_1703007), _1703009), hAPP(hAPP(c_List_Olist_OCons(_1703007), _1703011), c_List_Olist_ONil(_1703007)))) = _1703011)], (3384 ^ _779999) ^ [_830609, _830611, _830613, _830615] : [-(c_Nat_Ocompow(_830615, _830611) = c_Nat_Ocompow(_830613, _830609)), _830615 = _830613, _830611 = _830609], (51916 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (45095 ^ _779999) ^ [_1681288, _1681290, _1681292] : [_1681288 = hAPP(hAPP(c_List_Oappend(_1681290), _1681288), _1681292), -(_1681292 = c_List_Olist_ONil(_1681290))], (43663 ^ _779999) ^ [_1647369, _1647371, _1647373, _1647375] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1647371), hAPP(hAPP(c_List_Olist_OCons(_1647371), _1647373), _1647375)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647369)) = _1647373)], (2158 ^ _779999) ^ [_811564, _811566, _811568, _811570, _811572, _811574, _811576, _811578] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_811578, _811574, _811570, _811566) = c_SetInterval_Oord_OgreaterThanLessThan(_811576, _811572, _811568, _811564)), _811578 = _811576, _811574 = _811572, _811570 = _811568, _811566 = _811564], (51101 ^ _779999) ^ [_1813947, _1813949, _1813951] : [-(c_Equiv__Relations_Oequiv(_1813947, _1813949, _1813951)), c_Relation_Orefl__on(_1813947, _1813949, _1813951), c_Relation_Osym(_1813947, _1813951), c_Relation_Otrans(_1813947, _1813951)], (3682 ^ _779999) ^ [_835224, _835226, _835228, _835230, _835232, _835234, _835236, _835238] : [-(c_List_Olist_Olist__case(_835238, _835234, _835230, _835226) = c_List_Olist_Olist__case(_835236, _835232, _835228, _835224)), _835238 = _835236, _835234 = _835232, _835230 = _835228, _835226 = _835224], (40409 ^ _779999) ^ [_1566487, _1566489] : [-(hAPP(c_Relation_OImage(_1566487, _1566487, c_Relation_OId(_1566487)), _1566489) = _1566489)], (9650 ^ _779999) ^ [_944103, _944105, _944107] : [class_Orderings_Owellorder(_944103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944103), _944105), c_Orderings_Oord__class_OLeast(_944103, _944107))), hBOOL(hAPP(_944107, _944105))], (34903 ^ _779999) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (32713 ^ _779999) ^ [_1393700] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393700) = _1393700)], (30206 ^ _779999) ^ [_1346080, _1346082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346080)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1346080), _1346082)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1346080)), hAPP(c_Int_Onat, _1346082)))], (36961 ^ _779999) ^ [_1478255, _1478257, _1478259, _1478261, _1478263, _1478265, _1478267, _1478269] : [c_Equiv__Relations_Oequiv(_1478255, _1478257, _1478259), c_Equiv__Relations_Ocongruent2(_1478255, _1478261, _1478263, _1478259, _1478265, _1478267), hBOOL(hAPP(hAPP(c_member(_1478255), _1478269), _1478257)), -(c_Equiv__Relations_Ocongruent(_1478261, _1478263, _1478265, hAPP(_1478267, _1478269)))], (25996 ^ _779999) ^ [_1267526, _1267528, _1267530, _1267532, _1267534] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1267526, _1267528, _1267530)), _1267532), _1267534)), 26001 ^ _779999 : [(26004 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267528), _1267532), _1267534)))], (26002 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1267526, _1267532)))]], 26005 ^ _779999 : [(26008 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1267530), _1267532), _1267534)))], (26006 ^ _779999) ^ [] : [hBOOL(hAPP(_1267526, _1267532))]]], (22283 ^ _779999) ^ [_1192298, _1192300, _1192302, _1192304] : [c_Fun_Oinj__on(_1192298, _1192300, _1192302, c_Orderings_Otop__class_Otop(tc_fun(_1192298, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1192298, tc_fun(_1192304, _1192300), hAPP(hAPP(c_COMBB(_1192300, tc_fun(_1192304, _1192300), _1192298), c_COMBK(_1192300, _1192304)), _1192302), c_Orderings_Otop__class_Otop(tc_fun(_1192298, tc_HOL_Obool))))], (48957 ^ _779999) ^ [_1765846, _1765848, _1765850] : [-(hBOOL(hAPP(hAPP(c_member(_1765846), _1765848), hAPP(c_List_Oset(_1765846), _1765850)))), -(hAPP(c_List_OremoveAll(_1765846, _1765848), _1765850) = _1765850)], (41640 ^ _779999) ^ [_1594771, _1594773, _1594775, _1594777, _1594779, _1594781, _1594783] : [c_Finite__Set_Ofun__left__comm(_1594771, _1594773, _1594775), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1594771, _1594773, _1594775, _1594777, _1594779), _1594781)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1594771, _1594773, _1594775, _1594777, _1594779), _1594783)), -(_1594783 = _1594781)], (46628 ^ _779999) ^ [_1715263, _1715265, _1715267, _1715269] : [class_Groups_Ocomm__monoid__add(_1715263), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715263), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1715263), _1715265), c_List_Oupto(_1715267, _1715269))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1715263), _1715265), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1715267, _1715269))))], (21056 ^ _779999) ^ [_1162582] : [_1162582 = 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), _1162582)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37503 ^ _779999) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (14089 ^ _779999) ^ [_1031354, _1031356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1031354), _1031356))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031354), _1031356)))], (51838 ^ _779999) ^ [_1828912, _1828914] : [class_Orderings_Otop(_1828912), -(class_Orderings_Otop(tc_fun(_1828914, _1828912)))], (52094 ^ _779999) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (40479 ^ _779999) ^ [_1568120, _1568122, _1568124, _1568126, _1568128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568120, _1568120)), hAPP(hAPP(c_Product__Type_OPair(_1568120, _1568120), _1568122), _1568124)), c_Transitive__Closure_Otrancl(_1568120, _1568126))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568120, _1568120)), hAPP(hAPP(c_Product__Type_OPair(_1568120, _1568120), _1568124), _1568128)), c_Transitive__Closure_Ortrancl(_1568120, _1568126))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568120, _1568120)), hAPP(hAPP(c_Product__Type_OPair(_1568120, _1568120), _1568122), _1568128)), c_Transitive__Closure_Otrancl(_1568120, _1568126))))], (13963 ^ _779999) ^ [_1028843, _1028845, _1028847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028843), _1028845)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028845), _1028843)), _1028847) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028845), _1028847)), _1028843))], (25313 ^ _779999) ^ [_1255202, _1255204, _1255206] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1255202, _1255204, _1255206)) = 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), _1255204)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1255206))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34313 ^ _779999) ^ [_1421654, _1421656, _1421658] : [class_Groups_Omonoid__mult(_1421654), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421654), _1421656), 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)))), _1421658)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1421654), hAPP(hAPP(c_Power_Opower__class_Opower(_1421654), _1421656), _1421658)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (30483 ^ _779999) ^ [_1351276, _1351278, _1351280, _1351282] : [class_Divides_Osemiring__div(_1351276), -(c_Divides_Odiv__class_Omod(_1351276, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351276), _1351278), _1351280), _1351282) = c_Divides_Odiv__class_Omod(_1351276, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351276), _1351278), c_Divides_Odiv__class_Omod(_1351276, _1351280, _1351282)), _1351282))], (25966 ^ _779999) ^ [_1266951, _1266953, _1266955, _1266957, _1266959] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1266951, _1266953, _1266955)), _1266957), _1266959)), 25971 ^ _779999 : [(25974 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1266953), _1266957), _1266959)))], (25972 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1266951, _1266957)))]], 25975 ^ _779999 : [(25978 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1266955), _1266957), _1266959)))], (25976 ^ _779999) ^ [] : [hBOOL(hAPP(_1266951, _1266957))]]], (26113 ^ _779999) ^ [_1269785, _1269787, _1269789, _1269791] : [class_Groups_Ocomm__monoid__mult(_1269785), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1269787), _1269789))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269787, _1269785), _1269791), _1269789) = c_Groups_Oone__class_Oone(_1269785))], (7759 ^ _779999) ^ [_910575, _910577, _910579, _910581] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910575)), _910577, _910579, _910581), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _910575), _910577, hAPP(c_Nat_OSuc, _910579), _910581))], (37572 ^ _779999) ^ [] : [-(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))], (17965 ^ _779999) ^ [_1107031, _1107033, _1107035] : [class_Orderings_Oorder(_1107031), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107031, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1107031), _1107033)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107031, _1107033), _1107035)) = c_Orderings_Obot__class_Obot(tc_fun(_1107031, tc_HOL_Obool)))], (4170 ^ _779999) ^ [_842978, _842980, _842982, _842984, _842986, _842988, _842990, _842992] : [-(c_New__DSequence_Oneg__decr__bind(_842992, _842988, _842984, _842980) = c_New__DSequence_Oneg__decr__bind(_842990, _842986, _842982, _842978)), _842992 = _842990, _842988 = _842986, _842984 = _842982, _842980 = _842978], (51628 ^ _779999) ^ [_1825001, _1825003, _1825005] : [c_Fun_Obij__betw(_1825001, _1825003, _1825005, c_Orderings_Otop__class_Otop(tc_fun(_1825001, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1825003, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1825003, _1825001, c_Orderings_Otop__class_Otop(tc_fun(_1825003, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1825001, _1825003, c_Orderings_Otop__class_Otop(tc_fun(_1825001, tc_HOL_Obool)), _1825005)) = _1825005)], (48997 ^ _779999) ^ [_1766453, _1766455] : [-(hAPP(c_List_OremoveAll(_1766453, _1766455), c_List_Olist_ONil(_1766453)) = c_List_Olist_ONil(_1766453))], (46634 ^ _779999) ^ [_1715406, _1715408, _1715410] : [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, _1715406), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1715406)), _1715408)))), -(hBOOL(hAPP(hAPP(c_member(_1715406), hAPP(c_Product__Type_Ofst(_1715406, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1715406, _1715408), _1715410))), hAPP(c_List_Oset(_1715406), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1715406), _1715406), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1715406)), _1715408)))))], (3036 ^ _779999) ^ [_825223, _825225] : [_825225 = _825223, -(c_Relation_OField(_825225) = c_Relation_OField(_825223))], (30958 ^ _779999) ^ [_1360244, _1360246, _1360248] : [hBOOL(hAPP(_1360244, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1360246, _1360248))), 30961 ^ _779999 : [(30986 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1360248), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30989 ^ _779999 : [(30990 ^ _779999) ^ [_1360866, _1360868] : [-(hBOOL(hAPP(_1360244, _1360866))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1360248), _1360866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1360866), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1360246 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1360248), _1360868)), _1360866)]]], (30968 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360248)), 30971 ^ _779999 : [(30972 ^ _779999) ^ [_1360574, _1360576] : [-(hBOOL(hAPP(_1360244, _1360574))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1360574), _1360248)), _1360246 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1360248), _1360576)), _1360574)]]], (30962 ^ _779999) ^ [] : [_1360248 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1360244, _1360246)))]]], (24010 ^ _779999) ^ [_1228628, _1228630] : [class_Orderings_Olinorder(_1228628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1228628), _1228630)), -(c_Big__Operators_Olattice_OInf__fin(_1228628, c_Orderings_Oord__class_Omin(_1228628), _1228630) = hAPP(c_Finite__Set_Ofold1(_1228628, c_Orderings_Oord__class_Omin(_1228628)), _1228630))], (27130 ^ _779999) ^ [_1290570, _1290572] : [-(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, _1290570)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1290572))))], (38507 ^ _779999) ^ [_1518565, _1518567, _1518569, _1518571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518565), _1518567)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518569), _1518571)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1518565, _1518569)), hAPP(hAPP(c_Product__Type_OSigma(_1518565, _1518569), _1518567), hAPP(c_COMBK(tc_fun(_1518569, tc_HOL_Obool), _1518565), _1518571)))))], (20754 ^ _779999) ^ [_1156722, _1156724, _1156726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1156724), 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), _1156724), _1156726))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1156722))), _1156726)))], (49736 ^ _779999) ^ [_1783317, _1783319, _1783321, _1783323, _1783325] : [-(hAPP(c_New__DSequence_Opos__bind(_1783317, _1783319, _1783321, _1783323), _1783325) = hAPP(c_Lazy__Sequence_Obind(_1783317, _1783319, hAPP(_1783321, _1783325)), hAPP(hAPP(c_COMBC(_1783317, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1783319)), _1783323), _1783325)))], (40142 ^ _779999) ^ [_1559297, _1559299] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559297, _1559297)), hAPP(hAPP(c_Product__Type_OPair(_1559297, _1559297), 40143 ^ [_1559297, _1559299]), 40143 ^ [_1559297, _1559299])), c_Transitive__Closure_Otrancl(_1559297, _1559299)))), -(c_Wellfounded_Oacyclic(_1559297, _1559299))], (4792 ^ _779999) ^ [_852955, _852957, _852959, _852961, _852963, _852965, _852967, _852969, _852971, _852973] : [-(c_Nitpick_Opair__box_Opair__box__size(_852973, _852969, _852965, _852961, _852957) = c_Nitpick_Opair__box_Opair__box__size(_852971, _852967, _852963, _852959, _852955)), _852973 = _852971, _852969 = _852967, _852965 = _852963, _852961 = _852959, _852957 = _852955], (33711 ^ _779999) ^ [_1410740, _1410742] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410740)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410742)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1410742))), 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, _1410740))), 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), _1410740)), c_Int_Onat)))))], (14614 ^ _779999) ^ [_1041933, _1041935, _1041937, _1041939, _1041941, _1041943, _1041945] : [c_Big__Operators_Ocomm__monoid__big(_1041933, _1041935, _1041937, _1041939, _1041941), 14617 ^ _779999 : [(14624 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041935), _1041943))), -(hAPP(hAPP(_1041941, _1041945), _1041943) = _1041939)], (14618 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041935), _1041943)), -(hAPP(hAPP(_1041941, _1041945), _1041943) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1041933, _1041935, _1041937), _1041945), _1041939), _1041943))]]], (27388 ^ _779999) ^ [_1295211, _1295213, _1295215, _1295217] : [class_Rings_Ocomm__semiring__1(_1295211), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295211), hAPP(hAPP(c_Power_Opower__class_Opower(_1295211), _1295213), _1295215)), hAPP(hAPP(c_Power_Opower__class_Opower(_1295211), _1295213), _1295217)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1295211), _1295213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295215), _1295217)))], (49515 ^ _779999) ^ [_1778864, _1778866, _1778868] : [c_List_Olist__all(_1778864, _1778866, _1778868), -(c_List_Olist__all(_1778864, _1778866, hAPP(c_List_Orev(_1778864), _1778868)))], (15915 ^ _779999) ^ [_1066870] : [class_Lattices_Oab__semigroup__idem__mult(_1066870), -(c_Finite__Set_Ofun__left__comm__idem(_1066870, _1066870, c_Groups_Otimes__class_Otimes(_1066870)))], (30046 ^ _779999) ^ [_1343106] : [class_Rings_Oring__1(_1343106), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343106), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1343106))], (22799 ^ _779999) ^ [_1203028, _1203030, _1203032, _1203034] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203028, tc_fun(_1203030, tc_HOL_Obool)), _1203032), _1203034) = c_Orderings_Obot__class_Obot(tc_fun(_1203030, tc_HOL_Obool)), 22802 ^ _779999 : [(22803 ^ _779999) ^ [_1203144] : [hBOOL(hAPP(hAPP(c_member(_1203028), _1203144), _1203032)), -(hAPP(_1203034, _1203144) = c_Orderings_Obot__class_Obot(tc_fun(_1203030, tc_HOL_Obool)))]]], (35922 ^ _779999) ^ [_1456520, _1456522] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456520))), 35925 ^ _779999 : [(35932 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456522))), -(c_Divides_Odivmod__int(_1456520, _1456522) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456520), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456522))))], (35926 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456522)), -(c_Divides_Odivmod__int(_1456520, _1456522) = c_Divides_OnegDivAlg(_1456520, _1456522))]]], (41226 ^ _779999) ^ [_1586558, _1586560, _1586562, _1586564] : [41228 ^ _779999 : [(41233 ^ _779999) ^ [] : [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(_1586562, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41227 ^ [_1586558, _1586560, _1586562, _1586564]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1586562, 41227 ^ [_1586558, _1586560, _1586562, _1586564])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41231 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41227 ^ [_1586558, _1586560, _1586562, _1586564]), _1586560)))], (41229 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1586558), 41227 ^ [_1586558, _1586560, _1586562, _1586564])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1586558), _1586560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1586562, _1586558)), _1586564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1586564), hAPP(_1586562, _1586560))), 41247 ^ _779999 : [(41252 ^ _779999) ^ [] : [-(hAPP(_1586562, 41246 ^ [_1586558, _1586560, _1586562, _1586564]) = _1586564)], (41250 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41246 ^ [_1586558, _1586560, _1586562, _1586564]), _1586560)))], (41248 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1586558), 41246 ^ [_1586558, _1586560, _1586562, _1586564])))]]], (18171 ^ _779999) ^ [_1110750, _1110752] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1110750), hAPP(c_Nat_OSuc, _1110752)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1110750, _1110752))], (52104 ^ _779999) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (15713 ^ _779999) ^ [_1063467, _1063469, _1063471, _1063473, _1063475] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1063467), 15716 ^ _779999 : [(15717 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063469), _1063471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063473), _1063475)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063469), _1063475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063473), _1063471)), -(_1063469 = _1063473), -(_1063471 = _1063475)], (15727 ^ _779999) ^ [] : [15728 ^ _779999 : [(15731 ^ _779999) ^ [] : [_1063471 = _1063475], (15729 ^ _779999) ^ [] : [_1063469 = _1063473]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063469), _1063471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063473), _1063475)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063469), _1063475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063467), _1063473), _1063471)))]]], (51572 ^ _779999) ^ [_1823893, _1823895, _1823897, _1823899] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1823893, _1823895, _1823897, _1823899, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1823895)) = _1823897)], (38736 ^ _779999) ^ [_1526046, _1526048] : [-(c_Product__Type_Oapfst(_1526046, _1526046, _1526048, c_Fun_Oid(_1526046)) = c_Fun_Oid(tc_prod(_1526046, _1526048)))], (52074 ^ _779999) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (36687 ^ _779999) ^ [_1471992, _1471994, _1471996, _1471998, _1472000, _1472002] : [c_Equiv__Relations_Oequiv(_1471992, _1471994, _1471996), hBOOL(hAPP(hAPP(c_member(_1471992), _1471998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471992, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1471992, _1471992, _1471996), hAPP(hAPP(c_Set_Oinsert(_1471992), _1472000), c_Orderings_Obot__class_Obot(tc_fun(_1471992, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1471992, _1471992, _1471996), hAPP(hAPP(c_Set_Oinsert(_1471992), _1472002), c_Orderings_Obot__class_Obot(tc_fun(_1471992, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471992, _1471992)), hAPP(hAPP(c_Product__Type_OPair(_1471992, _1471992), _1472000), _1472002)), _1471996)))], (38435 ^ _779999) ^ [_1516265, _1516267, _1516269, _1516271, _1516273, _1516275] : [hBOOL(hAPP(hAPP(c_member(_1516265), _1516267), _1516269)), 38438 ^ _779999 : [(38445 ^ _779999) ^ [] : [_1516273 = _1516275, -(hAPP(hAPP(c_Product__Type_OSigma(_1516271, _1516265), _1516273), hAPP(c_COMBK(tc_fun(_1516265, tc_HOL_Obool), _1516271), _1516269)) = hAPP(hAPP(c_Product__Type_OSigma(_1516271, _1516265), _1516275), hAPP(c_COMBK(tc_fun(_1516265, tc_HOL_Obool), _1516271), _1516269)))], (38439 ^ _779999) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1516271, _1516265), _1516273), hAPP(c_COMBK(tc_fun(_1516265, tc_HOL_Obool), _1516271), _1516269)) = hAPP(hAPP(c_Product__Type_OSigma(_1516271, _1516265), _1516275), hAPP(c_COMBK(tc_fun(_1516265, tc_HOL_Obool), _1516271), _1516269)), -(_1516273 = _1516275)]]], (26034 ^ _779999) ^ [_1268303, _1268305, _1268307] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1268303), _1268305), _1268307) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1268303), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1268303, tc_Int_Oint), _1268305), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268307))), class_Groups_Ocomm__monoid__add(_1268303), class_Groups_Ocomm__monoid__mult(_1268303)], (8419 ^ _779999) ^ [_923917, _923919, _923921] : [hBOOL(hAPP(c_Predicate_OPowp(_923917, hAPP(hAPP(c_COMBC(_923917, tc_fun(_923917, tc_HOL_Obool), tc_HOL_Obool), c_member(_923917)), _923919)), _923921)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_923917, tc_HOL_Obool)), _923921), hAPP(c_Set_OPow(_923917), _923919))))], (19115 ^ _779999) ^ [_1128394, _1128396, _1128398] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128394), _1128396)), _1128398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128394), _1128398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128396), _1128398)))], (33057 ^ _779999) ^ [_1399603] : [class_Int_Onumber__ring(_1399603), -(c_Groups_Ozero__class_Ozero(_1399603) = hAPP(c_Int_Onumber__class_Onumber__of(_1399603), c_Int_OPls))], (26328 ^ _779999) ^ [_1273353, _1273355] : [class_Groups_Ogroup__add(_1273353), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273353), c_Groups_Ozero__class_Ozero(_1273353)), _1273355) = hAPP(c_Groups_Ouminus__class_Ouminus(_1273353), _1273355))], (7844 ^ _779999) ^ [_912458, _912460, _912462, _912464] : [hBOOL(hAPP(hAPP(c_member(_912458), _912460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912458, tc_HOL_Obool)), _912462), _912464))), 7847 ^ _779999 : [(7850 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912458), _912460), _912464))], (7848 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912458), _912460), _912462)))]]], (13197 ^ _779999) ^ [_1014953, _1014955] : [class_Groups_Omonoid__add(_1014953), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014953), c_Groups_Ozero__class_Ozero(_1014953)), _1014955) = _1014955)], (13341 ^ _779999) ^ [_1017561, _1017563] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017561), _1017563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 13344 ^ _779999 : [(13347 ^ _779999) ^ [] : [-(_1017563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13345 ^ _779999) ^ [] : [-(_1017561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6631 ^ _779999) ^ [_887922, _887924, _887926] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887922))), _887924), _887926)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _887922)), _887924), _887926)))], (20596 ^ _779999) ^ [_1154090] : [c_Nat__Transfer_Onat__set(_1154090), 20599 ^ _779999 : [(20600 ^ _779999) ^ [_1154156] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1154156), _1154090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154156)))]]], (15233 ^ _779999) ^ [_1053684, _1053686, _1053688, _1053690] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1053684, _1053688)), c_Sum__Type_OPlus(_1053684, _1053688, _1053686, _1053690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053684), _1053686)), hAPP(c_Finite__Set_Ocard(_1053688), _1053690))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053684), _1053686)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053688), _1053690))], (40045 ^ _779999) ^ [_1557167, _1557169, _1557171, _1557173] : [c_Com_Ocom_OLocal(_1557167, _1557169, _1557171) = hAPP(c_Com_Ocom_OBODY, _1557173)], (50377 ^ _779999) ^ [_1797610, _1797612] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1797610, _1797612), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797610)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45803 ^ _779999) ^ [_1697383, _1697385, _1697387] : [class_Lattices_Olattice(_1697383), -(c_Big__Operators_Olattice__class_OInf__fin(_1697383, hAPP(c_List_Oset(_1697383), hAPP(hAPP(c_List_Olist_OCons(_1697383), _1697385), _1697387))) = hAPP(c_List_Ofoldl(_1697383, _1697383, c_Lattices_Osemilattice__inf__class_Oinf(_1697383), _1697385), _1697387))], (1294 ^ _779999) ^ [_799282, _799284] : [-(class_Rings_Oordered__ring(_799282)), _799284 = _799282, class_Rings_Oordered__ring(_799284)], (13281 ^ _779999) ^ [_1016430, _1016432, _1016434, _1016436] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1016430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016430), _1016432), _1016434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016430), _1016432), _1016436)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016430), _1016434), _1016436))))], (8146 ^ _779999) ^ [_917898, _917900, _917902, _917904] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917898, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917898, tc_HOL_Obool)), _917900), _917902)), _917904) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917898, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917898, tc_HOL_Obool)), _917900), _917904)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917898, tc_HOL_Obool)), _917902), _917904)))], (40249 ^ _779999) ^ [_1561921, _1561923, _1561925, _1561927, _1561929] : [_1561921 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1561923, _1561925, _1561921, _1561927), _1561929) = hAPP(c_Product__Type_OPair(_1561923, _1561925), _1561929))], (34155 ^ _779999) ^ [_1418719, _1418721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1418719), _1418721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1418719)), c_Int_OBit1(_1418721))))], (2494 ^ _779999) ^ [_816786, _816788, _816790, _816792] : [-(c_Groups_Osgn__class_Osgn(_816792, _816788) = c_Groups_Osgn__class_Osgn(_816790, _816786)), _816792 = _816790, _816788 = _816786], (20272 ^ _779999) ^ [_1148953, _1148955] : [20273 ^ _779999 : [(20276 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148955))], (20274 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148953))]], 20277 ^ _779999 : [(20284 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148953), _1148955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1148953)), hAPP(c_Int_Onat, _1148955))))], (20278 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1148953)), hAPP(c_Int_Onat, _1148955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148953), _1148955)))]]], (47143 ^ _779999) ^ [_1726982, _1726984, _1726986, _1726988, _1726990] : [47145 ^ _779999 : [(47148 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1726982, _1726984, tc_HOL_Obool), _1726990), 47144 ^ [_1726982, _1726984, _1726986, _1726988, _1726990]))], (47146 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1726982, _1726984)), 47144 ^ [_1726982, _1726984, _1726986, _1726988, _1726990]), hAPP(c_List_Oset(tc_prod(_1726982, _1726984)), hAPP(hAPP(c_List_Ozip(_1726982, _1726984), _1726986), _1726988)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726982)), _1726986) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726984)), _1726988), -(c_List_Olist__all2(_1726982, _1726984, _1726990, _1726986, _1726988))], (38433 ^ _779999) ^ [_1516216, _1516218, _1516220] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516216, _1516218), c_Orderings_Obot__class_Obot(tc_fun(_1516216, tc_HOL_Obool))), _1516220) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516216, _1516218), tc_HOL_Obool)))], (21887 ^ _779999) ^ [_1180888, _1180890, _1180892, _1180894, _1180896] : [_1180888 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1180890, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1180890, tc_HOL_Obool), tc_fun(_1180890, tc_HOL_Obool), tc_fun(_1180890, tc_HOL_Obool)), c_Set_OCollect(_1180890)), _1180892)), c_Orderings_Oorder__class_Omono(tc_fun(_1180890, tc_HOL_Obool), tc_fun(_1180890, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1180890, tc_HOL_Obool), tc_fun(_1180890, tc_HOL_Obool), tc_fun(_1180890, tc_HOL_Obool)), c_Set_OCollect(_1180890)), _1180892)), hBOOL(hAPP(hAPP(c_member(_1180890), _1180894), _1180896)), 21901 ^ _779999 : [(21904 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1180892, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1180890, tc_HOL_Obool)), _1180896), _1180888)), 21900 ^ [_1180888, _1180890, _1180892, _1180894, _1180896]))], (21902 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180890), 21900 ^ [_1180888, _1180890, _1180892, _1180894, _1180896]), _1180896)))]], -(hBOOL(hAPP(hAPP(c_member(_1180890), _1180894), _1180888)))], (42516 ^ _779999) ^ [_1616975, _1616977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1616975, tc_HOL_Obool), tc_HOL_Obool)), _1616977), hAPP(c_Set_OPow(_1616975), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616975, tc_HOL_Obool), _1616977)))))], (46326 ^ _779999) ^ [_1708751, _1708753, _1708755, _1708757] : [-(_1708751 = c_List_Olist_ONil(_1708753)), -(hAPP(c_List_Ohd(_1708755), hAPP(hAPP(c_List_Omap(_1708753, _1708755), _1708757), _1708751)) = hAPP(_1708757, hAPP(c_List_Ohd(_1708753), _1708751)))], (7197 ^ _779999) ^ [_898839, _898841, _898843, _898845] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898839, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_898839), _898841), _898843)), _898845) = hAPP(hAPP(c_Set_Oinsert(_898839), _898841), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898839, tc_HOL_Obool)), _898843), _898845)))], (7127 ^ _779999) ^ [_897293, _897295, _897297, _897299, _897301] : [hBOOL(hAPP(hAPP(c_member(_897293), _897295), _897297)), -(hAPP(hAPP(c_Set_Oinsert(_897299), hAPP(_897301, _897295)), hAPP(c_Set_Oimage(_897293, _897299, _897301), _897297)) = hAPP(c_Set_Oimage(_897293, _897299, _897301), _897297))], (16827 ^ _779999) ^ [_1084321, _1084323, _1084325] : [class_Orderings_Oorder(_1084321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084321), _1084323), _1084325)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1084321, _1084325, _1084323) = c_Orderings_Obot__class_Obot(tc_fun(_1084321, tc_HOL_Obool)))], (20371 ^ _779999) ^ [_1150744, _1150746] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1150744, _1150746)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1150746), _1150744)))], (45235 ^ _779999) ^ [_1684428, _1684430, _1684432] : [-(hBOOL(hAPP(c_List_Odistinct(_1684428), hAPP(hAPP(c_List_Oappend(_1684428), _1684430), _1684432)))), hBOOL(hAPP(c_List_Odistinct(_1684428), _1684430)), hBOOL(hAPP(c_List_Odistinct(_1684428), _1684432)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684428, tc_HOL_Obool)), hAPP(c_List_Oset(_1684428), _1684430)), hAPP(c_List_Oset(_1684428), _1684432)) = c_Orderings_Obot__class_Obot(tc_fun(_1684428, tc_HOL_Obool))], (45382 ^ _779999) ^ [_1688261, _1688263, _1688265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688261, tc_HOL_Obool)), hAPP(c_List_Oset(_1688261), hAPP(hAPP(c_List_Odrop(_1688261), _1688263), _1688265))), hAPP(c_List_Oset(_1688261), _1688265))))], (7655 ^ _779999) ^ [_908616, _908618] : [_908616 = _908618, -(hAPP(c_Nat_OSuc, _908616) = hAPP(c_Nat_OSuc, _908618))], (33643 ^ _779999) ^ [_1409188, _1409190] : [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(_1409190))), 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)), _1409188))))), -(hAPP(c_Nat_OSuc, _1409188) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409190))], (24840 ^ _779999) ^ [_1245285, _1245287, _1245289] : [class_Orderings_Olinorder(_1245285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245285), _1245287)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245285), _1245289)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1245285, tc_HOL_Obool)), _1245287), _1245289) = c_Orderings_Obot__class_Obot(tc_fun(_1245285, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245285), c_Big__Operators_Olinorder__class_OMax(_1245285, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245285, tc_HOL_Obool)), _1245287), _1245289))), c_Big__Operators_Olinorder__class_OMax(_1245285, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1245285, tc_HOL_Obool)), _1245287), _1245289))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245285), c_Big__Operators_Olinorder__class_OMax(_1245285, _1245287)), c_Big__Operators_Olinorder__class_OMax(_1245285, _1245289)))], (51958 ^ _779999) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (44678 ^ _779999) ^ [_1671491, _1671493, _1671495, _1671497] : [_1671493 = c_List_Olist_ONil(_1671491), -(hAPP(hAPP(c_List_Olist__update(_1671491, _1671493), _1671495), _1671497) = c_List_Olist_ONil(_1671491))], (49998 ^ _779999) ^ [_1789418, _1789420, _1789422] : [c_List_Olist_ONil(_1789418) = c_List_Oreplicate(_1789418, _1789420, _1789422), -(_1789420 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19071 ^ _779999) ^ [_1127655] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1127655), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1127655)], (10153 ^ _779999) ^ [_955146] : [-(_955146 = 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)), _955146)))], (21062 ^ _779999) ^ [_1162675, _1162677] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1162675), _1162677))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1162675))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1162677))))], (11803 ^ _779999) ^ [_987411, _987413, _987415, _987417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987411), hAPP(c_Set_Oimage(_987413, _987411, _987415), _987417))), c_Fun_Oinj__on(_987413, _987411, _987415, _987417), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987413), _987417)))], (38168 ^ _779999) ^ [_1509095, _1509097, _1509099, _1509101] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509095), _1509097)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509095), _1509099)), -(_1509099 = c_Orderings_Obot__class_Obot(tc_fun(_1509095, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1509095, tc_HOL_Obool), tc_fun(_1509095, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1509095, tc_HOL_Obool), tc_fun(_1509095, tc_HOL_Obool)), _1509097), _1509099)), c_Wellfounded_Omax__ext(_1509095, _1509101)))), 38182 ^ _779999 : [(38185 ^ _779999) ^ [_1509500] : [hBOOL(hAPP(hAPP(c_member(_1509095), _1509500), _1509099)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509095, _1509095)), hAPP(hAPP(c_Product__Type_OPair(_1509095, _1509095), 38181 ^ [_1509095, _1509097, _1509099, _1509101]), _1509500)), _1509101))], (38183 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509095), 38181 ^ [_1509095, _1509097, _1509099, _1509101]), _1509097)))]]], (35528 ^ _779999) ^ [_1448780, _1448782, _1448784, _1448786, _1448788, _1448790] : [35529 ^ _779999 : [(35532 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1448786, _1448782), _1448784))], (35530 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1448780, _1448782), _1448784))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448788, tc_fun(_1448790, tc_HOL_Obool))), _1448786), _1448780), _1448782), _1448784)))], (15653 ^ _779999) ^ [_1062079, _1062081] : [class_Rings_Ocomm__semiring__1(_1062079), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062079), c_Groups_Ozero__class_Ozero(_1062079)), _1062081) = c_Groups_Ozero__class_Ozero(_1062079))], (18899 ^ _779999) ^ [_1124859, _1124861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124859), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124861), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124859), _1124861)))], (22493 ^ _779999) ^ [_1196214, _1196216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1196214), c_Orderings_Otop__class_Otop(tc_fun(_1196214, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1196214, _1196214, _1196216), c_Orderings_Otop__class_Otop(tc_fun(_1196214, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1196214, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1196214, _1196214, _1196216, c_Orderings_Otop__class_Otop(tc_fun(_1196214, tc_HOL_Obool))))], (31214 ^ _779999) ^ [_1364873, _1364875] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364873, _1364875)) = _1364875, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1364873), _1364875) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8411 ^ _779999) ^ [_923796, _923798, _923800, _923802, _923804, _923806] : [-(hBOOL(hAPP(hAPP(c_member(_923796), _923798), _923800))), -(hAPP(c_Fun_Ooverride__on(_923796, _923802, _923804, _923806, _923800), _923798) = hAPP(_923804, _923798))], (39501 ^ _779999) ^ [_1544051, _1544053, _1544055, _1544057, _1544059, _1544061] : [c_Fun_Oinj__on(_1544051, _1544053, hAPP(c_Fun_Ocomp(_1544055, _1544053, _1544051, _1544057), _1544059), _1544061), -(c_Fun_Oinj__on(_1544055, _1544053, _1544057, hAPP(c_Set_Oimage(_1544051, _1544055, _1544059), _1544061)))], (45845 ^ _779999) ^ [_1698382, _1698384] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1698382), hAPP(c_List_Oset(tc_Nat_Onat), _1698384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698382), 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)), _1698384))))], (34279 ^ _779999) ^ [_1421074, _1421076] : [class_Groups_Omonoid__mult(_1421074), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421074), _1421076), 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(_1421074), _1421076), _1421076))], (42853 ^ _779999) ^ [_1624554, _1624556, _1624558] : [42855 ^ _779999 : [(42858 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624554), _1624558), 42854 ^ [_1624554, _1624556, _1624558]))], (42856 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624554, tc_HOL_Obool)), 42854 ^ [_1624554, _1624556, _1624558]), _1624556)))]], -(hBOOL(hAPP(hAPP(c_member(_1624554), _1624558), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624554, tc_HOL_Obool), _1624556))))], (18445 ^ _779999) ^ [_1115792, _1115794, _1115796] : [class_Orderings_Oord(_1115792), 18448 ^ _779999 : [(18455 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115792), _1115794), _1115796)), -(hBOOL(hAPP(hAPP(c_member(_1115792), _1115794), hAPP(c_SetInterval_Oord__class_OlessThan(_1115792), _1115796))))], (18449 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1115792), _1115794), hAPP(c_SetInterval_Oord__class_OlessThan(_1115792), _1115796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115792), _1115794), _1115796)))]]], (46686 ^ _779999) ^ [_1716474, _1716476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716474)), hAPP(c_Code__Numeral_Onat__of, _1716476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1716474), _1716476)))], (17281 ^ _779999) ^ [_1093358, _1093360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1093360), _1093358))))], (20552 ^ _779999) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6863 ^ _779999) ^ [_892505, _892507, _892509] : [hBOOL(hAPP(hAPP(c_member(_892505), _892507), hAPP(hAPP(c_Set_Oinsert(_892505), _892509), c_Orderings_Obot__class_Obot(tc_fun(_892505, tc_HOL_Obool))))), -(_892507 = _892509)], (1544 ^ _779999) ^ [_802407, _802409] : [-(class_Finite__Set_Ofinite(_802407)), _802409 = _802407, class_Finite__Set_Ofinite(_802409)], (6889 ^ _779999) ^ [_893008, _893010, _893012, _893014] : [6890 ^ _779999 : [(6893 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893008), _893010), _893014))], (6891 ^ _779999) ^ [] : [_893010 = _893012]], -(hBOOL(hAPP(hAPP(c_member(_893008), _893010), hAPP(hAPP(c_Set_Oinsert(_893008), _893012), _893014))))], (14451 ^ _779999) ^ [_1038309, _1038311, _1038313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038309), _1038311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038309, tc_HOL_Obool)), _1038313), _1038311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1038309), _1038313)), hAPP(c_Finite__Set_Ocard(_1038309), _1038311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1038309, tc_HOL_Obool)), _1038313), _1038311)))], (14423 ^ _779999) ^ [_1037809, _1037811, _1037813, _1037815, _1037817] : [class_Groups_Ocomm__monoid__add(_1037809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037811), _1037813)), -(hBOOL(hAPP(hAPP(c_member(_1037811), _1037815), _1037813))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1037811, _1037809), _1037817), hAPP(hAPP(c_Set_Oinsert(_1037811), _1037815), _1037813)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037809), hAPP(_1037817, _1037815)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1037811, _1037809), _1037817), _1037813)))], (48703 ^ _779999) ^ [_1760336, _1760338] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1760336), _1760338) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1760336)), c_List_Oembed__list(_1760338))))], (42103 ^ _779999) ^ [_1607172, _1607174, _1607176, _1607178, _1607180, _1607182] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607172, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1607174, _1607172, _1607176), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607178, tc_fun(_1607174, tc_HOL_Obool)), _1607180), _1607182))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607178, tc_fun(_1607172, tc_HOL_Obool)), _1607180), hAPP(hAPP(c_COMBB(tc_fun(_1607174, tc_HOL_Obool), tc_fun(_1607172, tc_HOL_Obool), _1607178), c_Relation_OImage(_1607174, _1607172, _1607176)), _1607182)))))], (11396 ^ _779999) ^ [_978016, _978018, _978020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978016, tc_HOL_Obool)), _978018), _978020)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978016, tc_HOL_Obool)), _978020), _978018) = _978018)], (21806 ^ _779999) ^ [_1178439, _1178441, _1178443, _1178445] : [_1178439 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1178441, _1178443), 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)), _1178445))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1178441), _1178439)))], (37684 ^ _779999) ^ [_1497349, _1497351, _1497353, _1497355] : [hAPP(hAPP(c_Relation_Orel__comp(_1497349, _1497349, _1497349), _1497351), _1497353) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497349, _1497349), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1497349, _1497349, _1497349), _1497355), _1497353) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497349, _1497349), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1497349, _1497349, _1497349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1497349, _1497349), tc_HOL_Obool)), _1497351), _1497355)), _1497353) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497349, _1497349), tc_HOL_Obool)))], (1274 ^ _779999) ^ [_799032, _799034] : [-(class_Rings_Olinordered__idom(_799032)), _799034 = _799032, class_Rings_Olinordered__idom(_799034)], (4272 ^ _779999) ^ [_844771, _844773, _844775, _844777, _844779, _844781, _844783, _844785] : [-(c_New__Random__Sequence_Opos__empty(_844785, _844781, _844777, _844773) = c_New__Random__Sequence_Opos__empty(_844783, _844779, _844775, _844771)), _844785 = _844783, _844781 = _844779, _844777 = _844775, _844773 = _844771], (43841 ^ _779999) ^ [_1652034, _1652036, _1652038] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1652034)), _1652036), c_List_Olists(_1652034, _1652038))), 43844 ^ _779999 : [(43845 ^ _779999) ^ [_1652142] : [hBOOL(hAPP(hAPP(c_member(_1652034), _1652142), hAPP(c_List_Oset(_1652034), _1652036))), -(hBOOL(hAPP(hAPP(c_member(_1652034), _1652142), _1652038)))]]], (12651 ^ _779999) ^ [_1003829, _1003831, _1003833] : [class_Lattices_Olattice(_1003829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003829), _1003831)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003829), _1003833)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1003829, tc_HOL_Obool)), _1003831), _1003833) = c_Orderings_Obot__class_Obot(tc_fun(_1003829, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1003829), c_Big__Operators_Olattice__class_OSup__fin(_1003829, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003829, tc_HOL_Obool)), _1003831), _1003833))), c_Big__Operators_Olattice__class_OSup__fin(_1003829, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1003829, tc_HOL_Obool)), _1003831), _1003833))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1003829), c_Big__Operators_Olattice__class_OSup__fin(_1003829, _1003831)), c_Big__Operators_Olattice__class_OSup__fin(_1003829, _1003833)))], (14742 ^ _779999) ^ [_1044765, _1044767, _1044769] : [_1044765 = _1044769, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044765), _1044767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044769), _1044767))], (25239 ^ _779999) ^ [_1253859, _1253861] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1253859))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1253861)), hAPP(c_Int_Onat, _1253859)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253861), _1253859)), 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)))], (42470 ^ _779999) ^ [_1615704, _1615706, _1615708] : [-(hAPP(c_Relation_ODomain(_1615704, _1615706), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1615704, _1615706), tc_HOL_Obool), _1615708)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1615704, _1615706), tc_HOL_Obool), tc_fun(_1615704, tc_HOL_Obool)), _1615708), c_Relation_ODomain(_1615704, _1615706)))], (39511 ^ _779999) ^ [_1544358, _1544360, _1544362, _1544364, _1544366, _1544368, _1544370, _1544372, _1544374, _1544376] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1544358, _1544360), tc_prod(_1544362, _1544364), tc_prod(_1544366, _1544368), c_Product__Type_Omap__pair(_1544358, _1544362, _1544360, _1544364, _1544370, _1544372)), c_Product__Type_Omap__pair(_1544366, _1544358, _1544368, _1544360, _1544374, _1544376)) = c_Product__Type_Omap__pair(_1544366, _1544362, _1544368, _1544364, hAPP(c_Fun_Ocomp(_1544358, _1544362, _1544366, _1544370), _1544374), hAPP(c_Fun_Ocomp(_1544360, _1544364, _1544368, _1544372), _1544376)))], (51347 ^ _779999) ^ [_1818539, _1818541, _1818543, _1818545] : [hAPP(c_Set_Oimage(_1818539, _1818541, _1818543), c_Orderings_Otop__class_Otop(tc_fun(_1818539, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1818541, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1818539, _1818541, _1818543), hAPP(c_Set_Oimage(_1818541, _1818539, c_Hilbert__Choice_Oinv__into(_1818539, _1818541, c_Orderings_Otop__class_Otop(tc_fun(_1818539, tc_HOL_Obool)), _1818543)), _1818545)) = _1818545)], (5847 ^ _779999) ^ [_872851, _872853, _872855, _872857] : [5848 ^ _779999 : [(5851 ^ _779999) ^ [] : [hBOOL(hAPP(_872855, _872853))], (5849 ^ _779999) ^ [] : [hBOOL(hAPP(_872851, _872853))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_872857, tc_HOL_Obool)), _872855), _872851), _872853)))], (24694 ^ _779999) ^ [_1242610, _1242612, _1242614, _1242616, _1242618] : [class_Orderings_Olinorder(_1242610), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242610, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242610, _1242612, _1242614)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242610, _1242616, _1242618)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1242610, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242610), _1242612), _1242616), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1242610), _1242614), _1242618)))], (50046 ^ _779999) ^ [_1790291, _1790293, _1790295] : [-(_1790291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1790293), c_List_Oreplicate(_1790293, _1790291, _1790295)) = hAPP(hAPP(c_Set_Oinsert(_1790293), _1790295), c_Orderings_Obot__class_Obot(tc_fun(_1790293, tc_HOL_Obool))))], (43161 ^ _779999) ^ [_1631696, _1631698] : [-(c_List_Olenlex(_1631696, _1631698) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1631696), tc_List_Olist(_1631696), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1631696), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), tc_List_Olist(_1631696)), c_COMBS(tc_List_Olist(_1631696), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1631696)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1631696)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631696), tc_fun(tc_List_Olist(_1631696), tc_Nat_Onat), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631696), tc_Nat_Onat), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), tc_List_Olist(_1631696)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1631696))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1631696)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1631696))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1631696)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1631696), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), tc_List_Olist(_1631696)), c_COMBS(tc_List_Olist(_1631696), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1631696)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1631696)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631696), tc_fun(tc_List_Olist(_1631696), tc_Nat_Onat), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631696), tc_Nat_Onat), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), tc_List_Olist(_1631696)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1631696))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1631696)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1631696))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1631696)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631696), tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631696), tc_HOL_Obool)), tc_List_Olist(_1631696)), c_COMBC(tc_List_Olist(_1631696), tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631696), tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696))), tc_fun(tc_List_Olist(_1631696), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1631696)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1631696)), c_member(tc_prod(tc_List_Olist(_1631696), tc_List_Olist(_1631696))))), c_Product__Type_OPair(tc_List_Olist(_1631696), tc_List_Olist(_1631696))))), c_List_Olex(_1631696, _1631698)))))))], (6231 ^ _779999) ^ [_879623, _879625, _879627] : [-(_879623 = _879625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879627, tc_HOL_Obool)), _879623), _879625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879627, tc_HOL_Obool)), _879625), _879623))], (6294 ^ _779999) ^ [_880983, _880985, _880987, _880989] : [6295 ^ _779999 : [(6296 ^ _779999) ^ [_881093] : [hBOOL(hAPP(hAPP(c_member(_880983), _881093), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880983, tc_HOL_Obool)), _880985), _880987))), hBOOL(hAPP(_880989, _881093))]], 6304 ^ _779999 : [(6307 ^ _779999) ^ [] : [-(hBOOL(hAPP(_880989, 6303 ^ [_880983, _880985, _880987, _880989])))], (6305 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880983), 6303 ^ [_880983, _880985, _880987, _880989]), _880985)))]], 6309 ^ _779999 : [(6312 ^ _779999) ^ [] : [-(hBOOL(hAPP(_880989, 6308 ^ [_880983, _880985, _880987, _880989])))], (6310 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880983), 6308 ^ [_880983, _880985, _880987, _880989]), _880987)))]]], (20160 ^ _779999) ^ [_1147254] : [-(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)), _1147254)) = hAPP(c_Int_Onat, _1147254))], (21726 ^ _779999) ^ [_1175887, _1175889, _1175891] : [-(hAPP(c_Set_OCollect(_1175887), hAPP(hAPP(c_COMBS(_1175887, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175887), c_fdisj), _1175889)), _1175891)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1175887, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1175887), _1175889)), hAPP(c_Set_OCollect(_1175887), _1175891)))], (13872 ^ _779999) ^ [_1027356, _1027358] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027356), _1027358), 13877 ^ _779999 : [(13880 ^ _779999) ^ [] : [-(_1027358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13878 ^ _779999) ^ [] : [-(_1027356 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13881 ^ _779999 : [(13884 ^ _779999) ^ [] : [-(_1027358 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13882 ^ _779999) ^ [] : [-(_1027356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34531 ^ _779999) ^ [_1425371, _1425373, _1425375] : [class_Rings_Olinordered__idom(_1425371), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425371), c_Groups_Ozero__class_Ozero(_1425371)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425371), hAPP(hAPP(c_Power_Opower__class_Opower(_1425371), _1425373), 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(_1425371), _1425375), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (46356 ^ _779999) ^ [_1709342, _1709344, _1709346, _1709348, _1709350] : [c_Fun_Oinj__on(_1709342, _1709344, _1709346, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1709342, tc_HOL_Obool)), hAPP(c_List_Oset(_1709342), _1709348)), hAPP(c_List_Oset(_1709342), _1709350))), 46359 ^ _779999 : [(46366 ^ _779999) ^ [] : [_1709348 = _1709350, -(hAPP(hAPP(c_List_Omap(_1709342, _1709344), _1709346), _1709348) = hAPP(hAPP(c_List_Omap(_1709342, _1709344), _1709346), _1709350))], (46360 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Omap(_1709342, _1709344), _1709346), _1709348) = hAPP(hAPP(c_List_Omap(_1709342, _1709344), _1709346), _1709350), -(_1709348 = _1709350)]]], (20538 ^ _779999) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33785 ^ _779999) ^ [_1412249] : [class_Int_Onumber__ring(_1412249), -(c_Int_Oiszero(_1412249, hAPP(c_Int_Onumber__class_Onumber__of(_1412249), c_Int_OPls)))], (52248 ^ _779999) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (8338 ^ _779999) ^ [_921923, _921925, _921927, _921929, _921931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921923, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921923, tc_HOL_Obool)), hAPP(c_Set_Oimage(_921925, _921923, _921927), _921929)), hAPP(c_Set_Oimage(_921925, _921923, _921927), _921931))), hAPP(c_Set_Oimage(_921925, _921923, _921927), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921925, tc_HOL_Obool)), _921929), _921931)))))], (25680 ^ _779999) ^ [_1261467, _1261469, _1261471, _1261473] : [class_Groups_Ouminus(_1261467), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261469, _1261467)), _1261471), _1261473) = hAPP(c_Groups_Ouminus__class_Ouminus(_1261467), hAPP(_1261471, _1261473)))], (6751 ^ _779999) ^ [_890490, _890492, _890494, _890496, _890498, _890500] : [_890490 = hAPP(_890492, _890494), hBOOL(hAPP(hAPP(c_member(_890496), _890494), _890498)), -(hBOOL(hAPP(hAPP(c_member(_890500), _890490), hAPP(c_Set_Oimage(_890496, _890500, _890492), _890498))))], (46167 ^ _779999) ^ [_1704367, _1704369] : [-(_1704367 = c_List_Olist_ONil(_1704369)), -(c_Random_Oselect__weight(_1704369, hAPP(hAPP(c_List_Omap(_1704369, tc_prod(tc_Code__Numeral_Ocode__numeral, _1704369)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1704369), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1704367)) = c_Random_Oselect(_1704369, _1704367))], (21098 ^ _779999) ^ [_1163394, _1163396, _1163398] : [class_Orderings_Oorder(_1163394), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1163394, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1163394), _1163396)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1163394, _1163396, _1163398)) = c_Orderings_Obot__class_Obot(tc_fun(_1163394, tc_HOL_Obool)))], (20980 ^ _779999) ^ [_1161009, _1161011] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161009), _1161011)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1161009) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (52078 ^ _779999) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (51832 ^ _779999) ^ [_1828833, _1828835] : [class_Orderings_Oorder(_1828833), -(class_Orderings_Oorder(tc_fun(_1828835, _1828833)))], (72 ^ _779999) ^ [_781157, _781159, _781161, _781163, _781165, _781167, _781169, _781171, _781173, _781175, _781177, _781179] : [-(c_Finite__Set_Ofolding__image__simple(_781177, _781173, _781169, _781165, _781161, _781157)), c_Finite__Set_Ofolding__image__simple(_781179, _781175, _781171, _781167, _781163, _781159), _781179 = _781177, _781175 = _781173, _781171 = _781169, _781167 = _781165, _781163 = _781161, _781159 = _781157], (23990 ^ _779999) ^ [_1228268, _1228270, _1228272] : [class_Orderings_Olinorder(_1228268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1228268), _1228270)), hBOOL(hAPP(hAPP(c_member(_1228268), _1228272), _1228270)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1228268), _1228272), c_Big__Operators_Olattice_OInf__fin(_1228268, c_Orderings_Oord__class_Omin(_1228268), _1228270)) = c_Big__Operators_Olattice_OInf__fin(_1228268, c_Orderings_Oord__class_Omin(_1228268), _1228270))], (43341 ^ _779999) ^ [_1637999, _1638001, _1638003, _1638005] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637999), tc_List_Olist(_1637999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637999), tc_List_Olist(_1637999)), _1638001), _1638003)), c_List_Olistrel1(_1637999, hAPP(c_Relation_Oconverse(_1637999, _1637999), _1638005)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637999), tc_List_Olist(_1637999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637999), tc_List_Olist(_1637999)), _1638001), _1638003)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1637999), tc_List_Olist(_1637999)), c_List_Olistrel1(_1637999, _1638005)))))], (46308 ^ _779999) ^ [_1707753, _1707755, _1707757, _1707759] : [-(hAPP(c_List_Oset(_1707753), hAPP(hAPP(c_List_Omap(_1707755, _1707753), _1707757), _1707759)) = hAPP(c_Set_Oimage(_1707755, _1707753, _1707757), hAPP(c_List_Oset(_1707755), _1707759)))], (48432 ^ _779999) ^ [_1754645, _1754647, _1754649, _1754651, _1754653] : [c_List_Olist__all2(_1754645, _1754647, _1754649, hAPP(c_List_Orev(_1754645), _1754651), _1754653), -(c_List_Olist__all2(_1754645, _1754647, _1754649, _1754651, hAPP(c_List_Orev(_1754647), _1754653)))], (20748 ^ _779999) ^ [_1156579, _1156581] : [class_Orderings_Olinorder(_1156579), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1156579, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1156579), _1156581)), hAPP(hAPP(c_Set_Oinsert(_1156579), _1156581), c_Orderings_Obot__class_Obot(tc_fun(_1156579, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1156579), _1156581))], (37437 ^ _779999) ^ [_1489696, _1489698, _1489700, _1489702] : [-(hAPP(c_Relation_OField(_1489696), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1489696, _1489696)), hAPP(hAPP(c_Product__Type_OPair(_1489696, _1489696), _1489698), _1489700)), _1489702)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489696, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1489696), _1489698), hAPP(hAPP(c_Set_Oinsert(_1489696), _1489700), c_Orderings_Obot__class_Obot(tc_fun(_1489696, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1489696), _1489702)))], (45372 ^ _779999) ^ [_1688009, _1688011, _1688013, _1688015] : [-(hAPP(hAPP(c_List_Odrop(_1688009), _1688011), hAPP(hAPP(c_List_Otake(_1688009), _1688013), _1688015)) = hAPP(hAPP(c_List_Otake(_1688009), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1688013), _1688011)), hAPP(hAPP(c_List_Odrop(_1688009), _1688011), _1688015)))], (29460 ^ _779999) ^ [_1333086, _1333088, _1333090, _1333092] : [class_Divides_Osemiring__div(_1333086), -(_1333088 = c_Groups_Ozero__class_Ozero(_1333086)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1333086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333086), _1333090), _1333088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333086), _1333092), _1333088)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1333086), _1333090), _1333092))], (8460 ^ _779999) ^ [_924759, _924761] : [-(c_Enum_Oenum__the(_924759, _924761) = c_HOL_OThe(_924759, _924761))], (35574 ^ _779999) ^ [_1449828, _1449830, _1449832, _1449834, _1449836, _1449838, _1449840] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1449828, _1449830, tc_fun(_1449832, tc_HOL_Obool)), _1449834), hAPP(hAPP(c_Product__Type_OPair(_1449828, _1449830), _1449836), _1449838)), _1449840)), -(hBOOL(hAPP(hAPP(hAPP(_1449834, _1449836), _1449838), _1449840)))], (38481 ^ _779999) ^ [_1517460, _1517462, _1517464] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1517460, _1517462), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517460, _1517462), _1517464), hAPP(c_COMBK(tc_fun(_1517462, tc_HOL_Obool), _1517460), c_Orderings_Otop__class_Otop(tc_fun(_1517462, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1517460, _1517462), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1517460, tc_HOL_Obool)), _1517464)), hAPP(c_COMBK(tc_fun(_1517462, tc_HOL_Obool), _1517460), c_Orderings_Otop__class_Otop(tc_fun(_1517462, tc_HOL_Obool)))))], (33625 ^ _779999) ^ [_1408798, _1408800] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408798) = hAPP(c_Nat_OSuc, _1408800), -(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(_1408798))), 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)), _1408800))))))], (22319 ^ _779999) ^ [_1192926, _1192928, _1192930] : [class_Lattices_Obounded__lattice__top(_1192926), 22322 ^ _779999 : [(22331 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1192926), _1192928), _1192930) = c_Orderings_Otop__class_Otop(_1192926)), _1192928 = c_Orderings_Otop__class_Otop(_1192926), _1192930 = c_Orderings_Otop__class_Otop(_1192926)], (22323 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1192926), _1192928), _1192930) = c_Orderings_Otop__class_Otop(_1192926), 22326 ^ _779999 : [(22329 ^ _779999) ^ [] : [-(_1192930 = c_Orderings_Otop__class_Otop(_1192926))], (22327 ^ _779999) ^ [] : [-(_1192928 = c_Orderings_Otop__class_Otop(_1192926))]]]]], (3956 ^ _779999) ^ [_839509, _839511, _839513, _839515, _839517, _839519] : [-(c_List_Oremove1(_839519, _839515, _839511) = c_List_Oremove1(_839517, _839513, _839509)), _839519 = _839517, _839515 = _839513, _839511 = _839509], (35675 ^ _779999) ^ [_1452029, _1452031, _1452033, _1452035, _1452037, _1452039] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1452029, _1452031, _1452033), _1452035), hAPP(hAPP(c_Product__Type_OPair(_1452029, _1452031), _1452037), _1452039)) = hAPP(hAPP(_1452035, _1452037), _1452039))], (51333 ^ _779999) ^ [_1818246, _1818248, _1818250, _1818252, _1818254, _1818256] : [hAPP(c_Hilbert__Choice_Oinv__into(_1818246, _1818248, _1818250, _1818252), _1818254) = hAPP(c_Hilbert__Choice_Oinv__into(_1818246, _1818248, _1818250, _1818252), _1818256), hBOOL(hAPP(hAPP(c_member(_1818248), _1818254), hAPP(c_Set_Oimage(_1818246, _1818248, _1818252), _1818250))), hBOOL(hAPP(hAPP(c_member(_1818248), _1818256), hAPP(c_Set_Oimage(_1818246, _1818248, _1818252), _1818250))), -(_1818254 = _1818256)], (9800 ^ _779999) ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290] : [c_Nitpick_Ofold__graph_H(_947278, _947280, _947282, _947284, _947286, hAPP(hAPP(_947282, _947288), _947290)), 9805 ^ _779999 : [(9808 ^ _779999) ^ [] : [-(hAPP(hAPP(_947282, _947288), _947290) = _947284)], (9806 ^ _779999) ^ [] : [-(_947286 = c_Orderings_Obot__class_Obot(tc_fun(_947278, tc_HOL_Obool)))]], 9811 ^ _779999 : [(9816 ^ _779999) ^ [] : [-(c_Nitpick_Ofold__graph_H(_947278, _947280, _947282, _947284, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947278, tc_HOL_Obool)), _947286), hAPP(hAPP(c_Set_Oinsert(_947278), 9809 ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290]), c_Orderings_Obot__class_Obot(tc_fun(_947278, tc_HOL_Obool)))), 9810 ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290]))], (9814 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_947278), 9809 ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290]), _947286)))], (9812 ^ _779999) ^ [] : [-(hAPP(hAPP(_947282, _947288), _947290) = hAPP(hAPP(_947282, 9809 ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290]), 9810 ^ [_947278, _947280, _947282, _947284, _947286, _947288, _947290]))]]], (7173 ^ _779999) ^ [_898300, _898302, _898304, _898306] : [-(_898300 = c_Orderings_Obot__class_Obot(tc_fun(_898302, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_898302, _898304, hAPP(c_COMBK(_898304, _898302), _898306)), _898300) = hAPP(hAPP(c_Set_Oinsert(_898304), _898306), c_Orderings_Obot__class_Obot(tc_fun(_898304, tc_HOL_Obool))))], (48784 ^ _779999) ^ [_1762035, _1762037] : [-(c_List_OdropWhile(_1762035, _1762037, c_List_Olist_ONil(_1762035)) = c_List_Olist_ONil(_1762035))], (22289 ^ _779999) ^ [_1192445, _1192447] : [class_Orderings_Otop(_1192445), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192445), _1192447), c_Orderings_Otop__class_Otop(_1192445))))], (43453 ^ _779999) ^ [_1641486, _1641488, _1641490, _1641492] : [c_List_Olistrelp(_1641486, hAPP(hAPP(c_COMBC(_1641486, tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_fun(_1641486, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1641486, tc_fun(tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_fun(_1641486, tc_HOL_Obool)), _1641486), c_COMBC(_1641486, tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1641486, tc_prod(_1641486, _1641486)), tc_fun(_1641486, tc_fun(tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_HOL_Obool)), _1641486), hAPP(c_COMBB(tc_prod(_1641486, _1641486), tc_fun(tc_fun(tc_prod(_1641486, _1641486), tc_HOL_Obool), tc_HOL_Obool), _1641486), c_member(tc_prod(_1641486, _1641486)))), c_Product__Type_OPair(_1641486, _1641486)))), _1641488), _1641490, _1641492), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641486), tc_List_Olist(_1641486))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641486), tc_List_Olist(_1641486)), _1641490), _1641492)), c_List_Olistrel(_1641486, _1641488))))], (39233 ^ _779999) ^ [_1537527, _1537529, _1537531] : [39235 ^ _779999 : [(39238 ^ _779999) ^ [] : [hBOOL(hAPP(_1537529, 39234 ^ [_1537527, _1537529, _1537531]))], (39236 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537527), 39234 ^ [_1537527, _1537529, _1537531]), _1537531)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1537527, _1537529), _1537531)))], (51596 ^ _779999) ^ [_1824337, _1824339, _1824341, _1824343, _1824345, _1824347] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1824337, _1824339, _1824341, _1824343), _1824345), _1824347) = hAPP(_1824343, hAPP(hAPP(c_Product__Type_OPair(_1824337, _1824339), _1824345), _1824347)))], (19399 ^ _779999) ^ [_1133716, _1133718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133716)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1133716), _1133718)))], (19679 ^ _779999) ^ [_1138827, _1138829, _1138831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138827)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1138829), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1138831)), 19689 ^ _779999 : [(19695 ^ _779999) ^ [] : [-(_1138829 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19691 ^ [_1138827, _1138829, _1138831]), 19688 ^ [_1138827, _1138829, _1138831]))], (19693 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19691 ^ [_1138827, _1138829, _1138831]), _1138831)))], (19690 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19688 ^ [_1138827, _1138829, _1138831]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1138827))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1138829), _1138827) = _1138829)], (52082 ^ _779999) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (3580 ^ _779999) ^ [_833689, _833691] : [_833691 = _833689, -(c_Random_Orange(_833691) = c_Random_Orange(_833689))], (35095 ^ _779999) ^ [_1435515, _1435517, _1435519, _1435521] : [-(c_Nitpick_Oprod(_1435515, _1435517, _1435519, _1435521) = hAPP(c_Set_OCollect(tc_prod(_1435515, _1435517)), hAPP(c_Product__Type_Oprod_Oprod__case(_1435515, _1435517, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1435515, tc_fun(_1435517, tc_HOL_Obool), tc_fun(_1435517, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1435517, tc_HOL_Obool), tc_fun(_1435517, tc_HOL_Obool)), _1435515), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1435517)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1435515), c_fconj), hAPP(hAPP(c_COMBC(_1435515, tc_fun(_1435515, tc_HOL_Obool), tc_HOL_Obool), c_member(_1435515)), _1435519)))), hAPP(hAPP(c_COMBC(_1435517, tc_fun(_1435517, tc_HOL_Obool), tc_HOL_Obool), c_member(_1435517)), _1435521)))))], (26358 ^ _779999) ^ [_1273934, _1273936] : [class_Rings_Ocomm__ring__1(_1273934), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1273934), _1273936) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273934), hAPP(c_Groups_Ouminus__class_Ouminus(_1273934), c_Groups_Oone__class_Oone(_1273934))), _1273936))], (20948 ^ _779999) ^ [_1160229, _1160231, _1160233, _1160235, _1160237] : [class_Rings_Olinordered__idom(_1160229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160229), hAPP(c_Groups_Oabs__class_Oabs(_1160229), _1160231)), _1160233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160229), hAPP(c_Groups_Oabs__class_Oabs(_1160229), _1160235)), _1160237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160229), hAPP(c_Groups_Oabs__class_Oabs(_1160229), _1160231)), hAPP(c_Groups_Oabs__class_Oabs(_1160229), _1160235))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160229), _1160233), _1160237))))], (8078 ^ _779999) ^ [_916397, _916399, _916401, _916403] : [hBOOL(hAPP(hAPP(c_member(_916397), _916399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916397, tc_HOL_Obool)), _916401), _916403))), 8081 ^ _779999 : [(8084 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_916397), _916399), _916403))], (8082 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916397), _916399), _916401)))]]], (7570 ^ _779999) ^ [_907132, _907134, _907136, _907138] : [-(c_Com_Ocom_OSemi(_907132, _907134) = c_Com_Ocom_OSemi(_907136, _907138)), _907132 = _907136, _907134 = _907138], (32797 ^ _779999) ^ [_1395189] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395189)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395189))], (44996 ^ _779999) ^ [_1679110, _1679112, _1679114, _1679116] : [hAPP(hAPP(c_List_Oappend(_1679110), _1679112), _1679114) = hAPP(hAPP(c_List_Oappend(_1679110), _1679112), _1679116), -(_1679114 = _1679116)], (13736 ^ _779999) ^ [_1025021, _1025023, _1025025, _1025027, _1025029] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1025021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025021), _1025023), _1025025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025021), _1025027), _1025029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025021), _1025023), _1025027)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025021), _1025025), _1025029))))], (40691 ^ _779999) ^ [_1572535, _1572537, _1572539, _1572541] : [-(hAPP(c_Relation_Oconverse(_1572535, _1572535), hAPP(hAPP(c_Relation_Oinv__image(_1572537, _1572535), _1572539), _1572541)) = hAPP(hAPP(c_Relation_Oinv__image(_1572537, _1572535), hAPP(c_Relation_Oconverse(_1572537, _1572537), _1572539)), _1572541))], (4522 ^ _779999) ^ [_848732, _848734] : [_848734 = _848732, -(c_List_Ohd(_848734) = c_List_Ohd(_848732))], (38726 ^ _779999) ^ [_1525886, _1525888] : [-(c_Product__Type_Oapsnd(_1525886, _1525886, _1525888, c_Fun_Oid(_1525886)) = c_Fun_Oid(tc_prod(_1525888, _1525886)))], (22213 ^ _779999) ^ [_1191006] : [c_Orderings_Otop__class_Otop(tc_fun(_1191006, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1191006, tc_HOL_Obool))], (33937 ^ _779999) ^ [_1414974, _1414976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414974), _1414976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1414974)), c_Int_OBit0(_1414976))))], (29402 ^ _779999) ^ [_1332229, _1332231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332229)), 29405 ^ _779999 : [(29412 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332231), 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), _1332231), _1332229)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29406 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332231), _1332229)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332231), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (52286 ^ _779999) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (33041 ^ _779999) ^ [_1399398] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399398), c_Int_OPls) = _1399398)], (34137 ^ _779999) ^ [_1418361] : [-(c_Int_Osucc(c_Int_OBit1(_1418361)) = c_Int_OBit0(c_Int_Osucc(_1418361)))], (28974 ^ _779999) ^ [_1324151, _1324153, _1324155, _1324157] : [class_Fields_Olinordered__field(_1324151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324151), c_Groups_Ozero__class_Ozero(_1324151)), _1324153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324151), _1324155), _1324153)), _1324157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324151), _1324155), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324151), _1324157), _1324153))))], (9935 ^ _779999) ^ [_951054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951054), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8548 ^ _779999) ^ [_926218] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926218), _926218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38505 ^ _779999) ^ [_1518464, _1518466, _1518468, _1518470] : [-(hAPP(c_Set_Oimage(tc_prod(_1518464, _1518466), tc_prod(_1518466, _1518464), hAPP(c_Product__Type_Oprod_Oprod__case(_1518464, _1518466, tc_prod(_1518466, _1518464)), hAPP(c_COMBC(_1518466, _1518464, tc_prod(_1518466, _1518464)), c_Product__Type_OPair(_1518466, _1518464)))), hAPP(hAPP(c_Product__Type_OSigma(_1518464, _1518466), _1518468), hAPP(c_COMBK(tc_fun(_1518466, tc_HOL_Obool), _1518464), _1518470))) = hAPP(hAPP(c_Product__Type_OSigma(_1518466, _1518464), _1518470), hAPP(c_COMBK(tc_fun(_1518464, tc_HOL_Obool), _1518466), _1518468)))], (33121 ^ _779999) ^ [_1400610] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400610), 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), _1400610)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1400610)))], (8556 ^ _779999) ^ [_926345, _926347, _926349] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _926345)), _926347)), hAPP(c_Nat_OSuc, _926349)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926345), _926347)), _926349))], (39223 ^ _779999) ^ [_1537344, _1537346, _1537348] : [hBOOL(hAPP(c_Predicate_OPowp(_1537344, _1537346), _1537348)), 39226 ^ _779999 : [(39227 ^ _779999) ^ [_1537428] : [hBOOL(hAPP(hAPP(c_member(_1537344), _1537428), _1537348)), -(hBOOL(hAPP(_1537346, _1537428)))]]], (37327 ^ _779999) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (24820 ^ _779999) ^ [_1244815, _1244817, _1244819] : [class_Orderings_Olinorder(_1244815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244815), _1244817)), 24827 ^ _779999 : [(24834 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1244815, tc_HOL_Obool)), _1244817), hAPP(hAPP(c_Set_Oinsert(_1244815), _1244819), c_Orderings_Obot__class_Obot(tc_fun(_1244815, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1244815, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1244815, hAPP(hAPP(c_Set_Oinsert(_1244815), _1244819), _1244817)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244815), _1244819), c_Big__Operators_Olinorder__class_OMax(_1244815, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1244815, tc_HOL_Obool)), _1244817), hAPP(hAPP(c_Set_Oinsert(_1244815), _1244819), c_Orderings_Obot__class_Obot(tc_fun(_1244815, tc_HOL_Obool)))))))], (24828 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1244815, tc_HOL_Obool)), _1244817), hAPP(hAPP(c_Set_Oinsert(_1244815), _1244819), c_Orderings_Obot__class_Obot(tc_fun(_1244815, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1244815, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1244815, hAPP(hAPP(c_Set_Oinsert(_1244815), _1244819), _1244817)) = _1244819)]]], (30675 ^ _779999) ^ [_1355130, _1355132] : [class_Divides_Osemiring__div(_1355130), -(c_Divides_Odiv__class_Omod(_1355130, _1355132, c_Groups_Oone__class_Oone(_1355130)) = c_Groups_Ozero__class_Ozero(_1355130))], (11462 ^ _779999) ^ [_980001, _980003, _980005, _980007, _980009] : [class_Groups_Ocomm__monoid__add(_980001), hBOOL(hAPP(c_Finite__Set_Ofinite(_980003), _980005)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980003, _980001), _980007), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980003, tc_HOL_Obool)), _980005), _980009)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_980003, _980001), hAPP(hAPP(c_COMBC(_980003, _980001, _980001), hAPP(hAPP(c_COMBS(_980003, _980001, tc_fun(_980001, _980001)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_980001, tc_fun(_980001, _980001)), _980003), c_If(_980001)), hAPP(hAPP(c_COMBC(_980003, tc_fun(_980003, tc_HOL_Obool), tc_HOL_Obool), c_member(_980003)), _980009))), _980007)), c_Groups_Ozero__class_Ozero(_980001))), _980005))], (10855 ^ _779999) ^ [_967772, _967774, _967776, _967778] : [-(c_Partial__Function_Omk__less(_967772, _967774, _967776, _967778)), hBOOL(hAPP(hAPP(_967774, _967776), _967778)), -(hBOOL(hAPP(hAPP(_967774, _967778), _967776)))], (43926 ^ _779999) ^ [_1655182, _1655184, _1655186] : [-(hAPP(c_List_Oset(tc_List_Olist(_1655182)), c_Enum_On__lists(_1655182, _1655184, _1655186)) = hAPP(c_Set_OCollect(tc_List_Olist(_1655182)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1655182), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1655182)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655182), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1655182)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1655182)))), _1655184))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655182), tc_fun(_1655182, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1655182, tc_HOL_Obool), tc_fun(tc_fun(_1655182, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1655182)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1655182, tc_HOL_Obool))), c_List_Oset(_1655182))), hAPP(c_List_Oset(_1655182), _1655186)))))], (2834 ^ _779999) ^ [_822050, _822052, _822054, _822056, _822058, _822060, _822062, _822064] : [-(c_Product__Type_Oapsnd(_822064, _822060, _822056, _822052) = c_Product__Type_Oapsnd(_822062, _822058, _822054, _822050)), _822064 = _822062, _822060 = _822058, _822056 = _822054, _822052 = _822050], (35679 ^ _779999) ^ [_1452145, _1452147, _1452149, _1452151, _1452153] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1452145, _1452147, tc_HOL_Obool), _1452149), hAPP(hAPP(c_Product__Type_OPair(_1452145, _1452147), _1452151), _1452153))), -(hBOOL(hAPP(hAPP(_1452149, _1452151), _1452153)))], (51622 ^ _779999) ^ [_1824850, _1824852, _1824854] : [c_Fun_Obij__betw(_1824850, _1824852, _1824854, c_Orderings_Otop__class_Otop(tc_fun(_1824850, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1824852, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1824852, _1824850, c_Hilbert__Choice_Oinv__into(_1824850, _1824852, c_Orderings_Otop__class_Otop(tc_fun(_1824850, tc_HOL_Obool)), _1824854), c_Orderings_Otop__class_Otop(tc_fun(_1824852, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1824850, tc_HOL_Obool))))], (37272 ^ _779999) ^ [_1486129, _1486131, _1486133, _1486135, _1486137, _1486139, _1486141] : [hBOOL(hAPP(_1486129, _1486131)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1486133, _1486133)), hAPP(hAPP(c_Product__Type_OPair(_1486133, _1486133), _1486135), _1486137)), hAPP(_1486139, _1486131))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1486141, _1486133), tc_prod(_1486141, _1486133))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1486141, _1486133), tc_prod(_1486141, _1486133)), hAPP(hAPP(c_Product__Type_OPair(_1486141, _1486133), _1486131), _1486135)), hAPP(hAPP(c_Product__Type_OPair(_1486141, _1486133), _1486131), _1486137))), c_Recdef_Osame__fst(_1486141, _1486133, _1486129, _1486139))))], (16449 ^ _779999) ^ [_1077158, _1077160, _1077162] : [class_Rings_Olinordered__ring__strict(_1077158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077158), _1077160), c_Groups_Ozero__class_Ozero(_1077158))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077158), _1077162), c_Groups_Ozero__class_Ozero(_1077158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077158), c_Groups_Ozero__class_Ozero(_1077158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077158), _1077160), _1077162))))], (47763 ^ _779999) ^ [_1741676] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1741676) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1741676)))], (48444 ^ _779999) ^ [_1754897, _1754899, _1754901, _1754903, _1754905] : [c_List_Olist__all2(_1754897, _1754899, _1754901, hAPP(c_List_Orev(_1754897), _1754903), hAPP(c_List_Orev(_1754899), _1754905)), -(c_List_Olist__all2(_1754897, _1754899, _1754901, _1754903, _1754905))], (25332 ^ _779999) ^ [_1255595, _1255597] : [class_Groups_Oordered__ab__group__add(_1255595), -(c_Fun_Oinj__on(_1255595, _1255595, c_Groups_Ouminus__class_Ouminus(_1255595), _1255597))], (34819 ^ _779999) ^ [_1431214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431214), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1431214)), c_Int_OMin)))], (15099 ^ _779999) ^ [_1051133, _1051135, _1051137, _1051139, _1051141] : [hBOOL(hAPP(hAPP(c_member(_1051133), _1051135), c_SetInterval_Oord_OgreaterThanLessThan(_1051133, _1051137, _1051139, _1051141))), 15102 ^ _779999 : [(15105 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1051137, _1051135), _1051141)))], (15103 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1051137, _1051139), _1051135)))]]], (19435 ^ _779999) ^ [_1134409, _1134411] : [_1134409 = _1134411, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134409) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134411))], (32695 ^ _779999) ^ [_1393370, _1393372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393370), _1393372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1393370)), c_Int_OBit1(_1393372))))], (50905 ^ _779999) ^ [_1810042, _1810044, _1810046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1810042, _1810042), tc_HOL_Obool)), _1810044), _1810046)), c_Relation_Oantisym(_1810042, _1810046), -(c_Relation_Oantisym(_1810042, _1810044))], (30186 ^ _779999) ^ [_1345658, _1345660, _1345662] : [-(hBOOL(hAPP(_1345658, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1345660), _1345662)))), 30189 ^ _779999 : [(30192 ^ _779999) ^ [] : [hBOOL(hAPP(_1345658, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30190 ^ _779999) ^ [] : [-(_1345662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 30193 ^ _779999 : [(30198 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30196 ^ [_1345658, _1345660, _1345662]), _1345662)))], (30200 ^ _779999) ^ [] : [-(_1345660 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1345662), 30195 ^ [_1345658, _1345660, _1345662])), 30196 ^ [_1345658, _1345660, _1345662]))], (30202 ^ _779999) ^ [] : [hBOOL(hAPP(_1345658, 30195 ^ [_1345658, _1345660, _1345662]))], (30194 ^ _779999) ^ [] : [_1345662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (49076 ^ _779999) ^ [_1768363, _1768365] : [-(c_List_Omeasures(_1768363, _1768365) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1768363), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1768363, tc_List_Olist(tc_fun(_1768363, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768363, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1768363, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1768363), c_List_Omap(tc_fun(_1768363, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1768363, tc_Nat_Onat), _1768363, tc_Nat_Onat), c_COMBI(tc_fun(_1768363, tc_Nat_Onat))))), _1768365)))], (31405 ^ _779999) ^ [_1368275, _1368277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1368275)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368275), _1368277)), _1368275) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22928 ^ _779999) ^ [_1206903, _1206905, _1206907, _1206909, _1206911] : [hBOOL(hAPP(hAPP(c_member(_1206903), _1206905), _1206907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1206909, tc_HOL_Obool)), hAPP(_1206911, _1206905)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206903, tc_fun(_1206909, tc_HOL_Obool)), _1206907), _1206911))))], (2456 ^ _779999) ^ [_816233, _816235] : [_816235 = _816233, -(c_Enum_Oenum__class_Oenum__all(_816235) = c_Enum_Oenum__class_Oenum__all(_816233))], (35614 ^ _779999) ^ [_1450685, _1450687, _1450689, _1450691, _1450693, _1450695] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450685, tc_fun(_1450687, tc_HOL_Obool))), _1450689), _1450691), _1450693), _1450695)), -(hBOOL(hAPP(hAPP(_1450691, _1450693), _1450695)))], (40693 ^ _779999) ^ [_1572594, _1572596, _1572598] : [-(hAPP(c_Relation_Oconverse(_1572594, _1572596), hAPP(c_Relation_Oconverse(_1572596, _1572594), _1572598)) = _1572598)], (11428 ^ _779999) ^ [_978853, _978855, _978857, _978859] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978853, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978853, tc_HOL_Obool)), _978855), _978857)), _978859) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978853, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978853, tc_HOL_Obool)), _978855), _978859)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978853, tc_HOL_Obool)), _978857), _978859)))], (24420 ^ _779999) ^ [_1237380, _1237382, _1237384, _1237386, _1237388] : [class_Orderings_Olinorder(_1237380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237380), _1237382), _1237384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237380), _1237386), _1237388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237380), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237380), _1237382), _1237386)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237380), _1237384), _1237388))))], (42300 ^ _779999) ^ [_1611867, _1611869, _1611871, _1611873, _1611875] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611867, tc_fun(_1611869, tc_HOL_Obool)), _1611871), _1611873), _1611875)), 42303 ^ _779999 : [(42304 ^ _779999) ^ [_1611976] : [hBOOL(hAPP(hAPP(c_member(_1611867), _1611976), _1611871)), -(hBOOL(hAPP(hAPP(_1611873, _1611976), _1611875)))]]], (32409 ^ _779999) ^ [_1387833, _1387835, _1387837, _1387839] : [class_Fields_Olinordered__field__inverse__zero(_1387833), class_Int_Onumber(_1387833), 32416 ^ _779999 : [(32417 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387833), _1387835), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))), _1387839)), 32420 ^ _779999 : [(32427 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)))), 32430 ^ _779999 : [(32437 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)), c_Groups_Ozero__class_Ozero(_1387833)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), _1387839)))], (32431 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)), c_Groups_Ozero__class_Ozero(_1387833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387833), _1387839), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))), _1387835)))]]], (32421 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), _1387835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387833), _1387839), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)))))]]], (32443 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387833), _1387835), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))), _1387839))), 32446 ^ _779999 : [(32449 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), _1387835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387833), _1387839), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))))], (32447 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))))]], 32450 ^ _779999 : [(32453 ^ _779999) ^ [] : [32454 ^ _779999 : [(32457 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387833), _1387839), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837))), _1387835))], (32455 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)), c_Groups_Ozero__class_Ozero(_1387833))))]], 32458 ^ _779999 : [(32461 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), _1387839))], (32459 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)), c_Groups_Ozero__class_Ozero(_1387833)))]]], (32451 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387833), c_Groups_Ozero__class_Ozero(_1387833)), hAPP(c_Int_Onumber__class_Onumber__of(_1387833), _1387837)))]]]]], (8332 ^ _779999) ^ [_921690, _921692, _921694, _921696] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921690, tc_HOL_Obool)), _921692), hAPP(hAPP(c_Set_Oinsert(_921690), _921694), _921696)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921690, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921690, tc_HOL_Obool)), _921692), _921696)), hAPP(hAPP(c_Set_Oinsert(_921690), _921694), c_Orderings_Obot__class_Obot(tc_fun(_921690, tc_HOL_Obool)))))], (26895 ^ _779999) ^ [_1285051, _1285053, _1285055] : [class_Lattices_Oboolean__algebra(_1285051), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1285051), _1285053), _1285055) = c_Orderings_Obot__class_Obot(_1285051), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285051), _1285053), _1285055) = c_Orderings_Otop__class_Otop(_1285051), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1285051), _1285053) = _1285055)], (42618 ^ _779999) ^ [_1619312, _1619314, _1619316] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619312, tc_HOL_Obool)), _1619314), _1619316) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619312, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619312, tc_HOL_Obool)), _1619314), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619312, tc_HOL_Obool)), _1619316), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619312, tc_HOL_Obool), tc_HOL_Obool))))))], (52264 ^ _779999) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (38682 ^ _779999) ^ [_1523647, _1523649, _1523651] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523647), _1523649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1523647, _1523647), tc_HOL_Obool)), _1523651), hAPP(hAPP(c_Product__Type_OSigma(_1523647, _1523647), _1523649), hAPP(c_COMBK(tc_fun(_1523647, tc_HOL_Obool), _1523647), _1523649)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1523647, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1523647), _1523649), _1523651))))], (50656 ^ _779999) ^ [_1803911, _1803913] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803911, tc_HOL_Obool), _1803913) = hAPP(c_Set_OCollect(_1803911), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803911, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1803911), c_HOL_OEx(tc_fun(_1803911, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803911, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803911, tc_HOL_Obool), tc_HOL_Obool), _1803911), hAPP(c_COMBS(tc_fun(_1803911, 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(_1803911, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1803911, tc_HOL_Obool), tc_fun(tc_fun(_1803911, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1803911, tc_HOL_Obool))), _1803913)))), c_member(_1803911)))))], (17491 ^ _779999) ^ [_1097412, _1097414] : [_1097412 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1097412), _1097414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9024 ^ _779999) ^ [_934321, _934323, _934325, _934327] : [class_Orderings_Oorder(_934321), _934323 = _934325, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934321), _934327), _934325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934321), _934327), _934323)))], (39397 ^ _779999) ^ [_1541930, _1541932, _1541934, _1541936, _1541938, _1541940] : [-(hAPP(hAPP(c_Fun_Ocomp(_1541930, _1541932, _1541934, _1541936), _1541938), _1541940) = hAPP(_1541936, hAPP(_1541938, _1541940)))], (8206 ^ _779999) ^ [_919099, _919101, _919103] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_919099, tc_HOL_Obool)), _919101), hAPP(c_Set_OPow(_919099), _919103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919099, tc_HOL_Obool)), _919101), _919103)))], (43618 ^ _779999) ^ [_1646341, _1646343, _1646345, _1646347] : [-(hAPP(hAPP(c_List_Onth(_1646341), hAPP(hAPP(c_List_Olist_OCons(_1646341), _1646343), _1646345)), hAPP(c_Nat_OSuc, _1646347)) = hAPP(hAPP(c_List_Onth(_1646341), _1646345), _1646347))], (50510 ^ _779999) ^ [_1800750, _1800752] : [c_Relation_Otrans(_1800750, _1800752), 50513 ^ _779999 : [(50514 ^ _779999) ^ [_1800886, _1800888] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1800750, _1800750)), hAPP(hAPP(c_Product__Type_OPair(_1800750, _1800750), _1800888), _1800886)), _1800752)), 50517 ^ _779999 : [(50518 ^ _779999) ^ [_1801029] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1800750, _1800750)), hAPP(hAPP(c_Product__Type_OPair(_1800750, _1800750), _1800886), _1801029)), _1800752)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800750, _1800750)), hAPP(hAPP(c_Product__Type_OPair(_1800750, _1800750), _1800888), _1801029)), _1800752)))]]]]], (7167 ^ _779999) ^ [_898179, _898181, _898183, _898185] : [_898179 = c_Orderings_Obot__class_Obot(tc_fun(_898181, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_898181, _898183, hAPP(c_COMBK(_898183, _898181), _898185)), _898179) = c_Orderings_Obot__class_Obot(tc_fun(_898183, tc_HOL_Obool)))], (42862 ^ _779999) ^ [_1624770, _1624772, _1624774, _1624776] : [class_Lattices_Osemilattice__inf(_1624770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624770), _1624772)), 42872 ^ _779999 : [(42875 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624770), _1624774), 42871 ^ [_1624770, _1624772, _1624774, _1624776]))], (42873 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624770), 42871 ^ [_1624770, _1624772, _1624774, _1624776]), _1624772)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624770), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1624770), _1624774), _1624776)), hAPP(hAPP(c_Finite__Set_Ofold(_1624770, _1624770, c_Lattices_Osemilattice__inf__class_Oinf(_1624770)), _1624776), _1624772))))], (45326 ^ _779999) ^ [_1686876, _1686878] : [-(hAPP(c_List_Orotate1(_1686876), _1686878) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1686876), _1686876, c_List_Olist_ONil(_1686876), hAPP(hAPP(c_COMBB(tc_List_Olist(_1686876), tc_fun(tc_List_Olist(_1686876), tc_List_Olist(_1686876)), _1686876), hAPP(c_COMBC(tc_List_Olist(_1686876), tc_List_Olist(_1686876), tc_List_Olist(_1686876)), c_List_Oappend(_1686876))), hAPP(hAPP(c_COMBC(_1686876, tc_List_Olist(_1686876), tc_List_Olist(_1686876)), c_List_Olist_OCons(_1686876)), c_List_Olist_ONil(_1686876)))), _1686878))], (1764 ^ _779999) ^ [_805157, _805159] : [-(class_Groups_Osemigroup__add(_805157)), _805159 = _805157, class_Groups_Osemigroup__add(_805159)], (3676 ^ _779999) ^ [_835139, _835141] : [_835141 = _835139, -(c_Finite__Set_Ocard(_835141) = c_Finite__Set_Ocard(_835139))], (15543 ^ _779999) ^ [_1060247, _1060249, _1060251, _1060253] : [class_Rings_Ocomm__semiring__1(_1060247), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060247), _1060249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060247), _1060251), _1060253)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060247), _1060249), _1060251)), _1060253))], (38477 ^ _779999) ^ [_1517310, _1517312, _1517314] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517310, _1517312), _1517314), hAPP(c_COMBK(tc_fun(_1517312, tc_HOL_Obool), _1517310), c_Orderings_Obot__class_Obot(tc_fun(_1517312, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517310, _1517312), tc_HOL_Obool)))], (40915 ^ _779999) ^ [_1578260, _1578262, _1578264] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1578260, _1578260, _1578260), _1578262), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578260, _1578260), tc_HOL_Obool), _1578264), _1578262)) = hAPP(hAPP(c_Relation_Orel__comp(_1578260, _1578260, _1578260), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578260, _1578260), tc_HOL_Obool), _1578264), _1578262)), _1578262))], (26398 ^ _779999) ^ [_1274566, _1274568, _1274570] : [class_Lattices_Oboolean__algebra(_1274566), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274566), _1274568), _1274570) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1274566), _1274568), hAPP(c_Groups_Ouminus__class_Ouminus(_1274566), _1274570)))], (7938 ^ _779999) ^ [_913962, _913964] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _913962), _913964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _913964), _913962)))], (48294 ^ _779999) ^ [_1751578, _1751580, _1751582] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751578), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1751578))), _1751580))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751582), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1751578))), _1751580))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751578), _1751578), hAPP(hAPP(c_COMBC(tc_List_Olist(_1751578), tc_Nat_Onat, _1751578), c_List_Onth(_1751578)), _1751582)), hAPP(c_List_Ofilter(tc_List_Olist(_1751578), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1751578)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751582)), c_Nat_Osize__class_Osize(tc_List_Olist(_1751578)))), c_List_Otranspose(_1751578, _1751580))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1751578)), _1751580), _1751582))], (23849 ^ _779999) ^ [_1225365, _1225367, _1225369] : [class_Orderings_Olinorder(_1225365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1225365), _1225367)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1225365), _1225369)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1225365, tc_HOL_Obool)), _1225367), _1225369) = c_Orderings_Obot__class_Obot(tc_fun(_1225365, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225365), c_Big__Operators_Olinorder__class_OMin(_1225365, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1225365, tc_HOL_Obool)), _1225367), _1225369))), c_Big__Operators_Olinorder__class_OMin(_1225365, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1225365, tc_HOL_Obool)), _1225367), _1225369))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225365), c_Big__Operators_Olinorder__class_OMin(_1225365, _1225367)), c_Big__Operators_Olinorder__class_OMin(_1225365, _1225369)))], (40283 ^ _779999) ^ [_1563396, _1563398] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563396, _1563396)), hAPP(hAPP(c_Product__Type_OPair(_1563396, _1563396), _1563398), _1563398)), c_Relation_OId(_1563396))))], (48480 ^ _779999) ^ [_1755670, _1755672] : [-(_1755670 = c_List_Olist_ONil(_1755672)), -(hAPP(c_List_Ohd(_1755672), hAPP(c_List_Orev(_1755672), _1755670)) = c_List_Olast(_1755672, _1755670))], (11182 ^ _779999) ^ [_973762, _973764, _973766] : [class_Lattices_Osemilattice__inf(_973762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973762), _973764), _973766)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973762), _973764), _973766) = _973764)], (18721 ^ _779999) ^ [_1121502, _1121504] : [class_Rings_Osemiring__1(_1121502), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121502), _1121504) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1121502, hAPP(hAPP(c_COMBC(_1121502, _1121502, _1121502), c_Groups_Oplus__class_Oplus(_1121502)), c_Groups_Oone__class_Oone(_1121502)), _1121504, c_Groups_Ozero__class_Ozero(_1121502)))], (44320 ^ _779999) ^ [_1664646, _1664648, _1664650] : [-(hBOOL(hAPP(c_List_Odistinct(_1664646), hAPP(hAPP(c_List_Olist_OCons(_1664646), _1664648), _1664650)))), -(hBOOL(hAPP(hAPP(c_member(_1664646), _1664648), hAPP(c_List_Oset(_1664646), _1664650)))), hBOOL(hAPP(c_List_Odistinct(_1664646), _1664650))], (24212 ^ _779999) ^ [_1233379, _1233381, _1233383] : [class_Orderings_Olinorder(_1233379), hAPP(_1233381, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1233379), 24217 ^ [_1233379, _1233381, _1233383]), 24218 ^ [_1233379, _1233381, _1233383])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1233379), hAPP(_1233381, 24217 ^ [_1233379, _1233381, _1233383])), hAPP(_1233381, 24218 ^ [_1233379, _1233381, _1233383])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1233379), _1233383)), -(_1233383 = c_Orderings_Obot__class_Obot(tc_fun(_1233379, tc_HOL_Obool))), -(hAPP(_1233381, c_Big__Operators_Olattice_OInf__fin(_1233379, c_Orderings_Oord__class_Omin(_1233379), _1233383)) = c_Big__Operators_Olattice_OInf__fin(_1233379, c_Orderings_Oord__class_Omin(_1233379), hAPP(c_Set_Oimage(_1233379, _1233379, _1233381), _1233383)))], (22890 ^ _779999) ^ [_1205726, _1205728, _1205730, _1205732, _1205734, _1205736, _1205738] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205726, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205728, tc_fun(_1205726, tc_HOL_Obool)), _1205730), _1205732)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205734, tc_fun(_1205726, tc_HOL_Obool)), _1205736), _1205738)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205728, tc_fun(_1205726, tc_HOL_Obool)), _1205730), hAPP(hAPP(c_COMBB(tc_fun(_1205734, tc_fun(_1205726, tc_HOL_Obool)), tc_fun(_1205726, tc_HOL_Obool), _1205728), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205734, tc_fun(_1205726, tc_HOL_Obool)), _1205736)), hAPP(hAPP(c_COMBC(_1205728, tc_fun(_1205734, tc_fun(_1205726, tc_HOL_Obool)), tc_fun(_1205734, tc_fun(_1205726, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1205726, tc_HOL_Obool), tc_fun(_1205726, tc_HOL_Obool)), tc_fun(tc_fun(_1205734, tc_fun(_1205726, tc_HOL_Obool)), tc_fun(_1205734, tc_fun(_1205726, tc_HOL_Obool))), _1205728), c_COMBB(tc_fun(_1205726, tc_HOL_Obool), tc_fun(_1205726, tc_HOL_Obool), _1205734)), hAPP(hAPP(c_COMBB(tc_fun(_1205726, tc_HOL_Obool), tc_fun(tc_fun(_1205726, tc_HOL_Obool), tc_fun(_1205726, tc_HOL_Obool)), _1205728), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205726, tc_HOL_Obool))), _1205732))), _1205738))))], (3106 ^ _779999) ^ [_826314, _826316, _826318, _826320, _826322, _826324] : [-(c_Nitpick_Otimes__frac(_826324, _826320, _826316) = c_Nitpick_Otimes__frac(_826322, _826318, _826314)), _826324 = _826322, _826320 = _826318, _826316 = _826314], (41730 ^ _779999) ^ [_1596436, _1596438, _1596440, _1596442, _1596444, _1596446, _1596448] : [c_Finite__Set_Ofun__left__comm(_1596436, _1596438, _1596440), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1596436, _1596438, _1596440, _1596442, _1596444), _1596446)), hBOOL(hAPP(hAPP(c_member(_1596436), _1596448), _1596444)), 41742 ^ _779999 : [(41745 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1596436, _1596438, _1596440, _1596442, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596436, tc_HOL_Obool)), _1596444), hAPP(hAPP(c_Set_Oinsert(_1596436), _1596448), c_Orderings_Obot__class_Obot(tc_fun(_1596436, tc_HOL_Obool))))), 41741 ^ [_1596436, _1596438, _1596440, _1596442, _1596444, _1596446, _1596448])))], (41743 ^ _779999) ^ [] : [-(_1596446 = hAPP(hAPP(_1596440, _1596448), 41741 ^ [_1596436, _1596438, _1596440, _1596442, _1596444, _1596446, _1596448]))]]], (15433 ^ _779999) ^ [_1057489, _1057491] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1057489, _1057491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1057491)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14762 ^ _779999) ^ [_1045143, _1045145, _1045147] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045143), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045145), _1045147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045143), _1045147)))], (33873 ^ _779999) ^ [_1413746, _1413748, _1413750] : [-(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), _1413746)), 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))), _1413748))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1413750))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1413750)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413746), 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), _1413750), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1413748)))))], (6695 ^ _779999) ^ [_889440, _889442, _889444] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _889440)), _889442), _889444)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _889440))), _889442), _889444)))], (22900 ^ _779999) ^ [_1206189, _1206191, _1206193, _1206195, _1206197] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206189, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206191, tc_fun(_1206189, tc_HOL_Obool)), _1206193), _1206195)), _1206197) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206191, tc_fun(_1206189, tc_HOL_Obool)), _1206193), hAPP(hAPP(c_COMBC(_1206191, tc_fun(_1206189, tc_HOL_Obool), tc_fun(_1206189, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1206189, tc_HOL_Obool), tc_fun(tc_fun(_1206189, tc_HOL_Obool), tc_fun(_1206189, tc_HOL_Obool)), _1206191), c_Groups_Ominus__class_Ominus(tc_fun(_1206189, tc_HOL_Obool))), _1206195)), _1206197)))], (6255 ^ _779999) ^ [_880076, _880078, _880080, _880082] : [6257 ^ _779999 : [(6260 ^ _779999) ^ [] : [hBOOL(hAPP(_880082, 6256 ^ [_880076, _880078, _880080, _880082]))], (6258 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880076), 6256 ^ [_880076, _880078, _880080, _880082]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880076, tc_HOL_Obool)), _880078), _880080))))]], 6261 ^ _779999 : [(6268 ^ _779999) ^ [_880393] : [hBOOL(hAPP(hAPP(c_member(_880076), _880393), _880080)), -(hBOOL(hAPP(_880082, _880393)))], (6262 ^ _779999) ^ [_880296] : [hBOOL(hAPP(hAPP(c_member(_880076), _880296), _880078)), -(hBOOL(hAPP(_880082, _880296)))]]], (44476 ^ _779999) ^ [_1667915, _1667917, _1667919] : [hBOOL(hAPP(hAPP(c_member(_1667915), _1667917), hAPP(c_List_Oset(_1667915), _1667919))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667915)), c_List_Oremove1(_1667915, _1667917, _1667919)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667915)), _1667919)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49675 ^ _779999) ^ [_1781964, _1781966, _1781968] : [-(c_List_Olist__ex1(_1781964, _1781966, _1781968)), 49676 ^ _779999 : [(49677 ^ _779999) ^ [_1782058] : [hBOOL(hAPP(hAPP(c_member(_1781964), _1782058), hAPP(c_List_Oset(_1781964), _1781968))), hBOOL(hAPP(_1781966, _1782058)), 49685 ^ _779999 : [(49690 ^ _779999) ^ [] : [49684 ^ [_1781964, _1781966, _1781968, _1782058] = _1782058], (49688 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1781966, 49684 ^ [_1781964, _1781966, _1781968, _1782058])))], (49686 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781964), 49684 ^ [_1781964, _1781966, _1781968, _1782058]), hAPP(c_List_Oset(_1781964), _1781968))))]]]]], (43285 ^ _779999) ^ [_1636231, _1636233, _1636235] : [-(c_Random_Oselect__weight(_1636231, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1636231)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1636231), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1636233)), _1636235)) = c_Random_Oselect__weight(_1636231, _1636235))], (47896 ^ _779999) ^ [_1744282, _1744284, _1744286] : [class_Orderings_Olinorder(_1744282), c_List_Olinorder__class_Osorted(_1744282, _1744284), -(c_List_Olinorder__class_Osorted(_1744282, hAPP(hAPP(c_List_Otake(_1744282), _1744286), _1744284)))], (48963 ^ _779999) ^ [_1765902, _1765904, _1765906] : [-(c_List_Oinsert(_1765902, _1765904, c_List_Oremdups(_1765902, _1765906)) = c_List_Oremdups(_1765902, c_List_Oinsert(_1765902, _1765904, _1765906)))], (46652 ^ _779999) ^ [_1715908, _1715910] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1715908), _1715910) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1715908)), hAPP(c_Code__Numeral_Onat__of, _1715910))))], (6781 ^ _779999) ^ [_891083, _891085, _891087] : [c_Orderings_Obot__class_Obot(tc_fun(_891083, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_891083), _891085), _891087)], (10165 ^ _779999) ^ [_955279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955279), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8640 ^ _779999) ^ [_927881, _927883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927881), _927883)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927881), _927883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10013 ^ _779999) ^ [_952810, _952812] : [class_Enum_Oenum(_952810), 10016 ^ _779999 : [(10024 ^ _779999) ^ [] : [10025 ^ _779999 : [(10026 ^ _779999) ^ [_952990] : [hBOOL(hAPP(_952812, _952990))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_952810), _952812)))], (10017 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_952810), _952812)), -(hBOOL(hAPP(_952812, 10020 ^ [_952810, _952812])))]]], (50955 ^ _779999) ^ [_1811146, _1811148] : [c_Relation_Oantisym(_1811146, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1811146, _1811146), tc_HOL_Obool)), _1811148), c_Relation_OId(_1811146))), -(c_Relation_Oantisym(_1811146, _1811148))], (45167 ^ _779999) ^ [_1682535, _1682537, _1682539, _1682541] : [-(hAPP(hAPP(c_List_Onth(_1682535), hAPP(hAPP(c_List_Oappend(_1682535), _1682537), hAPP(hAPP(c_List_Olist_OCons(_1682535), _1682539), _1682541))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682535)), _1682537)) = _1682539)], (18303 ^ _779999) ^ [_1113040, _1113042, _1113044, _1113046, _1113048] : [class_Orderings_Olinorder(_1113040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1113040, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1113040, _1113042), _1113044)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1113040, _1113046), _1113048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113040), _1113044), _1113042))), 18314 ^ _779999 : [(18317 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113040), _1113044), _1113048)))], (18315 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113040), _1113046), _1113042)))]]], (52140 ^ _779999) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (43747 ^ _779999) ^ [_1649890, _1649892] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1649890), hAPP(c_List_Oset(_1649890), _1649892))))], (19521 ^ _779999) ^ [_1135830] : [19523 ^ _779999 : [(19526 ^ _779999) ^ [] : [hBOOL(hAPP(_1135830, 19522 ^ [_1135830]))], (19524 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19522 ^ [_1135830])))]], 19527 ^ _779999 : [(19528 ^ _779999) ^ [_1135957] : [-(hBOOL(hAPP(_1135830, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1135957))))]]], (30613 ^ _779999) ^ [_1353947, _1353949, _1353951] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353947), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1353949, _1353951)), _1353951) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353947), _1353949), _1353951))], (47040 ^ _779999) ^ [_1724715, _1724717, _1724719, _1724721, _1724723] : [c_List_Olist__all2(_1724715, _1724717, _1724719, _1724721, _1724723), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724715)), _1724721) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724717)), _1724723))], (1804 ^ _779999) ^ [_805657, _805659] : [-(class_Rings_Ozero__neq__one(_805657)), _805659 = _805657, class_Rings_Ozero__neq__one(_805659)], (52232 ^ _779999) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (11424 ^ _779999) ^ [_978685, _978687, _978689, _978691] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978685, tc_HOL_Obool)), _978687), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978685, tc_HOL_Obool)), _978689), _978691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978685, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978685, tc_HOL_Obool)), _978687), _978689)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978685, tc_HOL_Obool)), _978687), _978691)))], (2966 ^ _779999) ^ [_824148, _824150, _824152, _824154, _824156, _824158, _824160, _824162] : [-(c_Random_Oiterate(_824162, _824158, _824154, _824150) = c_Random_Oiterate(_824160, _824156, _824152, _824148)), _824162 = _824160, _824158 = _824156, _824154 = _824152, _824150 = _824148], (31709 ^ _779999) ^ [_1374754, _1374756] : [class_Int_Onumber__ring(_1374754), -(hAPP(c_Int_Oring__1__class_Oof__int(_1374754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1374756)) = hAPP(c_Int_Onumber__class_Onumber__of(_1374754), _1374756))], (30034 ^ _779999) ^ [_1342836, _1342838, _1342840] : [class_Rings_Oring__1(_1342836), -(hAPP(c_Int_Oring__1__class_Oof__int(_1342836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1342838), _1342840)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342836), hAPP(c_Int_Oring__1__class_Oof__int(_1342836), _1342838)), hAPP(c_Int_Oring__1__class_Oof__int(_1342836), _1342840)))], (38222 ^ _779999) ^ [_1510222] : [-(c_Nitpick_Ozero__frac(_1510222) = c_Nitpick_OAbs__Frac(_1510222, 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))))], (40457 ^ _779999) ^ [_1567591, _1567593, _1567595, _1567597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567591, _1567591)), hAPP(hAPP(c_Product__Type_OPair(_1567591, _1567591), _1567593), _1567595)), c_Transitive__Closure_Ortrancl(_1567591, _1567597))), -(_1567593 = _1567595), 40464 ^ _779999 : [(40467 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567591, _1567591)), hAPP(hAPP(c_Product__Type_OPair(_1567591, _1567591), _1567593), _1567595)), c_Transitive__Closure_Otrancl(_1567591, _1567597))))], (40465 ^ _779999) ^ [] : [_1567593 = _1567595]]], (8171 ^ _779999) ^ [_918397] : [hAPP(c_Nat_OSuc, _918397) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47765 ^ _779999) ^ [_1741708, _1741710, _1741712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741708), _1741710)), _1741712)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1741708, _1741712)), _1741710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741708), _1741710))], (42374 ^ _779999) ^ [_1613728, _1613730, _1613732] : [class_Complete__Lattice_Ocomplete__lattice(_1613728), class_Orderings_Olinorder(_1613728), 42381 ^ _779999 : [(42391 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613728), _1613730), c_Complete__Lattice_OSup__class_OSup(_1613728, _1613732)))), 42392 ^ _779999 : [(42393 ^ _779999) ^ [_1614034] : [hBOOL(hAPP(hAPP(c_member(_1613728), _1614034), _1613732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613728), _1613730), _1614034))]]], (42382 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613728), _1613730), c_Complete__Lattice_OSup__class_OSup(_1613728, _1613732))), 42386 ^ _779999 : [(42389 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613728), _1613730), 42385 ^ [_1613728, _1613730, _1613732])))], (42387 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613728), 42385 ^ [_1613728, _1613730, _1613732]), _1613732)))]]]]], (26352 ^ _779999) ^ [_1273815, _1273817, _1273819] : [class_Rings_Ocomm__ring__1(_1273815), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273815), _1273817), _1273819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273815), _1273817), hAPP(c_Groups_Ouminus__class_Ouminus(_1273815), _1273819)))], (30367 ^ _779999) ^ [_1348901, _1348903, _1348905] : [class_Fields_Olinordered__field__inverse__zero(_1348901), 30373 ^ _779999 : [(30378 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348901), 30372 ^ [_1348901, _1348903, _1348905]), _1348903)), _1348905))], (30376 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348901), 30372 ^ [_1348901, _1348903, _1348905]), c_Groups_Oone__class_Oone(_1348901))))], (30374 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348901), c_Groups_Ozero__class_Ozero(_1348901)), 30372 ^ [_1348901, _1348903, _1348905])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348901), _1348903), _1348905)))], (47655 ^ _779999) ^ [_1739825, _1739827, _1739829] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1739825), c_List_Oupt(_1739827, _1739829)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1739827), _1739825), _1739829))], (4314 ^ _779999) ^ [_845458, _845460, _845462, _845464, _845466, _845468, _845470, _845472] : [-(c_New__Random__Sequence_Oneg__map(_845472, _845468, _845464, _845460) = c_New__Random__Sequence_Oneg__map(_845470, _845466, _845462, _845458)), _845472 = _845470, _845468 = _845466, _845464 = _845462, _845460 = _845458], (10527 ^ _779999) ^ [_961174, _961176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961174), _961176)), 10530 ^ _779999 : [(10537 ^ _779999) ^ [] : [_961176 = _961174, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961176), hAPP(c_Nat_OSuc, _961174))))], (10531 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961176), hAPP(c_Nat_OSuc, _961174))), -(_961176 = _961174)]]], (19641 ^ _779999) ^ [_1138133, _1138135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138133)), 19650 ^ _779999 : [(19653 ^ _779999) ^ [] : [hBOOL(hAPP(_1138135, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19646 ^ [_1138133, _1138135]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 19647 ^ [_1138133, _1138135]), _1138133))))], (19651 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1138135, 19646 ^ [_1138133, _1138135])))]], 19654 ^ _779999 : [(19657 ^ _779999) ^ [] : [hBOOL(hAPP(_1138135, 19646 ^ [_1138133, _1138135]))], (19655 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1138135, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19646 ^ [_1138133, _1138135]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 19647 ^ [_1138133, _1138135]), _1138133)))))]], 19658 ^ _779999 : [(19668 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1138135, 19675 ^ [_1138133, _1138135]))), 19669 ^ _779999 : [(19670 ^ _779999) ^ [_1138680] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1138680), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1138133))), hBOOL(hAPP(_1138135, _1138680))]]], (19659 ^ _779999) ^ [] : [19660 ^ _779999 : [(19661 ^ _779999) ^ [_1138565] : [hBOOL(hAPP(_1138135, _1138565))]], 19663 ^ _779999 : [(19666 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1138135, 19662 ^ [_1138133, _1138135])))], (19664 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19662 ^ [_1138133, _1138135]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1138133))))]]]]], (21110 ^ _779999) ^ [_1163648, _1163650, _1163652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163652), 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), _1163652), _1163650))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1163648)))))], (34297 ^ _779999) ^ [_1421373] : [class_Rings_Osemiring__1(_1421373), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421373), c_Groups_Oone__class_Oone(_1421373)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1421373))], (46372 ^ _779999) ^ [_1709667, _1709669, _1709671, _1709673, _1709675] : [-(c_List_Olist_Olist__size(_1709667, _1709669, hAPP(hAPP(c_List_Omap(_1709671, _1709667), _1709673), _1709675)) = c_List_Olist_Olist__size(_1709671, hAPP(c_Fun_Ocomp(_1709667, tc_Nat_Onat, _1709671, _1709669), _1709673), _1709675))], (12900 ^ _779999) ^ [_1008803, _1008805, _1008807, _1008809] : [c_Finite__Set_Ofolding__one__idem(_1008803, _1008805, _1008807), -(hAPP(hAPP(_1008805, _1008809), _1008809) = _1008809)], (22892 ^ _779999) ^ [_1205929, _1205931, _1205933, _1205935, _1205937, _1205939] : [class_Complete__Lattice_Ocomplete__lattice(_1205929), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205931, tc_fun(_1205933, _1205929)), _1205935), _1205937), _1205939) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205931, _1205929), _1205935), hAPP(hAPP(c_COMBC(_1205931, _1205933, _1205929), _1205937), _1205939)))], (18808 ^ _779999) ^ [_1123231, _1123233, _1123235, _1123237] : [class_Orderings_Olinorder(_1123231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123231), _1123233), _1123235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123231), _1123235), _1123237)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123231, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1123231, _1123233, _1123235)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1123231, _1123235, _1123237)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1123231, _1123233), _1123237))], (20762 ^ _779999) ^ [_1156897, _1156899, _1156901, _1156903] : [class_Groups_Oordered__ab__group__add__abs(_1156897), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156897), hAPP(c_Groups_Oabs__class_Oabs(_1156897), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1156899, _1156897), _1156901), _1156903))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1156899, _1156897), hAPP(hAPP(c_COMBB(_1156897, _1156897, _1156899), c_Groups_Oabs__class_Oabs(_1156897)), _1156901)), _1156903))))], (46490 ^ _779999) ^ [_1712540, _1712542, _1712544] : [-(c_Enum_Osublists(_1712540, hAPP(hAPP(c_List_Olist_OCons(_1712540), _1712542), _1712544)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1712540)), tc_List_Olist(tc_List_Olist(_1712540))), c_Enum_Osublists(_1712540, _1712544)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1712540)), tc_List_Olist(tc_List_Olist(_1712540)), tc_List_Olist(tc_List_Olist(_1712540))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1712540)), tc_fun(tc_List_Olist(tc_List_Olist(_1712540)), tc_List_Olist(tc_List_Olist(_1712540))), tc_List_Olist(tc_List_Olist(_1712540))), c_List_Oappend(tc_List_Olist(_1712540))), hAPP(c_List_Omap(tc_List_Olist(_1712540), tc_List_Olist(_1712540)), hAPP(c_List_Olist_OCons(_1712540), _1712542)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1712540))))))], (11436 ^ _779999) ^ [_979233, _979235, _979237, _979239] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979233, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979233, tc_HOL_Obool)), _979235), _979237)), _979239) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979233, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979233, tc_HOL_Obool)), _979235), _979239)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979233, tc_HOL_Obool)), _979237), _979239)))], (32733 ^ _779999) ^ [_1394064] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394064))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1394064)))))], (45400 ^ _779999) ^ [_1688656, _1688658] : [_1688658 = c_List_Olist_ONil(_1688656), -(hAPP(c_List_Orotate1(_1688656), _1688658) = c_List_Olist_ONil(_1688656))], (7133 ^ _779999) ^ [_897440, _897442, _897444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897440, tc_HOL_Obool)), _897442), hAPP(hAPP(c_Set_Oinsert(_897440), _897444), c_Orderings_Obot__class_Obot(tc_fun(_897440, tc_HOL_Obool))))), -(_897442 = c_Orderings_Obot__class_Obot(tc_fun(_897440, tc_HOL_Obool))), -(_897442 = hAPP(hAPP(c_Set_Oinsert(_897440), _897444), c_Orderings_Obot__class_Obot(tc_fun(_897440, tc_HOL_Obool))))], (31164 ^ _779999) ^ [_1364026, _1364028] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364026, _1364028)), _1364026)))], (43088 ^ _779999) ^ [_1630115, _1630117, _1630119] : [c_Nitpick_Oless__eq__frac(_1630115, _1630117, _1630119), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1630115), c_Nitpick_Oplus__frac(_1630115, _1630117, c_Nitpick_Ouminus__frac(_1630115, _1630119)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41817 ^ _779999) ^ [_1598321, _1598323, _1598325, _1598327] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1598325), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598321, tc_fun(_1598325, tc_HOL_Obool)), _1598323), _1598327)))), 41818 ^ _779999 : [(41819 ^ _779999) ^ [_1598395] : [hBOOL(hAPP(hAPP(c_member(_1598321), _1598395), _1598323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598325), hAPP(_1598327, _1598395)))]]], (31271 ^ _779999) ^ [_1365730, _1365732] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365730, _1365732)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365730), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365732)))], (14968 ^ _779999) ^ [_1048612, _1048614, _1048616] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048612), _1048614)), -(hBOOL(hAPP(hAPP(c_member(_1048612), _1048616), _1048614))), -(hAPP(c_Finite__Set_Ocard(_1048612), hAPP(hAPP(c_Set_Oinsert(_1048612), _1048616), _1048614)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1048612), _1048614)))], (47577 ^ _779999) ^ [_1737650, _1737652, _1737654, _1737656] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1737650, tc_Nat_Onat), _1737650), c_Product__Type_Ofst(_1737650, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1737650, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1737650, tc_Nat_Onat)), _1737652), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1737650, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1737650, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1737650, tc_Nat_Onat), _1737654), _1737656))) = hAPP(hAPP(c_List_Omap(tc_prod(_1737650, tc_Nat_Onat), _1737650), c_Product__Type_Ofst(_1737650, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1737650, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1737650, tc_Nat_Onat)), _1737652), c_Product__Type_Osnd(_1737650, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1737650, tc_Nat_Onat), _1737654), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1737656)))))], (21088 ^ _779999) ^ [_1163199, _1163201, _1163203] : [class_Orderings_Olinorder(_1163199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163199), _1163201), _1163203)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1163199, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1163199), _1163201)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1163199, _1163201, _1163203)) = hAPP(c_SetInterval_Oord__class_OatMost(_1163199), _1163203))], (6345 ^ _779999) ^ [_882140, _882142, _882144, _882146] : [class_Lattices_Osemilattice__sup(_882140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882140), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_882140), _882142), _882144)), _882146)), 6352 ^ _779999 : [(6355 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882140), _882144), _882146)))], (6353 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882140), _882142), _882146)))]]], (39276 ^ _779999) ^ [_1538919, _1538921, _1538923, _1538925, _1538927, _1538929] : [hBOOL(hAPP(hAPP(c_member(_1538919), _1538921), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1538923, _1538925, tc_fun(_1538919, tc_HOL_Obool)), _1538927), _1538929))), 39281 ^ _779999 : [(39284 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538919), _1538921), hAPP(hAPP(_1538927, 39279 ^ [_1538919, _1538921, _1538923, _1538925, _1538927, _1538929]), 39280 ^ [_1538919, _1538921, _1538923, _1538925, _1538927, _1538929]))))], (39282 ^ _779999) ^ [] : [-(_1538929 = hAPP(hAPP(c_Product__Type_OPair(_1538923, _1538925), 39279 ^ [_1538919, _1538921, _1538923, _1538925, _1538927, _1538929]), 39280 ^ [_1538919, _1538921, _1538923, _1538925, _1538927, _1538929]))]]], (33305 ^ _779999) ^ [_1403459, _1403461] : [33306 ^ _779999 : [(33309 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403459), c_Int_OPls))], (33307 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403459), _1403461))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403459)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403461))))], (6857 ^ _779999) ^ [_892386, _892388, _892390] : [_892388 = _892390, -(hBOOL(hAPP(hAPP(c_member(_892386), _892388), hAPP(c_fequal, _892390))))], (17497 ^ _779999) ^ [_1097495, _1097497] : [-(_1097495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1097495), _1097497) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1097497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1097495), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1097497)))], (1674 ^ _779999) ^ [_804032, _804034] : [-(class_Rings_Olinordered__semiring(_804032)), _804034 = _804032, class_Rings_Olinordered__semiring(_804034)], (30120 ^ _779999) ^ [_1344449, _1344451, _1344453, _1344455] : [class_Rings_Oring__1(_1344449), -(hAPP(c_Int_Oring__1__class_Oof__int(_1344449), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344451, tc_Int_Oint), _1344453), _1344455)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344451, _1344449), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1344449, _1344451), c_Int_Oring__1__class_Oof__int(_1344449)), _1344453)), _1344455))], (25024 ^ _779999) ^ [_1249652, _1249654, _1249656] : [class_Orderings_Olinorder(_1249652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249652), _1249654)), -(_1249656 = c_Orderings_Obot__class_Obot(tc_fun(_1249652, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249652, tc_HOL_Obool)), _1249656), _1249654)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1249652), c_Big__Operators_Olattice_OSup__fin(_1249652, c_Orderings_Oord__class_Omax(_1249652), _1249656)), c_Big__Operators_Olattice_OSup__fin(_1249652, c_Orderings_Oord__class_Omax(_1249652), _1249654)) = c_Big__Operators_Olattice_OSup__fin(_1249652, c_Orderings_Oord__class_Omax(_1249652), _1249654))], (10321 ^ _779999) ^ [_957590, _957592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957590), _957592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957590), _957592))), -(_957590 = _957592)], (38252 ^ _779999) ^ [_1510954, _1510956, _1510958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1510954, _1510956)), _1510958)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1510956), hAPP(c_Relation_ORange(_1510954, _1510956), _1510958))))], (30872 ^ _779999) ^ [_1358719, _1358721, _1358723, _1358725] : [_1358719 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358721), _1358723)), _1358725), -(_1358721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358719, _1358721) = _1358725), 30879 ^ _779999 : [(30882 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1358725), _1358721))], (30880 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358721)))]], 30887 ^ _779999 : [(30890 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1358721), _1358725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1358725), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30888 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358721))]]], (4528 ^ _779999) ^ [_848817, _848819] : [_848819 = _848817, -(c_List_Odrop(_848819) = c_List_Odrop(_848817))], (5258 ^ _779999) ^ [_860484, _860486, _860488, _860490, _860492, _860494] : [-(c_Relation_Orel__comp(_860494, _860490, _860486) = c_Relation_Orel__comp(_860492, _860488, _860484)), _860494 = _860492, _860490 = _860488, _860486 = _860484], (14866 ^ _779999) ^ [_1046828, _1046830] : [-(_1046828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046828), _1046830) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046828), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1046830)))], (38357 ^ _779999) ^ [_1513709, _1513711, _1513713, _1513715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1513709, _1513711), tc_HOL_Obool)), _1513713), _1513715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513709, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1513709, _1513711), _1513713)), hAPP(c_Relation_ODomain(_1513709, _1513711), _1513715))))], (3156 ^ _779999) ^ [_827075, _827077] : [_827077 = _827075, -(c_Nitpick_Ofrac(_827077) = c_Nitpick_Ofrac(_827075))], (47908 ^ _779999) ^ [_1744457, _1744459, _1744461] : [class_Orderings_Olinorder(_1744457), c_List_Olinorder__class_Osorted(_1744457, _1744459), -(c_List_Olinorder__class_Osorted(_1744457, c_List_Oremove1(_1744457, _1744461, _1744459)))], (27552 ^ _779999) ^ [_1298195, _1298197, _1298199, _1298201] : [class_Rings_Olinordered__semidom(_1298195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298195), _1298197), _1298199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298195), c_Groups_Ozero__class_Ozero(_1298195)), _1298197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1298201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298195), hAPP(hAPP(c_Power_Opower__class_Opower(_1298195), _1298197), _1298201)), hAPP(hAPP(c_Power_Opower__class_Opower(_1298195), _1298199), _1298201))))], (30489 ^ _779999) ^ [_1351411, _1351413, _1351415, _1351417] : [class_Divides_Osemiring__div(_1351411), -(c_Divides_Odiv__class_Omod(_1351411, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351411), _1351413), _1351415), _1351417) = c_Divides_Odiv__class_Omod(_1351411, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351411), c_Divides_Odiv__class_Omod(_1351411, _1351413, _1351417)), _1351415), _1351417))], (2912 ^ _779999) ^ [_823323, _823325] : [_823325 = _823323, -(c_Com_Ocom_Ocom__size(_823325) = c_Com_Ocom_Ocom__size(_823323))], (50190 ^ _779999) ^ [_1793322, _1793324] : [hBOOL(hAPP(hAPP(c_List_Omember(_1793322), c_List_Olist_ONil(_1793322)), _1793324))], (6333 ^ _779999) ^ [_881785, _881787, _881789, _881791] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881785, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881785, tc_HOL_Obool)), _881787), _881789)), _881791) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881785, tc_HOL_Obool)), _881787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881785, tc_HOL_Obool)), _881789), _881791)))], (41757 ^ _779999) ^ [_1597035, _1597037, _1597039, _1597041, _1597043, _1597045] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597035, tc_fun(_1597037, tc_HOL_Obool)), _1597039), _1597041), _1597043)), hBOOL(hAPP(hAPP(c_member(_1597035), _1597045), _1597039)), -(hBOOL(hAPP(hAPP(_1597041, _1597045), _1597043)))], (51946 ^ _779999) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (23899 ^ _779999) ^ [_1226291] : [class_Orderings_Oord(_1226291), -(c_Orderings_Oord__class_Omin(_1226291) = c_Orderings_Oord_Omin(_1226291, c_Orderings_Oord__class_Oless__eq(_1226291)))], (23893 ^ _779999) ^ [_1226190] : [class_Orderings_Olinorder(_1226190), -(c_Orderings_Oord_Omax(_1226190, hAPP(c_COMBC(_1226190, _1226190, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1226190))) = c_Orderings_Oord__class_Omin(_1226190))], (46580 ^ _779999) ^ [_1714305, _1714307, _1714309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1714305), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714307), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1714307)), _1714309)))), -(hBOOL(hAPP(hAPP(c_member(_1714307), hAPP(c_Random_Opick(_1714307, _1714309), _1714305)), hAPP(c_List_Oset(_1714307), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714307), _1714307), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1714307)), _1714309)))))], (21032 ^ _779999) ^ [_1162174] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162174)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162174)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1162174)))], (38213 ^ _779999) ^ [_1510037, _1510039, _1510041, _1510043] : [38215 ^ _779999 : [(38218 ^ _779999) ^ [] : [c_Wellfounded_Owf(_1510039, hAPP(_1510041, 38214 ^ [_1510037, _1510039, _1510041, _1510043]))], (38216 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1510037, 38214 ^ [_1510037, _1510039, _1510041, _1510043])))]], -(c_Wellfounded_Owf(tc_prod(_1510043, _1510039), c_Recdef_Osame__fst(_1510043, _1510039, _1510037, _1510041)))], (5272 ^ _779999) ^ [_860705, _860707, _860709, _860711] : [-(c_Relation_Oinv__image(_860711, _860707) = c_Relation_Oinv__image(_860709, _860705)), _860711 = _860709, _860707 = _860705], (33233 ^ _779999) ^ [_1402287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1402287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1402287))))], (774 ^ _779999) ^ [_791846, _791848, _791850, _791852, _791854, _791856, _791858, _791860, _791862, _791864] : [-(c_List_Olist__all2(_791862, _791858, _791854, _791850, _791846)), c_List_Olist__all2(_791864, _791860, _791856, _791852, _791848), _791864 = _791862, _791860 = _791858, _791856 = _791854, _791852 = _791850, _791848 = _791846], (8126 ^ _779999) ^ [_917462, _917464, _917466, _917468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917462, tc_HOL_Obool)), _917464), _917466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917462, tc_HOL_Obool)), _917466), _917468)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917462, tc_HOL_Obool)), _917466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917462, tc_HOL_Obool)), _917468), _917464)) = _917464)], (16579 ^ _779999) ^ [_1079594, _1079596, _1079598] : [class_Rings_Olinordered__semidom(_1079594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079594), c_Groups_Oone__class_Oone(_1079594)), _1079596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079594), c_Groups_Oone__class_Oone(_1079594)), _1079598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079594), c_Groups_Oone__class_Oone(_1079594)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079594), _1079596), _1079598))))], (35063 ^ _779999) ^ [_1434916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434916)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1434916) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (29088 ^ _779999) ^ [_1326325, _1326327, _1326329, _1326331] : [class_Fields_Ofield__inverse__zero(_1326325), -(_1326327 = c_Groups_Ozero__class_Ozero(_1326325)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326325), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326325), _1326329), _1326327)), _1326331) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326325), _1326329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326325), _1326331), _1326327))), _1326327))], (19771 ^ _779999) ^ [_1140538, _1140540, _1140542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140538)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1140540), _1140542)), 19778 ^ _779999 : [(19779 ^ _779999) ^ [_1140734] : [19781 ^ _779999 : [(19787 ^ _779999) ^ [] : [-(_1140734 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19783 ^ [_1140538, _1140540, _1140542, _1140734]), 19780 ^ [_1140538, _1140540, _1140542, _1140734]))], (19785 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19783 ^ [_1140538, _1140540, _1140542, _1140734]), _1140542)))], (19782 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19780 ^ [_1140538, _1140540, _1140542, _1140734]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1140538))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140734), _1140540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140734), _1140538)), _1140540)))]]], (16257 ^ _779999) ^ [_1073654, _1073656, _1073658, _1073660] : [class_Rings_Olinordered__ring__strict(_1073654), 16260 ^ _779999 : [(16275 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073654), _1073656), _1073658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073654), _1073660), _1073658)))), 16276 ^ _779999 : [(16283 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073658), c_Groups_Ozero__class_Ozero(_1073654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073660), _1073656))], (16277 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), c_Groups_Ozero__class_Ozero(_1073654)), _1073658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073656), _1073660))]]], (16261 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073654), _1073656), _1073658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073654), _1073660), _1073658))), 16266 ^ _779999 : [(16269 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073656), _1073660)))], (16267 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), c_Groups_Ozero__class_Ozero(_1073654)), _1073658)))]], 16270 ^ _779999 : [(16273 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073660), _1073656)))], (16271 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073654), _1073658), c_Groups_Ozero__class_Ozero(_1073654))))]]]]], (22182 ^ _779999) ^ [_1190301, _1190303, _1190305, _1190307] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1190301), _1190303)), 22185 ^ _779999 : [(22186 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1190305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1190301, tc_fun(_1190305, tc_HOL_Obool)), _1190303), _1190307))), 22189 ^ _779999 : [(22190 ^ _779999) ^ [_1190485] : [hBOOL(hAPP(hAPP(c_member(_1190301), _1190485), _1190303)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1190305), hAPP(_1190307, _1190485))))]]], (22196 ^ _779999) ^ [] : [22198 ^ _779999 : [(22201 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1190305), hAPP(_1190307, 22197 ^ [_1190301, _1190303, _1190305, _1190307])))], (22199 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1190301), 22197 ^ [_1190301, _1190303, _1190305, _1190307]), _1190303)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1190305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1190301, tc_fun(_1190305, tc_HOL_Obool)), _1190303), _1190307))))]]], (51716 ^ _779999) ^ [_1826880, _1826882, _1826884, _1826886] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1826880, _1826882, _1826884), c_Product__Type_Ocurry(_1826880, _1826882, _1826884, _1826886)) = _1826886)], (43913 ^ _779999) ^ [_1654444, _1654446, _1654448, _1654450] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654444), tc_List_Olist(_1654444))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654444), tc_List_Olist(_1654444)), _1654446), _1654448)), c_List_Olistrel(_1654444, _1654450)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654444)), _1654446) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654444)), _1654448), 43919 ^ _779999 : [(43922 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1654444, _1654444, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1654444, tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_fun(_1654444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654444, tc_fun(tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_fun(_1654444, tc_HOL_Obool)), _1654444), c_COMBC(_1654444, tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654444, tc_prod(_1654444, _1654444)), tc_fun(_1654444, tc_fun(tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_HOL_Obool)), _1654444), hAPP(c_COMBB(tc_prod(_1654444, _1654444), tc_fun(tc_fun(tc_prod(_1654444, _1654444), tc_HOL_Obool), tc_HOL_Obool), _1654444), c_member(tc_prod(_1654444, _1654444)))), c_Product__Type_OPair(_1654444, _1654444)))), _1654450)), 43918 ^ [_1654444, _1654446, _1654448, _1654450]))], (43920 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654444, _1654444)), 43918 ^ [_1654444, _1654446, _1654448, _1654450]), hAPP(c_List_Oset(tc_prod(_1654444, _1654444)), hAPP(hAPP(c_List_Ozip(_1654444, _1654444), _1654446), _1654448)))))]]], (38211 ^ _779999) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (47348 ^ _779999) ^ [_1731069, _1731071, _1731073] : [-(c_List_Oconcat(_1731069, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1731069)), _1731071), _1731073)) = hAPP(hAPP(c_List_Oappend(_1731069), c_List_Oconcat(_1731069, _1731071)), c_List_Oconcat(_1731069, _1731073)))], (7358 ^ _779999) ^ [_902128, _902130, _902132, _902134, _902136] : [class_Orderings_Oorder(_902128), class_Orderings_Oorder(_902130), c_Orderings_Oorder__class_Omono(_902130, _902128, _902132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902130), _902134), _902136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902128), hAPP(_902132, _902134)), hAPP(_902132, _902136))))], (40261 ^ _779999) ^ [_1562106, _1562108, _1562110, _1562112] : [-(c_Transitive__Closure_Otrancl(_1562106, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1562106, _1562106)), hAPP(hAPP(c_Product__Type_OPair(_1562106, _1562106), _1562108), _1562110)), _1562112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562106, _1562106), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1562106, _1562112)), hAPP(c_Set_OCollect(tc_prod(_1562106, _1562106)), hAPP(c_Product__Type_Oprod_Oprod__case(_1562106, _1562106, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1562106, tc_fun(_1562106, tc_HOL_Obool), tc_fun(_1562106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1562106, tc_HOL_Obool), tc_fun(_1562106, tc_HOL_Obool)), _1562106), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562106)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562106), c_fconj), hAPP(hAPP(c_COMBC(_1562106, tc_fun(tc_prod(_1562106, _1562106), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1562106, _1562106), tc_fun(tc_fun(tc_prod(_1562106, _1562106), tc_HOL_Obool), tc_HOL_Obool), _1562106), c_member(tc_prod(_1562106, _1562106))), hAPP(hAPP(c_COMBC(_1562106, _1562106, tc_prod(_1562106, _1562106)), c_Product__Type_OPair(_1562106, _1562106)), _1562108))), c_Transitive__Closure_Ortrancl(_1562106, _1562112))))), hAPP(hAPP(c_COMBC(_1562106, tc_fun(tc_prod(_1562106, _1562106), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1562106, _1562106), tc_fun(tc_fun(tc_prod(_1562106, _1562106), tc_HOL_Obool), tc_HOL_Obool), _1562106), c_member(tc_prod(_1562106, _1562106))), hAPP(c_Product__Type_OPair(_1562106, _1562106), _1562110))), c_Transitive__Closure_Ortrancl(_1562106, _1562112)))))))], (1584 ^ _779999) ^ [_802907, _802909] : [-(class_Rings_Olinordered__comm__semiring__strict(_802907)), _802909 = _802907, class_Rings_Olinordered__comm__semiring__strict(_802909)], (38299 ^ _779999) ^ [_1512524, _1512526, _1512528, _1512530] : [hBOOL(hAPP(c_Predicate_ORangeP(_1512524, _1512526, _1512528), _1512530)), -(hBOOL(hAPP(hAPP(_1512528, 38302 ^ [_1512524, _1512526, _1512528, _1512530]), _1512530)))], (15843 ^ _779999) ^ [_1065595, _1065597, _1065599] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1065595), _1065597)), _1065599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065595), _1065599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065597), _1065599)))], (49548 ^ _779999) ^ [_1779495, _1779497, _1779499, _1779501] : [-(c_List_Olist__all(_1779495, _1779497, hAPP(hAPP(c_List_Oappend(_1779495), _1779499), _1779501))), c_List_Olist__all(_1779495, _1779497, _1779499), c_List_Olist__all(_1779495, _1779497, _1779501)], (12753 ^ _779999) ^ [_1005890, _1005892, _1005894] : [class_Lattices_Olattice(_1005890), hAPP(_1005892, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005890), 12758 ^ [_1005890, _1005892, _1005894]), 12759 ^ [_1005890, _1005892, _1005894])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005890), hAPP(_1005892, 12758 ^ [_1005890, _1005892, _1005894])), hAPP(_1005892, 12759 ^ [_1005890, _1005892, _1005894])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005890), _1005894)), -(_1005894 = c_Orderings_Obot__class_Obot(tc_fun(_1005890, tc_HOL_Obool))), -(hAPP(_1005892, c_Big__Operators_Olattice__class_OInf__fin(_1005890, _1005894)) = c_Big__Operators_Olattice__class_OInf__fin(_1005890, hAPP(c_Set_Oimage(_1005890, _1005890, _1005892), _1005894)))], (1434 ^ _779999) ^ [_801032, _801034] : [-(class_Lattices_Obounded__lattice__top(_801032)), _801034 = _801032, class_Lattices_Obounded__lattice__top(_801034)], (48202 ^ _779999) ^ [_1749703, _1749705, _1749707] : [class_Orderings_Olinorder(_1749703), hBOOL(hAPP(hAPP(c_member(_1749703), _1749705), hAPP(c_List_Oset(_1749703), _1749707))), c_List_Olinorder__class_Osorted(_1749703, _1749707), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1749703, _1749703, c_COMBI(_1749703)), _1749705), c_List_Oremove1(_1749703, _1749705, _1749707)) = _1749707)], (6999 ^ _779999) ^ [_894998, _895000, _895002, _895004] : [_894998 = _895000, 7002 ^ _779999 : [(7009 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895002), _895000), _895004)), -(hBOOL(hAPP(hAPP(c_member(_895002), _894998), _895004)))], (7003 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895002), _894998), _895004)), -(hBOOL(hAPP(hAPP(c_member(_895002), _895000), _895004)))]]], (23949 ^ _779999) ^ [_1227346, _1227348, _1227350] : [class_Orderings_Olinorder(_1227346), hAPP(_1227348, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1227346), 23954 ^ [_1227346, _1227348, _1227350]), 23955 ^ [_1227346, _1227348, _1227350])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1227346), hAPP(_1227348, 23954 ^ [_1227346, _1227348, _1227350])), hAPP(_1227348, 23955 ^ [_1227346, _1227348, _1227350])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1227346), _1227350)), -(_1227350 = c_Orderings_Obot__class_Obot(tc_fun(_1227346, tc_HOL_Obool))), -(hAPP(_1227348, c_Big__Operators_Olinorder__class_OMin(_1227346, _1227350)) = c_Big__Operators_Olinorder__class_OMin(_1227346, hAPP(c_Set_Oimage(_1227346, _1227346, _1227348), _1227350)))], (11042 ^ _779999) ^ [_971035, _971037, _971039, _971041] : [class_Lattices_Olattice(_971035), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971035), _971037), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971035), _971039), _971041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971035), _971039), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971035), _971037), _971041)))], (32833 ^ _779999) ^ [_1395883, _1395885] : [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), _1395883))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1395885), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1395883))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1395885), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395883))), 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), _1395885))), c_COMBI(tc_Int_Oint))))], (51970 ^ _779999) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (37986 ^ _779999) ^ [_1504933, _1504935, _1504937] : [c_Wellfounded_Owf(_1504933, _1504935), -(c_Wellfounded_Owf(_1504933, c_Wellfounded_Omlex__prod(_1504933, _1504937, _1504935)))], (26799 ^ _779999) ^ [_1282836, _1282838] : [class_Groups_Oordered__ab__group__add(_1282836), -(hAPP(c_Set_Oimage(_1282836, _1282836, c_Groups_Ouminus__class_Ouminus(_1282836)), hAPP(c_SetInterval_Oord__class_OatMost(_1282836), _1282838)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1282836), hAPP(c_Groups_Ouminus__class_Ouminus(_1282836), _1282838)))], (43136 ^ _779999) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4428 ^ _779999) ^ [_847279, _847281, _847283, _847285, _847287, _847289] : [-(c_List_Osplice(_847289, _847285, _847281) = c_List_Osplice(_847287, _847283, _847279)), _847289 = _847287, _847285 = _847283, _847281 = _847279], (17635 ^ _779999) ^ [_1100440, _1100442, _1100444, _1100446, _1100448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100440), _1100442)), 17638 ^ _779999 : [(17645 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100446), 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), _1100442), _1100440)), _1100444)), _1100448))), -(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), _1100440), _1100444)), _1100446)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100442), _1100444)), _1100448))))], (17639 ^ _779999) ^ [] : [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), _1100440), _1100444)), _1100446)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100442), _1100444)), _1100448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100446), 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), _1100442), _1100440)), _1100444)), _1100448))))]]], (18271 ^ _779999) ^ [_1112590, _1112592, _1112594] : [class_Orderings_Oorder(_1112590), 18274 ^ _779999 : [(18281 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112590), _1112592), _1112594))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1112590, _1112592), _1112594) = c_Orderings_Obot__class_Obot(tc_fun(_1112590, tc_HOL_Obool)))], (18275 ^ _779999) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1112590, _1112592), _1112594) = c_Orderings_Obot__class_Obot(tc_fun(_1112590, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112590), _1112592), _1112594))]]], (26550 ^ _779999) ^ [_1277363, _1277365, _1277367] : [class_Groups_Ocomm__monoid__add(_1277363), class_Groups_Ocomm__monoid__mult(_1277363), c_Nat__Transfer_Onat__set(_1277365), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1277363), _1277367), _1277365) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1277363), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1277363, tc_Nat_Onat), _1277367), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1277365)))], (21648 ^ _779999) ^ [_1174411] : [-(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)), _1174411)))))], (34185 ^ _779999) ^ [_1419287, _1419289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1419287)), c_Int_OBit0(_1419289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419287), _1419289)))], (1794 ^ _779999) ^ [_805532, _805534] : [-(class_Nat_Osemiring__char__0(_805532)), _805534 = _805532, class_Nat_Osemiring__char__0(_805534)], (46324 ^ _779999) ^ [_1708681, _1708683, _1708685, _1708687, _1708689] : [-(hAPP(hAPP(c_List_Omap(_1708681, _1708683), _1708685), hAPP(hAPP(c_List_Oappend(_1708681), _1708687), _1708689)) = hAPP(hAPP(c_List_Oappend(_1708683), hAPP(hAPP(c_List_Omap(_1708681, _1708683), _1708685), _1708687)), hAPP(hAPP(c_List_Omap(_1708681, _1708683), _1708685), _1708689)))], (26220 ^ _779999) ^ [_1271537, _1271539] : [class_Groups_Oordered__ab__group__add(_1271537), 26223 ^ _779999 : [(26230 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271537), _1271539), c_Groups_Ozero__class_Ozero(_1271537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271537), c_Groups_Ozero__class_Ozero(_1271537)), hAPP(c_Groups_Ouminus__class_Ouminus(_1271537), _1271539))))], (26224 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271537), c_Groups_Ozero__class_Ozero(_1271537)), hAPP(c_Groups_Ouminus__class_Ouminus(_1271537), _1271539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271537), _1271539), c_Groups_Ozero__class_Ozero(_1271537))))]]], (1474 ^ _779999) ^ [_801532, _801534] : [-(class_Lattices_Odistrib__lattice(_801532)), _801534 = _801532, class_Lattices_Odistrib__lattice(_801534)], (5508 ^ _779999) ^ [_864329, _864331, _864333, _864335] : [-(c_Product__Type_OPair(_864335, _864331) = c_Product__Type_OPair(_864333, _864329)), _864335 = _864333, _864331 = _864329], (17755 ^ _779999) ^ [_1102834, _1102836, _1102838, _1102840, _1102842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102834), _1102836)), -(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), _1102836), _1102838)), _1102840)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102834), _1102838)), _1102842)) = 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), _1102836), _1102834)), _1102838)), _1102840)), _1102842))], (19873 ^ _779999) ^ [_1142422, _1142424, _1142426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1142422, 19874 ^ [_1142422, _1142424, _1142426])), hAPP(_1142424, 19874 ^ [_1142422, _1142424, _1142426]))), -(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), _1142424), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1142426))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1142422), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1142426))) = 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)), _1142424)), _1142422)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1142426)))], (52252 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (23421 ^ _779999) ^ [_1217000, _1217002, _1217004] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217000), _1217002)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217004), _1217002)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1217000), _1217004)), _1217002))], (42135 ^ _779999) ^ [_1608160, _1608162, _1608164, _1608166, _1608168] : [-(_1608160 = c_Orderings_Obot__class_Obot(tc_fun(_1608162, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608162, tc_fun(_1608164, tc_HOL_Obool)), _1608160), hAPP(hAPP(c_COMBC(_1608162, tc_fun(_1608164, tc_HOL_Obool), tc_fun(_1608164, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608164, tc_HOL_Obool), tc_fun(tc_fun(_1608164, tc_HOL_Obool), tc_fun(_1608164, tc_HOL_Obool)), _1608162), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608164, tc_HOL_Obool))), _1608166)), _1608168)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608164, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608162, tc_fun(_1608164, tc_HOL_Obool)), _1608160), _1608166)), _1608168))], (33227 ^ _779999) ^ [_1402204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1402204))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1402204)))], (36807 ^ _779999) ^ [_1474613, _1474615, _1474617, _1474619, _1474621] : [c_Equiv__Relations_Oequiv(_1474613, _1474615, _1474617), 36810 ^ _779999 : [(36821 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474613, _1474613)), hAPP(hAPP(c_Product__Type_OPair(_1474613, _1474613), _1474619), _1474621)), _1474617))), hAPP(c_Relation_OImage(_1474613, _1474613, _1474617), hAPP(hAPP(c_Set_Oinsert(_1474613), _1474619), c_Orderings_Obot__class_Obot(tc_fun(_1474613, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1474613, _1474613, _1474617), hAPP(hAPP(c_Set_Oinsert(_1474613), _1474621), c_Orderings_Obot__class_Obot(tc_fun(_1474613, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1474613), _1474619), _1474615)), hBOOL(hAPP(hAPP(c_member(_1474613), _1474621), _1474615))], (36811 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1474613, _1474613)), hAPP(hAPP(c_Product__Type_OPair(_1474613, _1474613), _1474619), _1474621)), _1474617)), 36814 ^ _779999 : [(36819 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474613), _1474621), _1474615)))], (36817 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474613), _1474619), _1474615)))], (36815 ^ _779999) ^ [] : [-(hAPP(c_Relation_OImage(_1474613, _1474613, _1474617), hAPP(hAPP(c_Set_Oinsert(_1474613), _1474619), c_Orderings_Obot__class_Obot(tc_fun(_1474613, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1474613, _1474613, _1474617), hAPP(hAPP(c_Set_Oinsert(_1474613), _1474621), c_Orderings_Obot__class_Obot(tc_fun(_1474613, tc_HOL_Obool)))))]]]]], (27828 ^ _779999) ^ [_1303091, _1303093, _1303095, _1303097] : [class_Rings_Olinordered__semidom(_1303091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303091), c_Groups_Oone__class_Oone(_1303091)), _1303093)), 27835 ^ _779999 : [(27842 ^ _779999) ^ [] : [_1303095 = _1303097, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303091), _1303093), _1303095) = hAPP(hAPP(c_Power_Opower__class_Opower(_1303091), _1303093), _1303097))], (27836 ^ _779999) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1303091), _1303093), _1303095) = hAPP(hAPP(c_Power_Opower__class_Opower(_1303091), _1303093), _1303097), -(_1303095 = _1303097)]]], (37628 ^ _779999) ^ [_1494918, _1494920, _1494922, _1494924] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1494918, _1494920, _1494922, c_Code__Numeral_OSuc__code__numeral(_1494924)) = hAPP(_1494922, _1494924))], (30902 ^ _779999) ^ [_1359184, _1359186, _1359188, _1359190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1359186), _1359188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1359188), 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), _1359186), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359190, _1359184))), _1359188)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15141 ^ _779999) ^ [_1051959, _1051961, _1051963, _1051965] : [hBOOL(hAPP(hAPP(_1051963, _1051965), _1051961)), -(hBOOL(hAPP(hAPP(c_member(_1051959), _1051961), c_SetInterval_Oord_OgreaterThan(_1051959, _1051963, _1051965))))], (45055 ^ _779999) ^ [_1680570, _1680572, _1680574] : [class_Groups_Omonoid__add(_1680570), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1680570), hAPP(hAPP(c_List_Oappend(_1680570), _1680572), _1680574)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1680570), hAPP(c_List_Omonoid__add__class_Olistsum(_1680570), _1680572)), hAPP(c_List_Omonoid__add__class_Olistsum(_1680570), _1680574)))], (27510 ^ _779999) ^ [_1297482, _1297484] : [_1297482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297484), _1297482) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20306 ^ _779999) ^ [_1149532, _1149534] : [-(hBOOL(hAPP(_1149532, hAPP(c_Int_Onat, _1149534)))), 20310 ^ _779999 : [(20313 ^ _779999) ^ [] : [hBOOL(hAPP(_1149532, 20309 ^ [_1149532, _1149534]))], (20311 ^ _779999) ^ [] : [-(_1149534 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20309 ^ [_1149532, _1149534]))]], 20314 ^ _779999 : [(20317 ^ _779999) ^ [] : [hBOOL(hAPP(_1149532, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20315 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149534), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (43745 ^ _779999) ^ [_1649746, _1649748, _1649750] : [-(hAPP(c_List_Oset(_1649746), c_List_Osublist(_1649746, _1649748, _1649750)) = hAPP(c_Set_OCollect(_1649746), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1649746), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1649746, 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)), _1649746), 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)), _1649746), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1649746, tc_fun(tc_Nat_Onat, _1649746), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649746, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1649746), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1649746), c_COMBB(_1649746, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1649746), _1649748))))), 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(_1649746)), _1649748)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1649750))))))], (47496 ^ _779999) ^ [_1735056, _1735058, _1735060] : [hBOOL(hAPP(c_List_Odistinct(_1735056), _1735058)), -(hBOOL(hAPP(c_List_Odistinct(_1735056), hAPP(c_List_Ofilter(_1735056, _1735060), _1735058))))], (19441 ^ _779999) ^ [_1134494, _1134496] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134494) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134496), -(_1134494 = _1134496)], (26028 ^ _779999) ^ [_1268149, _1268151, _1268153, _1268155] : [hAPP(c_Com_Ocom_OBODY, _1268149) = c_Com_Ocom_OCond(_1268151, _1268153, _1268155)], (43389 ^ _779999) ^ [_1639501, _1639503, _1639505, _1639507] : [-(c_List_Olist_Olist__size(_1639501, _1639503, hAPP(hAPP(c_List_Olist_OCons(_1639501), _1639505), _1639507)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1639503, _1639505)), c_List_Olist_Olist__size(_1639501, _1639503, _1639507))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30742 ^ _779999) ^ [_1356214] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356214, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1356214)], (5490 ^ _779999) ^ [_864028, _864030, _864032, _864034, _864036, _864038, _864040, _864042] : [-(c_Fun_Ocomp(_864042, _864038, _864034, _864030) = c_Fun_Ocomp(_864040, _864036, _864032, _864028)), _864042 = _864040, _864038 = _864036, _864034 = _864032, _864030 = _864028], (12379 ^ _779999) ^ [_999161, _999163] : [class_Lattices_Olattice(_999161), -(c_Big__Operators_Olattice__class_OSup__fin(_999161, hAPP(hAPP(c_Set_Oinsert(_999161), _999163), c_Orderings_Obot__class_Obot(tc_fun(_999161, tc_HOL_Obool)))) = _999163)], (51551 ^ _779999) ^ [_1823558] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823558), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1823558 = hAPP(c_Code__Numeral_Onat__of, 51554 ^ [_1823558]))], (7418 ^ _779999) ^ [_903507, _903509, _903511] : [class_Lattices_Obounded__lattice__bot(_903507), 7421 ^ _779999 : [(7430 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903507), _903509), _903511) = c_Orderings_Obot__class_Obot(_903507)), _903509 = c_Orderings_Obot__class_Obot(_903507), _903511 = c_Orderings_Obot__class_Obot(_903507)], (7422 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903507), _903509), _903511) = c_Orderings_Obot__class_Obot(_903507), 7425 ^ _779999 : [(7428 ^ _779999) ^ [] : [-(_903511 = c_Orderings_Obot__class_Obot(_903507))], (7426 ^ _779999) ^ [] : [-(_903509 = c_Orderings_Obot__class_Obot(_903507))]]]]], (52090 ^ _779999) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (19447 ^ _779999) ^ [_1134600, _1134602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1134600), _1134602)), -(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)), _1134600)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1134602))))], (44156 ^ _779999) ^ [_1661006, _1661008, _1661010, _1661012, _1661014, _1661016] : [-(_1661006 = _1661008), -(hAPP(hAPP(c_List_Olist__update(_1661010, hAPP(hAPP(c_List_Olist__update(_1661010, _1661012), _1661006), _1661014)), _1661008), _1661016) = hAPP(hAPP(c_List_Olist__update(_1661010, hAPP(hAPP(c_List_Olist__update(_1661010, _1661012), _1661008), _1661016)), _1661006), _1661014))], (23135 ^ _779999) ^ [_1211870, _1211872] : [-(hAPP(c_Set_Ovimage(_1211870, _1211870, c_COMBI(_1211870)), _1211872) = _1211872)], (52150 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (31226 ^ _779999) ^ [_1365031, _1365033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1365031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365033, _1365031)), _1365031)))], (37574 ^ _779999) ^ [_1493375, _1493377, _1493379] : [class_Rings_Oring__1(_1493375), -(hAPP(c_Int_Oring__1__class_Oof__int(_1493375), 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), _1493377), _1493379)), 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(_1493375), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1493375), _1493377)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1493375), _1493379)))], (35093 ^ _779999) ^ [_1435395, _1435397] : [-(c_Fun_Oinj__on(tc_fun(_1435395, _1435397), tc_fun(tc_prod(_1435395, _1435397), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1435395, _1435397), tc_HOL_Obool), tc_fun(tc_prod(_1435395, _1435397), tc_HOL_Obool), tc_fun(_1435395, _1435397)), c_Set_OCollect(tc_prod(_1435395, _1435397))), hAPP(hAPP(c_COMBB(tc_fun(_1435395, tc_fun(_1435397, tc_HOL_Obool)), tc_fun(tc_prod(_1435395, _1435397), tc_HOL_Obool), tc_fun(_1435395, _1435397)), c_Product__Type_Oprod_Oprod__case(_1435395, _1435397, tc_HOL_Obool)), hAPP(c_COMBB(_1435397, tc_fun(_1435397, tc_HOL_Obool), _1435395), hAPP(c_COMBC(_1435397, _1435397, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1435395, _1435397), tc_HOL_Obool))))], (19353 ^ _779999) ^ [_1132880, _1132882, _1132884, _1132886, _1132888, _1132890] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132880), _1132882)), _1132884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132886), _1132888)), _1132890), 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), _1132886), _1132888)), _1132890)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132884), _1132880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132886), _1132880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132888), _1132882)))], (41069 ^ _779999) ^ [_1582189] : [-(c_Relation_Osingle__valued(_1582189, _1582189, c_Relation_OId(_1582189)))], (1714 ^ _779999) ^ [_804532, _804534] : [-(class_Groups_Oab__semigroup__add(_804532)), _804534 = _804532, class_Groups_Oab__semigroup__add(_804534)], (39032 ^ _779999) ^ [_1532994, _1532996] : [c_Wellfounded_Owf(_1532994, _1532996), -(c_Wellfounded_OwfP(_1532994, c_FunDef_Oin__rel(_1532994, _1532994, _1532996)))], (19989 ^ _779999) ^ [_1144533] : [19991 ^ _779999 : [(19994 ^ _779999) ^ [] : [hBOOL(hAPP(_1144533, hAPP(c_Int_Onat, 19990 ^ [_1144533])))], (19992 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19990 ^ [_1144533])))]], 19995 ^ _779999 : [(19996 ^ _779999) ^ [_1144666] : [-(hBOOL(hAPP(_1144533, _1144666)))]]], (13495 ^ _779999) ^ [_1020427, _1020429, _1020431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020427), _1020429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020429), _1020431))))], (51466 ^ _779999) ^ [_1821256, _1821258, _1821260, _1821262, _1821264] : [c_Fun_Oinj__on(_1821256, _1821258, _1821260, c_Orderings_Otop__class_Otop(tc_fun(_1821256, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1821258, _1821262, _1821256, hAPP(c_Fun_Ocomp(_1821256, _1821262, _1821258, _1821264), c_Hilbert__Choice_Oinv__into(_1821256, _1821258, c_Orderings_Otop__class_Otop(tc_fun(_1821256, tc_HOL_Obool)), _1821260))), _1821260) = _1821264)], (48705 ^ _779999) ^ [_1760379] : [-(c_List_Oembed__list(_1760379) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1760379))], (49806 ^ _779999) ^ [_1785070, _1785072, _1785074, _1785076, _1785078] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1785070, _1785072, _1785074), _1785076), _1785078)), -(hBOOL(hAPP(hAPP(_1785074, _1785078), _1785076)))], (22818 ^ _779999) ^ [_1203502, _1203504, _1203506, _1203508] : [_1203502 = c_Orderings_Obot__class_Obot(tc_fun(_1203504, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203504, tc_fun(_1203506, tc_HOL_Obool)), _1203502), hAPP(c_COMBK(tc_fun(_1203506, tc_HOL_Obool), _1203504), _1203508)) = c_Orderings_Obot__class_Obot(tc_fun(_1203506, tc_HOL_Obool)))], (49630 ^ _779999) ^ [_1781099, _1781101] : [c_List_Olist__ex1(_1781099, _1781101, c_List_Olist_ONil(_1781099))], (27584 ^ _779999) ^ [_1298808, _1298810, _1298812] : [class_Rings_Olinordered__semidom(_1298808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298808), c_Groups_Oone__class_Oone(_1298808)), _1298810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1298812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298808), c_Groups_Oone__class_Oone(_1298808)), hAPP(hAPP(c_Power_Opower__class_Opower(_1298808), _1298810), _1298812))))], (9614 ^ _779999) ^ [_943419, _943421, _943423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943419, tc_HOL_Obool)), _943421), _943423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943419, tc_HOL_Obool)), _943421), _943423)))], (37803 ^ _779999) ^ [_1500400, _1500402, _1500404, _1500406, _1500408, _1500410] : [c_Typedef_Otype__definition(_1500400, _1500402, _1500404, _1500406, _1500408), -(hAPP(_1500406, hAPP(_1500404, _1500410)) = _1500410)], (51892 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (6741 ^ _779999) ^ [_890305, _890307, _890309, _890311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890305, tc_HOL_Obool)), _890307), _890309)), hBOOL(hAPP(hAPP(c_member(_890305), _890311), _890307)), -(hBOOL(hAPP(hAPP(c_member(_890305), _890311), _890309)))], (38049 ^ _779999) ^ [_1506091, _1506093, _1506095] : [c_Wellfounded_Owf(_1506091, _1506093), -(hBOOL(hAPP(hAPP(c_member(_1506091), _1506095), c_Wellfounded_Oacc(_1506091, _1506093))))], (51089 ^ _779999) ^ [_1813755, _1813757] : [-(c_Relation_Osym(_1813755, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1813755, _1813755), tc_HOL_Obool)), _1813757), hAPP(c_Relation_Oconverse(_1813755, _1813755), _1813757))))], (33321 ^ _779999) ^ [_1403692] : [-(c_Int_Osucc(_1403692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1403692), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19203 ^ _779999) ^ [_1130143, _1130145, _1130147, _1130149] : [class_Orderings_Olinorder(_1130143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130143), _1130145), _1130147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130143), _1130147), _1130149)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1130143, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1130143, _1130145, _1130147)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1130143, _1130147, _1130149)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1130143, _1130145, _1130149))], (45975 ^ _779999) ^ [_1701137, _1701139, _1701141] : [class_Orderings_Olinorder(_1701137), -(hBOOL(hAPP(hAPP(c_member(_1701137), _1701139), hAPP(c_List_Oset(_1701137), _1701141)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1701137, _1701137, c_COMBI(_1701137), _1701139, _1701141) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701137, _1701137, c_COMBI(_1701137)), _1701139), _1701141))], (7093 ^ _779999) ^ [_896582, _896584, _896586, _896588] : [-(hBOOL(hAPP(hAPP(c_member(_896582), _896584), _896586))), 7096 ^ _779999 : [(7103 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896582, tc_HOL_Obool)), _896586), _896588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896582, tc_HOL_Obool)), _896586), hAPP(hAPP(c_Set_Oinsert(_896582), _896584), _896588))))], (7097 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896582, tc_HOL_Obool)), _896586), hAPP(hAPP(c_Set_Oinsert(_896582), _896584), _896588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896582, tc_HOL_Obool)), _896586), _896588)))]]], (13810 ^ _779999) ^ [_1026384, _1026386, _1026388] : [class_Groups_Oordered__comm__monoid__add(_1026384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026384), _1026386), c_Groups_Ozero__class_Ozero(_1026384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026384), _1026388), c_Groups_Ozero__class_Ozero(_1026384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026384), _1026386), _1026388)), c_Groups_Ozero__class_Ozero(_1026384))))], (29510 ^ _779999) ^ [_1333892, _1333894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1333892), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333894), _1333892)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333892), _1333894) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4644 ^ _779999) ^ [_850597, _850599, _850601, _850603, _850605, _850607, _850609, _850611, _850613, _850615, _850617, _850619] : [-(c_New__Random__Sequence_Opos__union(_850619, _850615, _850611, _850607, _850603, _850599) = c_New__Random__Sequence_Opos__union(_850617, _850613, _850609, _850605, _850601, _850597)), _850619 = _850617, _850615 = _850613, _850611 = _850609, _850607 = _850605, _850603 = _850601, _850599 = _850597], (23589 ^ _779999) ^ [_1220700, _1220702] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220700)), _1220702) = 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), _1220700)), _1220702))], (36108 ^ _779999) ^ [_1459801, _1459803] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1459801, _1459803), c_Divides_Odivmod__nat(_1459801, _1459803))))], (51936 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (22559 ^ _779999) ^ [_1197570, _1197572] : [class_Orderings_Olinorder(_1197570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197570), _1197572)), -(_1197572 = c_Orderings_Obot__class_Obot(tc_fun(_1197570, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1197570), c_Big__Operators_Olinorder__class_OMin(_1197570, _1197572)), _1197572)))], (43235 ^ _779999) ^ [_1634429, _1634431, _1634433] : [hAPP(hAPP(c_List_Olist_OCons(_1634429), _1634431), _1634433) = _1634433], (35954 ^ _779999) ^ [_1457046, _1457048] : [-(_1457046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35957 ^ _779999 : [(35964 ^ _779999) ^ [] : [-(_1457048 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1457046, _1457048) = 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, _1457048))), hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_fdisj, hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457048)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457046))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1457048), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1457046), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1457046, _1457048)), 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), _1457048))))), c_Divides_Opdivmod(_1457046, _1457048)))))], (35958 ^ _779999) ^ [] : [_1457048 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1457046, _1457048) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457046))]]], (5518 ^ _779999) ^ [_864478, _864480, _864482, _864484, _864486, _864488] : [-(c_Product__Type_Oprod_Oprod__case(_864488, _864484, _864480) = c_Product__Type_Oprod_Oprod__case(_864486, _864482, _864478)), _864488 = _864486, _864484 = _864482, _864480 = _864478], (20192 ^ _779999) ^ [_1147776, _1147778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147778)), 20199 ^ _779999 : [(20206 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147776), _1147778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1147776)), hAPP(c_Int_Onat, _1147778))))], (20200 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1147776)), hAPP(c_Int_Onat, _1147778))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147776), _1147778)))]]], (25257 ^ _779999) ^ [_1254048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254048)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254048))], (5630 ^ _779999) ^ [_866178, _866180, _866182, _866184] : [-(tc_prod(_866184, _866180) = tc_prod(_866182, _866178)), _866184 = _866182, _866180 = _866178], (14754 ^ _779999) ^ [_1044987, _1044989, _1044991] : [_1044989 = _1044991, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044987), _1044989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044987), _1044991))], (18824 ^ _779999) ^ [_1123531, _1123533] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123531), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1123533) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1123531, _1123533))], (33595 ^ _779999) ^ [_1408138] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408138) = 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(_1408138)))))], (6343 ^ _779999) ^ [_882076, _882078, _882080, _882082, _882084, _882086] : [-(hAPP(c_Set_Oimage(_882076, _882078, _882080), hAPP(c_Set_Oimage(_882082, _882076, _882084), _882086)) = hAPP(c_Set_Oimage(_882082, _882078, hAPP(hAPP(c_COMBB(_882076, _882078, _882082), _882080), _882084)), _882086))], (47463 ^ _779999) ^ [_1734417, _1734419, _1734421] : [47465 ^ _779999 : [(47468 ^ _779999) ^ [] : [hBOOL(hAPP(_1734419, 47464 ^ [_1734417, _1734419, _1734421]))], (47466 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734417), 47464 ^ [_1734417, _1734419, _1734421]), hAPP(c_List_Oset(_1734417), _1734421))))]], -(hAPP(c_List_Ofilter(_1734417, _1734419), _1734421) = _1734421)], (10567 ^ _779999) ^ [_961855, _961857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961855), hAPP(c_Nat_OSuc, _961857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961855), _961857)))], (43347 ^ _779999) ^ [_1638228, _1638230, _1638232, _1638234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638228), tc_List_Olist(_1638228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638228), tc_List_Olist(_1638228)), _1638230), _1638232)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1638228), tc_List_Olist(_1638228)), c_List_Olistrel1(_1638228, _1638234)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638228), tc_List_Olist(_1638228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638228), tc_List_Olist(_1638228)), _1638230), _1638232)), c_List_Olistrel1(_1638228, hAPP(c_Relation_Oconverse(_1638228, _1638228), _1638234)))))], (50660 ^ _779999) ^ [_1804241, _1804243, _1804245] : [-(c_List_Olist__ex(_1804241, _1804245, _1804243)), 50661 ^ _779999 : [(50662 ^ _779999) ^ [_1804298] : [hBOOL(hAPP(hAPP(c_member(_1804241), _1804298), hAPP(c_List_Oset(_1804241), _1804243))), hBOOL(hAPP(_1804245, _1804298))]]], (19217 ^ _779999) ^ [_1130408, _1130410, _1130412] : [class_Orderings_Olinorder(_1130408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130408), _1130410), _1130412)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1130408, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1130408), _1130410), c_Orderings_Obot__class_Obot(tc_fun(_1130408, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1130408, _1130410, _1130412)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1130408, _1130410), _1130412))], (7978 ^ _779999) ^ [_914562, _914564, _914566] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914562, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914562, tc_HOL_Obool)), _914564), _914566)), _914566) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914562, tc_HOL_Obool)), _914564), _914566))], (35572 ^ _779999) ^ [_1449786, _1449788, _1449790, _1449792] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1449786, tc_fun(_1449788, tc_HOL_Obool))), _1449790), _1449792))], (14846 ^ _779999) ^ [_1046480] : [class_Rings_Olinordered__semidom(_1046480), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046480), c_Groups_Ozero__class_Ozero(_1046480)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046480), c_Groups_Oone__class_Oone(_1046480)), c_Groups_Oone__class_Oone(_1046480)))))], (10974 ^ _779999) ^ [_969653, _969655] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969653, tc_HOL_Obool)), _969655), _969655) = _969655)], (36483 ^ _779999) ^ [_1467095, _1467097, _1467099] : [-(hAPP(c_Product__Type_Ofst(_1467095, _1467097), _1467099) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1467095, _1467097, _1467095), c_COMBK(_1467095, _1467097)), _1467099))], (35641 ^ _779999) ^ [_1451321, _1451323, _1451325, _1451327, _1451329, _1451331] : [hAPP(hAPP(c_Product__Type_OPair(_1451321, _1451323), _1451325), _1451327) = hAPP(hAPP(c_Product__Type_OPair(_1451321, _1451323), _1451329), _1451331), 35644 ^ _779999 : [(35647 ^ _779999) ^ [] : [-(_1451327 = _1451331)], (35645 ^ _779999) ^ [] : [-(_1451325 = _1451329)]]], (31721 ^ _779999) ^ [_1374976, _1374978, _1374980] : [class_Int_Onumber(_1374976), 31724 ^ _779999 : [(31731 ^ _779999) ^ [] : [_1374980 = hAPP(c_Int_Onumber__class_Onumber__of(_1374976), _1374978), -(hAPP(c_Int_Onumber__class_Onumber__of(_1374976), _1374978) = _1374980)], (31725 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1374976), _1374978) = _1374980, -(_1374980 = hAPP(c_Int_Onumber__class_Onumber__of(_1374976), _1374978))]]], (41384 ^ _779999) ^ [_1589908, _1589910, _1589912, _1589914] : [class_Lattices_Osemilattice__inf(_1589908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589908), _1589910)), hBOOL(hAPP(hAPP(c_member(_1589908), _1589912), _1589910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1589908), hAPP(hAPP(c_Finite__Set_Ofold(_1589908, _1589908, c_Lattices_Osemilattice__inf__class_Oinf(_1589908)), _1589914), _1589910)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1589908), _1589912), _1589914))))], (8136 ^ _779999) ^ [_917683, _917685, _917687, _917689] : [c_Natural_Oevaln(_917683, _917685, _917687, _917689), -(c_Natural_Oevaln(_917683, _917685, hAPP(c_Nat_OSuc, _917687), _917689))], (18965 ^ _779999) ^ [_1126025, _1126027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1126025), _1126027)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126025), _1126027)))], (34811 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (9896 ^ _779999) ^ [_950200, _950202, _950204, _950206, _950208] : [-(c_Fun_Oinj__on(_950200, _950202, _950204, hAPP(hAPP(c_Set_Oinsert(_950200), _950206), _950208))), c_Fun_Oinj__on(_950200, _950202, _950204, _950208), -(hBOOL(hAPP(hAPP(c_member(_950202), hAPP(_950204, _950206)), hAPP(c_Set_Oimage(_950200, _950202, _950204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950200, tc_HOL_Obool)), _950208), hAPP(hAPP(c_Set_Oinsert(_950200), _950206), c_Orderings_Obot__class_Obot(tc_fun(_950200, tc_HOL_Obool))))))))], (24262 ^ _779999) ^ [_1234459, _1234461, _1234463, _1234465] : [class_Groups_Oordered__ab__group__add(_1234459), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234459), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234459), _1234461), _1234463)), _1234465) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234459), _1234461), _1234465)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234459), _1234463), _1234465)))], (18757 ^ _779999) ^ [_1122211, _1122213, _1122215, _1122217, _1122219] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1122211, _1122211, _1122213, _1122215, _1122217), _1122219)), -(hBOOL(hAPP(hAPP(c_member(_1122211), _1122215), _1122217))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1122211, _1122213, hAPP(hAPP(c_Set_Oinsert(_1122211), _1122215), _1122217)), _1122219)))], (22714 ^ _779999) ^ [_1201023, _1201025, _1201027, _1201029, _1201031, _1201033] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201023, tc_fun(_1201025, tc_HOL_Obool)), _1201027), hAPP(hAPP(c_COMBC(_1201023, tc_fun(_1201029, tc_fun(_1201025, tc_HOL_Obool)), tc_fun(_1201025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1201029, tc_HOL_Obool), tc_fun(tc_fun(_1201029, tc_fun(_1201025, tc_HOL_Obool)), tc_fun(_1201025, tc_HOL_Obool)), _1201023), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201029, tc_fun(_1201025, tc_HOL_Obool))), _1201031)), _1201033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201029, tc_fun(_1201025, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201023, tc_fun(_1201029, tc_HOL_Obool)), _1201027), _1201031)), _1201033))], (36354 ^ _779999) ^ [_1464584, _1464586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464586), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1464584, _1464586) = 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), _1464584), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464586)))))], (20026 ^ _779999) ^ [_1145107] : [hAPP(c_Int_Onat, _1145107) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145107), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45412 ^ _779999) ^ [_1688916, _1688918, _1688920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688916)), _1688918)), _1688920)), -(hAPP(hAPP(c_List_Odrop(_1688916), _1688920), _1688918) = c_List_Olist_ONil(_1688916))], (48410 ^ _779999) ^ [_1754227, _1754229, _1754231] : [_1754229 = _1754231, -(hAPP(c_List_Orev(_1754227), _1754229) = hAPP(c_List_Orev(_1754227), _1754231))], (45061 ^ _779999) ^ [_1680721, _1680723, _1680725] : [_1680721 = c_List_Olist_ONil(_1680723), -(c_List_Obutlast(_1680723, hAPP(hAPP(c_List_Oappend(_1680723), _1680725), _1680721)) = c_List_Obutlast(_1680723, _1680725))], (30615 ^ _779999) ^ [_1353998, _1354000, _1354002] : [-(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, _1353998, _1354000)), _1354002), _1354000) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1353998), _1354002), _1354000))], (2090 ^ _779999) ^ [_810416, _810418, _810420, _810422, _810424, _810426] : [-(c_Partial__Function_Oflat__lub(_810426, _810422, _810418) = c_Partial__Function_Oflat__lub(_810424, _810420, _810416)), _810426 = _810424, _810422 = _810420, _810418 = _810416], (332 ^ _779999) ^ [_785105, _785107] : [-(c_Nitpick_Ounknown(_785105)), _785107 = _785105, c_Nitpick_Ounknown(_785107)], (19473 ^ _779999) ^ [_1135025] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1135025) = 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)), _1135025)))], (49308 ^ _779999) ^ [_1774525, _1774527, _1774529] : [c_List_Olist__ex(_1774525, _1774527, _1774529), 49312 ^ _779999 : [(49315 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1774527, hAPP(hAPP(c_List_Onth(_1774525), _1774529), 49311 ^ [_1774525, _1774527, _1774529]))))], (49313 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49311 ^ [_1774525, _1774527, _1774529]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774525)), _1774529))))]]], (33619 ^ _779999) ^ [_1408656, _1408658] : [class_Int_Onumber__ring(_1408656), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1408656), c_Groups_Oone__class_Oone(_1408656)), hAPP(c_Int_Onumber__class_Onumber__of(_1408656), _1408658)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408656), 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), _1408658))))], (21665 ^ _779999) ^ [_1174667, _1174669] : [hAPP(c_Set_OCollect(_1174667), _1174669) = c_Orderings_Obot__class_Obot(tc_fun(_1174667, tc_HOL_Obool)), 21668 ^ _779999 : [(21669 ^ _779999) ^ [_1174752] : [hBOOL(hAPP(_1174669, _1174752))]]], (36497 ^ _779999) ^ [_1467485, _1467487, _1467489, _1467491, _1467493] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1467485, _1467487, _1467489), _1467491), _1467493) = hAPP(hAPP(_1467491, hAPP(c_Product__Type_Ofst(_1467485, _1467487), _1467493)), hAPP(c_Product__Type_Osnd(_1467485, _1467487), _1467493)))], (15807 ^ _779999) ^ [_1065010, _1065012] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065010), _1065012) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1065010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1065012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52382 ^ _779999) ^ [_1834579, _1834581] : [hBOOL(hAPP(hAPP(c_fconj, _1834579), _1834581)), -(hBOOL(_1834581))], (30136 ^ _779999) ^ [_1344801, _1344803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344803), _1344801))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344803), _1344801) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1344803), _1344801)), _1344801)))], (15659 ^ _779999) ^ [_1062178, _1062180] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1062178, _1062180)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1062178), hAPP(c_Nat_OSuc, _1062180)))], (18421 ^ _779999) ^ [_1115326] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115326)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1115326), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1115326)))], (51604 ^ _779999) ^ [_1824518, _1824520] : [-(c_Fun_Obij__betw(_1824518, _1824518, c_Fun_Oid(_1824518), _1824520, _1824520))], (48655 ^ _779999) ^ [_1759333, _1759335, _1759337, _1759339, _1759341] : [hBOOL(hAPP(hAPP(c_member(_1759333), _1759335), hAPP(c_List_Oset(_1759333), _1759337))), -(hBOOL(hAPP(_1759339, _1759335))), -(c_List_OtakeWhile(_1759333, _1759339, hAPP(hAPP(c_List_Oappend(_1759333), _1759337), _1759341)) = c_List_OtakeWhile(_1759333, _1759339, _1759337))], (27516 ^ _779999) ^ [_1297565, _1297567] : [-(_1297565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297567), _1297565) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1297567), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1297565), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (34927 ^ _779999) ^ [_1432864] : [class_Int_Onumber__ring(_1432864), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1432864), c_Groups_Oone__class_Oone(_1432864)) = hAPP(c_Int_Onumber__class_Onumber__of(_1432864), c_Int_OMin))], (50587 ^ _779999) ^ [_1802458, _1802460] : [-(c_Relation_Otrans(_1802458, c_Transitive__Closure_Otrancl(_1802458, _1802460)))], (34053 ^ _779999) ^ [_1416924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1416924))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1416924)))], (22960 ^ _779999) ^ [_1207737, _1207739, _1207741, _1207743, _1207745] : [-(_1207737 = c_Orderings_Obot__class_Obot(tc_fun(_1207739, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1207741), _1207743), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207739, tc_fun(_1207741, tc_HOL_Obool)), _1207737), _1207745)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207739, tc_fun(_1207741, tc_HOL_Obool)), _1207737), hAPP(hAPP(c_COMBB(tc_fun(_1207741, tc_HOL_Obool), tc_fun(_1207741, tc_HOL_Obool), _1207739), hAPP(c_Set_Oinsert(_1207741), _1207743)), _1207745)))], (40155 ^ _779999) ^ [_1559534, _1559536] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559534, _1559534), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559534, _1559536)), hAPP(hAPP(c_Product__Type_OSigma(_1559534, _1559534), hAPP(c_Relation_OField(_1559534), _1559536)), hAPP(c_COMBK(tc_fun(_1559534, tc_HOL_Obool), _1559534), hAPP(c_Relation_OField(_1559534), _1559536))))))], (32761 ^ _779999) ^ [_1394556, _1394558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394556), _1394558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1394556)), c_Int_OBit1(_1394558))))], (45334 ^ _779999) ^ [_1687163, _1687165, _1687167] : [-(hAPP(hAPP(c_List_Oappend(_1687163), hAPP(hAPP(c_List_Otake(_1687163), _1687165), _1687167)), hAPP(hAPP(c_List_Odrop(_1687163), _1687165), _1687167)) = _1687167)], (41047 ^ _779999) ^ [_1581732, _1581734, _1581736, _1581738, _1581740] : [c_Relation_Osingle__valued(_1581732, _1581734, hAPP(c_Relation_Oconverse(_1581734, _1581732), _1581736)), -(hAPP(c_Relation_OImage(_1581734, _1581732, _1581736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581734, tc_HOL_Obool)), _1581738), _1581740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581732, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1581734, _1581732, _1581736), _1581738)), hAPP(c_Relation_OImage(_1581734, _1581732, _1581736), _1581740)))], (8748 ^ _779999) ^ [_929909, _929911, _929913, _929915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929909, tc_HOL_Obool)), _929911), hAPP(hAPP(c_Set_Oinsert(_929909), _929913), _929915))), 8751 ^ _779999 : [(8758 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929909), _929913), _929915))), 8761 ^ _779999 : [(8768 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929909), _929913), _929911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929909, tc_HOL_Obool)), _929911), _929915)))], (8762 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929909), _929913), _929911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929909, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929909, tc_HOL_Obool)), _929911), hAPP(hAPP(c_Set_Oinsert(_929909), _929913), c_Orderings_Obot__class_Obot(tc_fun(_929909, tc_HOL_Obool))))), _929915)))]]], (8752 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929909), _929913), _929915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929909, tc_HOL_Obool)), _929911), _929915)))]]], (42562 ^ _779999) ^ [_1618072] : [class_Complete__Lattice_Ocomplete__lattice(_1618072), -(c_Complete__Lattice_OSup__class_OSup(_1618072, c_Orderings_Obot__class_Obot(tc_fun(_1618072, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1618072))], (40489 ^ _779999) ^ [_1568393, _1568395, _1568397, _1568399, _1568401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568393, _1568393)), hAPP(hAPP(c_Product__Type_OPair(_1568393, _1568393), _1568395), _1568397)), c_Transitive__Closure_Ortrancl(_1568393, _1568399))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568393, _1568393)), hAPP(hAPP(c_Product__Type_OPair(_1568393, _1568393), _1568397), _1568401)), c_Transitive__Closure_Otrancl(_1568393, _1568399))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568393, _1568393)), hAPP(hAPP(c_Product__Type_OPair(_1568393, _1568393), _1568395), _1568401)), c_Transitive__Closure_Otrancl(_1568393, _1568399))))], (10255 ^ _779999) ^ [_956608, _956610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956608), _956610)), -(hAPP(c_Nat_OSuc, _956608) = _956610), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956608)), _956610)))], (14710 ^ _779999) ^ [_1044049, _1044051, _1044053] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044049), _1044051)), 14713 ^ _779999 : [(14720 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1044049), _1044053), _1044051))), -(hAPP(c_Finite__Set_Ocard(_1044049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044049, tc_HOL_Obool)), _1044051), hAPP(hAPP(c_Set_Oinsert(_1044049), _1044053), c_Orderings_Obot__class_Obot(tc_fun(_1044049, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1044049), _1044051))], (14714 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1044049), _1044053), _1044051)), -(hAPP(c_Finite__Set_Ocard(_1044049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044049, tc_HOL_Obool)), _1044051), hAPP(hAPP(c_Set_Oinsert(_1044049), _1044053), c_Orderings_Obot__class_Obot(tc_fun(_1044049, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044049), _1044051)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (6707 ^ _779999) ^ [_889688, _889690, _889692, _889694] : [_889688 = _889690, 6712 ^ _779999 : [(6715 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889692), _889694), _889690)))], (6713 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889692), _889694), _889688)))]], 6716 ^ _779999 : [(6719 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889692), _889694), _889690))], (6717 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889692), _889694), _889688))]]], (43395 ^ _779999) ^ [_1639744, _1639746, _1639748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1639744, _1639744), tc_HOL_Obool)), _1639746), _1639748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1639744), tc_List_Olist(_1639744)), tc_HOL_Obool)), c_List_Olistrel(_1639744, _1639746)), c_List_Olistrel(_1639744, _1639748))))], (3846 ^ _779999) ^ [_837814, _837816, _837818, _837820] : [-(c_List_Orotate(_837820, _837816) = c_List_Orotate(_837818, _837814)), _837820 = _837818, _837816 = _837814], (36390 ^ _779999) ^ [_1465170] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1465170)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1465170)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40705 ^ _779999) ^ [_1572882, _1572884, _1572886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572884, _1572882)), _1572886)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572882, _1572884)), hAPP(c_Relation_Oconverse(_1572884, _1572882), _1572886))))], (48458 ^ _779999) ^ [_1755182, _1755184, _1755186, _1755188, _1755190] : [-(c_List_Ofoldr(_1755182, _1755184, _1755186, _1755188, _1755190) = hAPP(c_List_Ofoldl(_1755184, _1755182, hAPP(c_COMBC(_1755182, _1755184, _1755184), _1755186), _1755190), hAPP(c_List_Orev(_1755182), _1755188)))], (5328 ^ _779999) ^ [_861535, _861537, _861539, _861541] : [-(c_Relation_Oconverse(_861541, _861537) = c_Relation_Oconverse(_861539, _861535)), _861541 = _861539, _861537 = _861535], (43757 ^ _779999) ^ [_1650124, _1650126, _1650128] : [-(hAPP(c_List_Oset(_1650124), hAPP(hAPP(c_List_Olist_OCons(_1650124), _1650126), _1650128)) = hAPP(hAPP(c_Set_Oinsert(_1650124), _1650126), hAPP(c_List_Oset(_1650124), _1650128)))], (5390 ^ _779999) ^ [_862458, _862460] : [_862460 = _862458, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_862460) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_862458))], (19169 ^ _779999) ^ [_1129448, _1129450, _1129452, _1129454] : [class_Orderings_Oorder(_1129448), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129448, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1129448, _1129450, _1129452)), c_SetInterval_Oord__class_OatLeastAtMost(_1129448, _1129452, _1129454)) = c_Orderings_Obot__class_Obot(tc_fun(_1129448, tc_HOL_Obool)))], (36070 ^ _779999) ^ [_1459202, _1459204] : [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), _1459202), _1459204))), 36073 ^ _779999 : [(36082 ^ _779999) ^ [] : [-(c_Divides_OnegDivAlg(_1459202, _1459204) = hAPP(c_Divides_Oadjust(_1459204), c_Divides_OnegDivAlg(_1459202, 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)))), _1459204)))), -(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), _1459202), _1459204)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1459204), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36074 ^ _779999) ^ [] : [36075 ^ _779999 : [(36078 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1459204), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36076 ^ _779999) ^ [] : [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), _1459202), _1459204)))]], -(c_Divides_OnegDivAlg(_1459202, _1459204) = 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), _1459202), _1459204)))]]], (3536 ^ _779999) ^ [_833021, _833023, _833025, _833027] : [-(c_HOL_OLet(_833027, _833023) = c_HOL_OLet(_833025, _833021)), _833027 = _833025, _833023 = _833021], (50995 ^ _779999) ^ [_1812073, _1812075] : [c_Relation_Osym(_1812073, _1812075), 50998 ^ _779999 : [(50999 ^ _779999) ^ [_1812179, _1812181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1812073, _1812073)), hAPP(hAPP(c_Product__Type_OPair(_1812073, _1812073), _1812181), _1812179)), _1812075)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812073, _1812073)), hAPP(hAPP(c_Product__Type_OPair(_1812073, _1812073), _1812179), _1812181)), _1812075)))]]], (21305 ^ _779999) ^ [_1167901, _1167903, _1167905] : [21307 ^ _779999 : [(21310 ^ _779999) ^ [] : [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(_1167903, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21306 ^ [_1167901, _1167903, _1167905]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1167903, 21306 ^ [_1167901, _1167903, _1167905])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21308 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21306 ^ [_1167901, _1167903, _1167905]), _1167901)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1167903, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1167905), hAPP(_1167903, _1167901))), 21320 ^ _779999 : [(21323 ^ _779999) ^ [] : [-(hAPP(_1167903, 21319 ^ [_1167901, _1167903, _1167905]) = _1167905)], (21321 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21319 ^ [_1167901, _1167903, _1167905]), _1167901)))]]], (31929 ^ _779999) ^ [_1378737, _1378739, _1378741] : [class_Int_Onumber__ring(_1378737), -(hAPP(c_Int_Onumber__class_Onumber__of(_1378737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1378739), _1378741)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1378737), hAPP(c_Int_Onumber__class_Onumber__of(_1378737), _1378739)), hAPP(c_Int_Onumber__class_Onumber__of(_1378737), _1378741)))], (29960 ^ _779999) ^ [_1341651, _1341653] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341651), _1341653)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341651)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341653)))], (11496 ^ _779999) ^ [_980942, _980944, _980946, _980948] : [hBOOL(hAPP(hAPP(c_member(_980942), _980944), _980946)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980942, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980942), _980944), _980948)), _980946) = hAPP(hAPP(c_Set_Oinsert(_980942), _980944), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980942, tc_HOL_Obool)), _980948), _980946)))], (4774 ^ _779999) ^ [_852700, _852702] : [_852702 = _852700, -(c_List_Olist_ONil(_852702) = c_List_Olist_ONil(_852700))], (44015 ^ _779999) ^ [_1657720, _1657722, _1657724, _1657726] : [-(hAPP(c_List_Oset(tc_prod(_1657720, _1657722)), hAPP(hAPP(c_List_Ozip(_1657720, _1657722), _1657724), _1657726)) = hAPP(c_Set_OCollect(tc_prod(_1657720, _1657722)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1657720, _1657722)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1657720, _1657722), 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(_1657720, _1657722)), 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(_1657720, _1657722)), 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(_1657720, _1657722), tc_fun(tc_Nat_Onat, tc_prod(_1657720, _1657722)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1657720, _1657722), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1657720, _1657722)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1657720, _1657722)), c_COMBB(tc_prod(_1657720, _1657722), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1657722, tc_prod(_1657720, _1657722)), hAPP(hAPP(c_COMBB(_1657720, tc_fun(_1657722, tc_prod(_1657720, _1657722)), tc_Nat_Onat), c_Product__Type_OPair(_1657720, _1657722)), hAPP(c_List_Onth(_1657720), _1657724))), hAPP(c_List_Onth(_1657722), _1657726)))))), 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(_1657720)), _1657724)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657722)), _1657726)))))))], (3586 ^ _779999) ^ [_833774, _833776, _833778, _833780] : [-(c_Code__Numeral_Onat__of__aux(_833780, _833776) = c_Code__Numeral_Onat__of__aux(_833778, _833774)), _833780 = _833778, _833776 = _833774], (4602 ^ _779999) ^ [_849902, _849904, _849906, _849908, _849910, _849912] : [-(c_List_Oreplicate(_849912, _849908, _849904) = c_List_Oreplicate(_849910, _849906, _849902)), _849912 = _849910, _849908 = _849906, _849904 = _849902], (34949 ^ _779999) ^ [_1433203, _1433205] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433203), _1433205), hAPP(c_Int_Onumber__class_Onumber__of(_1433203), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1433203), _1433205)), class_Fields_Ofield__inverse__zero(_1433203), class_Int_Onumber__ring(_1433203)], (24562 ^ _779999) ^ [_1239814, _1239816, _1239818] : [class_Orderings_Olinorder(_1239814), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239814), _1239816), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239814), _1239818), _1239816))))], (31245 ^ _779999) ^ [_1365371, _1365373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1365371), _1365373)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365371, _1365373) = _1365371)], (15829 ^ _779999) ^ [_1065310, _1065312, _1065314] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065310)), _1065312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065310)), _1065314), -(_1065312 = _1065314)], (27808 ^ _779999) ^ [_1302753, _1302755, _1302757] : [class_Rings_Olinordered__semidom(_1302753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302753), c_Groups_Oone__class_Oone(_1302753)), _1302755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302753), c_Groups_Oone__class_Oone(_1302753)), hAPP(hAPP(c_Power_Opower__class_Opower(_1302753), _1302755), _1302757))))], (50749 ^ _779999) ^ [_1807441, _1807443] : [c_Predicate_Otransp(_1807441, _1807443), -(c_Relation_Otrans(_1807441, hAPP(c_Set_OCollect(tc_prod(_1807441, _1807441)), hAPP(c_Product__Type_Oprod_Oprod__case(_1807441, _1807441, tc_HOL_Obool), _1807443))))], (52064 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (35380 ^ _779999) ^ [_1445742, _1445744, _1445746] : [class_Rings_Osemiring__1(_1445742), hBOOL(hAPP(hAPP(c_member(_1445742), _1445744), c_Nat_Osemiring__1__class_ONats(_1445742))), hBOOL(hAPP(hAPP(c_member(_1445742), _1445746), c_Nat_Osemiring__1__class_ONats(_1445742))), -(hBOOL(hAPP(hAPP(c_member(_1445742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1445742), _1445744), _1445746)), c_Nat_Osemiring__1__class_ONats(_1445742))))], (31953 ^ _779999) ^ [_1379311, _1379313, _1379315] : [class_Int_Onumber__ring(_1379311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379311), hAPP(c_Int_Onumber__class_Onumber__of(_1379311), _1379313)), hAPP(c_Int_Onumber__class_Onumber__of(_1379311), _1379315)) = hAPP(c_Int_Onumber__class_Onumber__of(_1379311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1379313), _1379315)))], (7811 ^ _779999) ^ [_911742, _911744, _911746, _911748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911742, tc_HOL_Obool)), _911744), hAPP(hAPP(c_Set_Oinsert(_911742), _911746), _911748)))), 7814 ^ _779999 : [(7817 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911742, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911742, tc_HOL_Obool)), _911744), hAPP(hAPP(c_Set_Oinsert(_911742), _911746), c_Orderings_Obot__class_Obot(tc_fun(_911742, tc_HOL_Obool))))), _911748))], (7815 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911742), _911746), _911744)))]], 7818 ^ _779999 : [(7821 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911742, tc_HOL_Obool)), _911744), _911748))], (7819 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_911742), _911746), _911744))]]], (51145 ^ _779999) ^ [_1814586, _1814588] : [c_Relation_Osym(_1814586, hAPP(c_Set_OCollect(tc_prod(_1814586, _1814586)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814586, _1814586, tc_HOL_Obool), _1814588))), -(c_Predicate_Osymp(_1814586, _1814588))], (40952 ^ _779999) ^ [_1579255, _1579257] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579255, _1579255), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1579257) = c_Relation_OId(_1579255))], (46929 ^ _779999) ^ [_1722212, _1722214, _1722216, _1722218] : [46931 ^ _779999 : [(46934 ^ _779999) ^ [] : [hBOOL(hAPP(_1722216, hAPP(hAPP(c_List_Onth(_1722212), _1722214), 46930 ^ [_1722212, _1722214, _1722216, _1722218])))], (46932 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46930 ^ [_1722212, _1722214, _1722216, _1722218]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722212)), _1722214))))]], hBOOL(hAPP(hAPP(c_member(_1722212), _1722218), hAPP(c_List_Oset(_1722212), _1722214))), -(hBOOL(hAPP(_1722216, _1722218)))], (41201 ^ _779999) ^ [_1585896, _1585898, _1585900, _1585902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585896, _1585896)), hAPP(hAPP(c_Product__Type_OPair(_1585896, _1585896), _1585898), _1585900)), c_Transitive__Closure_Otrancl(_1585896, _1585902))), 41205 ^ _779999 : [(41208 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585896, _1585896)), hAPP(hAPP(c_Product__Type_OPair(_1585896, _1585896), 41204 ^ [_1585896, _1585898, _1585900, _1585902]), _1585900)), _1585902)))], (41206 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585896, _1585896)), hAPP(hAPP(c_Product__Type_OPair(_1585896, _1585896), _1585898), 41204 ^ [_1585896, _1585898, _1585900, _1585902])), c_Transitive__Closure_Ortrancl(_1585896, _1585902))))]]], (33089 ^ _779999) ^ [_1400065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1400065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1400065))))], (7306 ^ _779999) ^ [_901101, _901103, _901105, _901107] : [c_Orderings_Obot__class_Obot(tc_fun(_901101, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_901103, _901101, _901105), _901107), -(_901107 = c_Orderings_Obot__class_Obot(tc_fun(_901103, tc_HOL_Obool)))], (4374 ^ _779999) ^ [_846446, _846448, _846450, _846452, _846454, _846456, _846458, _846460] : [-(c_New__Random__Sequence_Opos__bind(_846460, _846456, _846452, _846448) = c_New__Random__Sequence_Opos__bind(_846458, _846454, _846450, _846446)), _846460 = _846458, _846456 = _846454, _846452 = _846450, _846448 = _846446], (37672 ^ _779999) ^ [_1497007, _1497009, _1497011, _1497013, _1497015, _1497017, _1497019] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1497007, _1497009, _1497011), hAPP(hAPP(c_Relation_Orel__comp(_1497007, _1497013, _1497009), _1497015), _1497017)), _1497019) = hAPP(hAPP(c_Relation_Orel__comp(_1497007, _1497013, _1497011), _1497015), hAPP(hAPP(c_Relation_Orel__comp(_1497013, _1497009, _1497011), _1497017), _1497019)))], (7753 ^ _779999) ^ [_910466, _910468, _910470, _910472] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _910466), _910468, hAPP(c_Nat_OSuc, _910470), _910472), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910466)), _910468, _910470, _910472))], (5957 ^ _779999) ^ [_874869, _874871, _874873] : [class_Orderings_Oorder(_874869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874869), _874871), _874873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874869), _874873), _874871)), -(_874871 = _874873)], (33981 ^ _779999) ^ [_1415670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1415670)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415670), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16533 ^ _779999) ^ [_1078758, _1078760, _1078762] : [class_Rings_Olinordered__ring__strict(_1078758), 16536 ^ _779999 : [(16545 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078758), _1078760), _1078760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078758), _1078762), _1078762)) = c_Groups_Ozero__class_Ozero(_1078758)), _1078760 = c_Groups_Ozero__class_Ozero(_1078758), _1078762 = c_Groups_Ozero__class_Ozero(_1078758)], (16537 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078758), _1078760), _1078760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078758), _1078762), _1078762)) = c_Groups_Ozero__class_Ozero(_1078758), 16540 ^ _779999 : [(16543 ^ _779999) ^ [] : [-(_1078762 = c_Groups_Ozero__class_Ozero(_1078758))], (16541 ^ _779999) ^ [] : [-(_1078760 = c_Groups_Ozero__class_Ozero(_1078758))]]]]], (27698 ^ _779999) ^ [_1300743, _1300745, _1300747] : [class_Groups_Omonoid__mult(_1300743), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300743), hAPP(hAPP(c_Power_Opower__class_Opower(_1300743), _1300745), _1300747)), _1300745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300743), _1300745), hAPP(hAPP(c_Power_Opower__class_Opower(_1300743), _1300745), _1300747)))], (45406 ^ _779999) ^ [_1688753, _1688755, _1688757, _1688759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1688753), _1688755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1688757, tc_HOL_Obool)), hAPP(c_List_Oset(_1688757), hAPP(hAPP(c_List_Odrop(_1688757), _1688755), _1688759))), hAPP(c_List_Oset(_1688757), hAPP(hAPP(c_List_Odrop(_1688757), _1688753), _1688759)))))], (46560 ^ _779999) ^ [_1713891, _1713893] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1713891)), hAPP(c_Code__Numeral_Oof__nat, _1713893)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713891), _1713893)))], (982 ^ _779999) ^ [_794970, _794972, _794974, _794976] : [-(c_Relation_Oantisym(_794974, _794970)), c_Relation_Oantisym(_794976, _794972), _794976 = _794974, _794972 = _794970], (9212 ^ _779999) ^ [_937290, _937292, _937294] : [class_Orderings_Olinorder(_937290), 9215 ^ _779999 : [(9222 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937290), _937294), _937292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937290), _937292), _937294))], (9216 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937290), _937292), _937294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937290), _937294), _937292)))]]], (44668 ^ _779999) ^ [_1671287, _1671289, _1671291] : [-(hAPP(hAPP(c_List_Olist__update(_1671287, c_List_Olist_ONil(_1671287)), _1671289), _1671291) = c_List_Olist_ONil(_1671287))], (40106 ^ _779999) ^ [_1558489, _1558491] : [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), _1558489), _1558491)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558489), _1558491)))], (30826 ^ _779999) ^ [_1357895, _1357897] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357895, _1357897) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357895, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1357897)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45708 ^ _779999) ^ [_1695406, _1695408] : [class_Lattices_Oab__semigroup__idem__mult(_1695406), -(_1695408 = c_List_Olist_ONil(_1695406)), -(hAPP(c_Finite__Set_Ofold1(_1695406, c_Groups_Otimes__class_Otimes(_1695406)), hAPP(c_List_Oset(_1695406), _1695408)) = hAPP(c_List_Ofoldl(_1695406, _1695406, c_Groups_Otimes__class_Otimes(_1695406), hAPP(c_List_Ohd(_1695406), _1695408)), hAPP(c_List_Otl(_1695406), _1695408)))], (9156 ^ _779999) ^ [_936423, _936425, _936427, _936429, _936431, _936433, _936435] : [-(_936423 = _936425), -(c_Fun_Ofun__upd(_936427, _936429, c_Fun_Ofun__upd(_936427, _936429, _936431, _936423, _936433), _936425, _936435) = c_Fun_Ofun__upd(_936427, _936429, c_Fun_Ofun__upd(_936427, _936429, _936431, _936425, _936435), _936423, _936433))], (13824 ^ _779999) ^ [_1026639] : [class_Lattices_Osemilattice__sup(_1026639), -(c_Finite__Set_Ofun__left__comm__idem(_1026639, _1026639, c_Lattices_Osemilattice__sup__class_Osup(_1026639)))], (34149 ^ _779999) ^ [_1418618, _1418620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1418618)), c_Int_OBit1(_1418620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1418618), _1418620)))], (7400 ^ _779999) ^ [_903224, _903226] : [class_Orderings_Obot(_903224), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903224), c_Orderings_Obot__class_Obot(_903224)), _903226)))], (24338 ^ _779999) ^ [_1235979, _1235981] : [class_Orderings_Olinorder(_1235979), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235979), _1235981), _1235981) = _1235981)], (19283 ^ _779999) ^ [_1131551, _1131553, _1131555, _1131557, _1131559] : [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), _1131551), _1131553)), _1131555)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131551), _1131557)), _1131559))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131555), _1131551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131559), _1131551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131553), _1131557)))], (10816 ^ _779999) ^ [_966905, _966907, _966909, _966911, _966913] : [class_Groups_Oab__group__add(_966905), hBOOL(hAPP(c_Finite__Set_Ofinite(_966907), _966909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966907, tc_HOL_Obool)), _966911), _966909)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966907, _966905), _966913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966907, tc_HOL_Obool)), _966909), _966911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966905), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966907, _966905), _966913), _966909)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966907, _966905), _966913), _966911)))], (5396 ^ _779999) ^ [_862543, _862545] : [_862545 = _862543, -(c_Orderings_Oord__class_Oless(_862545) = c_Orderings_Oord__class_Oless(_862543))], (4050 ^ _779999) ^ [_841000, _841002, _841004, _841006, _841008, _841010, _841012, _841014] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_841014, _841010, _841006, _841002) = c_New__Random__Sequence_Opos__not__random__dseq(_841012, _841008, _841004, _841000)), _841014 = _841012, _841010 = _841008, _841006 = _841004, _841002 = _841000], (35197 ^ _779999) ^ [_1441646, _1441648, _1441650, _1441652] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1441646, _1441648)), hAPP(hAPP(c_Product__Type_OPair(_1441646, _1441648), _1441650), _1441652)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1441646, _1441648), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1441646, tc_fun(_1441648, tc_HOL_Obool))), _1441650), _1441652)))], (22174 ^ _779999) ^ [_1190186, _1190188, _1190190] : [class_Orderings_Otop(_1190186), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1190188, _1190186)), _1190190) = c_Orderings_Otop__class_Otop(_1190186))], (7910 ^ _779999) ^ [_913533, _913535] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _913533, _913535, _913533))], (10285 ^ _779999) ^ [_957019, _957021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _957019)), _957021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957019), _957021)))], (33699 ^ _779999) ^ [_1410597] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410597))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410597)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (43739 ^ _779999) ^ [_1649443, _1649445, _1649447] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649443), _1649445)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1649443)), hAPP(c_Set_OCollect(tc_List_Olist(_1649443)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1649443), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1649443)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649443), tc_fun(_1649443, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649443, tc_HOL_Obool), tc_fun(tc_fun(_1649443, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649443)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649443, tc_HOL_Obool))), c_List_Oset(_1649443))), _1649445))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649443), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1649443)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1649443)))), _1649447))))))], (36501 ^ _779999) ^ [_1467603, _1467605, _1467607] : [-(c_HOL_OThe(tc_prod(_1467603, _1467605), hAPP(c_Product__Type_Oprod_Oprod__case(_1467603, _1467605, tc_HOL_Obool), _1467607)) = c_HOL_OThe(tc_prod(_1467603, _1467605), hAPP(hAPP(c_COMBS(tc_prod(_1467603, _1467605), _1467605, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1467603, tc_fun(_1467605, tc_HOL_Obool), tc_prod(_1467603, _1467605)), _1467607), c_Product__Type_Ofst(_1467603, _1467605))), c_Product__Type_Osnd(_1467603, _1467605))))], (12245 ^ _779999) ^ [_996423, _996425, _996427, _996429, _996431] : [class_Groups_Oordered__ab__group__add(_996423), hBOOL(hAPP(c_Finite__Set_Ofinite(_996425), _996427)), 12255 ^ _779999 : [(12258 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996423), c_Groups_Ozero__class_Ozero(_996423)), hAPP(_996429, 12254 ^ [_996423, _996425, _996427, _996429, _996431])))], (12256 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_996425), 12254 ^ [_996423, _996425, _996427, _996429, _996431]), _996427)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_996425, _996423), _996429), _996427) = c_Groups_Ozero__class_Ozero(_996423), hBOOL(hAPP(hAPP(c_member(_996425), _996431), _996427)), -(hAPP(_996429, _996431) = c_Groups_Ozero__class_Ozero(_996423))], (8358 ^ _779999) ^ [_922523, _922525, _922527, _922529, _922531] : [c_Hoare__Mirabelle_Otriple__valid(_922523, _922525, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_922523), _922527), _922529), _922531)), 8361 ^ _779999 : [(8362 ^ _779999) ^ [_922644, _922646] : [hBOOL(hAPP(hAPP(_922527, _922646), _922644)), 8365 ^ _779999 : [(8366 ^ _779999) ^ [_922734] : [c_Natural_Oevaln(_922529, _922644, _922525, _922734), -(hBOOL(hAPP(hAPP(_922531, _922646), _922734)))]]]]], (45225 ^ _779999) ^ [_1684211, _1684213, _1684215] : [hBOOL(hAPP(c_List_Odistinct(_1684211), hAPP(hAPP(c_List_Oappend(_1684211), _1684213), _1684215))), 45228 ^ _779999 : [(45233 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684211, tc_HOL_Obool)), hAPP(c_List_Oset(_1684211), _1684213)), hAPP(c_List_Oset(_1684211), _1684215)) = c_Orderings_Obot__class_Obot(tc_fun(_1684211, tc_HOL_Obool)))], (45231 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1684211), _1684215)))], (45229 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1684211), _1684213)))]]], (40469 ^ _779999) ^ [_1567853, _1567855, _1567857, _1567859, _1567861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567853, _1567853)), hAPP(hAPP(c_Product__Type_OPair(_1567853, _1567853), _1567855), _1567857)), c_Transitive__Closure_Ortrancl(_1567853, _1567859))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567853, _1567853)), hAPP(hAPP(c_Product__Type_OPair(_1567853, _1567853), _1567857), _1567861)), _1567859)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567853, _1567853)), hAPP(hAPP(c_Product__Type_OPair(_1567853, _1567853), _1567855), _1567861)), c_Transitive__Closure_Otrancl(_1567853, _1567859))))], (44834 ^ _779999) ^ [_1675304, _1675306, _1675308, _1675310, _1675312, _1675314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675304), tc_List_Olist(_1675304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675304), tc_List_Olist(_1675304)), hAPP(hAPP(c_List_Oappend(_1675304), _1675306), hAPP(hAPP(c_List_Olist_OCons(_1675304), _1675308), c_List_Olist_ONil(_1675304)))), hAPP(hAPP(c_List_Oappend(_1675304), _1675310), hAPP(hAPP(c_List_Olist_OCons(_1675304), _1675312), c_List_Olist_ONil(_1675304))))), c_List_Olistrel1(_1675304, _1675314))), 44839 ^ _779999 : [(44842 ^ _779999) ^ [] : [-(_1675308 = _1675312)], (44840 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675304), tc_List_Olist(_1675304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675304), tc_List_Olist(_1675304)), _1675306), _1675310)), c_List_Olistrel1(_1675304, _1675314))))]], 44843 ^ _779999 : [(44846 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1675304, _1675304)), hAPP(hAPP(c_Product__Type_OPair(_1675304, _1675304), _1675308), _1675312)), _1675314)))], (44844 ^ _779999) ^ [] : [-(_1675306 = _1675310)]]], (23347 ^ _779999) ^ [_1215504, _1215506, _1215508, _1215510] : [class_Orderings_Olinorder(_1215504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215504), _1215506), _1215508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215504), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215504), _1215506), _1215510)), _1215508)))], (26528 ^ _779999) ^ [_1276946] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276946, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1276946, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1276946, tc_HOL_Obool)))], (44710 ^ _779999) ^ [_1672240, _1672242, _1672244, _1672246] : [-(hAPP(hAPP(c_List_Otake(_1672240), _1672242), hAPP(hAPP(c_List_Olist_OCons(_1672240), _1672244), _1672246)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1672240), c_List_Olist_ONil(_1672240), hAPP(hAPP(c_COMBB(tc_List_Olist(_1672240), tc_List_Olist(_1672240), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1672240), _1672244)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1672240), tc_List_Olist(_1672240)), c_List_Otake(_1672240)), _1672246)), _1672242))], (10415 ^ _779999) ^ [_959310, _959312, _959314] : [class_Groups_Ocomm__monoid__add(_959310), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_959312, _959310), _959314), c_Orderings_Obot__class_Obot(tc_fun(_959312, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_959310))], (38608 ^ _779999) ^ [_1521378, _1521380, _1521382, _1521384, _1521386, _1521388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521378, _1521380), tc_HOL_Obool)), _1521382), hAPP(hAPP(c_Product__Type_OSigma(_1521378, _1521380), _1521384), hAPP(c_COMBK(tc_fun(_1521380, tc_HOL_Obool), _1521378), _1521386)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521380, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1521378, _1521380, _1521382), _1521388)), _1521386)))], (24034 ^ _779999) ^ [_1229011, _1229013, _1229015] : [class_Orderings_Olinorder(_1229011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229011), _1229013)), -(_1229015 = c_Orderings_Obot__class_Obot(tc_fun(_1229011, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229011, tc_HOL_Obool)), _1229015), _1229013)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229011), c_Big__Operators_Olattice_OInf__fin(_1229011, c_Orderings_Oord__class_Omin(_1229011), _1229015)), c_Big__Operators_Olattice_OInf__fin(_1229011, c_Orderings_Oord__class_Omin(_1229011), _1229013)) = c_Big__Operators_Olattice_OInf__fin(_1229011, c_Orderings_Oord__class_Omin(_1229011), _1229013))], (27506 ^ _779999) ^ [_1297402] : [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, _1297402)))))], (34673 ^ _779999) ^ [_1428321, _1428323] : [class_Rings_Oring__1(_1428321), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428321), hAPP(c_Groups_Ouminus__class_Ouminus(_1428321), c_Groups_Oone__class_Oone(_1428321))), 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)))), _1428323))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1428321), c_Groups_Oone__class_Oone(_1428321)))], (37662 ^ _779999) ^ [_1496611, _1496613, _1496615, _1496617, _1496619, _1496621, _1496623] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496611, _1496613, _1496615), _1496617), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496619, tc_fun(tc_prod(_1496613, _1496615), tc_HOL_Obool)), _1496621), _1496623)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496619, tc_fun(tc_prod(_1496611, _1496615), tc_HOL_Obool)), _1496621), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1496613, _1496615), tc_HOL_Obool), tc_fun(tc_prod(_1496611, _1496615), tc_HOL_Obool), _1496619), hAPP(c_Relation_Orel__comp(_1496611, _1496613, _1496615), _1496617)), _1496623)))], (44146 ^ _779999) ^ [_1660681, _1660683, _1660685, _1660687] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660681)), hAPP(hAPP(c_List_Olist__update(_1660681, _1660683), _1660685), _1660687)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660681)), _1660683))], (25281 ^ _779999) ^ [_1254403] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254403))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1254403)) = _1254403)], (42251 ^ _779999) ^ [_1610715, _1610717, _1610719, _1610721] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1610715, tc_HOL_Obool)), _1610717), _1610719)), hBOOL(hAPP(hAPP(c_member(_1610715), _1610721), _1610717)), -(hBOOL(hAPP(hAPP(c_member(_1610715), _1610721), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1610715, tc_HOL_Obool), _1610719))))], (34035 ^ _779999) ^ [_1416597, _1416599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416597), _1416599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416597)), c_Int_OBit1(_1416599))))], (11016 ^ _779999) ^ [_970444, _970446, _970448] : [class_Lattices_Osemilattice__inf(_970444), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970444), _970446), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970444), _970446), _970448)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970444), _970446), _970448))], (39075 ^ _779999) ^ [_1534316, _1534318] : [c_Wellfounded_OwfP(_1534316, _1534318), -(c_Wellfounded_Oacyclic(_1534316, hAPP(c_Set_OCollect(tc_prod(_1534316, _1534316)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534316, _1534316, tc_HOL_Obool), _1534318))))], (25142 ^ _779999) ^ [_1251818, _1251820, _1251822] : [class_Orderings_Olinorder(_1251818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251818), _1251820)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251818), _1251822)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1251818, tc_HOL_Obool)), _1251820), _1251822) = c_Orderings_Obot__class_Obot(tc_fun(_1251818, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1251818), c_Big__Operators_Olattice_OSup__fin(_1251818, c_Orderings_Oord__class_Omax(_1251818), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251818, tc_HOL_Obool)), _1251820), _1251822))), c_Big__Operators_Olattice_OSup__fin(_1251818, c_Orderings_Oord__class_Omax(_1251818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1251818, tc_HOL_Obool)), _1251820), _1251822))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1251818), c_Big__Operators_Olattice_OSup__fin(_1251818, c_Orderings_Oord__class_Omax(_1251818), _1251820)), c_Big__Operators_Olattice_OSup__fin(_1251818, c_Orderings_Oord__class_Omax(_1251818), _1251822)))], (37142 ^ _779999) ^ [_1482827] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1482827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1482827)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7582 ^ _779999) ^ [_907335, _907337] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_907335, _907337)], (40037 ^ _779999) ^ [_1556960, _1556962, _1556964, _1556966, _1556968] : [c_Com_Ocom_OLocal(_1556960, _1556962, _1556964) = c_Com_Ocom_OSemi(_1556966, _1556968)], (17319 ^ _779999) ^ [_1093967, _1093969] : [-(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), _1093967), _1093969)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093969))], (45674 ^ _779999) ^ [_1694627, _1694629, _1694631] : [-(hAPP(hAPP(c_List_Otake(_1694627), _1694629), hAPP(c_List_Otl(_1694627), _1694631)) = hAPP(c_List_Otl(_1694627), hAPP(hAPP(c_List_Otake(_1694627), hAPP(c_Nat_OSuc, _1694629)), _1694631)))], (43477 ^ _779999) ^ [_1642635, _1642637, _1642639, _1642641, _1642643, _1642645] : [hBOOL(hAPP(hAPP(_1642635, _1642637), _1642639)), c_List_Olistrelp(_1642641, _1642635, _1642643, _1642645), -(c_List_Olistrelp(_1642641, _1642635, hAPP(hAPP(c_List_Olist_OCons(_1642641), _1642637), _1642643), hAPP(hAPP(c_List_Olist_OCons(_1642641), _1642639), _1642645)))], (50379 ^ _779999) ^ [_1797643, _1797645, _1797647, _1797649] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1797643, _1797645, _1797647, _1797649, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797645)) = _1797647)], (41526 ^ _779999) ^ [_1592730, _1592732, _1592734] : [class_Groups_Oab__semigroup__mult(_1592730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592730), _1592732)), -(hBOOL(hAPP(hAPP(c_member(_1592730), _1592734), _1592732))), -(hAPP(c_Finite__Set_Ofold1(_1592730, c_Groups_Otimes__class_Otimes(_1592730)), hAPP(hAPP(c_Set_Oinsert(_1592730), _1592734), _1592732)) = hAPP(hAPP(c_Finite__Set_Ofold(_1592730, _1592730, c_Groups_Otimes__class_Otimes(_1592730)), _1592734), _1592732))], (7647 ^ _779999) ^ [_908490] : [hAPP(c_Nat_OSuc, _908490) = _908490], (6965 ^ _779999) ^ [_894399, _894401, _894403] : [_894399 = c_Orderings_Obot__class_Obot(tc_fun(_894401, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_894401), _894403), _894399))], (24668 ^ _779999) ^ [_1242017, _1242019, _1242021, _1242023, _1242025] : [class_Lattices_Osemilattice__sup(_1242017), class_Orderings_Olinorder(_1242019), c_Orderings_Oorder__class_Omono(_1242019, _1242017, _1242021), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1242017), hAPP(_1242021, _1242023)), hAPP(_1242021, _1242025))), hAPP(_1242021, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242019), _1242023), _1242025)))))], (38380 ^ _779999) ^ [_1514269, _1514271, _1514273, _1514275] : [38381 ^ _779999 : [(38382 ^ _779999) ^ [_1514344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514269, _1514273)), hAPP(hAPP(c_Product__Type_OPair(_1514269, _1514273), _1514271), _1514344)), _1514275))]], -(hBOOL(hAPP(hAPP(c_member(_1514269), _1514271), hAPP(c_Relation_ODomain(_1514269, _1514273), _1514275))))], (52006 ^ _779999) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (10761 ^ _779999) ^ [_965554, _965556, _965558, _965560, _965562] : [c_Fun_Oinj__on(_965554, _965556, _965558, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965554, tc_HOL_Obool)), _965560), _965562)), 10764 ^ _779999 : [(10769 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965556, tc_HOL_Obool)), hAPP(c_Set_Oimage(_965554, _965556, _965558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965554, tc_HOL_Obool)), _965560), _965562))), hAPP(c_Set_Oimage(_965554, _965556, _965558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965554, tc_HOL_Obool)), _965562), _965560))) = c_Orderings_Obot__class_Obot(tc_fun(_965556, tc_HOL_Obool)))], (10767 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_965554, _965556, _965558, _965562))], (10765 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_965554, _965556, _965558, _965560))]]], (6335 ^ _779999) ^ [_881858, _881860, _881862, _881864] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881858, tc_HOL_Obool)), _881860), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881858, tc_HOL_Obool)), _881862), _881864)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881858, tc_HOL_Obool)), _881862), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881858, tc_HOL_Obool)), _881860), _881864)))], (42560 ^ _779999) ^ [_1618002, _1618004, _1618006] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618002, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1618002, tc_HOL_Obool), tc_HOL_Obool)), _1618004), _1618006)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618002, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618002, tc_HOL_Obool), _1618004)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618002, tc_HOL_Obool), _1618006)))], (44544 ^ _779999) ^ [_1669226, _1669228] : [-(c_List_Olist_Olist__size(_1669226, _1669228, c_List_Olist_ONil(_1669226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7025 ^ _779999) ^ [_895424, _895426, _895428] : [hBOOL(hAPP(hAPP(c_member(_895424), _895426), hAPP(hAPP(c_Set_Oinsert(_895424), _895428), c_Orderings_Obot__class_Obot(tc_fun(_895424, tc_HOL_Obool))))), -(_895426 = _895428)], (40735 ^ _779999) ^ [_1573575, _1573577, _1573579, _1573581, _1573583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573575, _1573577)), hAPP(hAPP(c_Product__Type_OPair(_1573575, _1573577), _1573579), _1573581)), hAPP(c_Relation_Oconverse(_1573577, _1573575), _1573583))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573577, _1573575)), hAPP(hAPP(c_Product__Type_OPair(_1573577, _1573575), _1573581), _1573579)), _1573583)))], (37598 ^ _779999) ^ [_1494044, _1494046, _1494048, _1494050] : [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), _1494044), _1494046)), 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), _1494048), _1494050)), 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), _1494044), _1494050)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1494048), _1494046))))], (35223 ^ _779999) ^ [_1442248, _1442250, _1442252] : [class_Enum_Oenum(_1442248), class_Enum_Oenum(_1442250), 35230 ^ _779999 : [(35237 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1442250), hAPP(hAPP(c_COMBB(tc_fun(_1442248, tc_HOL_Obool), tc_HOL_Obool, _1442250), c_Enum_Oenum__class_Oenum__ex(_1442248)), hAPP(hAPP(c_COMBB(tc_fun(_1442248, tc_prod(_1442250, _1442248)), tc_fun(_1442248, tc_HOL_Obool), _1442250), hAPP(c_COMBB(tc_prod(_1442250, _1442248), tc_HOL_Obool, _1442248), _1442252)), c_Product__Type_OPair(_1442250, _1442248))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1442250, _1442248)), _1442252)))], (35231 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1442250, _1442248)), _1442252)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1442250), hAPP(hAPP(c_COMBB(tc_fun(_1442248, tc_HOL_Obool), tc_HOL_Obool, _1442250), c_Enum_Oenum__class_Oenum__ex(_1442248)), hAPP(hAPP(c_COMBB(tc_fun(_1442248, tc_prod(_1442250, _1442248)), tc_fun(_1442248, tc_HOL_Obool), _1442250), hAPP(c_COMBB(tc_prod(_1442250, _1442248), tc_HOL_Obool, _1442248), _1442252)), c_Product__Type_OPair(_1442250, _1442248))))))]]], (16325 ^ _779999) ^ [_1074866, _1074868, _1074870, _1074872] : [class_Rings_Olinordered__ring__strict(_1074866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074866), c_Groups_Ozero__class_Ozero(_1074866)), _1074868)), 16332 ^ _779999 : [(16339 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074866), _1074870), _1074872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074866), _1074868), _1074870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074866), _1074868), _1074872))))], (16333 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074866), _1074868), _1074870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074866), _1074868), _1074872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074866), _1074870), _1074872)))]]], (31508 ^ _779999) ^ [_1369923, _1369925, _1369927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369923), _1369925)), c_Fun_Oinj__on(_1369923, tc_fun(tc_fun(_1369923, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1369923, tc_fun(tc_prod(_1369923, _1369923), tc_HOL_Obool), tc_fun(tc_fun(_1369923, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1369923, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1369923, _1369923), tc_HOL_Obool), tc_fun(tc_fun(_1369923, tc_HOL_Obool), tc_HOL_Obool)), _1369923), c_Equiv__Relations_Oquotient(_1369923)), hAPP(hAPP(c_COMBC(_1369923, tc_fun(_1369923, tc_HOL_Obool), tc_fun(_1369923, tc_HOL_Obool)), c_Set_Oinsert(_1369923)), c_Orderings_Obot__class_Obot(tc_fun(_1369923, tc_HOL_Obool))))), _1369927), _1369925), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1369923, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1369923), _1369925), _1369927)) = hAPP(c_Finite__Set_Ocard(_1369923), _1369925))], (9848 ^ _779999) ^ [_949095, _949097] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949095), hAPP(c_Nat_OSuc, _949097)) = 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), _949095), _949097)))], (3202 ^ _779999) ^ [_827764, _827766] : [_827766 = _827764, -(c_Nitpick_Onum(_827766) = c_Nitpick_Onum(_827764))], (27298 ^ _779999) ^ [_1293789, _1293791, _1293793] : [class_Rings_Odivision__ring(_1293789), -(_1293791 = c_Groups_Ozero__class_Ozero(_1293789)), 27305 ^ _779999 : [(27312 ^ _779999) ^ [] : [_1293793 = _1293791, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293789), _1293793), _1293791) = c_Groups_Oone__class_Oone(_1293789))], (27306 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293789), _1293793), _1293791) = c_Groups_Oone__class_Oone(_1293789), -(_1293793 = _1293791)]]], (45380 ^ _779999) ^ [_1688221, _1688223] : [-(hAPP(c_List_Oset(_1688221), hAPP(c_List_Orotate1(_1688221), _1688223)) = hAPP(c_List_Oset(_1688221), _1688223))], (52376 ^ _779999) ^ [_1834492, _1834494] : [hBOOL(hAPP(hAPP(c_fconj, _1834492), _1834494)), -(hBOOL(_1834492))], (18875 ^ _779999) ^ [_1124473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124473)), -(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)), _1124473))))], (40295 ^ _779999) ^ [_1563693, _1563695] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563693, _1563693), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1563693, _1563695)), c_Relation_OId(_1563693)) = c_Transitive__Closure_Ortrancl(_1563693, _1563695))], (18339 ^ _779999) ^ [_1113768, _1113770, _1113772, _1113774, _1113776, _1113778, _1113780] : [-(hBOOL(hAPP(hAPP(c_member(_1113768), _1113770), _1113772))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1113768, _1113774, _1113776, _1113778, _1113772), _1113780)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1113768, _1113774, _1113776, _1113778, hAPP(hAPP(c_Set_Oinsert(_1113768), _1113770), _1113772)), hAPP(hAPP(_1113776, _1113770), _1113780))))], (20044 ^ _779999) ^ [_1145378, _1145380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145378)), 20047 ^ _779999 : [(20054 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145380), _1145378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1145380)), hAPP(c_Int_Onat, _1145378))))], (20048 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1145380)), hAPP(c_Int_Onat, _1145378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145380), _1145378)))]]], (38489 ^ _779999) ^ [_1517797, _1517799, _1517801, _1517803, _1517805] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517797, _1517799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517797, tc_HOL_Obool)), _1517801), _1517803)), _1517805) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517797, _1517799), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517797, _1517799), _1517801), _1517805)), hAPP(hAPP(c_Product__Type_OSigma(_1517797, _1517799), _1517803), _1517805)))], (38483 ^ _779999) ^ [_1517552, _1517554, _1517556, _1517558, _1517560, _1517562] : [class_Groups_Ocomm__monoid__mult(_1517552), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517554, _1517552), hAPP(hAPP(c_COMBC(_1517554, tc_fun(_1517556, tc_HOL_Obool), _1517552), hAPP(hAPP(c_COMBB(tc_fun(_1517556, _1517552), tc_fun(tc_fun(_1517556, tc_HOL_Obool), _1517552), _1517554), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517556, _1517552)), _1517558)), _1517560)), _1517562) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1517554, _1517556), _1517552), hAPP(c_Product__Type_Oprod_Oprod__case(_1517554, _1517556, _1517552), _1517558)), hAPP(hAPP(c_Product__Type_OSigma(_1517554, _1517556), _1517562), hAPP(c_COMBK(tc_fun(_1517556, tc_HOL_Obool), _1517554), _1517560))))], (40523 ^ _779999) ^ [_1569082, _1569084, _1569086, _1569088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569082, _1569082)), hAPP(hAPP(c_Product__Type_OPair(_1569082, _1569082), _1569084), _1569086)), c_Transitive__Closure_Ortrancl(_1569082, _1569088))), hBOOL(hAPP(hAPP(c_member(_1569082), _1569086), c_Wellfounded_Oacc(_1569082, _1569088))), -(hBOOL(hAPP(hAPP(c_member(_1569082), _1569084), c_Wellfounded_Oacc(_1569082, _1569088))))], (51774 ^ _779999) ^ [_1828072, _1828074] : [class_Lattices_Obounded__lattice(_1828072), -(class_Lattices_Obounded__lattice__top(tc_fun(_1828074, _1828072)))], (6937 ^ _779999) ^ [_893910, _893912, _893914, _893916] : [6938 ^ _779999 : [(6941 ^ _779999) ^ [] : [hBOOL(hAPP(_893914, _893916))], (6939 ^ _779999) ^ [] : [_893912 = _893916]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_893910), _893912), _893914), _893916)))], (40789 ^ _779999) ^ [_1575042, _1575044, _1575046, _1575048, _1575050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575042, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575044, _1575042, _1575046), _1575048)), _1575050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575044, tc_HOL_Obool)), _1575048), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575044, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575042, _1575044, hAPP(c_Relation_Oconverse(_1575044, _1575042), _1575046)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575042, tc_HOL_Obool)), _1575050))))))], (42518 ^ _779999) ^ [_1617024, _1617026, _1617028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1617024, tc_HOL_Obool), tc_HOL_Obool)), _1617026), _1617028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1617024, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617024, tc_HOL_Obool), _1617028)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617024, tc_HOL_Obool), _1617026))))], (52016 ^ _779999) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (49738 ^ _779999) ^ [_1783378, _1783380, _1783382, _1783384, _1783386, _1783388, _1783390] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1783378, _1783380, _1783382, _1783384), _1783386), _1783388), _1783390) = c_New__DSequence_Opos__bind(_1783378, _1783380, hAPP(hAPP(hAPP(_1783382, _1783386), _1783388), _1783390), hAPP(hAPP(c_COMBC(_1783378, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1783380))), hAPP(hAPP(c_COMBC(_1783378, 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(_1783380)))), hAPP(hAPP(c_COMBC(_1783378, 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(_1783380))))), _1783384), _1783386)), _1783388)), _1783390)))], (51129 ^ _779999) ^ [_1814331, _1814333, _1814335] : [c_Equiv__Relations_Oequiv(_1814331, _1814333, _1814335), 51132 ^ _779999 : [(51137 ^ _779999) ^ [] : [-(c_Relation_Otrans(_1814331, _1814335))], (51135 ^ _779999) ^ [] : [-(c_Relation_Osym(_1814331, _1814335))], (51133 ^ _779999) ^ [] : [-(c_Relation_Orefl__on(_1814331, _1814333, _1814335))]]], (31457 ^ _779999) ^ [_1369132] : [_1369132 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1369132) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52272 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (256 ^ _779999) ^ [_783905, _783907, _783909, _783911, _783913, _783915, _783917, _783919, _783921, _783923, _783925, _783927] : [-(c_Equiv__Relations_Ocongruent2(_783925, _783921, _783917, _783913, _783909, _783905)), c_Equiv__Relations_Ocongruent2(_783927, _783923, _783919, _783915, _783911, _783907), _783927 = _783925, _783923 = _783921, _783919 = _783917, _783915 = _783913, _783911 = _783909, _783907 = _783905], (23437 ^ _779999) ^ [_1217474, _1217476, _1217478, _1217480, _1217482] : [class_Orderings_Olinorder(_1217474), class_Orderings_Olinorder(_1217476), c_Orderings_Oorder__class_Omono(_1217476, _1217474, _1217478), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217474), hAPP(_1217478, _1217480)), hAPP(_1217478, _1217482)) = hAPP(_1217478, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217476), _1217480), _1217482)))], (6371 ^ _779999) ^ [_882634, _882636, _882638, _882640] : [class_Lattices_Osemilattice__sup(_882634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882634), _882636), _882638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882634), _882640), _882638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_882634), _882636), _882640)), _882638)))], (47625 ^ _779999) ^ [_1739268, _1739270] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1739268), _1739270) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1739268, _1739270)))], (27422 ^ _779999) ^ [_1295845, _1295847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295845)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295847))))], (9987 ^ _779999) ^ [_952355, _952357] : [-(c_Fun_Oinj__on(_952355, _952355, c_COMBI(_952355), _952357))], (26306 ^ _779999) ^ [_1272982, _1272984] : [class_Groups_Ogroup__add(_1272982), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272982), hAPP(c_Groups_Ouminus__class_Ouminus(_1272982), _1272984)), _1272984) = c_Groups_Ozero__class_Ozero(_1272982))], (26548 ^ _779999) ^ [_1277314, _1277316] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277314, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277314, tc_HOL_Obool)), _1277316)), _1277316) = c_Orderings_Obot__class_Obot(tc_fun(_1277314, tc_HOL_Obool)))], (52114 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (43891 ^ _779999) ^ [_1653187, _1653189] : [-(c_List_Olists(_1653187, _1653189) = hAPP(c_Set_OCollect(tc_List_Olist(_1653187)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1653187), tc_fun(_1653187, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1653187, tc_HOL_Obool), tc_fun(tc_fun(_1653187, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1653187)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1653187, tc_HOL_Obool))), c_List_Oset(_1653187))), _1653189)))], (34247 ^ _779999) ^ [_1420593] : [class_Int_Onumber__ring(_1420593), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420593), c_Groups_Oone__class_Oone(_1420593)), c_Groups_Oone__class_Oone(_1420593)) = hAPP(c_Int_Onumber__class_Onumber__of(_1420593), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (3648 ^ _779999) ^ [_834697, _834699, _834701, _834703, _834705, _834707] : [-(c_Enum_On__lists(_834707, _834703, _834699) = c_Enum_On__lists(_834705, _834701, _834697)), _834707 = _834705, _834703 = _834701, _834699 = _834697], (24712 ^ _779999) ^ [_1243071, _1243073, _1243075, _1243077] : [class_Orderings_Olinorder(_1243071), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1243071, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1243071, _1243073, _1243075)), hAPP(c_SetInterval_Oord__class_OatLeast(_1243071), _1243077)) = c_SetInterval_Oord__class_OatLeastAtMost(_1243071, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243071), _1243073), _1243077), _1243075))], (1174 ^ _779999) ^ [_797782, _797784] : [-(class_Rings_Olinordered__semiring__1__strict(_797782)), _797784 = _797782, class_Rings_Olinordered__semiring__1__strict(_797784)], (35053 ^ _779999) ^ [_1434751, _1434753] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1434751), hAPP(hAPP(c_Power_Opower__class_Opower(_1434751), hAPP(c_Int_Onumber__class_Onumber__of(_1434751), c_Int_OMin)), _1434753)) = c_Groups_Oone__class_Oone(_1434751)), class_Int_Onumber__ring(_1434751), class_Rings_Olinordered__idom(_1434751)], (51910 ^ _779999) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (22113 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (9340 ^ _779999) ^ [_939057, _939059, _939061] : [class_Orderings_Olinorder(_939057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939057), _939059), _939061))), 9347 ^ _779999 : [(9354 ^ _779999) ^ [] : [_939059 = _939061, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939057), _939059), _939061)))], (9348 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939057), _939059), _939061)), -(_939059 = _939061)]]], (52344 ^ _779999) ^ [_1834111, _1834113] : [_1834111 = _1834113, -(hBOOL(hAPP(hAPP(c_fequal, _1834111), _1834113)))], (43409 ^ _779999) ^ [_1640117, _1640119, _1640121, _1640123, _1640125] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640117), tc_List_Olist(_1640117))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640117), tc_List_Olist(_1640117)), _1640119), _1640121)), c_List_Olistrel(_1640117, c_Transitive__Closure_Ortrancl(_1640117, _1640123)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640117), tc_List_Olist(_1640117))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640117), tc_List_Olist(_1640117)), _1640121), _1640125)), c_List_Olistrel(_1640117, c_Transitive__Closure_Ortrancl(_1640117, _1640123)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640117), tc_List_Olist(_1640117))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640117), tc_List_Olist(_1640117)), _1640119), _1640125)), c_List_Olistrel(_1640117, c_Transitive__Closure_Ortrancl(_1640117, _1640123)))))], (11430 ^ _779999) ^ [_978937, _978939, _978941, _978943] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978937, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978937, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978937, tc_HOL_Obool)), _978939), _978941)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978937, tc_HOL_Obool)), _978941), _978943))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978937, tc_HOL_Obool)), _978943), _978939)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978937, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978937, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978937, tc_HOL_Obool)), _978939), _978941)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978937, tc_HOL_Obool)), _978941), _978943))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978937, tc_HOL_Obool)), _978943), _978939)))], (20986 ^ _779999) ^ [_1161110, _1161112, _1161114] : [class_Rings_Oordered__ring__abs(_1161110), -(hAPP(c_Groups_Oabs__class_Oabs(_1161110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161110), _1161112), _1161114)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161110), hAPP(c_Groups_Oabs__class_Oabs(_1161110), _1161112)), hAPP(c_Groups_Oabs__class_Oabs(_1161110), _1161114))), 20993 ^ _779999 : [(20996 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161110), _1161112), c_Groups_Ozero__class_Ozero(_1161110)))], (20994 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161110), c_Groups_Ozero__class_Ozero(_1161110)), _1161112))]], 20997 ^ _779999 : [(21000 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161110), _1161114), c_Groups_Ozero__class_Ozero(_1161110)))], (20998 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161110), c_Groups_Ozero__class_Ozero(_1161110)), _1161114))]]], (15641 ^ _779999) ^ [_1061881, _1061883] : [class_Rings_Omult__zero(_1061881), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061881), c_Groups_Ozero__class_Ozero(_1061881)), _1061883) = c_Groups_Ozero__class_Ozero(_1061881))], (36264 ^ _779999) ^ [_1462807, _1462809, _1462811, _1462813, _1462815, _1462817] : [hAPP(c_Product__Type_Oapsnd(_1462807, _1462809, _1462811, _1462813), _1462815) = hAPP(c_Product__Type_Oapsnd(_1462807, _1462809, _1462811, _1462817), _1462815), -(hAPP(_1462813, hAPP(c_Product__Type_Osnd(_1462811, _1462807), _1462815)) = hAPP(_1462817, hAPP(c_Product__Type_Osnd(_1462811, _1462807), _1462815)))], (51994 ^ _779999) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (29632 ^ _779999) ^ [_1335856, _1335858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335856)), 29635 ^ _779999 : [(29642 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335858)), -(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), _1335858), _1335856))))], (29636 ^ _779999) ^ [] : [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), _1335858), _1335856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335858)))]]], (22573 ^ _779999) ^ [_1197750, _1197752] : [class_Orderings_Olinorder(_1197750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197750), _1197752)), -(_1197752 = c_Orderings_Obot__class_Obot(tc_fun(_1197750, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1197750), c_Big__Operators_Olinorder__class_OMax(_1197750, _1197752)), _1197752)))], (51588 ^ _779999) ^ [_1824098, _1824100, _1824102, _1824104, _1824106, _1824108] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1824098, _1824100, _1824102, _1824104, c_Lazy__Sequence_Olazy__sequence_OInsert(_1824100, _1824106, _1824108)) = hAPP(hAPP(hAPP(_1824104, _1824106), _1824108), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1824098, _1824100, _1824102, _1824104, _1824108)))], (29162 ^ _779999) ^ [_1327677, _1327679, _1327681] : [class_Fields_Olinordered__field(_1327677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327677), _1327679), _1327681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327677), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327677), _1327679), _1327681)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327677), c_Groups_Oone__class_Oone(_1327677)), c_Groups_Oone__class_Oone(_1327677)))), _1327681)))], (22180 ^ _779999) ^ [] : [-(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)))], (1088 ^ _779999) ^ [_796473, _796475, _796477, _796479] : [-(c_Predicate_Otransp(_796477, _796473)), c_Predicate_Otransp(_796479, _796475), _796479 = _796477, _796475 = _796473], (34167 ^ _779999) ^ [_1418942, _1418944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1418942), _1418944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1418942)), c_Int_OBit1(_1418944))))], (49750 ^ _779999) ^ [_1783755, _1783757, _1783759] : [-(hAPP(c_New__DSequence_Opos__single(_1783755, _1783757), _1783759) = hAPP(c_Lazy__Sequence_Osingle(_1783755), _1783757))], (25790 ^ _779999) ^ [_1263349, _1263351, _1263353] : [class_Rings_Oring(_1263349), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1263349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263349), _1263351), _1263353)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263349), hAPP(c_Groups_Ouminus__class_Ouminus(_1263349), _1263351)), _1263353))], (12605 ^ _779999) ^ [_1002882, _1002884, _1002886] : [class_Lattices_Olattice(_1002882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002882), _1002884)), 12612 ^ _779999 : [(12619 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002882, tc_HOL_Obool)), _1002884), hAPP(hAPP(c_Set_Oinsert(_1002882), _1002886), c_Orderings_Obot__class_Obot(tc_fun(_1002882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1002882, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1002882, hAPP(hAPP(c_Set_Oinsert(_1002882), _1002886), _1002884)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1002882), _1002886), c_Big__Operators_Olattice__class_OInf__fin(_1002882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002882, tc_HOL_Obool)), _1002884), hAPP(hAPP(c_Set_Oinsert(_1002882), _1002886), c_Orderings_Obot__class_Obot(tc_fun(_1002882, tc_HOL_Obool)))))))], (12613 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002882, tc_HOL_Obool)), _1002884), hAPP(hAPP(c_Set_Oinsert(_1002882), _1002886), c_Orderings_Obot__class_Obot(tc_fun(_1002882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1002882, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1002882, hAPP(hAPP(c_Set_Oinsert(_1002882), _1002886), _1002884)) = _1002886)]]], (47115 ^ _779999) ^ [_1726384, _1726386, _1726388, _1726390, _1726392, _1726394, _1726396, _1726398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726384), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726386)), _1726388))), c_List_Olist__all2(_1726386, _1726390, _1726392, _1726388, _1726394), hBOOL(hAPP(hAPP(_1726392, _1726396), _1726398)), -(c_List_Olist__all2(_1726386, _1726390, _1726392, hAPP(hAPP(c_List_Olist__update(_1726386, _1726388), _1726384), _1726396), hAPP(hAPP(c_List_Olist__update(_1726390, _1726394), _1726384), _1726398)))], (43419 ^ _779999) ^ [_1640456, _1640458] : [-(c_List_Olistrel(_1640456, c_Transitive__Closure_Ortrancl(_1640456, _1640458)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1640456), c_List_Olistrel1(_1640456, _1640458)))], (48741 ^ _779999) ^ [_1761226, _1761228, _1761230] : [-(c_List_OdropWhile(_1761226, _1761228, _1761230) = c_List_Olist_ONil(_1761226)), hBOOL(hAPP(_1761228, hAPP(c_List_Ohd(_1761226), c_List_OdropWhile(_1761226, _1761228, _1761230))))], (41998 ^ _779999) ^ [_1604285, _1604287, _1604289] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604285, tc_fun(_1604287, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1604285, tc_HOL_Obool))), _1604289) = c_Orderings_Otop__class_Otop(tc_fun(_1604287, tc_HOL_Obool)))], (41978 ^ _779999) ^ [_1603564, _1603566, _1603568, _1603570] : [-(hAPP(c_Set_OPow(_1603564), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603566, tc_fun(_1603564, tc_HOL_Obool)), _1603568), _1603570)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603566, tc_fun(tc_fun(_1603564, tc_HOL_Obool), tc_HOL_Obool)), _1603568), hAPP(hAPP(c_COMBB(tc_fun(_1603564, tc_HOL_Obool), tc_fun(tc_fun(_1603564, tc_HOL_Obool), tc_HOL_Obool), _1603566), c_Set_OPow(_1603564)), _1603570)))], (52324 ^ _779999) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (28722 ^ _779999) ^ [_1319435, _1319437, _1319439, _1319441, _1319443] : [class_Fields_Olinordered__field(_1319435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319435), c_Groups_Ozero__class_Ozero(_1319435)), _1319437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319435), _1319437), _1319439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319435), c_Groups_Ozero__class_Ozero(_1319435)), _1319441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319435), _1319441), _1319443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319435), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319435), _1319437), _1319443)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319435), _1319439), _1319441))))], (24482 ^ _779999) ^ [_1238471, _1238473, _1238475, _1238477] : [class_Orderings_Olinorder(_1238471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238471), _1238473), _1238475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238471), _1238473), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238471), _1238477), _1238475))))], (15333 ^ _779999) ^ [_1055473, _1055475, _1055477, _1055479, _1055481] : [class_Rings_Ocomm__semiring__1(_1055473), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), _1055475), _1055477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), _1055479), _1055481)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), _1055475), _1055479)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055473), _1055477), _1055481)))], (47338 ^ _779999) ^ [_1730823, _1730825] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730823)), c_List_Oconcat(_1730823, _1730825)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730823), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1730823))), _1730825)))], (42474 ^ _779999) ^ [_1615834, _1615836, _1615838] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615834, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615834, tc_HOL_Obool), _1615836)), _1615838) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1615834, tc_HOL_Obool), tc_fun(_1615834, tc_HOL_Obool)), _1615836), hAPP(hAPP(c_COMBC(tc_fun(_1615834, tc_HOL_Obool), tc_fun(_1615834, tc_HOL_Obool), tc_fun(_1615834, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615834, tc_HOL_Obool))), _1615838)))], (47597 ^ _779999) ^ [_1738408, _1738410, _1738412, _1738414, _1738416, _1738418] : [-(c_List_Ofoldr(_1738408, _1738410, _1738412, hAPP(hAPP(c_List_Oappend(_1738408), _1738414), _1738416), _1738418) = c_List_Ofoldr(_1738408, _1738410, _1738412, _1738414, c_List_Ofoldr(_1738408, _1738410, _1738412, _1738416, _1738418)))], (6027 ^ _779999) ^ [_875958, _875960, _875962] : [class_Orderings_Oorder(_875958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875958), _875960), _875962)), 6034 ^ _779999 : [(6041 ^ _779999) ^ [] : [_875962 = _875960, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875958), _875962), _875960)))], (6035 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875958), _875962), _875960)), -(_875962 = _875960)]]], (14325 ^ _779999) ^ [_1035808, _1035810, _1035812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035808), _1035810)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035810), _1035808))), _1035812) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035808), _1035812)))], (5454 ^ _779999) ^ [_863472, _863474] : [_863474 = _863472, -(c_Set_OCollect(_863474) = c_Set_OCollect(_863472))], (21982 ^ _779999) ^ [_1183959, _1183961, _1183963] : [class_Lattices_Odistrib__lattice(_1183959), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183959), _1183961)), -(_1183961 = c_Orderings_Obot__class_Obot(tc_fun(_1183959, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183959), _1183963)), -(_1183963 = c_Orderings_Obot__class_Obot(tc_fun(_1183959, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1183959), c_Big__Operators_Olattice__class_OInf__fin(_1183959, _1183961)), c_Big__Operators_Olattice__class_OInf__fin(_1183959, _1183963)) = c_Big__Operators_Olattice__class_OInf__fin(_1183959, hAPP(c_Set_OCollect(_1183959), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_HOL_Obool), tc_HOL_Obool, _1183959), c_HOL_OEx(_1183959)), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool)), tc_fun(_1183959, tc_HOL_Obool), _1183959), hAPP(c_COMBB(tc_fun(_1183959, tc_HOL_Obool), tc_HOL_Obool, _1183959), c_HOL_OEx(_1183959))), hAPP(hAPP(c_COMBC(_1183959, tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool)), tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_fun(tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool))), tc_fun(tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool)), tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool))), _1183959), c_COMBS(_1183959, tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_fun(_1183959, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1183959, tc_fun(tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool))), _1183959), hAPP(c_COMBB(tc_fun(_1183959, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool)), _1183959), c_COMBS(_1183959, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool)), tc_fun(_1183959, tc_fun(_1183959, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1183959), hAPP(c_COMBB(tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1183959), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1183959), c_fconj))), hAPP(hAPP(c_COMBC(_1183959, tc_fun(_1183959, tc_fun(_1183959, _1183959)), tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1183959, _1183959), tc_fun(_1183959, tc_HOL_Obool)), tc_fun(tc_fun(_1183959, tc_fun(_1183959, _1183959)), tc_fun(_1183959, tc_fun(_1183959, tc_HOL_Obool))), _1183959), c_COMBB(tc_fun(_1183959, _1183959), tc_fun(_1183959, tc_HOL_Obool), _1183959)), hAPP(hAPP(c_COMBB(tc_fun(_1183959, tc_HOL_Obool), tc_fun(tc_fun(_1183959, _1183959), tc_fun(_1183959, tc_HOL_Obool)), _1183959), c_COMBB(_1183959, tc_HOL_Obool, _1183959)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1183959)))))), hAPP(hAPP(c_COMBC(_1183959, tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1183959, tc_HOL_Obool), tc_fun(_1183959, tc_HOL_Obool)), _1183959), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1183959)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1183959), c_fconj), hAPP(hAPP(c_COMBC(_1183959, tc_fun(_1183959, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183959)), _1183961)))), hAPP(hAPP(c_COMBC(_1183959, tc_fun(_1183959, tc_HOL_Obool), tc_HOL_Obool), c_member(_1183959)), _1183963))))))))], (18933 ^ _779999) ^ [_1125492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1125492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125492)))], (15635 ^ _779999) ^ [_1061782, _1061784] : [class_Rings_Omult__zero(_1061782), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061782), _1061784), c_Groups_Ozero__class_Ozero(_1061782)) = c_Groups_Ozero__class_Ozero(_1061782))], (11899 ^ _779999) ^ [_989214, _989216, _989218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_989214), _989216)), 11902 ^ _779999 : [(11909 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_989214), _989218)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_989214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989214, tc_HOL_Obool)), _989218), _989216))))], (11903 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_989214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989214, tc_HOL_Obool)), _989218), _989216))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_989214), _989218)))]]], (13538 ^ _779999) ^ [_1021298, _1021300] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021298), _1021300)), _1021300) = _1021298)], (40900 ^ _779999) ^ [_1577944, _1577946, _1577948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577944, _1577944)), _1577946), c_Transitive__Closure_Ortrancl(_1577944, _1577948))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577944, _1577944)), _1577946), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1577944, _1577944), 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(_1577944, _1577944), tc_HOL_Obool), tc_fun(tc_prod(_1577944, _1577944), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1577944, _1577944), tc_HOL_Obool)), _1577948)))))], (50024 ^ _779999) ^ [_1789868, _1789870, _1789872, _1789874] : [hBOOL(hAPP(hAPP(c_member(_1789868), _1789870), hAPP(c_List_Oset(_1789868), c_List_Oreplicate(_1789868, _1789872, _1789874)))), 50027 ^ _779999 : [(50030 ^ _779999) ^ [] : [_1789872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50028 ^ _779999) ^ [] : [-(_1789870 = _1789874)]]], (52312 ^ _779999) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (49037 ^ _779999) ^ [_1767276, _1767278] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1767276)), _1767278)), 49043 ^ _779999 : [(49046 ^ _779999) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1767276), 49042 ^ [_1767276, _1767278]))], (49044 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1767276)), 49042 ^ [_1767276, _1767278]), hAPP(c_List_Oset(tc_List_Olist(_1767276)), _1767278))))]], 49050 ^ _779999 : [(49054 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1767276)), 49052 ^ [_1767276, _1767278]), hAPP(c_List_Oset(tc_List_Olist(_1767276)), _1767278))))], (49056 ^ _779999) ^ [] : [49049 ^ [_1767276, _1767278] = 49052 ^ [_1767276, _1767278]], (49058 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1767276, tc_HOL_Obool)), hAPP(c_List_Oset(_1767276), 49049 ^ [_1767276, _1767278])), hAPP(c_List_Oset(_1767276), 49052 ^ [_1767276, _1767278])) = c_Orderings_Obot__class_Obot(tc_fun(_1767276, tc_HOL_Obool))], (49051 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1767276)), 49049 ^ [_1767276, _1767278]), hAPP(c_List_Oset(tc_List_Olist(_1767276)), _1767278))))]], -(hBOOL(hAPP(c_List_Odistinct(_1767276), c_List_Oconcat(_1767276, _1767278))))], (19109 ^ _779999) ^ [_1128249, _1128251, _1128253] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1128251), _1128253)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128249), _1128251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128249), _1128253)))], (41787 ^ _779999) ^ [_1597654, _1597656, _1597658, _1597660, _1597662, _1597664] : [hBOOL(hAPP(hAPP(c_member(_1597654), _1597656), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597658, tc_fun(_1597654, tc_HOL_Obool)), _1597660), _1597662))), hBOOL(hAPP(hAPP(c_member(_1597658), _1597664), _1597660)), -(hBOOL(hAPP(hAPP(c_member(_1597654), _1597656), hAPP(_1597662, _1597664))))], (33915 ^ _779999) ^ [_1414591, _1414593] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1414591)), _1414593) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414591), _1414593)))], (48649 ^ _779999) ^ [_1759222, _1759224, _1759226] : [-(c_List_OtakeWhile(_1759222, _1759224, _1759226) = hAPP(hAPP(c_List_Otake(_1759222), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759222)), c_List_OtakeWhile(_1759222, _1759224, _1759226))), _1759226))], (4476 ^ _779999) ^ [_848027, _848029] : [_848029 = _848027, -(c_List_Otl(_848029) = c_List_Otl(_848027))], (23111 ^ _779999) ^ [_1211392, _1211394, _1211396, _1211398] : [class_Orderings_Olinorder(_1211392), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211392), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211392), _1211394), _1211396)), _1211398) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211392), _1211394), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211392), _1211396), _1211398)))], (39215 ^ _779999) ^ [_1537184] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39211 ^ [_1537184]), c_Int_OInteg)))], (31297 ^ _779999) ^ [_1366183, _1366185] : [class_Rings_Olinordered__idom(_1366183), 31300 ^ _779999 : [(31307 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366183), _1366185), c_Groups_Ozero__class_Ozero(_1366183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366183), c_Groups_Osgn__class_Osgn(_1366183, _1366185)), c_Groups_Ozero__class_Ozero(_1366183))))], (31301 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366183), c_Groups_Osgn__class_Osgn(_1366183, _1366185)), c_Groups_Ozero__class_Ozero(_1366183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366183), _1366185), c_Groups_Ozero__class_Ozero(_1366183))))]]], (34291 ^ _779999) ^ [] : [-(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))))))], (42528 ^ _779999) ^ [_1617343] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617343, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1617343, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1617343, tc_HOL_Obool)))], (37304 ^ _779999) ^ [_1487088, _1487090, _1487092, _1487094, _1487096, _1487098, _1487100] : [-(hAPP(c_Product__Type_Oapsnd(_1487088, _1487090, _1487092, _1487094), hAPP(c_Product__Type_Oapfst(_1487096, _1487092, _1487088, _1487098), _1487100)) = hAPP(c_Product__Type_Oapfst(_1487096, _1487092, _1487090, _1487098), hAPP(c_Product__Type_Oapsnd(_1487088, _1487090, _1487096, _1487094), _1487100)))], (51996 ^ _779999) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (28744 ^ _779999) ^ [_1319858, _1319860, _1319862, _1319864, _1319866] : [class_Fields_Olinordered__field(_1319858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319858), c_Groups_Ozero__class_Ozero(_1319858)), _1319860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319858), _1319860), _1319862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319858), c_Groups_Ozero__class_Ozero(_1319858)), _1319864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319858), _1319864), _1319866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319858), _1319860), _1319866)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319858), _1319862), _1319864))))], (45809 ^ _779999) ^ [_1697512, _1697514, _1697516] : [class_Orderings_Olinorder(_1697512), -(c_Big__Operators_Olinorder__class_OMin(_1697512, hAPP(c_List_Oset(_1697512), hAPP(hAPP(c_List_Olist_OCons(_1697512), _1697514), _1697516))) = hAPP(c_List_Ofoldl(_1697512, _1697512, c_Orderings_Oord__class_Omin(_1697512), _1697514), _1697516))], (52276 ^ _779999) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (45386 ^ _779999) ^ [_1688360, _1688362, _1688364] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688360)), hAPP(hAPP(c_List_Odrop(_1688360), _1688362), _1688364)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688360)), _1688364)), _1688362))], (29028 ^ _779999) ^ [_1325182, _1325184, _1325186, _1325188] : [class_Fields_Olinordered__field(_1325182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325182), _1325184), _1325186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325182), c_Groups_Ozero__class_Ozero(_1325182)), _1325188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325182), c_Groups_Ozero__class_Ozero(_1325182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325182), _1325186), _1325184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325182), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325182), _1325188), _1325186)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325182), _1325188), _1325184))))], (44910 ^ _779999) ^ [_1677163, _1677165, _1677167, _1677169, _1677171] : [-(hAPP(hAPP(c_List_Olist_OCons(_1677163), _1677165), _1677167) = hAPP(hAPP(c_List_Oappend(_1677163), _1677169), _1677171)), 44911 ^ _779999 : [(44918 ^ _779999) ^ [_1677346] : [hAPP(hAPP(c_List_Olist_OCons(_1677163), _1677165), _1677346) = _1677169, _1677167 = hAPP(hAPP(c_List_Oappend(_1677163), _1677346), _1677171)], (44912 ^ _779999) ^ [] : [_1677169 = c_List_Olist_ONil(_1677163), hAPP(hAPP(c_List_Olist_OCons(_1677163), _1677165), _1677167) = _1677171]]], (15929 ^ _779999) ^ [_1067169, _1067171, _1067173, _1067175, _1067177] : [class_Groups_Ocomm__monoid__add(_1067169), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1067169), _1067171), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067173), _1067175), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067177), _1067175))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1067169), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1067169, tc_Nat_Onat), _1067171), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1067175))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1067173, _1067177)))], (36328 ^ _779999) ^ [_1464147, _1464149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464147), 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)), _1464149)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1464147, _1464149) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1464147, _1464149)))], (44736 ^ _779999) ^ [_1672696] : [-(c_List_Olists(_1672696, c_Orderings_Obot__class_Obot(tc_fun(_1672696, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1672696)), c_List_Olist_ONil(_1672696)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1672696), tc_HOL_Obool))))], (40761 ^ _779999) ^ [_1574180, _1574182, _1574184] : [-(hAPP(c_Relation_ODomain(_1574180, _1574182), hAPP(c_Relation_Oconverse(_1574182, _1574180), _1574184)) = hAPP(c_Relation_ORange(_1574182, _1574180), _1574184))], (38590 ^ _779999) ^ [_1520883, _1520885, _1520887, _1520889] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1520883, _1520885)), hAPP(hAPP(c_Product__Type_OSigma(_1520883, _1520885), hAPP(hAPP(c_Set_Oinsert(_1520883), _1520887), c_Orderings_Obot__class_Obot(tc_fun(_1520883, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1520885, tc_HOL_Obool), _1520883), _1520889))) = hAPP(c_Finite__Set_Ocard(_1520885), _1520889))], (14816 ^ _779999) ^ [_1045959] : [class_Rings_Olinordered__semidom(_1045959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045959), c_Groups_Oone__class_Oone(_1045959)), c_Groups_Ozero__class_Ozero(_1045959)))], (49257 ^ _779999) ^ [_1773379, _1773381, _1773383, _1773385, _1773387] : [-(hAPP(c_List_Ofilter(_1773379, _1773381), _1773383) = hAPP(hAPP(c_List_Olist_OCons(_1773379), _1773385), _1773387)), 49258 ^ _779999 : [(49259 ^ _779999) ^ [_1773507, _1773509] : [_1773383 = hAPP(hAPP(c_List_Oappend(_1773379), _1773509), hAPP(hAPP(c_List_Olist_OCons(_1773379), _1773385), _1773507)), 49265 ^ _779999 : [(49268 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1773381, 49264 ^ [_1773379, _1773381, _1773383, _1773385, _1773387, _1773507, _1773509])))], (49266 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773379), 49264 ^ [_1773379, _1773381, _1773383, _1773385, _1773387, _1773507, _1773509]), hAPP(c_List_Oset(_1773379), _1773509))))]], hBOOL(hAPP(_1773381, _1773385)), _1773387 = hAPP(c_List_Ofilter(_1773379, _1773381), _1773507)]]], (32947 ^ _779999) ^ [_1397920] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397920)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397920)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397920))], (30860 ^ _779999) ^ [_1358497, _1358499] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358497, _1358499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1358497), _1358499)), _1358499)))], (860 ^ _779999) ^ [_793155, _793157, _793159, _793161, _793163, _793165] : [-(c_List_Olist__ex1(_793163, _793159, _793155)), c_List_Olist__ex1(_793165, _793161, _793157), _793165 = _793163, _793161 = _793159, _793157 = _793155], (49644 ^ _779999) ^ [_1781279, _1781281, _1781283] : [c_FunDef_Ois__measure(_1781279, _1781281), -(c_FunDef_Ois__measure(tc_prod(_1781283, _1781279), hAPP(hAPP(c_COMBB(_1781279, tc_Nat_Onat, tc_prod(_1781283, _1781279)), _1781281), c_Product__Type_Osnd(_1781283, _1781279))))], (25748 ^ _779999) ^ [_1262560, _1262562] : [class_Groups_Ogroup__add(_1262560), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1262560), hAPP(c_Groups_Ouminus__class_Ouminus(_1262560), _1262562)) = _1262562)], (36280 ^ _779999) ^ [_1463218, _1463220, _1463222] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1463218, _1463220), _1463222)), 36283 ^ _779999 : [(36284 ^ _779999) ^ [_1463303] : [hBOOL(hAPP(hAPP(_1463220, _1463303), _1463222)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1463218, _1463220), _1463303)))]]], (2942 ^ _779999) ^ [_823778, _823780, _823782, _823784] : [-(c_Com_Ocom_OWhile(_823784, _823780) = c_Com_Ocom_OWhile(_823782, _823778)), _823784 = _823782, _823780 = _823778], (44162 ^ _779999) ^ [_1661086, _1661088, _1661090, _1661092, _1661094, _1661096] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1661086, _1661088), hAPP(hAPP(c_List_Ozip(_1661086, _1661088), _1661090), _1661092)), _1661094), _1661096) = hAPP(hAPP(c_List_Ozip(_1661086, _1661088), hAPP(hAPP(c_List_Olist__update(_1661086, _1661090), _1661094), hAPP(c_Product__Type_Ofst(_1661086, _1661088), _1661096))), hAPP(hAPP(c_List_Olist__update(_1661088, _1661092), _1661094), hAPP(c_Product__Type_Osnd(_1661086, _1661088), _1661096))))], (7866 ^ _779999) ^ [_912834, _912836, _912838, _912840, _912842, _912844] : [hBOOL(hAPP(_912834, _912836)), c_Natural_Oevaln(_912838, _912836, _912840, _912842), c_Natural_Oevaln(c_Com_Ocom_OWhile(_912834, _912838), _912842, _912840, _912844), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_912834, _912838), _912836, _912840, _912844))], (26030 ^ _779999) ^ [_1268206, _1268208, _1268210, _1268212, _1268214] : [c_Com_Ocom_OCond(_1268206, _1268208, _1268210) = c_Com_Ocom_OWhile(_1268212, _1268214)], (46802 ^ _779999) ^ [_1718879, _1718881, _1718883, _1718885] : [hBOOL(hAPP(c_List_Olistsp(_1718879, hAPP(hAPP(c_COMBS(_1718879, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1718879), c_fconj), _1718881)), _1718883)), _1718885)), 46805 ^ _779999 : [(46808 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1718879, _1718883), _1718885)))], (46806 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1718879, _1718881), _1718885)))]]], (44788 ^ _779999) ^ [_1673644] : [-(c_List_Olistset(_1673644, c_List_Olist_ONil(tc_fun(_1673644, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1673644)), c_List_Olist_ONil(_1673644)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1673644), tc_HOL_Obool))))], (28070 ^ _779999) ^ [_1307711, _1307713, _1307715] : [class_Rings_Olinordered__semidom(_1307711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307711), c_Groups_Ozero__class_Ozero(_1307711)), _1307713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307711), _1307713), c_Groups_Oone__class_Oone(_1307711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307711), _1307713), hAPP(hAPP(c_Power_Opower__class_Opower(_1307711), _1307713), _1307715))), hAPP(hAPP(c_Power_Opower__class_Opower(_1307711), _1307713), _1307715))))], (20852 ^ _779999) ^ [_1158561, _1158563, _1158565] : [class_Groups_Oordered__ab__group__add__abs(_1158561), -(hAPP(c_Groups_Oabs__class_Oabs(_1158561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1158561), _1158563), _1158565)) = hAPP(c_Groups_Oabs__class_Oabs(_1158561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1158561), _1158565), _1158563)))], (34781 ^ _779999) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (46322 ^ _779999) ^ [_1708539, _1708541, _1708543, _1708545, _1708547, _1708549] : [-(hAPP(hAPP(c_List_Ozip(_1708539, _1708541), _1708543), hAPP(hAPP(c_List_Omap(_1708545, _1708541), _1708547), _1708549)) = hAPP(hAPP(c_List_Omap(tc_prod(_1708539, _1708545), tc_prod(_1708539, _1708541)), hAPP(c_Product__Type_Oprod_Oprod__case(_1708539, _1708545, tc_prod(_1708539, _1708541)), hAPP(hAPP(c_COMBC(_1708539, tc_fun(_1708545, _1708541), tc_fun(_1708545, tc_prod(_1708539, _1708541))), hAPP(hAPP(c_COMBB(tc_fun(_1708541, tc_prod(_1708539, _1708541)), tc_fun(tc_fun(_1708545, _1708541), tc_fun(_1708545, tc_prod(_1708539, _1708541))), _1708539), c_COMBB(_1708541, tc_prod(_1708539, _1708541), _1708545)), c_Product__Type_OPair(_1708539, _1708541))), _1708547))), hAPP(hAPP(c_List_Ozip(_1708539, _1708545), _1708543), _1708549)))], (2474 ^ _779999) ^ [_816488, _816490, _816492, _816494] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_816494, _816490) = c_Code__Numeral_Odiv__mod__code__numeral(_816492, _816488)), _816494 = _816492, _816490 = _816488], (4188 ^ _779999) ^ [_843279, _843281, _843283, _843285, _843287, _843289, _843291, _843293] : [-(c_Lazy__Sequence_Ohb__bind(_843293, _843289, _843285, _843281) = c_Lazy__Sequence_Ohb__bind(_843291, _843287, _843283, _843279)), _843293 = _843291, _843289 = _843287, _843285 = _843283, _843281 = _843279], (1404 ^ _779999) ^ [_800657, _800659] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800657)), _800659 = _800657, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800659)], (38527 ^ _779999) ^ [_1519136, _1519138, _1519140, _1519142, _1519144] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519136, _1519138), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519136, tc_HOL_Obool)), _1519140), _1519142)), _1519144) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1519136, _1519138), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519136, _1519138), _1519140), _1519144)), hAPP(hAPP(c_Product__Type_OSigma(_1519136, _1519138), _1519142), _1519144)))], (36404 ^ _779999) ^ [_1465527, _1465529] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1465527, _1465529) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1465527, _1465529)))], (34005 ^ _779999) ^ [_1416062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416062)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416062), c_Int_OPls)))], (46886 ^ _779999) ^ [_1720681, _1720683, _1720685] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1720681)), _1720685), c_List_Olists(_1720681, _1720683))), -(hBOOL(hAPP(c_List_Olistsp(_1720681, hAPP(hAPP(c_COMBC(_1720681, tc_fun(_1720681, tc_HOL_Obool), tc_HOL_Obool), c_member(_1720681)), _1720683)), _1720685)))], (32027 ^ _779999) ^ [_1380685, _1380687, _1380689, _1380691] : [class_Fields_Ofield__inverse__zero(_1380685), class_Int_Onumber(_1380685), 32034 ^ _779999 : [(32035 ^ _779999) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380685), _1380687), _1380689) = hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691), 32038 ^ _779999 : [(32045 ^ _779999) ^ [] : [_1380689 = c_Groups_Ozero__class_Ozero(_1380685), -(hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691) = c_Groups_Ozero__class_Ozero(_1380685))], (32039 ^ _779999) ^ [] : [-(_1380689 = c_Groups_Ozero__class_Ozero(_1380685)), -(_1380687 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380685), hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691)), _1380689))]]], (32051 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380685), _1380687), _1380689) = hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691)), 32054 ^ _779999 : [(32057 ^ _779999) ^ [] : [_1380687 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380685), hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691)), _1380689)], (32055 ^ _779999) ^ [] : [_1380689 = c_Groups_Ozero__class_Ozero(_1380685)]], 32058 ^ _779999 : [(32061 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380685), _1380691) = c_Groups_Ozero__class_Ozero(_1380685)], (32059 ^ _779999) ^ [] : [-(_1380689 = c_Groups_Ozero__class_Ozero(_1380685))]]]]], (28988 ^ _779999) ^ [_1324420, _1324422, _1324424, _1324426] : [class_Fields_Olinordered__field(_1324420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324420), _1324422), c_Groups_Ozero__class_Ozero(_1324420))), 28995 ^ _779999 : [(29002 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324420), _1324426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324420), _1324424), _1324422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324420), _1324424), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324420), _1324426), _1324422))))], (28996 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324420), _1324424), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324420), _1324426), _1324422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324420), _1324426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324420), _1324424), _1324422))))]]], (8906 ^ _779999) ^ [_932630, _932632, _932634] : [class_Orderings_Olinorder(_932630), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932630), _932632), _932634))), 8913 ^ _779999 : [(8920 ^ _779999) ^ [] : [_932634 = _932632, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932630), _932634), _932632))], (8914 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932630), _932634), _932632))), -(_932634 = _932632)]]], (44408 ^ _779999) ^ [_1666606, _1666608] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1666606), _1666608)), -(c_Nitpick_Ocard_H(_1666606, _1666608) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666606)), c_Hilbert__Choice_OEps(tc_List_Olist(_1666606), hAPP(hAPP(c_COMBS(tc_List_Olist(_1666606), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1666606)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1666606), tc_fun(_1666606, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1666606, tc_HOL_Obool), tc_fun(tc_fun(_1666606, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1666606)), c_fequal), c_List_Oset(_1666606))), _1666608))), c_List_Odistinct(_1666606)))))], (38238 ^ _779999) ^ [_1510650, _1510652, _1510654] : [hAPP(c_Relation_ORange(_1510650, _1510652), _1510654) = c_Orderings_Obot__class_Obot(tc_fun(_1510652, tc_HOL_Obool)), -(_1510654 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1510650, _1510652), tc_HOL_Obool)))], (40597 ^ _779999) ^ [_1570856, _1570858, _1570860, _1570862, _1570864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570856, _1570856)), hAPP(hAPP(c_Product__Type_OPair(_1570856, _1570856), _1570858), _1570860)), c_Transitive__Closure_Ortrancl(_1570856, _1570862))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570856, _1570856), tc_HOL_Obool)), _1570862), hAPP(hAPP(c_Product__Type_OSigma(_1570856, _1570856), _1570864), hAPP(c_COMBK(tc_fun(_1570856, tc_HOL_Obool), _1570856), _1570864)))), -(_1570858 = _1570860), -(hBOOL(hAPP(hAPP(c_member(_1570856), _1570858), _1570864)))], (3024 ^ _779999) ^ [_825053, _825055] : [_825055 = _825053, -(c_Set_OBall(_825055) = c_Set_OBall(_825053))], (5821 ^ _779999) ^ [_872057, _872059, _872061, _872063] : [c_Hoare__Mirabelle_Ohoare__derivs(_872057, _872059, _872061), c_Hoare__Mirabelle_Ohoare__derivs(_872057, _872063, _872059), -(c_Hoare__Mirabelle_Ohoare__derivs(_872057, _872063, _872061))], (51384 ^ _779999) ^ [_1819534, _1819536, _1819538, _1819540] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1819534, _1819536, c_Orderings_Otop__class_Otop(tc_fun(_1819534, tc_HOL_Obool)), _1819538), _1819540) = c_Hilbert__Choice_OEps(_1819534, hAPP(hAPP(c_COMBC(_1819534, _1819536, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1819536, tc_fun(_1819536, tc_HOL_Obool), _1819534), c_fequal), _1819538)), _1819540)))], (52394 ^ _779999) ^ [_1834753, _1834755] : [hBOOL(_1834753), -(hBOOL(hAPP(hAPP(c_fdisj, _1834755), _1834753)))], (41370 ^ _779999) ^ [_1589641, _1589643, _1589645, _1589647] : [class_Lattices_Osemilattice__sup(_1589641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589641), _1589643)), hBOOL(hAPP(hAPP(c_member(_1589641), _1589645), _1589643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1589641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1589641), _1589645), _1589647)), hAPP(hAPP(c_Finite__Set_Ofold(_1589641, _1589641, c_Lattices_Osemilattice__sup__class_Osup(_1589641)), _1589647), _1589643))))], (24604 ^ _779999) ^ [_1240723, _1240725, _1240727, _1240729] : [class_Orderings_Olinorder(_1240723), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240723), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240723), _1240725), _1240727)), _1240729) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240723), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240723), _1240725), _1240729)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240723), _1240727), _1240729)))], (49521 ^ _779999) ^ [_1778977, _1778979, _1778981] : [c_List_Olist__all(_1778977, _1778979, _1778981), 49524 ^ _779999 : [(49525 ^ _779999) ^ [_1779058] : [hBOOL(hAPP(hAPP(c_member(_1778977), _1779058), hAPP(c_List_Oset(_1778977), _1778981))), -(hBOOL(hAPP(_1778979, _1779058)))]]], (38159 ^ _779999) ^ [_1508702, _1508704, _1508706, _1508708] : [38161 ^ _779999 : [(38164 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1508704, hAPP(_1508706, 38160 ^ [_1508702, _1508704, _1508706, _1508708]))), hAPP(_1508704, 38160 ^ [_1508702, _1508704, _1508706, _1508708])))], (38162 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1508702, 38160 ^ [_1508702, _1508704, _1508706, _1508708])))]], -(c_Wellfounded_Owf(_1508708, hAPP(c_Set_OCollect(tc_prod(_1508708, _1508708)), hAPP(c_Product__Type_Oprod_Oprod__case(_1508708, _1508708, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1508708, tc_HOL_Obool), tc_fun(_1508708, tc_HOL_Obool), _1508708), hAPP(c_COMBS(_1508708, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508708), c_fconj), _1508702))), hAPP(hAPP(c_COMBC(_1508708, tc_fun(_1508708, _1508708), tc_fun(_1508708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508708, tc_HOL_Obool), tc_fun(tc_fun(_1508708, _1508708), tc_fun(_1508708, tc_HOL_Obool)), _1508708), c_COMBB(_1508708, tc_HOL_Obool, _1508708)), c_fequal)), _1508706))))))], (38890 ^ _779999) ^ [_1529971, _1529973, _1529975, _1529977, _1529979, _1529981, _1529983, _1529985] : [c_Fun_Oinj__on(_1529971, _1529973, _1529975, _1529977), c_Fun_Oinj__on(_1529979, _1529981, _1529983, _1529985), -(c_Fun_Oinj__on(tc_prod(_1529971, _1529979), tc_prod(_1529973, _1529981), c_Product__Type_Omap__pair(_1529971, _1529973, _1529979, _1529981, _1529975, _1529983), hAPP(hAPP(c_Product__Type_OSigma(_1529971, _1529979), _1529977), hAPP(c_COMBK(tc_fun(_1529979, tc_HOL_Obool), _1529971), _1529985))))], (36457 ^ _779999) ^ [_1466600, _1466602, _1466604, _1466606] : [_1466600 = _1466602, 36460 ^ _779999 : [(36463 ^ _779999) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1466604, _1466606), _1466600) = hAPP(c_Product__Type_Osnd(_1466604, _1466606), _1466602))], (36461 ^ _779999) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1466604, _1466606), _1466600) = hAPP(c_Product__Type_Ofst(_1466604, _1466606), _1466602))]]], (41350 ^ _779999) ^ [_1589217, _1589219, _1589221, _1589223, _1589225] : [class_Complete__Lattice_Ocomplete__lattice(_1589217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589219), _1589221)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1589217), _1589223), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1589219, _1589217), _1589221), _1589225)) = hAPP(hAPP(c_Finite__Set_Ofold(_1589219, _1589217, hAPP(hAPP(c_COMBB(_1589217, tc_fun(_1589217, _1589217), _1589219), c_Lattices_Osemilattice__sup__class_Osup(_1589217)), _1589225)), _1589223), _1589221))], (40697 ^ _779999) ^ [_1572708, _1572710] : [-(hAPP(c_Relation_OField(_1572708), hAPP(c_Relation_Oconverse(_1572708, _1572708), _1572710)) = hAPP(c_Relation_OField(_1572708), _1572710))], (8334 ^ _779999) ^ [_921773, _921775, _921777, _921779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921773, tc_HOL_Obool)), _921775), hAPP(hAPP(c_Set_Oinsert(_921773), _921777), _921779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921773, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921773, tc_HOL_Obool)), _921775), hAPP(hAPP(c_Set_Oinsert(_921773), _921777), c_Orderings_Obot__class_Obot(tc_fun(_921773, tc_HOL_Obool))))), _921779))], (52160 ^ _779999) ^ [_1831995] : [-(class_Nat_Osize(tc_List_Olist(_1831995)))], (32981 ^ _779999) ^ [_1398468, _1398470] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398468)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398470)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398470))))], (45718 ^ _779999) ^ [_1695566, _1695568, _1695570, _1695572] : [45719 ^ _779999 : [(45720 ^ _779999) ^ [_1695663, _1695665] : [_1695566 = hAPP(hAPP(c_List_Olist_OCons(_1695568), _1695665), _1695663)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695568), tc_List_Olist(_1695568))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695568), tc_List_Olist(_1695568)), _1695570), hAPP(hAPP(c_List_Oappend(_1695568), _1695570), _1695566))), c_List_Olexord(_1695568, _1695572))))], (50383 ^ _779999) ^ [_1797726, _1797728, _1797730] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797726) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1797726, _1797728, _1797730)], (45464 ^ _779999) ^ [_1690084, _1690086, _1690088, _1690090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690084), _1690086)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690088)), _1690090))), -(hAPP(hAPP(c_List_Onth(_1690088), hAPP(hAPP(c_List_Odrop(_1690088), _1690084), _1690090)), _1690086) = hAPP(hAPP(c_List_Onth(_1690088), _1690090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690084), _1690086)))], (36162 ^ _779999) ^ [_1460824, _1460826] : [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), _1460824), _1460826))), 36165 ^ _779999 : [(36172 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460826), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36175 ^ _779999 : [(36184 ^ _779999) ^ [] : [-(c_Nitpick_Onorm__frac(_1460824, _1460826) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1460824), _1460826)), 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), _1460824))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460826)))), -(_1460824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1460826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36176 ^ _779999) ^ [] : [36177 ^ _779999 : [(36180 ^ _779999) ^ [] : [_1460826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36178 ^ _779999) ^ [] : [_1460824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1460824, _1460826) = 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)))]]], (36166 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460826), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1460824, _1460826) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1460824), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1460826)))]]], (5768 ^ _779999) ^ [_868249, _868251] : [_868251 = _868249, -(c_Hoare__Mirabelle_Otriple_Otriple(_868251) = c_Hoare__Mirabelle_Otriple_Otriple(_868249))], (31273 ^ _779999) ^ [_1365772, _1365774] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365772), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365774)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365772, _1365774)))], (28788 ^ _779999) ^ [_1320704, _1320706, _1320708] : [class_Fields_Olinordered__field(_1320704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320704), c_Groups_Ozero__class_Ozero(_1320704)), _1320706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320704), _1320708), c_Groups_Ozero__class_Ozero(_1320704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320704), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320704), _1320706), _1320708)), c_Groups_Ozero__class_Ozero(_1320704))))], (13969 ^ _779999) ^ [_1028980, _1028982, _1028984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028980), _1028982)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028984), _1028982)), _1028980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028982), _1028980)))], (29914 ^ _779999) ^ [_1340906, _1340908, _1340910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1340906), _1340908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1340906), _1340910)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1340908), _1340910))))], (43831 ^ _779999) ^ [_1651817, _1651819, _1651821, _1651823, _1651825] : [hBOOL(hAPP(hAPP(c_member(_1651817), _1651819), hAPP(c_List_Oset(_1651817), _1651821))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651823), hAPP(_1651825, _1651819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651823), c_List_Olist_Olist__size(_1651817, _1651825, _1651821))))], (36262 ^ _779999) ^ [_1462726, _1462728, _1462730] : [-(hAPP(c_Product__Type_Osnd(_1462726, _1462728), _1462730) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1462726, _1462728, _1462728), hAPP(c_COMBK(tc_fun(_1462728, _1462728), _1462726), c_COMBI(_1462728))), _1462730))], (11532 ^ _779999) ^ [_981674, _981676, _981678, _981680, _981682] : [class_Lattices_Osemilattice__inf(_981674), class_Lattices_Osemilattice__inf(_981676), c_Orderings_Oorder__class_Omono(_981676, _981674, _981678), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981674), hAPP(_981678, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981676), _981680), _981682))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981674), hAPP(_981678, _981680)), hAPP(_981678, _981682)))))], (34985 ^ _779999) ^ [_1433783] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1433783)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1433783)))], (40243 ^ _779999) ^ [_1561694, _1561696, _1561698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561694, _1561694), tc_HOL_Obool)), _1561696), hAPP(hAPP(c_Product__Type_OSigma(_1561694, _1561694), _1561698), hAPP(c_COMBK(tc_fun(_1561694, tc_HOL_Obool), _1561694), _1561698)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561694, _1561694), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1561694, _1561696)), hAPP(hAPP(c_Product__Type_OSigma(_1561694, _1561694), _1561698), hAPP(c_COMBK(tc_fun(_1561694, tc_HOL_Obool), _1561694), _1561698)))))], (48707 ^ _779999) ^ [_1760407, _1760409, _1760411] : [hBOOL(hAPP(c_List_Odistinct(_1760407), _1760409)), hBOOL(hAPP(hAPP(c_member(_1760407), _1760411), hAPP(c_List_Oset(_1760407), _1760409))), -(c_List_OtakeWhile(_1760407, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760407), c_fNot), hAPP(hAPP(c_COMBC(_1760407, _1760407, tc_HOL_Obool), c_fequal), _1760411)), hAPP(c_List_Orev(_1760407), _1760409)) = hAPP(c_List_Orev(_1760407), hAPP(c_List_Otl(_1760407), c_List_OdropWhile(_1760407, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760407), c_fNot), hAPP(hAPP(c_COMBC(_1760407, _1760407, tc_HOL_Obool), c_fequal), _1760411)), _1760409))))], (39727 ^ _779999) ^ [_1549402, _1549404, _1549406, _1549408, _1549410, _1549412, _1549414, _1549416] : [c_Finite__Set_Ofolding(_1549402, _1549404, _1549406, _1549408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549402), _1549410)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549402), _1549412)), -(hAPP(c_Fun_Ocomp(_1549404, _1549404, _1549414, hAPP(_1549408, _1549412)), hAPP(c_Fun_Ocomp(_1549404, _1549404, _1549414, hAPP(_1549408, _1549410)), _1549416)) = hAPP(c_Fun_Ocomp(_1549404, _1549404, _1549414, hAPP(_1549408, _1549410)), hAPP(c_Fun_Ocomp(_1549404, _1549404, _1549414, hAPP(_1549408, _1549412)), _1549416)))], (168 ^ _779999) ^ [_782769, _782771] : [-(class_Rings_Odivision__ring__inverse__zero(_782769)), _782771 = _782769, class_Rings_Odivision__ring__inverse__zero(_782771)], (6191 ^ _779999) ^ [_878936, _878938, _878940, _878942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878936, tc_HOL_Obool)), _878938), _878940)), hBOOL(hAPP(_878938, _878942)), -(hBOOL(hAPP(_878940, _878942)))], (40255 ^ _779999) ^ [_1562026, _1562028, _1562030, _1562032, _1562034] : [-(_1562026 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1562028, _1562030, _1562026, _1562032), _1562034) = hAPP(hAPP(c_Product__Type_Oscomp(_1562030, _1562028, _1562030, tc_prod(_1562028, _1562030)), hAPP(_1562032, _1562034)), c_Random_Oiterate(_1562028, _1562030, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1562026), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1562032)))], (20900 ^ _779999) ^ [_1159447, _1159449] : [class_Groups_Oordered__ab__group__add__abs(_1159447), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159447), c_Groups_Ozero__class_Ozero(_1159447)), _1159449)), -(hAPP(c_Groups_Oabs__class_Oabs(_1159447), _1159449) = _1159449)], (6805 ^ _779999) ^ [_891560, _891562, _891564] : [class_Orderings_Obot(_891560), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_891562, _891560)), _891564) = c_Orderings_Obot__class_Obot(_891560))], (18251 ^ _779999) ^ [_1112234, _1112236] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1112234), _1112236)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112236), _1112234))], (30746 ^ _779999) ^ [_1356278, _1356280, _1356282] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356278), _1356280)), _1356282) = 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), _1356278), _1356282)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1356280), _1356282))), 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, _1356278, _1356282)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356280, _1356282))), _1356282)))], (45534 ^ _779999) ^ [_1691885, _1691887, _1691889, _1691891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1691885), _1691887)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691889)), _1691891))), -(hAPP(hAPP(c_List_Otake(_1691889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1691885), _1691887)), _1691891) = hAPP(hAPP(c_List_Oappend(_1691889), hAPP(hAPP(c_List_Otake(_1691889), _1691885), _1691891)), hAPP(hAPP(c_List_Otake(_1691889), _1691887), hAPP(hAPP(c_List_Odrop(_1691889), _1691885), _1691891))))], (19926 ^ _779999) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (6785 ^ _779999) ^ [_891178, _891180, _891182] : [class_Orderings_Obot(_891178), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_891180, _891178)), _891182) = c_Orderings_Obot__class_Obot(_891178))], (5312 ^ _779999) ^ [_861301, _861303] : [_861303 = _861301, -(c_Relation_OId(_861303) = c_Relation_OId(_861301))], (44270 ^ _779999) ^ [_1663691, _1663693, _1663695] : [hBOOL(hAPP(c_List_Odistinct(_1663691), _1663693)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1663691)), c_Enum_On__lists(_1663691, _1663695, _1663693))))], (42950 ^ _779999) ^ [_1626934, _1626936, _1626938, _1626940, _1626942, _1626944, _1626946] : [c_Finite__Set_Ofolding__image__simple__idem(_1626934, _1626936, _1626938, _1626940, _1626942, _1626944), -(hAPP(hAPP(_1626938, _1626946), _1626946) = _1626946)], (38279 ^ _779999) ^ [_1511632, _1511634] : [-(c_Nitpick_Onumber__of__frac(_1511632, _1511634) = c_Nitpick_OAbs__Frac(_1511632, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1511634), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48010 ^ _779999) ^ [_1746045, _1746047, _1746049, _1746051] : [class_Orderings_Olinorder(_1746045), -(c_List_Olinorder__class_Osorted(_1746045, hAPP(hAPP(c_List_Omap(_1746047, _1746045), _1746049), c_List_Olinorder__class_Osort__key(_1746047, _1746045, _1746049, _1746051))))], (45053 ^ _779999) ^ [_1680508, _1680510, _1680512] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680508)), hAPP(hAPP(c_List_Oappend(_1680508), _1680510), _1680512)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680508)), _1680510)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680508)), _1680512)))], (11306 ^ _779999) ^ [_976009, _976011, _976013, _976015] : [class_Lattices_Odistrib__lattice(_976009), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976009), _976011), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976009), _976013), _976015)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976009), _976011), _976013)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976009), _976011), _976015)))], (39475 ^ _779999) ^ [_1543572, _1543574, _1543576, _1543578, _1543580, _1543582] : [c_Fun_Oinj__on(_1543572, _1543574, _1543576, _1543578), 39478 ^ _779999 : [(39485 ^ _779999) ^ [] : [c_Fun_Oinj__on(_1543572, _1543580, hAPP(c_Fun_Ocomp(_1543574, _1543580, _1543572, _1543582), _1543576), _1543578), -(c_Fun_Oinj__on(_1543574, _1543580, _1543582, hAPP(c_Set_Oimage(_1543572, _1543574, _1543576), _1543578)))], (39479 ^ _779999) ^ [] : [c_Fun_Oinj__on(_1543574, _1543580, _1543582, hAPP(c_Set_Oimage(_1543572, _1543574, _1543576), _1543578)), -(c_Fun_Oinj__on(_1543572, _1543580, hAPP(c_Fun_Ocomp(_1543574, _1543580, _1543572, _1543582), _1543576), _1543578))]]], (33239 ^ _779999) ^ [_1402388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1402388)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402388), c_Int_OPls)))], (13912 ^ _779999) ^ [_1027891, _1027893] : [13913 ^ _779999 : [(13916 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027893))], (13914 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027891))]], -(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), _1027891), _1027893))))], (30306 ^ _779999) ^ [_1347754, _1347756, _1347758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347754)), 30309 ^ _779999 : [(30310 ^ _779999) ^ [] : [-(_1347756 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1347758), _1347754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1347754), _1347756)), _1347758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1347758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1347754), hAPP(c_Nat_OSuc, _1347756))))], (30320 ^ _779999) ^ [] : [_1347756 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1347758), _1347754), 30323 ^ _779999 : [(30326 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1347758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1347754), hAPP(c_Nat_OSuc, _1347756)))))], (30324 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1347754), _1347756)), _1347758)))]]]]], (7199 ^ _779999) ^ [_898906, _898908, _898910, _898912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898906, tc_HOL_Obool)), _898908), _898910)), hBOOL(hAPP(hAPP(c_member(_898906), _898912), _898908)), -(hBOOL(hAPP(hAPP(c_member(_898906), _898912), _898910)))], (13501 ^ _779999) ^ [_1020556, _1020558, _1020560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020556), _1020558)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020556), _1020560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020558), _1020560)))], (19861 ^ _779999) ^ [_1142273, _1142275] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142273), _1142275))), -(c_Nat__Transfer_Otsub(_1142275, _1142273) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8431 ^ _779999) ^ [_924213, _924215, _924217, _924219, _924221] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_924213, _924215, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_924213), _924217), _924219), _924221)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18085 ^ _779999) ^ [_1109199, _1109201] : [18093 ^ _779999 : [(18096 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1109201, 18092 ^ [_1109199, _1109201])))], (18094 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 18092 ^ [_1109199, _1109201]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109199))))]], 18086 ^ _779999 : [(18087 ^ _779999) ^ [_1109267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109267), _1109199)), hBOOL(hAPP(_1109201, _1109267))]]], (3608 ^ _779999) ^ [_834093, _834095] : [_834095 = _834093, -(c_Int_OBit1(_834095) = c_Int_OBit1(_834093))], (51938 ^ _779999) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52318 ^ _779999) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (17239 ^ _779999) ^ [_1092255, _1092257, _1092259, _1092261, _1092263, _1092265] : [class_Rings_Oordered__ring(_1092255), 17242 ^ _779999 : [(17249 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092255), _1092261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092255), _1092263), _1092257)), _1092259)), _1092265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092255), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), _1092257), _1092259)), _1092261)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), _1092263), _1092259)), _1092265))))], (17243 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092255), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), _1092257), _1092259)), _1092261)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), _1092263), _1092259)), _1092265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092255), _1092261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092255), _1092263), _1092257)), _1092259)), _1092265))))]]], (13041 ^ _779999) ^ [_1012047, _1012049, _1012051, _1012053] : [class_Groups_Ocancel__ab__semigroup__add(_1012047), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012047), _1012049), _1012051) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012047), _1012049), _1012053), -(_1012051 = _1012053)], (22882 ^ _779999) ^ [_1205328, _1205330, _1205332, _1205334, _1205336] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205328, tc_fun(_1205330, tc_HOL_Obool)), _1205332), hAPP(hAPP(c_COMBC(_1205328, tc_fun(_1205330, tc_HOL_Obool), tc_fun(_1205330, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205330, tc_HOL_Obool), tc_fun(tc_fun(_1205330, tc_HOL_Obool), tc_fun(_1205330, tc_HOL_Obool)), _1205328), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205330, tc_HOL_Obool))), _1205334)), _1205336)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205330, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205328, tc_fun(_1205330, tc_HOL_Obool)), _1205332), _1205334)), _1205336))], (29704 ^ _779999) ^ [_1337027, _1337029, _1337031, _1337033] : [class_Divides_Osemiring__div(_1337027), -(_1337029 = c_Groups_Ozero__class_Ozero(_1337027)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337027), _1337031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337027), _1337033), _1337029))), _1337029) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337027), _1337033), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337027), _1337031), _1337029)))], (17838 ^ _779999) ^ [_1104845, _1104847] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1104845), _1104847))))], (8449 ^ _779999) ^ [_924542, _924544, _924546, _924548] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_924542)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_924542), _924544), _924546), _924548)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51944 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (25096 ^ _779999) ^ [_1250835, _1250837, _1250839] : [class_Orderings_Olinorder(_1250835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250835), _1250837)), 25103 ^ _779999 : [(25110 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250835, tc_HOL_Obool)), _1250837), hAPP(hAPP(c_Set_Oinsert(_1250835), _1250839), c_Orderings_Obot__class_Obot(tc_fun(_1250835, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1250835, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1250835, c_Orderings_Oord__class_Omax(_1250835), hAPP(hAPP(c_Set_Oinsert(_1250835), _1250839), _1250837)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250835), _1250839), c_Big__Operators_Olattice_OSup__fin(_1250835, c_Orderings_Oord__class_Omax(_1250835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250835, tc_HOL_Obool)), _1250837), hAPP(hAPP(c_Set_Oinsert(_1250835), _1250839), c_Orderings_Obot__class_Obot(tc_fun(_1250835, tc_HOL_Obool)))))))], (25104 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250835, tc_HOL_Obool)), _1250837), hAPP(hAPP(c_Set_Oinsert(_1250835), _1250839), c_Orderings_Obot__class_Obot(tc_fun(_1250835, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1250835, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1250835, c_Orderings_Oord__class_Omax(_1250835), hAPP(hAPP(c_Set_Oinsert(_1250835), _1250839), _1250837)) = _1250839)]]], (45833 ^ _779999) ^ [_1698040, _1698042, _1698044, _1698046] : [class_Complete__Lattice_Ocomplete__lattice(_1698040), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1698042, _1698040), hAPP(c_List_Oset(_1698042), _1698044)), _1698046) = hAPP(c_List_Ofoldl(_1698040, _1698042, hAPP(c_COMBC(_1698042, _1698040, _1698040), hAPP(hAPP(c_COMBB(_1698040, tc_fun(_1698040, _1698040), _1698042), c_Lattices_Osemilattice__sup__class_Osup(_1698040)), _1698046)), c_Orderings_Obot__class_Obot(_1698040)), _1698044))], (35693 ^ _779999) ^ [_1452611, _1452613, _1452615, _1452617, _1452619] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1452611, _1452613, _1452615), _1452617), _1452619)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452611, _1452613)), hAPP(hAPP(c_Product__Type_OPair(_1452611, _1452613), _1452617), _1452619)), _1452615)))], (13796 ^ _779999) ^ [_1026129, _1026131, _1026133] : [class_Groups_Oordered__comm__monoid__add(_1026129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026129), c_Groups_Ozero__class_Ozero(_1026129)), _1026131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026129), c_Groups_Ozero__class_Ozero(_1026129)), _1026133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026129), c_Groups_Ozero__class_Ozero(_1026129)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026129), _1026131), _1026133))))], (41984 ^ _779999) ^ [_1603814, _1603816, _1603818, _1603820, _1603822, _1603824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603814, tc_fun(_1603816, tc_HOL_Obool)), _1603818), hAPP(hAPP(c_COMBB(_1603820, tc_fun(_1603816, tc_HOL_Obool), _1603814), _1603822), _1603824)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603820, tc_fun(_1603816, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1603814, _1603820, _1603824), _1603818)), _1603822))], (4622 ^ _779999) ^ [_850208, _850210, _850212, _850214, _850216, _850218, _850220, _850222, _850224, _850226] : [-(c_Predicate_Opred__comp(_850226, _850222, _850218, _850214, _850210) = c_Predicate_Opred__comp(_850224, _850220, _850216, _850212, _850208)), _850226 = _850224, _850222 = _850220, _850218 = _850216, _850214 = _850212, _850210 = _850208], (40929 ^ _779999) ^ [_1578618, _1578620, _1578622, _1578624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578618, _1578618)), _1578620), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578618, _1578618), tc_HOL_Obool), _1578622), _1578624))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578618, _1578618)), _1578620), c_Transitive__Closure_Ortrancl(_1578618, _1578624))))], (41920 ^ _779999) ^ [_1601634, _1601636, _1601638, _1601640, _1601642, _1601644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601636, _1601638)), hAPP(hAPP(c_Product__Type_OPair(_1601636, _1601638), _1601642), _1601644)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601634, tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601634, tc_HOL_Obool))), _1601640))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601634, tc_fun(_1601636, tc_fun(_1601638, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1601634, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_fun(_1601636, tc_fun(_1601638, tc_HOL_Obool)), _1601634), hAPP(c_COMBC(_1601636, tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_fun(_1601638, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601638, tc_fun(tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_fun(_1601638, tc_HOL_Obool)), _1601636), c_COMBC(_1601638, tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601638, tc_prod(_1601636, _1601638)), tc_fun(_1601638, tc_fun(tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_HOL_Obool)), _1601636), hAPP(c_COMBB(tc_prod(_1601636, _1601638), tc_fun(tc_fun(tc_prod(_1601636, _1601638), tc_HOL_Obool), tc_HOL_Obool), _1601638), c_member(tc_prod(_1601636, _1601638)))), c_Product__Type_OPair(_1601636, _1601638))))), _1601640)), _1601642), _1601644)))], (11845 ^ _779999) ^ [_988238, _988240, _988242] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988238), _988242)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988238), hAPP(hAPP(c_Set_Oinsert(_988238), _988240), _988242))))], (15006 ^ _779999) ^ [_1049269, _1049271, _1049273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049269), _1049271)), hBOOL(hAPP(hAPP(c_member(_1049269), _1049273), _1049271)), -(hAPP(c_Finite__Set_Ocard(_1049269), _1049271) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1049269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049269, tc_HOL_Obool)), _1049271), hAPP(hAPP(c_Set_Oinsert(_1049269), _1049273), c_Orderings_Obot__class_Obot(tc_fun(_1049269, tc_HOL_Obool)))))))], (40689 ^ _779999) ^ [_1572498, _1572500] : [-(hAPP(c_Relation_Oconverse(_1572498, _1572498), c_Relation_OId__on(_1572498, _1572500)) = c_Relation_OId__on(_1572498, _1572500))], (34259 ^ _779999) ^ [_1420797, _1420799] : [class_Rings_Oring__1__no__zero__divisors(_1420797), 34262 ^ _779999 : [(34269 ^ _779999) ^ [] : [_1420799 = c_Groups_Ozero__class_Ozero(_1420797), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1420797), _1420799), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1420797))], (34263 ^ _779999) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1420797), _1420799), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1420797), -(_1420799 = c_Groups_Ozero__class_Ozero(_1420797))]]], (41219 ^ _779999) ^ [_1586416, _1586418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586416, _1586416)), _1586418), c_Relation_OId(_1586416))), -(_1586418 = hAPP(hAPP(c_Product__Type_OPair(_1586416, _1586416), 41222 ^ [_1586416, _1586418]), 41222 ^ [_1586416, _1586418]))], (44176 ^ _779999) ^ [_1661504, _1661506, _1661508, _1661510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661504, tc_HOL_Obool)), hAPP(c_List_Oset(_1661504), hAPP(hAPP(c_List_Olist__update(_1661504, _1661506), _1661508), _1661510))), hAPP(hAPP(c_Set_Oinsert(_1661504), _1661510), hAPP(c_List_Oset(_1661504), _1661506)))))], (9114 ^ _779999) ^ [_935801, _935803, _935805] : [class_Orderings_Olinorder(_935801), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935801), _935803), _935805))), -(_935803 = _935805), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935801), _935805), _935803)))], (36859 ^ _779999) ^ [_1475761, _1475763, _1475765, _1475767, _1475769] : [hAPP(c_Relation_OImage(_1475761, _1475761, _1475763), hAPP(hAPP(c_Set_Oinsert(_1475761), _1475765), c_Orderings_Obot__class_Obot(tc_fun(_1475761, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475761, _1475761, _1475763), hAPP(hAPP(c_Set_Oinsert(_1475761), _1475767), c_Orderings_Obot__class_Obot(tc_fun(_1475761, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1475761, _1475769, _1475763), hBOOL(hAPP(hAPP(c_member(_1475761), _1475767), _1475769)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475761, _1475761)), hAPP(hAPP(c_Product__Type_OPair(_1475761, _1475761), _1475765), _1475767)), _1475763)))], (42622 ^ _779999) ^ [_1619466, _1619468, _1619470] : [class_Complete__Lattice_Ocomplete__lattice(_1619466), -(c_Complete__Lattice_OSup__class_OSup(_1619466, hAPP(hAPP(c_Set_Oinsert(_1619466), _1619468), hAPP(hAPP(c_Set_Oinsert(_1619466), _1619470), c_Orderings_Obot__class_Obot(tc_fun(_1619466, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1619466), _1619468), _1619470))], (43329 ^ _779999) ^ [_1637630, _1637632, _1637634, _1637636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637630), tc_List_Olist(_1637630))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637630), tc_List_Olist(_1637630)), _1637632), _1637634)), c_List_Olistrel1(_1637630, _1637636))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637630)), _1637632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637630)), _1637634))], (33461 ^ _779999) ^ [_1405910, _1405912] : [class_Int_Onumber__ring(_1405910), -(hAPP(c_Int_Onumber__class_Onumber__of(_1405910), c_Int_Opred(_1405912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405910), hAPP(c_Groups_Ouminus__class_Ouminus(_1405910), c_Groups_Oone__class_Oone(_1405910))), hAPP(c_Int_Onumber__class_Onumber__of(_1405910), _1405912)))], (37648 ^ _779999) ^ [_1495744, _1495746, _1495748, _1495750, _1495752] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1495744, _1495746, _1495748), _1495750), _1495752) = hAPP(c_Set_OCollect(tc_prod(_1495744, _1495748)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495744, _1495748, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1495748, tc_fun(_1495746, tc_HOL_Obool)), tc_fun(_1495748, tc_HOL_Obool), _1495744), hAPP(c_COMBB(tc_fun(_1495746, tc_HOL_Obool), tc_HOL_Obool, _1495748), c_HOL_OEx(_1495746))), hAPP(hAPP(c_COMBC(_1495744, tc_fun(_1495748, tc_fun(_1495746, tc_HOL_Obool)), tc_fun(_1495748, tc_fun(_1495746, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1495746, tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), tc_fun(tc_fun(_1495748, tc_fun(_1495746, tc_HOL_Obool)), tc_fun(_1495748, tc_fun(_1495746, tc_HOL_Obool))), _1495744), c_COMBB(tc_fun(_1495746, tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool), _1495748)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1495746, tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), _1495744), c_COMBS(_1495746, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_HOL_Obool), tc_fun(_1495746, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1495744), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495746), c_fconj)), hAPP(hAPP(c_COMBC(_1495744, tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_fun(tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), _1495744), c_COMBC(_1495746, tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_prod(_1495744, _1495746)), tc_fun(_1495746, tc_fun(tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_HOL_Obool)), _1495744), hAPP(c_COMBB(tc_prod(_1495744, _1495746), tc_fun(tc_fun(tc_prod(_1495744, _1495746), tc_HOL_Obool), tc_HOL_Obool), _1495746), c_member(tc_prod(_1495744, _1495746)))), c_Product__Type_OPair(_1495744, _1495746)))), _1495750))))), hAPP(hAPP(c_COMBC(_1495748, tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_fun(tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_fun(_1495746, tc_HOL_Obool)), _1495748), c_COMBC(_1495746, tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495746, tc_prod(_1495746, _1495748)), tc_fun(_1495746, tc_fun(tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_HOL_Obool)), _1495748), hAPP(c_COMBB(tc_prod(_1495746, _1495748), tc_fun(tc_fun(tc_prod(_1495746, _1495748), tc_HOL_Obool), tc_HOL_Obool), _1495746), c_member(tc_prod(_1495746, _1495748)))), hAPP(c_COMBC(_1495746, _1495748, tc_prod(_1495746, _1495748)), c_Product__Type_OPair(_1495746, _1495748))))), _1495752))))))], (37493 ^ _779999) ^ [_1490998, _1491000, _1491002, _1491004] : [_1490998 = _1491000, hBOOL(hAPP(hAPP(c_member(_1491002), _1490998), _1491004)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491002, _1491002)), hAPP(hAPP(c_Product__Type_OPair(_1491002, _1491002), _1490998), _1491000)), c_Relation_OId__on(_1491002, _1491004))))], (52108 ^ _779999) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (32403 ^ _779999) ^ [_1387658, _1387660, _1387662, _1387664] : [class_Int_Onumber__ring(_1387658), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387658), hAPP(c_Int_Onumber__class_Onumber__of(_1387658), _1387660)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387658), _1387662), hAPP(c_Int_Onumber__class_Onumber__of(_1387658), _1387664))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387658), hAPP(c_Int_Onumber__class_Onumber__of(_1387658), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1387660), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1387664)))), _1387662))], (5694 ^ _779999) ^ [_867122, _867124] : [_867124 = _867122, -(c_Orderings_Oord__class_Oless__eq(_867124) = c_Orderings_Oord__class_Oless__eq(_867122))], (43104 ^ _779999) ^ [_1630413, _1630415, _1630417, _1630419] : [class_Rings_Olinordered__semidom(_1630413), 43110 ^ _779999 : [(43113 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1630413), c_Groups_Ozero__class_Ozero(_1630413)), hAPP(_1630419, 43109 ^ [_1630413, _1630415, _1630417, _1630419])))], (43111 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630415), 43109 ^ [_1630413, _1630415, _1630417, _1630419]), _1630417)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1630413), c_Groups_Ozero__class_Ozero(_1630413)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1630415, _1630413), _1630419), _1630417))))], (44099 ^ _779999) ^ [_1659635, _1659637, _1659639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659635), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659637)), _1659639))), -(hAPP(hAPP(c_List_Otake(_1659637), _1659635), c_List_Obutlast(_1659637, _1659639)) = hAPP(hAPP(c_List_Otake(_1659637), _1659635), _1659639))], (9330 ^ _779999) ^ [_938937, _938939, _938941] : [class_Orderings_Olinorder(_938937), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938937), _938939), _938941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938937), _938941), _938939)))], (52330 ^ _779999) ^ [_1833825, _1833827, _1833829, _1833831] : [-(hAPP(hAPP(c_COMBK(_1833825, _1833827), _1833829), _1833831) = _1833829)], (52000 ^ _779999) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (19621 ^ _779999) ^ [_1137725, _1137727, _1137729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137725)), 19624 ^ _779999 : [(19625 ^ _779999) ^ [_1137859] : [19627 ^ _779999 : [(19633 ^ _779999) ^ [] : [-(_1137859 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19629 ^ [_1137725, _1137727, _1137729, _1137859]), 19626 ^ [_1137725, _1137727, _1137729, _1137859]))], (19631 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19629 ^ [_1137725, _1137727, _1137729, _1137859]), _1137727)))], (19628 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19626 ^ [_1137725, _1137727, _1137729, _1137859]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1137725))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137729), _1137859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137729), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1137859), _1137725))))]]], (1344 ^ _779999) ^ [_799907, _799909] : [-(class_Int_Onumber__ring(_799907)), _799909 = _799907, class_Int_Onumber__ring(_799909)], (41955 ^ _779999) ^ [_1602853, _1602855, _1602857, _1602859] : [41957 ^ _779999 : [(41960 ^ _779999) ^ [] : [hAPP(_1602859, 41956 ^ [_1602853, _1602855, _1602857, _1602859]) = c_Orderings_Otop__class_Otop(tc_fun(_1602855, tc_HOL_Obool))], (41958 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602853), 41956 ^ [_1602853, _1602855, _1602857, _1602859]), _1602857)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602853, tc_fun(_1602855, tc_HOL_Obool)), _1602857), _1602859) = c_Orderings_Otop__class_Otop(tc_fun(_1602855, tc_HOL_Obool)))], (22097 ^ _779999) ^ [] : [-(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))))], (44879 ^ _779999) ^ [_1676499, _1676501, _1676503, _1676505, _1676507] : [-(hAPP(hAPP(c_List_Oappend(_1676499), _1676501), _1676503) = hAPP(hAPP(c_List_Olist_OCons(_1676499), _1676505), _1676507)), 44880 ^ _779999 : [(44887 ^ _779999) ^ [_1676682] : [_1676501 = hAPP(hAPP(c_List_Olist_OCons(_1676499), _1676505), _1676682), hAPP(hAPP(c_List_Oappend(_1676499), _1676682), _1676503) = _1676507], (44881 ^ _779999) ^ [] : [_1676501 = c_List_Olist_ONil(_1676499), _1676503 = hAPP(hAPP(c_List_Olist_OCons(_1676499), _1676505), _1676507)]]], (47705 ^ _779999) ^ [_1740636, _1740638] : [47706 ^ _779999 : [(47709 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1740638), _1740636))], (47707 ^ _779999) ^ [] : [_1740638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1740636, _1740638) = c_List_Olist_ONil(tc_Nat_Onat))], (9048 ^ _779999) ^ [_934737, _934739, _934741, _934743] : [class_Orderings_Oord(_934737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934737), _934739), _934741)), _934741 = _934743, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934737), _934739), _934743)))], (52326 ^ _779999) ^ [_1833771] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1833771)))], (50698 ^ _779999) ^ [_1804959, _1804961, _1804963, _1804965] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1804959, tc_fun(_1804961, tc_HOL_Obool)), _1804963), _1804965) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1804961, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1804961, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1804959, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1804961, tc_HOL_Obool)), c_HOL_OEx(_1804959)), hAPP(hAPP(c_COMBB(tc_fun(_1804959, tc_HOL_Obool), tc_fun(_1804959, tc_HOL_Obool), tc_fun(_1804961, tc_HOL_Obool)), hAPP(c_COMBS(_1804959, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1804959), c_fconj), hAPP(hAPP(c_COMBC(_1804959, tc_fun(_1804959, tc_HOL_Obool), tc_HOL_Obool), c_member(_1804959)), _1804963)))), hAPP(hAPP(c_COMBC(tc_fun(_1804961, tc_HOL_Obool), tc_fun(_1804959, tc_fun(_1804961, tc_HOL_Obool)), tc_fun(_1804959, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1804961, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1804959, tc_fun(_1804961, tc_HOL_Obool)), tc_fun(_1804959, tc_HOL_Obool)), tc_fun(_1804961, tc_HOL_Obool)), c_COMBB(tc_fun(_1804961, tc_HOL_Obool), tc_HOL_Obool, _1804959)), c_fequal)), _1804965))))))], (46011 ^ _779999) ^ [_1701760, _1701762, _1701764, _1701766, _1701768] : [class_Orderings_Olinorder(_1701760), hBOOL(hAPP(hAPP(c_member(_1701760), hAPP(_1701762, _1701764)), hAPP(c_Set_Oimage(_1701766, _1701760, _1701762), hAPP(c_List_Oset(_1701766), _1701768)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1701766, _1701760, _1701762, _1701764, _1701768) = _1701768)], (15707 ^ _779999) ^ [_1063308, _1063310, _1063312, _1063314] : [class_Rings_Ocomm__semiring__1(_1063308), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063308), _1063310), _1063312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063308), _1063314), _1063312)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063308), _1063310), _1063314)), _1063312))], (45598 ^ _779999) ^ [_1693335, _1693337] : [-(_1693335 = c_List_Olist_ONil(_1693337)), -(hAPP(c_List_Ohd(_1693337), _1693335) = hAPP(hAPP(c_List_Onth(_1693337), _1693335), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19459 ^ _779999) ^ [_1134831, _1134833] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134831) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134833), -(_1134831 = _1134833)], (31212 ^ _779999) ^ [_1364837] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364837, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21289 ^ _779999) ^ [_1167563, _1167565, _1167567] : [class_Orderings_Olinorder(_1167563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167563), _1167565), _1167567)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1167563, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1167563, _1167565, _1167567)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1167563), _1167567)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1167563), _1167565))], (4402 ^ _779999) ^ [_846896, _846898, _846900, _846902] : [-(c_Lazy__Sequence_Ohb__single(_846902, _846898) = c_Lazy__Sequence_Ohb__single(_846900, _846896)), _846902 = _846900, _846898 = _846896], (15825 ^ _779999) ^ [_1065237] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065237), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33033 ^ _779999) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (31176 ^ _779999) ^ [_1364251, _1364253, _1364255] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364251, _1364253)), _1364255) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364251), _1364255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364253), _1364255)))], (15221 ^ _779999) ^ [_1053479, _1053481] : [class_Rings_Ocomm__semiring__1(_1053479), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053479), _1053481), c_Groups_Ozero__class_Ozero(_1053479)) = _1053481)], (21976 ^ _779999) ^ [_1183849] : [-(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)))), _1183849))))], (33455 ^ _779999) ^ [_1405791, _1405793] : [class_Int_Onumber__ring(_1405791), -(hAPP(c_Int_Onumber__class_Onumber__of(_1405791), c_Int_Osucc(_1405793)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405791), c_Groups_Oone__class_Oone(_1405791)), hAPP(c_Int_Onumber__class_Onumber__of(_1405791), _1405793)))], (6119 ^ _779999) ^ [_877563, _877565, _877567, _877569] : [class_Lattices_Osemilattice__sup(_877563), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877563), _877565), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877563), _877567), _877569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877563), _877567), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877563), _877565), _877569)))], (29724 ^ _779999) ^ [_1337383, _1337385, _1337387] : [class_Divides_Osemiring__div(_1337383), -(_1337385 = c_Groups_Ozero__class_Ozero(_1337383)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337383), _1337387), _1337385)), _1337385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337383), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1337383), _1337387), _1337385)), c_Groups_Oone__class_Oone(_1337383)))], (3726 ^ _779999) ^ [_835908, _835910, _835912, _835914, _835916, _835918] : [-(c_List_Osublist(_835918, _835914, _835910) = c_List_Osublist(_835916, _835912, _835908)), _835918 = _835916, _835914 = _835912, _835910 = _835908], (49714 ^ _779999) ^ [_1782759, _1782761, _1782763, _1782765, _1782767] : [-(hAPP(c_New__DSequence_Oneg__bind(_1782759, _1782761, _1782763, _1782765), _1782767) = c_Lazy__Sequence_Ohb__bind(_1782759, _1782761, hAPP(_1782763, _1782767), hAPP(hAPP(c_COMBC(_1782759, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1782761))), _1782765), _1782767)))], (7719 ^ _779999) ^ [_909648, _909650] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909648), _909650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909650)), _909648)))], (41059 ^ _779999) ^ [_1582022, _1582024, _1582026, _1582028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582022, _1582024), tc_HOL_Obool)), _1582026), _1582028)), c_Relation_Osingle__valued(_1582022, _1582024, _1582028), -(c_Relation_Osingle__valued(_1582022, _1582024, _1582026))], (37533 ^ _779999) ^ [_1492455, _1492457, _1492459, _1492461] : [c_FunDef_Oreduction__pair(_1492455, _1492457), -(c_FunDef_Oreduction__pair(_1492459, hAPP(hAPP(c_FunDef_Orp__inv__image(_1492455, _1492459), _1492457), _1492461)))], (11440 ^ _779999) ^ [_979401, _979403, _979405, _979407, _979409] : [c_Fun_Oinj__on(_979401, _979403, _979405, _979407), c_Fun_Oinj__on(_979401, _979403, _979405, _979409), -(c_Fun_Oinj__on(_979401, _979403, _979405, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979401, tc_HOL_Obool)), _979407), _979409)))], (15177 ^ _779999) ^ [_1052694, _1052696, _1052698, _1052700] : [hBOOL(hAPP(hAPP(_1052698, _1052696), _1052700)), -(hBOOL(hAPP(hAPP(c_member(_1052694), _1052696), c_SetInterval_Oord_OatMost(_1052694, _1052698, _1052700))))], (49794 ^ _779999) ^ [_1784826, _1784828, _1784830, _1784832, _1784834] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1784826, _1784828, _1784830), _1784832), _1784834)), -(hBOOL(hAPP(hAPP(_1784830, _1784834), _1784832)))], (36256 ^ _779999) ^ [_1462613, _1462615, _1462617, _1462619, _1462621] : [hAPP(c_Product__Type_Osnd(_1462613, _1462615), hAPP(hAPP(c_Product__Type_OPair(_1462613, _1462615), _1462617), _1462619)) = _1462621, -(_1462619 = _1462621)], (25866 ^ _779999) ^ [_1264841, _1264843, _1264845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264841, tc_HOL_Obool)), _1264845), _1264843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264841, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264841, tc_HOL_Obool)), _1264843)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264841, tc_HOL_Obool)), _1264845))))], (33705 ^ _779999) ^ [_1410688] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410688)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410688)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1410688)))], (47657 ^ _779999) ^ [_1739870, _1739872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739870), _1739872)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1739870, _1739872)) = _1739870)], (36447 ^ _779999) ^ [_1466394, _1466396, _1466398, _1466400] : [hAPP(c_Product__Type_Ofst(_1466394, _1466396), _1466398) = hAPP(c_Product__Type_Ofst(_1466394, _1466396), _1466400), hAPP(c_Product__Type_Osnd(_1466394, _1466396), _1466398) = hAPP(c_Product__Type_Osnd(_1466394, _1466396), _1466400), -(_1466398 = _1466400)], (4768 ^ _779999) ^ [_852615, _852617] : [_852617 = _852615, -(c_Lazy__Sequence_Oyield(_852617) = c_Lazy__Sequence_Oyield(_852615))], (20385 ^ _779999) ^ [_1150973, _1150975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150973)), 20388 ^ _779999 : [(20395 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150973), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1150973)), _1150975)))], (20389 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1150973)), _1150975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150973), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150975))))]]], (6655 ^ _779999) ^ [_888504, _888506, _888508, _888510, _888512] : [c_Hoare__Mirabelle_Ohoare__derivs(_888504, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_888504)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888504), _888506), hAPP(c_Com_Ocom_OBODY, _888508)), _888510)), _888512), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_888504)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888504), _888506), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888508))), _888510)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_888504), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_888504, _888512, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_888504)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888504), _888506), hAPP(c_Com_Ocom_OBODY, _888508)), _888510)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_888504), tc_HOL_Obool)))))], (26769 ^ _779999) ^ [_1282125, _1282127, _1282129, _1282131] : [hAPP(c_Set_Oimage(_1282125, _1282127, _1282129), c_Orderings_Otop__class_Otop(tc_fun(_1282125, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1282127, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282127, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1282127, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1282125, _1282127, _1282129), _1282131))), hAPP(c_Set_Oimage(_1282125, _1282127, _1282129), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1282125, tc_HOL_Obool)), _1282131)))))], (40369 ^ _779999) ^ [_1565500, _1565502, _1565504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565500, _1565500), tc_HOL_Obool)), _1565502), _1565504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565500, _1565500), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565500, _1565502)), c_Transitive__Closure_Ortrancl(_1565500, _1565504))))], (11386 ^ _779999) ^ [_977799, _977801, _977803] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977799, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977799, tc_HOL_Obool)), _977801), _977803)), _977801)))], (10249 ^ _779999) ^ [_956505, _956507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956505), _956507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956505), hAPP(c_Nat_OSuc, _956507))))], (48816 ^ _779999) ^ [_1762726, _1762728, _1762730] : [-(c_List_OdropWhile(_1762726, _1762728, _1762730) = hAPP(hAPP(c_List_Odrop(_1762726), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762726)), c_List_OtakeWhile(_1762726, _1762728, _1762730))), _1762730))], (15537 ^ _779999) ^ [_1060104, _1060106, _1060108, _1060110] : [class_Rings_Ocomm__semiring__1(_1060104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060104), _1060106), _1060108)), _1060110) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060104), _1060106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060104), _1060108), _1060110)))], (39389 ^ _779999) ^ [_1541700, _1541702, _1541704, _1541706, _1541708, _1541710, _1541712, _1541714, _1541716, _1541718, _1541720] : [hAPP(_1541700, hAPP(_1541702, _1541704)) = hAPP(_1541706, hAPP(_1541708, _1541710)), -(hAPP(hAPP(c_Fun_Ocomp(_1541712, _1541714, _1541716, _1541700), _1541702), _1541704) = hAPP(hAPP(c_Fun_Ocomp(_1541718, _1541714, _1541720, _1541706), _1541708), _1541710))], (47729 ^ _779999) ^ [_1741073, _1741075, _1741077, _1741079] : [c_List_Oupt(_1741073, _1741075) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1741077), _1741079), 47732 ^ _779999 : [(47737 ^ _779999) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741073), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1741075) = _1741079)], (47735 ^ _779999) ^ [] : [-(_1741073 = _1741077)], (47733 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741073), _1741075)))]]], (43719 ^ _779999) ^ [_1648965, _1648967, _1648969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648965)), _1648967)), _1648969)), -(hAPP(hAPP(c_List_Otake(_1648965), _1648969), _1648967) = _1648967)], (41268 ^ _779999) ^ [_1587404, _1587406, _1587408, _1587410] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1587404, _1587406, _1587408), _1587410), c_Orderings_Obot__class_Obot(tc_fun(_1587404, tc_HOL_Obool))) = _1587410)], (27764 ^ _779999) ^ [_1302078, _1302080, _1302082] : [class_Rings_Olinordered__semidom(_1302078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302078), c_Groups_Ozero__class_Ozero(_1302078)), _1302080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302078), c_Groups_Ozero__class_Ozero(_1302078)), hAPP(hAPP(c_Power_Opower__class_Opower(_1302078), _1302080), _1302082))))], (26869 ^ _779999) ^ [_1284584, _1284586, _1284588, _1284590] : [class_Groups_Ocomm__monoid__mult(_1284584), 26872 ^ _779999 : [(26879 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284586), _1284588))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284586, _1284584), _1284590), _1284588) = c_Groups_Oone__class_Oone(_1284584))], (26873 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284586), _1284588)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284586, _1284584), _1284590), _1284588) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1284584, _1284586, c_Groups_Otimes__class_Otimes(_1284584)), _1284590), c_Groups_Oone__class_Oone(_1284584)), _1284588))]]], (52172 ^ _779999) ^ [_1832148, _1832150] : [-(class_Enum_Oenum(tc_sum(_1832148, _1832150))), class_Enum_Oenum(_1832148), class_Enum_Oenum(_1832150)], (3322 ^ _779999) ^ [_829640, _829642, _829644, _829646] : [-(c_Nitpick_Ocard_H(_829646, _829642) = c_Nitpick_Ocard_H(_829644, _829640)), _829646 = _829644, _829642 = _829640], (52072 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (23457 ^ _779999) ^ [_1217802, _1217804, _1217806, _1217808] : [-(hAPP(c_Set_Ovimage(_1217802, _1217804, _1217806), hAPP(c_Set_OCollect(_1217804), _1217808)) = hAPP(c_Set_OCollect(_1217802), hAPP(hAPP(c_COMBB(_1217804, tc_HOL_Obool, _1217802), _1217808), _1217806)))], (47406 ^ _779999) ^ [_1733269, _1733271, _1733273, _1733275, _1733277] : [class_Orderings_Olinorder(_1733269), -(hAPP(c_List_Ofilter(_1733271, _1733273), c_List_Olinorder__class_Osort__key(_1733271, _1733269, _1733275, _1733277)) = c_List_Olinorder__class_Osort__key(_1733271, _1733269, _1733275, hAPP(c_List_Ofilter(_1733271, _1733273), _1733277)))], (50413 ^ _779999) ^ [_1798207, _1798209, _1798211] : [c_List_Oall__interval__int(_1798207, _1798209, _1798211), 50416 ^ _779999 : [(50417 ^ _779999) ^ [_1798285] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1798285), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1798209, _1798211))), -(hBOOL(hAPP(_1798207, _1798285)))]]], (13111 ^ _779999) ^ [_1013288, _1013290, _1013292, _1013294] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1013288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013288), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013288), _1013290), _1013292)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013288), _1013290), _1013294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013288), _1013292), _1013294)))], (50389 ^ _779999) ^ [_1797857, _1797859, _1797861] : [c_List_Olist__all(tc_Int_Oint, _1797857, c_List_Oupto(_1797859, _1797861)), -(c_List_Oall__interval__int(_1797857, _1797859, _1797861))], (25584 ^ _779999) ^ [_1259764, _1259766, _1259768] : [class_Groups_Oordered__ab__group__add(_1259764), 25587 ^ _779999 : [(25594 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259764), hAPP(c_Groups_Ouminus__class_Ouminus(_1259764), _1259768)), _1259766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259764), hAPP(c_Groups_Ouminus__class_Ouminus(_1259764), _1259766)), _1259768)))], (25588 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259764), hAPP(c_Groups_Ouminus__class_Ouminus(_1259764), _1259766)), _1259768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259764), hAPP(c_Groups_Ouminus__class_Ouminus(_1259764), _1259768)), _1259766)))]]], (47424 ^ _779999) ^ [_1733609, _1733611] : [-(hAPP(c_List_Ofilter(_1733609, _1733611), c_List_Olist_ONil(_1733609)) = c_List_Olist_ONil(_1733609))], (43669 ^ _779999) ^ [_1647488, _1647490, _1647492, _1647494] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1647490), hAPP(hAPP(c_List_Olist_OCons(_1647490), _1647492), _1647494)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647488)) = hAPP(hAPP(c_List_Onth(_1647490), _1647494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647488)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (19958 ^ _779999) ^ [_1144014] : [19959 ^ _779999 : [(19960 ^ _779999) ^ [_1144071] : [hBOOL(hAPP(_1144014, _1144071))]], 19962 ^ _779999 : [(19965 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1144014, hAPP(c_Int_Onat, 19961 ^ [_1144014]))))], (19963 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19961 ^ [_1144014])))]]], (51904 ^ _779999) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (25892 ^ _779999) ^ [_1265520, _1265522, _1265524, _1265526] : [class_Fields_Olinordered__field(_1265520), -(hAPP(c_Groups_Oabs__class_Oabs(_1265520), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265522, _1265520), _1265524), _1265526)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1265522, _1265520), hAPP(hAPP(c_COMBB(_1265520, _1265520, _1265522), c_Groups_Oabs__class_Oabs(_1265520)), _1265524)), _1265526))], (45193 ^ _779999) ^ [_1683237, _1683239, _1683241, _1683243] : [45194 ^ _779999 : [(45197 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1683237), _1683239), hAPP(c_List_Oset(_1683237), c_List_Obutlast(_1683237, _1683243))))], (45195 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1683237), _1683239), hAPP(c_List_Oset(_1683237), c_List_Obutlast(_1683237, _1683241))))]], -(hBOOL(hAPP(hAPP(c_member(_1683237), _1683239), hAPP(c_List_Oset(_1683237), c_List_Obutlast(_1683237, hAPP(hAPP(c_List_Oappend(_1683237), _1683241), _1683243))))))], (45490 ^ _779999) ^ [_1690798, _1690800, _1690802, _1690804, _1690806] : [-(hAPP(hAPP(c_List_Oappend(_1690798), _1690800), _1690802) = hAPP(hAPP(c_List_Oappend(_1690798), _1690804), _1690806)), 45493 ^ _779999 : [(45496 ^ _779999) ^ [] : [_1690800 = hAPP(hAPP(c_List_Otake(_1690798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690800)), _1690804), _1690802 = hAPP(hAPP(c_List_Oappend(_1690798), hAPP(hAPP(c_List_Odrop(_1690798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690800)), _1690804)), _1690806)], (45494 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690800)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690804))))]], 45501 ^ _779999 : [(45504 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Otake(_1690798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690804)), _1690800) = _1690804, hAPP(hAPP(c_List_Oappend(_1690798), hAPP(hAPP(c_List_Odrop(_1690798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690804)), _1690800)), _1690802) = _1690806], (45502 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690800)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690804)))]]], (44360 ^ _779999) ^ [_1665553, _1665555] : [44362 ^ _779999 : [(44366 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44364 ^ [_1665553, _1665555]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665553)), _1665555))))], (44368 ^ _779999) ^ [] : [44361 ^ [_1665553, _1665555] = 44364 ^ [_1665553, _1665555]], (44370 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1665553), _1665555), 44361 ^ [_1665553, _1665555]) = hAPP(hAPP(c_List_Onth(_1665553), _1665555), 44364 ^ [_1665553, _1665555]))], (44363 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44361 ^ [_1665553, _1665555]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665553)), _1665555))))]], -(hBOOL(hAPP(c_List_Odistinct(_1665553), _1665555)))], (25920 ^ _779999) ^ [_1266130, _1266132, _1266134, _1266136, _1266138, _1266140] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_1266130, _1266132, _1266134), _1266136, _1266138, _1266140)), 25921 ^ _779999 : [(25928 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1266130, _1266136))), c_Natural_Oevaln(_1266134, _1266136, _1266138, _1266140)], (25922 ^ _779999) ^ [] : [hBOOL(hAPP(_1266130, _1266136)), c_Natural_Oevaln(_1266132, _1266136, _1266138, _1266140)]]], (50218 ^ _779999) ^ [_1793834, _1793836, _1793838] : [hBOOL(hAPP(hAPP(c_member(_1793834), _1793838), hAPP(c_List_Oset(_1793834), _1793836))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1793834), _1793836), _1793838)))], (14651 ^ _779999) ^ [_1042696, _1042698, _1042700, _1042702, _1042704] : [class_Groups_Ocomm__monoid__add(_1042696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042698), _1042700)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042698), _1042702)), 14665 ^ _779999 : [(14668 ^ _779999) ^ [] : [hAPP(_1042704, 14664 ^ [_1042696, _1042698, _1042700, _1042702, _1042704]) = c_Groups_Ozero__class_Ozero(_1042696)], (14666 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042698), 14664 ^ [_1042696, _1042698, _1042700, _1042702, _1042704]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1042698, tc_HOL_Obool)), _1042700), _1042702))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042698, _1042696), _1042704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042698, tc_HOL_Obool)), _1042700), _1042702)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042696), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042698, _1042696), _1042704), _1042700)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042698, _1042696), _1042704), _1042702)))], (7932 ^ _779999) ^ [_913879] : [_913879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _913879), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35039 ^ _779999) ^ [_1434520] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1434520), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1434520))], (46099 ^ _779999) ^ [_1703055, _1703057, _1703059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703055), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703057)), _1703059))), -(c_List_Olast(_1703057, hAPP(hAPP(c_List_Odrop(_1703057), _1703055), _1703059)) = c_List_Olast(_1703057, _1703059))], (24586 ^ _779999) ^ [_1240246, _1240248, _1240250, _1240252] : [class_Orderings_Olinorder(_1240246), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240246), _1240248), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240246), _1240250), _1240252)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240246), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240246), _1240248), _1240250)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240246), _1240248), _1240252)))], (37184 ^ _779999) ^ [_1483951, _1483953, _1483955, _1483957, _1483959, _1483961, _1483963, _1483965] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1483951, _1483953), tc_prod(_1483951, _1483953))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1483951, _1483953), tc_prod(_1483951, _1483953)), hAPP(hAPP(c_Product__Type_OPair(_1483951, _1483953), _1483955), _1483957)), hAPP(hAPP(c_Product__Type_OPair(_1483951, _1483953), _1483959), _1483961))), c_Wellfounded_Olex__prod(_1483951, _1483953, _1483963, _1483965)))), 37185 ^ _779999 : [(37188 ^ _779999) ^ [] : [_1483955 = _1483959, hBOOL(hAPP(hAPP(c_member(tc_prod(_1483953, _1483953)), hAPP(hAPP(c_Product__Type_OPair(_1483953, _1483953), _1483957), _1483961)), _1483965))], (37186 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1483951, _1483951)), hAPP(hAPP(c_Product__Type_OPair(_1483951, _1483951), _1483955), _1483959)), _1483963))]]], (10223 ^ _779999) ^ [_956124, _956126] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956124), _956126))), 10226 ^ _779999 : [(10233 ^ _779999) ^ [] : [_956124 = _956126, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956124), hAPP(c_Nat_OSuc, _956126))))], (10227 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956124), hAPP(c_Nat_OSuc, _956126))), -(_956124 = _956126)]]], (38781 ^ _779999) ^ [_1527049, _1527051, _1527053, _1527055, _1527057, _1527059] : [class_Groups_Ocomm__monoid__add(_1527049), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527051), _1527053)), 38791 ^ _779999 : [(38794 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527055), hAPP(_1527057, 38790 ^ [_1527049, _1527051, _1527053, _1527055, _1527057, _1527059])))], (38792 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527051), 38790 ^ [_1527049, _1527051, _1527053, _1527055, _1527057, _1527059]), _1527053)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527051, _1527049), hAPP(hAPP(c_COMBS(_1527051, tc_fun(_1527055, tc_HOL_Obool), _1527049), hAPP(hAPP(c_COMBB(tc_fun(_1527055, _1527049), tc_fun(tc_fun(_1527055, tc_HOL_Obool), _1527049), _1527051), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527055, _1527049)), _1527059)), _1527057)), _1527053) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1527051, _1527055), _1527049), hAPP(c_Product__Type_Oprod_Oprod__case(_1527051, _1527055, _1527049), _1527059)), hAPP(hAPP(c_Product__Type_OSigma(_1527051, _1527055), _1527053), _1527057)))], (47494 ^ _779999) ^ [_1734993, _1734995, _1734997, _1734999] : [-(hAPP(c_List_Ofilter(_1734993, _1734995), hAPP(hAPP(c_List_Oappend(_1734993), _1734997), _1734999)) = hAPP(hAPP(c_List_Oappend(_1734993), hAPP(c_List_Ofilter(_1734993, _1734995), _1734997)), hAPP(c_List_Ofilter(_1734993, _1734995), _1734999)))], (146 ^ _779999) ^ [_782416, _782418, _782420, _782422, _782424, _782426, _782428, _782430] : [-(c_Natural_Oevaln(_782428, _782424, _782420, _782416)), c_Natural_Oevaln(_782430, _782426, _782422, _782418), _782430 = _782428, _782426 = _782424, _782422 = _782420, _782418 = _782416], (14331 ^ _779999) ^ [_1035957, _1035959, _1035961] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035957), _1035959)), 14334 ^ _779999 : [(14341 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1035957), _1035961), _1035959))), -(hAPP(c_Finite__Set_Ocard(_1035957), hAPP(hAPP(c_Set_Oinsert(_1035957), _1035961), _1035959)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1035957), _1035959)))], (14335 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1035957), _1035961), _1035959)), -(hAPP(c_Finite__Set_Ocard(_1035957), hAPP(hAPP(c_Set_Oinsert(_1035957), _1035961), _1035959)) = hAPP(c_Finite__Set_Ocard(_1035957), _1035959))]]], (47715 ^ _779999) ^ [_1740795, _1740797] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1740795, _1740797)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1740797), _1740795))], (20130 ^ _779999) ^ [_1146699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146699)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1146699)) = _1146699)], (28208 ^ _779999) ^ [_1310261, _1310263, _1310265, _1310267] : [class_Fields_Olinordered__field__inverse__zero(_1310261), 28211 ^ _779999 : [(28212 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310261), _1310263), _1310265)), _1310267)), 28215 ^ _779999 : [(28222 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310265))), 28225 ^ _779999 : [(28232 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), _1310265), c_Groups_Ozero__class_Ozero(_1310261)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310267)))], (28226 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), _1310265), c_Groups_Ozero__class_Ozero(_1310261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310261), _1310267), _1310265)), _1310263)))]]], (28216 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), _1310263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310261), _1310267), _1310265))))]]], (28238 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310261), _1310263), _1310265)), _1310267))), 28241 ^ _779999 : [(28244 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), _1310263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310261), _1310267), _1310265)))], (28242 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310265)))]], 28245 ^ _779999 : [(28248 ^ _779999) ^ [] : [28249 ^ _779999 : [(28252 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310261), _1310267), _1310265)), _1310263))], (28250 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), _1310265), c_Groups_Ozero__class_Ozero(_1310261))))]], 28253 ^ _779999 : [(28256 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310267))], (28254 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), _1310265), c_Groups_Ozero__class_Ozero(_1310261)))]]], (28246 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310265))]]]]], (44154 ^ _779999) ^ [_1660952, _1660954, _1660956, _1660958, _1660960] : [-(hAPP(hAPP(c_List_Olist__update(_1660952, hAPP(hAPP(c_List_Olist__update(_1660952, _1660954), _1660956), _1660958)), _1660956), _1660960) = hAPP(hAPP(c_List_Olist__update(_1660952, _1660954), _1660956), _1660960))], (46732 ^ _779999) ^ [_1717287, _1717289] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1717287, _1717289) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1717287), hAPP(c_Code__Numeral_Onat__of, _1717289))))], (4022 ^ _779999) ^ [_840550, _840552, _840554, _840556] : [-(c_List_Omeasures(_840556, _840552) = c_List_Omeasures(_840554, _840550)), _840556 = _840554, _840552 = _840550], (46334 ^ _779999) ^ [_1708876, _1708878, _1708880, _1708882, _1708884, _1708886] : [-(hBOOL(hAPP(hAPP(c_member(_1708876), _1708878), hAPP(c_List_Oset(_1708876), _1708880)))), -(hAPP(hAPP(c_List_Omap(_1708876, _1708882), c_Fun_Ofun__upd(_1708876, _1708882, _1708884, _1708878, _1708886)), _1708880) = hAPP(hAPP(c_List_Omap(_1708876, _1708882), _1708884), _1708880))], (51037 ^ _779999) ^ [_1812939, _1812941, _1812943] : [c_Relation_Osym(_1812939, _1812941), c_Relation_Osym(_1812939, _1812943), -(c_Relation_Osym(_1812939, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812939, _1812939), tc_HOL_Obool)), _1812941), _1812943)))], (15525 ^ _779999) ^ [_1059784, _1059786, _1059788, _1059790, _1059792] : [class_Rings_Ocomm__semiring__1(_1059784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), _1059786), _1059788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), _1059790), _1059792)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), _1059786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), _1059788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059784), _1059790), _1059792))))], (32741 ^ _779999) ^ [_1394211, _1394213] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394211)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394213)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1394211), _1394213)))], (13618 ^ _779999) ^ [_1022968, _1022970] : [class_Groups_Olinordered__ab__group__add(_1022968), 13621 ^ _779999 : [(13628 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022968), c_Groups_Ozero__class_Ozero(_1022968)), _1022970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022968), c_Groups_Ozero__class_Ozero(_1022968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022968), _1022970), _1022970))))], (13622 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022968), c_Groups_Ozero__class_Ozero(_1022968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022968), _1022970), _1022970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022968), c_Groups_Ozero__class_Ozero(_1022968)), _1022970)))]]], (20401 ^ _779999) ^ [_1151232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151232)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1151232)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1151232)))], (49812 ^ _779999) ^ [_1785177, _1785179, _1785181, _1785183, _1785185] : [hBOOL(hAPP(hAPP(_1785181, _1785185), _1785183)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1785177, _1785179, _1785181), _1785183), _1785185)))], (42836 ^ _779999) ^ [_1624190, _1624192, _1624194, _1624196] : [class_Orderings_Olinorder(_1624190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624190), _1624192)), 42846 ^ _779999 : [(42849 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624190), _1624194), 42845 ^ [_1624190, _1624192, _1624194, _1624196]))], (42847 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624190), 42845 ^ [_1624190, _1624192, _1624194, _1624196]), _1624192)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624190), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1624190), _1624194), _1624196)), hAPP(hAPP(c_Finite__Set_Ofold(_1624190, _1624190, c_Orderings_Oord__class_Omin(_1624190)), _1624196), _1624192))))], (42600 ^ _779999) ^ [_1618815] : [class_Complete__Lattice_Ocomplete__lattice(_1618815), -(c_Complete__Lattice_OInf__class_OInf(_1618815, c_Orderings_Otop__class_Otop(tc_fun(_1618815, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1618815))], (3790 ^ _779999) ^ [_836890, _836892] : [_836892 = _836890, -(c_SetInterval_Oord__class_OatMost(_836892) = c_SetInterval_Oord__class_OatMost(_836890))], (50551 ^ _779999) ^ [_1801863, _1801865] : [-(hBOOL(hAPP(_1801865, 50558 ^ [_1801863, _1801865]))), 50552 ^ _779999 : [(50553 ^ _779999) ^ [_1801924] : [hBOOL(hAPP(hAPP(c_member(_1801863), _1801924), c_Orderings_Otop__class_Otop(tc_fun(_1801863, tc_HOL_Obool)))), hBOOL(hAPP(_1801865, _1801924))]]], (40077 ^ _779999) ^ [_1557772, _1557774, _1557776, _1557778, _1557780, _1557782, _1557784] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1557772, _1557774, _1557776, _1557778), _1557780), _1557782), _1557784) = hAPP(hAPP(_1557782, hAPP(c_Product__Type_Ofst(_1557774, _1557776), hAPP(_1557780, _1557784))), hAPP(c_Product__Type_Osnd(_1557774, _1557776), hAPP(_1557780, _1557784))))], (44832 ^ _779999) ^ [_1675190, _1675192, _1675194, _1675196] : [-(c_List_Osublist(_1675190, hAPP(hAPP(c_List_Olist_OCons(_1675190), _1675192), _1675194), _1675196) = hAPP(hAPP(c_List_Oappend(_1675190), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1675190)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1675196)), hAPP(hAPP(c_List_Olist_OCons(_1675190), _1675192), c_List_Olist_ONil(_1675190))), c_List_Olist_ONil(_1675190))), c_List_Osublist(_1675190, _1675194, 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)), _1675196)))))], (378 ^ _779999) ^ [_785776, _785778, _785780, _785782, _785784, _785786] : [-(c_Hoare__Mirabelle_Ohoare__valids(_785784, _785780, _785776)), c_Hoare__Mirabelle_Ohoare__valids(_785786, _785782, _785778), _785786 = _785784, _785782 = _785780, _785778 = _785776], (8840 ^ _779999) ^ [_931850, _931852, _931854] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _931850), _931852)), _931854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _931850), _931854)), _931852))], (18183 ^ _779999) ^ [_1110963, _1110965, _1110967] : [class_Rings_Olinordered__semidom(_1110963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110965), _1110967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110963), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110963), _1110965)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110963), _1110967))))], (27716 ^ _779999) ^ [_1301108, _1301110, _1301112, _1301114] : [class_Groups_Omonoid__mult(_1301108), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301108), _1301110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1301112), _1301114)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301108), hAPP(hAPP(c_Power_Opower__class_Opower(_1301108), _1301110), _1301112)), _1301114))], (20024 ^ _779999) ^ [] : [-(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))))], (10065 ^ _779999) ^ [_953625, _953627, _953629, _953631, _953633, _953635] : [c_Fun_Oinj__on(_953625, _953627, _953629, _953631), -(_953633 = _953635), hBOOL(hAPP(hAPP(c_member(_953625), _953633), _953631)), hBOOL(hAPP(hAPP(c_member(_953625), _953635), _953631)), hAPP(_953629, _953633) = hAPP(_953629, _953635)], (11921 ^ _779999) ^ [_989612, _989614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_989612), _989614)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_989612, tc_HOL_Obool)), hAPP(c_Set_OPow(_989612), _989614))))], (25388 ^ _779999) ^ [_1256477, _1256479, _1256481, _1256483, _1256485] : [hBOOL(hAPP(_1256477, _1256479)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1256481), _1256479), _1256483)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1256477, _1256481, _1256485)), _1256479), _1256483)))], (43657 ^ _779999) ^ [_1647282, _1647284, _1647286, _1647288] : [-(_1647282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1647284), hAPP(hAPP(c_List_Olist_OCons(_1647284), _1647286), _1647288)), _1647282) = hAPP(hAPP(c_List_Onth(_1647284), _1647288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647282), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46462 ^ _779999) ^ [_1711830, _1711832, _1711834, _1711836] : [c_Fun_Oinj__on(_1711830, _1711832, _1711834, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1711830, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1711830), tc_fun(_1711830, tc_HOL_Obool), c_List_Oset(_1711830)), _1711836))), -(c_Fun_Oinj__on(tc_List_Olist(_1711830), tc_List_Olist(_1711832), hAPP(c_List_Omap(_1711830, _1711832), _1711834), _1711836))], (22990 ^ _779999) ^ [_1208376, _1208378, _1208380, _1208382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208376, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208376, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22991 ^ [_1208376, _1208378, _1208380, _1208382])), _1208378)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208376, 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), 22991 ^ [_1208376, _1208378, _1208380, _1208382]), _1208380))), _1208382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208376, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208376, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1208378)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1208376, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1208382))))], (7157 ^ _779999) ^ [_897967, _897969, _897971, _897973] : [c_Hoare__Mirabelle_Ohoare__derivs(_897967, _897969, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_897967)), _897971), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_897967), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_897967, _897969, _897973), -(c_Hoare__Mirabelle_Ohoare__derivs(_897967, _897969, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_897967)), _897971), _897973)))], (40829 ^ _779999) ^ [_1576079, _1576081, _1576083, _1576085, _1576087] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576079, _1576079)), hAPP(hAPP(c_Product__Type_OPair(_1576079, _1576079), hAPP(_1576081, hAPP(c_Nat_OSuc, 40830 ^ [_1576079, _1576081, _1576083, _1576085, _1576087]))), hAPP(_1576081, 40830 ^ [_1576079, _1576081, _1576083, _1576085, _1576087]))), c_Transitive__Closure_Ortrancl(_1576079, _1576083))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576079, _1576079)), hAPP(hAPP(c_Product__Type_OPair(_1576079, _1576079), hAPP(_1576081, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1576085), _1576087))), hAPP(_1576081, _1576085))), c_Transitive__Closure_Ortrancl(_1576079, _1576083))))], (40307 ^ _779999) ^ [_1563936, _1563938, _1563940, _1563942, _1563944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563936, _1563936)), hAPP(hAPP(c_Product__Type_OPair(_1563936, _1563936), _1563938), _1563940)), _1563942)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563936, _1563936)), hAPP(hAPP(c_Product__Type_OPair(_1563936, _1563936), _1563940), _1563944)), c_Transitive__Closure_Ortrancl(_1563936, _1563942))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563936, _1563936)), hAPP(hAPP(c_Product__Type_OPair(_1563936, _1563936), _1563938), _1563944)), c_Transitive__Closure_Ortrancl(_1563936, _1563942))))], (7825 ^ _779999) ^ [_912106, _912108, _912110, _912112, _912114] : [hBOOL(hAPP(hAPP(c_member(_912106), _912108), hAPP(c_Set_Oimage(_912110, _912106, _912112), _912114))), 7829 ^ _779999 : [(7832 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912110), 7828 ^ [_912106, _912108, _912110, _912112, _912114]), _912114)))], (7830 ^ _779999) ^ [] : [-(_912108 = hAPP(_912112, 7828 ^ [_912106, _912108, _912110, _912112, _912114]))]]], (35723 ^ _779999) ^ [_1453221, _1453223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453221), 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)), _1453223)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1453221, _1453223), c_Divides_OnegDivAlg(_1453221, _1453223))))], (22972 ^ _779999) ^ [_1207990, _1207992, _1207994, _1207996, _1207998] : [-(_1207990 = c_Orderings_Obot__class_Obot(tc_fun(_1207992, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207994, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207992, tc_fun(_1207994, tc_HOL_Obool)), _1207990), _1207996)), _1207998) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207992, tc_fun(_1207994, tc_HOL_Obool)), _1207990), hAPP(hAPP(c_COMBC(_1207992, tc_fun(_1207994, tc_HOL_Obool), tc_fun(_1207994, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1207994, tc_HOL_Obool), tc_fun(tc_fun(_1207994, tc_HOL_Obool), tc_fun(_1207994, tc_HOL_Obool)), _1207992), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207994, tc_HOL_Obool))), _1207996)), _1207998)))], (51690 ^ _779999) ^ [_1826298, _1826300, _1826302, _1826304, _1826306] : [c_Fun_Obij__betw(_1826298, _1826300, _1826302, c_Orderings_Otop__class_Otop(tc_fun(_1826298, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1826300, tc_HOL_Obool))), c_Fun_Obij__betw(_1826300, _1826304, _1826306, c_Orderings_Otop__class_Otop(tc_fun(_1826300, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1826304, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1826298, _1826304, hAPP(c_Fun_Ocomp(_1826300, _1826304, _1826298, _1826306), _1826302), c_Orderings_Otop__class_Otop(tc_fun(_1826298, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1826304, tc_HOL_Obool))))], (52058 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (51888 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (34807 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44078 ^ _779999) ^ [_1659099, _1659101, _1659103, _1659105] : [44080 ^ _779999 : [(44083 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1659103, 44079 ^ [_1659099, _1659101, _1659103, _1659105])), hAPP(_1659105, 44079 ^ [_1659099, _1659101, _1659103, _1659105])))], (44081 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659099), 44079 ^ [_1659099, _1659101, _1659103, _1659105]), hAPP(c_List_Oset(_1659099), _1659101))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1659099, _1659103, _1659101)), c_List_Olist_Olist__size(_1659099, _1659105, _1659101))))], (5781 ^ _779999) ^ [_871353, _871355, _871357, _871359, _871361, _871363, _871365] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871353), _871355), _871357), _871359) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871353), _871361), _871363), _871365), 5784 ^ _779999 : [(5789 ^ _779999) ^ [] : [-(_871359 = _871365)], (5787 ^ _779999) ^ [] : [-(_871357 = _871363)], (5785 ^ _779999) ^ [] : [-(_871355 = _871361)]]], (21518 ^ _779999) ^ [_1171759, _1171761, _1171763] : [class_Lattices_Oab__semigroup__idem__mult(_1171759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171759), _1171761)), -(_1171761 = c_Orderings_Obot__class_Obot(tc_fun(_1171759, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171759), _1171763)), -(_1171763 = c_Orderings_Obot__class_Obot(tc_fun(_1171759, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1171759, c_Groups_Otimes__class_Otimes(_1171759)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1171759, tc_HOL_Obool)), _1171761), _1171763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171759), hAPP(c_Finite__Set_Ofold1(_1171759, c_Groups_Otimes__class_Otimes(_1171759)), _1171761)), hAPP(c_Finite__Set_Ofold1(_1171759, c_Groups_Otimes__class_Otimes(_1171759)), _1171763)))], (23925 ^ _779999) ^ [_1226822, _1226824, _1226826] : [class_Orderings_Olinorder(_1226822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1226822), _1226824)), hBOOL(hAPP(hAPP(c_member(_1226822), _1226826), _1226824)), 23936 ^ _779999 : [(23943 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1226822, tc_HOL_Obool)), _1226824), hAPP(hAPP(c_Set_Oinsert(_1226822), _1226826), c_Orderings_Obot__class_Obot(tc_fun(_1226822, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1226822, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1226822, c_Orderings_Oord__class_Omin(_1226822), _1226824) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1226822), _1226826), c_Big__Operators_Olattice_OInf__fin(_1226822, c_Orderings_Oord__class_Omin(_1226822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1226822, tc_HOL_Obool)), _1226824), hAPP(hAPP(c_Set_Oinsert(_1226822), _1226826), c_Orderings_Obot__class_Obot(tc_fun(_1226822, tc_HOL_Obool)))))))], (23937 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1226822, tc_HOL_Obool)), _1226824), hAPP(hAPP(c_Set_Oinsert(_1226822), _1226826), c_Orderings_Obot__class_Obot(tc_fun(_1226822, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1226822, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1226822, c_Orderings_Oord__class_Omin(_1226822), _1226824) = _1226826)]]], (46219 ^ _779999) ^ [_1705414, _1705416, _1705418, _1705420, _1705422] : [class_Groups_Oab__group__add(_1705414), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705414), hAPP(hAPP(c_List_Omap(_1705416, _1705414), hAPP(hAPP(c_COMBS(_1705416, _1705414, _1705414), hAPP(hAPP(c_COMBB(_1705414, tc_fun(_1705414, _1705414), _1705416), c_Groups_Ominus__class_Ominus(_1705414)), _1705418)), _1705420)), _1705422)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1705414), hAPP(c_List_Omonoid__add__class_Olistsum(_1705414), hAPP(hAPP(c_List_Omap(_1705416, _1705414), _1705418), _1705422))), hAPP(c_List_Omonoid__add__class_Olistsum(_1705414), hAPP(hAPP(c_List_Omap(_1705416, _1705414), _1705420), _1705422))))], (21671 ^ _779999) ^ [_1174775, _1174777] : [-(hBOOL(hAPP(_1174777, 21672 ^ [_1174775, _1174777]))), -(hAPP(c_Set_OCollect(_1174775), _1174777) = c_Orderings_Obot__class_Obot(tc_fun(_1174775, tc_HOL_Obool)))], (43094 ^ _779999) ^ [_1630226, _1630228, _1630230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1630226), c_Nitpick_Oplus__frac(_1630226, _1630228, c_Nitpick_Ouminus__frac(_1630226, _1630230)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1630226, _1630228, _1630230))], (6213 ^ _779999) ^ [_879299, _879301, _879303, _879305] : [hBOOL(hAPP(_879299, _879301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879303, tc_HOL_Obool)), _879299), _879305)), -(hBOOL(hAPP(_879305, _879301)))], (30238 ^ _779999) ^ [_1346644, _1346646] : [class_Rings_Olinordered__idom(_1346644), 30241 ^ _779999 : [(30248 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346644), c_Groups_Ozero__class_Ozero(_1346644)), hAPP(c_Int_Oring__1__class_Oof__int(_1346644), _1346646))))], (30242 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346644), c_Groups_Ozero__class_Ozero(_1346644)), hAPP(c_Int_Oring__1__class_Oof__int(_1346644), _1346646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346646)))]]], (44608 ^ _779999) ^ [_1670287] : [-(hAPP(c_List_Oset(_1670287), c_List_Olist_ONil(_1670287)) = c_Orderings_Obot__class_Obot(tc_fun(_1670287, tc_HOL_Obool)))], (7733 ^ _779999) ^ [_909839, _909841, _909843, _909845, _909847] : [class_Orderings_Oorder(_909839), c_Orderings_Oorder__class_Omono(_909839, tc_fun(_909841, tc_HOL_Obool), _909843), -(c_Orderings_Oorder__class_Omono(_909839, tc_fun(_909841, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_909839, tc_fun(_909841, tc_HOL_Obool), tc_fun(_909841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_909841, tc_HOL_Obool), tc_fun(tc_fun(_909841, tc_HOL_Obool), tc_fun(_909841, tc_HOL_Obool)), _909839), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909841, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_909839, tc_fun(_909841, tc_HOL_Obool), tc_fun(_909841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_909841, tc_HOL_Obool), tc_fun(tc_fun(_909841, tc_HOL_Obool), tc_fun(_909841, tc_HOL_Obool)), _909839), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909841, tc_HOL_Obool))), _909843)), _909845))), _909847)))], (41540 ^ _779999) ^ [_1592954, _1592956, _1592958] : [class_Lattices_Olattice(_1592954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592954), _1592956)), -(hBOOL(hAPP(hAPP(c_member(_1592954), _1592958), _1592956))), -(c_Big__Operators_Olattice__class_OSup__fin(_1592954, hAPP(hAPP(c_Set_Oinsert(_1592954), _1592958), _1592956)) = hAPP(hAPP(c_Finite__Set_Ofold(_1592954, _1592954, c_Lattices_Osemilattice__sup__class_Osup(_1592954)), _1592958), _1592956))], (50761 ^ _779999) ^ [_1807653, _1807655, _1807657, _1807659, _1807661] : [c_Predicate_Otransp(_1807653, _1807655), hBOOL(hAPP(hAPP(_1807655, _1807657), _1807659)), hBOOL(hAPP(hAPP(_1807655, _1807659), _1807661)), -(hBOOL(hAPP(hAPP(_1807655, _1807657), _1807661)))], (45604 ^ _779999) ^ [_1693382, _1693384] : [-(_1693382 = c_List_Olist_ONil(_1693384)), -(hAPP(c_List_Orotate1(_1693384), _1693382) = hAPP(hAPP(c_List_Oappend(_1693384), hAPP(c_List_Otl(_1693384), _1693382)), hAPP(hAPP(c_List_Olist_OCons(_1693384), hAPP(c_List_Ohd(_1693384), _1693382)), c_List_Olist_ONil(_1693384))))], (44560 ^ _779999) ^ [_1669484, _1669486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1669484), _1669486)), -(c_List_Oupto(_1669486, _1669484) = c_List_Olist_ONil(tc_Int_Oint))], (46237 ^ _779999) ^ [_1706031, _1706033, _1706035] : [class_Groups_Omonoid__add(_1706031), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1706031), hAPP(hAPP(c_List_Omap(_1706033, _1706031), hAPP(c_COMBK(_1706031, _1706033), c_Groups_Ozero__class_Ozero(_1706031))), _1706035)) = c_Groups_Ozero__class_Ozero(_1706031))], (15555 ^ _779999) ^ [_1060533, _1060535, _1060537] : [class_Rings_Ocomm__semiring__1(_1060533), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060533), _1060535), _1060537) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060533), _1060537), _1060535))], (21866 ^ _779999) ^ [_1180447, _1180449, _1180451, _1180453, _1180455] : [_1180447 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1180449, tc_HOL_Obool), _1180451), c_Orderings_Oorder__class_Omono(tc_fun(_1180449, tc_HOL_Obool), tc_fun(_1180449, tc_HOL_Obool), _1180451), hBOOL(hAPP(hAPP(c_member(_1180449), _1180453), _1180447)), 21880 ^ _779999 : [(21883 ^ _779999) ^ [] : [hBOOL(hAPP(_1180455, 21879 ^ [_1180447, _1180449, _1180451, _1180453, _1180455]))], (21881 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180449), 21879 ^ [_1180447, _1180449, _1180451, _1180453, _1180455]), hAPP(_1180451, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1180449, tc_HOL_Obool)), _1180447), hAPP(c_Set_OCollect(_1180449), _1180455))))))]], -(hBOOL(hAPP(_1180455, _1180453)))], (7924 ^ _779999) ^ [_913761] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _913761)))], (47681 ^ _779999) ^ [_1740252, _1740254, _1740256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1740252), _1740254)), _1740256)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1740254), c_List_Oupt(_1740252, _1740256)) = c_List_Oupt(_1740252, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1740252), _1740254)))], (15873 ^ _779999) ^ [_1066220, _1066222, _1066224] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066220), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066222), _1066224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066220), _1066222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066220), _1066224)))], (37650 ^ _779999) ^ [_1496192, _1496194, _1496196, _1496198, _1496200, _1496202, _1496204, _1496206] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1496192, _1496194)), hAPP(hAPP(c_Product__Type_OPair(_1496192, _1496194), _1496196), _1496198)), _1496200)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1496194, _1496202)), hAPP(hAPP(c_Product__Type_OPair(_1496194, _1496202), _1496198), _1496204)), _1496206)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496192, _1496202)), hAPP(hAPP(c_Product__Type_OPair(_1496192, _1496202), _1496196), _1496204)), hAPP(hAPP(c_Relation_Orel__comp(_1496192, _1496194, _1496202), _1496200), _1496206))))], (47619 ^ _779999) ^ [_1738899, _1738901] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738899))), c_List_Otranspose(_1738899, _1738901)) = c_List_Ofoldr(tc_List_Olist(_1738899), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1738899)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1738899))), _1738901, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48386 ^ _779999) ^ [_1753682, _1753684, _1753686, _1753688] : [-(hAPP(c_List_Orev(_1753682), hAPP(hAPP(c_List_Omap(_1753684, _1753682), _1753686), _1753688)) = hAPP(hAPP(c_List_Omap(_1753684, _1753682), _1753686), hAPP(c_List_Orev(_1753684), _1753688)))], (19924 ^ _779999) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1484 ^ _779999) ^ [_801657, _801659] : [-(class_Lattices_Oboolean__algebra(_801657)), _801659 = _801657, class_Lattices_Oboolean__algebra(_801659)], (1394 ^ _779999) ^ [_800532, _800534] : [-(class_Rings_Oidom(_800532)), _800534 = _800532, class_Rings_Oidom(_800534)], (5999 ^ _779999) ^ [_875520, _875522, _875524, _875526] : [class_Orderings_Oorder(_875520), _875522 = _875524, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875520), _875526), _875524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875520), _875526), _875522)))], (8399 ^ _779999) ^ [_923520, _923522, _923524] : [hBOOL(hAPP(hAPP(c_member(_923520), _923522), _923524)), -(hAPP(hAPP(c_Set_Oinsert(_923520), _923522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923520, tc_HOL_Obool)), _923524), hAPP(hAPP(c_Set_Oinsert(_923520), _923522), c_Orderings_Obot__class_Obot(tc_fun(_923520, tc_HOL_Obool))))) = _923524)], (7394 ^ _779999) ^ [_903019, _903021, _903023, _903025] : [hBOOL(hAPP(hAPP(c_member(_903019), _903025), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903019, tc_HOL_Obool)), _903021), _903023))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903019, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_903019, tc_fun(_903019, tc_HOL_Obool), tc_HOL_Obool), c_member(_903019)), _903021)), hAPP(hAPP(c_COMBC(_903019, tc_fun(_903019, tc_HOL_Obool), tc_HOL_Obool), c_member(_903019)), _903023)), _903025)))], (26048 ^ _779999) ^ [_1268627, _1268629, _1268631] : [c_Com_Ocom_OCond(_1268627, _1268629, _1268631) = c_Com_Ocom_OSKIP], (38493 ^ _779999) ^ [_1517990, _1517992, _1517994, _1517996, _1517998] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517990, _1517992), _1517994), hAPP(hAPP(c_COMBS(_1517990, tc_fun(_1517992, tc_HOL_Obool), tc_fun(_1517992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517992, tc_HOL_Obool), tc_fun(tc_fun(_1517992, tc_HOL_Obool), tc_fun(_1517992, tc_HOL_Obool)), _1517990), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517992, tc_HOL_Obool))), _1517996)), _1517998)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517990, _1517992), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517990, _1517992), _1517994), _1517996)), hAPP(hAPP(c_Product__Type_OSigma(_1517990, _1517992), _1517994), _1517998)))], (13131 ^ _779999) ^ [_1013678, _1013680, _1013682, _1013684, _1013686] : [class_Groups_Oordered__ab__semigroup__add(_1013678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013678), _1013680), _1013682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013678), _1013684), _1013686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013678), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013678), _1013680), _1013684)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013678), _1013682), _1013686))))], (51844 ^ _779999) ^ [_1828991, _1828993] : [class_Orderings_Oord(_1828991), -(class_Orderings_Oord(tc_fun(_1828993, _1828991)))], (25716 ^ _779999) ^ [_1262078, _1262080, _1262082] : [class_Groups_Ogroup__add(_1262078), 25719 ^ _779999 : [(25726 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1262078), _1262082) = _1262080, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1262078), _1262080) = _1262082)], (25720 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1262078), _1262080) = _1262082, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1262078), _1262082) = _1262080)]]], (1014 ^ _779999) ^ [_795432, _795434, _795436, _795438, _795440, _795442] : [-(c_Relation_Orefl__on(_795440, _795436, _795432)), c_Relation_Orefl__on(_795442, _795438, _795434), _795442 = _795440, _795438 = _795436, _795434 = _795432], (24592 ^ _779999) ^ [_1240405, _1240407, _1240409, _1240411] : [class_Orderings_Olinorder(_1240405), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240405), _1240407), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240405), _1240409), _1240411)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240405), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240405), _1240407), _1240409)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1240405), _1240407), _1240411)))], (37196 ^ _779999) ^ [_1484341, _1484343] : [c_Equiv__Relations_Oequiv(_1484341, c_Orderings_Otop__class_Otop(tc_fun(_1484341, tc_HOL_Obool)), _1484343), -(c_Equiv__Relations_Oequivp(_1484341, hAPP(hAPP(c_COMBC(_1484341, tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_fun(_1484341, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484341, tc_fun(tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_fun(_1484341, tc_HOL_Obool)), _1484341), c_COMBC(_1484341, tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484341, tc_prod(_1484341, _1484341)), tc_fun(_1484341, tc_fun(tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_HOL_Obool)), _1484341), hAPP(c_COMBB(tc_prod(_1484341, _1484341), tc_fun(tc_fun(tc_prod(_1484341, _1484341), tc_HOL_Obool), tc_HOL_Obool), _1484341), c_member(tc_prod(_1484341, _1484341)))), c_Product__Type_OPair(_1484341, _1484341)))), _1484343)))], (9388 ^ _779999) ^ [_939792, _939794, _939796] : [class_Orderings_Olinorder(_939792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939792), _939794), _939796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939792), _939796), _939794))], (42051 ^ _779999) ^ [_1605957, _1605959, _1605961, _1605963, _1605965, _1605967, _1605969] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605957, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605959, tc_fun(_1605957, tc_HOL_Obool)), _1605961), _1605963)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605965, tc_fun(_1605957, tc_HOL_Obool)), _1605967), _1605969)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605959, tc_fun(_1605957, tc_HOL_Obool)), _1605961), hAPP(hAPP(c_COMBB(tc_fun(_1605965, tc_fun(_1605957, tc_HOL_Obool)), tc_fun(_1605957, tc_HOL_Obool), _1605959), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605965, tc_fun(_1605957, tc_HOL_Obool)), _1605967)), hAPP(hAPP(c_COMBC(_1605959, tc_fun(_1605965, tc_fun(_1605957, tc_HOL_Obool)), tc_fun(_1605965, tc_fun(_1605957, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1605957, tc_HOL_Obool), tc_fun(_1605957, tc_HOL_Obool)), tc_fun(tc_fun(_1605965, tc_fun(_1605957, tc_HOL_Obool)), tc_fun(_1605965, tc_fun(_1605957, tc_HOL_Obool))), _1605959), c_COMBB(tc_fun(_1605957, tc_HOL_Obool), tc_fun(_1605957, tc_HOL_Obool), _1605965)), hAPP(hAPP(c_COMBB(tc_fun(_1605957, tc_HOL_Obool), tc_fun(tc_fun(_1605957, tc_HOL_Obool), tc_fun(_1605957, tc_HOL_Obool)), _1605959), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605957, tc_HOL_Obool))), _1605963))), _1605969))))], (21026 ^ _779999) ^ [_1162080] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1162080) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1162080))], (35795 ^ _779999) ^ [_1454463, _1454465] : [c_Nitpick_Orefl_H(_1454463, _1454465), 35798 ^ _779999 : [(35799 ^ _779999) ^ [_1454541] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454463, _1454463)), hAPP(hAPP(c_Product__Type_OPair(_1454463, _1454463), _1454541), _1454541)), _1454465)))]]], (46586 ^ _779999) ^ [_1714496, _1714498, _1714500, _1714502, _1714504] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714496)), _1714498) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714500)), _1714502), 46589 ^ _779999 : [(46598 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1714496, _1714500), _1714498), _1714502) = _1714504), hAPP(hAPP(c_List_Omap(tc_prod(_1714496, _1714500), _1714496), c_Product__Type_Ofst(_1714496, _1714500)), _1714504) = _1714498, hAPP(hAPP(c_List_Omap(tc_prod(_1714496, _1714500), _1714500), c_Product__Type_Osnd(_1714496, _1714500)), _1714504) = _1714502], (46590 ^ _779999) ^ [] : [hAPP(hAPP(c_List_Ozip(_1714496, _1714500), _1714498), _1714502) = _1714504, 46593 ^ _779999 : [(46596 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1714496, _1714500), _1714500), c_Product__Type_Osnd(_1714496, _1714500)), _1714504) = _1714502)], (46594 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1714496, _1714500), _1714496), c_Product__Type_Ofst(_1714496, _1714500)), _1714504) = _1714498)]]]]], (30607 ^ _779999) ^ [_1353842] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1353842) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5550 ^ _779999) ^ [_865000, _865002, _865004, _865006] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_865006, _865002) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_865004, _865000)), _865006 = _865004, _865002 = _865000], (50224 ^ _779999) ^ [_1793953, _1793955, _1793957, _1793959, _1793961, _1793963] : [-(c_Nitpick_Opair__box_Opair__box__size(_1793953, _1793955, _1793957, _1793959, c_Nitpick_Opair__box_OPairBox(_1793953, _1793955, _1793961, _1793963)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1793957, _1793961)), hAPP(_1793959, _1793963))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37972 ^ _779999) ^ [_1504691, _1504693, _1504695] : [c_Wellfounded_Owf(_1504691, _1504693), -(c_Wellfounded_Owf(_1504691, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1504691, _1504691), tc_HOL_Obool)), _1504693), _1504695)))], (48352 ^ _779999) ^ [_1752942, _1752944, _1752946] : [_1752946 = hAPP(hAPP(c_List_Olist_OCons(_1752942), _1752944), c_List_Olist_ONil(_1752942)), -(hAPP(hAPP(c_List_Olist_OCons(_1752942), _1752944), c_List_Olist_ONil(_1752942)) = hAPP(c_List_Orev(_1752942), _1752946))], (43573 ^ _779999) ^ [_1644942, _1644944, _1644946, _1644948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644942), tc_List_Olist(_1644942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644942), tc_List_Olist(_1644942)), _1644944), _1644946)), c_List_Olistrel(_1644942, _1644948))), 43576 ^ _779999 : [(43579 ^ _779999) ^ [_1645171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645171), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644942)), _1644944))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1644942, _1644942)), hAPP(hAPP(c_Product__Type_OPair(_1644942, _1644942), hAPP(hAPP(c_List_Onth(_1644942), _1644944), _1645171)), hAPP(hAPP(c_List_Onth(_1644942), _1644946), _1645171))), _1644948)))], (43577 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644942)), _1644944) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644942)), _1644946))]]], (37632 ^ _779999) ^ [_1494988, _1494990, _1494992] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1494988, _1494990, _1494992, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1494990)], (2104 ^ _779999) ^ [_810637, _810639, _810641, _810643] : [-(c_Orderings_Oord__class_OLeast(_810643, _810639) = c_Orderings_Oord__class_OLeast(_810641, _810637)), _810643 = _810641, _810639 = _810637], (9162 ^ _779999) ^ [_936489, _936491, _936493, _936495, _936497, _936499] : [-(_936489 = _936491), -(hAPP(c_Fun_Ofun__upd(_936493, _936495, _936497, _936491, _936499), _936489) = hAPP(_936497, _936489))], (39379 ^ _779999) ^ [_1541453, _1541455] : [-(c_Hilbert__Choice_OEps(_1541453, hAPP(hAPP(c_COMBC(_1541453, _1541453, tc_HOL_Obool), c_fequal), _1541455)) = _1541455)], (13008 ^ _779999) ^ [_1011286] : [-(c_Finite__Set_Ofun__left__comm__idem(_1011286, tc_fun(_1011286, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1011286, tc_HOL_Obool), tc_fun(tc_fun(_1011286, tc_HOL_Obool), tc_fun(_1011286, tc_HOL_Obool)), _1011286), hAPP(c_COMBC(tc_fun(_1011286, tc_HOL_Obool), tc_fun(_1011286, tc_HOL_Obool), tc_fun(_1011286, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1011286, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1011286, tc_fun(_1011286, tc_HOL_Obool), tc_fun(_1011286, tc_HOL_Obool)), c_Set_Oinsert(_1011286)), c_Orderings_Obot__class_Obot(tc_fun(_1011286, tc_HOL_Obool))))))], (26172 ^ _779999) ^ [_1270727, _1270729] : [class_Groups_Olinordered__ab__group__add(_1270727), 26175 ^ _779999 : [(26182 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270727), _1270729), c_Groups_Ozero__class_Ozero(_1270727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270727), _1270729), hAPP(c_Groups_Ouminus__class_Ouminus(_1270727), _1270729))))], (26176 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270727), _1270729), hAPP(c_Groups_Ouminus__class_Ouminus(_1270727), _1270729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270727), _1270729), c_Groups_Ozero__class_Ozero(_1270727))))]]], (47396 ^ _779999) ^ [_1732638, _1732640, _1732642, _1732644] : [-(c_List_Oconcat(_1732638, hAPP(hAPP(c_List_Omap(_1732640, tc_List_Olist(_1732638)), hAPP(hAPP(c_COMBC(_1732640, tc_List_Olist(_1732638), tc_List_Olist(_1732638)), hAPP(hAPP(c_COMBB(_1732638, tc_fun(tc_List_Olist(_1732638), tc_List_Olist(_1732638)), _1732640), c_List_Olist_OCons(_1732638)), _1732642)), c_List_Olist_ONil(_1732638))), _1732644)) = hAPP(hAPP(c_List_Omap(_1732640, _1732638), _1732642), _1732644))], (46376 ^ _779999) ^ [_1709794, _1709796, _1709798, _1709800, _1709802] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1709794), tc_List_Olist(_1709796), tc_List_Olist(_1709798), hAPP(c_List_Omap(_1709794, _1709796), _1709800)), hAPP(c_List_Omap(_1709798, _1709794), _1709802)) = hAPP(c_List_Omap(_1709798, _1709796), hAPP(c_Fun_Ocomp(_1709794, _1709796, _1709798, _1709800), _1709802)))], (20417 ^ _779999) ^ [_1151482, _1151484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151482), _1151484)), -(c_Nat__Transfer_Otsub(_1151484, _1151482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1151484), _1151482))], (51856 ^ _779999) ^ [_1829149, _1829151] : [class_Groups_Ouminus(_1829149), -(class_Groups_Ouminus(tc_fun(_1829151, _1829149)))], (18639 ^ _779999) ^ [_1119768, _1119770, _1119772, _1119774] : [class_Orderings_Olinorder(_1119768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119768), _1119770), _1119772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119768), _1119772), _1119774)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119768, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1119768, _1119770, _1119772)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1119768, _1119772, _1119774)) = c_SetInterval_Oord__class_OatLeastAtMost(_1119768, _1119770, _1119774))], (29694 ^ _779999) ^ [_1336797, _1336799, _1336801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336797)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1336801), _1336797)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336799), _1336801)), _1336797))], (41320 ^ _779999) ^ [_1588548, _1588550, _1588552, _1588554] : [class_Orderings_Olinorder(_1588548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588548), _1588550)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1588548, _1588548, c_Orderings_Oord__class_Omax(_1588548)), _1588552), hAPP(hAPP(c_Set_Oinsert(_1588548), _1588554), _1588550)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1588548), _1588554), hAPP(hAPP(c_Finite__Set_Ofold(_1588548, _1588548, c_Orderings_Oord__class_Omax(_1588548)), _1588552), _1588550)))], (22164 ^ _779999) ^ [_1189962, _1189964, _1189966, _1189968, _1189970] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1189962, tc_fun(_1189964, tc_HOL_Obool)), _1189966), _1189968), _1189970))), 22165 ^ _779999 : [(22166 ^ _779999) ^ [_1190034] : [hBOOL(hAPP(hAPP(c_member(_1189962), _1190034), _1189966)), hBOOL(hAPP(hAPP(_1189968, _1190034), _1189970))]]], (6661 ^ _779999) ^ [_888769, _888771, _888773, _888775, _888777] : [class_Lattices_Osemilattice__sup(_888769), class_Lattices_Osemilattice__sup(_888771), c_Orderings_Oorder__class_Omono(_888771, _888769, _888773), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_888769), hAPP(_888773, _888775)), hAPP(_888773, _888777))), hAPP(_888773, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_888771), _888775), _888777)))))], (44610 ^ _779999) ^ [_1670337, _1670339] : [c_Orderings_Obot__class_Obot(tc_fun(_1670337, tc_HOL_Obool)) = hAPP(c_List_Oset(_1670337), _1670339), -(_1670339 = c_List_Olist_ONil(_1670337))], (40299 ^ _779999) ^ [_1563787, _1563789] : [-(c_Transitive__Closure_Otrancl(_1563787, c_Transitive__Closure_Ortrancl(_1563787, _1563789)) = c_Transitive__Closure_Ortrancl(_1563787, _1563789))], (41905 ^ _779999) ^ [_1600876, _1600878, _1600880, _1600882, _1600884] : [41907 ^ _779999 : [(41910 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1600876), _1600878), hAPP(_1600884, 41906 ^ [_1600876, _1600878, _1600880, _1600882, _1600884])))], (41908 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600880), 41906 ^ [_1600876, _1600878, _1600880, _1600882, _1600884]), _1600882)))]], -(hBOOL(hAPP(hAPP(c_member(_1600876), _1600878), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600880, tc_fun(_1600876, tc_HOL_Obool)), _1600882), _1600884))))], (50468 ^ _779999) ^ [_1799746, _1799748, _1799750, _1799752] : [-(hAPP(c_Relation_OImage(_1799746, _1799748, hAPP(c_Set_OCollect(tc_prod(_1799746, _1799748)), hAPP(c_Product__Type_Oprod_Oprod__case(_1799746, _1799748, tc_HOL_Obool), _1799750))), _1799752) = hAPP(c_Set_OCollect(_1799748), hAPP(hAPP(c_COMBB(tc_fun(_1799746, tc_HOL_Obool), tc_HOL_Obool, _1799748), c_HOL_OEx(_1799746)), hAPP(hAPP(c_COMBB(tc_fun(_1799746, tc_HOL_Obool), tc_fun(_1799746, tc_HOL_Obool), _1799748), hAPP(c_COMBS(_1799746, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1799746), c_fconj), hAPP(hAPP(c_COMBC(_1799746, tc_fun(_1799746, tc_HOL_Obool), tc_HOL_Obool), c_member(_1799746)), _1799752)))), hAPP(c_COMBC(_1799746, _1799748, tc_HOL_Obool), _1799750)))))], (52092 ^ _779999) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (35400 ^ _779999) ^ [_1446092, _1446094] : [class_Rings_Osemiring__1(_1446092), -(hBOOL(hAPP(hAPP(c_member(_1446092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1446092), _1446094)), c_Nat_Osemiring__1__class_ONats(_1446092))))], (30222 ^ _779999) ^ [_1346382, _1346384] : [class_Rings_Olinordered__idom(_1346382), 30225 ^ _779999 : [(30232 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1346384), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346382), hAPP(c_Int_Oring__1__class_Oof__int(_1346382), _1346384)), c_Groups_Ozero__class_Ozero(_1346382))))], (30226 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346382), hAPP(c_Int_Oring__1__class_Oof__int(_1346382), _1346384)), c_Groups_Ozero__class_Ozero(_1346382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1346384), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44488 ^ _779999) ^ [_1668130, _1668132, _1668134] : [class_Orderings_Olinorder(_1668130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1668130), _1668132)), -(c_List_Olinorder__class_Osorted__list__of__set(_1668130, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1668130, tc_HOL_Obool)), _1668132), hAPP(hAPP(c_Set_Oinsert(_1668130), _1668134), c_Orderings_Obot__class_Obot(tc_fun(_1668130, tc_HOL_Obool))))) = c_List_Oremove1(_1668130, _1668134, c_List_Olinorder__class_Osorted__list__of__set(_1668130, _1668132)))], (26594 ^ _779999) ^ [_1278375, _1278377, _1278379] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278375, tc_HOL_Obool)), _1278377), _1278379) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278375, tc_HOL_Obool)), _1278377), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278375, tc_HOL_Obool)), _1278379)))], (23829 ^ _779999) ^ [_1224895, _1224897, _1224899] : [class_Orderings_Olinorder(_1224895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224895), _1224897)), 23836 ^ _779999 : [(23843 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1224895, tc_HOL_Obool)), _1224897), hAPP(hAPP(c_Set_Oinsert(_1224895), _1224899), c_Orderings_Obot__class_Obot(tc_fun(_1224895, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1224895, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1224895, hAPP(hAPP(c_Set_Oinsert(_1224895), _1224899), _1224897)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224895), _1224899), c_Big__Operators_Olinorder__class_OMin(_1224895, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1224895, tc_HOL_Obool)), _1224897), hAPP(hAPP(c_Set_Oinsert(_1224895), _1224899), c_Orderings_Obot__class_Obot(tc_fun(_1224895, tc_HOL_Obool)))))))], (23837 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1224895, tc_HOL_Obool)), _1224897), hAPP(hAPP(c_Set_Oinsert(_1224895), _1224899), c_Orderings_Obot__class_Obot(tc_fun(_1224895, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1224895, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1224895, hAPP(hAPP(c_Set_Oinsert(_1224895), _1224899), _1224897)) = _1224899)]]], (51960 ^ _779999) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (12920 ^ _779999) ^ [_1009145, _1009147, _1009149, _1009151, _1009153] : [class_Groups_Ocomm__monoid__add(_1009145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009147), _1009149)), hBOOL(hAPP(hAPP(c_member(_1009147), _1009151), _1009149)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009147, _1009145), _1009153), _1009149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009145), hAPP(_1009153, _1009151)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009147, _1009145), _1009153), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009147, tc_HOL_Obool)), _1009149), hAPP(hAPP(c_Set_Oinsert(_1009147), _1009151), c_Orderings_Obot__class_Obot(tc_fun(_1009147, tc_HOL_Obool)))))))], (18513 ^ _779999) ^ [_1117166, _1117168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117166), _1117168)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1117166), hAPP(c_Nat_OSuc, _1117168)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1117168), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1117166), _1117168)))], (32897 ^ _779999) ^ [_1396947, _1396949] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1396947) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1396949)), 32900 ^ _779999 : [(32903 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396949)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32901 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396947))))]], 32904 ^ _779999 : [(32907 ^ _779999) ^ [] : [32908 ^ _779999 : [(32911 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396947) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32909 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396949))))]], 32912 ^ _779999 : [(32915 ^ _779999) ^ [] : [_1396947 = _1396949], (32913 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396949)))]]], (32905 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396947)))]]], (44706 ^ _779999) ^ [_1672107, _1672109, _1672111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672107), tc_List_Olist(_1672107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672107), tc_List_Olist(_1672107)), c_List_Olist_ONil(_1672107)), _1672109)), c_List_Olex(_1672107, _1672111)))], (44672 ^ _779999) ^ [_1671388, _1671390, _1671392, _1671394] : [hAPP(hAPP(c_List_Olist__update(_1671388, _1671390), _1671392), _1671394) = c_List_Olist_ONil(_1671388), -(_1671390 = c_List_Olist_ONil(_1671388))], (33201 ^ _779999) ^ [_1401802] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401802), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401802), c_Int_OPls)))], (35131 ^ _779999) ^ [] : [-(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))], (39843 ^ _779999) ^ [_1552327, _1552329, _1552331, _1552333, _1552335] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1552327, _1552329, _1552331), _1552333), _1552335))), hBOOL(hAPP(hAPP(_1552329, _1552333), _1552335)), hBOOL(hAPP(_1552331, _1552335))], (47482 ^ _779999) ^ [_1734794, _1734796, _1734798, _1734800] : [hBOOL(hAPP(_1734794, _1734796)), -(hAPP(c_List_Ofilter(_1734798, _1734794), hAPP(hAPP(c_List_Olist_OCons(_1734798), _1734796), _1734800)) = hAPP(hAPP(c_List_Olist_OCons(_1734798), _1734796), hAPP(c_List_Ofilter(_1734798, _1734794), _1734800)))], (37146 ^ _779999) ^ [_1482902, _1482904, _1482906, _1482908, _1482910, _1482912] : [-(c_Product__Type_Oprod_Oprod__rec(_1482902, _1482904, _1482906, _1482908, hAPP(hAPP(c_Product__Type_OPair(_1482902, _1482904), _1482910), _1482912)) = hAPP(hAPP(_1482908, _1482910), _1482912))], (5752 ^ _779999) ^ [_868019, _868021, _868023, _868025] : [-(tc_fun(_868025, _868021) = tc_fun(_868023, _868019)), _868025 = _868023, _868021 = _868019], (3214 ^ _779999) ^ [_827934, _827936, _827938, _827940, _827942, _827944] : [-(c_Product__Type_Ointernal__split(_827944, _827940, _827936) = c_Product__Type_Ointernal__split(_827942, _827938, _827934)), _827944 = _827942, _827940 = _827938, _827936 = _827934], (33161 ^ _779999) ^ [_1401204] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401204), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401204)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1401204)))], (4094 ^ _779999) ^ [_841692, _841694, _841696, _841698, _841700, _841702] : [-(c_List_OtakeWhile(_841702, _841698, _841694) = c_List_OtakeWhile(_841700, _841696, _841692)), _841702 = _841700, _841698 = _841696, _841694 = _841692], (34017 ^ _779999) ^ [_1416273, _1416275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416273)), c_Int_OBit1(_1416275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416273), _1416275)))], (35824 ^ _779999) ^ [_1455019, _1455021] : [35825 ^ _779999 : [(35828 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1455021), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35826 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1455019), _1455021))]], -(c_Divides_OposDivAlg(_1455019, _1455021) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455019))], (26052 ^ _779999) ^ [_1268704, _1268706, _1268708, _1268710] : [class_Rings_Ocomm__semiring__1(_1268704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268706), _1268708)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1268706, _1268704), _1268710), _1268708) = c_Groups_Ozero__class_Ozero(_1268704)), 26061 ^ _779999 : [(26062 ^ _779999) ^ [_1268885] : [hBOOL(hAPP(hAPP(c_member(_1268706), _1268885), _1268708)), hAPP(_1268710, _1268885) = c_Groups_Ozero__class_Ozero(_1268704)]]], (34071 ^ _779999) ^ [_1417212, _1417214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417212), _1417214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1417212)), c_Int_OBit0(_1417214))))], (11100 ^ _779999) ^ [_972340, _972342, _972344] : [class_Lattices_Olattice(_972340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972340), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972340), _972342), _972344)), _972342)))], (34617 ^ _779999) ^ [_1427207, _1427209] : [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), _1427207))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1427209))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427207))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427209)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427207)))], (31004 ^ _779999) ^ [_1361121, _1361123, _1361125] : [-(hBOOL(hAPP(_1361121, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361123, _1361125)))), 31007 ^ _779999 : [(31010 ^ _779999) ^ [] : [hBOOL(hAPP(_1361121, _1361123))], (31008 ^ _779999) ^ [] : [-(_1361125 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 31013 ^ _779999 : [(31014 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361125)))], (31020 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31016 ^ [_1361121, _1361123, _1361125]), _1361125)))], (31024 ^ _779999) ^ [] : [hBOOL(hAPP(_1361121, 31016 ^ [_1361121, _1361123, _1361125]))], (31022 ^ _779999) ^ [] : [-(_1361123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361125), 31015 ^ [_1361121, _1361123, _1361125])), 31016 ^ [_1361121, _1361123, _1361125]))], (31018 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31016 ^ [_1361121, _1361123, _1361125])))]], 31025 ^ _779999 : [(31026 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1361125), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31032 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31028 ^ [_1361121, _1361123, _1361125]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31036 ^ _779999) ^ [] : [hBOOL(hAPP(_1361121, 31028 ^ [_1361121, _1361123, _1361125]))], (31034 ^ _779999) ^ [] : [-(_1361123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361125), 31027 ^ [_1361121, _1361123, _1361125])), 31028 ^ [_1361121, _1361123, _1361125]))], (31030 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1361125), 31028 ^ [_1361121, _1361123, _1361125])))]]], (10579 ^ _779999) ^ [_962074, _962076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962074), _962076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962074)), _962076)))], (32941 ^ _779999) ^ [_1397829] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397829))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397829)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37359 ^ _779999) ^ [_1488284, _1488286, _1488288, _1488290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1488284), _1488286)), 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)), _1488284), _1488288)), 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)), _1488286), _1488290)), 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)), _1488286), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1488288), _1488290))), c_FunDef_Omin__strict)))], (51724 ^ _779999) ^ [_1827134, _1827136, _1827138, _1827140] : [c_Fun_Obij__betw(_1827134, _1827136, _1827138, c_Orderings_Otop__class_Otop(tc_fun(_1827134, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1827136, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1827134, _1827136, _1827138), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1827134, tc_HOL_Obool)), _1827140)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1827136, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1827134, _1827136, _1827138), _1827140)))], (50070 ^ _779999) ^ [_1790661, _1790663, _1790665, _1790667, _1790669, _1790671] : [-(c_New__Random__Sequence_Opos__union(_1790661, _1790663, _1790665, _1790667, _1790669, _1790671) = c_New__DSequence_Opos__union(_1790661, hAPP(hAPP(hAPP(_1790663, _1790667), _1790669), _1790671), hAPP(hAPP(hAPP(_1790665, _1790667), _1790669), _1790671)))], (50486 ^ _779999) ^ [_1800269, _1800271, _1800273, _1800275] : [c_Relation_Otrans(_1800269, _1800271), c_Relation_Otrans(_1800273, _1800275), -(c_Relation_Otrans(tc_prod(_1800269, _1800273), c_Wellfounded_Olex__prod(_1800269, _1800273, _1800271, _1800275)))], (7604 ^ _779999) ^ [_907683, _907685, _907687, _907689] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_907683, _907685)), _907687), _907689)), 7608 ^ _779999 : [(7611 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907685), 7607 ^ [_907683, _907685, _907687, _907689]), _907689)))], (7609 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907683), _907687), 7607 ^ [_907683, _907685, _907687, _907689])))]]], (49734 ^ _779999) ^ [_1783281, _1783283, _1783285, _1783287] : [-(c_New__Random__Sequence_Opos__empty(_1783281, _1783283, _1783285, _1783287) = c_New__DSequence_Opos__empty(_1783281))], (41412 ^ _779999) ^ [_1590442, _1590444, _1590446, _1590448] : [class_Orderings_Olinorder(_1590442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590442), _1590444)), hBOOL(hAPP(hAPP(c_member(_1590442), _1590446), _1590444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1590442), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1590442), _1590446), _1590448)), hAPP(hAPP(c_Finite__Set_Ofold(_1590442, _1590442, c_Orderings_Oord__class_Omax(_1590442)), _1590448), _1590444))))], (41692 ^ _779999) ^ [_1595745, _1595747, _1595749, _1595751, _1595753] : [c_Finite__Set_Ofun__left__comm(_1595745, _1595747, _1595749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595745), _1595751)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1595745, _1595747, _1595749, _1595753, _1595751), hAPP(hAPP(c_Finite__Set_Ofold(_1595745, _1595747, _1595749), _1595753), _1595751))))], (46728 ^ _779999) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (11384 ^ _779999) ^ [_977724, _977726, _977728, _977730] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977724, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977724), _977726), _977728)), hAPP(hAPP(c_Set_Oinsert(_977724), _977726), _977730)) = hAPP(hAPP(c_Set_Oinsert(_977724), _977726), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977724, tc_HOL_Obool)), _977728), _977730)))], (46498 ^ _779999) ^ [_1712794, _1712796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712794), _1712796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1712794)), hAPP(c_Code__Numeral_Oof__nat, _1712796))))], (10976 ^ _779999) ^ [_969689, _969691] : [class_Lattices_Osemilattice__inf(_969689), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_969689), _969691), _969691) = _969691)], (36551 ^ _779999) ^ [_1468570, _1468572, _1468574, _1468576, _1468578, _1468580] : [hBOOL(hAPP(_1468570, _1468572)), hBOOL(hAPP(_1468574, _1468576)), 36558 ^ _779999 : [(36561 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1468574, hAPP(c_Product__Type_Osnd(_1468578, _1468580), hAPP(hAPP(c_Product__Type_OPair(_1468578, _1468580), _1468572), _1468576)))))], (36559 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1468570, hAPP(c_Product__Type_Ofst(_1468578, _1468580), hAPP(hAPP(c_Product__Type_OPair(_1468578, _1468580), _1468572), _1468576)))))]]], (36414 ^ _779999) ^ [_1465717, _1465719] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465717, _1465717)), hAPP(hAPP(c_Product__Type_OPair(_1465717, _1465717), 36415 ^ [_1465717, _1465719]), 36415 ^ [_1465717, _1465719])), _1465719))), -(c_Relation_Oirrefl(_1465717, _1465719))], (9186 ^ _779999) ^ [_936822, _936824, _936826, _936828] : [-(c_Nitpick_Ofold__graph_H(_936822, _936824, _936826, _936828, c_Orderings_Obot__class_Obot(tc_fun(_936822, tc_HOL_Obool)), _936828))], (43775 ^ _779999) ^ [_1650471, _1650473, _1650475, _1650477] : [-(hBOOL(hAPP(hAPP(c_member(_1650471), _1650473), hAPP(c_List_Oset(_1650471), _1650475)))), hBOOL(hAPP(hAPP(c_member(_1650471), _1650473), hAPP(c_List_Oset(_1650471), c_List_Osublist(_1650471, _1650475, _1650477))))], (52032 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (34339 ^ _779999) ^ [_1422110] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1422110))), 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), _1422110), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (19481 ^ _779999) ^ [_1135177, _1135179] : [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)), _1135177)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1135179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1135177), _1135179)))], (27710 ^ _779999) ^ [_1300983, _1300985, _1300987] : [class_Rings_Osemiring__1(_1300983), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1300983), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1300985), _1300987)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1300983), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1300983), _1300985)), _1300987))], (33425 ^ _779999) ^ [] : [-(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))))))], (33011 ^ _779999) ^ [_1398911, _1398913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1398911), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398913)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398911)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398913))], (37118 ^ _779999) ^ [_1482394, _1482396, _1482398, _1482400, _1482402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1482394, _1482396)), hAPP(_1482394, _1482398))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482400, _1482400)), hAPP(hAPP(c_Product__Type_OPair(_1482400, _1482400), _1482396), _1482398)), c_Wellfounded_Omlex__prod(_1482400, _1482394, _1482402))))], (17943 ^ _779999) ^ [_1106611, _1106613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106611), _1106613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106611)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106613))))], (16189 ^ _779999) ^ [_1072369, _1072371, _1072373, _1072375, _1072377] : [class_Rings_Oordered__semiring(_1072369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072369), _1072371), _1072373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072369), _1072375), _1072377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072369), c_Groups_Ozero__class_Ozero(_1072369)), _1072373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072369), c_Groups_Ozero__class_Ozero(_1072369)), _1072375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072369), _1072371), _1072375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072369), _1072373), _1072377))))], (18147 ^ _779999) ^ [_1110327, _1110329] : [class_Rings_Olinordered__semidom(_1110327), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110327), c_Groups_Ozero__class_Ozero(_1110327)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110327), _1110329))))], (34417 ^ _779999) ^ [_1423511, _1423513] : [class_Rings_Olinordered__idom(_1423511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423511), hAPP(hAPP(c_Power_Opower__class_Opower(_1423511), _1423513), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1423511)))], (40687 ^ _779999) ^ [_1572429, _1572431, _1572433, _1572435, _1572437] : [-(hAPP(c_Relation_Oconverse(_1572429, _1572431), hAPP(hAPP(c_Relation_Orel__comp(_1572429, _1572433, _1572431), _1572435), _1572437)) = hAPP(hAPP(c_Relation_Orel__comp(_1572431, _1572433, _1572429), hAPP(c_Relation_Oconverse(_1572433, _1572431), _1572437)), hAPP(c_Relation_Oconverse(_1572429, _1572433), _1572435)))], (47256 ^ _779999) ^ [_1729180, _1729182, _1729184] : [-(c_List_Oconcat(_1729180, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729180)), _1729182), _1729184)) = hAPP(hAPP(c_List_Oappend(_1729180), _1729182), c_List_Oconcat(_1729180, _1729184)))], (25116 ^ _779999) ^ [_1251323, _1251325, _1251327] : [class_Orderings_Olinorder(_1251323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251323), _1251325)), -(_1251325 = c_Orderings_Obot__class_Obot(tc_fun(_1251323, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251323), _1251327)), -(_1251327 = c_Orderings_Obot__class_Obot(tc_fun(_1251323, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1251323, tc_HOL_Obool)), _1251325), _1251327) = c_Orderings_Obot__class_Obot(tc_fun(_1251323, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1251323, c_Orderings_Oord__class_Omax(_1251323), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251323, tc_HOL_Obool)), _1251325), _1251327)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1251323), c_Big__Operators_Olattice_OSup__fin(_1251323, c_Orderings_Oord__class_Omax(_1251323), _1251325)), c_Big__Operators_Olattice_OSup__fin(_1251323, c_Orderings_Oord__class_Omax(_1251323), _1251327)))], (20508 ^ _779999) ^ [_1152889, _1152891] : [c_Nat__Transfer_Onat__set(_1152889), c_Nat__Transfer_Onat__set(_1152891), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1152889), _1152891)))], (30609 ^ _779999) ^ [_1353869] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1353869, _1353869) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46049 ^ _779999) ^ [_1702409, _1702411, _1702413] : [-(_1702409 = c_List_Olist_ONil(_1702411)), -(c_List_Olast(_1702411, hAPP(hAPP(c_List_Oappend(_1702411), _1702413), _1702409)) = c_List_Olast(_1702411, _1702409))], (19465 ^ _779999) ^ [_1134916, _1134918] : [_1134916 = _1134918, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134916) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134918))], (32861 ^ _779999) ^ [_1396382, _1396384] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1396382) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396384)), _1396382 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396384)), 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), _1396384)))], (48416 ^ _779999) ^ [_1754346, _1754348, _1754350] : [hAPP(c_List_Orev(_1754346), _1754348) = _1754350, -(_1754348 = hAPP(c_List_Orev(_1754346), _1754350))], (11472 ^ _779999) ^ [_980322, _980324, _980326, _980328] : [class_Lattices_Olattice(_980322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980322), _980324), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_980322), _980326), _980328))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_980322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980322), _980324), _980326)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980322), _980324), _980328)))))], (39164 ^ _779999) ^ [_1535606] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1535606), c_Int_OInteg)), -(_1535606 = hAPP(c_Int_ORep__Integ, 39167 ^ [_1535606]))], (47516 ^ _779999) ^ [_1735596, _1735598, _1735600, _1735602] : [-(c_List_Otranspose(_1735596, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735598), tc_List_Olist(_1735596)), hAPP(c_List_Omap(_1735598, _1735596), _1735600)), _1735602)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735598), tc_List_Olist(_1735596)), hAPP(c_List_Omap(_1735598, _1735596), _1735600)), c_List_Otranspose(_1735598, _1735602)))], (42896 ^ _779999) ^ [_1625498, _1625500, _1625502] : [class_Divides_Osemiring__div(_1625498), -(_1625500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1625498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1625498), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1625498), _1625500), _1625502)), _1625502)), c_Divides_Odiv__class_Omod(_1625498, _1625500, _1625502)))], (32959 ^ _779999) ^ [_1398081, _1398083] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398081)))), 32962 ^ _779999 : [(32969 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398083)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398081), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398083)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398081), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398083))))], (32963 ^ _779999) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398083))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398081), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398083)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398081))]]], (47522 ^ _779999) ^ [_1735826, _1735828, _1735830, _1735832] : [hBOOL(hAPP(hAPP(c_member(_1735826), _1735828), hAPP(c_List_Oset(_1735826), _1735830))), -(hBOOL(hAPP(_1735832, _1735828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735826)), hAPP(c_List_Ofilter(_1735826, _1735832), _1735830))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735826)), _1735830))))], (29322 ^ _779999) ^ [_1330930, _1330932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1330930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330932)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1330932), _1330930)), _1330932) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1330932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1330930), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (23069 ^ _779999) ^ [_1210495, _1210497, _1210499] : [class_Orderings_Olinorder(_1210495), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210495), _1210497), _1210499) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210495), _1210499), _1210497))], (35880 ^ _779999) ^ [_1455823, _1455825] : [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), _1455823))), 35883 ^ _779999 : [(35890 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455825)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455823)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455825), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455823)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455823)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455825), 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), _1455823)))))], (35884 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455825)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455823))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455825), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1455823)) = 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), _1455825)))]]], (45273 ^ _779999) ^ [_1685252, _1685254, _1685256, _1685258] : [-(c_List_Osublist(_1685252, hAPP(hAPP(c_List_Oappend(_1685252), _1685254), _1685256), _1685258) = hAPP(hAPP(c_List_Oappend(_1685252), c_List_Osublist(_1685252, _1685254, _1685258)), c_List_Osublist(_1685252, _1685256, 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(_1685252)), _1685254)))), _1685258)))))], (4462 ^ _779999) ^ [_847806, _847808, _847810, _847812, _847814, _847816] : [-(c_Lazy__Sequence_Obind(_847816, _847812, _847808) = c_Lazy__Sequence_Obind(_847814, _847810, _847806)), _847816 = _847814, _847812 = _847810, _847808 = _847806], (4566 ^ _779999) ^ [_849370, _849372, _849374, _849376] : [-(c_List_Oconcat(_849376, _849372) = c_List_Oconcat(_849374, _849370)), _849376 = _849374, _849372 = _849370], (26590 ^ _779999) ^ [_1278261, _1278263] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278261, tc_HOL_Obool)), _1278263) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278261, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1278261, tc_HOL_Obool))), _1278263))], (25338 ^ _779999) ^ [_1255674, _1255676, _1255678] : [-(hBOOL(hAPP(hAPP(c_member(_1255674), _1255676), _1255678))), -(hBOOL(hAPP(hAPP(c_member(_1255674), _1255676), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1255674, tc_HOL_Obool)), _1255678))))], (50524 ^ _779999) ^ [_1801192, _1801194] : [50527 ^ _779999 : [(50533 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1801192, _1801192)), hAPP(hAPP(c_Product__Type_OPair(_1801192, _1801192), 50525 ^ [_1801192, _1801194]), 50529 ^ [_1801192, _1801194])), _1801194))], (50531 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801192, _1801192)), hAPP(hAPP(c_Product__Type_OPair(_1801192, _1801192), 50526 ^ [_1801192, _1801194]), 50529 ^ [_1801192, _1801194])), _1801194)))], (50528 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801192, _1801192)), hAPP(hAPP(c_Product__Type_OPair(_1801192, _1801192), 50525 ^ [_1801192, _1801194]), 50526 ^ [_1801192, _1801194])), _1801194)))]], -(c_Relation_Otrans(_1801192, _1801194))], (42970 ^ _779999) ^ [_1627318, _1627320, _1627322, _1627324, _1627326, _1627328, _1627330, _1627332] : [c_Finite__Set_Ofolding__image__simple__idem(_1627318, _1627320, _1627322, _1627324, _1627326, _1627328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627320), _1627330)), -(hAPP(_1627328, hAPP(hAPP(c_Set_Oinsert(_1627320), _1627332), _1627330)) = hAPP(hAPP(_1627322, hAPP(_1627326, _1627332)), hAPP(_1627328, _1627330)))], (32065 ^ _779999) ^ [_1381280, _1381282, _1381284, _1381286] : [class_Fields_Ofield__inverse__zero(_1381280), class_Int_Onumber(_1381280), 32072 ^ _779999 : [(32073 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381280), _1381284), _1381286), 32076 ^ _779999 : [(32083 ^ _779999) ^ [] : [_1381286 = c_Groups_Ozero__class_Ozero(_1381280), -(hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282) = c_Groups_Ozero__class_Ozero(_1381280))], (32077 ^ _779999) ^ [] : [-(_1381286 = c_Groups_Ozero__class_Ozero(_1381280)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381280), hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282)), _1381286) = _1381284)]]], (32089 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381280), _1381284), _1381286)), 32092 ^ _779999 : [(32095 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381280), hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282)), _1381286) = _1381284], (32093 ^ _779999) ^ [] : [_1381286 = c_Groups_Ozero__class_Ozero(_1381280)]], 32096 ^ _779999 : [(32099 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381280), _1381282) = c_Groups_Ozero__class_Ozero(_1381280)], (32097 ^ _779999) ^ [] : [-(_1381286 = c_Groups_Ozero__class_Ozero(_1381280))]]]]], (37624 ^ _779999) ^ [_1494849] : [-(_1494849 = 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), 37621 ^ [_1494849]), 37622 ^ [_1494849])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38394 ^ _779999) ^ [_1514717, _1514719, _1514721] : [-(hAPP(c_Relation_ODomain(_1514717, _1514719), hAPP(c_Set_OCollect(tc_prod(_1514717, _1514719)), hAPP(c_Product__Type_Oprod_Oprod__case(_1514717, _1514719, tc_HOL_Obool), _1514721))) = hAPP(c_Set_OCollect(_1514717), hAPP(hAPP(c_COMBB(tc_fun(_1514719, tc_HOL_Obool), tc_HOL_Obool, _1514717), c_HOL_OEx(_1514719)), _1514721)))], (42189 ^ _779999) ^ [_1609435, _1609437, _1609439, _1609441, _1609443] : [_1609435 = c_Orderings_Obot__class_Obot(tc_fun(_1609437, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609437, tc_fun(_1609439, tc_HOL_Obool)), _1609435), hAPP(hAPP(c_COMBB(tc_fun(_1609439, tc_HOL_Obool), tc_fun(_1609439, tc_HOL_Obool), _1609437), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609439, tc_HOL_Obool)), _1609441)), _1609443)) = c_Orderings_Otop__class_Otop(tc_fun(_1609439, tc_HOL_Obool)))], (10996 ^ _779999) ^ [_970057, _970059, _970061] : [class_Lattices_Osemilattice__inf(_970057), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970057), _970059), _970061) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970057), _970061), _970059))], (23219 ^ _779999) ^ [_1213282, _1213284, _1213286, _1213288] : [class_Orderings_Olinorder(_1213282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213282), _1213284), _1213286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213282), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213282), _1213288), _1213284)), _1213286)))], (47258 ^ _779999) ^ [_1729231, _1729233] : [-(c_List_Oconcat(_1729231, _1729233) = hAPP(c_List_Ofoldl(tc_List_Olist(_1729231), tc_List_Olist(_1729231), c_List_Oappend(_1729231), c_List_Olist_ONil(_1729231)), _1729233))], (41310 ^ _779999) ^ [_1588325, _1588327, _1588329, _1588331] : [class_Orderings_Olinorder(_1588325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588325), _1588327)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1588325, _1588325, c_Orderings_Oord__class_Omin(_1588325)), _1588329), hAPP(hAPP(c_Set_Oinsert(_1588325), _1588331), _1588327)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1588325), _1588331), hAPP(hAPP(c_Finite__Set_Ofold(_1588325, _1588325, c_Orderings_Oord__class_Omin(_1588325)), _1588329), _1588327)))], (33961 ^ _779999) ^ [_1415391] : [_1415391 = c_Int_OPls, -(c_Int_OBit0(_1415391) = c_Int_OPls)], (3366 ^ _779999) ^ [_830308, _830310, _830312, _830314, _830316, _830318, _830320, _830322] : [-(c_Nat_Onat_Onat__case(_830322, _830318, _830314, _830310) = c_Nat_Onat_Onat__case(_830320, _830316, _830312, _830308)), _830322 = _830320, _830318 = _830316, _830314 = _830312, _830310 = _830308], (18607 ^ _779999) ^ [_1119129, _1119131, _1119133, _1119135] : [class_Groups_Ocomm__monoid__add(_1119129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119131), _1119133)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1119129), _1119135), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1119131), _1119133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119129), hAPP(_1119135, _1119131)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1119129), _1119135), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1119131)), _1119133))))], (34777 ^ _779999) ^ [] : [-(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))], (43901 ^ _779999) ^ [_1653715, _1653717, _1653719, _1653721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653715), tc_List_Olist(_1653715))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653715), tc_List_Olist(_1653715)), _1653717), _1653719)), c_List_Olistrel(_1653715, _1653721))), 43904 ^ _779999 : [(43907 ^ _779999) ^ [_1654051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653715, _1653715)), _1654051), hAPP(c_List_Oset(tc_prod(_1653715, _1653715)), hAPP(hAPP(c_List_Ozip(_1653715, _1653715), _1653717), _1653719)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1653715, _1653715, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1653715, tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_fun(_1653715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1653715, tc_fun(tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_fun(_1653715, tc_HOL_Obool)), _1653715), c_COMBC(_1653715, tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1653715, tc_prod(_1653715, _1653715)), tc_fun(_1653715, tc_fun(tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_HOL_Obool)), _1653715), hAPP(c_COMBB(tc_prod(_1653715, _1653715), tc_fun(tc_fun(tc_prod(_1653715, _1653715), tc_HOL_Obool), tc_HOL_Obool), _1653715), c_member(tc_prod(_1653715, _1653715)))), c_Product__Type_OPair(_1653715, _1653715)))), _1653721)), _1654051)))], (43905 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653715)), _1653717) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653715)), _1653719))]]], (11388 ^ _779999) ^ [_977847, _977849, _977851] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977847, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977847, tc_HOL_Obool)), _977849), _977851)), _977851)))], (46079 ^ _779999) ^ [_1702803, _1702805, _1702807] : [_1702803 = c_List_Olist_ONil(_1702805), -(c_List_Olast(_1702805, hAPP(hAPP(c_List_Olist_OCons(_1702805), _1702807), _1702803)) = _1702807)], (42115 ^ _779999) ^ [_1607475, _1607477, _1607479, _1607481] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607475, tc_fun(_1607477, tc_HOL_Obool)), _1607479), _1607481) = hAPP(c_Set_OCollect(_1607477), hAPP(hAPP(c_COMBB(tc_fun(_1607475, tc_HOL_Obool), tc_HOL_Obool, _1607477), c_HOL_OAll(_1607475)), hAPP(hAPP(c_COMBB(tc_fun(_1607475, tc_HOL_Obool), tc_fun(_1607475, tc_HOL_Obool), _1607477), hAPP(c_COMBS(_1607475, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1607475), c_fimplies), hAPP(hAPP(c_COMBC(_1607475, tc_fun(_1607475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1607475)), _1607479)))), hAPP(hAPP(c_COMBC(_1607477, tc_fun(_1607475, tc_fun(_1607477, tc_HOL_Obool)), tc_fun(_1607475, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1607477, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1607475, tc_fun(_1607477, tc_HOL_Obool)), tc_fun(_1607475, tc_HOL_Obool)), _1607477), c_COMBB(tc_fun(_1607477, tc_HOL_Obool), tc_HOL_Obool, _1607475)), c_member(_1607477))), _1607481)))))], (17059 ^ _779999) ^ [_1088597, _1088599, _1088601, _1088603] : [class_Rings_Olinordered__semiring(_1088597), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088597), _1088599), _1088601)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088597), _1088599), _1088603))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088597), c_Groups_Ozero__class_Ozero(_1088597)), _1088599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088597), _1088601), _1088603)))], (48430 ^ _779999) ^ [_1754577, _1754579] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754577)), hAPP(c_List_Orev(_1754577), _1754579)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754577)), _1754579))], (34989 ^ _779999) ^ [_1433849, _1433851] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1433849), _1433851) = c_Groups_Oone__class_Oone(tc_Int_Oint), 34994 ^ _779999 : [(34997 ^ _779999) ^ [] : [-(_1433851 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34995 ^ _779999) ^ [] : [-(_1433849 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 34998 ^ _779999 : [(35001 ^ _779999) ^ [] : [-(_1433851 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (34999 ^ _779999) ^ [] : [-(_1433849 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (44546 ^ _779999) ^ [_1669257] : [class_Orderings_Olinorder(_1669257), -(c_List_Olinorder__class_Osorted__list__of__set(_1669257, c_Orderings_Obot__class_Obot(tc_fun(_1669257, tc_HOL_Obool))) = c_List_Olist_ONil(_1669257))], (52154 ^ _779999) ^ [_1831920] : [class_Lazy__Sequence_Osmall__lazy(_1831920), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1831920)))], (15647 ^ _779999) ^ [_1061980, _1061982] : [class_Rings_Ocomm__semiring__1(_1061980), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061980), _1061982), c_Groups_Ozero__class_Ozero(_1061980)) = c_Groups_Ozero__class_Ozero(_1061980))], (42789 ^ _779999) ^ [_1623208, _1623210, _1623212, _1623214, _1623216, _1623218] : [-(_1623208 = c_Orderings_Obot__class_Obot(tc_fun(_1623210, tc_HOL_Obool))), 42795 ^ _779999 : [(42798 ^ _779999) ^ [] : [c_Fun_Oinj__on(_1623212, _1623214, _1623216, hAPP(_1623218, 42794 ^ [_1623208, _1623210, _1623212, _1623214, _1623216, _1623218]))], (42796 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623210), 42794 ^ [_1623208, _1623210, _1623212, _1623214, _1623216, _1623218]), _1623208)))]], -(c_Fun_Oinj__on(_1623212, _1623214, _1623216, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623210, tc_fun(_1623212, tc_HOL_Obool)), _1623208), _1623218)))], (37831 ^ _779999) ^ [_1501456, _1501458, _1501460, _1501462, _1501464, _1501466, _1501468] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501456, _1501460)), hAPP(hAPP(c_Product__Type_OPair(_1501456, _1501460), _1501466), _1501468)), hAPP(hAPP(c_Relation_Orel__comp(_1501456, _1501458, _1501460), _1501462), _1501464))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1501456, _1501458, _1501460, hAPP(hAPP(c_COMBC(_1501456, tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_fun(_1501458, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501458, tc_fun(tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_fun(_1501458, tc_HOL_Obool)), _1501456), c_COMBC(_1501458, tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501458, tc_prod(_1501456, _1501458)), tc_fun(_1501458, tc_fun(tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_HOL_Obool)), _1501456), hAPP(c_COMBB(tc_prod(_1501456, _1501458), tc_fun(tc_fun(tc_prod(_1501456, _1501458), tc_HOL_Obool), tc_HOL_Obool), _1501458), c_member(tc_prod(_1501456, _1501458)))), c_Product__Type_OPair(_1501456, _1501458)))), _1501462), hAPP(hAPP(c_COMBC(_1501458, tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_fun(_1501460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501460, tc_fun(tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_fun(_1501460, tc_HOL_Obool)), _1501458), c_COMBC(_1501460, tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501460, tc_prod(_1501458, _1501460)), tc_fun(_1501460, tc_fun(tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_HOL_Obool)), _1501458), hAPP(c_COMBB(tc_prod(_1501458, _1501460), tc_fun(tc_fun(tc_prod(_1501458, _1501460), tc_HOL_Obool), tc_HOL_Obool), _1501460), c_member(tc_prod(_1501458, _1501460)))), c_Product__Type_OPair(_1501458, _1501460)))), _1501464)), _1501466), _1501468)))], (40417 ^ _779999) ^ [_1566656, _1566658, _1566660] : [_1566658 = _1566660, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566656, _1566656)), hAPP(hAPP(c_Product__Type_OPair(_1566656, _1566656), _1566658), _1566660)), c_Relation_OId(_1566656))))], (31172 ^ _779999) ^ [_1364155, _1364157] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1364155), _1364157) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1364155, _1364157)), _1364157))], (40629 ^ _779999) ^ [_1571356, _1571358, _1571360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571356), _1571358)), -(c_Random_Ominus__shift(_1571360, _1571356, _1571358) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1571360), _1571356)), _1571358))], (5604 ^ _779999) ^ [_865795, _865797] : [_865797 = _865795, -(tc_List_Olist(_865797) = tc_List_Olist(_865795))], (22281 ^ _779999) ^ [_1192226, _1192228, _1192230, _1192232, _1192234] : [-(hAPP(c_Set_Oimage(_1192226, _1192228, hAPP(hAPP(c_COMBB(_1192230, _1192228, _1192226), _1192232), _1192234)), c_Orderings_Otop__class_Otop(tc_fun(_1192226, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1192230, _1192228, _1192232), hAPP(c_Set_Oimage(_1192226, _1192230, _1192234), c_Orderings_Otop__class_Otop(tc_fun(_1192226, tc_HOL_Obool)))))], (48016 ^ _779999) ^ [_1746152, _1746154, _1746156, _1746158, _1746160] : [class_Orderings_Olinorder(_1746152), c_List_Olinorder__class_Osorted(_1746152, hAPP(hAPP(c_List_Omap(_1746154, _1746152), _1746156), _1746158)), -(c_List_Olinorder__class_Osorted(_1746152, hAPP(hAPP(c_List_Omap(_1746154, _1746152), _1746156), c_List_Olinorder__class_Oinsort__insert__key(_1746154, _1746152, _1746156, _1746160, _1746158))))], (43167 ^ _779999) ^ [_1632365, _1632367, _1632369] : [-(hAPP(c_List_Olexn(_1632365, _1632367), hAPP(c_Nat_OSuc, _1632369)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1632365), tc_List_Olist(_1632365)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1632365, tc_List_Olist(_1632365)), tc_prod(_1632365, tc_List_Olist(_1632365))), tc_prod(tc_List_Olist(_1632365), tc_List_Olist(_1632365)), c_Product__Type_Omap__pair(tc_prod(_1632365, tc_List_Olist(_1632365)), tc_List_Olist(_1632365), tc_prod(_1632365, tc_List_Olist(_1632365)), tc_List_Olist(_1632365), hAPP(c_Product__Type_Oprod_Oprod__case(_1632365, tc_List_Olist(_1632365), tc_List_Olist(_1632365)), c_List_Olist_OCons(_1632365)), hAPP(c_Product__Type_Oprod_Oprod__case(_1632365, tc_List_Olist(_1632365), tc_List_Olist(_1632365)), c_List_Olist_OCons(_1632365)))), c_Wellfounded_Olex__prod(_1632365, tc_List_Olist(_1632365), _1632367, hAPP(c_List_Olexn(_1632365, _1632367), _1632369)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1632365), tc_List_Olist(_1632365))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1632365), tc_List_Olist(_1632365), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1632365), tc_fun(tc_List_Olist(_1632365), tc_HOL_Obool), tc_fun(tc_List_Olist(_1632365), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1632365), tc_HOL_Obool), tc_fun(tc_List_Olist(_1632365), tc_HOL_Obool)), tc_List_Olist(_1632365)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1632365))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1632365)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1632365), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1632365)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1632365)))), hAPP(c_Nat_OSuc, _1632369))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1632365), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1632365)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1632365)))), hAPP(c_Nat_OSuc, _1632369)))))))], (51023 ^ _779999) ^ [_1812745, _1812747] : [c_Relation_Osym(_1812745, _1812747), -(c_Relation_Osym(_1812745, c_Transitive__Closure_Ortrancl(_1812745, _1812747)))], (46111 ^ _779999) ^ [_1703265, _1703267, _1703269, _1703271] : [hAPP(hAPP(c_List_Oappend(_1703265), _1703267), hAPP(hAPP(c_List_Olist_OCons(_1703265), _1703269), c_List_Olist_ONil(_1703265))) = _1703271, 46114 ^ _779999 : [(46119 ^ _779999) ^ [] : [-(c_List_Olast(_1703265, _1703271) = _1703269)], (46117 ^ _779999) ^ [] : [-(c_List_Obutlast(_1703265, _1703271) = _1703267)], (46115 ^ _779999) ^ [] : [_1703271 = c_List_Olist_ONil(_1703265)]]], (22519 ^ _779999) ^ [_1196750, _1196752, _1196754, _1196756, _1196758] : [c_Fun_Oinj__on(_1196750, _1196752, _1196754, c_Orderings_Otop__class_Otop(tc_fun(_1196750, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1196750, _1196752, _1196754), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1196750, tc_HOL_Obool)), _1196756), _1196758)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1196752, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1196750, _1196752, _1196754), _1196756)), hAPP(c_Set_Oimage(_1196750, _1196752, _1196754), _1196758)))], (5662 ^ _779999) ^ [_866646, _866648, _866650, _866652, _866654, _866656] : [-(c_COMBC(_866656, _866652, _866648) = c_COMBC(_866654, _866650, _866646)), _866656 = _866654, _866652 = _866650, _866648 = _866646], (21945 ^ _779999) ^ [_1182781, _1182783] : [-(hAPP(c_Set_OPow(_1182781), _1182783) = hAPP(c_Set_OCollect(tc_fun(_1182781, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1182781, tc_HOL_Obool), tc_fun(_1182781, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1182781, tc_HOL_Obool))), _1182783)))], (46904 ^ _779999) ^ [_1721546, _1721548, _1721550, _1721552, _1721554] : [c_List_Olist__all2(_1721546, _1721548, _1721550, _1721552, _1721554), 46907 ^ _779999 : [(46910 ^ _779999) ^ [_1721712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1721546, _1721548)), _1721712), hAPP(c_List_Oset(tc_prod(_1721546, _1721548)), hAPP(hAPP(c_List_Ozip(_1721546, _1721548), _1721552), _1721554)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1721546, _1721548, tc_HOL_Obool), _1721550), _1721712)))], (46908 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721546)), _1721552) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721548)), _1721554))]]], (14288 ^ _779999) ^ [_1035090, _1035092, _1035094] : [hBOOL(hAPP(_1035090, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035092), _1035094))), 14291 ^ _779999 : [(14298 ^ _779999) ^ [_1035275] : [_1035092 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035094), _1035275), -(hBOOL(hAPP(_1035090, _1035275)))], (14292 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035092), _1035094)), -(hBOOL(hAPP(_1035090, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (47022 ^ _779999) ^ [_1724418, _1724420, _1724422] : [_1724418 = _1724420, -(c_List_Olist__all2(_1724422, _1724422, c_fequal, _1724418, _1724420))], (31935 ^ _779999) ^ [_1378872, _1378874, _1378876] : [class_Int_Onumber__ring(_1378872), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1378872), hAPP(c_Int_Onumber__class_Onumber__of(_1378872), _1378874)), hAPP(c_Int_Onumber__class_Onumber__of(_1378872), _1378876)) = hAPP(c_Int_Onumber__class_Onumber__of(_1378872), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1378874), _1378876)))], (17425 ^ _779999) ^ [_1095969, _1095971, _1095973, _1095975] : [class_Groups_Ocomm__monoid__add(_1095969), 17428 ^ _779999 : [(17435 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1095971)), _1095973))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1095969), _1095975), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1095973, hAPP(c_Nat_OSuc, _1095971))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095969), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1095969), _1095975), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1095973, _1095971))), hAPP(_1095975, hAPP(c_Nat_OSuc, _1095971))))], (17429 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1095971)), _1095973)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1095969), _1095975), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1095973, hAPP(c_Nat_OSuc, _1095971))) = c_Groups_Ozero__class_Ozero(_1095969))]]], (46320 ^ _779999) ^ [_1708358, _1708360, _1708362, _1708364, _1708366, _1708368, _1708370, _1708372] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1708358, _1708360), _1708362), _1708364), hAPP(hAPP(c_List_Ozip(_1708358, _1708360), _1708366), hAPP(hAPP(c_List_Omap(_1708368, _1708360), _1708370), _1708372))) = hAPP(hAPP(c_List_Omap(tc_prod(_1708358, _1708368), _1708362), hAPP(c_Product__Type_Oprod_Oprod__case(_1708358, _1708368, _1708362), hAPP(hAPP(c_COMBB(tc_fun(_1708368, tc_prod(_1708358, _1708360)), tc_fun(_1708368, _1708362), _1708358), hAPP(c_COMBB(tc_prod(_1708358, _1708360), _1708362, _1708368), _1708364)), hAPP(hAPP(c_COMBC(_1708358, tc_fun(_1708368, _1708360), tc_fun(_1708368, tc_prod(_1708358, _1708360))), hAPP(hAPP(c_COMBB(tc_fun(_1708360, tc_prod(_1708358, _1708360)), tc_fun(tc_fun(_1708368, _1708360), tc_fun(_1708368, tc_prod(_1708358, _1708360))), _1708358), c_COMBB(_1708360, tc_prod(_1708358, _1708360), _1708368)), c_Product__Type_OPair(_1708358, _1708360))), _1708370)))), hAPP(hAPP(c_List_Ozip(_1708358, _1708368), _1708366), _1708372)))], (38006 ^ _779999) ^ [_1505245, _1505247, _1505249, _1505251] : [c_Wellfounded_Owf(_1505245, _1505247), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505245, _1505245)), hAPP(hAPP(c_Product__Type_OPair(_1505245, _1505245), _1505249), _1505251)), _1505247)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505245, _1505245)), hAPP(hAPP(c_Product__Type_OPair(_1505245, _1505245), _1505251), _1505249)), _1505247))], (9724 ^ _779999) ^ [_945324, _945326] : [class_Complete__Lattice_Ocomplete__lattice(_945324), c_Orderings_Oorder__class_Omono(_945324, _945324, _945326), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945324), hAPP(_945326, c_Inductive_Ocomplete__lattice__class_Ogfp(_945324, _945326))), c_Inductive_Ocomplete__lattice__class_Ogfp(_945324, _945326))))], (45267 ^ _779999) ^ [_1685149, _1685151, _1685153, _1685155, _1685157] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685149), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685151)), _1685153)))), -(hAPP(hAPP(c_List_Olist__update(_1685151, hAPP(hAPP(c_List_Oappend(_1685151), _1685153), _1685155)), _1685149), _1685157) = hAPP(hAPP(c_List_Oappend(_1685151), _1685153), hAPP(hAPP(c_List_Olist__update(_1685151, _1685155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685149), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685151)), _1685153))), _1685157)))], (19121 ^ _779999) ^ [_1128546, _1128548, _1128550, _1128552] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1128546, _1128548, _1128550), _1128552)), _1128550 = c_Orderings_Obot__class_Obot(tc_fun(_1128546, tc_HOL_Obool))], (20020 ^ _779999) ^ [_1145002] : [-(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)), _1145002)) = _1145002)], (25378 ^ _779999) ^ [_1256300, _1256302, _1256304, _1256306, _1256308] : [-(hBOOL(hAPP(_1256300, _1256302))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1256304), _1256302), _1256306)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1256300, _1256308, _1256304)), _1256302), _1256306)))], (6409 ^ _779999) ^ [_883293, _883295, _883297] : [class_Lattices_Osemilattice__sup(_883293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883293), _883295), _883297)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883293), _883295), _883297) = _883297)], (40585 ^ _779999) ^ [_1570640, _1570642] : [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), _1570640), _1570642)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1570640), _1570642)))], (13997 ^ _779999) ^ [_1029487, _1029489, _1029491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029487), _1029489)), 14000 ^ _779999 : [(14007 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029491), _1029487)), _1029489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029489), _1029487))))], (14001 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029489), _1029487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029491), _1029487)), _1029489)))]]], (47438 ^ _779999) ^ [_1733901, _1733903, _1733905] : [47440 ^ _779999 : [(47443 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1733903, 47439 ^ [_1733901, _1733903, _1733905])))], (47441 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733901), 47439 ^ [_1733901, _1733903, _1733905]), hAPP(c_List_Oset(_1733901), _1733905))))]], -(hAPP(c_List_Ofilter(_1733901, _1733903), _1733905) = c_List_Olist_ONil(_1733901))], (38097 ^ _779999) ^ [_1507221, _1507223, _1507225] : [c_Wellfounded_Owf(_1507221, _1507223), c_Wellfounded_Owf(_1507221, _1507225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507221, _1507221), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507221, _1507221, _1507221), _1507223), _1507225)), _1507223)), -(c_Wellfounded_Owf(_1507221, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507221, _1507221), tc_HOL_Obool)), _1507223), _1507225)))], (15869 ^ _779999) ^ [_1066129] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066129), _1066129))))], (18659 ^ _779999) ^ [_1120160, _1120162] : [class_Orderings_Oorder(_1120160), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1120160, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1120160), _1120162), c_Orderings_Obot__class_Obot(tc_fun(_1120160, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1120160), _1120162)) = hAPP(hAPP(c_Set_Oinsert(_1120160), _1120162), c_Orderings_Obot__class_Obot(tc_fun(_1120160, tc_HOL_Obool))))], (47532 ^ _779999) ^ [_1736000, _1736002, _1736004] : [-(c_List_Opartition(_1736000, _1736002, _1736004) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736000), tc_List_Olist(_1736000)), hAPP(c_List_Ofilter(_1736000, _1736002), _1736004)), hAPP(c_List_Ofilter(_1736000, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1736000, c_fNot), _1736002)), _1736004)))], (46730 ^ _779999) ^ [_1717250, _1717252] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1717250), _1717252) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1717250), _1717252))], (40777 ^ _779999) ^ [_1574632, _1574634, _1574636, _1574638] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574632, _1574632)), hAPP(hAPP(c_Product__Type_OPair(_1574632, _1574632), _1574634), _1574636)), c_Transitive__Closure_Otrancl(_1574632, hAPP(c_Relation_Oconverse(_1574632, _1574632), _1574638)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574632, _1574632)), hAPP(hAPP(c_Product__Type_OPair(_1574632, _1574632), _1574634), _1574636)), hAPP(c_Relation_Oconverse(_1574632, _1574632), c_Transitive__Closure_Otrancl(_1574632, _1574638)))))], (45255 ^ _779999) ^ [_1684871, _1684873, _1684875, _1684877] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684871), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684873)), _1684875)))), -(hAPP(hAPP(c_List_Onth(_1684873), hAPP(hAPP(c_List_Oappend(_1684873), _1684875), _1684877)), _1684871) = hAPP(hAPP(c_List_Onth(_1684873), _1684877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1684871), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684873)), _1684875))))], (46428 ^ _779999) ^ [_1711014, _1711016, _1711018] : [c_Fun_Oinj__on(tc_List_Olist(_1711014), tc_List_Olist(_1711016), hAPP(c_List_Omap(_1711014, _1711016), _1711018), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1711014), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1711014, _1711016, _1711018, c_Orderings_Otop__class_Otop(tc_fun(_1711014, tc_HOL_Obool))))], (15107 ^ _779999) ^ [_1051282, _1051284, _1051286, _1051288, _1051290] : [-(hBOOL(hAPP(hAPP(c_member(_1051282), _1051284), c_SetInterval_Oord_OgreaterThanLessThan(_1051282, _1051286, _1051288, _1051290)))), hBOOL(hAPP(hAPP(_1051286, _1051288), _1051284)), hBOOL(hAPP(hAPP(_1051286, _1051284), _1051290))], (14081 ^ _779999) ^ [_1031210, _1031212] : [14082 ^ _779999 : [(14085 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031210), _1031212)))], (14083 ^ _779999) ^ [] : [_1031212 = c_Orderings_Obot__class_Obot(tc_fun(_1031210, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1031210), _1031212) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43531 ^ _779999) ^ [_1644018, _1644020, _1644022] : [c_Equiv__Relations_Oequiv(_1644018, _1644020, _1644022), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1644018), c_List_Olists(_1644018, _1644020), c_List_Olistrel(_1644018, _1644022)))], (51826 ^ _779999) ^ [_1828754, _1828756] : [class_Lattices_Olattice(_1828754), -(class_Lattices_Olattice(tc_fun(_1828756, _1828754)))], (45995 ^ _779999) ^ [_1701460, _1701462, _1701464] : [class_Orderings_Olinorder(_1701460), hBOOL(hAPP(hAPP(c_member(_1701460), _1701462), hAPP(c_List_Oset(_1701460), _1701464))), -(c_List_Olinorder__class_Oinsort__insert__key(_1701460, _1701460, c_COMBI(_1701460), _1701462, _1701464) = _1701464)], (38525 ^ _779999) ^ [_1519026, _1519028, _1519030, _1519032, _1519034] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519026, _1519028), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519026, tc_HOL_Obool)), _1519030), _1519032)), hAPP(c_COMBK(tc_fun(_1519028, tc_HOL_Obool), _1519026), _1519034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1519026, _1519028), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519026, _1519028), _1519030), hAPP(c_COMBK(tc_fun(_1519028, tc_HOL_Obool), _1519026), _1519034))), hAPP(hAPP(c_Product__Type_OSigma(_1519026, _1519028), _1519032), hAPP(c_COMBK(tc_fun(_1519028, tc_HOL_Obool), _1519026), _1519034))))], (30681 ^ _779999) ^ [_1355221, _1355223, _1355225] : [class_Divides_Osemiring__div(_1355221), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1355221), c_Divides_Odiv__class_Omod(_1355221, _1355223, _1355225)), _1355225) = c_Groups_Ozero__class_Ozero(_1355221))], (11348 ^ _779999) ^ [_977008, _977010, _977012, _977014] : [hBOOL(hAPP(hAPP(c_member(_977008), _977010), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977008, tc_HOL_Obool)), _977012), _977014))), -(hBOOL(hAPP(hAPP(c_member(_977008), _977010), _977014)))], (3346 ^ _779999) ^ [_830010, _830012, _830014, _830016] : [-(c_List_Olistset(_830016, _830012) = c_List_Olistset(_830014, _830010)), _830016 = _830014, _830012 = _830010], (52278 ^ _779999) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (36749 ^ _779999) ^ [_1473432, _1473434, _1473436, _1473438, _1473440, _1473442, _1473444] : [c_Equiv__Relations_Oequiv(_1473432, _1473434, _1473436), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473432, tc_HOL_Obool)), _1473438), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473432), _1473434), _1473436))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473432, tc_HOL_Obool)), _1473440), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473432), _1473434), _1473436))), hBOOL(hAPP(hAPP(c_member(_1473432), _1473442), _1473438)), hBOOL(hAPP(hAPP(c_member(_1473432), _1473444), _1473440)), 36768 ^ _779999 : [(36775 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473432, _1473432)), hAPP(hAPP(c_Product__Type_OPair(_1473432, _1473432), _1473442), _1473444)), _1473436)), -(_1473438 = _1473440)], (36769 ^ _779999) ^ [] : [_1473438 = _1473440, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473432, _1473432)), hAPP(hAPP(c_Product__Type_OPair(_1473432, _1473432), _1473442), _1473444)), _1473436)))]]], (11574 ^ _779999) ^ [_982833, _982835, _982837, _982839] : [class_Groups_Ocomm__monoid__add(_982833), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_982835), _982837))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_982835, _982833), _982839), _982837) = c_Groups_Ozero__class_Ozero(_982833))], (38135 ^ _779999) ^ [_1508214, _1508216, _1508218, _1508220] : [c_FunDef_Oreduction__pair(_1508214, _1508216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool)), _1508218), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool), tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool)), _1508216))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool)), _1508220), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool), tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool)), _1508216))), c_Wellfounded_Owf(_1508214, _1508220), -(c_Wellfounded_Owf(_1508214, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508214, _1508214), tc_HOL_Obool)), _1508218), _1508220)))], (40179 ^ _779999) ^ [_1560136, _1560138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560136, _1560136)), c_Transitive__Closure_Otrancl(_1560136, _1560138))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560136, _1560136)), _1560138)))], (23591 ^ _779999) ^ [_1220745, _1220747, _1220749] : [class_Orderings_Olinorder(_1220745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220745), _1220747)), hBOOL(hAPP(hAPP(c_member(_1220745), _1220749), _1220747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220745), hAPP(c_Finite__Set_Ofold1(_1220745, c_Orderings_Oord__class_Omin(_1220745)), _1220747)), _1220749)))], (29046 ^ _779999) ^ [_1325541, _1325543, _1325545, _1325547] : [class_Fields_Olinordered__field(_1325541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325541), _1325543), _1325545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325541), _1325547), c_Groups_Ozero__class_Ozero(_1325541))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325541), c_Groups_Ozero__class_Ozero(_1325541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325541), _1325543), _1325545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325541), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325541), _1325547), _1325543)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325541), _1325547), _1325545))))], (16625 ^ _779999) ^ [_1080643, _1080645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1080643), hAPP(c_Nat_OSuc, _1080645))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1080643, hAPP(c_Nat_OSuc, _1080645)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1080645)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1080643, _1080645)))], (17820 ^ _779999) ^ [_1104501, _1104503, _1104505, _1104507, _1104509] : [class_Groups_Oab__semigroup__mult(_1104501), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1104501, _1104501, c_Groups_Otimes__class_Otimes(_1104501), _1104503, _1104505), _1104507)), hBOOL(hAPP(hAPP(c_member(_1104501), _1104509), _1104505)), -(hBOOL(hAPP(hAPP(c_member(_1104501), _1104503), _1104505))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1104501, _1104501, c_Groups_Otimes__class_Otimes(_1104501), _1104509, hAPP(hAPP(c_Set_Oinsert(_1104501), _1104503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1104501, tc_HOL_Obool)), _1104505), hAPP(hAPP(c_Set_Oinsert(_1104501), _1104509), c_Orderings_Obot__class_Obot(tc_fun(_1104501, tc_HOL_Obool)))))), _1104507)))], (27344 ^ _779999) ^ [_1294427, _1294429, _1294431] : [class_Rings_Odivision__ring(_1294427), -(_1294429 = c_Groups_Ozero__class_Ozero(_1294427)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294427), hAPP(c_Groups_Ouminus__class_Ouminus(_1294427), _1294431)), hAPP(c_Groups_Ouminus__class_Ouminus(_1294427), _1294429)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294427), _1294431), _1294429))], (49628 ^ _779999) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (4516 ^ _779999) ^ [_848647, _848649] : [_848649 = _848647, -(c_List_Otake(_848649) = c_List_Otake(_848647))], (52290 ^ _779999) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (37668 ^ _779999) ^ [_1496825, _1496827, _1496829, _1496831, _1496833, _1496835] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496825, _1496827, _1496829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496825, _1496827), tc_HOL_Obool)), _1496831), _1496833)), _1496835) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496825, _1496829), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1496825, _1496827, _1496829), _1496831), _1496835)), hAPP(hAPP(c_Relation_Orel__comp(_1496825, _1496827, _1496829), _1496833), _1496835)))], (1774 ^ _779999) ^ [_805282, _805284] : [-(class_Divides_Osemiring__div(_805282)), _805284 = _805282, class_Divides_Osemiring__div(_805284)], (40177 ^ _779999) ^ [_1560081, _1560083] : [-(hAPP(c_Relation_ORange(_1560081, _1560081), c_Transitive__Closure_Otrancl(_1560081, _1560083)) = hAPP(c_Relation_ORange(_1560081, _1560081), _1560083))], (30693 ^ _779999) ^ [_1355425, _1355427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355427)), -(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, _1355425, _1355427))))], (31232 ^ _779999) ^ [_1365145, _1365147] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365145, _1365147) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1365145 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1365147), 31235 ^ [_1365145, _1365147]))], (39087 ^ _779999) ^ [_1534500, _1534502, _1534504] : [c_Predicate_Oreflp(_1534500, _1534502), -(hBOOL(hAPP(hAPP(_1534502, _1534504), _1534504)))], (10683 ^ _779999) ^ [_963956, _963958] : [class_Complete__Lattice_Ocomplete__lattice(_963956), c_Orderings_Oorder__class_Omono(_963956, _963956, _963958), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963956), hAPP(_963958, c_Inductive_Ocomplete__lattice__class_Olfp(_963956, _963958))), c_Inductive_Ocomplete__lattice__class_Olfp(_963956, _963958))))], (18365 ^ _779999) ^ [_1114380, _1114382, _1114384, _1114386] : [class_Orderings_Oorder(_1114380), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1114380, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1114380, _1114382), _1114384)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1114380, _1114384), _1114386)) = c_Orderings_Obot__class_Obot(tc_fun(_1114380, tc_HOL_Obool)))], (52126 ^ _779999) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (21632 ^ _779999) ^ [_1174062, _1174064, _1174066] : [hBOOL(hAPP(_1174062, _1174064)), -(hBOOL(hAPP(hAPP(c_member(_1174066), _1174064), hAPP(c_Set_OCollect(_1174066), _1174062))))], (15345 ^ _779999) ^ [_1055793, _1055795, _1055797, _1055799] : [class_Rings_Ocomm__semiring__1(_1055793), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055793), _1055795), _1055797)), _1055799) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055793), _1055795), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055793), _1055797), _1055799)))], (14834 ^ _779999) ^ [_1046300, _1046302] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046300), _1046302))), -(hAPP(c_Finite__Set_Ocard(_1046300), _1046302) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45083 ^ _779999) ^ [_1681072, _1681074, _1681076] : [-(c_List_Olist_ONil(_1681072) = hAPP(hAPP(c_List_Oappend(_1681072), _1681074), _1681076)), _1681074 = c_List_Olist_ONil(_1681072), _1681076 = c_List_Olist_ONil(_1681072)], (33035 ^ _779999) ^ [_1399319] : [-(c_Int_Osucc(c_Int_Opred(_1399319)) = _1399319)], (40134 ^ _779999) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (11256 ^ _779999) ^ [_975076, _975078, _975080, _975082] : [class_Lattices_Osemilattice__inf(_975076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975076), _975078), _975080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975076), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975076), _975078), _975082)), _975080)))], (47129 ^ _779999) ^ [_1726683, _1726685, _1726687, _1726689, _1726691, _1726693, _1726695, _1726697] : [c_List_Olist__all2(_1726683, _1726685, _1726687, _1726689, _1726691), hBOOL(hAPP(hAPP(_1726687, _1726693), _1726695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726697), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726685)), _1726691))), -(c_List_Olist__all2(_1726683, _1726685, _1726687, hAPP(hAPP(c_List_Olist__update(_1726683, _1726689), _1726697), _1726693), hAPP(hAPP(c_List_Olist__update(_1726685, _1726691), _1726697), _1726695)))], (9168 ^ _779999) ^ [_936545, _936547, _936549, _936551, _936553] : [hAPP(_936545, _936547) = _936549, -(c_Fun_Ofun__upd(_936551, _936553, _936545, _936547, _936549) = _936545)], (47340 ^ _779999) ^ [_1730876, _1730878] : [-(hAPP(c_List_Oset(_1730876), c_List_Oconcat(_1730876, _1730878)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1730876), tc_fun(_1730876, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1730876)), _1730878)), c_List_Oset(_1730876)))], (50058 ^ _779999) ^ [_1790464, _1790466, _1790468] : [-(_1790464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1790466), c_List_Oreplicate(_1790466, _1790464, _1790468)) = hAPP(hAPP(c_Set_Oinsert(_1790466), _1790468), c_Orderings_Obot__class_Obot(tc_fun(_1790466, tc_HOL_Obool))))], (48637 ^ _779999) ^ [_1759037, _1759039, _1759041, _1759043] : [hBOOL(hAPP(_1759037, _1759039)), -(c_List_OtakeWhile(_1759041, _1759037, hAPP(hAPP(c_List_Olist_OCons(_1759041), _1759039), _1759043)) = hAPP(hAPP(c_List_Olist_OCons(_1759041), _1759039), c_List_OtakeWhile(_1759041, _1759037, _1759043)))], (49888 ^ _779999) ^ [_1787415, _1787417, _1787419] : [-(_1787415 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1787417), c_List_Oreplicate(_1787417, _1787415, _1787419)) = _1787419)], (15203 ^ _779999) ^ [_1053192, _1053194] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1053192, _1053194)) = 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(_1053192)), c_Com_Ocom_Ocom__size(_1053194))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15781 ^ _779999) ^ [_1064579, _1064581, _1064583] : [15782 ^ _779999 : [(15785 ^ _779999) ^ [] : [_1064581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15783 ^ _779999) ^ [] : [_1064579 = _1064583]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064579), _1064581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064583), _1064581))], (19938 ^ _779999) ^ [_1143717, _1143719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143719)), 19945 ^ _779999 : [(19952 ^ _779999) ^ [] : [_1143717 = _1143719, -(hAPP(c_Int_Onat, _1143717) = hAPP(c_Int_Onat, _1143719))], (19946 ^ _779999) ^ [] : [hAPP(c_Int_Onat, _1143717) = hAPP(c_Int_Onat, _1143719), -(_1143717 = _1143719)]]], (26787 ^ _779999) ^ [_1282590, _1282592] : [class_Groups_Oordered__ab__group__add(_1282590), -(hAPP(c_Set_Oimage(_1282590, _1282590, c_Groups_Ouminus__class_Ouminus(_1282590)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1282590), _1282592)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1282590), hAPP(c_Groups_Ouminus__class_Ouminus(_1282590), _1282592)))], (31548 ^ _779999) ^ [_1370877, _1370879] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1370877), c_Orderings_Obot__class_Obot(tc_fun(_1370877, tc_HOL_Obool))), _1370879) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1370877, tc_HOL_Obool), tc_HOL_Obool)))], (18617 ^ _779999) ^ [_1119362, _1119364] : [class_Rings_Olinordered__semidom(_1119362), 18620 ^ _779999 : [(18627 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119362), c_Groups_Ozero__class_Ozero(_1119362)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119362), _1119364))))], (18621 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119362), c_Groups_Ozero__class_Ozero(_1119362)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119362), _1119364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119364)))]]], (34901 ^ _779999) ^ [_1432463] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1432463) = c_Int_Opred(_1432463))], (21734 ^ _779999) ^ [_1176203, _1176205, _1176207] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1176203, tc_HOL_Obool)), _1176205), _1176207) = hAPP(c_Set_OCollect(_1176203), hAPP(hAPP(c_COMBS(_1176203, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1176203), c_fdisj), hAPP(hAPP(c_COMBC(_1176203, tc_fun(_1176203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176203)), _1176205))), hAPP(hAPP(c_COMBC(_1176203, tc_fun(_1176203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176203)), _1176207))))], (14111 ^ _779999) ^ [_1031777, _1031779, _1031781] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031777), _1031779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1031777, tc_HOL_Obool)), _1031781), _1031779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1031777), _1031779)), hAPP(c_Finite__Set_Ocard(_1031777), _1031781))), -(_1031781 = _1031779)], (41436 ^ _779999) ^ [_1590904, _1590906, _1590908] : [class_Lattices_Olattice(_1590904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590904), _1590906)), -(c_Big__Operators_Olattice__class_OSup__fin(_1590904, hAPP(hAPP(c_Set_Oinsert(_1590904), _1590908), _1590906)) = hAPP(hAPP(c_Finite__Set_Ofold(_1590904, _1590904, c_Lattices_Osemilattice__sup__class_Osup(_1590904)), _1590908), _1590906))], (22435 ^ _779999) ^ [] : [-(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)))], (13951 ^ _779999) ^ [_1028581, _1028583, _1028585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028581), _1028585)), _1028583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028583), _1028585))))], (35970 ^ _779999) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (31655 ^ _779999) ^ [_1373800, _1373802, _1373804] : [class_Orderings_Olinorder(_1373800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373800), _1373802)), 31665 ^ _779999 : [(31668 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373800), 31664 ^ [_1373800, _1373802, _1373804]), _1373804))], (31666 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373800), 31664 ^ [_1373800, _1373802, _1373804]), _1373802)))]], hBOOL(hAPP(hAPP(c_member(_1373800), _1373804), _1373802)), -(c_Big__Operators_Olinorder__class_OMax(_1373800, _1373802) = _1373804)], (35687 ^ _779999) ^ [_1452342, _1452344, _1452346] : [-(c_HOL_OThe(tc_prod(_1452342, _1452344), _1452346) = c_HOL_OThe(tc_prod(_1452342, _1452344), hAPP(c_Product__Type_Oprod_Oprod__case(_1452342, _1452344, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1452344, tc_prod(_1452342, _1452344)), tc_fun(_1452344, tc_HOL_Obool), _1452342), hAPP(c_COMBB(tc_prod(_1452342, _1452344), tc_HOL_Obool, _1452344), _1452346)), c_Product__Type_OPair(_1452342, _1452344)))))], (39296 ^ _779999) ^ [_1539513, _1539515, _1539517] : [39298 ^ _779999 : [(39301 ^ _779999) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1539513, hAPP(c_Nat_OSuc, _1539517), 39297 ^ [_1539513, _1539515, _1539517])], (39299 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1539513)), 39297 ^ [_1539513, _1539515, _1539517]), _1539515)))]], 39302 ^ _779999 : [(39303 ^ _779999) ^ [_1539686] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1539513)), _1539686), _1539515)), -(c_Hoare__Mirabelle_Otriple__valid(_1539513, _1539517, _1539686))]]], (41554 ^ _779999) ^ [_1593168, _1593170, _1593172] : [class_Lattices_Olattice(_1593168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593168), _1593170)), -(hBOOL(hAPP(hAPP(c_member(_1593168), _1593172), _1593170))), -(c_Big__Operators_Olattice__class_OInf__fin(_1593168, hAPP(hAPP(c_Set_Oinsert(_1593168), _1593172), _1593170)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593168, _1593168, c_Lattices_Osemilattice__inf__class_Oinf(_1593168)), _1593172), _1593170))], (43505 ^ _779999) ^ [_1643211, _1643213, _1643215, _1643217, _1643219] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643211), tc_List_Olist(_1643211))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643211), tc_List_Olist(_1643211)), _1643213), hAPP(hAPP(c_List_Olist_OCons(_1643211), _1643215), _1643217))), c_List_Olistrel(_1643211, _1643219))), 43510 ^ _779999 : [(43515 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643211), tc_List_Olist(_1643211))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643211), tc_List_Olist(_1643211)), 43509 ^ [_1643211, _1643213, _1643215, _1643217, _1643219]), _1643217)), c_List_Olistrel(_1643211, _1643219))))], (43513 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643211, _1643211)), hAPP(hAPP(c_Product__Type_OPair(_1643211, _1643211), 43508 ^ [_1643211, _1643213, _1643215, _1643217, _1643219]), _1643215)), _1643219)))], (43511 ^ _779999) ^ [] : [-(_1643213 = hAPP(hAPP(c_List_Olist_OCons(_1643211), 43508 ^ [_1643211, _1643213, _1643215, _1643217, _1643219]), 43509 ^ [_1643211, _1643213, _1643215, _1643217, _1643219]))]]], (48937 ^ _779999) ^ [_1765427, _1765429, _1765431, _1765433, _1765435] : [c_Fun_Oinj__on(_1765427, _1765429, _1765431, hAPP(hAPP(c_Set_Oinsert(_1765427), _1765433), hAPP(c_List_Oset(_1765427), _1765435))), -(hAPP(hAPP(c_List_Omap(_1765427, _1765429), _1765431), hAPP(c_List_OremoveAll(_1765427, _1765433), _1765435)) = hAPP(c_List_OremoveAll(_1765429, hAPP(_1765431, _1765433)), hAPP(hAPP(c_List_Omap(_1765427, _1765429), _1765431), _1765435)))], (45301 ^ _779999) ^ [_1686152, _1686154, _1686156, _1686158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686152), tc_List_Olist(_1686152))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686152), tc_List_Olist(_1686152)), _1686154), _1686156)), c_List_Olistrel1(_1686152, _1686158))), 45306 ^ _779999 : [(45313 ^ _779999) ^ [] : [-(_1686156 = hAPP(hAPP(c_List_Oappend(_1686152), 45308 ^ [_1686152, _1686154, _1686156, _1686158]), hAPP(hAPP(c_List_Olist_OCons(_1686152), 45305 ^ [_1686152, _1686154, _1686156, _1686158]), 45309 ^ [_1686152, _1686154, _1686156, _1686158])))], (45311 ^ _779999) ^ [] : [-(_1686154 = hAPP(hAPP(c_List_Oappend(_1686152), 45308 ^ [_1686152, _1686154, _1686156, _1686158]), hAPP(hAPP(c_List_Olist_OCons(_1686152), 45304 ^ [_1686152, _1686154, _1686156, _1686158]), 45309 ^ [_1686152, _1686154, _1686156, _1686158])))], (45307 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1686152, _1686152)), hAPP(hAPP(c_Product__Type_OPair(_1686152, _1686152), 45304 ^ [_1686152, _1686154, _1686156, _1686158]), 45305 ^ [_1686152, _1686154, _1686156, _1686158])), _1686158)))]]], (1694 ^ _779999) ^ [_804282, _804284] : [-(class_Groups_Oab__semigroup__mult(_804282)), _804284 = _804282, class_Groups_Oab__semigroup__mult(_804284)], (12270 ^ _779999) ^ [_996921, _996923, _996925, _996927, _996929, _996931] : [class_Groups_Oordered__ab__group__add(_996921), hBOOL(hAPP(c_Finite__Set_Ofinite(_996923), _996925)), 12280 ^ _779999 : [(12283 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996921), c_Groups_Ozero__class_Ozero(_996921)), hAPP(_996927, 12279 ^ [_996921, _996923, _996925, _996927, _996929, _996931])))], (12281 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_996923), 12279 ^ [_996921, _996923, _996925, _996927, _996929, _996931]), _996925)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_996923, _996921), _996927), _996925) = _996929, hBOOL(hAPP(hAPP(c_member(_996923), _996931), _996925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996921), hAPP(_996927, _996931)), _996929)))], (52246 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (8340 ^ _779999) ^ [_922028, _922030, _922032, _922034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922028, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922028, tc_HOL_Obool)), _922030), _922032)), _922034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922028, tc_HOL_Obool)), _922030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922028, tc_HOL_Obool)), _922032), _922034))))], (37586 ^ _779999) ^ [_1493706, _1493708] : [-(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), _1493706), _1493708)), 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), _1493708), _1493706)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (4726 ^ _779999) ^ [_851920, _851922, _851924, _851926, _851928, _851930, _851932, _851934, _851936, _851938] : [-(c_Option_Ooption_Ooption__case(_851938, _851934, _851930, _851926, _851922) = c_Option_Ooption_Ooption__case(_851936, _851932, _851928, _851924, _851920)), _851938 = _851936, _851934 = _851932, _851930 = _851928, _851926 = _851924, _851922 = _851920], (52120 ^ _779999) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (8393 ^ _779999) ^ [_923443, _923445, _923447] : [-(hBOOL(hAPP(hAPP(c_member(_923443), _923445), _923447))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923443, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_923443), _923445), _923447)), hAPP(hAPP(c_Set_Oinsert(_923443), _923445), c_Orderings_Obot__class_Obot(tc_fun(_923443, tc_HOL_Obool)))) = _923447)], (39350 ^ _779999) ^ [_1540871, _1540873, _1540875, _1540877, _1540879, _1540881, _1540883] : [hAPP(c_Fun_Ocomp(_1540871, _1540873, _1540875, _1540877), _1540879) = hAPP(c_Fun_Ocomp(_1540873, _1540873, _1540875, c_Fun_Oid(_1540873)), _1540881), -(hAPP(_1540877, hAPP(_1540879, _1540883)) = hAPP(_1540881, _1540883))], (25498 ^ _779999) ^ [_1258474, _1258476] : [class_Groups_Olinordered__ab__group__add(_1258474), 25501 ^ _779999 : [(25508 ^ _779999) ^ [] : [_1258476 = c_Groups_Ozero__class_Ozero(_1258474), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1258474), _1258476) = _1258476)], (25502 ^ _779999) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1258474), _1258476) = _1258476, -(_1258476 = c_Groups_Ozero__class_Ozero(_1258474))]]], (750 ^ _779999) ^ [_791528, _791530] : [-(c_List_Onat__list(_791528)), _791530 = _791528, c_List_Onat__list(_791530)], (30212 ^ _779999) ^ [_1346203, _1346205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346205)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1346203)), hAPP(c_Int_Onat, _1346205)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1346203), _1346205)))], (2 ^ _779999) ^ [_780026] : [-(_780026 = _780026)], (35278 ^ _779999) ^ [_1443453, _1443455, _1443457] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443453, _1443453), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443455), _1443457))), -(_1443453 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43187 ^ _779999) ^ [_1633215, _1633217, _1633219, _1633221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633215)), _1633217)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633215)), _1633219))), _1633217 = hAPP(hAPP(c_List_Olist_OCons(_1633215), _1633221), _1633219)], (8451 ^ _779999) ^ [_924589, _924591, _924593, _924595] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _924589), _924591, _924593, _924595), 8455 ^ _779999 : [(8458 ^ _779999) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _924589)), _924591, 8454 ^ [_924589, _924591, _924593, _924595], _924595))], (8456 ^ _779999) ^ [] : [-(_924593 = hAPP(c_Nat_OSuc, 8454 ^ [_924589, _924591, _924593, _924595]))]]], (15421 ^ _779999) ^ [_1057255, _1057257, _1057259, _1057261] : [-(c_Sum__Type_OPlus(_1057255, _1057257, _1057259, _1057261) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1057255, _1057257), tc_HOL_Obool))), _1057259 = c_Orderings_Obot__class_Obot(tc_fun(_1057255, tc_HOL_Obool)), _1057261 = c_Orderings_Obot__class_Obot(tc_fun(_1057257, tc_HOL_Obool))], (10607 ^ _779999) ^ [_962551, _962553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962553), _962551)), -(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), _962551), _962553))))], (11996 ^ _779999) ^ [_991247, _991249, _991251, _991253, _991255] : [class_Groups_Ocomm__monoid__add(_991247), class_Groups_Oordered__ab__semigroup__add(_991247), hBOOL(hAPP(c_Finite__Set_Ofinite(_991249), _991251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991249, tc_HOL_Obool)), _991253), _991251)), 12014 ^ _779999 : [(12017 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991247), c_Groups_Ozero__class_Ozero(_991247)), hAPP(_991255, 12013 ^ [_991247, _991249, _991251, _991253, _991255])))], (12015 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_991249), 12013 ^ [_991247, _991249, _991251, _991253, _991255]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_991249, tc_HOL_Obool)), _991251), _991253))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991247), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991249, _991247), _991255), _991253)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991249, _991247), _991255), _991251))))], (2604 ^ _779999) ^ [_818473, _818475, _818477, _818479] : [-(c_Divides_Odivmod__nat__rel(_818479, _818475) = c_Divides_Odivmod__nat__rel(_818477, _818473)), _818479 = _818477, _818475 = _818473], (32521 ^ _779999) ^ [_1390016, _1390018, _1390020, _1390022] : [class_Fields_Olinordered__field__inverse__zero(_1390016), class_Int_Onumber(_1390016), 32528 ^ _779999 : [(32529 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390016), _1390020), _1390022))), 32532 ^ _779999 : [(32539 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), c_Groups_Ozero__class_Ozero(_1390016)), _1390022))), 32542 ^ _779999 : [(32549 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), _1390022), c_Groups_Ozero__class_Ozero(_1390016)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), c_Groups_Ozero__class_Ozero(_1390016))))], (32543 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), _1390022), c_Groups_Ozero__class_Ozero(_1390016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), _1390020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), _1390022))))]]], (32533 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), c_Groups_Ozero__class_Ozero(_1390016)), _1390022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), _1390022)), _1390020)))]]], (32555 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390016), _1390020), _1390022)))), 32558 ^ _779999 : [(32561 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), _1390022)), _1390020))], (32559 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), c_Groups_Ozero__class_Ozero(_1390016)), _1390022)))]], 32562 ^ _779999 : [(32565 ^ _779999) ^ [] : [32566 ^ _779999 : [(32569 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), _1390020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), _1390022)))], (32567 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), _1390022), c_Groups_Ozero__class_Ozero(_1390016))))]], 32570 ^ _779999 : [(32573 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390016), hAPP(c_Int_Onumber__class_Onumber__of(_1390016), _1390018)), c_Groups_Ozero__class_Ozero(_1390016)))], (32571 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), _1390022), c_Groups_Ozero__class_Ozero(_1390016)))]]], (32563 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390016), c_Groups_Ozero__class_Ozero(_1390016)), _1390022))]]]]], (34769 ^ _779999) ^ [_1430560] : [c_Int_OBit0(_1430560) = c_Int_OMin], (44105 ^ _779999) ^ [_1659776, _1659778] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659776)), c_List_Obutlast(_1659776, _1659778)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659776)), _1659778)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17933 ^ _779999) ^ [_1106385, _1106387, _1106389] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106385)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106387)), _1106389)) = 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), _1106385), _1106387))), _1106389))], (37144 ^ _779999) ^ [_1482864] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1482864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1482864)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29480 ^ _779999) ^ [_1333410, _1333412] : [class_Divides_Osemiring__div(_1333410), -(_1333412 = c_Groups_Ozero__class_Ozero(_1333410)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1333410), _1333412), _1333412) = c_Groups_Oone__class_Oone(_1333410))], (29078 ^ _779999) ^ [_1326147, _1326149, _1326151, _1326153] : [class_Fields_Ofield(_1326147), -(_1326149 = c_Groups_Ozero__class_Ozero(_1326147)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326147), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326147), _1326151), _1326149)), _1326153) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326147), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326147), _1326151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326147), _1326149), _1326153))), _1326149))], (51862 ^ _779999) ^ [_1829228, _1829230] : [class_Groups_Ominus(_1829228), -(class_Groups_Ominus(tc_fun(_1829230, _1829228)))], (1424 ^ _779999) ^ [_800907, _800909] : [-(class_Complete__Lattice_Ocomplete__lattice(_800907)), _800909 = _800907, class_Complete__Lattice_Ocomplete__lattice(_800909)], (10379 ^ _779999) ^ [_958542, _958544, _958546, _958548, _958550] : [class_Groups_Oab__group__add(_958542), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958544, _958542), hAPP(hAPP(c_COMBS(_958544, _958542, _958542), hAPP(hAPP(c_COMBB(_958542, tc_fun(_958542, _958542), _958544), c_Groups_Ominus__class_Ominus(_958542)), _958546)), _958548)), _958550) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958542), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958544, _958542), _958546), _958550)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958544, _958542), _958548), _958550)))], (16795 ^ _779999) ^ [_1083883, _1083885, _1083887] : [class_Orderings_Oorder(_1083883), 16798 ^ _779999 : [(16805 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083883), _1083885), _1083887))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1083883, _1083885, _1083887) = c_Orderings_Obot__class_Obot(tc_fun(_1083883, tc_HOL_Obool)))], (16799 ^ _779999) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1083883, _1083885, _1083887) = c_Orderings_Obot__class_Obot(tc_fun(_1083883, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083883), _1083885), _1083887))]]], (15275 ^ _779999) ^ [_1054451, _1054453, _1054455, _1054457] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1054451, _1054453)), c_Sum__Type_OPlus(_1054451, _1054453, _1054455, _1054457))), 15278 ^ _779999 : [(15281 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054453), _1054457)))], (15279 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054451), _1054455)))]]], (29962 ^ _779999) ^ [_1341697, _1341699] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341697)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341699)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341697), _1341699)))], (48026 ^ _779999) ^ [_1746339, _1746341, _1746343, _1746345, _1746347] : [class_Orderings_Olinorder(_1746339), c_List_Olinorder__class_Osorted(_1746339, hAPP(hAPP(c_List_Omap(_1746341, _1746339), _1746343), _1746345)), -(c_List_Olinorder__class_Osorted(_1746339, hAPP(hAPP(c_List_Omap(_1746341, _1746339), _1746343), c_List_Oremove1(_1746341, _1746347, _1746345))))], (24802 ^ _779999) ^ [_1244578, _1244580, _1244582] : [class_Orderings_Olinorder(_1244578), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244578), _1244580)), -(hBOOL(hAPP(hAPP(c_member(_1244578), _1244582), _1244580))), -(_1244580 = c_Orderings_Obot__class_Obot(tc_fun(_1244578, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1244578, hAPP(hAPP(c_Set_Oinsert(_1244578), _1244582), _1244580)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244578), _1244582), c_Big__Operators_Olinorder__class_OMax(_1244578, _1244580)))], (19127 ^ _779999) ^ [_1128665, _1128667, _1128669] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1128665, _1128667, c_Orderings_Obot__class_Obot(tc_fun(_1128665, tc_HOL_Obool))), _1128669))], (20427 ^ _779999) ^ [_1151677, _1151679] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1151677, _1151679)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1151679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1151677), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (32215 ^ _779999) ^ [_1384054, _1384056, _1384058, _1384060] : [class_Fields_Olinordered__field__inverse__zero(_1384054), class_Int_Onumber(_1384054), 32222 ^ _779999 : [(32223 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384054), _1384056), _1384058)), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060))), 32226 ^ _779999 : [(32233 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), _1384058))), 32236 ^ _779999 : [(32243 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384058), c_Groups_Ozero__class_Ozero(_1384054)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060))))], (32237 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384058), c_Groups_Ozero__class_Ozero(_1384054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384054), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)), _1384058)), _1384056)))]]], (32227 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), _1384058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384054), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)), _1384058))))]]], (32249 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384054), _1384056), _1384058)), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)))), 32252 ^ _779999 : [(32255 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384054), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)), _1384058)))], (32253 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), _1384058)))]], 32256 ^ _779999 : [(32259 ^ _779999) ^ [] : [32260 ^ _779999 : [(32263 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384054), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)), _1384058)), _1384056))], (32261 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384058), c_Groups_Ozero__class_Ozero(_1384054))))]], 32264 ^ _779999 : [(32267 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), hAPP(c_Int_Onumber__class_Onumber__of(_1384054), _1384060)))], (32265 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), _1384058), c_Groups_Ozero__class_Ozero(_1384054)))]]], (32257 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384054), c_Groups_Ozero__class_Ozero(_1384054)), _1384058))]]]]], (37751 ^ _779999) ^ [_1499500, _1499502, _1499504, _1499506, _1499508] : [c_Typedef_Otype__definition(_1499500, _1499502, _1499504, _1499506, _1499508), -(hAPP(c_Set_Oimage(_1499500, _1499502, _1499504), c_Orderings_Otop__class_Otop(tc_fun(_1499500, tc_HOL_Obool))) = _1499508)], (7504 ^ _779999) ^ [_905449, _905451, _905453] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_905449, _905451, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905449)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905449), _905453), c_Com_Ocom_OSKIP), _905453)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905449), tc_HOL_Obool)))))], (38680 ^ _779999) ^ [_1523367, _1523369, _1523371, _1523373] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523367, _1523369), _1523371), _1523373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523367, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), _1523371), hAPP(hAPP(c_COMBS(_1523367, tc_fun(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523369, tc_HOL_Obool), tc_fun(tc_fun(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), _1523367), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), _1523373)), hAPP(hAPP(c_COMBC(_1523367, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523369, tc_fun(tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), _1523367), c_COMBC(_1523369, tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523369, tc_prod(_1523367, _1523369)), tc_fun(_1523369, tc_fun(tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))), _1523367), hAPP(c_COMBB(tc_prod(_1523367, _1523369), tc_fun(tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool), tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool)), _1523369), c_Set_Oinsert(tc_prod(_1523367, _1523369)))), c_Product__Type_OPair(_1523367, _1523369)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523367, _1523369), tc_HOL_Obool))))))], (9000 ^ _779999) ^ [_933942, _933944, _933946] : [class_Orderings_Oorder(_933942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933942), _933944), _933946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933942), _933946), _933944))], (32975 ^ _779999) ^ [_1398363, _1398365] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398363))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398363)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398365)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22215 ^ _779999) ^ [_1191039] : [class_Finite__Set_Ofinite(_1191039), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1191039), c_Orderings_Otop__class_Otop(tc_fun(_1191039, tc_HOL_Obool)))))], (40269 ^ _779999) ^ [_1562795, _1562797, _1562799, _1562801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562795, _1562795)), hAPP(hAPP(c_Product__Type_OPair(_1562795, _1562795), _1562799), _1562801)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool)), _1562797), c_Relation_OId(_1562795)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562795, tc_fun(_1562795, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1562795, tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_fun(_1562795, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562795, tc_fun(tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_fun(_1562795, tc_HOL_Obool)), _1562795), c_COMBC(_1562795, tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562795, tc_prod(_1562795, _1562795)), tc_fun(_1562795, tc_fun(tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_HOL_Obool)), _1562795), hAPP(c_COMBB(tc_prod(_1562795, _1562795), tc_fun(tc_fun(tc_prod(_1562795, _1562795), tc_HOL_Obool), tc_HOL_Obool), _1562795), c_member(tc_prod(_1562795, _1562795)))), c_Product__Type_OPair(_1562795, _1562795)))), _1562797)), c_fequal), _1562799), _1562801)))], (35103 ^ _779999) ^ [_1435729, _1435731] : [-(_1435729 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1435729, _1435731) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1435729), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1435731)))], (24748 ^ _779999) ^ [_1243680, _1243682, _1243684] : [class_Orderings_Olinorder(_1243680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1243680), _1243682)), -(_1243684 = c_Orderings_Obot__class_Obot(tc_fun(_1243680, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1243680, tc_HOL_Obool)), _1243684), _1243682)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243680), c_Big__Operators_Olinorder__class_OMax(_1243680, _1243684)), c_Big__Operators_Olinorder__class_OMax(_1243680, _1243682)) = c_Big__Operators_Olinorder__class_OMax(_1243680, _1243682))], (42550 ^ _779999) ^ [_1617837, _1617839, _1617841] : [class_Complete__Lattice_Ocomplete__lattice(_1617837), hBOOL(hAPP(hAPP(c_member(_1617837), _1617839), _1617841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1617837), c_Complete__Lattice_OInf__class_OInf(_1617837, _1617841)), _1617839)))], (31421 ^ _779999) ^ [_1368553, _1368555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368555)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1368553), hAPP(c_Int_Onat, _1368555)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368553, _1368555)))], (39038 ^ _779999) ^ [_1533094, _1533096] : [c_Wellfounded_OwfP(_1533094, hAPP(hAPP(c_COMBC(_1533094, tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_fun(_1533094, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533094, tc_fun(tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_fun(_1533094, tc_HOL_Obool)), _1533094), c_COMBC(_1533094, tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533094, tc_prod(_1533094, _1533094)), tc_fun(_1533094, tc_fun(tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_HOL_Obool)), _1533094), hAPP(c_COMBB(tc_prod(_1533094, _1533094), tc_fun(tc_fun(tc_prod(_1533094, _1533094), tc_HOL_Obool), tc_HOL_Obool), _1533094), c_member(tc_prod(_1533094, _1533094)))), c_Product__Type_OPair(_1533094, _1533094)))), _1533096)), -(c_Wellfounded_Owf(_1533094, _1533096))], (22229 ^ _779999) ^ [_1191303, _1191305] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1191303, tc_HOL_Obool)), _1191305), c_Orderings_Otop__class_Otop(tc_fun(_1191303, tc_HOL_Obool))) = _1191305)], (27063 ^ _779999) ^ [_1288927, _1288929, _1288931, _1288933, _1288935, _1288937] : [class_Groups_Ocomm__monoid__mult(_1288927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288929), _1288931)), 27070 ^ _779999 : [(27077 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288929), _1288933), _1288931))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288929, _1288927), hAPP(hAPP(c_COMBC(_1288929, _1288927, _1288927), hAPP(hAPP(c_COMBS(_1288929, _1288927, tc_fun(_1288927, _1288927)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1288927, tc_fun(_1288927, _1288927)), _1288929), c_If(_1288927)), hAPP(hAPP(c_COMBC(_1288929, _1288929, tc_HOL_Obool), c_fequal), _1288933))), _1288935)), _1288937)), _1288931) = hAPP(hAPP(c_Power_Opower__class_Opower(_1288927), _1288937), hAPP(c_Finite__Set_Ocard(_1288929), _1288931)))], (27071 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1288929), _1288933), _1288931)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1288929, _1288927), hAPP(hAPP(c_COMBC(_1288929, _1288927, _1288927), hAPP(hAPP(c_COMBS(_1288929, _1288927, tc_fun(_1288927, _1288927)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1288927, tc_fun(_1288927, _1288927)), _1288929), c_If(_1288927)), hAPP(hAPP(c_COMBC(_1288929, _1288929, tc_HOL_Obool), c_fequal), _1288933))), _1288935)), _1288937)), _1288931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288927), hAPP(_1288935, _1288933)), hAPP(hAPP(c_Power_Opower__class_Opower(_1288927), _1288937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1288929), _1288931)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (21925 ^ _779999) ^ [_1182138, _1182140, _1182142] : [class_Lattices_Odistrib__lattice(_1182138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182138), _1182140)), -(_1182140 = c_Orderings_Obot__class_Obot(tc_fun(_1182138, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1182138), _1182142), c_Big__Operators_Olattice__class_OSup__fin(_1182138, _1182140)) = c_Big__Operators_Olattice__class_OSup__fin(_1182138, hAPP(c_Set_OCollect(_1182138), hAPP(hAPP(c_COMBB(tc_fun(_1182138, tc_HOL_Obool), tc_HOL_Obool, _1182138), c_HOL_OEx(_1182138)), hAPP(hAPP(c_COMBC(_1182138, tc_fun(_1182138, tc_HOL_Obool), tc_fun(_1182138, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1182138, tc_HOL_Obool), tc_fun(_1182138, tc_HOL_Obool)), _1182138), c_COMBS(_1182138, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182138, tc_HOL_Obool), tc_fun(_1182138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1182138), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1182138), c_fconj)), hAPP(hAPP(c_COMBC(_1182138, tc_fun(_1182138, _1182138), tc_fun(_1182138, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182138, tc_HOL_Obool), tc_fun(tc_fun(_1182138, _1182138), tc_fun(_1182138, tc_HOL_Obool)), _1182138), c_COMBB(_1182138, tc_HOL_Obool, _1182138)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1182138), _1182142))))), hAPP(hAPP(c_COMBC(_1182138, tc_fun(_1182138, tc_HOL_Obool), tc_HOL_Obool), c_member(_1182138)), _1182140))))))], (47583 ^ _779999) ^ [_1737919] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1737919)), c_List_Otranspose__rel(_1737919)), c_List_Olist_ONil(tc_List_Olist(_1737919)))), -(c_List_Otranspose(_1737919, c_List_Olist_ONil(tc_List_Olist(_1737919))) = c_List_Olist_ONil(tc_List_Olist(_1737919)))], (11594 ^ _779999) ^ [_983081, _983083, _983085, _983087, _983089] : [c_Orderings_Oorder__class_Omono(tc_fun(_983081, tc_HOL_Obool), tc_fun(_983083, tc_HOL_Obool), _983085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983083, tc_HOL_Obool)), hAPP(_983085, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983081, tc_HOL_Obool)), _983087), _983089))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983083, tc_HOL_Obool)), hAPP(_983085, _983087)), hAPP(_983085, _983089)))))], (5879 ^ _779999) ^ [_873463, _873465, _873467, _873469, _873471, _873473] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_873463, _873465, _873467, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873463), _873469), _873471), _873473)) = hAPP(hAPP(hAPP(_873467, _873469), _873471), _873473))], (46306 ^ _779999) ^ [_1707717, _1707719] : [-(hAPP(hAPP(c_List_Omap(_1707717, _1707717), c_COMBI(_1707717)), _1707719) = _1707719)], (1964 ^ _779999) ^ [_807657, _807659] : [-(class_Nat_Osize(_807657)), _807659 = _807657, class_Nat_Osize(_807659)], (18881 ^ _779999) ^ [_1124577, _1124579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124579), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124577), _1124579))), -(_1124577 = _1124579)], (3254 ^ _779999) ^ [_828538, _828540, _828542, _828544, _828546, _828548, _828550, _828552, _828554, _828556, _828558, _828560] : [-(c_Product__Type_Omap__pair(_828560, _828556, _828552, _828548, _828544, _828540) = c_Product__Type_Omap__pair(_828558, _828554, _828550, _828546, _828542, _828538)), _828560 = _828558, _828556 = _828554, _828552 = _828550, _828548 = _828546, _828544 = _828542, _828540 = _828538], (33313 ^ _779999) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (13780 ^ _779999) ^ [_1025846, _1025848] : [class_Groups_Olinordered__ab__group__add(_1025846), 13783 ^ _779999 : [(13790 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025846), _1025848), c_Groups_Ozero__class_Ozero(_1025846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025846), _1025848), _1025848)), c_Groups_Ozero__class_Ozero(_1025846))))], (13784 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025846), _1025848), _1025848)), c_Groups_Ozero__class_Ozero(_1025846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025846), _1025848), c_Groups_Ozero__class_Ozero(_1025846))))]]], (37106 ^ _779999) ^ [_1482112, _1482114, _1482116, _1482118, _1482120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1482112, _1482114)), hAPP(_1482112, _1482116))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1482118, _1482118)), hAPP(hAPP(c_Product__Type_OPair(_1482118, _1482118), _1482114), _1482116)), _1482120)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482118, _1482118)), hAPP(hAPP(c_Product__Type_OPair(_1482118, _1482118), _1482114), _1482116)), c_Wellfounded_Omlex__prod(_1482118, _1482112, _1482120))))], (9999 ^ _779999) ^ [_952565, _952567, _952569, _952571, _952573, _952575] : [c_Fun_Oinj__on(_952565, _952567, _952569, _952571), hAPP(_952569, _952573) = _952575, hBOOL(hAPP(hAPP(c_member(_952565), _952573), _952571)), -(hAPP(c_Fun_Othe__inv__into(_952565, _952567, _952571, _952569), _952575) = _952573)], (39805 ^ _779999) ^ [_1551202, _1551204, _1551206, _1551208, _1551210] : [c_Hoare__Mirabelle_Ohoare__derivs(_1551202, _1551204, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1551202)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1551202), c_Hoare__Mirabelle_Opeek__and(_1551202, _1551206, _1551208)), _1551210), _1551206)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1551202), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1551202, _1551204, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1551202)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1551202), _1551206), c_Com_Ocom_OWhile(_1551208, _1551210)), c_Hoare__Mirabelle_Opeek__and(_1551202, _1551206, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1551208)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1551202), tc_HOL_Obool)))))], (49023 ^ _779999) ^ [_1767022, _1767024, _1767026] : [-(hBOOL(hAPP(hAPP(c_member(_1767022), _1767024), hAPP(c_List_Oset(_1767022), _1767026)))), -(c_List_Oinsert(_1767022, _1767024, _1767026) = hAPP(hAPP(c_List_Olist_OCons(_1767022), _1767024), _1767026))], (21395 ^ _779999) ^ [_1169595, _1169597, _1169599, _1169601] : [c_Finite__Set_Ofolding__one(_1169595, _1169597, _1169599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169595), _1169601)), -(hAPP(_1169599, _1169601) = hAPP(c_Finite__Set_Ofold1(_1169595, _1169597), _1169601))], (37290 ^ _779999) ^ [_1486733, _1486735, _1486737, _1486739, _1486741, _1486743] : [hAPP(c_Product__Type_Oapfst(_1486733, _1486735, _1486737, _1486739), _1486741) = hAPP(c_Product__Type_Oapfst(_1486733, _1486735, _1486737, _1486743), _1486741), -(hAPP(_1486739, hAPP(c_Product__Type_Ofst(_1486733, _1486737), _1486741)) = hAPP(_1486743, hAPP(c_Product__Type_Ofst(_1486733, _1486737), _1486741)))], (7926 ^ _779999) ^ [_913798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _913798), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_913798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31620 ^ _779999) ^ [_1373004, _1373006, _1373008] : [-(hAPP(c_Relation_OImage(_1373004, _1373006, _1373008), c_Orderings_Obot__class_Obot(tc_fun(_1373004, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1373006, tc_HOL_Obool)))], (43153 ^ _779999) ^ [_1631493, _1631495, _1631497, _1631499, _1631501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631493), tc_List_Olist(_1631493))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631493), tc_List_Olist(_1631493)), _1631495), _1631497)), hAPP(c_List_Olexn(_1631493, _1631499), _1631501))), 43156 ^ _779999 : [(43159 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631493)), _1631497) = _1631501)], (43157 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631493)), _1631495) = _1631501)]]], (8114 ^ _779999) ^ [_917169, _917171, _917173] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917169, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917169, tc_HOL_Obool)), _917171), _917173)), _917171)))], (22716 ^ _779999) ^ [_1201142, _1201144, _1201146, _1201148, _1201150, _1201152] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201142, tc_fun(_1201144, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201146, tc_fun(_1201142, tc_HOL_Obool)), _1201148), _1201150)), _1201152) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201146, tc_fun(_1201144, tc_HOL_Obool)), _1201148), hAPP(hAPP(c_COMBC(_1201146, tc_fun(_1201142, tc_fun(_1201144, tc_HOL_Obool)), tc_fun(_1201144, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1201142, tc_HOL_Obool), tc_fun(tc_fun(_1201142, tc_fun(_1201144, tc_HOL_Obool)), tc_fun(_1201144, tc_HOL_Obool)), _1201146), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201142, tc_fun(_1201144, tc_HOL_Obool))), _1201150)), _1201152)))], (44222 ^ _779999) ^ [_1662461, _1662463, _1662465, _1662467] : [_1662461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662463)), _1662465)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1662463, hAPP(hAPP(c_List_Olist__update(_1662463, _1662465), _1662461), _1662467)) = c_List_Obutlast(_1662463, _1662465))], (13957 ^ _779999) ^ [_1028706, _1028708, _1028710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028706), _1028708)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028708), _1028710)), _1028706) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028708), _1028706)), _1028710))], (11484 ^ _779999) ^ [_980683, _980685, _980687, _980689] : [hBOOL(hAPP(hAPP(c_member(_980683), _980685), _980687)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980683, tc_HOL_Obool)), _980687), hAPP(hAPP(c_Set_Oinsert(_980683), _980685), _980689)) = hAPP(hAPP(c_Set_Oinsert(_980683), _980685), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980683, tc_HOL_Obool)), _980687), _980689)))], (11356 ^ _779999) ^ [_977185, _977187] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977185, tc_HOL_Obool)), _977187), c_Orderings_Obot__class_Obot(tc_fun(_977185, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_977185, tc_HOL_Obool)))], (33861 ^ _779999) ^ [_1413517, _1413519] : [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), _1413517))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1413519)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1413517))) = 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), _1413519), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413517)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36539 ^ _779999) ^ [_1468312, _1468314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468312), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1468314), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468312), _1468314) = 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), _1468312), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468314)))))], (45797 ^ _779999) ^ [_1697254, _1697256, _1697258] : [class_Lattices_Olattice(_1697254), -(c_Big__Operators_Olattice__class_OSup__fin(_1697254, hAPP(c_List_Oset(_1697254), hAPP(hAPP(c_List_Olist_OCons(_1697254), _1697256), _1697258))) = hAPP(c_List_Ofoldl(_1697254, _1697254, c_Lattices_Osemilattice__sup__class_Osup(_1697254), _1697256), _1697258))], (34897 ^ _779999) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (40175 ^ _779999) ^ [_1560041, _1560043] : [-(hAPP(c_Relation_ODomain(_1560041, _1560041), c_Transitive__Closure_Otrancl(_1560041, _1560043)) = hAPP(c_Relation_ODomain(_1560041, _1560041), _1560043))], (13381 ^ _779999) ^ [_1018221, _1018223, _1018225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018221), _1018223)), _1018225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018221), _1018225)))], (8550 ^ _779999) ^ [_926247] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926247), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _926247)], (51061 ^ _779999) ^ [_1813312, _1813314] : [hAPP(c_Relation_Oconverse(_1813312, _1813312), _1813314) = _1813314, -(c_Relation_Osym(_1813312, _1813314))], (18041 ^ _779999) ^ [_1108317, _1108319, _1108321, _1108323] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1108317, _1108319, _1108321, _1108323, c_Orderings_Obot__class_Obot(tc_fun(_1108317, tc_HOL_Obool))), _1108323)))], (26811 ^ _779999) ^ [_1283082, _1283084, _1283086, _1283088, _1283090] : [class_Groups_Ocomm__monoid__mult(_1283082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283084), _1283086)), -(hBOOL(hAPP(hAPP(c_member(_1283084), _1283088), _1283086))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283084, _1283082), _1283090), hAPP(hAPP(c_Set_Oinsert(_1283084), _1283088), _1283086)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283082), hAPP(_1283090, _1283088)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1283084, _1283082), _1283090), _1283086)))], (20846 ^ _779999) ^ [_1158422, _1158424, _1158426] : [class_Rings_Olinordered__idom(_1158422), -(hAPP(c_Groups_Oabs__class_Oabs(_1158422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158422), _1158424), _1158426)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158422), hAPP(c_Groups_Oabs__class_Oabs(_1158422), _1158424)), hAPP(c_Groups_Oabs__class_Oabs(_1158422), _1158426)))], (44047 ^ _779999) ^ [_1658525] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1658525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44050 ^ _779999 : [(44051 ^ _779999) ^ [_1658600] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658600), hAPP(c_List_Oset(tc_Nat_Onat), _1658525))), -(_1658600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5592 ^ _779999) ^ [_865625, _865627] : [_865627 = _865625, -(c_Lattices_Osemilattice__inf__class_Oinf(_865627) = c_Lattices_Osemilattice__inf__class_Oinf(_865625))], (19349 ^ _779999) ^ [_1132818, _1132820] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1132818, _1132820))))], (7446 ^ _779999) ^ [_904013] : [-(c_Hoare__Mirabelle_OMGT(_904013) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _904013), c_Natural_Oevalc(_904013)))], (48264 ^ _779999) ^ [_1750995, _1750997, _1750999, _1751001, _1751003] : [class_Orderings_Olinorder(_1750995), c_Fun_Oinj__on(_1750997, _1750995, _1750999, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1750997, tc_HOL_Obool)), hAPP(c_List_Oset(_1750997), _1751001)), hAPP(c_List_Oset(_1750997), _1751003))), c_List_Olinorder__class_Osorted(_1750995, hAPP(hAPP(c_List_Omap(_1750997, _1750995), _1750999), _1751001)), hBOOL(hAPP(c_List_Odistinct(_1750995), hAPP(hAPP(c_List_Omap(_1750997, _1750995), _1750999), _1751001))), c_List_Olinorder__class_Osorted(_1750995, hAPP(hAPP(c_List_Omap(_1750997, _1750995), _1750999), _1751003)), hBOOL(hAPP(c_List_Odistinct(_1750995), hAPP(hAPP(c_List_Omap(_1750997, _1750995), _1750999), _1751003))), hAPP(c_List_Oset(_1750997), _1751001) = hAPP(c_List_Oset(_1750997), _1751003), -(_1751001 = _1751003)], (13439 ^ _779999) ^ [_1019371, _1019373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019371), _1019373)), _1019371))], (46259 ^ _779999) ^ [_1706667, _1706669, _1706671, _1706673, _1706675] : [hAPP(hAPP(c_List_Omap(_1706667, _1706669), _1706671), _1706673) = hAPP(hAPP(c_List_Omap(_1706667, _1706669), _1706675), _1706673), 46262 ^ _779999 : [(46263 ^ _779999) ^ [_1706790] : [hBOOL(hAPP(hAPP(c_member(_1706667), _1706790), hAPP(c_List_Oset(_1706667), _1706673))), -(hAPP(_1706671, _1706790) = hAPP(_1706675, _1706790))]]], (46820 ^ _779999) ^ [_1719282, _1719284, _1719286, _1719288] : [hBOOL(hAPP(c_List_Olistsp(_1719282, _1719284), hAPP(hAPP(c_List_Olist_OCons(_1719282), _1719286), _1719288))), 46823 ^ _779999 : [(46826 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1719282, _1719284), _1719288)))], (46824 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1719284, _1719286)))]]], (9712 ^ _779999) ^ [_945123, _945125, _945127, _945129] : [-(c_Nat_Onat_Onat__case(_945123, _945125, _945127, hAPP(c_Nat_OSuc, _945129)) = hAPP(_945127, _945129))], (49846 ^ _779999) ^ [_1786446, _1786448] : [class_Lazy__Sequence_Osmall__lazy(_1786446), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786446), _1786448) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1786446), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1786446)), c_List_Olist_ONil(_1786446)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786446))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1786448)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1786446, tc_List_Olist(_1786446)), tc_List_Olist(_1786446), c_Lazy__Sequence_Oproduct(_1786446, tc_List_Olist(_1786446), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786446, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786448), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786448), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1786446, tc_List_Olist(_1786446), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786446))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1786446), tc_List_Olist(_1786446)), tc_fun(tc_List_Olist(_1786446), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786446))), _1786446), hAPP(c_COMBB(tc_List_Olist(_1786446), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786446)), tc_List_Olist(_1786446)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1786446)))), c_List_Olist_OCons(_1786446))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1786446)))))], (38656 ^ _779999) ^ [_1522555, _1522557, _1522559, _1522561] : [-(_1522555 = c_Orderings_Obot__class_Obot(tc_fun(_1522557, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1522557, _1522559), _1522559, c_Product__Type_Osnd(_1522557, _1522559)), hAPP(hAPP(c_Product__Type_OSigma(_1522557, _1522559), _1522555), hAPP(c_COMBK(tc_fun(_1522559, tc_HOL_Obool), _1522557), _1522561))) = _1522561)], (50102 ^ _779999) ^ [_1791169, _1791171, _1791173] : [class_Fields_Olinordered__field(_1791169), 50108 ^ _779999 : [(50111 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791169), _1791171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1791169), _1791173), 50107 ^ [_1791169, _1791171, _1791173])))], (50109 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1791169), c_Groups_Ozero__class_Ozero(_1791169)), 50107 ^ [_1791169, _1791171, _1791173])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791169), _1791171), _1791173)))], (4456 ^ _779999) ^ [_847721, _847723] : [_847723 = _847721, -(c_If(_847723) = c_If(_847721))], (47164 ^ _779999) ^ [_1727504, _1727506] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727504)), c_List_Oremdups(_1727504, _1727506))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727504)), _1727506))))], (22151 ^ _779999) ^ [_1189661, _1189663] : [-(c_Sum__Type_OPlus(_1189661, _1189663, c_Orderings_Otop__class_Otop(tc_fun(_1189661, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1189663, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1189661, _1189663), tc_HOL_Obool)))], (41009 ^ _779999) ^ [_1580820] : [-(c_Nat_Ofunpow(_1580820) = c_Nat_Ocompow(_1580820, _1580820))], (26346 ^ _779999) ^ [_1273696, _1273698, _1273700] : [class_Groups_Ogroup__add(_1273696), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273696), _1273698), _1273700) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273696), _1273698), hAPP(c_Groups_Ouminus__class_Ouminus(_1273696), _1273700)))], (43543 ^ _779999) ^ [_1644237, _1644239, _1644241, _1644243] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644237)), hAPP(hAPP(c_List_Olist_OCons(_1644237), _1644239), _1644241)), c_List_Olists(_1644237, _1644243))), 43546 ^ _779999 : [(43549 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644237)), _1644241), c_List_Olists(_1644237, _1644243))))], (43547 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644237), _1644239), _1644243)))]]], (40136 ^ _779999) ^ [_1559169, _1559171] : [c_Wellfounded_Oacyclic(_1559169, _1559171), 40139 ^ _779999 : [(40140 ^ _779999) ^ [_1559254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559169, _1559169)), hAPP(hAPP(c_Product__Type_OPair(_1559169, _1559169), _1559254), _1559254)), c_Transitive__Closure_Otrancl(_1559169, _1559171)))]]], (42022 ^ _779999) ^ [_1604948, _1604950, _1604952, _1604954, _1604956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604948, tc_HOL_Obool)), _1604950), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604952, tc_fun(_1604948, tc_HOL_Obool)), _1604954), _1604956))), 42025 ^ _779999 : [(42026 ^ _779999) ^ [_1605081] : [hBOOL(hAPP(hAPP(c_member(_1604952), _1605081), _1604954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604948, tc_HOL_Obool)), _1604950), hAPP(_1604956, _1605081))))]]], (13237 ^ _779999) ^ [_1015574, _1015576, _1015578, _1015580] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1015574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015574), _1015576), _1015578)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015574), _1015576), _1015580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015574), _1015578), _1015580)))], (46105 ^ _779999) ^ [_1703182, _1703184] : [-(_1703182 = c_List_Olist_ONil(_1703184)), -(hAPP(hAPP(c_List_Oappend(_1703184), c_List_Obutlast(_1703184, _1703182)), hAPP(hAPP(c_List_Olist_OCons(_1703184), c_List_Olast(_1703184, _1703182)), c_List_Olist_ONil(_1703184))) = _1703182)], (41982 ^ _779999) ^ [_1603730, _1603732, _1603734, _1603736, _1603738] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603730, tc_fun(_1603732, tc_HOL_Obool)), _1603734), hAPP(hAPP(c_COMBB(tc_fun(_1603732, tc_HOL_Obool), tc_fun(_1603732, tc_HOL_Obool), _1603730), hAPP(c_Set_Oinsert(_1603732), _1603736)), _1603738)) = hAPP(hAPP(c_Set_Oinsert(_1603732), _1603736), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603730, tc_fun(_1603732, tc_HOL_Obool)), _1603734), _1603738)))], (52200 ^ _779999) ^ [_1832505, _1832507] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1832505, _1832507))), class_Lazy__Sequence_Osmall__lazy(_1832505), class_Lazy__Sequence_Osmall__lazy(_1832507)], (8806 ^ _779999) ^ [_931214, _931216, _931218, _931220] : [class_Complete__Lattice_Ocomplete__lattice(_931214), _931216 = c_Inductive_Ocomplete__lattice__class_Ogfp(_931214, _931218), c_Orderings_Oorder__class_Omono(_931214, _931214, _931218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931214), _931220), hAPP(_931218, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931214), _931220), _931216)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931214), _931220), _931216)))], (45668 ^ _779999) ^ [_1694561, _1694563, _1694565] : [-(_1694561 = c_List_Olist_ONil(_1694563)), -(hAPP(c_List_Otl(_1694563), hAPP(hAPP(c_List_Oappend(_1694563), _1694561), _1694565)) = hAPP(hAPP(c_List_Oappend(_1694563), hAPP(c_List_Otl(_1694563), _1694561)), _1694565))], (41624 ^ _779999) ^ [_1594359, _1594361, _1594363, _1594365, _1594367, _1594369] : [c_Finite__Set_Ofun__left__comm(_1594359, _1594361, _1594363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594359), _1594365)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594359, _1594361, _1594363), _1594367), hAPP(hAPP(c_Set_Oinsert(_1594359), _1594369), _1594365)) = hAPP(hAPP(_1594363, _1594369), hAPP(hAPP(c_Finite__Set_Ofold(_1594359, _1594361, _1594363), _1594367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594359, tc_HOL_Obool)), _1594365), hAPP(hAPP(c_Set_Oinsert(_1594359), _1594369), c_Orderings_Obot__class_Obot(tc_fun(_1594359, tc_HOL_Obool)))))))], (34337 ^ _779999) ^ [_1422073] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1422073)), 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, _1422073, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20170 ^ _779999) ^ [_1147426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1147426))))], (47761 ^ _779999) ^ [_1741638, _1741640] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1741638, _1741640) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1741638, hAPP(c_Nat_OSuc, _1741640))))], (41988 ^ _779999) ^ [_1603968, _1603970, _1603972, _1603974, _1603976, _1603978] : [-(hAPP(c_Set_Ovimage(_1603968, _1603970, _1603972), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603974, tc_fun(_1603970, tc_HOL_Obool)), _1603976), _1603978)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603974, tc_fun(_1603968, tc_HOL_Obool)), _1603976), hAPP(hAPP(c_COMBB(tc_fun(_1603970, tc_HOL_Obool), tc_fun(_1603968, tc_HOL_Obool), _1603974), c_Set_Ovimage(_1603968, _1603970, _1603972)), _1603978)))], (42476 ^ _779999) ^ [_1615917, _1615919, _1615921, _1615923] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615917, tc_fun(_1615919, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615917, tc_HOL_Obool), _1615921)), _1615923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1615917, tc_HOL_Obool), tc_fun(_1615919, tc_HOL_Obool)), _1615921), hAPP(hAPP(c_COMBC(tc_fun(_1615917, tc_HOL_Obool), tc_fun(_1615917, tc_fun(_1615919, tc_HOL_Obool)), tc_fun(_1615919, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615917, tc_fun(_1615919, tc_HOL_Obool))), _1615923)))], (35272 ^ _779999) ^ [_1443414] : [-(_1443414 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1443414), 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)))))], (37467 ^ _779999) ^ [_1490314, _1490316] : [-(c_Relation_OId__on(_1490314, _1490316) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490314, tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool)), _1490316), hAPP(hAPP(c_COMBC(_1490314, tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool), tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1490314, _1490314), tc_fun(tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool), tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool)), _1490314), c_Set_Oinsert(tc_prod(_1490314, _1490314))), hAPP(hAPP(c_COMBS(_1490314, _1490314, tc_prod(_1490314, _1490314)), c_Product__Type_OPair(_1490314, _1490314)), c_COMBI(_1490314)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490314, _1490314), tc_HOL_Obool)))))], (25616 ^ _779999) ^ [_1260330, _1260332, _1260334] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260330, tc_Nat_Onat), _1260332), _1260334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260330, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1260330), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260332)), _1260334))], (33315 ^ _779999) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (20697 ^ _779999) ^ [_1155620, _1155622] : [c_Nat__Transfer_Onat__set(_1155620), c_Nat__Transfer_Onat__set(_1155622), 20704 ^ _779999 : [(20711 ^ _779999) ^ [] : [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), _1155620)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1155620), _1155622)))], (20705 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1155620), _1155622)), -(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), _1155620)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155622))))]]], (25200 ^ _779999) ^ [_1253055, _1253057, _1253059] : [class_Orderings_Olinorder(_1253055), hAPP(_1253057, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1253055), 25205 ^ [_1253055, _1253057, _1253059]), 25206 ^ [_1253055, _1253057, _1253059])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1253055), hAPP(_1253057, 25205 ^ [_1253055, _1253057, _1253059])), hAPP(_1253057, 25206 ^ [_1253055, _1253057, _1253059])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253055), _1253059)), -(_1253059 = c_Orderings_Obot__class_Obot(tc_fun(_1253055, tc_HOL_Obool))), -(hAPP(_1253057, c_Big__Operators_Olinorder__class_OMax(_1253055, _1253059)) = c_Big__Operators_Olinorder__class_OMax(_1253055, hAPP(c_Set_Oimage(_1253055, _1253055, _1253057), _1253059)))], (8224 ^ _779999) ^ [_919502, _919504, _919506, _919508, _919510] : [hAPP(c_Set_Oimage(_919502, _919504, _919506), _919508) = _919510, -(hAPP(c_Set_Oimage(tc_fun(_919502, tc_HOL_Obool), tc_fun(_919504, tc_HOL_Obool), c_Set_Oimage(_919502, _919504, _919506)), hAPP(c_Set_OPow(_919502), _919508)) = hAPP(c_Set_OPow(_919504), _919510))], (11825 ^ _779999) ^ [_987915, _987917] : [class_Finite__Set_Ofinite(_987915), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987915), _987917)))], (26410 ^ _779999) ^ [_1274776] : [class_Lattices_Oboolean__algebra(_1274776), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1274776), c_Orderings_Obot__class_Obot(_1274776)) = c_Orderings_Otop__class_Otop(_1274776))], (47278 ^ _779999) ^ [_1729583] : [-(c_List_Oconcat(_1729583, c_List_Olist_ONil(tc_List_Olist(_1729583))) = c_List_Olist_ONil(_1729583))], (38386 ^ _779999) ^ [_1514429, _1514431, _1514433, _1514435, _1514437] : [-(hAPP(c_Relation_ODomain(_1514429, _1514431), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1514429, _1514431)), hAPP(hAPP(c_Product__Type_OPair(_1514429, _1514431), _1514433), _1514435)), _1514437)) = hAPP(hAPP(c_Set_Oinsert(_1514429), _1514433), hAPP(c_Relation_ODomain(_1514429, _1514431), _1514437)))], (49125 ^ _779999) ^ [_1770038, _1770040, _1770042, _1770044] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1770038, _1770040, _1770042, _1770044) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1770038, _1770040), _1770042), _1770044)))], (6399 ^ _779999) ^ [_883132, _883134, _883136] : [class_Lattices_Osemilattice__sup(_883132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883132), _883134), _883136)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883132), _883136), _883134) = _883136)], (22720 ^ _779999) ^ [_1201380, _1201382, _1201384, _1201386, _1201388] : [class_Complete__Lattice_Ocomplete__lattice(_1201380), 22723 ^ _779999 : [(22724 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201382, _1201380), _1201384), _1201386)), _1201388)), 22727 ^ _779999 : [(22728 ^ _779999) ^ [_1201561] : [hBOOL(hAPP(hAPP(c_member(_1201382), _1201561), _1201384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201380), hAPP(_1201386, _1201561)), _1201388)))]]], (22734 ^ _779999) ^ [] : [22736 ^ _779999 : [(22739 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201380), hAPP(_1201386, 22735 ^ [_1201380, _1201382, _1201384, _1201386, _1201388])), _1201388))], (22737 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201382), 22735 ^ [_1201380, _1201382, _1201384, _1201386, _1201388]), _1201384)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201382, _1201380), _1201384), _1201386)), _1201388)))]]], (32811 ^ _779999) ^ [_1395371, _1395373] : [class_Int_Onumber__ring(_1395371), -(hAPP(c_Int_Onumber__class_Onumber__of(_1395371), c_Int_OBit1(_1395373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395371), c_Groups_Oone__class_Oone(_1395371)), hAPP(c_Int_Onumber__class_Onumber__of(_1395371), _1395373))), hAPP(c_Int_Onumber__class_Onumber__of(_1395371), _1395373)))], (40801 ^ _779999) ^ [_1575430, _1575432, _1575434] : [c_Relation_Orefl__on(_1575430, _1575432, _1575434), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575430, _1575430), tc_HOL_Obool)), _1575434), hAPP(hAPP(c_Relation_Orel__comp(_1575430, _1575430, _1575430), hAPP(c_Relation_Oconverse(_1575430, _1575430), _1575434)), _1575434))))], (47052 ^ _779999) ^ [_1724944, _1724946, _1724948, _1724950] : [_1724950 = c_List_Olist_ONil(_1724946), -(c_List_Olist__all2(_1724944, _1724946, _1724948, c_List_Olist_ONil(_1724944), _1724950))], (46654 ^ _779999) ^ [_1715969, _1715971] : [hAPP(c_Code__Numeral_Onat__of, _1715969) = hAPP(c_Code__Numeral_Onat__of, _1715971), -(_1715969 = _1715971)], (37580 ^ _779999) ^ [] : [-(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))))))], (24642 ^ _779999) ^ [_1241556, _1241558] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1241556), _1241558)), _1241558) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1241556), _1241558))], (51067 ^ _779999) ^ [_1813418, _1813420] : [c_Relation_Osym(_1813418, hAPP(c_Relation_Oconverse(_1813418, _1813418), _1813420)), -(c_Relation_Osym(_1813418, _1813420))], (7749 ^ _779999) ^ [_910279, _910281] : [-(c_Set_Othe__elem(_910279, _910281) = c_HOL_OThe(_910279, hAPP(hAPP(c_COMBB(tc_fun(_910279, tc_HOL_Obool), tc_HOL_Obool, _910279), hAPP(c_fequal, _910281)), hAPP(hAPP(c_COMBC(_910279, tc_fun(_910279, tc_HOL_Obool), tc_fun(_910279, tc_HOL_Obool)), c_Set_Oinsert(_910279)), c_Orderings_Obot__class_Obot(tc_fun(_910279, tc_HOL_Obool))))))], (47695 ^ _779999) ^ [_1740534, _1740536] : [c_List_Oupt(_1740534, _1740536) = c_List_Olist_ONil(tc_Nat_Onat), -(_1740536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1740536), _1740534)))], (28434 ^ _779999) ^ [_1314537, _1314539, _1314541, _1314543] : [class_Fields_Olinordered__field(_1314537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314537), _1314539), _1314541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314537), c_Groups_Ozero__class_Ozero(_1314537)), _1314543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314537), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314537), _1314539), _1314543)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314537), _1314541), _1314543))))], (46484 ^ _779999) ^ [_1712367, _1712369, _1712371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712367), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712369)), _1712371))), -(hAPP(c_Random_Opick(_1712369, hAPP(hAPP(c_List_Omap(_1712369, tc_prod(tc_Code__Numeral_Ocode__numeral, _1712369)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1712369), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1712371)), hAPP(c_Code__Numeral_Oof__nat, _1712367)) = hAPP(hAPP(c_List_Onth(_1712369), _1712371), _1712367))], (33553 ^ _779999) ^ [_1407404, _1407406] : [class_Int_Onumber__ring(_1407404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407404), c_Groups_Oone__class_Oone(_1407404)), hAPP(c_Int_Onumber__class_Onumber__of(_1407404), _1407406)) = hAPP(c_Int_Onumber__class_Onumber__of(_1407404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1407406)))], (5887 ^ _779999) ^ [_873709, _873711, _873713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873709, tc_HOL_Obool)), _873711), _873713)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873709, tc_HOL_Obool)), _873711), _873713) = _873713)], (2932 ^ _779999) ^ [_823629, _823631, _823633, _823635] : [-(c_Com_Ocom_OSemi(_823635, _823631) = c_Com_Ocom_OSemi(_823633, _823629)), _823635 = _823633, _823631 = _823629], (32689 ^ _779999) ^ [_1393269, _1393271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1393269)), c_Int_OBit1(_1393271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393269), _1393271)))], (8926 ^ _779999) ^ [_932889, _932891, _932893] : [class_Orderings_Olinorder(_932889), -(_932891 = _932893), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932889), _932891), _932893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932889), _932893), _932891)))], (33613 ^ _779999) ^ [_1408529, _1408531] : [class_Int_Onumber__ring(_1408529), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1408529), hAPP(c_Int_Onumber__class_Onumber__of(_1408529), _1408531)), c_Groups_Oone__class_Oone(_1408529)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1408531), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (49770 ^ _779999) ^ [_1784310, _1784312] : [c_Wellfounded_Oacyclic(_1784310, hAPP(c_Set_OCollect(tc_prod(_1784310, _1784310)), hAPP(c_Product__Type_Oprod_Oprod__case(_1784310, _1784310, tc_HOL_Obool), _1784312))), -(c_Wellfounded_Oacyclic(_1784310, hAPP(c_Set_OCollect(tc_prod(_1784310, _1784310)), hAPP(c_Product__Type_Oprod_Oprod__case(_1784310, _1784310, tc_HOL_Obool), c_Predicate_Oconversep(_1784310, _1784310, _1784312)))))], (33213 ^ _779999) ^ [_1401994] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401994) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401994), c_Int_OPls)))], (10125 ^ _779999) ^ [_954648] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _954648))], (22103 ^ _779999) ^ [_1188520, _1188522, _1188524, _1188526, _1188528, _1188530] : [hBOOL(hAPP(hAPP(c_member(_1188520), _1188522), _1188524)), hBOOL(hAPP(hAPP(_1188526, _1188522), _1188528)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1188520, tc_fun(_1188530, tc_HOL_Obool)), _1188524), _1188526), _1188528)))], (45985 ^ _779999) ^ [_1701293, _1701295, _1701297, _1701299, _1701301] : [class_Orderings_Olinorder(_1701293), hBOOL(hAPP(c_List_Odistinct(_1701295), _1701297)), -(hBOOL(hAPP(c_List_Odistinct(_1701295), c_List_Olinorder__class_Oinsort__insert__key(_1701295, _1701293, _1701299, _1701301, _1701297))))], (43443 ^ _779999) ^ [_1641130, _1641132, _1641134, _1641136, _1641138, _1641140] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1641130, _1641130)), hAPP(hAPP(c_Product__Type_OPair(_1641130, _1641130), _1641132), _1641134)), _1641136)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641130), tc_List_Olist(_1641130))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641130), tc_List_Olist(_1641130)), _1641138), _1641140)), c_List_Olistrel(_1641130, _1641136))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641130), tc_List_Olist(_1641130))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641130), tc_List_Olist(_1641130)), hAPP(hAPP(c_List_Olist_OCons(_1641130), _1641132), _1641138)), hAPP(hAPP(c_List_Olist_OCons(_1641130), _1641134), _1641140))), c_List_Olistrel(_1641130, _1641136))))], (40647 ^ _779999) ^ [_1571612, _1571614] : [-(_1571612 = _1571614), -(c_Random_Oinc__shift(_1571612, _1571614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1571614), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (29938 ^ _779999) ^ [_1341306] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341306)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341306))], (35029 ^ _779999) ^ [_1434361] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1434361)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1434361)))], (37505 ^ _779999) ^ [_1491211, _1491213, _1491215, _1491217, _1491219, _1491221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool)), _1491213), _1491215)), c_Wellfounded_Omax__ext(_1491211, _1491217))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool)), _1491219), _1491221)), c_Wellfounded_Omax__ext(_1491211, _1491217))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1491211, tc_HOL_Obool), tc_fun(_1491211, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491211, tc_HOL_Obool)), _1491213), _1491219)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491211, tc_HOL_Obool)), _1491215), _1491221))), c_Wellfounded_Omax__ext(_1491211, _1491217))))], (41174 ^ _779999) ^ [_1584964, _1584966, _1584968, _1584970, _1584972] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584964, _1584964)), hAPP(hAPP(c_Product__Type_OPair(_1584964, _1584964), _1584966), _1584968)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584964, _1584964), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1584970)), _1584972))), 41178 ^ _779999 : [(41181 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584964, _1584964)), hAPP(hAPP(c_Product__Type_OPair(_1584964, _1584964), 41177 ^ [_1584964, _1584966, _1584968, _1584970, _1584972]), _1584968)), _1584972)))], (41179 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584964, _1584964)), hAPP(hAPP(c_Product__Type_OPair(_1584964, _1584964), _1584966), 41177 ^ [_1584964, _1584966, _1584968, _1584970, _1584972])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584964, _1584964), tc_HOL_Obool), _1584970), _1584972))))]]], (4576 ^ _779999) ^ [_849519, _849521] : [_849521 = _849519, -(c_List_Oappend(_849521) = c_List_Oappend(_849519))], (27107 ^ _779999) ^ [_1290080, _1290082, _1290084, _1290086, _1290088] : [class_Groups_Ocomm__monoid__mult(_1290080), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290082), _1290084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290082, tc_HOL_Obool)), _1290086), _1290084)), 27121 ^ _779999 : [(27124 ^ _779999) ^ [] : [hAPP(_1290088, 27120 ^ [_1290080, _1290082, _1290084, _1290086, _1290088]) = c_Groups_Oone__class_Oone(_1290080)], (27122 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290082), 27120 ^ [_1290080, _1290082, _1290084, _1290086, _1290088]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290082, tc_HOL_Obool)), _1290084), _1290086))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290082, _1290080), _1290088), _1290084) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290082, _1290080), _1290088), _1290086))], (29940 ^ _779999) ^ [_1341338] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1341338), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1341338)], (4088 ^ _779999) ^ [_841607, _841609] : [_841609 = _841607, -(c_List_Odistinct(_841609) = c_List_Odistinct(_841607))], (45518 ^ _779999) ^ [_1691557, _1691559, _1691561, _1691563] : [-(hAPP(c_List_Orotate1(_1691557), c_List_Olist_ONil(_1691557)) = c_List_Olist_ONil(_1691557))], (14071 ^ _779999) ^ [_1031055, _1031057] : [hAPP(c_Finite__Set_Ocard(_1031055), _1031057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1031057 = c_Orderings_Obot__class_Obot(tc_fun(_1031055, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031055), _1031057))], (33179 ^ _779999) ^ [_1401461, _1401463] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401461), _1401463), hAPP(c_Int_Onumber__class_Onumber__of(_1401461), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1401461)), class_Fields_Ofield__inverse__zero(_1401461), class_Int_Onumber__ring(_1401461)], (48965 ^ _779999) ^ [_1765939, _1765941, _1765943, _1765945] : [-(hBOOL(hAPP(_1765939, _1765941))), -(hAPP(c_List_OremoveAll(_1765943, _1765941), hAPP(c_List_Ofilter(_1765943, _1765939), _1765945)) = hAPP(c_List_Ofilter(_1765943, _1765939), _1765945))], (16387 ^ _779999) ^ [_1076012, _1076014, _1076016] : [class_Rings_Olinordered__semiring__strict(_1076012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076012), c_Groups_Ozero__class_Ozero(_1076012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076012), _1076014), _1076016))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076012), c_Groups_Ozero__class_Ozero(_1076012)), _1076014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076012), c_Groups_Ozero__class_Ozero(_1076012)), _1076016)))], (11300 ^ _779999) ^ [_975850, _975852, _975854, _975856] : [class_Lattices_Odistrib__lattice(_975850), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975850), _975852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975850), _975854), _975856)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975850), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975850), _975852), _975854)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975850), _975852), _975856)))], (30715 ^ _779999) ^ [_1355793, _1355795] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355793, _1355795) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1355793 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1355795), 30718 ^ [_1355793, _1355795]))], (52416 ^ _779999) ^ [_1834974, _1834976] : [hBOOL(_1834974), -(hBOOL(hAPP(hAPP(c_fimplies, _1834976), _1834974)))], (12669 ^ _779999) ^ [_1004177, _1004179, _1004181] : [class_Lattices_Olattice(_1004177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004177), _1004179)), -(_1004179 = c_Orderings_Obot__class_Obot(tc_fun(_1004177, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004177), _1004181)), -(_1004181 = c_Orderings_Obot__class_Obot(tc_fun(_1004177, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004177, tc_HOL_Obool)), _1004179), _1004181) = c_Orderings_Obot__class_Obot(tc_fun(_1004177, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1004177, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004177, tc_HOL_Obool)), _1004179), _1004181)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1004177), c_Big__Operators_Olattice__class_OInf__fin(_1004177, _1004179)), c_Big__Operators_Olattice__class_OInf__fin(_1004177, _1004181)))], (47336 ^ _779999) ^ [_1730760, _1730762, _1730764, _1730766] : [-(hAPP(hAPP(c_List_Omap(_1730760, _1730762), _1730764), c_List_Oconcat(_1730760, _1730766)) = c_List_Oconcat(_1730762, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730760), tc_List_Olist(_1730762)), hAPP(c_List_Omap(_1730760, _1730762), _1730764)), _1730766)))], (44762 ^ _779999) ^ [_1673178, _1673180] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1673178), tc_List_Olist(_1673178), c_List_Olistrel(_1673178, _1673180)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1673178)), c_List_Olist_ONil(_1673178)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1673178), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1673178)), c_List_Olist_ONil(_1673178)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1673178), tc_HOL_Obool))))], (43271 ^ _779999) ^ [_1635450, _1635452, _1635454] : [-(c_List_Oset__Cons(_1635450, _1635452, _1635454) = hAPP(c_Set_OCollect(tc_List_Olist(_1635450)), hAPP(hAPP(c_COMBB(tc_fun(_1635450, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1635450)), c_HOL_OEx(_1635450)), hAPP(hAPP(c_COMBB(tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_fun(_1635450, tc_HOL_Obool), tc_List_Olist(_1635450)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_HOL_Obool, _1635450), c_HOL_OEx(tc_List_Olist(_1635450)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1635450), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1635450, tc_fun(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), tc_fun(tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), tc_List_Olist(_1635450)), c_COMBS(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1635450, tc_fun(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), tc_List_Olist(_1635450)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635450), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), _1635450), c_COMBS(tc_List_Olist(_1635450), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1635450)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1635450), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1635450)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1635450), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_List_Olist(_1635450))), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1635450), tc_List_Olist(_1635450)), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_fun(tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_List_Olist(_1635450))), tc_fun(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool))), tc_List_Olist(_1635450)), c_COMBB(tc_fun(tc_List_Olist(_1635450), tc_List_Olist(_1635450)), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), _1635450)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1635450), tc_List_Olist(_1635450)), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), tc_List_Olist(_1635450)), c_COMBB(tc_List_Olist(_1635450), tc_HOL_Obool, tc_List_Olist(_1635450))), c_fequal))), c_List_Olist_OCons(_1635450)))))), hAPP(hAPP(c_COMBC(_1635450, tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool)), _1635450), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1635450))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1635450), c_fconj), hAPP(hAPP(c_COMBC(_1635450, tc_fun(_1635450, tc_HOL_Obool), tc_HOL_Obool), c_member(_1635450)), _1635452)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1635450), tc_fun(tc_List_Olist(_1635450), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1635450))), _1635454)))))))], (52076 ^ _779999) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (35406 ^ _779999) ^ [_1446219, _1446221, _1446223, _1446225, _1446227] : [hBOOL(hAPP(hAPP(c_member(_1446219), _1446221), hAPP(c_Relation_OImage(_1446223, _1446219, _1446225), hAPP(hAPP(c_Set_Oinsert(_1446223), _1446227), c_Orderings_Obot__class_Obot(tc_fun(_1446223, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446223, _1446219)), hAPP(hAPP(c_Product__Type_OPair(_1446223, _1446219), _1446227), _1446221)), _1446225)))], (51416 ^ _779999) ^ [_1820161, _1820163, _1820165, _1820167, _1820169] : [c_Fun_Oinj__on(_1820161, _1820163, _1820165, _1820167), hBOOL(hAPP(hAPP(c_member(_1820161), _1820169), _1820167)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1820161, _1820163, _1820167, _1820165), hAPP(_1820165, _1820169)) = _1820169)], (12139 ^ _779999) ^ [_994250, _994252, _994254, _994256, _994258, _994260, _994262, _994264] : [c_Finite__Set_Ofolding__image__simple(_994250, _994252, _994254, _994256, _994258, _994260), hBOOL(hAPP(c_Finite__Set_Ofinite(_994252), _994262)), hBOOL(hAPP(c_Finite__Set_Ofinite(_994252), _994264)), -(hAPP(hAPP(_994254, hAPP(_994260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_994252, tc_HOL_Obool)), _994262), _994264))), hAPP(_994260, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994252, tc_HOL_Obool)), _994262), _994264))) = hAPP(hAPP(_994254, hAPP(_994260, _994262)), hAPP(_994260, _994264)))], (3700 ^ _779999) ^ [_835525, _835527, _835529, _835531] : [-(c_Random_Oselect__weight(_835531, _835527) = c_Random_Oselect__weight(_835529, _835525)), _835531 = _835529, _835527 = _835525], (23563 ^ _779999) ^ [_1220200, _1220202] : [class_Orderings_Olinorder(_1220200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220200), _1220202)), -(c_Big__Operators_Olinorder__class_OMin(_1220200, _1220202) = hAPP(c_Finite__Set_Ofold1(_1220200, c_Orderings_Oord__class_Omin(_1220200)), _1220202))], (25904 ^ _779999) ^ [_1265818, _1265820] : [-(hAPP(c_Set_OCollect(_1265818), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1265818), c_fNot), _1265820)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1265818, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1265818), _1265820)))], (11002 ^ _779999) ^ [_970166, _970168, _970170] : [class_Lattices_Olattice(_970166), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970166), _970168), _970170) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970166), _970170), _970168))], (13722 ^ _779999) ^ [_1024766, _1024768, _1024770] : [class_Groups_Oordered__comm__monoid__add(_1024766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024766), _1024768), c_Groups_Ozero__class_Ozero(_1024766))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024766), _1024770), c_Groups_Ozero__class_Ozero(_1024766))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024766), _1024768), _1024770)), c_Groups_Ozero__class_Ozero(_1024766))))], (44568 ^ _779999) ^ [_1669644, _1669646, _1669648] : [hAPP(hAPP(c_List_Olist_OCons(_1669644), _1669646), _1669648) = c_List_Olist_ONil(_1669644)], (5292 ^ _779999) ^ [_861003, _861005, _861007, _861009] : [-(c_Relation_OId__on(_861009, _861005) = c_Relation_OId__on(_861007, _861003)), _861009 = _861007, _861005 = _861003], (34227 ^ _779999) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (15259 ^ _779999) ^ [_1054140, _1054142, _1054144, _1054146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1054140, _1054142)), c_Sum__Type_OPlus(_1054140, _1054142, _1054144, _1054146))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054140), _1054144)))], (40711 ^ _779999) ^ [_1573021, _1573023, _1573025] : [c_Relation_Orefl__on(_1573021, _1573023, hAPP(c_Relation_Oconverse(_1573021, _1573021), _1573025)), -(c_Relation_Orefl__on(_1573021, _1573023, _1573025))], (47327 ^ _779999) ^ [_1730569, _1730571] : [47329 ^ _779999 : [(47332 ^ _779999) ^ [] : [47328 ^ [_1730569, _1730571] = c_List_Olist_ONil(_1730569)], (47330 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730569)), 47328 ^ [_1730569, _1730571]), hAPP(c_List_Oset(tc_List_Olist(_1730569)), _1730571))))]], -(c_List_Olist_ONil(_1730569) = c_List_Oconcat(_1730569, _1730571))], (49876 ^ _779999) ^ [_1787241, _1787243, _1787245] : [-(c_List_Oreplicate(_1787241, hAPP(c_Nat_OSuc, _1787243), _1787245) = hAPP(hAPP(c_List_Olist_OCons(_1787241), _1787245), c_List_Oreplicate(_1787241, _1787243, _1787245)))], (47771 ^ _779999) ^ [_1741839, _1741841] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1741839, _1741841) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1741839), hAPP(c_Nat_OSuc, _1741841))))], (36513 ^ _779999) ^ [_1467851, _1467853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467853)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467851), _1467853) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1467851, _1467853)))], (49371 ^ _779999) ^ [_1775858, _1775860, _1775862] : [c_List_Olist__ex(_1775858, _1775860, _1775862), -(c_List_Olist__ex(_1775858, _1775860, hAPP(c_List_Orev(_1775858), _1775862)))], (22673 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (50381 ^ _779999) ^ [_1797680, _1797682] : [-(c_Lazy__Sequence_Oappend(_1797680, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797680), _1797682) = _1797682)], (17365 ^ _779999) ^ [_1094836] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1094836)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25358 ^ _779999) ^ [_1255976, _1255978, _1255980, _1255982, _1255984, _1255986] : [hBOOL(hAPP(_1255976, _1255978)), c_Natural_Oevaln(_1255980, _1255978, _1255982, _1255984), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_1255976, _1255980, _1255986), _1255978, _1255982, _1255984))], (50282 ^ _779999) ^ [_1795216, _1795218, _1795220, _1795222] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1795216, _1795218)), c_Nitpick_Opair__box_OPairBox(_1795216, _1795218, _1795220, _1795222)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20884 ^ _779999) ^ [_1159194, _1159196] : [class_Groups_Oordered__ab__group__add__abs(_1159194), 20887 ^ _779999 : [(20894 ^ _779999) ^ [] : [_1159196 = c_Groups_Ozero__class_Ozero(_1159194), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159194), hAPP(c_Groups_Oabs__class_Oabs(_1159194), _1159196)), c_Groups_Ozero__class_Ozero(_1159194))))], (20888 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159194), hAPP(c_Groups_Oabs__class_Oabs(_1159194), _1159196)), c_Groups_Ozero__class_Ozero(_1159194))), -(_1159196 = c_Groups_Ozero__class_Ozero(_1159194))]]], (4290 ^ _779999) ^ [_845072, _845074] : [_845074 = _845072, -(c_New__DSequence_Opos__empty(_845074) = c_New__DSequence_Opos__empty(_845072))], (34761 ^ _779999) ^ [_1430406, _1430408] : [class_Int_Onumber__ring(_1430406), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430406), hAPP(c_Int_Onumber__class_Onumber__of(_1430406), 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)))), _1430408)) = c_Groups_Oone__class_Oone(_1430406))], (33589 ^ _779999) ^ [_1408047] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1408047)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408047) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41582 ^ _779999) ^ [_1593596, _1593598, _1593600] : [class_Orderings_Olinorder(_1593596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593596), _1593598)), -(hBOOL(hAPP(hAPP(c_member(_1593596), _1593600), _1593598))), -(c_Big__Operators_Olinorder__class_OMax(_1593596, hAPP(hAPP(c_Set_Oinsert(_1593596), _1593600), _1593598)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593596, _1593596, c_Orderings_Oord__class_Omax(_1593596)), _1593600), _1593598))], (31965 ^ _779999) ^ [_1379615, _1379617, _1379619] : [class_Int_Onumber__ring(_1379615), -(hAPP(c_Int_Onumber__class_Onumber__of(_1379615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1379617), _1379619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379615), hAPP(c_Int_Onumber__class_Onumber__of(_1379615), _1379617)), hAPP(c_Int_Onumber__class_Onumber__of(_1379615), _1379619)))], (39435 ^ _779999) ^ [_1542716, _1542718, _1542720] : [39436 ^ _779999 : [(39437 ^ _779999) ^ [_1542770] : [hBOOL(hAPP(_1542716, _1542770))]], _1542718 = c_Hilbert__Choice_OEps(_1542720, _1542716), -(hBOOL(hAPP(_1542716, _1542718)))], (33913 ^ _779999) ^ [_1414548, _1414550] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1414548)), c_Int_OBit0(_1414550)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414548), _1414550)))], (13247 ^ _779999) ^ [_1015769, _1015771, _1015773, _1015775] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1015769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015769), _1015771), _1015773)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015769), _1015775), _1015773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015769), _1015771), _1015775)))], (42732 ^ _779999) ^ [_1621835, _1621837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1621835, tc_HOL_Obool)), _1621837)), 42738 ^ _779999 : [(42741 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1621835), 42737 ^ [_1621835, _1621837]))], (42739 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1621835, tc_HOL_Obool)), 42737 ^ [_1621835, _1621837]), _1621837)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1621835), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621835, tc_HOL_Obool), _1621837))))], (35041 ^ _779999) ^ [] : [-(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))], (22307 ^ _779999) ^ [_1192736, _1192738] : [class_Lattices_Obounded__lattice__top(_1192736), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1192736), c_Orderings_Otop__class_Otop(_1192736)), _1192738) = _1192738)], (9190 ^ _779999) ^ [_936898, _936900, _936902, _936904] : [class_Orderings_Oord(_936898), 9193 ^ _779999 : [(9202 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936900, _936898)), _936902), _936904))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936900, _936898)), _936902), _936904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936900, _936898)), _936904), _936902)))], (9194 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936900, _936898)), _936902), _936904)), 9197 ^ _779999 : [(9200 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936900, _936898)), _936904), _936902))], (9198 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936900, _936898)), _936902), _936904)))]]]]], (50004 ^ _779999) ^ [_1789505, _1789507, _1789509] : [_1789507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1789505) = c_List_Oreplicate(_1789505, _1789507, _1789509))], (32919 ^ _779999) ^ [_1397360, _1397362, _1397364] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397360))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397360)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397362)), _1397364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1397362)), _1397364))], (16987 ^ _779999) ^ [_1087213, _1087215, _1087217, _1087219, _1087221] : [class_Rings_Olinordered__semiring__strict(_1087213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), _1087215), _1087217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087213), _1087219), _1087221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087213), c_Groups_Ozero__class_Ozero(_1087213)), _1087215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), c_Groups_Ozero__class_Ozero(_1087213)), _1087219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087213), _1087215), _1087219)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087213), _1087217), _1087221))))], (19183 ^ _779999) ^ [_1129747, _1129749, _1129751, _1129753] : [class_Orderings_Oorder(_1129747), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129747, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1129747, _1129749, _1129751)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1129747, _1129751, _1129753)) = c_Orderings_Obot__class_Obot(tc_fun(_1129747, tc_HOL_Obool)))], (44984 ^ _779999) ^ [_1678865, _1678867, _1678869, _1678871] : [hAPP(hAPP(c_List_Oappend(_1678865), _1678867), _1678869) = hAPP(hAPP(c_List_Oappend(_1678865), _1678871), _1678869), -(_1678867 = _1678871)], (52182 ^ _779999) ^ [_1832277, _1832279] : [-(class_Nat_Osize(tc_sum(_1832277, _1832279)))], (35673 ^ _779999) ^ [_1451923, _1451925, _1451927, _1451929, _1451931, _1451933, _1451935, _1451937] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1451923, _1451925, _1451927), _1451929), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1451931, _1451933, tc_prod(_1451923, _1451925)), _1451935), _1451937)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1451931, _1451933, _1451927), hAPP(hAPP(c_COMBB(tc_fun(_1451933, tc_prod(_1451923, _1451925)), tc_fun(_1451933, _1451927), _1451931), hAPP(c_COMBB(tc_prod(_1451923, _1451925), _1451927, _1451933), hAPP(c_Product__Type_Oprod_Oprod__case(_1451923, _1451925, _1451927), _1451929))), _1451935)), _1451937))], (32327 ^ _779999) ^ [_1386192, _1386194, _1386196, _1386198] : [class_Fields_Olinordered__field__inverse__zero(_1386192), class_Int_Onumber(_1386192), 32334 ^ _779999 : [(32335 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386194), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386192), _1386196), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)))), 32338 ^ _779999 : [(32345 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), c_Groups_Ozero__class_Ozero(_1386192)), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)))), 32348 ^ _779999 : [(32355 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)), c_Groups_Ozero__class_Ozero(_1386192)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386194), c_Groups_Ozero__class_Ozero(_1386192))))], (32349 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)), c_Groups_Ozero__class_Ozero(_1386192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386192), _1386194), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)))))]]], (32339 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), c_Groups_Ozero__class_Ozero(_1386192)), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386192), _1386194), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))), _1386196)))]]], (32361 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386194), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386192), _1386196), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))))), 32364 ^ _779999 : [(32367 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386192), _1386194), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))), _1386196))], (32365 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), c_Groups_Ozero__class_Ozero(_1386192)), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))))]], 32368 ^ _779999 : [(32371 ^ _779999) ^ [] : [32372 ^ _779999 : [(32375 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386192), _1386194), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198))))], (32373 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)), c_Groups_Ozero__class_Ozero(_1386192))))]], 32376 ^ _779999 : [(32379 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), _1386194), c_Groups_Ozero__class_Ozero(_1386192)))], (32377 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)), c_Groups_Ozero__class_Ozero(_1386192)))]]], (32369 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386192), c_Groups_Ozero__class_Ozero(_1386192)), hAPP(c_Int_Onumber__class_Onumber__of(_1386192), _1386198)))]]]]], (43082 ^ _779999) ^ [_1629980, _1629982, _1629984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1629980), c_Nitpick_Oplus__frac(_1629980, _1629982, c_Nitpick_Ouminus__frac(_1629980, _1629984)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1629980, _1629982, _1629984))], (44944 ^ _779999) ^ [_1677926, _1677928, _1677930, _1677932] : [-(hAPP(hAPP(c_List_Oappend(_1677926), hAPP(hAPP(c_List_Olist_OCons(_1677926), _1677928), _1677930)), _1677932) = hAPP(hAPP(c_List_Olist_OCons(_1677926), _1677928), hAPP(hAPP(c_List_Oappend(_1677926), _1677930), _1677932)))], (9298 ^ _779999) ^ [_938519, _938521, _938523] : [class_Orderings_Oorder(_938519), 9301 ^ _779999 : [(9302 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938519), _938521), _938523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938519), _938521), _938523))), -(_938521 = _938523)], (9312 ^ _779999) ^ [] : [9313 ^ _779999 : [(9316 ^ _779999) ^ [] : [_938521 = _938523], (9314 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938519), _938521), _938523))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938519), _938521), _938523)))]]], (33571 ^ _779999) ^ [_1407762, _1407764] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407762), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407762)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407764)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1407762), _1407764)))], (9596 ^ _779999) ^ [_943132, _943134, _943136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943132, tc_HOL_Obool)), _943134), _943136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943132, tc_HOL_Obool)), _943134), _943136))), -(_943134 = _943136)], (32755 ^ _779999) ^ [_1394455, _1394457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1394455)), c_Int_OBit1(_1394457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394455), _1394457)))], (33899 ^ _779999) ^ [_1414309, _1414311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1414309)), c_Int_OBit0(_1414311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414309), _1414311)))], (41124 ^ _779999) ^ [_1583456, _1583458, _1583460, _1583462, _1583464] : [c_Relation_Osingle__valued(_1583456, _1583456, _1583458), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583456, _1583456)), hAPP(hAPP(c_Product__Type_OPair(_1583456, _1583456), _1583460), _1583462)), c_Transitive__Closure_Ortrancl(_1583456, _1583458))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583456, _1583456)), hAPP(hAPP(c_Product__Type_OPair(_1583456, _1583456), _1583460), _1583464)), c_Transitive__Closure_Ortrancl(_1583456, _1583458))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583456, _1583456)), hAPP(hAPP(c_Product__Type_OPair(_1583456, _1583456), _1583462), _1583464)), c_Transitive__Closure_Ortrancl(_1583456, _1583458)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583456, _1583456)), hAPP(hAPP(c_Product__Type_OPair(_1583456, _1583456), _1583464), _1583462)), c_Transitive__Closure_Ortrancl(_1583456, _1583458))))], (6579 ^ _779999) ^ [_886598, _886600, _886602, _886604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886598, tc_HOL_Obool)), _886600), _886602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886598, tc_HOL_Obool)), _886604), _886602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886598, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886598, tc_HOL_Obool)), _886600), _886604)), _886602)))], (40231 ^ _779999) ^ [_1561424, _1561426, _1561428, _1561430] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561424, _1561424)), _1561426), c_Transitive__Closure_Otrancl(_1561424, _1561428))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561424, _1561424), tc_HOL_Obool)), _1561428), _1561430)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561424, _1561424)), _1561426), c_Transitive__Closure_Otrancl(_1561424, _1561430))))], (30569 ^ _779999) ^ [_1353159, _1353161, _1353163, _1353165] : [class_Divides_Osemiring__div(_1353159), -(c_Divides_Odiv__class_Omod(_1353159, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353159), c_Divides_Odiv__class_Omod(_1353159, _1353161, _1353163)), _1353165), _1353163) = c_Divides_Odiv__class_Omod(_1353159, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353159), _1353161), _1353165), _1353163))], (9150 ^ _779999) ^ [_936369, _936371, _936373, _936375, _936377, _936379] : [-(_936369 = _936371), -(hAPP(c_Fun_Ofun__upd(_936373, _936375, _936377, _936371, _936379), _936369) = hAPP(_936377, _936369))], (232 ^ _779999) ^ [_783587, _783589] : [-(class_Fields_Ofield__inverse__zero(_783587)), _783589 = _783587, class_Fields_Ofield__inverse__zero(_783589)], (15935 ^ _779999) ^ [_1067352, _1067354, _1067356, _1067358, _1067360, _1067362, _1067364] : [class_Rings_Osemiring__0(_1067352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067352), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067354, _1067352), _1067356), _1067358)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067360, _1067352), _1067362), _1067364)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067354, _1067352), hAPP(hAPP(c_COMBC(_1067354, tc_fun(_1067360, tc_HOL_Obool), _1067352), hAPP(hAPP(c_COMBB(tc_fun(_1067360, _1067352), tc_fun(tc_fun(_1067360, tc_HOL_Obool), _1067352), _1067354), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067360, _1067352)), hAPP(hAPP(c_COMBC(_1067354, tc_fun(_1067360, _1067352), tc_fun(_1067360, _1067352)), hAPP(hAPP(c_COMBB(tc_fun(_1067352, _1067352), tc_fun(tc_fun(_1067360, _1067352), tc_fun(_1067360, _1067352)), _1067354), c_COMBB(_1067352, _1067352, _1067360)), hAPP(hAPP(c_COMBB(_1067352, tc_fun(_1067352, _1067352), _1067354), c_Groups_Otimes__class_Otimes(_1067352)), _1067356))), _1067362))), _1067364)), _1067358))], (46716 ^ _779999) ^ [_1716997, _1716999] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1716997), _1716999) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716997)), hAPP(c_Code__Numeral_Onat__of, _1716999))))], (42281 ^ _779999) ^ [_1611336, _1611338, _1611340, _1611342, _1611344, _1611346, _1611348] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611336, tc_fun(_1611338, tc_fun(_1611340, tc_HOL_Obool))), _1611342), _1611344), _1611346), _1611348)), 42284 ^ _779999 : [(42285 ^ _779999) ^ [_1611464] : [hBOOL(hAPP(hAPP(c_member(_1611336), _1611464), _1611342)), -(hBOOL(hAPP(hAPP(hAPP(_1611344, _1611464), _1611346), _1611348)))]]], (42486 ^ _779999) ^ [_1616311, _1616313, _1616315, _1616317] : [-(hAPP(c_Set_Ovimage(_1616311, _1616313, _1616315), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616313, tc_HOL_Obool), _1616317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1616313, tc_HOL_Obool), tc_fun(_1616311, tc_HOL_Obool)), _1616317), c_Set_Ovimage(_1616311, _1616313, _1616315)))], (38111 ^ _779999) ^ [_1507482] : [class_Orderings_Owellorder(_1507482), -(c_Wellfounded_Owf(_1507482, hAPP(c_Set_OCollect(tc_prod(_1507482, _1507482)), hAPP(c_Product__Type_Oprod_Oprod__case(_1507482, _1507482, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1507482)))))], (11771 ^ _779999) ^ [_986842, _986844, _986846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986842), _986844)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_986842), hAPP(hAPP(c_Set_Oinsert(_986842), _986846), _986844))))], (46257 ^ _779999) ^ [_1706591, _1706593, _1706595, _1706597] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706591)), hAPP(hAPP(c_List_Omap(_1706593, _1706591), _1706595), _1706597)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706593)), _1706597))], (18861 ^ _779999) ^ [_1124209] : [-(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)), _1124209))))], (16153 ^ _779999) ^ [_1071677, _1071679, _1071681, _1071683] : [class_Rings_Oordered__ring(_1071677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071677), _1071679), _1071681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071677), _1071683), c_Groups_Ozero__class_Ozero(_1071677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071677), _1071683), _1071681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071677), _1071683), _1071679))))], (43072 ^ _779999) ^ [_1629755, _1629757] : [-(c_Nitpick_Oinverse__frac(_1629755, _1629757) = hAPP(hAPP(c_Nitpick_Ofrac(_1629755), hAPP(c_Nitpick_Odenom(_1629755), _1629757)), hAPP(c_Nitpick_Onum(_1629755), _1629757)))], (44690 ^ _779999) ^ [_1671709, _1671711] : [-(_1671711 = c_List_Olist_ONil(_1671709)), -(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(_1671709)), _1671711))))], (12469 ^ _779999) ^ [_1000612, _1000614, _1000616] : [class_Lattices_Olattice(_1000612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000612), _1000614)), -(_1000616 = c_Orderings_Obot__class_Obot(tc_fun(_1000612, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000612, tc_HOL_Obool)), _1000616), _1000614)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1000612), c_Big__Operators_Olattice__class_OSup__fin(_1000612, _1000616)), c_Big__Operators_Olattice__class_OSup__fin(_1000612, _1000614)) = c_Big__Operators_Olattice__class_OSup__fin(_1000612, _1000614))], (20443 ^ _779999) ^ [_1151938, _1151940] : [c_Nat__Transfer_Onat__set(_1151938), c_Nat__Transfer_Onat__set(_1151940), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1151938), _1151940) = 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), _1151938)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1151940))))], (13608 ^ _779999) ^ [_1022865] : [-(c_Finite__Set_Ofun__left__comm__idem(_1022865, tc_fun(_1022865, tc_HOL_Obool), c_Set_Oinsert(_1022865)))], (38034 ^ _779999) ^ [_1505816] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1505816)))], (15497 ^ _779999) ^ [_1058974, _1058976, _1058978, _1058980, _1058982] : [class_Groups_Ocomm__monoid__mult(_1058974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058976), _1058978)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058976), _1058980)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058974), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1058974, _1058976, c_Groups_Otimes__class_Otimes(_1058974)), _1058982), c_Groups_Oone__class_Oone(_1058974)), _1058978)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1058974, _1058976, c_Groups_Otimes__class_Otimes(_1058974)), _1058982), c_Groups_Oone__class_Oone(_1058974)), _1058980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058974), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1058974, _1058976, c_Groups_Otimes__class_Otimes(_1058974)), _1058982), c_Groups_Oone__class_Oone(_1058974)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1058976, tc_HOL_Obool)), _1058978), _1058980))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1058974, _1058976, c_Groups_Otimes__class_Otimes(_1058974)), _1058982), c_Groups_Oone__class_Oone(_1058974)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1058976, tc_HOL_Obool)), _1058978), _1058980))))], (8142 ^ _779999) ^ [_917778, _917780, _917782] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917778, tc_HOL_Obool)), _917780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917778, tc_HOL_Obool)), _917782), _917780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917778, tc_HOL_Obool)), _917780), _917782))], (14828 ^ _779999) ^ [_1046173, _1046175] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046173), _1046175)), -(hAPP(c_Finite__Set_Ocard(_1046173), _1046175) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1046173, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1046173), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046175))], (10437 ^ _779999) ^ [_959712, _959714] : [class_Complete__Lattice_Ocomplete__lattice(_959712), c_Orderings_Oorder__class_Omono(_959712, _959712, _959714), -(c_Inductive_Ocomplete__lattice__class_Olfp(_959712, _959714) = hAPP(_959714, c_Inductive_Ocomplete__lattice__class_Olfp(_959712, _959714)))], (34883 ^ _779999) ^ [_1432236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1432236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1432236))))], (34029 ^ _779999) ^ [_1416496, _1416498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416496)), c_Int_OBit1(_1416498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416496), _1416498)))], (42745 ^ _779999) ^ [_1622093, _1622095, _1622097] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1622093, tc_HOL_Obool)), _1622095), _1622097))), 42751 ^ _779999 : [(42755 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1622093, tc_HOL_Obool)), 42753 ^ [_1622093, _1622095, _1622097]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1622093, tc_HOL_Obool)), _1622095), _1622097))))], (42757 ^ _779999) ^ [] : [42750 ^ [_1622093, _1622095, _1622097] = 42753 ^ [_1622093, _1622095, _1622097]], (42759 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622093, tc_HOL_Obool)), 42750 ^ [_1622093, _1622095, _1622097]), 42753 ^ [_1622093, _1622095, _1622097]) = c_Orderings_Obot__class_Obot(tc_fun(_1622093, tc_HOL_Obool))], (42752 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1622093, tc_HOL_Obool)), 42750 ^ [_1622093, _1622095, _1622097]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1622093, tc_HOL_Obool)), _1622095), _1622097))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622093, tc_HOL_Obool)), _1622095), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622093, tc_HOL_Obool), _1622097)) = c_Orderings_Obot__class_Obot(tc_fun(_1622093, tc_HOL_Obool)))], (35472 ^ _779999) ^ [_1447722, _1447724, _1447726, _1447728, _1447730] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1447722, _1447724), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1447726), _1447728))), -(_1447724 = 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), _1447730), _1447722), _1447724), 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), _1447730), _1447726)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1447730), _1447728)), _1447724))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1447730), _1447728), _1447724)))))], (40906 ^ _779999) ^ [_1578151, _1578153] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578151, _1578151)), hAPP(hAPP(c_Product__Type_OPair(_1578151, _1578151), 40907 ^ [_1578151, _1578153]), 40907 ^ [_1578151, _1578153])), c_Transitive__Closure_Otrancl(_1578151, _1578153)))), -(c_Wellfounded_Oacyclic(_1578151, _1578153))], (26520 ^ _779999) ^ [_1276780, _1276782] : [_1276782 = c_Orderings_Obot__class_Obot(tc_fun(_1276780, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276780, tc_HOL_Obool)), _1276782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276780, tc_HOL_Obool)), _1276782))))], (44594 ^ _779999) ^ [_1670079, _1670081] : [_1670079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1670081, _1670079, c_List_Olist_ONil(_1670081)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1670081)), c_List_Olist_ONil(_1670081)), c_List_Olist_ONil(tc_List_Olist(_1670081))))], (10613 ^ _779999) ^ [_962656, _962658] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962656), _962658)), hAPP(c_Nat_OSuc, _962656))))], (35633 ^ _779999) ^ [_1451116, _1451118, _1451120] : [hBOOL(hAPP(_1451116, hAPP(hAPP(c_Product__Type_OPair(_1451118, _1451120), 35634 ^ [_1451116, _1451118, _1451120]), 35635 ^ [_1451116, _1451118, _1451120]))), 35638 ^ _779999 : [(35639 ^ _779999) ^ [_1451263] : [-(hBOOL(hAPP(_1451116, _1451263)))]]], (12455 ^ _779999) ^ [_1000404, _1000406, _1000408] : [class_Lattices_Olattice(_1000404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000404), _1000406)), -(_1000406 = c_Orderings_Obot__class_Obot(tc_fun(_1000404, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1000404, hAPP(hAPP(c_Set_Oinsert(_1000404), _1000408), _1000406)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1000404), _1000408), c_Big__Operators_Olattice__class_OInf__fin(_1000404, _1000406)))], (3018 ^ _779999) ^ [_824968, _824970] : [_824970 = _824968, -(c_Nat_Ofunpow(_824970) = c_Nat_Ofunpow(_824968))], (38365 ^ _779999) ^ [_1513932, _1513934, _1513936] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1513932, _1513934)), _1513936)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1513932), hAPP(c_Relation_ODomain(_1513932, _1513934), _1513936))))], (27480 ^ _779999) ^ [_1296983, _1296985] : [-(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), _1296983)), _1296985))))], (49440 ^ _779999) ^ [_1777247, _1777249, _1777251] : [-(hBOOL(hAPP(hAPP(c_member(_1777247), _1777249), hAPP(c_List_Oset(_1777247), _1777251)))), 49441 ^ _779999 : [(49442 ^ _779999) ^ [_1777336, _1777338] : [_1777251 = hAPP(hAPP(c_List_Oappend(_1777247), _1777338), hAPP(hAPP(c_List_Olist_OCons(_1777247), _1777249), _1777336)), -(hBOOL(hAPP(hAPP(c_member(_1777247), _1777249), hAPP(c_List_Oset(_1777247), _1777336))))]]], (9674 ^ _779999) ^ [_944458, _944460] : [class_Complete__Lattice_Ocomplete__lattice(_944458), c_Orderings_Oorder__class_Omono(_944458, _944458, _944460), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_944458, _944460) = hAPP(_944460, c_Inductive_Ocomplete__lattice__class_Ogfp(_944458, _944460)))], (39356 ^ _779999) ^ [_1541012, _1541014, _1541016, _1541018, _1541020, _1541022, _1541024] : [-(hAPP(c_Product__Type_Oapsnd(_1541012, _1541014, _1541016, _1541018), hAPP(c_Product__Type_Oapsnd(_1541020, _1541012, _1541016, _1541022), _1541024)) = hAPP(c_Product__Type_Oapsnd(_1541020, _1541014, _1541016, hAPP(c_Fun_Ocomp(_1541012, _1541014, _1541020, _1541018), _1541022)), _1541024))], (30852 ^ _779999) ^ [_1358255, _1358257, _1358259] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358255), _1358257)), _1358259) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358255), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1358257), _1358259))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358255), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358257, _1358259))), _1358259)))], (27021 ^ _779999) ^ [_1287937, _1287939, _1287941, _1287943, _1287945] : [class_Groups_Ocomm__monoid__mult(_1287937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287939), _1287941)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287939), _1287943)), 27035 ^ _779999 : [(27038 ^ _779999) ^ [] : [hAPP(_1287945, 27034 ^ [_1287937, _1287939, _1287941, _1287943, _1287945]) = c_Groups_Oone__class_Oone(_1287937)], (27036 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1287939), 27034 ^ [_1287937, _1287939, _1287941, _1287943, _1287945]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287939, tc_HOL_Obool)), _1287941), _1287943))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287939, _1287937), _1287945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287939, tc_HOL_Obool)), _1287941), _1287943)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287937), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287939, _1287937), _1287945), _1287941)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287939, _1287937), _1287945), _1287943)))], (27996 ^ _779999) ^ [_1306255, _1306257, _1306259, _1306261] : [class_Rings_Olinordered__semidom(_1306255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306255), c_Groups_Oone__class_Oone(_1306255)), _1306257)), 28003 ^ _779999 : [(28010 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306259), _1306261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306255), hAPP(hAPP(c_Power_Opower__class_Opower(_1306255), _1306257), _1306259)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306255), _1306257), _1306261))))], (28004 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306255), hAPP(hAPP(c_Power_Opower__class_Opower(_1306255), _1306257), _1306259)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306255), _1306257), _1306261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306259), _1306261)))]]], (27774 ^ _779999) ^ [_1302261, _1302263, _1302265] : [class_Power_Opower(_1302261), class_Rings_Omult__zero(_1302261), class_Rings_Ono__zero__divisors(_1302261), class_Rings_Ozero__neq__one(_1302261), 27789 ^ _779999 : [(27798 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1302261), _1302263), _1302265) = c_Groups_Ozero__class_Ozero(_1302261)), _1302263 = c_Groups_Ozero__class_Ozero(_1302261), -(_1302265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27790 ^ _779999) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1302261), _1302263), _1302265) = c_Groups_Ozero__class_Ozero(_1302261), 27793 ^ _779999 : [(27796 ^ _779999) ^ [] : [_1302265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27794 ^ _779999) ^ [] : [-(_1302263 = c_Groups_Ozero__class_Ozero(_1302261))]]]]], (4786 ^ _779999) ^ [_852870, _852872] : [_852872 = _852870, -(c_List_Omember(_852872) = c_List_Omember(_852870))], (27354 ^ _779999) ^ [_1294575, _1294577, _1294579] : [class_Rings_Odivision__ring(_1294575), -(_1294577 = c_Groups_Ozero__class_Ozero(_1294575)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1294575), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294575), _1294579), _1294577)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294575), _1294579), hAPP(c_Groups_Ouminus__class_Ouminus(_1294575), _1294577)))], (7181 ^ _779999) ^ [_898418, _898420, _898422, _898424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898418, tc_HOL_Obool)), _898420), _898422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898418, tc_HOL_Obool)), _898420), hAPP(hAPP(c_Set_Oinsert(_898418), _898424), _898422))))], (51563 ^ _779999) ^ [_1823724, _1823726] : [51565 ^ _779999 : [(51568 ^ _779999) ^ [] : [hBOOL(hAPP(_1823724, hAPP(c_Code__Numeral_Oof__nat, 51564 ^ [_1823724, _1823726])))], (51566 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51564 ^ [_1823724, _1823726]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1823724, _1823726)))], (31200 ^ _779999) ^ [_1364623] : [class_Groups_Osgn__if(_1364623), -(c_Groups_Osgn__class_Osgn(_1364623, c_Groups_Ozero__class_Ozero(_1364623)) = c_Groups_Ozero__class_Ozero(_1364623))], (38517 ^ _779999) ^ [_1518768, _1518770, _1518772] : [c_Equiv__Relations_Oequiv(_1518768, _1518770, _1518772), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518768, _1518768), tc_HOL_Obool)), _1518772), hAPP(hAPP(c_Product__Type_OSigma(_1518768, _1518768), _1518770), hAPP(c_COMBK(tc_fun(_1518768, tc_HOL_Obool), _1518768), _1518770)))))], (25674 ^ _779999) ^ [_1261354, _1261356, _1261358] : [_1261356 = _1261358, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261354, tc_HOL_Obool)), _1261356) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261354, tc_HOL_Obool)), _1261358))], (6851 ^ _779999) ^ [_892291, _892293, _892295] : [hBOOL(hAPP(hAPP(c_member(_892291), _892293), hAPP(c_fequal, _892295))), -(_892293 = _892295)], (2562 ^ _779999) ^ [_817786, _817788, _817790, _817792] : [-(c_Divides_OposDivAlg(_817792, _817788) = c_Divides_OposDivAlg(_817790, _817786)), _817792 = _817790, _817788 = _817786], (34755 ^ _779999) ^ [_1430283, _1430285] : [class_Int_Onumber__ring(_1430283), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430283), hAPP(c_Int_Onumber__class_Onumber__of(_1430283), 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)))), _1430285))) = hAPP(c_Int_Onumber__class_Onumber__of(_1430283), c_Int_OMin))], (24282 ^ _779999) ^ [_1234802, _1234804] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1234802)), hAPP(c_Nat_OSuc, _1234804)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1234802), _1234804)))], (31789 ^ _779999) ^ [_1375992, _1375994, _1375996] : [class_Int_Onumber(_1375992), class_Orderings_Olinorder(_1375992), 31796 ^ _779999 : [(31803 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375992), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375996)), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375994)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375992), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375994)), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375996))))], (31797 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375992), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375994)), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375996))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375992), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375996)), hAPP(c_Int_Onumber__class_Onumber__of(_1375992), _1375994)))]]], (7219 ^ _779999) ^ [_899276, _899278, _899280, _899282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899276, tc_HOL_Obool)), _899278), _899280)), hBOOL(hAPP(hAPP(c_member(_899276), _899282), _899278)), -(hBOOL(hAPP(hAPP(c_member(_899276), _899282), _899280)))], (27168 ^ _779999) ^ [_1291404, _1291406] : [class_Rings_Odivision__ring(_1291404), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291404), _1291406), c_Groups_Oone__class_Oone(_1291404)) = _1291406)], (6101 ^ _779999) ^ [_877134, _877136, _877138, _877140] : [class_Lattices_Osemilattice__sup(_877134), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877134), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877134), _877136), _877138)), _877140) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877134), _877136), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_877134), _877138), _877140)))], (6483 ^ _779999) ^ [_884555, _884557, _884559] : [class_Lattices_Olattice(_884555), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884555), _884557), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_884555), _884559), _884557))))], (35982 ^ _779999) ^ [_1457614, _1457616] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457614), _1457616)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457614), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1457616)))], (20768 ^ _779999) ^ [_1157060, _1157062, _1157064, _1157066] : [class_Groups_Oordered__ab__group__add__abs(_1157060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157060), c_Groups_Ozero__class_Ozero(_1157060)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1157062, _1157060), hAPP(hAPP(c_COMBB(_1157060, _1157060, _1157062), c_Groups_Oabs__class_Oabs(_1157060)), _1157064)), _1157066))))], (27426 ^ _779999) ^ [_1295924, _1295926] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1295924), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1295926)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1295924), _1295926))], (42291 ^ _779999) ^ [_1611583, _1611585, _1611587, _1611589, _1611591, _1611593, _1611595] : [42293 ^ _779999 : [(42296 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1611591, 42292 ^ [_1611583, _1611585, _1611587, _1611589, _1611591, _1611593, _1611595]), _1611593), _1611595))], (42294 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611583), 42292 ^ [_1611583, _1611585, _1611587, _1611589, _1611591, _1611593, _1611595]), _1611589)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611583, tc_fun(_1611585, tc_fun(_1611587, tc_HOL_Obool))), _1611589), _1611591), _1611593), _1611595)))], (10940 ^ _779999) ^ [_969103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969103), _969103))], (4700 ^ _779999) ^ [_851537, _851539] : [_851539 = _851537, -(c_Lazy__Sequence_Osingle(_851539) = c_Lazy__Sequence_Osingle(_851537))], (1224 ^ _779999) ^ [_798407, _798409] : [-(class_Rings_Oring__no__zero__divisors(_798407)), _798409 = _798407, class_Rings_Oring__no__zero__divisors(_798409)], (34107 ^ _779999) ^ [_1417907] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417907))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1417907)))))], (33039 ^ _779999) ^ [_1399372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1399372) = _1399372)], (30669 ^ _779999) ^ [_1355003, _1355005, _1355007, _1355009] : [class_Divides_Osemiring__div(_1355003), -(c_Divides_Odiv__class_Omod(_1355003, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355003), _1355005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355003), _1355007), _1355009)), _1355009) = c_Divides_Odiv__class_Omod(_1355003, _1355005, _1355009))], (11192 ^ _779999) ^ [_973923, _973925, _973927] : [class_Lattices_Osemilattice__inf(_973923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973923), _973925), _973927)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973923), _973927), _973925) = _973925)], (45364 ^ _779999) ^ [_1687774, _1687776, _1687778, _1687780, _1687782] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1687774, _1687776)), _1687778), hAPP(hAPP(c_List_Ozip(_1687774, _1687776), _1687780), _1687782)) = hAPP(hAPP(c_List_Ozip(_1687774, _1687776), hAPP(hAPP(c_List_Odrop(_1687774), _1687778), _1687780)), hAPP(hAPP(c_List_Odrop(_1687776), _1687778), _1687782)))], (4482 ^ _779999) ^ [_848112, _848114, _848116, _848118, _848120, _848122, _848124, _848126] : [-(c_Lazy__Sequence_Oproduct(_848126, _848122, _848118, _848114) = c_Lazy__Sequence_Oproduct(_848124, _848120, _848116, _848112)), _848126 = _848124, _848122 = _848120, _848118 = _848116, _848114 = _848112], (932 ^ _779999) ^ [_794231, _794233, _794235, _794237] : [-(c_Predicate_Oreflp(_794235, _794231)), c_Predicate_Oreflp(_794237, _794233), _794237 = _794235, _794233 = _794231], (28940 ^ _779999) ^ [_1323501, _1323503, _1323505, _1323507] : [class_Fields_Olinordered__field(_1323501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323501), c_Groups_Ozero__class_Ozero(_1323501)), _1323503)), 28947 ^ _779999 : [(28954 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323501), _1323505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323501), _1323507), _1323503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323501), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323501), _1323505), _1323503)), _1323507)))], (28948 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323501), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323501), _1323505), _1323503)), _1323507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323501), _1323505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323501), _1323507), _1323503))))]]], (37337 ^ _779999) ^ [_1487833, _1487835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1487833), _1487835)), -(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), _1487833), _1487835)), c_Wellfounded_Oless__than)))], (16435 ^ _779999) ^ [_1076903, _1076905, _1076907] : [class_Rings_Olinordered__semiring__strict(_1076903), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076903), _1076905), c_Groups_Ozero__class_Ozero(_1076903))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076903), c_Groups_Ozero__class_Ozero(_1076903)), _1076907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076903), _1076905), _1076907)), c_Groups_Ozero__class_Ozero(_1076903))))], (44684 ^ _779999) ^ [_1671615, _1671617] : [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(_1671615)), _1671617))), _1671617 = c_List_Olist_ONil(_1671615)], (46269 ^ _779999) ^ [_1706911, _1706913, _1706915, _1706917, _1706919] : [46271 ^ _779999 : [(46274 ^ _779999) ^ [] : [hAPP(_1706915, 46270 ^ [_1706911, _1706913, _1706915, _1706917, _1706919]) = hAPP(_1706919, 46270 ^ [_1706911, _1706913, _1706915, _1706917, _1706919])], (46272 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706911), 46270 ^ [_1706911, _1706913, _1706915, _1706917, _1706919]), hAPP(c_List_Oset(_1706911), _1706917))))]], -(hAPP(hAPP(c_List_Omap(_1706911, _1706913), _1706915), _1706917) = hAPP(hAPP(c_List_Omap(_1706911, _1706913), _1706919), _1706917))], (17009 ^ _779999) ^ [_1087636, _1087638, _1087640, _1087642, _1087644] : [class_Rings_Olinordered__semiring__strict(_1087636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087636), _1087638), _1087640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087636), _1087642), _1087644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087636), c_Groups_Ozero__class_Ozero(_1087636)), _1087638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087636), c_Groups_Ozero__class_Ozero(_1087636)), _1087642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087636), _1087638), _1087642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087636), _1087640), _1087644))))], (51634 ^ _779999) ^ [_1825146, _1825148, _1825150, _1825152, _1825154] : [c_Fun_Obij__betw(_1825146, _1825148, _1825150, c_Orderings_Otop__class_Otop(tc_fun(_1825146, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1825148, tc_HOL_Obool))), c_Fun_Obij__betw(_1825152, _1825146, _1825154, c_Orderings_Otop__class_Otop(tc_fun(_1825152, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1825146, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1825152, _1825148, c_Orderings_Otop__class_Otop(tc_fun(_1825152, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1825146, _1825148, _1825152, _1825150), _1825154)) = hAPP(c_Fun_Ocomp(_1825146, _1825152, _1825148, c_Hilbert__Choice_Oinv__into(_1825152, _1825146, c_Orderings_Otop__class_Otop(tc_fun(_1825152, tc_HOL_Obool)), _1825154)), c_Hilbert__Choice_Oinv__into(_1825146, _1825148, c_Orderings_Otop__class_Otop(tc_fun(_1825146, tc_HOL_Obool)), _1825150)))], (39583 ^ _779999) ^ [_1545962, _1545964, _1545966, _1545968, _1545970, _1545972, _1545974] : [c_Fun_Oinj__on(_1545962, _1545964, _1545966, hAPP(c_Set_Oimage(_1545968, _1545962, _1545970), _1545972)), c_Fun_Oinj__on(_1545968, _1545962, _1545970, _1545972), hBOOL(hAPP(hAPP(c_member(_1545964), _1545974), hAPP(c_Set_Oimage(_1545962, _1545964, _1545966), hAPP(c_Set_Oimage(_1545968, _1545962, _1545970), _1545972)))), -(hAPP(c_Fun_Othe__inv__into(_1545968, _1545964, _1545972, hAPP(c_Fun_Ocomp(_1545962, _1545964, _1545968, _1545966), _1545970)), _1545974) = hAPP(hAPP(c_Fun_Ocomp(_1545962, _1545968, _1545964, c_Fun_Othe__inv__into(_1545968, _1545962, _1545972, _1545970)), c_Fun_Othe__inv__into(_1545962, _1545964, hAPP(c_Set_Oimage(_1545968, _1545962, _1545970), _1545972), _1545966)), _1545974))], (47637 ^ _779999) ^ [_1739524, _1739526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1739524), _1739526)), -(c_List_Oupt(_1739524, hAPP(c_Nat_OSuc, _1739526)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1739524, _1739526)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1739526), c_List_Olist_ONil(tc_Nat_Onat))))], (46251 ^ _779999) ^ [_1706440, _1706442, _1706444, _1706446, _1706448, _1706450, _1706452] : [hAPP(hAPP(c_List_Omap(_1706440, _1706442), _1706444), _1706446) = hAPP(hAPP(c_List_Omap(_1706448, _1706442), _1706450), _1706452), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706440)), _1706446) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706448)), _1706452))], (2438 ^ _779999) ^ [_815932, _815934, _815936, _815938, _815940, _815942, _815944, _815946] : [-(c_Nitpick_Oprod(_815946, _815942, _815938, _815934) = c_Nitpick_Oprod(_815944, _815940, _815936, _815932)), _815946 = _815944, _815942 = _815940, _815938 = _815936, _815934 = _815932], (8425 ^ _779999) ^ [_924062, _924064, _924066] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_924062, tc_HOL_Obool)), _924066), hAPP(c_Set_OPow(_924062), _924064))), -(hBOOL(hAPP(c_Predicate_OPowp(_924062, hAPP(hAPP(c_COMBC(_924062, tc_fun(_924062, tc_HOL_Obool), tc_HOL_Obool), c_member(_924062)), _924064)), _924066)))], (19227 ^ _779999) ^ [_1130621, _1130623, _1130625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130621)), _1130621 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1130621), _1130625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130623), _1130621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1130625)))], (23137 ^ _779999) ^ [_1211904, _1211906, _1211908] : [class_Orderings_Olinorder(_1211904), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211904), _1211906), _1211908)), _1211906)))], (13534 ^ _779999) ^ [_1021210, _1021212, _1021214] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1021210), _1021212)), _1021214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1021210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021212), _1021214)))], (50052 ^ _779999) ^ [_1790363, _1790365, _1790367] : [_1790363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1790365), c_List_Oreplicate(_1790365, _1790363, _1790367)) = c_Orderings_Obot__class_Obot(tc_fun(_1790365, tc_HOL_Obool)))], (49430 ^ _779999) ^ [_1776992, _1776994, _1776996] : [hBOOL(hAPP(hAPP(c_member(_1776992), _1776994), hAPP(c_List_Oset(_1776992), _1776996))), 49435 ^ _779999 : [(49438 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1776992), _1776994), hAPP(c_List_Oset(_1776992), 49434 ^ [_1776992, _1776994, _1776996])))], (49436 ^ _779999) ^ [] : [-(_1776996 = hAPP(hAPP(c_List_Oappend(_1776992), 49433 ^ [_1776992, _1776994, _1776996]), hAPP(hAPP(c_List_Olist_OCons(_1776992), _1776994), 49434 ^ [_1776992, _1776994, _1776996])))]]], (23143 ^ _779999) ^ [_1212011, _1212013, _1212015] : [class_Orderings_Olinorder(_1212011), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212011), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212011), _1212013), _1212015)), _1212015)))], (476 ^ _779999) ^ [_787305, _787307, _787309, _787311, _787313, _787315] : [-(c_Relation_Ototal__on(_787313, _787309, _787305)), c_Relation_Ototal__on(_787315, _787311, _787307), _787315 = _787313, _787311 = _787309, _787307 = _787305], (35091 ^ _779999) ^ [_1435349] : [-(c_Int_Oint__ge__less__than(_1435349) = 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), _1435349)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38949 ^ _779999) ^ [_1531480, _1531482] : [-(c_Relation_Orefl__on(_1531480, _1531482, c_Relation_OId__on(_1531480, _1531482)))], (46316 ^ _779999) ^ [_1708111, _1708113, _1708115, _1708117, _1708119, _1708121] : [-(hAPP(hAPP(c_List_Ozip(_1708111, _1708113), hAPP(hAPP(c_List_Omap(_1708115, _1708111), _1708117), _1708119)), _1708121) = hAPP(hAPP(c_List_Omap(tc_prod(_1708115, _1708113), tc_prod(_1708111, _1708113)), hAPP(c_Product__Type_Oprod_Oprod__case(_1708115, _1708113, tc_prod(_1708111, _1708113)), hAPP(hAPP(c_COMBB(_1708111, tc_fun(_1708113, tc_prod(_1708111, _1708113)), _1708115), c_Product__Type_OPair(_1708111, _1708113)), _1708117))), hAPP(hAPP(c_List_Ozip(_1708115, _1708113), _1708119), _1708121)))], (38634 ^ _779999) ^ [_1521887, _1521889, _1521891, _1521893] : [-(hAPP(c_Set_OCollect(tc_prod(_1521887, _1521889)), hAPP(c_Product__Type_Oprod_Oprod__case(_1521887, _1521889, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1521887, tc_fun(_1521889, tc_HOL_Obool), tc_fun(_1521889, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1521889, tc_HOL_Obool), tc_fun(_1521889, tc_HOL_Obool)), _1521887), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521889)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521887), c_fconj), _1521891))), _1521893))) = hAPP(hAPP(c_Product__Type_OSigma(_1521887, _1521889), hAPP(c_Set_OCollect(_1521887), _1521891)), hAPP(c_COMBK(tc_fun(_1521889, tc_HOL_Obool), _1521887), hAPP(c_Set_OCollect(_1521889), _1521893))))], (50785 ^ _779999) ^ [_1808013, _1808015] : [c_Predicate_Oreflp(_1808013, _1808015), c_Predicate_Osymp(_1808013, _1808015), c_Predicate_Otransp(_1808013, _1808015), -(c_Equiv__Relations_Oequivp(_1808013, _1808015))], (51700 ^ _779999) ^ [_1826533, _1826535, _1826537, _1826539, _1826541] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1826533, _1826535, tc_HOL_Obool, _1826537), _1826539), _1826541)), -(hBOOL(hAPP(_1826537, hAPP(hAPP(c_Product__Type_OPair(_1826533, _1826535), _1826539), _1826541))))], (6771 ^ _779999) ^ [_890843, _890845, _890847, _890849] : [6772 ^ _779999 : [(6775 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890843), _890845), _890849))], (6773 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890843), _890845), _890847))]], -(hBOOL(hAPP(hAPP(c_member(_890843), _890845), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890843, tc_HOL_Obool)), _890849), _890847))))], (6797 ^ _779999) ^ [_891401, _891403] : [hBOOL(hAPP(hAPP(c_member(_891401), _891403), c_Orderings_Obot__class_Obot(tc_fun(_891401, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_891401, tc_HOL_Obool)), _891403)))], (44702 ^ _779999) ^ [_1671959, _1671961] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671959), tc_List_Olist(_1671959))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671959), tc_List_Olist(_1671959)), c_List_Olist_ONil(_1671959)), c_List_Olist_ONil(_1671959))), c_List_Olistrel(_1671959, _1671961))))], (48490 ^ _779999) ^ [_1755822, _1755824, _1755826] : [-(hAPP(c_List_Orev(_1755822), hAPP(hAPP(c_List_Odrop(_1755822), _1755824), _1755826)) = hAPP(hAPP(c_List_Otake(_1755822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755822)), _1755826)), _1755824)), hAPP(c_List_Orev(_1755822), _1755826)))], (41865 ^ _779999) ^ [_1599760, _1599762, _1599764, _1599766, _1599768] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599760, tc_fun(_1599762, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1599760), _1599764), _1599766)), _1599768) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599762, tc_HOL_Obool)), hAPP(_1599768, _1599764)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599760, tc_fun(_1599762, tc_HOL_Obool)), _1599766), _1599768)))], (47082 ^ _779999) ^ [_1725590, _1725592, _1725594, _1725596, _1725598] : [-(c_List_Olist__all2(_1725590, _1725592, _1725594, _1725596, _1725598)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725590)), _1725596) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725592)), _1725598), 47088 ^ _779999 : [(47091 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1725594, hAPP(hAPP(c_List_Onth(_1725590), _1725596), 47087 ^ [_1725590, _1725592, _1725594, _1725596, _1725598])), hAPP(hAPP(c_List_Onth(_1725592), _1725598), 47087 ^ [_1725590, _1725592, _1725594, _1725596, _1725598])))], (47089 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47087 ^ [_1725590, _1725592, _1725594, _1725596, _1725598]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725590)), _1725596))))]]], (16893 ^ _779999) ^ [_1085440, _1085442, _1085444] : [class_Orderings_Oorder(_1085440), _1085442 = _1085444, -(c_SetInterval_Oord__class_OatLeastAtMost(_1085440, _1085442, _1085444) = hAPP(hAPP(c_Set_Oinsert(_1085440), _1085442), c_Orderings_Obot__class_Obot(tc_fun(_1085440, tc_HOL_Obool))))], (27662 ^ _779999) ^ [_1300119] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1300119) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15243 ^ _779999) ^ [_1053889, _1053891, _1053893, _1053895] : [15244 ^ _779999 : [(15247 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053893), _1053895)))], (15245 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1053889), _1053891)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1053889, _1053893)), c_Sum__Type_OPlus(_1053889, _1053893, _1053891, _1053895)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17137 ^ _779999) ^ [_1090069, _1090071, _1090073] : [class_Rings_Olinordered__ring(_1090069), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090069), c_Groups_Ozero__class_Ozero(_1090069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090069), _1090071), _1090071)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090069), _1090073), _1090073)))))], (45440 ^ _779999) ^ [_1689583, _1689585, _1689587, _1689589] : [-(hAPP(hAPP(c_List_Oappend(_1689583), _1689585), _1689587) = _1689589), _1689585 = hAPP(hAPP(c_List_Otake(_1689583), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689583)), _1689585)), _1689589), _1689587 = hAPP(hAPP(c_List_Odrop(_1689583), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689583)), _1689585)), _1689589)], (11294 ^ _779999) ^ [_975741, _975743, _975745] : [class_Lattices_Olattice(_975741), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975741), _975743), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975741), _975743), _975745)) = _975743)], (51674 ^ _779999) ^ [_1826007, _1826009, _1826011, _1826013, _1826015, _1826017, _1826019, _1826021] : [c_Fun_Obij__betw(_1826007, _1826009, _1826011, _1826013, _1826015), 51677 ^ _779999 : [(51684 ^ _779999) ^ [] : [c_Fun_Obij__betw(_1826007, _1826017, hAPP(c_Fun_Ocomp(_1826009, _1826017, _1826007, _1826019), _1826011), _1826013, _1826021), -(c_Fun_Obij__betw(_1826009, _1826017, _1826019, _1826015, _1826021))], (51678 ^ _779999) ^ [] : [c_Fun_Obij__betw(_1826009, _1826017, _1826019, _1826015, _1826021), -(c_Fun_Obij__betw(_1826007, _1826017, hAPP(c_Fun_Ocomp(_1826009, _1826017, _1826007, _1826019), _1826011), _1826013, _1826021))]]], (14241 ^ _779999) ^ [_1034148, _1034150, _1034152, _1034154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1034148), hAPP(c_Set_Oimage(_1034150, _1034148, _1034152), _1034154))), hAPP(c_Finite__Set_Ocard(_1034150), _1034154))), c_Fun_Oinj__on(_1034150, _1034148, _1034152, _1034154)], (51926 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (34599 ^ _779999) ^ [_1426761, _1426763, _1426765] : [class_Rings_Ocomm__semiring__1(_1426761), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426761), _1426763), 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)))), _1426765))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426761), _1426763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426761), hAPP(hAPP(c_Power_Opower__class_Opower(_1426761), _1426763), _1426765)), hAPP(hAPP(c_Power_Opower__class_Opower(_1426761), _1426763), _1426765))))], (14515 ^ _779999) ^ [_1039821, _1039823, _1039825, _1039827, _1039829] : [class_Groups_Ocomm__monoid__add(_1039821), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039823), _1039825)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039823), _1039827)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1039823, tc_HOL_Obool)), _1039825), _1039827) = c_Orderings_Obot__class_Obot(tc_fun(_1039823, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039823, _1039821), _1039829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1039823, tc_HOL_Obool)), _1039825), _1039827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039821), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039823, _1039821), _1039829), _1039825)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039823, _1039821), _1039829), _1039827)))], (15883 ^ _779999) ^ [_1066403, _1066405] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066403), _1066405) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1066403 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1066405 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (8116 ^ _779999) ^ [_917217, _917219, _917221, _917223, _917225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917217, tc_HOL_Obool)), _917219), _917221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917217, tc_HOL_Obool)), _917223), _917225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917217, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917217, tc_HOL_Obool)), _917219), _917225)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917217, tc_HOL_Obool)), _917221), _917223))))], (26340 ^ _779999) ^ [_1273577, _1273579, _1273581] : [class_Groups_Oab__group__add(_1273577), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273577), _1273579), _1273581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273577), _1273579), hAPP(c_Groups_Ouminus__class_Ouminus(_1273577), _1273581)))], (36549 ^ _779999) ^ [_1468503, _1468505, _1468507, _1468509, _1468511] : [-(c_Product__Type_Oprod_Oprod__size(_1468503, _1468505, _1468507, _1468509, _1468511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1468507, hAPP(c_Product__Type_Ofst(_1468503, _1468505), _1468511))), hAPP(_1468509, hAPP(c_Product__Type_Osnd(_1468503, _1468505), _1468511)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14145 ^ _779999) ^ [_1032410, _1032412, _1032414] : [class_Groups_Oordered__comm__monoid__add(_1032410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032410), c_Groups_Ozero__class_Ozero(_1032410)), _1032412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032410), c_Groups_Ozero__class_Ozero(_1032410)), _1032414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032410), c_Groups_Ozero__class_Ozero(_1032410)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032410), _1032412), _1032414))))], (44398 ^ _779999) ^ [_1666420, _1666422] : [class_Groups_Ocomm__monoid__add(_1666420), hBOOL(hAPP(c_List_Odistinct(_1666420), _1666422)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666420), _1666422) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1666420, _1666420), c_COMBI(_1666420)), hAPP(c_List_Oset(_1666420), _1666422)))], (34767 ^ _779999) ^ [_1430526] : [c_Int_OMin = c_Int_OBit0(_1430526)], (23367 ^ _779999) ^ [_1215862, _1215864, _1215866, _1215868] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1215862), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215862), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215862), _1215864), _1215866)), _1215868) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215862), _1215864), _1215868)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215862), _1215866), _1215868)))], (14225 ^ _779999) ^ [_1033864, _1033866, _1033868, _1033870] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1033864), _1033866)), 14228 ^ _779999 : [(14235 ^ _779999) ^ [] : [hAPP(c_Finite__Set_Ocard(_1033868), hAPP(c_Set_Oimage(_1033864, _1033868, _1033870), _1033866)) = hAPP(c_Finite__Set_Ocard(_1033864), _1033866), -(c_Fun_Oinj__on(_1033864, _1033868, _1033870, _1033866))], (14229 ^ _779999) ^ [] : [c_Fun_Oinj__on(_1033864, _1033868, _1033870, _1033866), -(hAPP(c_Finite__Set_Ocard(_1033868), hAPP(c_Set_Oimage(_1033864, _1033868, _1033870), _1033866)) = hAPP(c_Finite__Set_Ocard(_1033864), _1033866))]]], (43459 ^ _779999) ^ [_1641863, _1641865, _1641867, _1641869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641863), tc_List_Olist(_1641863))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641863), tc_List_Olist(_1641863)), _1641867), _1641869)), c_List_Olistrel(_1641863, _1641865))), -(c_List_Olistrelp(_1641863, hAPP(hAPP(c_COMBC(_1641863, tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_fun(_1641863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1641863, tc_fun(tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_fun(_1641863, tc_HOL_Obool)), _1641863), c_COMBC(_1641863, tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1641863, tc_prod(_1641863, _1641863)), tc_fun(_1641863, tc_fun(tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_HOL_Obool)), _1641863), hAPP(c_COMBB(tc_prod(_1641863, _1641863), tc_fun(tc_fun(tc_prod(_1641863, _1641863), tc_HOL_Obool), tc_HOL_Obool), _1641863), c_member(tc_prod(_1641863, _1641863)))), c_Product__Type_OPair(_1641863, _1641863)))), _1641865), _1641867, _1641869))], (7440 ^ _779999) ^ [_903834, _903836, _903838, _903840, _903842] : [c_Orderings_Oorder__class_Omono(tc_fun(_903834, tc_HOL_Obool), tc_fun(_903836, tc_HOL_Obool), _903838), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903836, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903836, tc_HOL_Obool)), hAPP(_903838, _903840)), hAPP(_903838, _903842))), hAPP(_903838, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903834, tc_HOL_Obool)), _903840), _903842)))))], (47260 ^ _779999) ^ [_1729275, _1729277, _1729279] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1729275), tc_List_Olist(_1729275), c_List_Oappend(_1729275), _1729277), _1729279) = hAPP(hAPP(c_List_Oappend(_1729275), _1729277), c_List_Oconcat(_1729275, _1729279)))], (38277 ^ _779999) ^ [_1511604] : [-(c_Nitpick_Oone__frac(_1511604) = c_Nitpick_OAbs__Frac(_1511604, 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))))], (51450 ^ _779999) ^ [_1820922, _1820924, _1820926, _1820928, _1820930] : [c_Fun_Oinj__on(_1820922, _1820924, _1820926, _1820928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1820922, tc_HOL_Obool)), _1820930), _1820928)), -(hAPP(c_Set_Oimage(_1820924, _1820922, c_Hilbert__Choice_Oinv__into(_1820922, _1820924, _1820928, _1820926)), hAPP(c_Set_Oimage(_1820922, _1820924, _1820926), _1820930)) = _1820930)], (50718 ^ _779999) ^ [_1806472, _1806474, _1806476, _1806478] : [class_Complete__Lattice_Ocomplete__lattice(_1806472), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1806474, _1806472), _1806476), _1806478) = c_Complete__Lattice_OInf__class_OInf(_1806472, hAPP(c_Set_OCollect(_1806472), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool), tc_HOL_Obool, _1806472), c_HOL_OEx(tc_fun(_1806474, _1806472))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool), tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool), _1806472), hAPP(c_COMBS(tc_fun(_1806474, _1806472), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1806474, _1806472)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1806474, _1806472), tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1806474, _1806472))), _1806476)))), hAPP(hAPP(c_COMBC(_1806472, tc_fun(tc_fun(_1806474, _1806472), _1806472), tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806472, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1806474, _1806472), _1806472), tc_fun(tc_fun(_1806474, _1806472), tc_HOL_Obool)), _1806472), c_COMBB(_1806472, tc_HOL_Obool, tc_fun(_1806474, _1806472))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1806474, _1806472), _1806474, _1806472), c_COMBI(tc_fun(_1806474, _1806472))), _1806478)))))))], (20357 ^ _779999) ^ [_1150455, _1150457] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1150455), _1150457) = 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)), _1150455)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1150457))))], (16755 ^ _779999) ^ [_1083148, _1083150] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1083148), hAPP(c_Nat_OSuc, _1083150)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1083148), _1083150)))], (36392 ^ _779999) ^ [_1465227, _1465229, _1465231, _1465233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465227, _1465227)), hAPP(hAPP(c_Product__Type_OPair(_1465227, _1465227), _1465229), _1465231)), hAPP(c_Wellfounded_Omeasure(_1465227), _1465233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1465233, _1465229)), hAPP(_1465233, _1465231))))], (19037 ^ _779999) ^ [_1127057, _1127059, _1127061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127057), _1127059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127061), _1127057)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127061), _1127059))))], (19381 ^ _779999) ^ [_1133415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1133415)), -(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)), _1133415))))], (8474 ^ _779999) ^ [_925038, _925040, _925042] : [class_Groups_Ogroup__add(_925038), 8477 ^ _779999 : [(8484 ^ _779999) ^ [] : [_925040 = _925042, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925038), _925040), _925042) = c_Groups_Ozero__class_Ozero(_925038))], (8478 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925038), _925040), _925042) = c_Groups_Ozero__class_Ozero(_925038), -(_925040 = _925042)]]], (40401 ^ _779999) ^ [_1566331, _1566333] : [-(hAPP(c_Relation_ORange(_1566331, _1566331), c_Transitive__Closure_Ortrancl(_1566331, _1566333)) = c_Orderings_Otop__class_Otop(tc_fun(_1566331, tc_HOL_Obool)))], (47506 ^ _779999) ^ [_1735265, _1735267, _1735269] : [-(c_List_Oremdups(_1735265, hAPP(c_List_Ofilter(_1735265, _1735267), _1735269)) = hAPP(c_List_Ofilter(_1735265, _1735267), c_List_Oremdups(_1735265, _1735269)))], (39022 ^ _779999) ^ [_1532803, _1532805, _1532807, _1532809] : [c_Relation_Orefl__on(_1532803, _1532805, _1532807), hBOOL(hAPP(hAPP(c_member(_1532803), _1532809), _1532805)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532803, _1532803)), hAPP(hAPP(c_Product__Type_OPair(_1532803, _1532803), _1532809), _1532809)), _1532807)))], (10107 ^ _779999) ^ [_954339, _954341, _954343, _954345, _954347, _954349] : [c_Fun_Oinj__on(_954339, _954341, _954343, _954345), hAPP(_954343, _954347) = hAPP(_954343, _954349), hBOOL(hAPP(hAPP(c_member(_954339), _954347), _954345)), hBOOL(hAPP(hAPP(c_member(_954339), _954349), _954345)), -(_954347 = _954349)], (4962 ^ _779999) ^ [_855786, _855788] : [_855788 = _855786, -(c_Nat_Osize__class_Osize(_855788) = c_Nat_Osize__class_Osize(_855786))], (47687 ^ _779999) ^ [_1740389, _1740391] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1740389), _1740391)) = c_List_Oupt(_1740389, _1740391))], (10167 ^ _779999) ^ [_955313] : [-(_955313 = 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)), _955313)))], (25233 ^ _779999) ^ [_1253754, _1253756] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1253754)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1253756)), hAPP(c_Int_Onat, _1253754)) = hAPP(c_Int_Onat, _1253756))], (15511 ^ _779999) ^ [_1059399, _1059401] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1059399, _1059401))))], (36140 ^ _779999) ^ [_1460501, _1460503] : [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), _1460501), _1460503))), 36143 ^ _779999 : [(36152 ^ _779999) ^ [] : [-(c_Divides_OposDivAlg(_1460501, _1460503) = hAPP(c_Divides_Oadjust(_1460503), c_Divides_OposDivAlg(_1460501, 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)))), _1460503)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460501), _1460503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1460503), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36144 ^ _779999) ^ [] : [36145 ^ _779999 : [(36148 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1460503), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36146 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460501), _1460503))]], -(c_Divides_OposDivAlg(_1460501, _1460503) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460501))]]], (51210 ^ _779999) ^ [_1815578, _1815580, _1815582, _1815584] : [c_Equiv__Relations_Opart__equivp(_1815578, _1815580), hBOOL(hAPP(hAPP(_1815580, _1815582), _1815584)), -(hBOOL(hAPP(hAPP(_1815580, _1815584), _1815582)))], (15327 ^ _779999) ^ [_1055378] : [class_Rings_Oring__1(_1055378), -(hBOOL(hAPP(hAPP(c_member(_1055378), c_Groups_Oone__class_Oone(_1055378)), c_Int_Oring__1__class_OInts(_1055378))))], (6791 ^ _779999) ^ [_891290, _891292] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_891290, tc_HOL_Obool)), _891292)), -(hBOOL(hAPP(hAPP(c_member(_891290), _891292), c_Orderings_Obot__class_Obot(tc_fun(_891290, tc_HOL_Obool)))))], (14247 ^ _779999) ^ [_1034278, _1034280, _1034282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034278), _1034280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1034278, tc_HOL_Obool)), _1034282), _1034280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1034278), _1034282)), hAPP(c_Finite__Set_Ocard(_1034278), _1034280))))], (32147 ^ _779999) ^ [_1382654, _1382656, _1382658] : [class_Int_Onumber__ring(_1382654), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382654), hAPP(c_Groups_Ouminus__class_Ouminus(_1382654), hAPP(c_Int_Onumber__class_Onumber__of(_1382654), _1382656))), _1382658) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382654), hAPP(c_Int_Onumber__class_Onumber__of(_1382654), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1382656))), _1382658))], (37935 ^ _779999) ^ [_1503985, _1503987, _1503989] : [c_Wellfounded_Owf(_1503985, _1503987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1503985, _1503985), tc_HOL_Obool)), _1503989), _1503987)), -(c_Wellfounded_Owf(_1503985, _1503989))], (48824 ^ _779999) ^ [_1762963, _1762965, _1762967, _1762969, _1762971] : [class_Groups_Omonoid__add(_1762963), 48830 ^ _779999 : [(48835 ^ _779999) ^ [] : [hAPP(_1762971, 48829 ^ [_1762963, _1762965, _1762967, _1762969, _1762971]) = c_Groups_Ozero__class_Ozero(_1762963)], (48833 ^ _779999) ^ [] : [hBOOL(hAPP(_1762969, 48829 ^ [_1762963, _1762965, _1762967, _1762969, _1762971]))], (48831 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762965), 48829 ^ [_1762963, _1762965, _1762967, _1762969, _1762971]), hAPP(c_List_Oset(_1762965), _1762967))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1762963), hAPP(hAPP(c_List_Omap(_1762965, _1762963), _1762971), hAPP(c_List_Ofilter(_1762965, _1762969), _1762967))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1762963), hAPP(hAPP(c_List_Omap(_1762965, _1762963), _1762971), _1762967)))], (18863 ^ _779999) ^ [_1124249] : [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)), _1124249)), _1124249)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124249), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48422 ^ _779999) ^ [_1754441, _1754443, _1754445] : [_1754443 = hAPP(c_List_Orev(_1754441), _1754445), -(hAPP(c_List_Orev(_1754441), _1754443) = _1754445)], (26618 ^ _779999) ^ [_1278929, _1278931, _1278933] : [class_Groups_Oordered__ab__group__add(_1278929), -(hAPP(c_Set_Oimage(_1278929, _1278929, c_Groups_Ouminus__class_Ouminus(_1278929)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1278929, _1278931, _1278933)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1278929, hAPP(c_Groups_Ouminus__class_Ouminus(_1278929), _1278933), hAPP(c_Groups_Ouminus__class_Ouminus(_1278929), _1278931)))], (38351 ^ _779999) ^ [_1513590, _1513592, _1513594] : [_1513594 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513590, _1513592), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1513590, _1513592), _1513594) = c_Orderings_Obot__class_Obot(tc_fun(_1513590, tc_HOL_Obool)))], (13530 ^ _779999) ^ [_1021108, _1021110, _1021112] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021108), _1021110)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021112), _1021110)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1021108), _1021112))], (8247 ^ _779999) ^ [_919981, _919983, _919985, _919987] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_919981, _919983)), _919985), _919987))), 8248 ^ _779999 : [(8255 ^ _779999) ^ [] : [hBOOL(hAPP(_919981, _919985)), 8258 ^ _779999 : [(8259 ^ _779999) ^ [_920200] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_919983), _919985), _920200)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_919981, _919983)), _920200), _919987))]]], (8249 ^ _779999) ^ [] : [_919987 = _919985, -(hBOOL(hAPP(_919981, _919985)))]]], (13483 ^ _779999) ^ [_1020193, _1020195, _1020197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020193), _1020195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020193), _1020197)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1020195), _1020197))))], (39411 ^ _779999) ^ [_1542281, _1542283] : [39412 ^ _779999 : [(39413 ^ _779999) ^ [_1542327] : [hBOOL(hAPP(_1542281, _1542327))]], -(hBOOL(hAPP(_1542281, c_Hilbert__Choice_OEps(_1542283, _1542281))))], (38275 ^ _779999) ^ [_1511522, _1511524, _1511526, _1511528] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1511522, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1511524, _1511522), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1511524, _1511522), tc_HOL_Obool)), _1511526), _1511528))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511522, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1511524, _1511522), _1511526)), hAPP(c_Relation_ORange(_1511524, _1511522), _1511528)))))], (38363 ^ _779999) ^ [_1513860, _1513862, _1513864, _1513866] : [-(hAPP(c_Relation_ODomain(_1513860, _1513862), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1513860, _1513862), tc_HOL_Obool)), _1513864), _1513866)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1513860, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1513860, _1513862), _1513864)), hAPP(c_Relation_ODomain(_1513860, _1513862), _1513866)))], (18951 ^ _779999) ^ [_1125776, _1125778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125776), _1125778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125776), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1125778), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (27376 ^ _779999) ^ [_1294985, _1294987, _1294989] : [class_Rings_Ocomm__semiring__1(_1294985), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1294985), _1294987), hAPP(c_Nat_OSuc, _1294989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294985), _1294987), hAPP(hAPP(c_Power_Opower__class_Opower(_1294985), _1294987), _1294989)))], (35602 ^ _779999) ^ [_1450419, _1450421, _1450423, _1450425, _1450427, _1450429] : [hBOOL(hAPP(hAPP(_1450419, _1450421), _1450423)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450425, tc_fun(_1450427, tc_HOL_Obool))), _1450419), _1450429), _1450421), _1450423)))], (7627 ^ _779999) ^ [_908175] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _908175), _908175)))], (12906 ^ _779999) ^ [_1008898, _1008900, _1008902, _1008904, _1008906] : [c_Finite__Set_Ofolding__one__idem(_1008898, _1008900, _1008902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008898), _1008904)), hBOOL(hAPP(hAPP(c_member(_1008898), _1008906), _1008904)), -(hAPP(hAPP(_1008900, _1008906), hAPP(_1008902, _1008904)) = hAPP(_1008902, _1008904))], (36060 ^ _779999) ^ [_1458933, _1458935, _1458937, _1458939, _1458941] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1458933, _1458935), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1458937), _1458939))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1458935)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1458941), _1458933), _1458935), 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), _1458941), _1458937)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1458941), _1458939)), _1458935))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1458941), _1458939), _1458935)))))], (44414 ^ _779999) ^ [_1666843, _1666845] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1666843), _1666845))), -(c_Nitpick_Ocard_H(_1666843, _1666845) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52210 ^ _779999) ^ [_1832634, _1832636] : [-(class_Finite__Set_Ofinite(tc_prod(_1832634, _1832636))), class_Finite__Set_Ofinite(_1832634), class_Finite__Set_Ofinite(_1832636)], (27932 ^ _779999) ^ [_1305101, _1305103, _1305105, _1305107] : [class_Rings_Olinordered__semidom(_1305101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305101), hAPP(hAPP(c_Power_Opower__class_Opower(_1305101), _1305103), hAPP(c_Nat_OSuc, _1305105))), hAPP(hAPP(c_Power_Opower__class_Opower(_1305101), _1305107), hAPP(c_Nat_OSuc, _1305105)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305101), c_Groups_Ozero__class_Ozero(_1305101)), _1305107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305101), _1305103), _1305107)))], (2426 ^ _779999) ^ [_815762, _815764] : [_815764 = _815762, -(c_Int_Opred(_815764) = c_Int_Opred(_815762))], (2706 ^ _779999) ^ [_820078, _820080, _820082, _820084, _820086, _820088] : [-(c_Wellfounded_Omlex__prod(_820088, _820084, _820080) = c_Wellfounded_Omlex__prod(_820086, _820082, _820078)), _820088 = _820086, _820084 = _820082, _820080 = _820078], (8391 ^ _779999) ^ [_923367, _923369, _923371] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_923367, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_923367, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_923367), _923369)), hAPP(c_Set_OPow(_923367), _923371))), hAPP(c_Set_OPow(_923367), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923367, tc_HOL_Obool)), _923369), _923371)))))], (23469 ^ _779999) ^ [_1218138, _1218140, _1218142, _1218144] : [-(hAPP(c_Set_Ovimage(_1218138, _1218140, _1218142), _1218144) = hAPP(c_Set_OCollect(_1218138), hAPP(hAPP(c_COMBC(_1218138, tc_fun(_1218140, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1218140, tc_fun(tc_fun(_1218140, tc_HOL_Obool), tc_HOL_Obool), _1218138), c_member(_1218140)), _1218142)), _1218144)))], (44640 ^ _779999) ^ [_1670867, _1670869, _1670871] : [-(_1670867 = c_List_Olist_ONil(_1670869)), -(c_List_Obutlast(_1670869, hAPP(hAPP(c_List_Olist_OCons(_1670869), _1670871), _1670867)) = hAPP(hAPP(c_List_Olist_OCons(_1670869), _1670871), c_List_Obutlast(_1670869, _1670867)))], (5620 ^ _779999) ^ [_866029, _866031, _866033, _866035] : [-(tc_Nitpick_Opair__box(_866035, _866031) = tc_Nitpick_Opair__box(_866033, _866029)), _866035 = _866033, _866031 = _866029], (1884 ^ _779999) ^ [_806657, _806659] : [-(class_Orderings_Oorder(_806657)), _806659 = _806657, class_Orderings_Oorder(_806659)], (10030 ^ _779999) ^ [_953053, _953055] : [class_Enum_Oenum(_953053), 10033 ^ _779999 : [(10040 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_953053), _953055)), -(hBOOL(hAPP(_953055, 10043 ^ [_953053, _953055])))], (10034 ^ _779999) ^ [] : [10035 ^ _779999 : [(10036 ^ _779999) ^ [_953155] : [hBOOL(hAPP(_953055, _953155))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_953053), _953055)))]]], (49948 ^ _779999) ^ [_1788587, _1788589, _1788591, _1788593, _1788595] : [c_List_Oreplicate(_1788587, _1788589, _1788591) = c_List_Oreplicate(_1788587, _1788593, _1788595), 49951 ^ _779999 : [(49954 ^ _779999) ^ [] : [-(_1788589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1788591 = _1788595)], (49952 ^ _779999) ^ [] : [-(_1788589 = _1788593)]]], (9888 ^ _779999) ^ [_949981, _949983, _949985, _949987, _949989] : [c_Fun_Oinj__on(_949981, _949983, _949985, hAPP(hAPP(c_Set_Oinsert(_949981), _949987), _949989)), 9891 ^ _779999 : [(9894 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_949983), hAPP(_949985, _949987)), hAPP(c_Set_Oimage(_949981, _949983, _949985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949981, tc_HOL_Obool)), _949989), hAPP(hAPP(c_Set_Oinsert(_949981), _949987), c_Orderings_Obot__class_Obot(tc_fun(_949981, tc_HOL_Obool)))))))], (9892 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_949981, _949983, _949985, _949989))]]], (40275 ^ _779999) ^ [_1563222, _1563224, _1563226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563222, _1563222)), _1563224), _1563226)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563222, _1563222)), _1563224), c_Transitive__Closure_Ortrancl(_1563222, _1563226))))], (46660 ^ _779999) ^ [_1716054, _1716056] : [_1716054 = _1716056, -(hAPP(c_Code__Numeral_Onat__of, _1716054) = hAPP(c_Code__Numeral_Onat__of, _1716056))], (7554 ^ _779999) ^ [_906881] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _906881), _906881)))], (39551 ^ _779999) ^ [_1545228, _1545230, _1545232, _1545234] : [-(c_Hilbert__Choice_OEps(tc_prod(_1545228, _1545230), hAPP(c_Product__Type_Oprod_Oprod__case(_1545228, _1545230, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1545228, tc_fun(_1545230, tc_HOL_Obool), tc_fun(_1545230, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545230, tc_HOL_Obool), tc_fun(_1545230, tc_HOL_Obool)), _1545228), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545230)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545228), c_fconj), hAPP(c_fequal, _1545232)))), hAPP(c_fequal, _1545234)))) = hAPP(hAPP(c_Product__Type_OPair(_1545228, _1545230), _1545232), _1545234))], (13572 ^ _779999) ^ [_1022093, _1022095, _1022097, _1022099] : [class_Groups_Ocomm__monoid__add(_1022093), 13575 ^ _779999 : [(13582 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022095), _1022097))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1022095, _1022093), _1022099), _1022097) = c_Groups_Ozero__class_Ozero(_1022093))], (13576 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022095), _1022097)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1022095, _1022093), _1022099), _1022097) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1022093, _1022095, c_Groups_Oplus__class_Oplus(_1022093)), _1022099), c_Groups_Ozero__class_Ozero(_1022093)), _1022097))]]], (37116 ^ _779999) ^ [_1482359] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1482359)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1482359)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20606 ^ _779999) ^ [_1154247] : [20608 ^ _779999 : [(20611 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20607 ^ [_1154247]))], (20609 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 20607 ^ [_1154247]), _1154247)))]], -(c_Nat__Transfer_Onat__set(_1154247))], (26564 ^ _779999) ^ [_1277608, _1277610] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277608, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277608, tc_HOL_Obool)), _1277610)), _1277610) = c_Orderings_Otop__class_Otop(tc_fun(_1277608, tc_HOL_Obool)))], (30092 ^ _779999) ^ [_1343949, _1343951, _1343953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1343949)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1343949), _1343951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1343949), _1343953)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1343951), _1343953))], (45093 ^ _779999) ^ [_1681235, _1681237] : [-(hAPP(hAPP(c_List_Oappend(_1681235), _1681237), c_List_Olist_ONil(_1681235)) = _1681237)], (49509 ^ _779999) ^ [_1778775, _1778777, _1778779] : [c_List_Olist__all(_1778775, _1778777, hAPP(c_List_Orev(_1778775), _1778779)), -(c_List_Olist__all(_1778775, _1778777, _1778779))], (33051 ^ _779999) ^ [_1399516] : [class_Int_Onumber__ring(_1399516), -(hAPP(c_Int_Onumber__class_Onumber__of(_1399516), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1399516))], (7492 ^ _779999) ^ [_904971, _904973, _904975, _904977, _904979] : [7495 ^ _779999 : [(7498 ^ _779999) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_904973, _904975, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_904973)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_904973), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _904973), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 7494 ^ [_904971, _904973, _904975, _904977, _904979]))), _904977), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _904973), hAPP(_904979, 7493 ^ [_904971, _904973, _904975, _904977, _904979])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_904973), tc_HOL_Obool))))], (7496 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_904971, 7493 ^ [_904971, _904973, _904975, _904977, _904979]), 7494 ^ [_904971, _904973, _904975, _904977, _904979])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_904973, _904975, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_904973)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_904973), _904971), _904977), _904979)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_904973), tc_HOL_Obool)))))], (34309 ^ _779999) ^ [_1421587] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1421587), 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), _1421587), _1421587))], (12385 ^ _779999) ^ [_999268, _999270, _999272] : [class_Lattices_Olattice(_999268), hBOOL(hAPP(c_Finite__Set_Ofinite(_999268), _999270)), hBOOL(hAPP(hAPP(c_member(_999268), _999272), _999270)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999268), _999272), c_Big__Operators_Olattice__class_OSup__fin(_999268, _999270)) = c_Big__Operators_Olattice__class_OSup__fin(_999268, _999270))], (34041 ^ _779999) ^ [_1416716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1416716)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416716), c_Int_OPls)))], (46450 ^ _779999) ^ [_1711503, _1711505, _1711507, _1711509, _1711511] : [-(c_Enum_Oproduct(_1711503, _1711505, hAPP(hAPP(c_List_Olist_OCons(_1711503), _1711507), _1711509), _1711511) = hAPP(hAPP(c_List_Oappend(tc_prod(_1711503, _1711505)), hAPP(hAPP(c_List_Omap(_1711505, tc_prod(_1711503, _1711505)), hAPP(c_Product__Type_OPair(_1711503, _1711505), _1711507)), _1711511)), c_Enum_Oproduct(_1711503, _1711505, _1711509, _1711511)))], (22880 ^ _779999) ^ [_1205238, _1205240, _1205242, _1205244, _1205246] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205238, tc_fun(_1205240, tc_HOL_Obool)), _1205242), hAPP(hAPP(c_COMBB(tc_fun(_1205240, tc_HOL_Obool), tc_fun(_1205240, tc_HOL_Obool), _1205238), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205240, tc_HOL_Obool)), _1205244)), _1205246)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205240, tc_HOL_Obool)), _1205244), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205238, tc_fun(_1205240, tc_HOL_Obool)), _1205242), _1205246)))], (9538 ^ _779999) ^ [_942056, _942058, _942060, _942062, _942064] : [class_Groups_Oordered__ab__group__add(_942056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_942056), _942058), _942060) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_942056), _942062), _942064), 9545 ^ _779999 : [(9552 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942056), _942062), _942064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942056), _942058), _942060)))], (9546 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942056), _942058), _942060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942056), _942062), _942064)))]]], (21658 ^ _779999) ^ [_1174595, _1174597] : [-(hBOOL(hAPP(_1174597, 21659 ^ [_1174595, _1174597]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1174595, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1174595), _1174597))], (7145 ^ _779999) ^ [_897691, _897693, _897695] : [hAPP(hAPP(c_COMBC(_897691, tc_fun(_897691, tc_HOL_Obool), tc_HOL_Obool), c_member(_897691)), _897693) = hAPP(hAPP(c_COMBC(_897691, tc_fun(_897691, tc_HOL_Obool), tc_HOL_Obool), c_member(_897691)), _897695), -(_897693 = _897695)], (49758 ^ _779999) ^ [_1783953, _1783955] : [-(c_List_Osplice(_1783953, _1783955, c_List_Olist_ONil(_1783953)) = _1783955)], (6911 ^ _779999) ^ [_893459, _893461, _893463, _893465, _893467] : [-(hAPP(hAPP(c_Set_Oinsert(_893459), _893461), hAPP(hAPP(c_Set_Oinsert(_893459), _893463), c_Orderings_Obot__class_Obot(tc_fun(_893459, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_893459), _893465), hAPP(hAPP(c_Set_Oinsert(_893459), _893467), c_Orderings_Obot__class_Obot(tc_fun(_893459, tc_HOL_Obool))))), 6912 ^ _779999 : [(6919 ^ _779999) ^ [] : [_893461 = _893467, _893463 = _893465], (6913 ^ _779999) ^ [] : [_893461 = _893465, _893463 = _893467]]], (44792 ^ _779999) ^ [_1673921, _1673923, _1673925, _1673927, _1673929, _1673931] : [-(hAPP(c_List_Olist_Olist__case(_1673921, _1673923, _1673925, _1673927), hAPP(hAPP(c_List_Olist_OCons(_1673923), _1673929), _1673931)) = hAPP(hAPP(_1673927, _1673929), _1673931))], (42347 ^ _779999) ^ [_1613268, _1613270, _1613272] : [class_Complete__Lattice_Ocomplete__lattice(_1613268), class_Orderings_Olinorder(_1613268), 42354 ^ _779999 : [(42364 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613268), c_Complete__Lattice_OInf__class_OInf(_1613268, _1613270)), _1613272))), 42365 ^ _779999 : [(42366 ^ _779999) ^ [_1613574] : [hBOOL(hAPP(hAPP(c_member(_1613268), _1613574), _1613270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613268), _1613574), _1613272))]]], (42355 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613268), c_Complete__Lattice_OInf__class_OInf(_1613268, _1613270)), _1613272)), 42359 ^ _779999 : [(42362 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1613268), 42358 ^ [_1613268, _1613270, _1613272]), _1613272)))], (42360 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613268), 42358 ^ [_1613268, _1613270, _1613272]), _1613270)))]]]]], (2514 ^ _779999) ^ [_817084, _817086] : [_817086 = _817084, -(c_Divides_Oadjust(_817086) = c_Divides_Oadjust(_817084))], (4582 ^ _779999) ^ [_849604, _849606, _849608, _849610] : [-(c_List_Omap(_849610, _849606) = c_List_Omap(_849608, _849604)), _849610 = _849608, _849606 = _849604], (51031 ^ _779999) ^ [_1812856, _1812858] : [c_Relation_Osym(_1812856, _1812858), -(c_Relation_Osym(_1812856, c_Transitive__Closure_Otrancl(_1812856, _1812858)))], (8280 ^ _779999) ^ [_920616, _920618, _920620] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_920616, _920618)), _920620), _920620))), 8281 ^ _779999 : [(8284 ^ _779999) ^ [_920716] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_920618), _920620), _920716)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_920616, _920618)), _920716), _920620))], (8282 ^ _779999) ^ [] : [-(hBOOL(hAPP(_920616, _920620)))]]], (828 ^ _779999) ^ [_792677, _792679, _792681, _792683, _792685, _792687, _792689, _792691] : [-(c_Nat__Transfer_Otransfer__morphism(_792689, _792685, _792681, _792677)), c_Nat__Transfer_Otransfer__morphism(_792691, _792687, _792683, _792679), _792691 = _792689, _792687 = _792685, _792683 = _792681, _792679 = _792677], (49852 ^ _779999) ^ [_1786803, _1786805, _1786807] : [-(_1786803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1786805), c_List_Oreplicate(_1786805, _1786803, _1786807)) = c_List_Oreplicate(_1786805, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1786803), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1786807))], (46280 ^ _779999) ^ [_1707233, _1707235, _1707237, _1707239, _1707241] : [hAPP(hAPP(c_List_Omap(_1707233, _1707235), _1707237), _1707239) = hAPP(hAPP(c_List_Omap(_1707233, _1707235), _1707237), _1707241), c_Fun_Oinj__on(_1707233, _1707235, _1707237, c_Orderings_Otop__class_Otop(tc_fun(_1707233, tc_HOL_Obool))), -(_1707239 = _1707241)], (44800 ^ _779999) ^ [_1674264, _1674266, _1674268] : [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), _1674264), _1674266))), -(hBOOL(hAPP(hAPP(_1674268, _1674264), _1674266))), 44807 ^ _779999 : [(44810 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 44805 ^ [_1674264, _1674266, _1674268]), 44806 ^ [_1674264, _1674266, _1674268])), -(hBOOL(hAPP(hAPP(_1674268, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 44805 ^ [_1674264, _1674266, _1674268]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 44806 ^ [_1674264, _1674266, _1674268])))], (44816 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1674268, 44805 ^ [_1674264, _1674266, _1674268]), 44806 ^ [_1674264, _1674266, _1674268]))], (44808 ^ _779999) ^ [] : [-(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), 44805 ^ [_1674264, _1674266, _1674268]), 44806 ^ [_1674264, _1674266, _1674268]))))]]], (44057 ^ _779999) ^ [_1658693] : [44059 ^ _779999 : [(44062 ^ _779999) ^ [] : [44058 ^ [_1658693] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44060 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44058 ^ [_1658693]), hAPP(c_List_Oset(tc_Nat_Onat), _1658693))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1658693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40795 ^ _779999) ^ [_1575233, _1575235, _1575237, _1575239, _1575241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575235, tc_HOL_Obool)), _1575239), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575235, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575233, _1575235, hAPP(c_Relation_Oconverse(_1575235, _1575233), _1575237)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575233, tc_HOL_Obool)), _1575241))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575233, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575235, _1575233, _1575237), _1575239)), _1575241)))], (25297 ^ _779999) ^ [_1254828, _1254830, _1254832, _1254834, _1254836] : [class_Groups_Ocomm__monoid__mult(_1254828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254830), _1254832)), hBOOL(hAPP(hAPP(c_member(_1254830), _1254834), _1254832)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1254830, _1254828), _1254836), _1254832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254828), hAPP(_1254836, _1254834)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1254830, _1254828), _1254836), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254830, tc_HOL_Obool)), _1254832), hAPP(hAPP(c_Set_Oinsert(_1254830), _1254834), c_Orderings_Obot__class_Obot(tc_fun(_1254830, tc_HOL_Obool)))))))], (38388 ^ _779999) ^ [_1514500, _1514502, _1514504, _1514506] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514500, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1514500, _1514502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1514500, _1514502), tc_HOL_Obool)), _1514504), _1514506))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514500, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1514500, _1514502), _1514504)), hAPP(c_Relation_ODomain(_1514500, _1514502), _1514506)))))], (31339 ^ _779999) ^ [_1366996, _1366998] : [class_Rings_Olinordered__idom(_1366996), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366996), c_Groups_Osgn__class_Osgn(_1366996, _1366998)), hAPP(c_Groups_Oabs__class_Oabs(_1366996), _1366998)) = _1366998)], (25878 ^ _779999) ^ [_1265145, _1265147, _1265149, _1265151] : [-(hAPP(c_Set_Ovimage(_1265145, _1265147, _1265149), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1265147, tc_HOL_Obool)), _1265151)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1265145, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1265145, _1265147, _1265149), _1265151)))], (41972 ^ _779999) ^ [_1603355, _1603357, _1603359, _1603361, _1603363, _1603365] : [class_Complete__Lattice_Ocomplete__lattice(_1603355), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603357, _1603355), _1603359), hAPP(hAPP(c_COMBB(tc_fun(_1603361, _1603355), _1603355, _1603357), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603361, _1603355), _1603363)), _1603365)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603361, _1603355), _1603363), hAPP(hAPP(c_COMBB(tc_fun(_1603357, _1603355), _1603355, _1603361), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603357, _1603355), _1603359)), hAPP(c_COMBC(_1603357, _1603361, _1603355), _1603365))))], (48697 ^ _779999) ^ [_1760255] : [c_List_Onat__list(_1760255), -(c_List_Oembed__list(c_List_Oreturn__list(_1760255)) = _1760255)], (30501 ^ _779999) ^ [_1351689, _1351691, _1351693, _1351695] : [class_Divides_Osemiring__div(_1351689), -(c_Divides_Odiv__class_Omod(_1351689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351689), _1351691), _1351693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351689), _1351691), _1351695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351689), _1351691), c_Divides_Odiv__class_Omod(_1351689, _1351693, _1351695)))], (21646 ^ _779999) ^ [_1174380] : [-(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)), _1174380)))))], (20806 ^ _779999) ^ [_1157714, _1157716] : [class_Groups_Oordered__ab__group__add__abs(_1157714), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157714), _1157716), hAPP(c_Groups_Oabs__class_Oabs(_1157714), _1157716))))], (5160 ^ _779999) ^ [_858911, _858913, _858915, _858917, _858919, _858921, _858923, _858925] : [-(c_Wellfounded_Olex__prod(_858925, _858921, _858917, _858913) = c_Wellfounded_Olex__prod(_858923, _858919, _858915, _858911)), _858925 = _858923, _858921 = _858919, _858917 = _858915, _858913 = _858911], (33693 ^ _779999) ^ [_1410458, _1410460] : [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(_1410458))), 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)), _1410460)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410458)), hAPP(c_Nat_OSuc, _1410460))))], (51055 ^ _779999) ^ [_1813227, _1813229] : [c_Relation_Osym(_1813227, _1813229), -(hAPP(c_Relation_Oconverse(_1813227, _1813227), _1813229) = _1813229)], (39383 ^ _779999) ^ [_1541522, _1541524, _1541526, _1541528, _1541530, _1541532] : [-(hAPP(hAPP(c_Fun_Ocomp(_1541522, _1541524, _1541526, _1541528), _1541530), _1541532) = hAPP(_1541528, hAPP(_1541530, _1541532)))], (19117 ^ _779999) ^ [_1128451, _1128453, _1128455] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128453), _1128455)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128451), _1128453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128451), _1128455)))], (31977 ^ _779999) ^ [_1379861, _1379863] : [class_Int_Onumber__ring(_1379861), -(hAPP(c_Int_Onumber__class_Onumber__of(_1379861), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1379863)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1379861), hAPP(c_Int_Onumber__class_Onumber__of(_1379861), _1379863)))], (39373 ^ _779999) ^ [_1541347, _1541349] : [39374 ^ _779999 : [(39375 ^ _779999) ^ [_1541393] : [hBOOL(hAPP(_1541347, _1541393))]], -(hBOOL(hAPP(_1541347, c_Hilbert__Choice_OEps(_1541349, _1541347))))], (29862 ^ _779999) ^ [_1339974, _1339976] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339974))), -(c_SMT_Oz3div(_1339976, _1339974) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1339976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339974))))], (52280 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (19998 ^ _779999) ^ [_1144699, _1144701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144701)), 20005 ^ _779999 : [(20012 ^ _779999) ^ [] : [_1144699 = _1144701, -(hAPP(c_Int_Onat, _1144699) = hAPP(c_Int_Onat, _1144701))], (20006 ^ _779999) ^ [] : [hAPP(c_Int_Onat, _1144699) = hAPP(c_Int_Onat, _1144701), -(_1144699 = _1144701)]]], (34605 ^ _779999) ^ [_1426930, _1426932, _1426934] : [class_Groups_Omonoid__mult(_1426930), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426930), _1426932), 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)))), _1426934))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426930), _1426932), hAPP(hAPP(c_Power_Opower__class_Opower(_1426930), hAPP(hAPP(c_Power_Opower__class_Opower(_1426930), _1426932), _1426934)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34559 ^ _779999) ^ [_1425910, _1425912, _1425914] : [class_Rings_Olinordered__idom(_1425910), 34562 ^ _779999 : [(34563 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425910), c_Groups_Ozero__class_Ozero(_1425910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425910), hAPP(hAPP(c_Power_Opower__class_Opower(_1425910), _1425912), 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(_1425910), _1425914), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1425912 = c_Groups_Ozero__class_Ozero(_1425910), _1425914 = c_Groups_Ozero__class_Ozero(_1425910)], (34573 ^ _779999) ^ [] : [34574 ^ _779999 : [(34577 ^ _779999) ^ [] : [-(_1425914 = c_Groups_Ozero__class_Ozero(_1425910))], (34575 ^ _779999) ^ [] : [-(_1425912 = c_Groups_Ozero__class_Ozero(_1425910))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425910), c_Groups_Ozero__class_Ozero(_1425910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425910), hAPP(hAPP(c_Power_Opower__class_Opower(_1425910), _1425912), 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(_1425910), _1425914), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (34713 ^ _779999) ^ [_1429110] : [-(_1429110 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 34716 ^ _779999 : [(34723 ^ _779999) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1429110, 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, _1429110) = 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), _1429110), 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)))], (34717 ^ _779999) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1429110, 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, _1429110) = 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), _1429110), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (15183 ^ _779999) ^ [_1052809, _1052811] : [class_Rings_Olinordered__idom(_1052809), hBOOL(hAPP(hAPP(c_member(_1052809), _1052811), c_Int_Oring__1__class_OInts(_1052809))), 15190 ^ _779999 : [(15197 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052809), _1052811), c_Groups_Ozero__class_Ozero(_1052809))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052809), c_Groups_Oone__class_Oone(_1052809)), _1052811)), _1052811)), c_Groups_Ozero__class_Ozero(_1052809))))], (15191 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052809), c_Groups_Oone__class_Oone(_1052809)), _1052811)), _1052811)), c_Groups_Ozero__class_Ozero(_1052809))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052809), _1052811), c_Groups_Ozero__class_Ozero(_1052809))))]]], (27476 ^ _779999) ^ [_1296917] : [-(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), _1296917))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37019 ^ _779999) ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641] : [c_Equiv__Relations_Oequiv(_1479629, _1479631, _1479633), c_Equiv__Relations_Ocongruent(_1479629, tc_fun(_1479635, tc_HOL_Obool), _1479633, _1479637), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479629, tc_fun(_1479635, tc_HOL_Obool)), _1479639), _1479637) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479629, tc_fun(_1479635, tc_HOL_Obool)), _1479641), _1479637), hBOOL(hAPP(hAPP(c_member(tc_fun(_1479629, tc_HOL_Obool)), _1479639), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479629), _1479631), _1479633))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1479629, tc_HOL_Obool)), _1479641), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479629), _1479631), _1479633))), 37041 ^ _779999 : [(37045 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479629), 37043 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641]), _1479631)))], (37047 ^ _779999) ^ [] : [-(hAPP(_1479637, 37040 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641]) = hAPP(_1479637, 37043 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641]))], (37049 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479629, _1479629)), hAPP(hAPP(c_Product__Type_OPair(_1479629, _1479629), 37040 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641]), 37043 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641])), _1479633))], (37042 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479629), 37040 ^ [_1479629, _1479631, _1479633, _1479635, _1479637, _1479639, _1479641]), _1479631)))]], -(_1479639 = _1479641)], (20760 ^ _779999) ^ [_1156869] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1156869))))], (27328 ^ _779999) ^ [_1294205, _1294207] : [class_Rings_Odivision__ring__inverse__zero(_1294205), 27331 ^ _779999 : [(27338 ^ _779999) ^ [] : [-(_1294207 = c_Groups_Ozero__class_Ozero(_1294205)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294205), _1294207), _1294207) = c_Groups_Oone__class_Oone(_1294205))], (27332 ^ _779999) ^ [] : [_1294207 = c_Groups_Ozero__class_Ozero(_1294205), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294205), _1294207), _1294207) = c_Groups_Ozero__class_Ozero(_1294205))]]], (33719 ^ _779999) ^ [_1411148, _1411150] : [class_Int_Onumber__ring(_1411148), 33722 ^ _779999 : [(33729 ^ _779999) ^ [] : [c_Int_Oiszero(_1411148, hAPP(c_Int_Onumber__class_Onumber__of(_1411148), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411148), _1411150) = c_Groups_Oone__class_Oone(_1411148))], (33723 ^ _779999) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1411148), _1411150) = c_Groups_Oone__class_Oone(_1411148), -(c_Int_Oiszero(_1411148, hAPP(c_Int_Onumber__class_Onumber__of(_1411148), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (45684 ^ _779999) ^ [_1694917, _1694919, _1694921] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1694917, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694919)), _1694921)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1694919, _1694917), _1694921) = _1694921)], (37905 ^ _779999) ^ [_1503496, _1503498, _1503500, _1503502] : [c_Wellfounded_Owf(_1503496, _1503498), -(c_Wellfounded_Owf(_1503500, hAPP(hAPP(c_Relation_Oinv__image(_1503496, _1503500), _1503498), _1503502)))], (26482 ^ _779999) ^ [_1276089, _1276091, _1276093] : [class_Groups_Oordered__ab__group__add__abs(_1276089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276089), hAPP(c_Groups_Oabs__class_Oabs(_1276089), _1276091)), _1276093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276089), hAPP(c_Groups_Ouminus__class_Ouminus(_1276089), _1276091)), _1276093)))], (43759 ^ _779999) ^ [_1650177, _1650179, _1650181, _1650183] : [hBOOL(hAPP(hAPP(c_member(_1650177), _1650179), hAPP(c_List_Oset(_1650177), hAPP(hAPP(c_List_Olist_OCons(_1650177), _1650181), _1650183)))), -(_1650179 = _1650181), -(hBOOL(hAPP(hAPP(c_member(_1650177), _1650179), hAPP(c_List_Oset(_1650177), _1650183))))], (9142 ^ _779999) ^ [_936211, _936213, _936215, _936217, _936219] : [-(hAPP(c_Fun_Ofun__upd(_936211, _936213, _936215, _936217, _936219), _936217) = _936219)], (31345 ^ _779999) ^ [_1367103, _1367105] : [class_Rings_Olinordered__idom(_1367103), -(hAPP(c_Groups_Oabs__class_Oabs(_1367103), _1367105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367103), _1367105), c_Groups_Osgn__class_Osgn(_1367103, _1367105)))], (46757 ^ _779999) ^ [_1717800, _1717802] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1717800), _1717802) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1717800, 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)))), _1717802))))], (8314 ^ _779999) ^ [_921299, _921301, _921303, _921305] : [hBOOL(hAPP(hAPP(c_member(_921299), _921301), _921303)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921299, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_921299), _921301), _921305)), _921303) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921299, tc_HOL_Obool)), _921305), _921303))], (32739 ^ _779999) ^ [_1394165, _1394167] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394165)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394167)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394165), _1394167)))], (26050 ^ _779999) ^ [_1268673, _1268675, _1268677] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1268673, _1268675, _1268677)], (40051 ^ _779999) ^ [_1557337, _1557339, _1557341, _1557343, _1557345] : [c_Com_Ocom_OWhile(_1557337, _1557339) = c_Com_Ocom_OLocal(_1557341, _1557343, _1557345)], (37222 ^ _779999) ^ [_1485218, _1485220, _1485222, _1485224] : [c_Equiv__Relations_Oequivp(_1485218, _1485220), hBOOL(hAPP(hAPP(_1485220, _1485222), _1485224)), -(hBOOL(hAPP(hAPP(_1485220, _1485224), _1485222)))], (17087 ^ _779999) ^ [_1089135, _1089137, _1089139, _1089141] : [class_Rings_Olinordered__semiring__strict(_1089135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089135), _1089137), _1089139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089135), _1089141), _1089139))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089135), c_Groups_Ozero__class_Ozero(_1089135)), _1089139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089135), _1089137), _1089141)))], (45640 ^ _779999) ^ [_1693998, _1694000, _1694002] : [-(c_List_Orotate(_1693998, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1694000), _1694002)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1693998), tc_List_Olist(_1693998), tc_List_Olist(_1693998), c_List_Orotate(_1693998, _1694000)), c_List_Orotate(_1693998, _1694002)))], (45328 ^ _779999) ^ [_1686970, _1686972, _1686974, _1686976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686970), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686972)), _1686974))), -(hAPP(hAPP(c_List_Olist__update(_1686972, _1686974), _1686970), _1686976) = hAPP(hAPP(c_List_Oappend(_1686972), hAPP(hAPP(c_List_Otake(_1686972), _1686970), _1686974)), hAPP(hAPP(c_List_Olist_OCons(_1686972), _1686976), hAPP(hAPP(c_List_Odrop(_1686972), hAPP(c_Nat_OSuc, _1686970)), _1686974))))], (29560 ^ _779999) ^ [_1334719, _1334721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334719), _1334721)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1334719), _1334721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18828 ^ _779999) ^ [_1123611, _1123613] : [-(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)), _1123611)), 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), _1123613), _1123611))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1123611), _1123613))], (24462 ^ _779999) ^ [_1238149, _1238151, _1238153] : [class_Orderings_Olinorder(_1238149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238149), _1238151), _1238153)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238149), _1238153), _1238151) = _1238153)], (7673 ^ _779999) ^ [_908899, _908901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _908899), hAPP(c_Nat_OSuc, _908901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _908899), _908901))), -(_908899 = hAPP(c_Nat_OSuc, _908901))], (22095 ^ _779999) ^ [_1188361, _1188363, _1188365] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1188361, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1188363)), _1188365) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1188361, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1188361, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1188363)), _1188365)), hAPP(_1188365, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47234 ^ _779999) ^ [_1728759, _1728761, _1728763] : [hBOOL(hAPP(hAPP(c_member(_1728759), _1728761), hAPP(c_List_Oset(_1728759), _1728763))), -(c_List_Oremdups(_1728759, hAPP(hAPP(c_List_Olist_OCons(_1728759), _1728761), _1728763)) = c_List_Oremdups(_1728759, _1728763))], (13359 ^ _779999) ^ [_1017815] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017815), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1017815)], (26434 ^ _779999) ^ [_1275250, _1275252] : [class_Lattices_Oboolean__algebra(_1275250), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275250), _1275252), hAPP(c_Groups_Ouminus__class_Ouminus(_1275250), _1275252)) = c_Orderings_Otop__class_Otop(_1275250))], (38941 ^ _779999) ^ [_1531333, _1531335] : [c_Wellfounded_Owf(_1531333, hAPP(c_Set_OCollect(tc_prod(_1531333, _1531333)), hAPP(c_Product__Type_Oprod_Oprod__case(_1531333, _1531333, tc_HOL_Obool), _1531335))), -(c_Wellfounded_OwfP(_1531333, _1531335))], (33911 ^ _779999) ^ [_1414517] : [-(c_Int_OBit0(_1414517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414517), _1414517))], (36487 ^ _779999) ^ [_1467192, _1467194, _1467196] : [-(_1467192 = hAPP(hAPP(c_Product__Type_OPair(_1467194, _1467196), hAPP(c_Product__Type_Ofst(_1467194, _1467196), _1467192)), hAPP(c_Product__Type_Osnd(_1467194, _1467196), _1467192)))], (22099 ^ _779999) ^ [_1188451, _1188453] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1188451, tc_HOL_Obool)), _1188453)))], (48332 ^ _779999) ^ [_1752579, _1752581] : [c_List_Olist_ONil(_1752579) = hAPP(c_List_Orev(_1752579), _1752581), -(_1752581 = c_List_Olist_ONil(_1752579))], (15585 ^ _779999) ^ [_1061092, _1061094, _1061096] : [class_Rings_Ono__zero__divisors(_1061092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061092), _1061094), _1061096) = c_Groups_Ozero__class_Ozero(_1061092), -(_1061094 = c_Groups_Ozero__class_Ozero(_1061092)), -(_1061096 = c_Groups_Ozero__class_Ozero(_1061092))], (5885 ^ _779999) ^ [_873643, _873645, _873647] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873643, tc_HOL_Obool)), _873645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_873643, tc_HOL_Obool)), _873647), _873645))))], (26046 ^ _779999) ^ [_1268574, _1268576, _1268578, _1268580, _1268582] : [c_Com_Ocom_OSemi(_1268574, _1268576) = c_Com_Ocom_OCond(_1268578, _1268580, _1268582)], (36421 ^ _779999) ^ [_1465788, _1465790, _1465792] : [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), _1465788), _1465790))), -(hBOOL(hAPP(hAPP(_1465792, _1465788), _1465790))), 36428 ^ _779999 : [(36431 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36427 ^ [_1465788, _1465790, _1465792]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1465792, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36426 ^ [_1465788, _1465790, _1465792])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36427 ^ [_1465788, _1465790, _1465792]))))], (36437 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1465792, 36426 ^ [_1465788, _1465790, _1465792]), 36427 ^ [_1465788, _1465790, _1465792]))], (36429 ^ _779999) ^ [] : [-(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), 36426 ^ [_1465788, _1465790, _1465792]), 36427 ^ [_1465788, _1465790, _1465792]))))]]], (50537 ^ _779999) ^ [_1801612, _1801614, _1801616, _1801618] : [c_Relation_Otrans(_1801612, _1801614), -(c_Relation_Otrans(_1801616, hAPP(hAPP(c_Relation_Oinv__image(_1801612, _1801616), _1801614), _1801618)))], (37923 ^ _779999) ^ [_1503793, _1503795] : [c_Wellfounded_Owf(_1503793, _1503795), -(c_Wellfounded_Owf(_1503793, hAPP(hAPP(c_Relation_Orel__comp(_1503793, _1503793, _1503793), _1503795), _1503795)))], (17723 ^ _779999) ^ [_1102160, _1102162, _1102164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102160)), 17726 ^ _779999 : [(17733 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102162), _1102164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102160), _1102162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102160), _1102164))))], (17727 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102160), _1102162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102160), _1102164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102162), _1102164)))]]], (40301 ^ _779999) ^ [_1563821, _1563823] : [-(c_Transitive__Closure_Ortrancl(_1563821, c_Transitive__Closure_Otrancl(_1563821, _1563823)) = c_Transitive__Closure_Ortrancl(_1563821, _1563823))], (42117 ^ _779999) ^ [_1607658, _1607660, _1607662, _1607664, _1607666] : [_1607658 = c_Orderings_Obot__class_Obot(tc_fun(_1607660, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607660, tc_fun(_1607662, tc_HOL_Obool)), _1607658), hAPP(hAPP(c_COMBB(tc_fun(_1607662, tc_HOL_Obool), tc_fun(_1607662, tc_HOL_Obool), _1607660), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607662, tc_HOL_Obool)), _1607664)), _1607666)) = c_Orderings_Otop__class_Otop(tc_fun(_1607662, tc_HOL_Obool)))], (49072 ^ _779999) ^ [_1768266, _1768268] : [-(c_Wellfounded_Owf(_1768266, c_List_Omeasures(_1768266, _1768268)))], (9174 ^ _779999) ^ [_936667, _936669, _936671, _936673, _936675, _936677] : [_936667 = _936669, -(hAPP(c_Fun_Ofun__upd(_936671, _936673, _936675, _936669, _936677), _936667) = _936677)], (1454 ^ _779999) ^ [_801282, _801284] : [-(class_Lattices_Osemilattice__sup(_801282)), _801284 = _801282, class_Lattices_Osemilattice__sup(_801284)], (37306 ^ _779999) ^ [_1487155, _1487157, _1487159, _1487161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1487155), _1487157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1487159), _1487161)), -(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), _1487155), _1487159)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1487157), _1487161))), c_FunDef_Opair__less)))], (27598 ^ _779999) ^ [_1299049, _1299051, _1299053, _1299055] : [class_Rings_Olinordered__semidom(_1299049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299049), c_Groups_Oone__class_Oone(_1299049)), _1299051)), 27605 ^ _779999 : [(27612 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299053), _1299055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299049), hAPP(hAPP(c_Power_Opower__class_Opower(_1299049), _1299051), _1299053)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299049), _1299051), _1299055))))], (27606 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299049), hAPP(hAPP(c_Power_Opower__class_Opower(_1299049), _1299051), _1299053)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299049), _1299051), _1299055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299053), _1299055)))]]], (37441 ^ _779999) ^ [_1489828, _1489830, _1489832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1489828, _1489828), tc_HOL_Obool)), _1489830), _1489832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489828, tc_HOL_Obool)), hAPP(c_Relation_OField(_1489828), _1489830)), hAPP(c_Relation_OField(_1489828), _1489832))))], (13105 ^ _779999) ^ [_1013175, _1013177, _1013179, _1013181, _1013183] : [c_Finite__Set_Ofun__left__comm__idem(_1013175, _1013177, _1013179), -(c_Finite__Set_Ofun__left__comm__idem(_1013181, _1013177, hAPP(hAPP(c_COMBB(_1013175, tc_fun(_1013177, _1013177), _1013181), _1013179), _1013183)))], (46492 ^ _779999) ^ [_1712689, _1712691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1712689)), hAPP(c_Code__Numeral_Oof__nat, _1712691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712689), _1712691)))], (44210 ^ _779999) ^ [_1662160, _1662162, _1662164, _1662166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662162)), _1662164))), -(hAPP(hAPP(c_List_Onth(_1662162), hAPP(hAPP(c_List_Olist__update(_1662162, _1662164), _1662160), _1662166)), _1662160) = _1662166)], (34379 ^ _779999) ^ [_1422832, _1422834, _1422836] : [class_Rings_Olinordered__semidom(_1422832), hAPP(hAPP(c_Power_Opower__class_Opower(_1422832), _1422834), 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(_1422832), _1422836), 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(_1422832), c_Groups_Ozero__class_Ozero(_1422832)), _1422834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422832), c_Groups_Ozero__class_Ozero(_1422832)), _1422836)), -(_1422834 = _1422836)], (35745 ^ _779999) ^ [_1453605, _1453607] : [35746 ^ _779999 : [(35749 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453607), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35747 ^ _779999) ^ [] : [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), _1453605), _1453607)))]], -(c_Divides_OnegDivAlg(_1453605, _1453607) = 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), _1453605), _1453607)))], (43751 ^ _779999) ^ [_1649979, _1649981, _1649983, _1649985] : [hBOOL(hAPP(hAPP(c_member(_1649979), _1649981), hAPP(c_List_Oset(_1649979), hAPP(hAPP(c_List_Otake(_1649979), _1649983), _1649985)))), -(hBOOL(hAPP(hAPP(c_member(_1649979), _1649981), hAPP(c_List_Oset(_1649979), _1649985))))], (42606 ^ _779999) ^ [_1618908, _1618910, _1618912] : [class_Complete__Lattice_Ocomplete__lattice(_1618908), -(c_Complete__Lattice_OInf__class_OInf(_1618908, hAPP(hAPP(c_Set_Oinsert(_1618908), _1618910), _1618912)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1618908), _1618910), c_Complete__Lattice_OInf__class_OInf(_1618908, _1618912)))], (40033 ^ _779999) ^ [_1556833, _1556835, _1556837, _1556839, _1556841, _1556843] : [c_Com_Ocom_OLocal(_1556833, _1556835, _1556837) = c_Com_Ocom_OCond(_1556839, _1556841, _1556843)], (35424 ^ _779999) ^ [_1446620, _1446622, _1446624, _1446626] : [-(hAPP(c_Relation_OImage(_1446620, _1446622, _1446624), hAPP(hAPP(c_Set_Oinsert(_1446620), _1446626), c_Orderings_Obot__class_Obot(tc_fun(_1446620, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1446622), hAPP(hAPP(c_COMBC(_1446622, tc_fun(tc_prod(_1446620, _1446622), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1446620, _1446622), tc_fun(tc_fun(tc_prod(_1446620, _1446622), tc_HOL_Obool), tc_HOL_Obool), _1446622), c_member(tc_prod(_1446620, _1446622))), hAPP(c_Product__Type_OPair(_1446620, _1446622), _1446626))), _1446624)))], (11651 ^ _779999) ^ [_984264, _984266, _984268, _984270] : [class_Complete__Lattice_Ocomplete__lattice(_984264), _984266 = c_Inductive_Ocomplete__lattice__class_Olfp(_984264, _984268), c_Orderings_Oorder__class_Omono(_984264, _984264, _984268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984264), hAPP(_984268, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_984264), _984266), _984270))), _984270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984264), _984266), _984270)))], (2350 ^ _779999) ^ [_814618, _814620] : [_814620 = _814618, -(c_Natural_Oevalc(_814620) = c_Natural_Oevalc(_814618))], (6155 ^ _779999) ^ [_878299, _878301, _878303] : [class_Lattices_Osemilattice__sup(_878299), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878299), _878301), _878303) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878299), _878303), _878301))], (188 ^ _779999) ^ [_783019, _783021] : [-(class_Fields_Ofield(_783019)), _783021 = _783019, class_Fields_Ofield(_783021)], (49377 ^ _779999) ^ [_1775971, _1775973, _1775975] : [c_List_Olist__ex(_1775971, _1775973, _1775975), 49381 ^ _779999 : [(49384 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1775973, 49380 ^ [_1775971, _1775973, _1775975])))], (49382 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775971), 49380 ^ [_1775971, _1775973, _1775975]), hAPP(c_List_Oset(_1775971), _1775975))))]]], (5206 ^ _779999) ^ [_859616, _859618, _859620, _859622] : [-(c_Complete__Lattice_OSup__class_OSup(_859622, _859618) = c_Complete__Lattice_OSup__class_OSup(_859620, _859616)), _859622 = _859620, _859618 = _859616], (50184 ^ _779999) ^ [_1793191, _1793193, _1793195] : [hBOOL(hAPP(hAPP(c_List_Omember(_1793191), _1793195), _1793193)), -(hBOOL(hAPP(hAPP(c_member(_1793191), _1793193), hAPP(c_List_Oset(_1793191), _1793195))))], (46574 ^ _779999) ^ [_1714168, _1714170] : [hBOOL(hAPP(c_List_Odistinct(_1714168), _1714170)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1714168, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714168), tc_fun(_1714168, tc_HOL_Obool)), c_List_Oset(_1714168)), c_Enum_Osublists(_1714168, _1714170)))))], (2020 ^ _779999) ^ [_809271, _809273, _809275, _809277, _809279, _809281, _809283, _809285] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_809285, _809281, _809277, _809273) = c_Hoare__Mirabelle_Otriple_Otriple__case(_809283, _809279, _809275, _809271)), _809285 = _809283, _809281 = _809279, _809277 = _809275, _809273 = _809271], (22842 ^ _779999) ^ [_1204015, _1204017, _1204019, _1204021] : [22844 ^ _779999 : [(22847 ^ _779999) ^ [] : [hAPP(_1204021, 22843 ^ [_1204015, _1204017, _1204019, _1204021]) = c_Orderings_Obot__class_Obot(tc_fun(_1204015, tc_HOL_Obool))], (22845 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1204017), 22843 ^ [_1204015, _1204017, _1204019, _1204021]), _1204019)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1204015, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1204017, tc_fun(_1204015, tc_HOL_Obool)), _1204019), _1204021))], (42231 ^ _779999) ^ [_1610338, _1610340] : [class_Complete__Lattice_Ocomplete__lattice(_1610338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610338), _1610340)), -(c_Complete__Lattice_OSup__class_OSup(_1610338, _1610340) = hAPP(hAPP(c_Finite__Set_Ofold(_1610338, _1610338, c_Lattices_Osemilattice__sup__class_Osup(_1610338)), c_Orderings_Obot__class_Obot(_1610338)), _1610340))], (19033 ^ _779999) ^ [_1126969, _1126971, _1126973] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126971), _1126973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126969), _1126973)))], (45370 ^ _779999) ^ [_1687942, _1687944, _1687946, _1687948] : [-(hAPP(hAPP(c_List_Otake(_1687942), _1687944), hAPP(hAPP(c_List_Odrop(_1687942), _1687946), _1687948)) = hAPP(hAPP(c_List_Odrop(_1687942), _1687946), hAPP(hAPP(c_List_Otake(_1687942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1687944), _1687946)), _1687948)))], (18055 ^ _779999) ^ [_1108577, _1108579, _1108581] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1108577, tc_Nat_Onat), _1108579), _1108581)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1108577, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1108577), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1108579)), _1108581))], (14159 ^ _779999) ^ [_1032665, _1032667, _1032669, _1032671] : [class_Groups_Oordered__comm__monoid__add(_1032665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032665), c_Groups_Ozero__class_Ozero(_1032665)), _1032667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032665), _1032669), _1032671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032665), _1032669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032665), _1032667), _1032671))))], (42574 ^ _779999) ^ [_1618272, _1618274, _1618276] : [class_Complete__Lattice_Ocomplete__lattice(_1618272), -(c_Complete__Lattice_OSup__class_OSup(_1618272, hAPP(hAPP(c_Set_Oinsert(_1618272), _1618274), _1618276)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1618272), _1618274), c_Complete__Lattice_OSup__class_OSup(_1618272, _1618276)))], (49792 ^ _779999) ^ [_1784767, _1784769, _1784771] : [-(c_Predicate_Oconversep(_1784767, _1784769, c_Predicate_Oconversep(_1784769, _1784767, _1784771)) = _1784771)], (24654 ^ _779999) ^ [_1241782, _1241784, _1241786] : [class_Orderings_Olinorder(_1241782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1241782), _1241784)), hBOOL(hAPP(hAPP(c_member(_1241782), _1241786), _1241784)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241782), _1241786), c_Big__Operators_Olinorder__class_OMax(_1241782, _1241784)) = c_Big__Operators_Olinorder__class_OMax(_1241782, _1241784))], (44027 ^ _779999) ^ [_1658175, _1658177] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1658175, _1658177) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1658175), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1658177)))], (46710 ^ _779999) ^ [_1716897] : [-(hAPP(c_Code__Numeral_Onat__of, _1716897) = c_Code__Numeral_Onat__of__aux(_1716897, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19411 ^ _779999) ^ [_1133947, _1133949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133947)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1133947), _1133949)))], (24940 ^ _779999) ^ [_1248169, _1248171] : [class_Orderings_Olinorder(_1248169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248169), _1248171)), -(_1248171 = c_Orderings_Obot__class_Obot(tc_fun(_1248169, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248169), c_Big__Operators_Olattice_OInf__fin(_1248169, c_Orderings_Oord__class_Omin(_1248169), _1248171)), c_Big__Operators_Olattice_OSup__fin(_1248169, c_Orderings_Oord__class_Omax(_1248169), _1248171))))], (31809 ^ _779999) ^ [_1376319, _1376321, _1376323, _1376325] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376319), _1376321), _1376323)), hAPP(c_Int_Onumber__class_Onumber__of(_1376319), _1376325)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376319), _1376321), hAPP(c_Int_Onumber__class_Onumber__of(_1376319), _1376325))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376319), _1376323), hAPP(c_Int_Onumber__class_Onumber__of(_1376319), _1376325)))), class_Int_Onumber(_1376319), class_Rings_Osemiring(_1376319)], (20870 ^ _779999) ^ [_1158886] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1158886)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1158886))], (19541 ^ _779999) ^ [] : [-(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))))], (18019 ^ _779999) ^ [_1107950, _1107952, _1107954, _1107956, _1107958] : [class_Orderings_Olinorder(_1107950), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107950, _1107952), _1107954) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1107950, _1107956), _1107958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107950), _1107952), _1107954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107950), _1107956), _1107958)), -(_1107954 = _1107958)], (20498 ^ _779999) ^ [_1152754, _1152756] : [c_Nat__Transfer_Onat__set(_1152754), c_Nat__Transfer_Onat__set(_1152756), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1152754), _1152756)))], (9456 ^ _779999) ^ [_940713, _940715, _940717] : [class_Orderings_Oorder(_940713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940713), _940715), _940717)), -(_940717 = _940715), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940713), _940715), _940717)))], (47836 ^ _779999) ^ [_1743417, _1743419] : [class_Orderings_Olinorder(_1743417), -(c_List_Olinorder__class_Osorted(_1743417, hAPP(hAPP(c_List_Olist_OCons(_1743417), _1743419), c_List_Olist_ONil(_1743417))))], (26526 ^ _779999) ^ [_1276905] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276905, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1276905, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1276905, tc_HOL_Obool)))], (37584 ^ _779999) ^ [_1493677] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1493677)) = _1493677)], (2406 ^ _779999) ^ [_815456, _815458] : [_815458 = _815456, -(c_Int_Oring__1__class_OInts(_815458) = c_Int_Oring__1__class_OInts(_815456))], (37903 ^ _779999) ^ [_1503465] : [-(c_Wellfounded_Owf(_1503465, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1503465, _1503465), tc_HOL_Obool))))], (34987 ^ _779999) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (15941 ^ _779999) ^ [_1067691, _1067693, _1067695, _1067697, _1067699] : [class_Rings_Osemiring__0(_1067691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067691), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067693, _1067691), _1067695), _1067697)), _1067699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067693, _1067691), hAPP(hAPP(c_COMBC(_1067693, _1067691, _1067691), hAPP(hAPP(c_COMBB(_1067691, tc_fun(_1067691, _1067691), _1067693), c_Groups_Otimes__class_Otimes(_1067691)), _1067695)), _1067699)), _1067697))], (42472 ^ _779999) ^ [_1615767, _1615769, _1615771] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615767, tc_HOL_Obool)), _1615769), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615767, tc_HOL_Obool), _1615771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1615767, tc_HOL_Obool), tc_fun(_1615767, tc_HOL_Obool)), _1615771), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615767, tc_HOL_Obool)), _1615769)))], (48188 ^ _779999) ^ [_1749482, _1749484] : [class_Orderings_Olinorder(_1749482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749482), _1749484)), 48195 ^ _779999 : [(48200 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1749482), c_List_Olinorder__class_Osorted__list__of__set(_1749482, _1749484))))], (48198 ^ _779999) ^ [] : [-(c_List_Olinorder__class_Osorted(_1749482, c_List_Olinorder__class_Osorted__list__of__set(_1749482, _1749484)))], (48196 ^ _779999) ^ [] : [-(hAPP(c_List_Oset(_1749482), c_List_Olinorder__class_Osorted__list__of__set(_1749482, _1749484)) = _1749484)]]], (46278 ^ _779999) ^ [_1707168, _1707170, _1707172, _1707174, _1707176] : [-(hAPP(hAPP(c_List_Otake(_1707168), _1707170), hAPP(hAPP(c_List_Omap(_1707172, _1707168), _1707174), _1707176)) = hAPP(hAPP(c_List_Omap(_1707172, _1707168), _1707174), hAPP(hAPP(c_List_Otake(_1707172), _1707170), _1707176)))], (27674 ^ _779999) ^ [_1300341, _1300343] : [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), _1300341), _1300343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1300341))), -(_1300343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47178 ^ _779999) ^ [_1727768, _1727770] : [_1727770 = c_List_Olist_ONil(_1727768), -(c_List_Oremdups(_1727768, _1727770) = c_List_Olist_ONil(_1727768))], (33029 ^ _779999) ^ [_1399258] : [c_Int_OPls = c_Int_OBit1(_1399258)], (40927 ^ _779999) ^ [_1578556, _1578558, _1578560, _1578562] : [-(hAPP(hAPP(c_Nat_Ocompow(_1578556, _1578556), _1578558), hAPP(hAPP(c_Nat_Ocompow(_1578556, _1578556), _1578560), _1578562)) = hAPP(hAPP(c_Nat_Ocompow(_1578556, _1578556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1578560), _1578558)), _1578562))], (8506 ^ _779999) ^ [_925520, _925522] : [class_Groups_Ogroup__add(_925520), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925520), _925522), _925522) = c_Groups_Ozero__class_Ozero(_925520))], (28920 ^ _779999) ^ [_1323120, _1323122, _1323124, _1323126] : [class_Fields_Olinordered__field(_1323120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323120), c_Groups_Ozero__class_Ozero(_1323120)), _1323122)), 28927 ^ _779999 : [(28934 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323120), _1323124), _1323122)), _1323126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323120), _1323124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323120), _1323126), _1323122))))], (28928 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323120), _1323124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323120), _1323126), _1323122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323120), _1323124), _1323122)), _1323126)))]]], (1734 ^ _779999) ^ [_804782, _804784] : [-(class_Rings_Ono__zero__divisors(_804782)), _804784 = _804782, class_Rings_Ono__zero__divisors(_804784)], (25860 ^ _779999) ^ [_1264694, _1264696, _1264698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264694, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264694, tc_HOL_Obool)), _1264696)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264694, tc_HOL_Obool)), _1264698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264694, tc_HOL_Obool)), _1264698), _1264696)))], (18591 ^ _779999) ^ [_1118809, _1118811, _1118813, _1118815] : [class_Orderings_Oorder(_1118809), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1118809, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1118809, _1118811), _1118813)), c_SetInterval_Oord__class_OatLeastAtMost(_1118809, _1118813, _1118815)) = c_Orderings_Obot__class_Obot(tc_fun(_1118809, tc_HOL_Obool)))], (8668 ^ _779999) ^ [_928322, _928324, _928326, _928328, _928330] : [class_Groups_Oab__group__add(_928322), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928322), _928324), _928326) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928322), _928328), _928330), 8675 ^ _779999 : [(8682 ^ _779999) ^ [] : [_928328 = _928330, -(_928324 = _928326)], (8676 ^ _779999) ^ [] : [_928324 = _928326, -(_928328 = _928330)]]], (36667 ^ _779999) ^ [_1470981, _1470983] : [_1470981 = _1470983, -(hAPP(c_Int_ORep__Integ, _1470981) = hAPP(c_Int_ORep__Integ, _1470983))], (27860 ^ _779999) ^ [_1303692, _1303694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1303692)), -(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), _1303692), _1303694))))], (17955 ^ _779999) ^ [_1106832, _1106834, _1106836] : [class_Orderings_Olinorder(_1106832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106832), _1106834), _1106836)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106832, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1106832), _1106834)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1106832, _1106834), _1106836)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1106832), _1106836))], (47534 ^ _779999) ^ [_1736064, _1736066, _1736068] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1736064, tc_HOL_Obool)), hAPP(c_List_Oset(_1736064), _1736066)), hAPP(hAPP(c_Set_Oinsert(_1736064), _1736068), c_Orderings_Obot__class_Obot(tc_fun(_1736064, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1736064), hAPP(c_List_Ofilter(_1736064, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1736064), c_fNot), hAPP(hAPP(c_COMBC(_1736064, _1736064, tc_HOL_Obool), c_fequal), _1736068))), _1736066)))], (38580 ^ _779999) ^ [_1520646, _1520648, _1520650, _1520652, _1520654, _1520656] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1520646, _1520648)), hAPP(hAPP(c_Product__Type_OPair(_1520646, _1520648), _1520650), _1520652)), hAPP(hAPP(c_Product__Type_OSigma(_1520646, _1520648), _1520654), _1520656)))), hBOOL(hAPP(hAPP(c_member(_1520646), _1520650), _1520654)), hBOOL(hAPP(hAPP(c_member(_1520648), _1520652), hAPP(_1520656, _1520650)))], (52230 ^ _779999) ^ [_1832892, _1832894] : [-(class_Nat_Osize(tc_prod(_1832892, _1832894)))], (7689 ^ _779999) ^ [_909141, _909143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909141)), hAPP(c_Nat_OSuc, _909143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _909141), _909143)))], (25042 ^ _779999) ^ [_1249984, _1249986, _1249988] : [class_Orderings_Olinorder(_1249984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249984), _1249986)), hBOOL(hAPP(hAPP(c_member(_1249984), _1249988), _1249986)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1249984), _1249988), c_Big__Operators_Olattice_OSup__fin(_1249984, c_Orderings_Oord__class_Omax(_1249984), _1249986)) = _1249988)], (41914 ^ _779999) ^ [_1601151, _1601153, _1601155, _1601157, _1601159, _1601161] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601151, tc_fun(_1601153, tc_fun(_1601155, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1601151, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_fun(_1601153, tc_fun(_1601155, tc_HOL_Obool)), _1601151), hAPP(c_COMBC(_1601153, tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_fun(_1601155, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601155, tc_fun(tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_fun(_1601155, tc_HOL_Obool)), _1601153), c_COMBC(_1601155, tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601155, tc_prod(_1601153, _1601155)), tc_fun(_1601155, tc_fun(tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_HOL_Obool)), _1601153), hAPP(c_COMBB(tc_prod(_1601153, _1601155), tc_fun(tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool), tc_HOL_Obool), _1601155), c_member(tc_prod(_1601153, _1601155)))), c_Product__Type_OPair(_1601153, _1601155))))), _1601157)), _1601159), _1601161)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601153, _1601155)), hAPP(hAPP(c_Product__Type_OPair(_1601153, _1601155), _1601159), _1601161)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601151, tc_fun(tc_prod(_1601153, _1601155), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601151, tc_HOL_Obool))), _1601157))))], (38459 ^ _779999) ^ [_1516955, _1516957, _1516959, _1516961] : [hAPP(hAPP(c_Product__Type_OSigma(_1516955, _1516957), _1516959), hAPP(c_COMBK(tc_fun(_1516957, tc_HOL_Obool), _1516955), _1516961)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516955, _1516957), tc_HOL_Obool)), -(_1516959 = c_Orderings_Obot__class_Obot(tc_fun(_1516955, tc_HOL_Obool))), -(_1516961 = c_Orderings_Obot__class_Obot(tc_fun(_1516957, tc_HOL_Obool)))], (4442 ^ _779999) ^ [_847500, _847502, _847504, _847506, _847508, _847510] : [-(c_Predicate_Oconversep(_847510, _847506, _847502) = c_Predicate_Oconversep(_847508, _847504, _847500)), _847510 = _847508, _847506 = _847504, _847502 = _847500], (43239 ^ _779999) ^ [_1634514, _1634516, _1634518] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634514)), hAPP(hAPP(c_List_Olist_OCons(_1634514), _1634516), _1634518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634514)), _1634518)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21728 ^ _779999) ^ [_1175960, _1175962, _1175964] : [-(hAPP(c_Set_OCollect(_1175960), hAPP(hAPP(c_COMBS(_1175960, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175960), c_fconj), _1175962)), _1175964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1175960, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1175960), _1175962)), hAPP(c_Set_OCollect(_1175960), _1175964)))], (48580 ^ _779999) ^ [_1757884, _1757886, _1757888] : [class_Orderings_Olinorder(_1757884), c_List_Olinorder__class_Osorted(_1757884, _1757886), -(c_List_Olinorder__class_Osorted(_1757884, c_List_OtakeWhile(_1757884, _1757888, _1757886)))], (2356 ^ _779999) ^ [_814703, _814705] : [_814705 = _814703, -(c_SetInterval_Oord__class_OatLeast(_814705) = c_SetInterval_Oord__class_OatLeast(_814703))], (29258 ^ _779999) ^ [_1329573, _1329575, _1329577, _1329579] : [class_Fields_Olinordered__field(_1329573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329573), c_Groups_Ozero__class_Ozero(_1329573)), _1329575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329573), _1329577), _1329575)), _1329579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329573), _1329577), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329573), _1329579), _1329575))))], (36218 ^ _779999) ^ [_1461811, _1461813, _1461815] : [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), _1461811), _1461813))), -(hBOOL(hAPP(hAPP(_1461815, _1461811), _1461813))), 36225 ^ _779999 : [(36228 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1461815, 36223 ^ [_1461811, _1461813, _1461815]), 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)))), 36224 ^ [_1461811, _1461813, _1461815])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36223 ^ [_1461811, _1461813, _1461815]), 36224 ^ [_1461811, _1461813, _1461815]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36224 ^ [_1461811, _1461813, _1461815]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36238 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1461815, 36223 ^ [_1461811, _1461813, _1461815]), 36224 ^ [_1461811, _1461813, _1461815]))], (36226 ^ _779999) ^ [] : [-(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), 36223 ^ [_1461811, _1461813, _1461815]), 36224 ^ [_1461811, _1461813, _1461815]))))]]], (1824 ^ _779999) ^ [_805907, _805909] : [-(class_Orderings_Olinorder(_805907)), _805909 = _805907, class_Orderings_Olinorder(_805909)], (14173 ^ _779999) ^ [_1032918, _1032920, _1032922, _1032924] : [class_Groups_Oordered__comm__monoid__add(_1032918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032918), c_Groups_Ozero__class_Ozero(_1032918)), _1032920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032918), _1032922), _1032924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032918), _1032922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032918), _1032920), _1032924))))], (21692 ^ _779999) ^ [_1175107, _1175109, _1175111] : [hBOOL(hAPP(hAPP(c_member(_1175107), _1175109), hAPP(c_Set_OCollect(_1175107), _1175111))), -(hBOOL(hAPP(_1175111, _1175109)))], (51165 ^ _779999) ^ [_1814914, _1814916] : [c_Equiv__Relations_Opart__equivp(_1814914, _1814916), 51169 ^ _779999 : [(51174 ^ _779999) ^ [] : [-(c_Predicate_Otransp(_1814914, _1814916))], (51172 ^ _779999) ^ [] : [-(c_Predicate_Osymp(_1814914, _1814916))], (51170 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1814916, 51168 ^ [_1814914, _1814916]), 51168 ^ [_1814914, _1814916])))]]], (4706 ^ _779999) ^ [_851622, _851624, _851626, _851628] : [-(c_Lazy__Sequence_Osmall__lazy_H(_851628, _851624) = c_Lazy__Sequence_Osmall__lazy_H(_851626, _851622)), _851628 = _851626, _851624 = _851622], (11478 ^ _779999) ^ [_980495, _980497, _980499, _980501] : [class_Lattices_Olattice(_980495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980495), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980495), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_980495), _980497), _980499)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_980495), _980497), _980501))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_980495), _980497), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980495), _980499), _980501)))))], (22946 ^ _779999) ^ [_1207404, _1207406, _1207408, _1207410, _1207412] : [-(_1207404 = c_Orderings_Obot__class_Obot(tc_fun(_1207406, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207406, tc_fun(_1207408, tc_HOL_Obool)), _1207404), hAPP(hAPP(c_COMBB(tc_fun(_1207408, tc_HOL_Obool), tc_fun(_1207408, tc_HOL_Obool), _1207406), hAPP(c_Set_Oinsert(_1207408), _1207410)), _1207412)) = hAPP(hAPP(c_Set_Oinsert(_1207408), _1207410), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1207406, tc_fun(_1207408, tc_HOL_Obool)), _1207404), _1207412)))], (52096 ^ _779999) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (26290 ^ _779999) ^ [_1272726, _1272728, _1272730] : [class_Groups_Ogroup__add(_1272726), 26293 ^ _779999 : [(26300 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272726), _1272728), _1272730) = c_Groups_Ozero__class_Ozero(_1272726), -(_1272728 = hAPP(c_Groups_Ouminus__class_Ouminus(_1272726), _1272730))], (26294 ^ _779999) ^ [] : [_1272728 = hAPP(c_Groups_Ouminus__class_Ouminus(_1272726), _1272730), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272726), _1272728), _1272730) = c_Groups_Ozero__class_Ozero(_1272726))]]], (31313 ^ _779999) ^ [_1366451, _1366453] : [class_Rings_Olinordered__idom(_1366451), 31316 ^ _779999 : [(31323 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366451), c_Groups_Ozero__class_Ozero(_1366451)), _1366453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366451), c_Groups_Ozero__class_Ozero(_1366451)), c_Groups_Osgn__class_Osgn(_1366451, _1366453))))], (31317 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366451), c_Groups_Ozero__class_Ozero(_1366451)), c_Groups_Osgn__class_Osgn(_1366451, _1366453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366451), c_Groups_Ozero__class_Ozero(_1366451)), _1366453)))]]], (8824 ^ _779999) ^ [_931519, _931521, _931523] : [class_Complete__Lattice_Ocomplete__lattice(_931519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931519), _931521), hAPP(_931523, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931519), _931521), c_Inductive_Ocomplete__lattice__class_Ogfp(_931519, _931523))))), c_Orderings_Oorder__class_Omono(_931519, _931519, _931523), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931519), _931521), c_Inductive_Ocomplete__lattice__class_Ogfp(_931519, _931523))), hAPP(_931523, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_931519), _931521), c_Inductive_Ocomplete__lattice__class_Ogfp(_931519, _931523))))))], (40988 ^ _779999) ^ [_1580301, _1580303, _1580305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580301, _1580301)), _1580303), c_Transitive__Closure_Otrancl(_1580301, _1580305))), 40992 ^ _779999 : [(40995 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580301, _1580301)), _1580303), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580301, _1580301), tc_HOL_Obool), 40991 ^ [_1580301, _1580303, _1580305]), _1580305))))], (40993 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40991 ^ [_1580301, _1580303, _1580305])))]]], (8417 ^ _779999) ^ [_923859, _923861, _923863, _923865] : [-(c_Fun_Ooverride__on(_923859, _923861, _923863, _923865, c_Orderings_Obot__class_Obot(tc_fun(_923859, tc_HOL_Obool))) = _923863)], (44276 ^ _779999) ^ [_1663798, _1663800, _1663802, _1663804] : [hBOOL(hAPP(c_List_Odistinct(_1663798), _1663800)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1663798, _1663802)), hAPP(hAPP(c_List_Ozip(_1663798, _1663802), _1663800), _1663804))))], (14031 ^ _779999) ^ [_1030165, _1030167, _1030169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030165), _1030167)), _1030169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030169), _1030167))))], (49200 ^ _779999) ^ [_1771793, _1771795, _1771797, _1771799, _1771801] : [hAPP(hAPP(c_List_Olist_OCons(_1771793), _1771795), _1771797) = hAPP(c_List_Ofilter(_1771793, _1771799), _1771801), 49205 ^ _779999 : [(49214 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1771799, _1771795)))], (49216 ^ _779999) ^ [] : [-(_1771797 = hAPP(c_List_Ofilter(_1771793, _1771799), 49204 ^ [_1771793, _1771795, _1771797, _1771799, _1771801]))], (49208 ^ _779999) ^ [_1772107] : [hBOOL(hAPP(hAPP(c_member(_1771793), _1772107), hAPP(c_List_Oset(_1771793), 49203 ^ [_1771793, _1771795, _1771797, _1771799, _1771801]))), hBOOL(hAPP(_1771799, _1772107))], (49206 ^ _779999) ^ [] : [-(_1771801 = hAPP(hAPP(c_List_Oappend(_1771793), 49203 ^ [_1771793, _1771795, _1771797, _1771799, _1771801]), hAPP(hAPP(c_List_Olist_OCons(_1771793), _1771795), 49204 ^ [_1771793, _1771795, _1771797, _1771799, _1771801])))]]], (29520 ^ _779999) ^ [_1334053, _1334055, _1334057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334053), 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)), _1334055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334055), _1334057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1334053), _1334055)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1334053), _1334057))))], (6201 ^ _779999) ^ [_879101, _879103, _879105] : [_879101 = _879103, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879105, tc_HOL_Obool)), _879103), _879101)))], (49636 ^ _779999) ^ [_1781177, _1781179] : [-(c_FunDef_Ois__measure(_1781177, _1781179))], (18557 ^ _779999) ^ [_1118155, _1118157, _1118159, _1118161, _1118163] : [class_Groups_Oab__semigroup__mult(_1118155), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1118155, _1118155, c_Groups_Otimes__class_Otimes(_1118155), _1118157, _1118159), _1118161)), -(hBOOL(hAPP(hAPP(c_member(_1118155), _1118157), _1118159))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1118155, _1118155, c_Groups_Otimes__class_Otimes(_1118155), _1118163, hAPP(hAPP(c_Set_Oinsert(_1118155), _1118157), _1118159)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118155), _1118163), _1118161))))], (44570 ^ _779999) ^ [_1669681] : [-(c_Enum_Osublists(_1669681, c_List_Olist_ONil(_1669681)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1669681)), c_List_Olist_ONil(_1669681)), c_List_Olist_ONil(tc_List_Olist(_1669681))))], (52148 ^ _779999) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (5566 ^ _779999) ^ [_865234, _865236] : [_865236 = _865234, -(c_Orderings_Otop__class_Otop(_865236) = c_Orderings_Otop__class_Otop(_865234))], (22407 ^ _779999) ^ [_1194524, _1194526, _1194528, _1194530, _1194532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194524), hAPP(c_Set_Oimage(_1194526, _1194524, _1194528), c_Orderings_Otop__class_Otop(tc_fun(_1194526, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1194530), hAPP(c_Set_Oimage(_1194526, _1194530, hAPP(hAPP(c_COMBB(_1194524, _1194530, _1194526), _1194532), _1194528)), c_Orderings_Otop__class_Otop(tc_fun(_1194526, tc_HOL_Obool))))))], (1414 ^ _779999) ^ [_800782, _800784] : [-(class_Orderings_Owellorder(_800782)), _800784 = _800782, class_Orderings_Owellorder(_800784)], (48625 ^ _779999) ^ [_1758855, _1758857, _1758859] : [hBOOL(hAPP(c_List_Odistinct(_1758855), _1758857)), -(hBOOL(hAPP(c_List_Odistinct(_1758855), c_List_OtakeWhile(_1758855, _1758859, _1758857))))], (7070 ^ _779999) ^ [_896181, _896183] : [class_Enum_Oenum(_896181), 7073 ^ _779999 : [(7080 ^ _779999) ^ [] : [hBOOL(hAPP(_896183, 7081 ^ [_896181, _896183])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_896181), _896183)))], (7074 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_896181), _896183)), 7077 ^ _779999 : [(7078 ^ _779999) ^ [_896307] : [-(hBOOL(hAPP(_896183, _896307)))]]]]], (6419 ^ _779999) ^ [_883454, _883456, _883458, _883460] : [class_Lattices_Osemilattice__sup(_883454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883454), _883456), _883458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883454), _883456), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_883454), _883460), _883458))))], (25754 ^ _779999) ^ [_1262655, _1262657, _1262659] : [class_Groups_Oab__group__add(_1262655), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1262655), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262655), _1262657), _1262659)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262655), _1262659), _1262657))], (52146 ^ _779999) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (47426 ^ _779999) ^ [_1733644] : [-(c_List_Otranspose(_1733644, c_List_Olist_ONil(tc_List_Olist(_1733644))) = c_List_Olist_ONil(tc_List_Olist(_1733644)))], (7972 ^ _779999) ^ [_914425, _914427, _914429, _914431, _914433] : [class_Groups_Ominus(_914425), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914427, _914425)), _914429), _914431), _914433) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_914425), hAPP(_914429, _914433)), hAPP(_914431, _914433)))], (33153 ^ _779999) ^ [_1401070] : [-(c_Int_Opred(_1401070) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1401070), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37815 ^ _779999) ^ [_1500614, _1500616, _1500618, _1500620, _1500622, _1500624] : [c_Typedef_Otype__definition(_1500614, _1500616, _1500618, _1500620, _1500622), hBOOL(hAPP(hAPP(c_member(_1500616), _1500624), _1500622)), -(hAPP(_1500618, hAPP(_1500620, _1500624)) = _1500624)], (10884 ^ _779999) ^ [_968291, _968293, _968295, _968297] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968291, tc_HOL_Obool)), _968293), _968295), _968297)), 10887 ^ _779999 : [(10890 ^ _779999) ^ [] : [-(hBOOL(hAPP(_968295, _968297)))], (10888 ^ _779999) ^ [] : [-(hBOOL(hAPP(_968293, _968297)))]]], (45785 ^ _779999) ^ [_1697024, _1697026] : [class_Complete__Lattice_Ocomplete__lattice(_1697024), -(c_Complete__Lattice_OSup__class_OSup(_1697024, hAPP(c_List_Oset(_1697024), _1697026)) = hAPP(c_List_Ofoldl(_1697024, _1697024, c_Lattices_Osemilattice__sup__class_Osup(_1697024), c_Orderings_Obot__class_Obot(_1697024)), _1697026))], (43737 ^ _779999) ^ [_1649379, _1649381, _1649383, _1649385] : [-(hAPP(hAPP(c_List_Otake(_1649379), hAPP(c_Nat_OSuc, _1649381)), hAPP(hAPP(c_List_Olist_OCons(_1649379), _1649383), _1649385)) = hAPP(hAPP(c_List_Olist_OCons(_1649379), _1649383), hAPP(hAPP(c_List_Otake(_1649379), _1649381), _1649385)))], (47510 ^ _779999) ^ [_1735353, _1735355, _1735357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735355))), c_List_Otranspose(_1735355, _1735357)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1735355)), c_List_Otranspose(_1735355, _1735357)), _1735353) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735355), _1735355), hAPP(hAPP(c_COMBC(tc_List_Olist(_1735355), tc_Nat_Onat, _1735355), c_List_Onth(_1735355)), _1735353)), hAPP(c_List_Ofilter(tc_List_Olist(_1735355), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1735355)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735353)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735355)))), _1735357)))], (25872 ^ _779999) ^ [_1264994, _1264996, _1264998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264994, tc_HOL_Obool)), _1264996), _1264998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264994, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264994, tc_HOL_Obool)), _1264998)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264994, tc_HOL_Obool)), _1264996))))], (43177 ^ _779999) ^ [_1632928, _1632930, _1632932, _1632934] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632928), tc_List_Olist(_1632928))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632928), tc_List_Olist(_1632928)), _1632930), _1632932)), c_List_Olex(_1632928, _1632934)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632928), tc_List_Olist(_1632928))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632928), tc_List_Olist(_1632928)), _1632930), _1632932)), c_List_Olexord(_1632928, _1632934))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632928)), _1632930) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632928)), _1632932)], (49742 ^ _779999) ^ [_1783560, _1783562, _1783564, _1783566, _1783568] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1783560), _1783562), _1783564), _1783566), _1783568) = c_New__DSequence_Oneg__single(_1783560, _1783562))], (49936 ^ _779999) ^ [_1788311, _1788313, _1788315, _1788317] : [49937 ^ _779999 : [(49940 ^ _779999) ^ [] : [_1788313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49938 ^ _779999) ^ [] : [hBOOL(hAPP(_1788317, _1788315))]], 49941 ^ _779999 : [(49942 ^ _779999) ^ [_1788436] : [hBOOL(hAPP(hAPP(c_member(_1788311), _1788436), hAPP(c_List_Oset(_1788311), c_List_Oreplicate(_1788311, _1788313, _1788315)))), -(hBOOL(hAPP(_1788317, _1788436)))]]], (36999 ^ _779999) ^ [_1479042, _1479044, _1479046, _1479048, _1479050, _1479052, _1479054, _1479056, _1479058] : [c_Equiv__Relations_Oequiv(_1479042, _1479044, _1479046), c_Equiv__Relations_Oequiv(_1479048, _1479050, _1479052), c_Equiv__Relations_Ocongruent2(_1479042, _1479048, tc_fun(_1479054, tc_HOL_Obool), _1479046, _1479052, _1479056), hBOOL(hAPP(hAPP(c_member(_1479048), _1479058), _1479050)), -(c_Equiv__Relations_Ocongruent(_1479042, tc_fun(_1479054, tc_HOL_Obool), _1479046, hAPP(hAPP(c_COMBB(tc_fun(_1479048, tc_fun(_1479054, tc_HOL_Obool)), tc_fun(_1479054, tc_HOL_Obool), _1479042), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479048, tc_fun(_1479054, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1479048, _1479048, _1479052), hAPP(hAPP(c_Set_Oinsert(_1479048), _1479058), c_Orderings_Obot__class_Obot(tc_fun(_1479048, tc_HOL_Obool)))))), _1479056)))], (6897 ^ _779999) ^ [_893197, _893199, _893201, _893203, _893205] : [hAPP(hAPP(c_Set_Oinsert(_893197), _893199), hAPP(hAPP(c_Set_Oinsert(_893197), _893201), c_Orderings_Obot__class_Obot(tc_fun(_893197, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_893197), _893203), hAPP(hAPP(c_Set_Oinsert(_893197), _893205), c_Orderings_Obot__class_Obot(tc_fun(_893197, tc_HOL_Obool)))), 6902 ^ _779999 : [(6905 ^ _779999) ^ [] : [-(_893201 = _893205)], (6903 ^ _779999) ^ [] : [-(_893199 = _893203)]], 6906 ^ _779999 : [(6909 ^ _779999) ^ [] : [-(_893201 = _893203)], (6907 ^ _779999) ^ [] : [-(_893199 = _893205)]]], (43979 ^ _779999) ^ [_1656819, _1656821, _1656823, _1656825] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656819, _1656819)), hAPP(hAPP(c_Product__Type_OPair(_1656819, _1656819), _1656821), _1656823)), hAPP(c_List_Oset(tc_prod(_1656819, _1656819)), hAPP(hAPP(c_List_Ozip(_1656819, _1656819), _1656825), _1656825)))), 43982 ^ _779999 : [(43985 ^ _779999) ^ [] : [-(_1656821 = _1656823)], (43983 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656819), _1656821), hAPP(c_List_Oset(_1656819), _1656825))))]]], (52266 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (8538 ^ _779999) ^ [_926065, _926067] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926065), _926067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926067), _926065) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_926065 = _926067)], (50066 ^ _779999) ^ [_1790578, _1790580, _1790582, _1790584] : [-(hAPP(c_New__DSequence_Opos__union(_1790578, _1790580, _1790582), _1790584) = c_Lazy__Sequence_Oappend(_1790578, hAPP(_1790580, _1790584), hAPP(_1790582, _1790584)))], (3720 ^ _779999) ^ [_835823, _835825] : [_835825 = _835823, -(c_List_Otranspose__rel(_835825) = c_List_Otranspose__rel(_835823))], (2614 ^ _779999) ^ [_818622, _818624, _818626, _818628] : [-(c_Set_Othe__elem(_818628, _818624) = c_Set_Othe__elem(_818626, _818622)), _818628 = _818626, _818624 = _818622], (12359 ^ _779999) ^ [_998868, _998870] : [class_Lattices_Olattice(_998868), hBOOL(hAPP(c_Finite__Set_Ofinite(_998868), _998870)), -(_998870 = c_Orderings_Obot__class_Obot(tc_fun(_998868, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998868), c_Big__Operators_Olattice__class_OInf__fin(_998868, _998870)), c_Big__Operators_Olattice__class_OSup__fin(_998868, _998870))))], (50084 ^ _779999) ^ [_1790881] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1790881) = c_Lazy__Sequence_Osmall__lazy_H(_1790881, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1790881)))], (40982 ^ _779999) ^ [_1580121, _1580123, _1580125] : [-(hAPP(hAPP(c_Nat_Ocompow(_1580121, _1580121), hAPP(c_Nat_OSuc, _1580123)), _1580125) = hAPP(c_Fun_Ocomp(_1580121, _1580121, _1580121, _1580125), hAPP(hAPP(c_Nat_Ocompow(_1580121, _1580121), _1580123), _1580125)))], (22123 ^ _779999) ^ [_1188993, _1188995, _1188997, _1188999] : [hBOOL(hAPP(hAPP(c_member(_1188995), _1188999), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1188993, tc_fun(_1188995, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1188993, tc_HOL_Obool))), _1188997))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1188993, tc_fun(_1188995, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1188993, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1188995, tc_HOL_Obool), tc_fun(_1188995, tc_HOL_Obool), _1188993), hAPP(c_COMBC(_1188995, tc_fun(_1188995, tc_HOL_Obool), tc_HOL_Obool), c_member(_1188995))), _1188997)), _1188999)))], (42699 ^ _779999) ^ [_1620951, _1620953, _1620955] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1620951, tc_HOL_Obool)), _1620953)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620951), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620951, tc_HOL_Obool), _1620953))), 42709 ^ _779999 : [(42712 ^ _779999) ^ [] : [hAPP(c_Finite__Set_Ocard(_1620951), 42708 ^ [_1620951, _1620953, _1620955]) = _1620955], (42710 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1620951, tc_HOL_Obool)), 42708 ^ [_1620951, _1620953, _1620955]), _1620953)))]], 42716 ^ _779999 : [(42720 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1620951, tc_HOL_Obool)), 42718 ^ [_1620951, _1620953, _1620955]), _1620953)))], (42722 ^ _779999) ^ [] : [42715 ^ [_1620951, _1620953, _1620955] = 42718 ^ [_1620951, _1620953, _1620955]], (42724 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620951, tc_HOL_Obool)), 42715 ^ [_1620951, _1620953, _1620955]), 42718 ^ [_1620951, _1620953, _1620955]) = c_Orderings_Obot__class_Obot(tc_fun(_1620951, tc_HOL_Obool))], (42717 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1620951, tc_HOL_Obool)), 42715 ^ [_1620951, _1620953, _1620955]), _1620953)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1620955), hAPP(c_Finite__Set_Ocard(tc_fun(_1620951, tc_HOL_Obool)), _1620953)) = hAPP(c_Finite__Set_Ocard(_1620951), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620951, tc_HOL_Obool), _1620953)))], (27458 ^ _779999) ^ [_1296631, _1296633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296631)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296633)))), 27461 ^ _779999 : [(27464 ^ _779999) ^ [] : [-(_1296633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27462 ^ _779999) ^ [] : [-(_1296631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29970 ^ _779999) ^ [_1341830, _1341832] : [class_Int_Oring__char__0(_1341830), 29973 ^ _779999 : [(29980 ^ _779999) ^ [] : [_1341832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1341830) = hAPP(c_Int_Oring__1__class_Oof__int(_1341830), _1341832))], (29974 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_1341830) = hAPP(c_Int_Oring__1__class_Oof__int(_1341830), _1341832), -(_1341832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25000 ^ _779999) ^ [_1249269, _1249271] : [class_Orderings_Olinorder(_1249269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249269), _1249271)), -(c_Big__Operators_Olattice_OSup__fin(_1249269, c_Orderings_Oord__class_Omax(_1249269), _1249271) = hAPP(c_Finite__Set_Ofold1(_1249269, c_Orderings_Oord__class_Omax(_1249269)), _1249271))], (9606 ^ _779999) ^ [_943260, _943262, _943264] : [9607 ^ _779999 : [(9610 ^ _779999) ^ [] : [_943262 = _943264], (9608 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943260, tc_HOL_Obool)), _943262), _943264))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943260, tc_HOL_Obool)), _943262), _943264)))], (46444 ^ _779999) ^ [_1711344, _1711346, _1711348, _1711350] : [class_Rings_Osemiring__1(_1711344), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711344), hAPP(hAPP(c_List_Omap(_1711346, _1711344), hAPP(c_COMBK(_1711344, _1711346), _1711348)), _1711350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1711344), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1711344), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711346)), _1711350))), _1711348))], (40337 ^ _779999) ^ [_1564743, _1564745] : [-(c_Transitive__Closure_Ortrancl(_1564743, c_Transitive__Closure_Ortrancl(_1564743, _1564745)) = c_Transitive__Closure_Ortrancl(_1564743, _1564745))], (42041 ^ _779999) ^ [_1605469, _1605471, _1605473, _1605475, _1605477] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605469, tc_fun(_1605471, tc_HOL_Obool)), _1605473), hAPP(hAPP(c_COMBB(tc_fun(_1605471, tc_HOL_Obool), tc_fun(_1605471, tc_HOL_Obool), _1605469), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605471, tc_HOL_Obool)), _1605475)), _1605477)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605471, tc_HOL_Obool)), _1605475), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605469, tc_fun(_1605471, tc_HOL_Obool)), _1605473), _1605477)))], (45648 ^ _779999) ^ [_1694180, _1694182, _1694184] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694180)), hAPP(c_List_Orotate(_1694180, _1694182), _1694184)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694180)), _1694184))], (11074 ^ _779999) ^ [_971823, _971825, _971827, _971829, _971831] : [class_Lattices_Olattice(_971823), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971825, _971823)), _971827), _971829), _971831) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971823), hAPP(_971827, _971831)), hAPP(_971829, _971831)))], (2114 ^ _779999) ^ [_810786, _810788, _810790, _810792, _810794, _810796, _810798, _810800, _810802, _810804] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_810804, _810800, _810796, _810792, _810788) = c_SetInterval_Oord_OgreaterThanAtMost(_810802, _810798, _810794, _810790, _810786)), _810804 = _810802, _810800 = _810798, _810796 = _810794, _810792 = _810790, _810788 = _810786], (14201 ^ _779999) ^ [_1033426, _1033428, _1033430] : [class_Groups_Oordered__comm__monoid__add(_1033426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033426), _1033428), c_Groups_Ozero__class_Ozero(_1033426))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033426), _1033430), c_Groups_Ozero__class_Ozero(_1033426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033426), _1033428), _1033430)), c_Groups_Ozero__class_Ozero(_1033426))))], (35659 ^ _779999) ^ [_1451647, _1451649, _1451651, _1451653, _1451655, _1451657] : [hAPP(hAPP(c_Product__Type_OPair(_1451647, _1451649), _1451651), _1451653) = hAPP(hAPP(c_Product__Type_OPair(_1451647, _1451649), _1451655), _1451657), 35662 ^ _779999 : [(35665 ^ _779999) ^ [] : [-(_1451653 = _1451657)], (35663 ^ _779999) ^ [] : [-(_1451651 = _1451655)]]], (52004 ^ _779999) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (14013 ^ _779999) ^ [_1029776, _1029778, _1029780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029776), _1029778)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029778), _1029776)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029780), _1029778)), _1029776))], (6643 ^ _779999) ^ [_888196, _888198, _888200, _888202, _888204] : [c_Hoare__Mirabelle_Otriple__valid(_888196, _888198, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888196), _888200), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888202))), _888204)), -(c_Hoare__Mirabelle_Otriple__valid(_888196, hAPP(c_Nat_OSuc, _888198), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_888196), _888200), hAPP(c_Com_Ocom_OBODY, _888202)), _888204)))], (15855 ^ _779999) ^ [_1065843, _1065845, _1065847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1065843), _1065845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065847), _1065843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065847), _1065845))))], (23435 ^ _779999) ^ [_1217400, _1217402, _1217404, _1217406, _1217408] : [-(hAPP(c_Set_Ovimage(_1217400, _1217402, _1217404), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1217402, tc_HOL_Obool)), _1217406), _1217408)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1217400, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1217400, _1217402, _1217404), _1217406)), hAPP(c_Set_Ovimage(_1217400, _1217402, _1217404), _1217408)))], (51900 ^ _779999) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (29316 ^ _779999) ^ [_1330837] : [class_Power_Opower(_1330837), -(c_Power_Opower__class_Opower(_1330837) = c_Power_Opower_Opower(_1330837, c_Groups_Oone__class_Oone(_1330837), c_Groups_Otimes__class_Otimes(_1330837)))], (30663 ^ _779999) ^ [_1354876, _1354878, _1354880, _1354882] : [class_Divides_Osemiring__div(_1354876), -(c_Divides_Odiv__class_Omod(_1354876, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354876), _1354878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354876), _1354880), _1354882)), _1354880) = c_Divides_Odiv__class_Omod(_1354876, _1354878, _1354880))], (10203 ^ _779999) ^ [_955751, _955753] : [10204 ^ _779999 : [(10207 ^ _779999) ^ [] : [_955751 = _955753], (10205 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955751), _955753))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955751), hAPP(c_Nat_OSuc, _955753))))], (38964 ^ _779999) ^ [_1531734, _1531736, _1531738] : [c_Wellfounded_OwfP(_1531734, _1531736), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1531734, _1531736), _1531738)))], (17291 ^ _779999) ^ [_1093517, _1093519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1093517), _1093519))))], (41634 ^ _779999) ^ [_1594630, _1594632, _1594634, _1594636, _1594638] : [c_Finite__Set_Ofun__left__comm(_1594630, _1594632, _1594634), -(hAPP(c_Fun_Ocomp(_1594632, _1594632, _1594632, hAPP(_1594634, _1594636)), hAPP(_1594634, _1594638)) = hAPP(c_Fun_Ocomp(_1594632, _1594632, _1594632, hAPP(_1594634, _1594638)), hAPP(_1594634, _1594636)))], (22779 ^ _779999) ^ [_1202624, _1202626, _1202628, _1202630, _1202632] : [-(hBOOL(hAPP(hAPP(c_member(_1202624), _1202626), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1202628, tc_fun(_1202624, tc_HOL_Obool)), _1202630), _1202632)))), 22780 ^ _779999 : [(22781 ^ _779999) ^ [_1202706] : [hBOOL(hAPP(hAPP(c_member(_1202628), _1202706), _1202630)), hBOOL(hAPP(hAPP(c_member(_1202624), _1202626), hAPP(_1202632, _1202706)))]]], (25251 ^ _779999) ^ [_1254014] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1254014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254014)))], (23495 ^ _779999) ^ [_1218803, _1218805, _1218807] : [class_Orderings_Olinorder(_1218803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218803), _1218805)), hBOOL(hAPP(hAPP(c_member(_1218803), _1218807), _1218805)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1218803), _1218807), c_Big__Operators_Olinorder__class_OMin(_1218803, _1218805)) = c_Big__Operators_Olinorder__class_OMin(_1218803, _1218805))], (43821 ^ _779999) ^ [_1651618, _1651620, _1651622, _1651624, _1651626] : [hBOOL(hAPP(hAPP(c_member(_1651618), _1651620), hAPP(c_List_Oset(_1651618), _1651622))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651624), hAPP(_1651626, _1651620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651624), c_List_Olist_Olist__size(_1651618, _1651626, _1651622))))], (21758 ^ _779999) ^ [_1176826, _1176828] : [-(hAPP(c_Set_OCollect(_1176826), hAPP(hAPP(c_COMBC(_1176826, _1176826, tc_HOL_Obool), c_fequal), _1176828)) = hAPP(hAPP(c_Set_Oinsert(_1176826), _1176828), c_Orderings_Obot__class_Obot(tc_fun(_1176826, tc_HOL_Obool))))], (43802 ^ _779999) ^ [_1651136, _1651138, _1651140] : [43804 ^ _779999 : [(43807 ^ _779999) ^ [] : [hBOOL(hAPP(_1651140, hAPP(hAPP(c_List_Onth(_1651136), _1651138), 43803 ^ [_1651136, _1651138, _1651140])))], (43805 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43803 ^ [_1651136, _1651138, _1651140]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651136)), _1651138))))]], 43808 ^ _779999 : [(43809 ^ _779999) ^ [_1651338] : [hBOOL(hAPP(hAPP(c_member(_1651136), _1651338), hAPP(c_List_Oset(_1651136), _1651138))), -(hBOOL(hAPP(_1651140, _1651338)))]]], (45965 ^ _779999) ^ [_1700965, _1700967, _1700969, _1700971, _1700973] : [class_Orderings_Olinorder(_1700965), -(hBOOL(hAPP(hAPP(c_member(_1700965), hAPP(_1700967, _1700969)), hAPP(c_Set_Oimage(_1700971, _1700965, _1700967), hAPP(c_List_Oset(_1700971), _1700973))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1700971, _1700965, _1700967, _1700969, _1700973) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700971, _1700965, _1700967), _1700969), _1700973))], (39187 ^ _779999) ^ [_1536348, _1536350, _1536352] : [-(c_Relation_Orefl__on(_1536348, _1536350, _1536352)), 39191 ^ _779999 : [(39194 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1536348, _1536348, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1536348, tc_fun(_1536348, tc_HOL_Obool), tc_fun(_1536348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536348, tc_HOL_Obool), tc_fun(_1536348, tc_HOL_Obool)), _1536348), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536348)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536348), c_fconj), hAPP(hAPP(c_COMBC(_1536348, tc_fun(_1536348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536348)), _1536350)))), hAPP(hAPP(c_COMBC(_1536348, tc_fun(_1536348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536348)), _1536350))), 39190 ^ [_1536348, _1536350, _1536352]))], (39192 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536348, _1536348)), 39190 ^ [_1536348, _1536350, _1536352]), _1536352)))]], 39196 ^ _779999 : [(39199 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536348, _1536348)), hAPP(hAPP(c_Product__Type_OPair(_1536348, _1536348), 39195 ^ [_1536348, _1536350, _1536352]), 39195 ^ [_1536348, _1536350, _1536352])), _1536352))], (39197 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536348), 39195 ^ [_1536348, _1536350, _1536352]), _1536350)))]]], (11118 ^ _779999) ^ [_972661, _972663, _972665] : [class_Lattices_Osemilattice__inf(_972661), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972661), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972661), _972663), _972665)), _972665)))], (38811 ^ _779999) ^ [_1527863, _1527865, _1527867, _1527869] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527863), _1527865)), 38817 ^ _779999 : [(38820 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527867), hAPP(_1527869, 38816 ^ [_1527863, _1527865, _1527867, _1527869])))], (38818 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527863), 38816 ^ [_1527863, _1527865, _1527867, _1527869]), _1527865)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1527863, _1527867)), hAPP(hAPP(c_Product__Type_OSigma(_1527863, _1527867), _1527865), _1527869))))], (43119 ^ _779999) ^ [_1630744, _1630746, _1630748, _1630750, _1630752, _1630754] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1630744, _1630746, _1630748), _1630750), hAPP(hAPP(c_Product__Type_OPair(_1630744, _1630746), _1630752), _1630754)) = hAPP(hAPP(_1630750, _1630752), _1630754))], (18173 ^ _779999) ^ [_1110788, _1110790, _1110792] : [class_Rings_Olinordered__semidom(_1110788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110788), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110788), _1110790)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110788), _1110792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110790), _1110792)))], (43895 ^ _779999) ^ [_1653391, _1653393, _1653395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1653391), _1653393)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1653391)), hAPP(c_Set_OCollect(tc_List_Olist(_1653391)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1653391), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1653391)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1653391), tc_fun(_1653391, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1653391, tc_HOL_Obool), tc_fun(tc_fun(_1653391, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1653391)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1653391, tc_HOL_Obool))), c_List_Oset(_1653391))), _1653393))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1653391), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1653391)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1653391)))), _1653395))))))], (3570 ^ _779999) ^ [_833540, _833542, _833544, _833546] : [-(c_Random_Oselect(_833546, _833542) = c_Random_Oselect(_833544, _833540)), _833546 = _833544, _833542 = _833540], (46838 ^ _779999) ^ [_1719625, _1719627, _1719629, _1719631] : [hBOOL(hAPP(c_List_Olistsp(_1719625, _1719627), hAPP(hAPP(c_List_Oappend(_1719625), _1719629), _1719631))), 46841 ^ _779999 : [(46844 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1719625, _1719627), _1719631)))], (46842 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1719625, _1719627), _1719629)))]]], (47842 ^ _779999) ^ [_1743512, _1743514] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1743512, _1743514)))], (44634 ^ _779999) ^ [_1670764, _1670766, _1670768] : [_1670764 = c_List_Olist_ONil(_1670766), -(c_List_Obutlast(_1670766, hAPP(hAPP(c_List_Olist_OCons(_1670766), _1670768), _1670764)) = c_List_Olist_ONil(_1670766))], (31849 ^ _779999) ^ [_1377291, _1377293, _1377295] : [class_Int_Onumber__ring(_1377291), class_Rings_Olinordered__idom(_1377291), 31856 ^ _779999 : [(31863 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1377293), _1377295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377291), hAPP(c_Int_Onumber__class_Onumber__of(_1377291), _1377293)), hAPP(c_Int_Onumber__class_Onumber__of(_1377291), _1377295))))], (31857 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377291), hAPP(c_Int_Onumber__class_Onumber__of(_1377291), _1377293)), hAPP(c_Int_Onumber__class_Onumber__of(_1377291), _1377295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1377293), _1377295)))]]], (20150 ^ _779999) ^ [_1147063, _1147065, _1147067] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1147063), _1147065), _1147067) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1147063), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1147063, tc_Int_Oint), _1147065), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1147067))), class_Groups_Ocomm__monoid__add(_1147063), class_Groups_Ocomm__monoid__mult(_1147063)], (27872 ^ _779999) ^ [_1303884, _1303886, _1303888, _1303890] : [class_Groups_Omonoid__mult(_1303884), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303884), _1303886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1303888), _1303890)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303884), hAPP(hAPP(c_Power_Opower__class_Opower(_1303884), _1303886), _1303888)), hAPP(hAPP(c_Power_Opower__class_Opower(_1303884), _1303886), _1303890)))], (8710 ^ _779999) ^ [_929113, _929115] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _929113), _929115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _929113)), _929115)))], (21849 ^ _779999) ^ [_1180064, _1180066, _1180068, _1180070] : [hBOOL(hAPP(hAPP(c_member(_1180064), _1180066), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1180064, tc_HOL_Obool), _1180068))), c_Orderings_Oorder__class_Omono(tc_fun(_1180064, tc_HOL_Obool), tc_fun(_1180064, tc_HOL_Obool), _1180068), 21859 ^ _779999 : [(21862 ^ _779999) ^ [] : [hBOOL(hAPP(_1180070, 21858 ^ [_1180064, _1180066, _1180068, _1180070]))], (21860 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180064), 21858 ^ [_1180064, _1180066, _1180068, _1180070]), hAPP(_1180068, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1180064, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1180064, tc_HOL_Obool), _1180068)), hAPP(c_Set_OCollect(_1180064), _1180070))))))]], -(hBOOL(hAPP(_1180070, _1180066)))], (21574 ^ _779999) ^ [_1172799, _1172801] : [class_Groups_Oab__semigroup__mult(_1172799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172799), _1172801)), -(_1172801 = c_Orderings_Obot__class_Obot(tc_fun(_1172799, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1172799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172799), 21587 ^ [_1172799, _1172801]), 21588 ^ [_1172799, _1172801])), hAPP(hAPP(c_Set_Oinsert(_1172799), 21587 ^ [_1172799, _1172801]), hAPP(hAPP(c_Set_Oinsert(_1172799), 21588 ^ [_1172799, _1172801]), c_Orderings_Obot__class_Obot(tc_fun(_1172799, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1172799), hAPP(c_Finite__Set_Ofold1(_1172799, c_Groups_Otimes__class_Otimes(_1172799)), _1172801)), _1172801)))], (51928 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (21980 ^ _779999) ^ [_1183918] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1183918) = 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), _1183918), c_Int_Onat)))))], (45043 ^ _779999) ^ [_1680199, _1680201, _1680203, _1680205, _1680207, _1680209] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680199)), _1680201) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680203)), _1680205), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680199)), _1680207) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680203)), _1680209), -(hAPP(hAPP(c_List_Ozip(_1680199, _1680203), hAPP(hAPP(c_List_Oappend(_1680199), _1680201), _1680207)), hAPP(hAPP(c_List_Oappend(_1680203), _1680205), _1680209)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1680199, _1680203)), hAPP(hAPP(c_List_Ozip(_1680199, _1680203), _1680201), _1680205)), hAPP(hAPP(c_List_Ozip(_1680199, _1680203), _1680207), _1680209)))], (49748 ^ _779999) ^ [_1783707, _1783709, _1783711, _1783713, _1783715] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1783707), _1783709), _1783711), _1783713), _1783715) = c_New__DSequence_Opos__single(_1783707, _1783709))], (42819 ^ _779999) ^ [_1623826, _1623828, _1623830, _1623832] : [class_Orderings_Olinorder(_1623826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623826), _1623828)), 42829 ^ _779999 : [(42832 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1623826), 42828 ^ [_1623826, _1623828, _1623830, _1623832]), _1623830))], (42830 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623826), 42828 ^ [_1623826, _1623828, _1623830, _1623832]), _1623828)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1623826), hAPP(hAPP(c_Finite__Set_Ofold(_1623826, _1623826, c_Orderings_Oord__class_Omax(_1623826)), _1623832), _1623828)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1623826), _1623830), _1623832))))], (6609 ^ _779999) ^ [_887163, _887165] : [class_Lattices_Olattice(_887163), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_887163), _887165), _887165) = _887165)], (20100 ^ _779999) ^ [_1146293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146293)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1146293)) = _1146293)], (23303 ^ _779999) ^ [_1214775, _1214777, _1214779, _1214781] : [class_Orderings_Olinorder(_1214775), 23306 ^ _779999 : [(23315 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214775), _1214779), _1214781)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), _1214779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), _1214781))], (23307 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214775), _1214779), _1214781))), 23310 ^ _779999 : [(23313 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), _1214781)))], (23311 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214775), _1214777), _1214779)))]]]]], (33487 ^ _779999) ^ [_1406353, _1406355] : [class_Int_Onumber__ring(_1406353), class_Rings_Olinordered__idom(_1406353), 33494 ^ _779999 : [(33501 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1406355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406353), c_Groups_Oone__class_Oone(_1406353)), hAPP(c_Int_Onumber__class_Onumber__of(_1406353), _1406355))))], (33495 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406353), c_Groups_Oone__class_Oone(_1406353)), hAPP(c_Int_Onumber__class_Onumber__of(_1406353), _1406355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1406355)))]]], (42919 ^ _779999) ^ [_1626165, _1626167] : [-(c_Wellfounded_Owf(_1626165, _1626167)), 42922 ^ _779999 : [(42925 ^ _779999) ^ [_1626385] : [hBOOL(hAPP(hAPP(c_member(_1626165), _1626385), 42920 ^ [_1626165, _1626167])), 42929 ^ _779999 : [(42932 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626165), 42928 ^ [_1626165, _1626167, _1626385]), 42920 ^ [_1626165, _1626167])))], (42930 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626165, _1626165)), hAPP(hAPP(c_Product__Type_OPair(_1626165, _1626165), 42928 ^ [_1626165, _1626167, _1626385]), _1626385)), _1626167)))]]], (42923 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626165), 42921 ^ [_1626165, _1626167]), 42920 ^ [_1626165, _1626167])))]]], (31611 ^ _779999) ^ [_1372776, _1372778, _1372780, _1372782] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1372776, tc_HOL_Obool)), _1372778), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372776), _1372780), _1372782))), 31615 ^ _779999 : [(31618 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372776), 31614 ^ [_1372776, _1372778, _1372780, _1372782]), _1372780)))], (31616 ^ _779999) ^ [] : [-(_1372778 = hAPP(c_Relation_OImage(_1372776, _1372776, _1372782), hAPP(hAPP(c_Set_Oinsert(_1372776), 31614 ^ [_1372776, _1372778, _1372780, _1372782]), c_Orderings_Obot__class_Obot(tc_fun(_1372776, tc_HOL_Obool)))))]]], (41889 ^ _779999) ^ [_1600384, _1600386, _1600388, _1600390] : [hBOOL(hAPP(hAPP(c_member(_1600386), _1600390), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600384, tc_fun(_1600386, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1600384, tc_HOL_Obool))), _1600388))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600384, tc_fun(_1600386, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1600384, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1600386, tc_HOL_Obool), tc_fun(_1600386, tc_HOL_Obool), _1600384), hAPP(c_COMBC(_1600386, tc_fun(_1600386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1600386))), _1600388)), _1600390)))], (48778 ^ _779999) ^ [_1761971, _1761973, _1761975, _1761977] : [-(hBOOL(hAPP(_1761971, _1761973))), -(c_List_OdropWhile(_1761975, _1761971, hAPP(hAPP(c_List_Olist_OCons(_1761975), _1761973), _1761977)) = hAPP(hAPP(c_List_Olist_OCons(_1761975), _1761973), _1761977))], (26468 ^ _779999) ^ [_1275842, _1275844, _1275846] : [class_Groups_Oordered__ab__group__add__abs(_1275842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275842), _1275844), _1275846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275842), hAPP(c_Groups_Ouminus__class_Ouminus(_1275842), _1275844)), _1275846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275842), hAPP(c_Groups_Oabs__class_Oabs(_1275842), _1275844)), _1275846)))], (39513 ^ _779999) ^ [_1544453, _1544455, _1544457, _1544459, _1544461, _1544463] : [class_Groups_Ocomm__monoid__add(_1544453), c_Fun_Oinj__on(_1544455, _1544457, _1544459, _1544461), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544457, _1544453), _1544463), hAPP(c_Set_Oimage(_1544455, _1544457, _1544459), _1544461)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544455, _1544453), hAPP(c_Fun_Ocomp(_1544457, _1544453, _1544455, _1544463), _1544459)), _1544461))], (41192 ^ _779999) ^ [_1585588, _1585590, _1585592, _1585594, _1585596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585588, _1585588)), hAPP(hAPP(c_Product__Type_OPair(_1585588, _1585588), _1585590), _1585592)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585588, _1585588), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585594)), _1585596))), 41196 ^ _779999 : [(41199 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585588, _1585588)), hAPP(hAPP(c_Product__Type_OPair(_1585588, _1585588), 41195 ^ [_1585588, _1585590, _1585592, _1585594, _1585596]), _1585592)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585588, _1585588), tc_HOL_Obool), _1585594), _1585596))))], (41197 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585588, _1585588)), hAPP(hAPP(c_Product__Type_OPair(_1585588, _1585588), _1585590), 41195 ^ [_1585588, _1585590, _1585592, _1585594, _1585596])), _1585596)))]]], (39741 ^ _779999) ^ [_1549727, _1549729, _1549731, _1549733] : [c_Finite__Set_Ofolding(_1549727, _1549729, _1549731, _1549733), -(hAPP(_1549733, c_Orderings_Obot__class_Obot(tc_fun(_1549727, tc_HOL_Obool))) = c_Fun_Oid(_1549729))], (39129 ^ _779999) ^ [_1535127, _1535129] : [c_Nitpick_Owf_H(_1535127, _1535129), 39132 ^ _779999 : [(39135 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535127, _1535127)), _1535129))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (39133 ^ _779999) ^ [] : [-(c_Wellfounded_Oacyclic(_1535127, _1535129))]]], (46648 ^ _779999) ^ [_1715850] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1715850)) = _1715850)], (36290 ^ _779999) ^ [_1463404, _1463406, _1463408] : [36292 ^ _779999 : [(36295 ^ _779999) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1463404, _1463406), 36291 ^ [_1463404, _1463406, _1463408]))], (36293 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1463406, 36291 ^ [_1463404, _1463406, _1463408]), _1463408)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1463404, _1463406), _1463408)))], (14411 ^ _779999) ^ [_1037453, _1037455, _1037457] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037453), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037453, tc_HOL_Obool)), _1037455), _1037457))), -(hAPP(c_Finite__Set_Ocard(_1037453), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037453, tc_HOL_Obool)), _1037455), _1037457)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1037453), _1037455)), hAPP(c_Finite__Set_Ocard(_1037453), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037453, tc_HOL_Obool)), _1037455), _1037457))))], (40747 ^ _779999) ^ [_1573915, _1573917] : [c_Wellfounded_Owf(_1573915, hAPP(c_Relation_Oconverse(_1573915, _1573915), _1573917)), -(c_Wellfounded_Owf(_1573915, hAPP(c_Relation_Oconverse(_1573915, _1573915), c_Transitive__Closure_Otrancl(_1573915, _1573917))))], (49886 ^ _779999) ^ [_1787368, _1787370, _1787372, _1787374] : [-(hAPP(hAPP(c_List_Otake(_1787368), _1787370), c_List_Oreplicate(_1787368, _1787372, _1787374)) = c_List_Oreplicate(_1787368, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1787370), _1787372), _1787374))], (38592 ^ _779999) ^ [_1520956, _1520958, _1520960, _1520962, _1520964, _1520966] : [hBOOL(hAPP(hAPP(c_member(_1520956), _1520958), _1520960)), 38595 ^ _779999 : [(38602 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520962, tc_HOL_Obool)), _1520964), _1520966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520962, _1520956), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520962, _1520956), _1520964), hAPP(c_COMBK(tc_fun(_1520956, tc_HOL_Obool), _1520962), _1520960))), hAPP(hAPP(c_Product__Type_OSigma(_1520962, _1520956), _1520966), hAPP(c_COMBK(tc_fun(_1520956, tc_HOL_Obool), _1520962), _1520960)))))], (38596 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520962, _1520956), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520962, _1520956), _1520964), hAPP(c_COMBK(tc_fun(_1520956, tc_HOL_Obool), _1520962), _1520960))), hAPP(hAPP(c_Product__Type_OSigma(_1520962, _1520956), _1520966), hAPP(c_COMBK(tc_fun(_1520956, tc_HOL_Obool), _1520962), _1520960)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520962, tc_HOL_Obool)), _1520964), _1520966)))]]], (10847 ^ _779999) ^ [_967637, _967639, _967641, _967643] : [c_Partial__Function_Omk__less(_967637, _967639, _967641, _967643), 10850 ^ _779999 : [(10853 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_967639, _967643), _967641))], (10851 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_967639, _967641), _967643)))]]], (45002 ^ _779999) ^ [_1679219, _1679221, _1679223, _1679225] : [_1679223 = _1679225, -(hAPP(hAPP(c_List_Oappend(_1679219), _1679221), _1679223) = hAPP(hAPP(c_List_Oappend(_1679219), _1679221), _1679225))], (4882 ^ _779999) ^ [_854508, _854510, _854512, _854514] : [-(c_HOL_OThe(_854514, _854510) = c_HOL_OThe(_854512, _854508)), _854514 = _854512, _854510 = _854508], (17529 ^ _779999) ^ [_1098086, _1098088, _1098090, _1098092, _1098094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098086), _1098088)), 17532 ^ _779999 : [(17539 ^ _779999) ^ [] : [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), _1098088), _1098086)), _1098090)), _1098092)), _1098094)), -(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), _1098088), _1098090)), _1098092)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1098086), _1098090)), _1098094))))], (17533 ^ _779999) ^ [] : [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), _1098088), _1098090)), _1098092)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1098086), _1098090)), _1098094))), -(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), _1098088), _1098086)), _1098090)), _1098092)), _1098094)))]]], (51438 ^ _779999) ^ [_1820632, _1820634, _1820636, _1820638] : [c_Fun_Oinj__on(_1820632, _1820634, _1820636, c_Orderings_Otop__class_Otop(tc_fun(_1820632, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1820634, _1820632, c_Hilbert__Choice_Oinv__into(_1820632, _1820634, c_Orderings_Otop__class_Otop(tc_fun(_1820632, tc_HOL_Obool)), _1820636)), hAPP(c_Set_Oimage(_1820632, _1820634, _1820636), _1820638)) = _1820638)], (27318 ^ _779999) ^ [_1294091, _1294093] : [class_Rings_Odivision__ring(_1294091), -(_1294093 = c_Groups_Ozero__class_Ozero(_1294091)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294091), _1294093), _1294093) = c_Groups_Oone__class_Oone(_1294091))], (46332 ^ _779999) ^ [_1708815, _1708817, _1708819, _1708821, _1708823] : [-(hAPP(hAPP(c_List_Odrop(_1708815), _1708817), hAPP(hAPP(c_List_Omap(_1708819, _1708815), _1708821), _1708823)) = hAPP(hAPP(c_List_Omap(_1708819, _1708815), _1708821), hAPP(hAPP(c_List_Odrop(_1708819), _1708817), _1708823)))], (19880 ^ _779999) ^ [_1142655, _1142657, _1142659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142655)), 19886 ^ _779999 : [(19889 ^ _779999) ^ [] : [hBOOL(hAPP(_1142657, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19885 ^ [_1142655, _1142657, _1142659]), _1142655)))], (19887 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1142657, 19885 ^ [_1142655, _1142657, _1142659])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142659)), 19894 ^ _779999 : [(19895 ^ _779999) ^ [_1142944] : [hBOOL(hAPP(_1142657, _1142944)), -(hBOOL(hAPP(_1142657, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142659), _1142655)))))]]], (26284 ^ _779999) ^ [_1272621, _1272623] : [class_Groups_Ogroup__add(_1272621), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272621), _1272623), hAPP(c_Groups_Ouminus__class_Ouminus(_1272621), _1272623)) = c_Groups_Ozero__class_Ozero(_1272621))], (26793 ^ _779999) ^ [_1282713, _1282715] : [class_Groups_Oordered__ab__group__add(_1282713), -(hAPP(c_Set_Oimage(_1282713, _1282713, c_Groups_Ouminus__class_Ouminus(_1282713)), hAPP(c_SetInterval_Oord__class_OlessThan(_1282713), _1282715)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1282713), hAPP(c_Groups_Ouminus__class_Ouminus(_1282713), _1282715)))], (39358 ^ _779999) ^ [_1541079, _1541081, _1541083, _1541085, _1541087, _1541089] : [-(hAPP(hAPP(c_Fun_Ocomp(_1541079, _1541081, _1541083, hAPP(c_COMBK(_1541081, _1541079), _1541085)), _1541087), _1541089) = _1541085)], (37557 ^ _779999) ^ [_1493005, _1493007, _1493009, _1493011] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493005), _1493011) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493009), _1493007), -(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), _1493005), _1493007)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493009), _1493011))), c_Int_Ointrel)))], (800 ^ _779999) ^ [_792291, _792293, _792295, _792297] : [-(c_List_Olinorder__class_Osorted(_792295, _792291)), c_List_Olinorder__class_Osorted(_792297, _792293), _792297 = _792295, _792293 = _792291], (38738 ^ _779999) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (5194 ^ _779999) ^ [_859446, _859448] : [_859448 = _859446, -(c_Wellfounded_Ofinite__psubset(_859448) = c_Wellfounded_Ofinite__psubset(_859446))], (18830 ^ _779999) ^ [_1123676, _1123678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123676), _1123678)), -(_1123678 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123676), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18833 ^ [_1123676, _1123678])))], (37154 ^ _779999) ^ [_1483018, _1483020, _1483022, _1483024, _1483026, _1483028] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1483018, _1483020)), hAPP(hAPP(c_Product__Type_OPair(_1483018, _1483020), _1483022), _1483024)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1483018, _1483020), tc_HOL_Obool), _1483026))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1483018, _1483020), tc_HOL_Obool), tc_fun(tc_prod(_1483018, _1483020), tc_HOL_Obool), _1483026), 37165 ^ _779999 : [(37168 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1483028, 37163 ^ [_1483018, _1483020, _1483022, _1483024, _1483026, _1483028]), 37164 ^ [_1483018, _1483020, _1483022, _1483024, _1483026, _1483028]))], (37166 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483018, _1483020)), hAPP(hAPP(c_Product__Type_OPair(_1483018, _1483020), 37163 ^ [_1483018, _1483020, _1483022, _1483024, _1483026, _1483028]), 37164 ^ [_1483018, _1483020, _1483022, _1483024, _1483026, _1483028])), hAPP(_1483026, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1483018, _1483020), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1483018, _1483020), tc_HOL_Obool), _1483026)), hAPP(c_Set_OCollect(tc_prod(_1483018, _1483020)), hAPP(c_Product__Type_Oprod_Oprod__case(_1483018, _1483020, tc_HOL_Obool), _1483028)))))))]], -(hBOOL(hAPP(hAPP(_1483028, _1483022), _1483024)))], (8588 ^ _779999) ^ [_926956, _926958, _926960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926956), _926958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _926956), _926960)), 8595 ^ _779999 : [(8602 ^ _779999) ^ [] : [_926958 = _926960, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926958), _926956) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926960), _926956))], (8596 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926958), _926956) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926960), _926956), -(_926958 = _926960)]]], (39261 ^ _779999) ^ [_1538479, _1538481, _1538483] : [c_Wellfounded_OwfP(_1538479, hAPP(_1538481, 39262 ^ [_1538479, _1538481, _1538483])), 39269 ^ _779999 : [(39272 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538479, tc_HOL_Obool)), c_Predicate_ODomainP(_1538479, _1538479, hAPP(_1538481, 39267 ^ [_1538479, _1538481, _1538483]))), c_Predicate_ORangeP(_1538479, _1538479, hAPP(_1538481, 39268 ^ [_1538479, _1538481, _1538483]))) = c_Orderings_Obot__class_Obot(tc_fun(_1538479, tc_HOL_Obool))], (39270 ^ _779999) ^ [] : [hAPP(_1538481, 39267 ^ [_1538479, _1538481, _1538483]) = hAPP(_1538481, 39268 ^ [_1538479, _1538481, _1538483])]], -(c_Wellfounded_OwfP(_1538479, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1538483, tc_fun(_1538479, tc_fun(_1538479, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1538483, tc_HOL_Obool))), _1538481)))], (43959 ^ _779999) ^ [_1656201, _1656203, _1656205, _1656207, _1656209, _1656211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656201, _1656203)), hAPP(hAPP(c_Product__Type_OPair(_1656201, _1656203), _1656205), _1656207)), hAPP(c_List_Oset(tc_prod(_1656201, _1656203)), hAPP(hAPP(c_List_Ozip(_1656201, _1656203), _1656209), _1656211)))), 43962 ^ _779999 : [(43965 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656203), _1656207), hAPP(c_List_Oset(_1656203), _1656211))))], (43963 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656201), _1656205), hAPP(c_List_Oset(_1656201), _1656209))))]]], (45861 ^ _779999) ^ [_1698748, _1698750, _1698752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1698748), tc_List_Olist(_1698748))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1698748), tc_List_Olist(_1698748)), c_List_Olist_ONil(_1698748)), _1698750)), c_List_Olexord(_1698748, _1698752))), -(_1698750 = hAPP(hAPP(c_List_Olist_OCons(_1698748), 45864 ^ [_1698748, _1698750, _1698752]), 45865 ^ [_1698748, _1698750, _1698752]))], (15845 ^ _779999) ^ [_1065652, _1065654, _1065656, _1065658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1065652), _1065654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1065656), _1065658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065652), _1065656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065654), _1065658))))], (7294 ^ _779999) ^ [_900848, _900850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900848, tc_HOL_Obool)), _900850), c_Orderings_Obot__class_Obot(tc_fun(_900848, tc_HOL_Obool)))), -(_900850 = c_Orderings_Obot__class_Obot(tc_fun(_900848, tc_HOL_Obool)))], (44336 ^ _779999) ^ [_1664959, _1664961] : [hBOOL(hAPP(c_List_Odistinct(_1664959), _1664961)), -(hAPP(c_Finite__Set_Ocard(_1664959), hAPP(c_List_Oset(_1664959), _1664961)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664959)), _1664961))], (25368 ^ _779999) ^ [_1256140, _1256142, _1256144, _1256146, _1256148, _1256150] : [-(hBOOL(hAPP(_1256140, _1256142))), c_Natural_Oevaln(_1256144, _1256142, _1256146, _1256148), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_1256140, _1256150, _1256144), _1256142, _1256146, _1256148))], (52274 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17301 ^ _779999) ^ [_1093676, _1093678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093678)), -(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), _1093678), _1093676))))], (38957 ^ _779999) ^ [_1531616, _1531618] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1531616, _1531618), 38958 ^ [_1531616, _1531618])), -(c_Wellfounded_OwfP(_1531616, _1531618))], (46524 ^ _779999) ^ [_1713196, _1713198] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713196), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713198), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 46531 ^ _779999 : [(46538 ^ _779999) ^ [] : [_1713196 = _1713198, -(hAPP(c_Code__Numeral_Oof__nat, _1713196) = hAPP(c_Code__Numeral_Oof__nat, _1713198))], (46532 ^ _779999) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1713196) = hAPP(c_Code__Numeral_Oof__nat, _1713198), -(_1713196 = _1713198)]]], (6501 ^ _779999) ^ [_884876, _884878, _884880, _884882, _884884] : [class_Orderings_Oord(_884876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884878, _884876)), _884880), _884882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884876), hAPP(_884880, _884884)), hAPP(_884882, _884884))))], (2762 ^ _779999) ^ [_820940, _820942, _820944, _820946] : [-(c_Nitpick_Onumber__of__frac(_820946, _820942) = c_Nitpick_Onumber__of__frac(_820944, _820940)), _820946 = _820944, _820942 = _820940], (13203 ^ _779999) ^ [_1015048, _1015050] : [class_Groups_Ocomm__monoid__add(_1015048), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015048), c_Groups_Ozero__class_Ozero(_1015048)), _1015050) = _1015050)], (26032 ^ _779999) ^ [_1268265, _1268267, _1268269, _1268271, _1268273] : [c_Com_Ocom_OWhile(_1268265, _1268267) = c_Com_Ocom_OCond(_1268269, _1268271, _1268273)], (23419 ^ _779999) ^ [_1216956, _1216958, _1216960] : [-(hAPP(c_Set_Ovimage(_1216956, _1216958, _1216960), c_Orderings_Obot__class_Obot(tc_fun(_1216958, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1216956, tc_HOL_Obool)))], (18519 ^ _779999) ^ [_1117289, _1117291] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117289), _1117291))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1117289), hAPP(c_Nat_OSuc, _1117291)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (5364 ^ _779999) ^ [_862067, _862069, _862071, _862073, _862075, _862077] : [-(c_Finite__Set_Ofold__image(_862077, _862073, _862069) = c_Finite__Set_Ofold__image(_862075, _862071, _862067)), _862077 = _862075, _862073 = _862071, _862069 = _862067], (34831 ^ _779999) ^ [_1431410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1431410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1431410))))], (15171 ^ _779999) ^ [_1052585, _1052587, _1052589, _1052591] : [hBOOL(hAPP(hAPP(c_member(_1052585), _1052587), c_SetInterval_Oord_OatMost(_1052585, _1052589, _1052591))), -(hBOOL(hAPP(hAPP(_1052589, _1052587), _1052591)))], (42532 ^ _779999) ^ [_1617455, _1617457, _1617459] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617455, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1617455, tc_HOL_Obool)), _1617457), _1617459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617455, tc_HOL_Obool)), _1617457), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617455, tc_HOL_Obool), _1617459)))], (20176 ^ _779999) ^ [_1147517, _1147519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147517)), 20179 ^ _779999 : [(20186 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147517), _1147519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1147517)), hAPP(c_Int_Onat, _1147519))))], (20180 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1147517)), hAPP(c_Int_Onat, _1147519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147517), _1147519)))]]], (32707 ^ _779999) ^ [_1393593, _1393595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393593), _1393595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1393593)), c_Int_OBit1(_1393595))))], (47882 ^ _779999) ^ [_1744090, _1744092] : [class_Orderings_Olinorder(_1744090), -(_1744092 = c_List_Olist_ONil(_1744090)), c_List_Olinorder__class_Osorted(_1744090, _1744092), -(c_List_Olinorder__class_Osorted(_1744090, c_List_Obutlast(_1744090, _1744092)))], (33993 ^ _779999) ^ [_1415878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1415878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1415878)))], (46892 ^ _779999) ^ [_1720826, _1720828, _1720830, _1720832] : [-(c_List_Opartition(_1720826, _1720828, hAPP(hAPP(c_List_Olist_OCons(_1720826), _1720830), _1720832)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1720826), tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1720826), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1720826), tc_fun(tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), tc_fun(tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), tc_List_Olist(_1720826)), c_COMBS(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_fun(tc_List_Olist(_1720826), tc_fun(tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), tc_List_Olist(_1720826)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_fun(tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_List_Olist(_1720826)), hAPP(c_If(tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), hAPP(_1720828, _1720830)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1720826), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_List_Olist(_1720826)), c_Product__Type_OPair(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), hAPP(c_List_Olist_OCons(_1720826), _1720830))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720826), tc_fun(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826))), tc_fun(tc_fun(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_fun(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), tc_List_Olist(_1720826)), c_COMBB(tc_List_Olist(_1720826), tc_prod(tc_List_Olist(_1720826), tc_List_Olist(_1720826)), tc_List_Olist(_1720826))), c_Product__Type_OPair(tc_List_Olist(_1720826), tc_List_Olist(_1720826)))), hAPP(c_List_Olist_OCons(_1720826), _1720830)))), c_List_Opartition(_1720826, _1720828, _1720832)))], (23043 ^ _779999) ^ [_1209988, _1209990, _1209992, _1209994, _1209996, _1209998, _1210000, _1210002] : [hBOOL(hAPP(hAPP(c_member(_1209988), _1209990), _1209992)), hBOOL(hAPP(hAPP(hAPP(_1209994, _1209990), _1209996), _1209998)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1209988, tc_fun(_1210000, tc_fun(_1210002, tc_HOL_Obool))), _1209992), _1209994), _1209996), _1209998)))], (45586 ^ _779999) ^ [_1693228, _1693230, _1693232] : [-(_1693228 = c_List_Olist_ONil(_1693230)), -(hAPP(c_List_Ohd(_1693230), hAPP(hAPP(c_List_Oappend(_1693230), _1693228), _1693232)) = hAPP(c_List_Ohd(_1693230), _1693228))], (20818 ^ _779999) ^ [_1157904, _1157906] : [class_Groups_Oordered__ab__group__add__abs(_1157904), 20821 ^ _779999 : [(20828 ^ _779999) ^ [] : [_1157906 = c_Groups_Ozero__class_Ozero(_1157904), -(hAPP(c_Groups_Oabs__class_Oabs(_1157904), _1157906) = c_Groups_Ozero__class_Ozero(_1157904))], (20822 ^ _779999) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1157904), _1157906) = c_Groups_Ozero__class_Ozero(_1157904), -(_1157906 = c_Groups_Ozero__class_Ozero(_1157904))]]], (50072 ^ _779999) ^ [_1790732, _1790734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1790732), _1790734)), -(c_Lazy__Sequence_Osmall__lazy_H(_1790732, _1790734) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (6047 ^ _779999) ^ [_876258, _876260, _876262] : [class_Orderings_Opreorder(_876258), _876260 = _876262, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876258), _876260), _876262)))], (44536 ^ _779999) ^ [_1669076, _1669078] : [-(c_List_Oremove1(_1669076, _1669078, c_List_Olist_ONil(_1669076)) = c_List_Olist_ONil(_1669076))], (11837 ^ _779999) ^ [_988081] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_988081), c_Orderings_Obot__class_Obot(tc_fun(_988081, tc_HOL_Obool)))))], (49117 ^ _779999) ^ [_1769626, _1769628, _1769630, _1769632, _1769634] : [49118 ^ _779999 : [(49121 ^ _779999) ^ [] : [hBOOL(hAPP(_1769634, hAPP(hAPP(c_List_Ozip(_1769626, _1769630), hAPP(hAPP(c_List_Otake(_1769626), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769626)), _1769628)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769630)), _1769632))), _1769628)), hAPP(hAPP(c_List_Otake(_1769630), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769626)), _1769628)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769630)), _1769632))), _1769632))))], (49119 ^ _779999) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769626)), hAPP(hAPP(c_List_Otake(_1769626), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769626)), _1769628)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769630)), _1769632))), _1769628)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769630)), hAPP(hAPP(c_List_Otake(_1769630), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769626)), _1769628)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769630)), _1769632))), _1769632)))]], -(hBOOL(hAPP(_1769634, hAPP(hAPP(c_List_Ozip(_1769626, _1769630), _1769628), _1769632))))], (17347 ^ _779999) ^ [_1094497, _1094499, _1094501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094497), _1094499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094497), _1094501))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1094497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1094499), _1094501)))], (45746 ^ _779999) ^ [_1696267, _1696269, _1696271, _1696273, _1696275, _1696277] : [-(hAPP(c_List_Ofoldl(_1696267, _1696269, _1696271, _1696273), hAPP(hAPP(c_List_Oappend(_1696269), _1696275), _1696277)) = hAPP(c_List_Ofoldl(_1696267, _1696269, _1696271, hAPP(c_List_Ofoldl(_1696267, _1696269, _1696271, _1696273), _1696275)), _1696277))], (43076 ^ _779999) ^ [_1629869, _1629871, _1629873] : [c_Nitpick_Oless__frac(_1629869, _1629871, _1629873), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1629869), c_Nitpick_Oplus__frac(_1629869, _1629871, c_Nitpick_Ouminus__frac(_1629869, _1629873)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36781 ^ _779999) ^ [_1474076, _1474078, _1474080, _1474082, _1474084, _1474086, _1474088] : [c_Equiv__Relations_Oequiv(_1474076, _1474078, _1474080), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474076, tc_HOL_Obool)), _1474082), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474076), _1474078), _1474080))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474076, tc_HOL_Obool)), _1474084), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474076), _1474078), _1474080))), hBOOL(hAPP(hAPP(c_member(_1474076), _1474086), _1474082)), hBOOL(hAPP(hAPP(c_member(_1474076), _1474088), _1474084)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1474076, _1474076)), hAPP(hAPP(c_Product__Type_OPair(_1474076, _1474076), _1474086), _1474088)), _1474080)), -(_1474082 = _1474084)], (39326 ^ _779999) ^ [_1540201, _1540203, _1540205] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1540201, _1540203, _1540205)), 39328 ^ _779999 : [(39329 ^ _779999) ^ [_1540347] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1540201)), _1540347), _1540203)), -(c_Hoare__Mirabelle_Otriple__valid(_1540201, 39327 ^ [_1540201, _1540203, _1540205], _1540347))], (39338 ^ _779999) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1540201, 39327 ^ [_1540201, _1540203, _1540205], 39334 ^ [_1540201, _1540203, _1540205])], (39336 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1540201)), 39334 ^ [_1540201, _1540203, _1540205]), _1540205)))]]], (33127 ^ _779999) ^ [_1400668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400668), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400668)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22595 ^ _779999) ^ [_1198129, _1198131, _1198133] : [class_Orderings_Olinorder(_1198129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198129, tc_HOL_Obool)), _1198131), _1198133)), -(_1198131 = c_Orderings_Obot__class_Obot(tc_fun(_1198129, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198129), _1198133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198129), c_Big__Operators_Olinorder__class_OMax(_1198129, _1198131)), c_Big__Operators_Olinorder__class_OMax(_1198129, _1198133))))], (20651 ^ _779999) ^ [_1154923, _1154925] : [c_Nat__Transfer_Onat__set(_1154923), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1154925), _1154923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154925)))], (16055 ^ _779999) ^ [_1069836, _1069838, _1069840] : [class_Rings_Oordered__cancel__semiring(_1069836), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069836), c_Groups_Ozero__class_Ozero(_1069836)), _1069838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069836), _1069840), c_Groups_Ozero__class_Ozero(_1069836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069836), _1069840), _1069838)), c_Groups_Ozero__class_Ozero(_1069836))))], (286 ^ _779999) ^ [_784450, _784452, _784454, _784456, _784458, _784460] : [-(c_Orderings_Oorder__class_Omono(_784458, _784454, _784450)), c_Orderings_Oorder__class_Omono(_784460, _784456, _784452), _784460 = _784458, _784456 = _784454, _784452 = _784450], (20916 ^ _779999) ^ [_1159706, _1159708] : [class_Groups_Oordered__ab__group__add__abs(_1159706), 20919 ^ _779999 : [(20926 ^ _779999) ^ [] : [-(_1159708 = c_Groups_Ozero__class_Ozero(_1159706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159706), c_Groups_Ozero__class_Ozero(_1159706)), hAPP(c_Groups_Oabs__class_Oabs(_1159706), _1159708))))], (20920 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159706), c_Groups_Ozero__class_Ozero(_1159706)), hAPP(c_Groups_Oabs__class_Oabs(_1159706), _1159708))), _1159708 = c_Groups_Ozero__class_Ozero(_1159706)]]], (42658 ^ _779999) ^ [_1620105, _1620107, _1620109] : [class_Complete__Lattice_Ocomplete__lattice(_1620105), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620105), _1620107)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1620105), _1620109), c_Complete__Lattice_OInf__class_OInf(_1620105, _1620107)) = hAPP(hAPP(c_Finite__Set_Ofold(_1620105, _1620105, c_Lattices_Osemilattice__inf__class_Oinf(_1620105)), _1620109), _1620107))], (46217 ^ _779999) ^ [_1705342, _1705344, _1705346, _1705348, _1705350, _1705352] : [-(hAPP(hAPP(c_List_Omap(_1705342, _1705344), _1705346), hAPP(hAPP(c_List_Olist__update(_1705342, _1705348), _1705350), _1705352)) = hAPP(hAPP(c_List_Olist__update(_1705344, hAPP(hAPP(c_List_Omap(_1705342, _1705344), _1705346), _1705348)), _1705350), hAPP(_1705346, _1705352)))], (36110 ^ _779999) ^ [_1459834, _1459836] : [-(c_Divides_Odivmod__nat(_1459834, _1459836) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1459834, _1459836)))], (26598 ^ _779999) ^ [_1278489, _1278491, _1278493, _1278495, _1278497] : [class_Groups_Ocomm__monoid__mult(_1278489), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278491), _1278493)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1278491, _1278489), hAPP(hAPP(c_COMBS(_1278491, _1278489, _1278489), hAPP(hAPP(c_COMBB(_1278489, tc_fun(_1278489, _1278489), _1278491), c_Groups_Otimes__class_Otimes(_1278489)), _1278495)), _1278497)), _1278493) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278489), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1278491, _1278489), _1278495), _1278493)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1278491, _1278489), _1278497), _1278493)))], (13836 ^ _779999) ^ [_1026797, _1026799, _1026801, _1026803] : [c_Fun_Oinj__on(_1026797, _1026799, _1026801, _1026803), -(hAPP(c_Finite__Set_Ocard(_1026799), hAPP(c_Set_Oimage(_1026797, _1026799, _1026801), _1026803)) = hAPP(c_Finite__Set_Ocard(_1026797), _1026803))], (3970 ^ _779999) ^ [_839730, _839732, _839734, _839736] : [-(c_List_OremoveAll(_839736, _839732) = c_List_OremoveAll(_839734, _839730)), _839736 = _839734, _839732 = _839730], (8980 ^ _779999) ^ [_933636, _933638, _933640] : [class_Orderings_Oorder(_933636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933636), _933638), _933640)), _933640 = _933638], (2672 ^ _779999) ^ [_819543, _819545, _819547, _819549, _819551, _819553, _819555, _819557] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_819557, _819553, _819549, _819545) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_819555, _819551, _819547, _819543)), _819557 = _819555, _819553 = _819551, _819549 = _819547, _819545 = _819543], (41895 ^ _779999) ^ [_1600633, _1600635, _1600637, _1600639, _1600641] : [hBOOL(hAPP(hAPP(c_member(_1600633), _1600635), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600637, tc_fun(_1600633, tc_HOL_Obool)), _1600639), _1600641))), 41898 ^ _779999 : [(41899 ^ _779999) ^ [_1600757] : [hBOOL(hAPP(hAPP(c_member(_1600637), _1600757), _1600639)), -(hBOOL(hAPP(hAPP(c_member(_1600633), _1600635), hAPP(_1600641, _1600757))))]]], (47447 ^ _779999) ^ [_1734018, _1734020, _1734022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734018)), hAPP(c_List_Ofilter(_1734018, _1734020), _1734022))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734018)), _1734022))))], (3430 ^ _779999) ^ [_831290, _831292, _831294, _831296] : [-(c_Big__Operators_Olinorder__class_OMin(_831296, _831292) = c_Big__Operators_Olinorder__class_OMin(_831294, _831290)), _831296 = _831294, _831292 = _831290], (50819 ^ _779999) ^ [_1808489, _1808491] : [-(c_Equiv__Relations_Oequivp(_1808489, _1808491)), c_Predicate_Oreflp(_1808489, _1808491), c_Predicate_Osymp(_1808489, _1808491), c_Predicate_Otransp(_1808489, _1808491)], (27508 ^ _779999) ^ [_1297436] : [-(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, _1297436)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12153 ^ _779999) ^ [_994583, _994585, _994587, _994589, _994591] : [c_Finite__Set_Ofolding__one(_994583, _994585, _994587), hBOOL(hAPP(c_Finite__Set_Ofinite(_994583), _994589)), -(hBOOL(hAPP(hAPP(c_member(_994583), _994591), _994589))), -(_994589 = c_Orderings_Obot__class_Obot(tc_fun(_994583, tc_HOL_Obool))), -(hAPP(_994587, hAPP(hAPP(c_Set_Oinsert(_994583), _994591), _994589)) = hAPP(hAPP(_994585, _994591), hAPP(_994587, _994589)))], (7448 ^ _779999) ^ [_904046, _904048] : [-(c_Set_Othe__elem(_904046, hAPP(hAPP(c_Set_Oinsert(_904046), _904048), c_Orderings_Obot__class_Obot(tc_fun(_904046, tc_HOL_Obool)))) = _904048)], (45658 ^ _779999) ^ [_1694372, _1694374, _1694376] : [_1694376 = c_List_Olist_ONil(_1694372), -(hAPP(c_List_Orotate(_1694372, _1694374), _1694376) = c_List_Olist_ONil(_1694372))], (41797 ^ _779999) ^ [_1597871, _1597873, _1597875, _1597877, _1597879, _1597881, _1597883, _1597885] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597871, tc_fun(_1597873, tc_fun(_1597875, tc_HOL_Obool))), _1597877), _1597879), _1597881), _1597883)), hBOOL(hAPP(hAPP(c_member(_1597871), _1597885), _1597877)), -(hBOOL(hAPP(hAPP(hAPP(_1597879, _1597885), _1597881), _1597883)))], (43781 ^ _779999) ^ [_1650595, _1650597] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1650595), tc_fun(_1650595, tc_HOL_Obool), c_List_Oset(_1650595)), hAPP(c_List_Oset(tc_List_Olist(_1650595)), c_Enum_Osublists(_1650595, _1650597))) = hAPP(c_Set_OPow(_1650595), hAPP(c_List_Oset(_1650595), _1650597)))], (38947 ^ _779999) ^ [_1531442] : [-(c_Wellfounded_OwfP(_1531442, hAPP(c_COMBK(tc_fun(_1531442, tc_HOL_Obool), _1531442), hAPP(c_COMBK(tc_HOL_Obool, _1531442), c_fFalse))))], (47212 ^ _779999) ^ [_1728371, _1728373] : [-(c_List_Oremdups(_1728371, c_List_Oremdups(_1728371, _1728373)) = c_List_Oremdups(_1728371, _1728373))], (50407 ^ _779999) ^ [_1798141, _1798143, _1798145] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1798141), _1798143, _1798145)), -(c_List_Olist__ex(tc_Int_Oint, _1798141, c_List_Oupto(_1798143, _1798145)))], (41837 ^ _779999) ^ [_1599012, _1599014, _1599016, _1599018, _1599020, _1599022] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599012, tc_fun(_1599014, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1599016, tc_fun(_1599012, tc_HOL_Obool)), _1599018), _1599020)), _1599022) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599016, tc_fun(_1599014, tc_HOL_Obool)), _1599018), hAPP(hAPP(c_COMBC(_1599016, tc_fun(_1599012, tc_fun(_1599014, tc_HOL_Obool)), tc_fun(_1599014, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599012, tc_HOL_Obool), tc_fun(tc_fun(_1599012, tc_fun(_1599014, tc_HOL_Obool)), tc_fun(_1599014, tc_HOL_Obool)), _1599016), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599012, tc_fun(_1599014, tc_HOL_Obool))), _1599020)), _1599022)))], (35087 ^ _779999) ^ [] : [-(c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), c_fequal)), c_Nitpick_Oint__gcd))), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (10601 ^ _779999) ^ [_962452, _962454] : [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), _962452), _962454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962454), _962452)))], (44007 ^ _779999) ^ [_1657532, _1657534, _1657536, _1657538] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657532)), _1657534), hAPP(c_List_Oset(tc_List_Olist(_1657532)), c_Enum_On__lists(_1657532, _1657536, _1657538)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657532)), _1657534) = _1657536)], (47156 ^ _779999) ^ [_1727321, _1727323, _1727325, _1727327, _1727329] : [c_Finite__Set_Ofun__left__comm(_1727321, _1727323, _1727325), -(hAPP(hAPP(c_Finite__Set_Ofold(_1727321, _1727323, _1727325), _1727327), hAPP(c_List_Oset(_1727321), _1727329)) = hAPP(c_List_Ofoldl(_1727323, _1727321, hAPP(c_COMBC(_1727321, _1727323, _1727323), _1727325), _1727327), c_List_Oremdups(_1727321, _1727329)))], (19795 ^ _779999) ^ [_1141010, _1141012, _1141014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141010)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141012), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1141014)), 19805 ^ _779999 : [(19811 ^ _779999) ^ [] : [-(_1141012 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19807 ^ [_1141010, _1141012, _1141014]), 19804 ^ [_1141010, _1141012, _1141014]))], (19809 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19807 ^ [_1141010, _1141012, _1141014]), _1141014)))], (19806 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19804 ^ [_1141010, _1141012, _1141014]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1141010))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141012), _1141010) = _1141012)], (49830 ^ _779999) ^ [_1785512, _1785514, _1785516, _1785518] : [-(c_Predicate_Oconversep(_1785512, _1785514, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1785512, tc_fun(_1785514, tc_HOL_Obool))), _1785516), _1785518)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1785514, tc_fun(_1785512, tc_HOL_Obool))), c_Predicate_Oconversep(_1785512, _1785514, _1785516)), c_Predicate_Oconversep(_1785512, _1785514, _1785518)))], (47595 ^ _779999) ^ [_1738349, _1738351, _1738353, _1738355, _1738357, _1738359] : [-(c_List_Ofoldr(_1738349, _1738351, _1738353, hAPP(hAPP(c_List_Olist_OCons(_1738349), _1738355), _1738357), _1738359) = hAPP(hAPP(_1738353, _1738355), c_List_Ofoldr(_1738349, _1738351, _1738353, _1738357, _1738359)))], (1864 ^ _779999) ^ [_806407, _806409] : [-(class_Rings_Osemiring__0(_806407)), _806409 = _806407, class_Rings_Osemiring__0(_806409)], (43165 ^ _779999) ^ [_1632299, _1632301, _1632303] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632299)), c_List_Osublist(_1632299, _1632301, _1632303)) = 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(_1632299)), _1632301)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1632303)))))], (23373 ^ _779999) ^ [_1216021, _1216023, _1216025, _1216027] : [class_Groups_Oordered__ab__group__add(_1216021), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216021), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216021), _1216023), _1216025)), _1216027) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216021), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216021), _1216023), _1216027)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216021), _1216025), _1216027)))], (23229 ^ _779999) ^ [_1213461, _1213463, _1213465] : [class_Orderings_Olinorder(_1213461), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213461), _1213463), _1213465)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213461), _1213463), _1213465) = _1213463)], (41990 ^ _779999) ^ [_1604052] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604052, tc_HOL_Obool) = c_Set_OBall(_1604052))], (45067 ^ _779999) ^ [_1680826, _1680828, _1680830] : [-(_1680826 = c_List_Olist_ONil(_1680828)), -(c_List_Obutlast(_1680828, hAPP(hAPP(c_List_Oappend(_1680828), _1680830), _1680826)) = hAPP(hAPP(c_List_Oappend(_1680828), _1680830), c_List_Obutlast(_1680828, _1680826)))], (342 ^ _779999) ^ [_785230, _785232, _785234, _785236, _785238, _785240, _785242, _785244] : [-(c_Equiv__Relations_Ocongruent(_785242, _785238, _785234, _785230)), c_Equiv__Relations_Ocongruent(_785244, _785240, _785236, _785232), _785244 = _785242, _785240 = _785238, _785236 = _785234, _785232 = _785230], (40263 ^ _779999) ^ [_1562374, _1562376, _1562378, _1562380] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562374, tc_fun(_1562374, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1562374, tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_fun(_1562374, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562374, tc_fun(tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_fun(_1562374, tc_HOL_Obool)), _1562374), c_COMBC(_1562374, tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562374, tc_prod(_1562374, _1562374)), tc_fun(_1562374, tc_fun(tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_HOL_Obool)), _1562374), hAPP(c_COMBB(tc_prod(_1562374, _1562374), tc_fun(tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool), tc_HOL_Obool), _1562374), c_member(tc_prod(_1562374, _1562374)))), c_Product__Type_OPair(_1562374, _1562374)))), _1562376)), c_fequal), _1562378), _1562380)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562374, _1562374)), hAPP(hAPP(c_Product__Type_OPair(_1562374, _1562374), _1562378), _1562380)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562374, _1562374), tc_HOL_Obool)), _1562376), c_Relation_OId(_1562374)))))], (38244 ^ _779999) ^ [_1510763, _1510765, _1510767] : [_1510767 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1510763, _1510765), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1510763, _1510765), _1510767) = c_Orderings_Obot__class_Obot(tc_fun(_1510765, tc_HOL_Obool)))], (42187 ^ _779999) ^ [] : [-(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)))], (40671 ^ _779999) ^ [_1572103, _1572105] : [-(c_Transitive__Closure_Otrancl(_1572103, hAPP(c_Relation_Oconverse(_1572103, _1572103), _1572105)) = hAPP(c_Relation_Oconverse(_1572103, _1572103), c_Transitive__Closure_Otrancl(_1572103, _1572105)))], (13939 ^ _779999) ^ [_1028391, _1028393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028391), _1028393))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028391), _1028393)) = _1028391)], (19835 ^ _779999) ^ [_1141757, _1141759, _1141761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141757)), 19838 ^ _779999 : [(19839 ^ _779999) ^ [_1141891] : [19841 ^ _779999 : [(19847 ^ _779999) ^ [] : [-(_1141891 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19843 ^ [_1141757, _1141759, _1141761, _1141891]), 19840 ^ [_1141757, _1141759, _1141761, _1141891]))], (19845 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19843 ^ [_1141757, _1141759, _1141761, _1141891]), _1141759)))], (19842 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19840 ^ [_1141757, _1141759, _1141761, _1141891]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1141757))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141891), _1141761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1141891), _1141757)), _1141761)))]]], (19119 ^ _779999) ^ [_1128508, _1128510] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1128508)), _1128510) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1128508, _1128510))], (34059 ^ _779999) ^ [_1417007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1417007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1417007))))], (8614 ^ _779999) ^ [_927390, _927392, _927394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _927390), _927392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927390), _927394)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927392), _927394))))], (17810 ^ _779999) ^ [_1104288, _1104290, _1104292] : [class_Orderings_Olinorder(_1104288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104288), _1104290), _1104292)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1104288, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1104288, _1104290), _1104292)), hAPP(hAPP(c_Set_Oinsert(_1104288), _1104292), c_Orderings_Obot__class_Obot(tc_fun(_1104288, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1104288, _1104290, _1104292))], (34211 ^ _779999) ^ [_1419821, _1419823] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1419821), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1419823))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1419821), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419823))), 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))))], (37349 ^ _779999) ^ [_1488081, _1488083, _1488085, _1488087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1488081), _1488083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1488085), _1488087)), -(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), _1488081), _1488085)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1488083), _1488087))), c_FunDef_Opair__leq)))], (6701 ^ _779999) ^ [_889561, _889563, _889565] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _889561))), _889563), _889565)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _889561)), _889563), _889565)))], (34423 ^ _779999) ^ [_1423621, _1423623] : [class_Rings_Olinordered__idom(_1423621), 34426 ^ _779999 : [(34433 ^ _779999) ^ [] : [-(_1423623 = c_Groups_Ozero__class_Ozero(_1423621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423621), c_Groups_Ozero__class_Ozero(_1423621)), hAPP(hAPP(c_Power_Opower__class_Opower(_1423621), _1423623), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34427 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423621), c_Groups_Ozero__class_Ozero(_1423621)), hAPP(hAPP(c_Power_Opower__class_Opower(_1423621), _1423623), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1423623 = c_Groups_Ozero__class_Ozero(_1423621)]]], (20790 ^ _779999) ^ [_1157440, _1157442] : [class_Groups_Oordered__ab__group__add__abs(_1157440), -(hAPP(c_Groups_Oabs__class_Oabs(_1157440), hAPP(c_Groups_Oabs__class_Oabs(_1157440), _1157442)) = hAPP(c_Groups_Oabs__class_Oabs(_1157440), _1157442))], (43465 ^ _779999) ^ [_1642246, _1642248, _1642250, _1642252, _1642254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642246), tc_List_Olist(_1642246))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642246), tc_List_Olist(_1642246)), hAPP(hAPP(c_List_Olist_OCons(_1642246), _1642248), _1642250)), _1642252)), c_List_Olistrel(_1642246, _1642254))), 43470 ^ _779999 : [(43475 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642246), tc_List_Olist(_1642246))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642246), tc_List_Olist(_1642246)), _1642250), 43469 ^ [_1642246, _1642248, _1642250, _1642252, _1642254])), c_List_Olistrel(_1642246, _1642254))))], (43473 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1642246, _1642246)), hAPP(hAPP(c_Product__Type_OPair(_1642246, _1642246), _1642248), 43468 ^ [_1642246, _1642248, _1642250, _1642252, _1642254])), _1642254)))], (43471 ^ _779999) ^ [] : [-(_1642252 = hAPP(hAPP(c_List_Olist_OCons(_1642246), 43468 ^ [_1642246, _1642248, _1642250, _1642252, _1642254]), 43469 ^ [_1642246, _1642248, _1642250, _1642252, _1642254]))]]], (14401 ^ _779999) ^ [_1037228, _1037230, _1037232] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037228), _1037230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037228, tc_HOL_Obool)), _1037230), _1037232)), -(hAPP(c_Finite__Set_Ocard(_1037228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037228, tc_HOL_Obool)), _1037232), _1037230)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1037228), _1037232)), hAPP(c_Finite__Set_Ocard(_1037228), _1037230)))], (19255 ^ _779999) ^ [_1131079, _1131081, _1131083] : [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), _1131079), _1131081)), _1131083))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131083), _1131079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131081)))], (37551 ^ _779999) ^ [_1492858, _1492860, _1492862, _1492864] : [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), _1492858), _1492860)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492862), _1492864))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1492858), _1492864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1492862), _1492860))], (34773 ^ _779999) ^ [] : [c_Int_OPls = c_Int_OMin], (6830 ^ _779999) ^ [_891957, _891959] : [-(_891959 = c_Orderings_Obot__class_Obot(tc_fun(_891957, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_891957), 6833 ^ [_891957, _891959]), _891959)))], (23081 ^ _779999) ^ [_1210713, _1210715, _1210717] : [class_Orderings_Olinorder(_1210713), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210713), _1210715), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210713), _1210715), _1210717)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210713), _1210715), _1210717))], (34115 ^ _779999) ^ [_1418039] : [-(c_Int_Opred(c_Int_OBit1(_1418039)) = c_Int_OBit0(_1418039))], (18535 ^ _779999) ^ [_1117540, _1117542, _1117544] : [class_Orderings_Olinorder(_1117540), 18538 ^ _779999 : [(18545 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117540), _1117542), _1117544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1117540, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1117540), _1117542)), hAPP(c_SetInterval_Oord__class_OlessThan(_1117540), _1117544))))], (18539 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1117540, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1117540), _1117542)), hAPP(c_SetInterval_Oord__class_OlessThan(_1117540), _1117544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117540), _1117542), _1117544)))]]], (34871 ^ _779999) ^ [_1432040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1432040), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1432040)), c_Int_OMin)))], (38992 ^ _779999) ^ [_1532216, _1532218, _1532220, _1532222, _1532224] : [c_Relation_Orefl__on(_1532216, _1532218, _1532220), c_Relation_Orefl__on(_1532216, _1532222, _1532224), -(c_Relation_Orefl__on(_1532216, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1532216, tc_HOL_Obool)), _1532218), _1532222), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1532216, _1532216), tc_HOL_Obool)), _1532220), _1532224)))], (51559 ^ _779999) ^ [_1823661] : [-(_1823661 = hAPP(c_Code__Numeral_Oof__nat, 51557 ^ [_1823661]))], (38234 ^ _779999) ^ [_1510506, _1510508, _1510510, _1510512] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510506, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510506, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1510508, _1510506), _1510510)), hAPP(c_Relation_ORange(_1510508, _1510506), _1510512))), hAPP(c_Relation_ORange(_1510508, _1510506), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1510508, _1510506), tc_HOL_Obool)), _1510510), _1510512)))))], (48058 ^ _779999) ^ [_1746992, _1746994, _1746996, _1746998, _1747000] : [class_Orderings_Olinorder(_1746992), c_List_Olinorder__class_Osorted(_1746992, hAPP(hAPP(c_List_Omap(_1746994, _1746992), _1746996), _1746998)), -(c_List_Olinorder__class_Osorted(_1746992, hAPP(hAPP(c_List_Omap(_1746994, _1746992), _1746996), hAPP(c_List_Ofilter(_1746994, _1747000), _1746998))))], (6837 ^ _779999) ^ [_892026, _892028] : [hBOOL(hAPP(hAPP(c_member(_892026), _892028), c_Orderings_Obot__class_Obot(tc_fun(_892026, tc_HOL_Obool))))], (17862 ^ _779999) ^ [_1105207, _1105209, _1105211] : [class_Nat_Osemiring__char__0(_1105207), 17865 ^ _779999 : [(17872 ^ _779999) ^ [] : [_1105209 = _1105211, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105207), _1105209) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105207), _1105211))], (17866 ^ _779999) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105207), _1105209) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105207), _1105211), -(_1105209 = _1105211)]]], (45766 ^ _779999) ^ [_1696653, _1696655] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1696653), _1696655) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1696653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45772 ^ _779999 : [(45775 ^ _779999) ^ [] : [45771 ^ [_1696653, _1696655] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45773 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45771 ^ [_1696653, _1696655]), hAPP(c_List_Oset(tc_Nat_Onat), _1696655))))]]], (6589 ^ _779999) ^ [_886817, _886819, _886821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886817, tc_HOL_Obool)), _886819), _886821)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886817, tc_HOL_Obool)), _886821), _886819) = _886821)], (11266 ^ _779999) ^ [_975255, _975257, _975259, _975261] : [class_Lattices_Osemilattice__inf(_975255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975255), _975257), _975259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975255), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975255), _975261), _975257)), _975259)))], (52050 ^ _779999) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (40669 ^ _779999) ^ [_1572028, _1572030, _1572032, _1572034] : [-(hAPP(c_Relation_Oconverse(_1572028, _1572030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572028, _1572030), tc_HOL_Obool)), _1572032), _1572034)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572030, _1572028), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1572028, _1572030), _1572032)), hAPP(c_Relation_Oconverse(_1572028, _1572030), _1572034)))], (42261 ^ _779999) ^ [_1610912, _1610914, _1610916, _1610918] : [hBOOL(hAPP(hAPP(c_member(_1610912), _1610914), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1610912, tc_HOL_Obool), _1610916))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1610912, tc_HOL_Obool)), _1610918), _1610916)), -(hBOOL(hAPP(hAPP(c_member(_1610912), _1610914), _1610918)))], (22301 ^ _779999) ^ [_1192637, _1192639] : [class_Lattices_Obounded__lattice__top(_1192637), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1192637), _1192639), c_Orderings_Otop__class_Otop(_1192637)) = c_Orderings_Otop__class_Otop(_1192637))], (47954 ^ _779999) ^ [_1745235, _1745237, _1745239] : [class_Orderings_Olinorder(_1745235), c_List_Olinorder__class_Osorted(_1745235, _1745237), -(c_List_Olinorder__class_Osorted(_1745235, hAPP(hAPP(c_List_Odrop(_1745235), _1745239), _1745237)))], (27212 ^ _779999) ^ [_1292256, _1292258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292256)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1292256)), _1292258) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1292256), _1292258)))], (51492 ^ _779999) ^ [_1821935, _1821937, _1821939] : [hAPP(c_Fun_Ocomp(_1821935, _1821937, _1821937, _1821939), c_Hilbert__Choice_Oinv__into(_1821935, _1821937, c_Orderings_Otop__class_Otop(tc_fun(_1821935, tc_HOL_Obool)), _1821939)) = c_Fun_Oid(_1821937), -(hAPP(c_Set_Oimage(_1821935, _1821937, _1821939), c_Orderings_Otop__class_Otop(tc_fun(_1821935, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1821937, tc_HOL_Obool)))], (50212 ^ _779999) ^ [_1793721, _1793723, _1793725] : [hBOOL(hAPP(hAPP(c_List_Omember(_1793721), _1793723), _1793725)), -(hBOOL(hAPP(hAPP(c_member(_1793721), _1793725), hAPP(c_List_Oset(_1793721), _1793723))))], (27644 ^ _779999) ^ [_1299892, _1299894] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1299892), _1299894) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1299894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1299892 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23433 ^ _779999) ^ [_1217326, _1217328, _1217330, _1217332, _1217334] : [-(hAPP(c_Set_Ovimage(_1217326, _1217328, _1217330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1217328, tc_HOL_Obool)), _1217332), _1217334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1217326, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1217326, _1217328, _1217330), _1217332)), hAPP(c_Set_Ovimage(_1217326, _1217328, _1217330), _1217334)))], (33343 ^ _779999) ^ [_1404028, _1404030] : [class_Int_Onumber__ring(_1404028), class_Rings_Olinordered__idom(_1404028), 33350 ^ _779999 : [(33357 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404030), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404028), hAPP(c_Int_Onumber__class_Onumber__of(_1404028), _1404030)), c_Groups_Ozero__class_Ozero(_1404028))))], (33351 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404028), hAPP(c_Int_Onumber__class_Onumber__of(_1404028), _1404030)), c_Groups_Ozero__class_Ozero(_1404028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404030), c_Int_OPls)))]]], (4 ^ _779999) ^ [_780049, _780051] : [_780051 = _780049, -(_780049 = _780051)], (36276 ^ _779999) ^ [_1463111, _1463113, _1463115, _1463117, _1463119] : [-(hAPP(c_Product__Type_Osnd(_1463111, _1463113), hAPP(c_Product__Type_Oapsnd(_1463115, _1463113, _1463111, _1463117), _1463119)) = hAPP(_1463117, hAPP(c_Product__Type_Osnd(_1463111, _1463115), _1463119)))], (42424 ^ _779999) ^ [_1614622, _1614624, _1614626] : [class_Complete__Lattice_Ocomplete__lattice(_1614622), 42427 ^ _779999 : [(42428 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614622), _1614624), c_Complete__Lattice_OInf__class_OInf(_1614622, _1614626))), 42431 ^ _779999 : [(42432 ^ _779999) ^ [_1614780] : [hBOOL(hAPP(hAPP(c_member(_1614622), _1614780), _1614626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614622), _1614624), _1614780)))]]], (42438 ^ _779999) ^ [] : [42440 ^ _779999 : [(42443 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614622), _1614624), 42439 ^ [_1614622, _1614624, _1614626]))], (42441 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614622), 42439 ^ [_1614622, _1614624, _1614626]), _1614626)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614622), _1614624), c_Complete__Lattice_OInf__class_OInf(_1614622, _1614626))))]]], (50 ^ _779999) ^ [_780804, _780806, _780808, _780810, _780812, _780814, _780816, _780818] : [-(c_Partial__Function_Omk__less(_780816, _780812, _780808, _780804)), c_Partial__Function_Omk__less(_780818, _780814, _780810, _780806), _780818 = _780816, _780814 = _780812, _780810 = _780808, _780806 = _780804], (46055 ^ _779999) ^ [_1702475, _1702477, _1702479] : [_1702475 = c_List_Olist_ONil(_1702477), -(c_List_Olast(_1702477, hAPP(hAPP(c_List_Oappend(_1702477), _1702479), _1702475)) = c_List_Olast(_1702477, _1702479))], (37626 ^ _779999) ^ [] : [-(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))], (18843 ^ _779999) ^ [_1123909] : [-(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), _1123909))))], (28868 ^ _779999) ^ [_1322167, _1322169, _1322171, _1322173] : [class_Fields_Olinordered__field__inverse__zero(_1322167), 28871 ^ _779999 : [(28872 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322167), _1322169), _1322171)), _1322173)), 28875 ^ _779999 : [(28882 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322171))), 28885 ^ _779999 : [(28892 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322171), c_Groups_Ozero__class_Ozero(_1322167)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322173)))], (28886 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322171), c_Groups_Ozero__class_Ozero(_1322167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322167), _1322173), _1322171)), _1322169)))]]], (28876 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322167), _1322173), _1322171))))]]], (28898 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322167), _1322169), _1322171)), _1322173))), 28901 ^ _779999 : [(28904 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322167), _1322173), _1322171)))], (28902 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322171)))]], 28905 ^ _779999 : [(28908 ^ _779999) ^ [] : [28909 ^ _779999 : [(28912 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322167), _1322173), _1322171)), _1322169))], (28910 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322171), c_Groups_Ozero__class_Ozero(_1322167))))]], 28913 ^ _779999 : [(28916 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322173))], (28914 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), _1322171), c_Groups_Ozero__class_Ozero(_1322167)))]]], (28906 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322167), c_Groups_Ozero__class_Ozero(_1322167)), _1322171))]]]]], (534 ^ _779999) ^ [_788196, _788198, _788200, _788202, _788204, _788206] : [-(c_Finite__Set_Ofolding__one(_788204, _788200, _788196)), c_Finite__Set_Ofolding__one(_788206, _788202, _788198), _788206 = _788204, _788202 = _788200, _788198 = _788196], (47428 ^ _779999) ^ [_1733696, _1733698, _1733700] : [hAPP(c_List_Ofilter(_1733696, _1733698), _1733700) = c_List_Olist_ONil(_1733696), 47431 ^ _779999 : [(47432 ^ _779999) ^ [_1733793] : [hBOOL(hAPP(hAPP(c_member(_1733696), _1733793), hAPP(c_List_Oset(_1733696), _1733700))), hBOOL(hAPP(_1733698, _1733793))]]], (49634 ^ _779999) ^ [_1781152, _1781154] : [-(c_FunDef_Ois__measure(_1781152, _1781154))], (49062 ^ _779999) ^ [_1767993, _1767995, _1767997, _1767999, _1768001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1767993, _1767995)), hAPP(_1767993, _1767997))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1767999, _1767999)), hAPP(hAPP(c_Product__Type_OPair(_1767999, _1767999), _1767995), _1767997)), c_List_Omeasures(_1767999, _1768001))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767999, _1767999)), hAPP(hAPP(c_Product__Type_OPair(_1767999, _1767999), _1767995), _1767997)), c_List_Omeasures(_1767999, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1767999, tc_Nat_Onat)), _1767993), _1768001)))))], (11106 ^ _779999) ^ [_972447, _972449, _972451] : [class_Lattices_Osemilattice__inf(_972447), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972447), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972447), _972449), _972451)), _972449)))], (45634 ^ _779999) ^ [_1693889, _1693891, _1693893] : [hBOOL(hAPP(c_List_Odistinct(_1693889), _1693893)), -(hBOOL(hAPP(c_List_Odistinct(_1693889), hAPP(c_List_Orotate(_1693889, _1693891), _1693893))))], (7623 ^ _779999) ^ [_908094, _908096, _908098] : [c_Com_Ocom_OSemi(_908094, _908096) = hAPP(c_Com_Ocom_OBODY, _908098)], (26318 ^ _779999) ^ [_1273192, _1273194, _1273196] : [class_Groups_Ogroup__add(_1273192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273192), _1273194), _1273196) = c_Groups_Ozero__class_Ozero(_1273192), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1273192), _1273194) = _1273196)], (45394 ^ _779999) ^ [_1688565, _1688567] : [hAPP(c_List_Orotate1(_1688565), _1688567) = c_List_Olist_ONil(_1688565), -(_1688567 = c_List_Olist_ONil(_1688565))], (38469 ^ _779999) ^ [_1517117, _1517119, _1517121, _1517123] : [38470 ^ _779999 : [(38473 ^ _779999) ^ [] : [_1517123 = c_Orderings_Obot__class_Obot(tc_fun(_1517119, tc_HOL_Obool))], (38471 ^ _779999) ^ [] : [_1517121 = c_Orderings_Obot__class_Obot(tc_fun(_1517117, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1517117, _1517119), _1517121), hAPP(c_COMBK(tc_fun(_1517119, tc_HOL_Obool), _1517117), _1517123)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517117, _1517119), tc_HOL_Obool)))], (42980 ^ _779999) ^ [_1627533, _1627535, _1627537, _1627539, _1627541, _1627543, _1627545, _1627547] : [c_Finite__Set_Ofolding__image__simple__idem(_1627533, _1627535, _1627537, _1627539, _1627541, _1627543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627535), _1627545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627535, tc_HOL_Obool)), _1627547), _1627545)), -(hAPP(hAPP(_1627537, hAPP(_1627543, _1627547)), hAPP(_1627543, _1627545)) = hAPP(_1627543, _1627545))], (43561 ^ _779999) ^ [_1644635, _1644637, _1644639] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644635)), _1644637), c_List_Olists(_1644635, c_Wellfounded_Oacc(_1644635, _1644639)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644635)), _1644637), c_Wellfounded_Oacc(tc_List_Olist(_1644635), c_List_Olistrel1(_1644635, _1644639)))))], (2820 ^ _779999) ^ [_821829, _821831, _821833, _821835, _821837, _821839] : [-(c_Predicate_ORangeP(_821839, _821835, _821831) = c_Predicate_ORangeP(_821837, _821833, _821829)), _821839 = _821837, _821835 = _821833, _821831 = _821829], (40403 ^ _779999) ^ [_1566370, _1566372] : [-(hAPP(c_Relation_ODomain(_1566370, _1566370), c_Transitive__Closure_Ortrancl(_1566370, _1566372)) = c_Orderings_Otop__class_Otop(tc_fun(_1566370, tc_HOL_Obool)))], (17681 ^ _779999) ^ [_1101410, _1101412, _1101414] : [17682 ^ _779999 : [(17685 ^ _779999) ^ [] : [_1101412 = _1101414], (17683 ^ _779999) ^ [] : [_1101410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101410), _1101412) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101410), _1101414))], (48592 ^ _779999) ^ [_1758073, _1758075, _1758077, _1758079] : [hBOOL(hAPP(hAPP(c_member(_1758073), _1758075), hAPP(c_List_Oset(_1758073), c_List_OtakeWhile(_1758073, _1758077, _1758079)))), 48595 ^ _779999 : [(48598 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1758077, _1758075)))], (48596 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758073), _1758075), hAPP(c_List_Oset(_1758073), _1758079))))]]], (44144 ^ _779999) ^ [_1660637, _1660639, _1660641] : [-(hAPP(hAPP(c_List_Olist__update(_1660637, _1660639), _1660641), hAPP(hAPP(c_List_Onth(_1660637), _1660639), _1660641)) = _1660639)], (8626 ^ _779999) ^ [_927636, _927638] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _927636), _927638)), _927636)))], (24858 ^ _779999) ^ [_1245633, _1245635, _1245637] : [class_Orderings_Olinorder(_1245633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245633), _1245635)), -(_1245635 = c_Orderings_Obot__class_Obot(tc_fun(_1245633, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245633), _1245637)), -(_1245637 = c_Orderings_Obot__class_Obot(tc_fun(_1245633, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1245633, tc_HOL_Obool)), _1245635), _1245637) = c_Orderings_Obot__class_Obot(tc_fun(_1245633, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1245633, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245633, tc_HOL_Obool)), _1245635), _1245637)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245633), c_Big__Operators_Olinorder__class_OMax(_1245633, _1245635)), c_Big__Operators_Olinorder__class_OMax(_1245633, _1245637)))], (21804 ^ _779999) ^ [_1178291, _1178293, _1178295, _1178297, _1178299, _1178301] : [-(hAPP(c_Set_Oimage(_1178291, _1178293, hAPP(hAPP(c_COMBS(_1178291, _1178293, _1178293), hAPP(hAPP(c_COMBS(_1178291, _1178293, tc_fun(_1178293, _1178293)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1178293, tc_fun(_1178293, _1178293)), _1178291), c_If(_1178293)), _1178295)), _1178297)), _1178299)), _1178301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178293, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1178291, _1178293, _1178297), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1178291, tc_HOL_Obool)), _1178301), hAPP(c_Set_OCollect(_1178291), _1178295)))), hAPP(c_Set_Oimage(_1178291, _1178293, _1178299), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1178291, tc_HOL_Obool)), _1178301), hAPP(c_Set_OCollect(_1178291), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1178291), c_fNot), _1178295))))))], (37670 ^ _779999) ^ [_1496916, _1496918, _1496920, _1496922, _1496924, _1496926] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496916, _1496918, _1496920), _1496922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496918, _1496920), tc_HOL_Obool)), _1496924), _1496926)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496916, _1496920), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1496916, _1496918, _1496920), _1496922), _1496924)), hAPP(hAPP(c_Relation_Orel__comp(_1496916, _1496918, _1496920), _1496922), _1496926)))], (46085 ^ _779999) ^ [_1702902, _1702904, _1702906] : [-(_1702902 = c_List_Olist_ONil(_1702904)), -(c_List_Olast(_1702904, hAPP(hAPP(c_List_Olist_OCons(_1702904), _1702906), _1702902)) = c_List_Olast(_1702904, _1702902))], (40935 ^ _779999) ^ [_1578787, _1578789, _1578791] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578787, _1578787)), _1578789), c_Transitive__Closure_Ortrancl(_1578787, _1578791))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578787, _1578787)), _1578789), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1578787, _1578787), tc_HOL_Obool), 40938 ^ [_1578787, _1578789, _1578791]), _1578791))))], (26775 ^ _779999) ^ [_1282320, _1282322, _1282324] : [class_Groups_Oordered__ab__group__add(_1282320), -(hAPP(c_Set_Oimage(_1282320, _1282320, c_Groups_Ouminus__class_Ouminus(_1282320)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1282320, _1282322, _1282324)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1282320, hAPP(c_Groups_Ouminus__class_Ouminus(_1282320), _1282324)), hAPP(c_Groups_Ouminus__class_Ouminus(_1282320), _1282322)))], (39681 ^ _779999) ^ [_1548317, _1548319, _1548321, _1548323, _1548325, _1548327, _1548329, _1548331] : [c_Finite__Set_Ofolding__image(_1548317, _1548319, _1548321, _1548323, _1548325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548319), _1548327)), -(hAPP(hAPP(_1548325, hAPP(hAPP(c_COMBS(_1548319, _1548317, _1548317), hAPP(hAPP(c_COMBB(_1548317, tc_fun(_1548317, _1548317), _1548319), _1548321), _1548329)), _1548331)), _1548327) = hAPP(hAPP(_1548321, hAPP(hAPP(_1548325, _1548329), _1548327)), hAPP(hAPP(_1548325, _1548331), _1548327)))], (30407 ^ _779999) ^ [_1349713, _1349715, _1349717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1349713)), 30410 ^ _779999 : [(30411 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1349715, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1349717), _1349713)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349717, _1349713))), 30414 ^ _779999 : [(30415 ^ _779999) ^ [_1349914, _1349916] : [-(hBOOL(hAPP(hAPP(_1349715, _1349916), _1349914))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1349914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1349914), _1349713)), _1349717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1349713), _1349916)), _1349914)]]], (30429 ^ _779999) ^ [] : [30432 ^ _779999 : [(30435 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30431 ^ [_1349713, _1349715, _1349717]), _1349713)))], (30437 ^ _779999) ^ [] : [-(_1349717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1349713), 30430 ^ [_1349713, _1349715, _1349717])), 30431 ^ [_1349713, _1349715, _1349717]))], (30439 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1349715, 30430 ^ [_1349713, _1349715, _1349717]), 30431 ^ [_1349713, _1349715, _1349717]))], (30433 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30431 ^ [_1349713, _1349715, _1349717])))]], -(hBOOL(hAPP(hAPP(_1349715, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1349717), _1349713)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349717, _1349713))))]]], (23429 ^ _779999) ^ [_1217208, _1217210, _1217212] : [-(hAPP(c_Set_Ovimage(_1217208, _1217210, _1217212), c_Orderings_Otop__class_Otop(tc_fun(_1217210, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1217208, tc_HOL_Obool)))], (18111 ^ _779999) ^ [_1109664, _1109666, _1109668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109664), _1109666)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1109664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109666), _1109668)) = 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, _1109664), _1109666)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1109666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109666), _1109668))))], (5871 ^ _779999) ^ [_873316, _873318] : [class_Orderings_Opreorder(_873316), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873316), _873318), _873318)))], (45173 ^ _779999) ^ [_1682743, _1682745, _1682747, _1682749, _1682751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682743), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682745)), _1682747))), -(hAPP(hAPP(c_List_Olist__update(_1682745, hAPP(hAPP(c_List_Oappend(_1682745), _1682747), _1682749)), _1682743), _1682751) = hAPP(hAPP(c_List_Oappend(_1682745), hAPP(hAPP(c_List_Olist__update(_1682745, _1682747), _1682743), _1682751)), _1682749))], (32795 ^ _779999) ^ [_1395157] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1395157) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395157)))], (41747 ^ _779999) ^ [_1596820, _1596822, _1596824, _1596826] : [class_Complete__Lattice_Ocomplete__lattice(_1596820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596822), _1596824)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596822, _1596820), _1596824), _1596826) = hAPP(hAPP(c_Finite__Set_Ofold(_1596822, _1596820, hAPP(hAPP(c_COMBB(_1596820, tc_fun(_1596820, _1596820), _1596822), c_Lattices_Osemilattice__inf__class_Oinf(_1596820)), _1596826)), c_Orderings_Otop__class_Otop(_1596820)), _1596824))], (7643 ^ _779999) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (9244 ^ _779999) ^ [_937708, _937710, _937712] : [class_Orderings_Olinorder(_937708), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937708), _937710), _937712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937708), _937712), _937710)))], (15841 ^ _779999) ^ [_1065538, _1065540, _1065542] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065538), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1065540), _1065542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065538), _1065540)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065538), _1065542)))], (33905 ^ _779999) ^ [_1414410, _1414412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414410), _1414412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1414410)), c_Int_OBit0(_1414412))))], (38856 ^ _779999) ^ [_1529068, _1529070, _1529072, _1529074, _1529076, _1529078, _1529080] : [-(hAPP(c_Product__Type_Osnd(_1529068, _1529070), hAPP(c_Product__Type_Omap__pair(_1529072, _1529068, _1529074, _1529070, _1529076, _1529078), _1529080)) = hAPP(_1529078, hAPP(c_Product__Type_Osnd(_1529072, _1529074), _1529080)))], (48488 ^ _779999) ^ [_1755767, _1755769] : [-(hAPP(c_List_Orev(_1755767), _1755769) = hAPP(c_List_Ofoldl(tc_List_Olist(_1755767), _1755767, hAPP(c_COMBC(_1755767, tc_List_Olist(_1755767), tc_List_Olist(_1755767)), c_List_Olist_OCons(_1755767)), c_List_Olist_ONil(_1755767)), _1755769))], (14772 ^ _779999) ^ [_1045313] : [class_Rings_Ozero__neq__one(_1045313), c_Groups_Ozero__class_Ozero(_1045313) = c_Groups_Oone__class_Oone(_1045313)], (33435 ^ _779999) ^ [_1405482, _1405484] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405482), c_Int_OPls))), 33438 ^ _779999 : [(33445 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405484), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405482)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405482), _1405484)))], (33439 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405484), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405482)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405482))]]], (51220 ^ _779999) ^ [_1815750, _1815752] : [c_Equiv__Relations_Opart__equivp(_1815750, _1815752), 51224 ^ _779999 : [(51237 ^ _779999) ^ [_1816092, _1816094] : [-(hBOOL(hAPP(hAPP(_1815752, _1816094), _1816092))), hBOOL(hAPP(hAPP(_1815752, _1816094), _1816094)), hBOOL(hAPP(hAPP(_1815752, _1816092), _1816092)), hAPP(_1815752, _1816094) = hAPP(_1815752, _1816092)], (51227 ^ _779999) ^ [_1815923, _1815925] : [hBOOL(hAPP(hAPP(_1815752, _1815925), _1815923)), 51230 ^ _779999 : [(51235 ^ _779999) ^ [] : [-(hAPP(_1815752, _1815925) = hAPP(_1815752, _1815923))], (51233 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1815752, _1815923), _1815923)))], (51231 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1815752, _1815925), _1815925)))]]], (51225 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1815752, 51223 ^ [_1815750, _1815752]), 51223 ^ [_1815750, _1815752])))]]], (34707 ^ _779999) ^ [_1429034] : [_1429034 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1429034) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27570 ^ _779999) ^ [_1298524, _1298526, _1298528, _1298530] : [class_Fields_Ofield(_1298524), -(_1298526 = c_Groups_Ozero__class_Ozero(_1298524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1298528), _1298530)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1298524), _1298526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1298530), _1298528)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298524), hAPP(hAPP(c_Power_Opower__class_Opower(_1298524), _1298526), _1298530)), hAPP(hAPP(c_Power_Opower__class_Opower(_1298524), _1298526), _1298528)))], (21760 ^ _779999) ^ [_1176891, _1176893, _1176895] : [hBOOL(hAPP(_1176891, _1176893)), -(hAPP(c_Set_OCollect(_1176895), hAPP(hAPP(c_COMBS(_1176895, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1176895), c_fconj), hAPP(c_fequal, _1176893))), _1176891)) = hAPP(hAPP(c_Set_Oinsert(_1176895), _1176893), c_Orderings_Obot__class_Obot(tc_fun(_1176895, tc_HOL_Obool))))], (11450 ^ _779999) ^ [_979597, _979599, _979601, _979603] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979597, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_979597, tc_fun(_979597, tc_HOL_Obool), tc_HOL_Obool), c_member(_979597)), _979599)), hAPP(hAPP(c_COMBC(_979597, tc_fun(_979597, tc_HOL_Obool), tc_HOL_Obool), c_member(_979597)), _979601)), _979603)), -(hBOOL(hAPP(hAPP(c_member(_979597), _979603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979597, tc_HOL_Obool)), _979599), _979601))))], (29366 ^ _779999) ^ [_1331655, _1331657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331657)), -(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), _1331655), _1331657))))], (12505 ^ _779999) ^ [_1001240, _1001242, _1001244] : [class_Lattices_Olattice(_1001240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001240), _1001242)), -(_1001242 = c_Orderings_Obot__class_Obot(tc_fun(_1001240, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001240), _1001244)), -(_1001244 = c_Orderings_Obot__class_Obot(tc_fun(_1001240, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1001240, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001240, tc_HOL_Obool)), _1001242), _1001244)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1001240), c_Big__Operators_Olattice__class_OSup__fin(_1001240, _1001242)), c_Big__Operators_Olattice__class_OSup__fin(_1001240, _1001244)))], (20540 ^ _779999) ^ [_1153315, _1153317] : [c_Nat__Transfer_Ois__nat(_1153315), c_Nat__Transfer_Ois__nat(_1153317), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153315), _1153317)))], (51912 ^ _779999) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (40405 ^ _779999) ^ [_1566409, _1566411, _1566413] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1566409, _1566411, _1566411), _1566413), c_Relation_OId(_1566411)) = _1566413)], (2552 ^ _779999) ^ [_817637, _817639, _817641, _817643] : [-(c_Divides_OnegDivAlg(_817643, _817639) = c_Divides_OnegDivAlg(_817641, _817637)), _817643 = _817641, _817639 = _817637], (52054 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (39713 ^ _779999) ^ [_1549121, _1549123, _1549125, _1549127, _1549129, _1549131] : [c_Finite__Set_Ofolding(_1549121, _1549123, _1549125, _1549127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549121), _1549129)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549121), _1549131)), -(hAPP(c_Fun_Ocomp(_1549123, _1549123, _1549123, hAPP(_1549127, _1549131)), hAPP(_1549127, _1549129)) = hAPP(c_Fun_Ocomp(_1549123, _1549123, _1549123, hAPP(_1549127, _1549129)), hAPP(_1549127, _1549131)))], (10830 ^ _779999) ^ [_967222, _967224, _967226, _967228, _967230] : [class_Groups_Ocomm__monoid__add(_967222), class_Groups_Oordered__ab__semigroup__add(_967222), 10840 ^ _779999 : [(10843 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967222), hAPP(_967228, 10839 ^ [_967222, _967224, _967226, _967228, _967230])), hAPP(_967230, 10839 ^ [_967222, _967224, _967226, _967228, _967230])))], (10841 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_967224), 10839 ^ [_967222, _967224, _967226, _967228, _967230]), _967226)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967222), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_967224, _967222), _967228), _967226)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_967224, _967222), _967230), _967226))))], (21546 ^ _779999) ^ [_1172265, _1172267, _1172269] : [class_Orderings_Olinorder(_1172265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172265), _1172267), _1172269)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1172265, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1172265, _1172267, _1172269)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1172265), _1172269)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1172265), _1172267))], (50163 ^ _779999) ^ [_1792648, _1792650, _1792652, _1792654, _1792656] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1792648, _1792650, _1792652, _1792654, _1792656) = c_Option_Ooption_Ooption__case(_1792648, tc_prod(_1792650, tc_Lazy__Sequence_Olazy__sequence(_1792650)), _1792652, hAPP(c_Product__Type_Oprod_Oprod__case(_1792650, tc_Lazy__Sequence_Olazy__sequence(_1792650), _1792648), _1792654), hAPP(c_Lazy__Sequence_Oyield(_1792650), _1792656)))], (8300 ^ _779999) ^ [_921086, _921088] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_921086, _921088)], (3306 ^ _779999) ^ [_829406, _829408] : [_829408 = _829406, -(c_Power_Opower__class_Opower(_829408) = c_Power_Opower__class_Opower(_829406))], (51005 ^ _779999) ^ [_1812336, _1812338] : [51008 ^ _779999 : [(51011 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1812336, _1812336)), hAPP(hAPP(c_Product__Type_OPair(_1812336, _1812336), 51007 ^ [_1812336, _1812338]), 51006 ^ [_1812336, _1812338])), _1812338))], (51009 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812336, _1812336)), hAPP(hAPP(c_Product__Type_OPair(_1812336, _1812336), 51006 ^ [_1812336, _1812338]), 51007 ^ [_1812336, _1812338])), _1812338)))]], -(c_Relation_Osym(_1812336, _1812338))], (23413 ^ _779999) ^ [_1216855] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216855) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45289 ^ _779999) ^ [_1685710, _1685712, _1685714, _1685716, _1685718, _1685720, _1685722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685710, _1685710)), hAPP(hAPP(c_Product__Type_OPair(_1685710, _1685710), _1685712), _1685714)), _1685716)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1685710), tc_List_Olist(_1685710))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1685710), tc_List_Olist(_1685710)), hAPP(hAPP(c_List_Oappend(_1685710), _1685718), hAPP(hAPP(c_List_Olist_OCons(_1685710), _1685712), _1685720))), hAPP(hAPP(c_List_Oappend(_1685710), _1685718), hAPP(hAPP(c_List_Olist_OCons(_1685710), _1685714), _1685722)))), c_List_Olexord(_1685710, _1685716))))], (6675 ^ _779999) ^ [_889032, _889034, _889036, _889038] : [class_Orderings_Oorder(_889032), class_Enum_Oenum(_889034), 6682 ^ _779999 : [(6689 ^ _779999) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_889034), hAPP(hAPP(c_COMBS(_889034, _889032, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_889032, tc_fun(_889032, tc_HOL_Obool), _889034), c_Orderings_Oord__class_Oless__eq(_889032)), _889036)), _889038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889034, _889032)), _889036), _889038)))], (6683 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889034, _889032)), _889036), _889038)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_889034), hAPP(hAPP(c_COMBS(_889034, _889032, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_889032, tc_fun(_889032, tc_HOL_Obool), _889034), c_Orderings_Oord__class_Oless__eq(_889032)), _889036)), _889038))))]]], (41833 ^ _779999) ^ [_1598803, _1598805, _1598807, _1598809, _1598811] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598803, tc_HOL_Obool)), _1598805), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598807, tc_fun(_1598803, tc_HOL_Obool)), _1598809), _1598811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598807, tc_fun(_1598803, tc_HOL_Obool)), _1598809), hAPP(hAPP(c_COMBB(tc_fun(_1598803, tc_HOL_Obool), tc_fun(_1598803, tc_HOL_Obool), _1598807), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598803, tc_HOL_Obool)), _1598805)), _1598811)))], (15481 ^ _779999) ^ [_1058536, _1058538, _1058540, _1058542] : [class_Groups_Oab__group__add(_1058536), 15484 ^ _779999 : [(15491 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058538), _1058540))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1058536), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1058536, _1058536), hAPP(hAPP(c_COMBB(_1058536, tc_fun(_1058536, _1058536), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1058536)), _1058542)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1058536, tc_Nat_Onat), _1058542), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1058538, _1058540)) = c_Groups_Ozero__class_Ozero(_1058536))], (15485 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058538), _1058540)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1058536), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1058536, _1058536), hAPP(hAPP(c_COMBB(_1058536, tc_fun(_1058536, _1058536), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1058536)), _1058542)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1058536, tc_Nat_Onat), _1058542), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1058538, _1058540)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058536), hAPP(_1058542, _1058538)), hAPP(_1058542, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058540), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (44946 ^ _779999) ^ [_1677987, _1677989, _1677991, _1677993, _1677995, _1677997] : [hAPP(hAPP(c_List_Olist_OCons(_1677987), _1677989), _1677991) = _1677993, _1677995 = hAPP(hAPP(c_List_Oappend(_1677987), _1677991), _1677997), -(hAPP(hAPP(c_List_Olist_OCons(_1677987), _1677989), _1677995) = hAPP(hAPP(c_List_Oappend(_1677987), _1677993), _1677997))], (7950 ^ _779999) ^ [_914095, _914097, _914099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914095), _914097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914097), _914099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914095), _914099)))], (34933 ^ _779999) ^ [_1432961] : [class_Int_Onumber__ring(_1432961), -(hAPP(c_Int_Onumber__class_Onumber__of(_1432961), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1432961), c_Groups_Oone__class_Oone(_1432961)))], (23587 ^ _779999) ^ [_1220655, _1220657] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1220655), hAPP(c_Nat_OSuc, _1220657)) = 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)), _1220657)), _1220655))], (39171 ^ _779999) ^ [_1535729, _1535731, _1535733] : [c_Relation_Orefl__on(_1535729, _1535731, _1535733), 39174 ^ _779999 : [(39181 ^ _779999) ^ [_1536213] : [hBOOL(hAPP(hAPP(c_member(_1535729), _1536213), _1535731)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1535729, _1535729)), hAPP(hAPP(c_Product__Type_OPair(_1535729, _1535729), _1536213), _1536213)), _1535733)))], (39175 ^ _779999) ^ [_1535940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535729, _1535729)), _1535940), _1535733)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1535729, _1535729, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1535729, tc_fun(_1535729, tc_HOL_Obool), tc_fun(_1535729, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1535729, tc_HOL_Obool), tc_fun(_1535729, tc_HOL_Obool)), _1535729), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1535729)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535729), c_fconj), hAPP(hAPP(c_COMBC(_1535729, tc_fun(_1535729, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535729)), _1535731)))), hAPP(hAPP(c_COMBC(_1535729, tc_fun(_1535729, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535729)), _1535731))), _1535940)))]]], (13467 ^ _779999) ^ [_1019891, _1019893, _1019895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1019891), _1019893)), _1019895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1019893), _1019895)))], (25247 ^ _779999) ^ [_1253956] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1253956)))], (40836 ^ _779999) ^ [_1576390, _1576392, _1576394] : [c_Relation_Ototal__on(_1576390, _1576392, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576390, _1576390), tc_HOL_Obool)), _1576394), c_Relation_OId(_1576390))), -(c_Relation_Ototal__on(_1576390, _1576392, _1576394))], (52132 ^ _779999) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (35691 ^ _779999) ^ [_1452526] : [-(c_Divides_Oadjust(_1452526) = 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)), _1452526))))), 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)), _1452526))))), 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))))))))], (7356 ^ _779999) ^ [_902095, _902097] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_902095, _902097, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_902095), tc_HOL_Obool))))], (49021 ^ _779999) ^ [_1766959, _1766961, _1766963] : [-(hAPP(c_List_Oset(_1766959), hAPP(c_List_OremoveAll(_1766959, _1766961), _1766963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1766959, tc_HOL_Obool)), hAPP(c_List_Oset(_1766959), _1766963)), hAPP(hAPP(c_Set_Oinsert(_1766959), _1766961), c_Orderings_Obot__class_Obot(tc_fun(_1766959, tc_HOL_Obool)))))], (37150 ^ _779999) ^ [] : [-(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))], (40345 ^ _779999) ^ [_1564910, _1564912, _1564914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564910, _1564910), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564910, _1564910), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564910, _1564912)), c_Transitive__Closure_Ortrancl(_1564910, _1564914))), c_Transitive__Closure_Ortrancl(_1564910, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564910, _1564910), tc_HOL_Obool)), _1564912), _1564914)))))], (30110 ^ _779999) ^ [_1344290, _1344292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1344290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344292), _1344290)), _1344292)))], (39056 ^ _779999) ^ [_1533848, _1533850] : [c_Relation_Orefl__on(_1533848, c_Orderings_Otop__class_Otop(tc_fun(_1533848, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1533848, _1533848)), hAPP(c_Product__Type_Oprod_Oprod__case(_1533848, _1533848, tc_HOL_Obool), _1533850))), -(c_Predicate_Oreflp(_1533848, _1533850))], (48338 ^ _779999) ^ [_1752670, _1752672] : [_1752672 = c_List_Olist_ONil(_1752670), -(c_List_Olist_ONil(_1752670) = hAPP(c_List_Orev(_1752670), _1752672))], (30734 ^ _779999) ^ [_1356099, _1356101] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1356099), _1356101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356099, _1356101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (1604 ^ _779999) ^ [_803157, _803159] : [-(class_Rings_Olinordered__semiring__strict(_803157)), _803159 = _803157, class_Rings_Olinordered__semiring__strict(_803159)], (47791 ^ _779999) ^ [_1742288, _1742290, _1742292, _1742294, _1742296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1742290), _1742292))), -(hAPP(hAPP(c_List_Onth(_1742294), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1742294), _1742296), c_List_Oupt(_1742292, _1742290))), _1742288) = hAPP(_1742296, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1742292), _1742288)))], (31128 ^ _779999) ^ [_1363464, _1363466] : [class_Groups_Osgn__if(_1363464), 31131 ^ _779999 : [(31138 ^ _779999) ^ [] : [-(_1363466 = c_Groups_Ozero__class_Ozero(_1363464)), 31141 ^ _779999 : [(31148 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363464), c_Groups_Ozero__class_Ozero(_1363464)), _1363466))), -(c_Groups_Osgn__class_Osgn(_1363464, _1363466) = hAPP(c_Groups_Ouminus__class_Ouminus(_1363464), c_Groups_Oone__class_Oone(_1363464)))], (31142 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363464), c_Groups_Ozero__class_Ozero(_1363464)), _1363466)), -(c_Groups_Osgn__class_Osgn(_1363464, _1363466) = c_Groups_Oone__class_Oone(_1363464))]]], (31132 ^ _779999) ^ [] : [_1363466 = c_Groups_Ozero__class_Ozero(_1363464), -(c_Groups_Osgn__class_Osgn(_1363464, _1363466) = c_Groups_Ozero__class_Ozero(_1363464))]]], (22351 ^ _779999) ^ [_1193477, _1193479] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193477), c_Orderings_Otop__class_Otop(tc_fun(_1193477, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1193477), _1193479) = hAPP(c_Finite__Set_Ocard(_1193477), c_Orderings_Otop__class_Otop(tc_fun(_1193477, tc_HOL_Obool))), -(_1193479 = c_Orderings_Otop__class_Otop(tc_fun(_1193477, tc_HOL_Obool)))], (12773 ^ _779999) ^ [_1006293, _1006295, _1006297] : [class_Lattices_Olattice(_1006293), hAPP(_1006295, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006293), 12778 ^ [_1006293, _1006295, _1006297]), 12779 ^ [_1006293, _1006295, _1006297])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006293), hAPP(_1006295, 12778 ^ [_1006293, _1006295, _1006297])), hAPP(_1006295, 12779 ^ [_1006293, _1006295, _1006297])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006293), _1006297)), -(_1006297 = c_Orderings_Obot__class_Obot(tc_fun(_1006293, tc_HOL_Obool))), -(hAPP(_1006295, c_Big__Operators_Olattice__class_OSup__fin(_1006293, _1006297)) = c_Big__Operators_Olattice__class_OSup__fin(_1006293, hAPP(c_Set_Oimage(_1006293, _1006293, _1006295), _1006297)))], (33363 ^ _779999) ^ [_1404342, _1404344] : [class_Int_Onumber__ring(_1404342), class_Rings_Olinordered__idom(_1404342), 33370 ^ _779999 : [(33377 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1404344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404342), c_Groups_Ozero__class_Ozero(_1404342)), hAPP(c_Int_Onumber__class_Onumber__of(_1404342), _1404344))))], (33371 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404342), c_Groups_Ozero__class_Ozero(_1404342)), hAPP(c_Int_Onumber__class_Onumber__of(_1404342), _1404344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1404344)))]]], (29912 ^ _779999) ^ [_1340855, _1340857, _1340859] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1340855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1340857), _1340859)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1340855), _1340857)), _1340859))], (49978 ^ _779999) ^ [_1789037, _1789039, _1789041, _1789043] : [-(hAPP(hAPP(c_List_Oappend(_1789037), c_List_Oreplicate(_1789037, _1789039, _1789041)), c_List_Oreplicate(_1789037, _1789043, _1789041)) = hAPP(hAPP(c_List_Oappend(_1789037), c_List_Oreplicate(_1789037, _1789043, _1789041)), c_List_Oreplicate(_1789037, _1789039, _1789041)))], (33037 ^ _779999) ^ [_1399346] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1399346) = c_Int_OPls)], (34099 ^ _779999) ^ [_1417747, _1417749] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1417747))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1417749))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417747)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417749)))], (10409 ^ _779999) ^ [_959201, _959203, _959205] : [class_Groups_Ocomm__monoid__add(_959201), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_959203, _959201), _959205), c_Orderings_Obot__class_Obot(tc_fun(_959203, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_959201))], (8167 ^ _779999) ^ [_918327] : [hAPP(c_Nat_OSuc, _918327) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45161 ^ _779999) ^ [_1682436, _1682438, _1682440] : [_1682436 = _1682438, -(_1682436 = hAPP(hAPP(c_List_Oappend(_1682440), c_List_Olist_ONil(_1682440)), _1682438))], (47250 ^ _779999) ^ [_1729069, _1729071] : [class_Orderings_Olinorder(_1729069), -(c_List_Olinorder__class_Osorted__list__of__set(_1729069, hAPP(c_List_Oset(_1729069), _1729071)) = c_List_Olinorder__class_Osort__key(_1729069, _1729069, c_COMBI(_1729069), c_List_Oremdups(_1729069, _1729071)))], (18826 ^ _779999) ^ [_1123570, _1123572] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1123570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123572), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1123570, _1123572))], (17031 ^ _779999) ^ [_1088059, _1088061, _1088063, _1088065] : [class_Rings_Olinordered__semiring(_1088059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088059), _1088061), _1088063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088059), _1088065), _1088063))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088059), c_Groups_Ozero__class_Ozero(_1088059)), _1088063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088059), _1088061), _1088065)))], (36697 ^ _779999) ^ [_1472293, _1472295, _1472297, _1472299, _1472301] : [c_Equiv__Relations_Oequiv(_1472293, _1472295, _1472297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472293, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472293, _1472293, _1472297), hAPP(hAPP(c_Set_Oinsert(_1472293), _1472299), c_Orderings_Obot__class_Obot(tc_fun(_1472293, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472293, _1472293, _1472297), hAPP(hAPP(c_Set_Oinsert(_1472293), _1472301), c_Orderings_Obot__class_Obot(tc_fun(_1472293, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1472293), _1472299), _1472295)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472293, _1472293)), hAPP(hAPP(c_Product__Type_OPair(_1472293, _1472293), _1472301), _1472299)), _1472297)))], (26640 ^ _779999) ^ [_1279426, _1279428] : [class_Orderings_Olinorder(_1279426), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279426, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1279426), _1279428)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1279426), _1279428))], (46512 ^ _779999) ^ [_1713023, _1713025] : [_1713023 = _1713025, -(hAPP(c_Code__Numeral_Oof__nat, _1713023) = hAPP(c_Code__Numeral_Oof__nat, _1713025))], (5344 ^ _779999) ^ [_861769, _861771, _861773, _861775] : [-(c_Hilbert__Choice_OEps(_861775, _861771) = c_Hilbert__Choice_OEps(_861773, _861769)), _861775 = _861773, _861771 = _861769], (43620 ^ _779999) ^ [_1646397, _1646399, _1646401] : [-(hAPP(hAPP(c_List_Onth(_1646397), hAPP(hAPP(c_List_Olist_OCons(_1646397), _1646399), _1646401)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1646399)], (45358 ^ _779999) ^ [_1687669, _1687671] : [hBOOL(hAPP(c_List_Odistinct(_1687669), _1687671)), -(hBOOL(hAPP(c_List_Odistinct(_1687669), hAPP(c_List_Orotate1(_1687669), _1687671))))], (30040 ^ _779999) ^ [_1342971, _1342973, _1342975] : [class_Rings_Oring__1(_1342971), -(hAPP(c_Int_Oring__1__class_Oof__int(_1342971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1342973), _1342975)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342971), hAPP(c_Int_Oring__1__class_Oof__int(_1342971), _1342973)), hAPP(c_Int_Oring__1__class_Oof__int(_1342971), _1342975)))], (17842 ^ _779999) ^ [_1104906, _1104908] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1104906, _1104908))))], (7661 ^ _779999) ^ [_908707, _908709] : [hAPP(c_Nat_OSuc, _908707) = hAPP(c_Nat_OSuc, _908709), -(_908707 = _908709)], (34113 ^ _779999) ^ [_1418008] : [-(c_Int_Opred(c_Int_OBit0(_1418008)) = c_Int_OBit1(c_Int_Opred(_1418008)))], (28312 ^ _779999) ^ [_1312282, _1312284, _1312286] : [class_Fields_Ofield__inverse__zero(_1312282), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312282), hAPP(c_Groups_Ouminus__class_Ouminus(_1312282), _1312284)), hAPP(c_Groups_Ouminus__class_Ouminus(_1312282), _1312286)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312282), _1312284), _1312286))], (34023 ^ _779999) ^ [_1416374, _1416376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1416374), _1416376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1416374)), c_Int_OBit1(_1416376))))], (5610 ^ _779999) ^ [_865880, _865882, _865884, _865886] : [-(tc_sum(_865886, _865882) = tc_sum(_865884, _865880)), _865886 = _865884, _865882 = _865880], (8017 ^ _779999) ^ [_915281, _915283, _915285, _915287] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_915281, _915283), _915285, _915287, _915285)), 8018 ^ _779999 : [(8021 ^ _779999) ^ [_915368] : [c_Natural_Oevaln(_915283, _915285, _915287, _915368), c_Natural_Oevaln(c_Com_Ocom_OWhile(_915281, _915283), _915368, _915287, _915285)], (8019 ^ _779999) ^ [] : [-(hBOOL(hAPP(_915281, _915285)))]]], (26646 ^ _779999) ^ [_1279537, _1279539] : [class_Orderings_Olinorder(_1279537), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279537, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1279537), _1279539)) = hAPP(c_SetInterval_Oord__class_OatMost(_1279537), _1279539))], (21766 ^ _779999) ^ [_1177050, _1177052, _1177054] : [-(hBOOL(hAPP(_1177050, _1177052))), -(hAPP(c_Set_OCollect(_1177054), hAPP(hAPP(c_COMBS(_1177054, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177054), c_fconj), hAPP(c_fequal, _1177052))), _1177050)) = c_Orderings_Obot__class_Obot(tc_fun(_1177054, tc_HOL_Obool)))], (15613 ^ _779999) ^ [_1061484, _1061486, _1061488] : [class_Rings_Oring__no__zero__divisors(_1061484), 15616 ^ _779999 : [(15617 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061484), _1061486), _1061488) = c_Groups_Ozero__class_Ozero(_1061484), -(_1061486 = c_Groups_Ozero__class_Ozero(_1061484)), -(_1061488 = c_Groups_Ozero__class_Ozero(_1061484))], (15627 ^ _779999) ^ [] : [15628 ^ _779999 : [(15631 ^ _779999) ^ [] : [_1061488 = c_Groups_Ozero__class_Ozero(_1061484)], (15629 ^ _779999) ^ [] : [_1061486 = c_Groups_Ozero__class_Ozero(_1061484)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061484), _1061486), _1061488) = c_Groups_Ozero__class_Ozero(_1061484))]]], (24232 ^ _779999) ^ [_1233794, _1233796, _1233798] : [class_Orderings_Olinorder(_1233794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1233794), _1233796)), hBOOL(hAPP(hAPP(c_member(_1233794), _1233798), _1233796)), 24243 ^ _779999 : [(24250 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1233794, tc_HOL_Obool)), _1233796), hAPP(hAPP(c_Set_Oinsert(_1233794), _1233798), c_Orderings_Obot__class_Obot(tc_fun(_1233794, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1233794, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1233794, _1233796) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1233794), _1233798), c_Big__Operators_Olinorder__class_OMax(_1233794, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1233794, tc_HOL_Obool)), _1233796), hAPP(hAPP(c_Set_Oinsert(_1233794), _1233798), c_Orderings_Obot__class_Obot(tc_fun(_1233794, tc_HOL_Obool)))))))], (24244 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1233794, tc_HOL_Obool)), _1233796), hAPP(hAPP(c_Set_Oinsert(_1233794), _1233798), c_Orderings_Obot__class_Obot(tc_fun(_1233794, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1233794, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1233794, _1233796) = _1233798)]]], (18159 ^ _779999) ^ [_1110559, _1110561] : [class_Rings_Olinordered__semidom(_1110559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110559), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110559), _1110561)), c_Groups_Ozero__class_Ozero(_1110559)))], (11961 ^ _779999) ^ [_990436, _990438, _990440, _990442, _990444, _990446, _990448, _990450] : [c_Finite__Set_Ofolding__image__simple(_990436, _990438, _990440, _990442, _990444, _990446), hBOOL(hAPP(c_Finite__Set_Ofinite(_990438), _990448)), hBOOL(hAPP(hAPP(c_member(_990438), _990450), _990448)), -(hAPP(_990446, _990448) = hAPP(hAPP(_990440, hAPP(_990444, _990450)), hAPP(_990446, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990438, tc_HOL_Obool)), _990448), hAPP(hAPP(c_Set_Oinsert(_990438), _990450), c_Orderings_Obot__class_Obot(tc_fun(_990438, tc_HOL_Obool)))))))], (27966 ^ _779999) ^ [_1305792, _1305794] : [class_Power_Opower(_1305792), class_Rings_Osemiring__0(_1305792), 27973 ^ _779999 : [(27980 ^ _779999) ^ [] : [-(_1305794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305792), c_Groups_Ozero__class_Ozero(_1305792)), _1305794) = c_Groups_Ozero__class_Ozero(_1305792))], (27974 ^ _779999) ^ [] : [_1305794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305792), c_Groups_Ozero__class_Ozero(_1305792)), _1305794) = c_Groups_Oone__class_Oone(_1305792))]]], (29666 ^ _779999) ^ [_1336343, _1336345] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336343), _1336345) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29667 ^ _779999 : [(29676 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1336343), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336345), _1336343))], (29670 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336343), _1336345))], (29668 ^ _779999) ^ [] : [_1336345 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (11332 ^ _779999) ^ [_976674, _976676, _976678, _976680] : [-(hBOOL(hAPP(hAPP(c_member(_976674), _976676), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976674, tc_HOL_Obool)), _976678), _976680)))), hBOOL(hAPP(hAPP(c_member(_976674), _976676), _976678)), hBOOL(hAPP(hAPP(c_member(_976674), _976676), _976680))], (48788 ^ _779999) ^ [_1762133, _1762135, _1762137, _1762139, _1762141] : [hBOOL(hAPP(hAPP(c_member(_1762133), _1762135), hAPP(c_List_Oset(_1762133), _1762137))), -(hBOOL(hAPP(_1762139, _1762135))), -(c_List_OdropWhile(_1762133, _1762139, hAPP(hAPP(c_List_Oappend(_1762133), _1762137), _1762141)) = hAPP(hAPP(c_List_Oappend(_1762133), c_List_OdropWhile(_1762133, _1762139, _1762137)), _1762141))], (11112 ^ _779999) ^ [_972554, _972556, _972558] : [class_Lattices_Olattice(_972554), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972554), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_972554), _972556), _972558)), _972558)))], (45548 ^ _779999) ^ [_1692312, _1692314, _1692316, _1692318, _1692320] : [-(hAPP(hAPP(c_List_Ozip(_1692312, _1692314), hAPP(hAPP(c_List_Oappend(_1692312), _1692316), _1692318)), _1692320) = hAPP(hAPP(c_List_Oappend(tc_prod(_1692312, _1692314)), hAPP(hAPP(c_List_Ozip(_1692312, _1692314), _1692316), hAPP(hAPP(c_List_Otake(_1692314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692312)), _1692316)), _1692320))), hAPP(hAPP(c_List_Ozip(_1692312, _1692314), _1692318), hAPP(hAPP(c_List_Odrop(_1692314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692312)), _1692316)), _1692320))))], (26107 ^ _779999) ^ [_1269676, _1269678, _1269680] : [class_Groups_Ocomm__monoid__mult(_1269676), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1269678, _1269676), _1269680), c_Orderings_Obot__class_Obot(tc_fun(_1269678, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1269676))], (34537 ^ _779999) ^ [_1425514, _1425516, _1425518] : [class_Rings_Olinordered__idom(_1425514), 34540 ^ _779999 : [(34549 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425514), hAPP(hAPP(c_Power_Opower__class_Opower(_1425514), _1425516), 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(_1425514), _1425518), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1425514)))), _1425516 = c_Groups_Ozero__class_Ozero(_1425514), _1425518 = c_Groups_Ozero__class_Ozero(_1425514)], (34541 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425514), hAPP(hAPP(c_Power_Opower__class_Opower(_1425514), _1425516), 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(_1425514), _1425518), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1425514))), 34544 ^ _779999 : [(34547 ^ _779999) ^ [] : [-(_1425518 = c_Groups_Ozero__class_Ozero(_1425514))], (34545 ^ _779999) ^ [] : [-(_1425516 = c_Groups_Ozero__class_Ozero(_1425514))]]]]], (19387 ^ _779999) ^ [_1133500] : [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)), _1133500))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1133500)))], (51894 ^ _779999) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (36721 ^ _779999) ^ [_1472853, _1472855, _1472857, _1472859, _1472861] : [c_Equiv__Relations_Oequiv(_1472853, _1472855, _1472857), hBOOL(hAPP(hAPP(c_member(tc_fun(_1472853, tc_HOL_Obool)), _1472859), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472853), _1472855), _1472857))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1472853, tc_HOL_Obool)), _1472861), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472853), _1472855), _1472857))), -(_1472859 = _1472861), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472853, tc_HOL_Obool)), _1472859), _1472861) = c_Orderings_Obot__class_Obot(tc_fun(_1472853, tc_HOL_Obool)))], (40581 ^ _779999) ^ [_1570455] : [-(c_Relation_OId(_1570455) = hAPP(c_Set_OCollect(tc_prod(_1570455, _1570455)), hAPP(hAPP(c_COMBB(tc_fun(_1570455, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1570455, _1570455)), c_HOL_OEx(_1570455)), hAPP(hAPP(c_COMBC(tc_prod(_1570455, _1570455), tc_fun(_1570455, tc_prod(_1570455, _1570455)), tc_fun(_1570455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1570455, _1570455), tc_HOL_Obool), tc_fun(tc_fun(_1570455, tc_prod(_1570455, _1570455)), tc_fun(_1570455, tc_HOL_Obool)), tc_prod(_1570455, _1570455)), c_COMBB(tc_prod(_1570455, _1570455), tc_HOL_Obool, _1570455)), c_fequal)), hAPP(hAPP(c_COMBS(_1570455, _1570455, tc_prod(_1570455, _1570455)), c_Product__Type_OPair(_1570455, _1570455)), c_COMBI(_1570455))))))], (24700 ^ _779999) ^ [_1242769, _1242771, _1242773, _1242775, _1242777] : [class_Orderings_Olinorder(_1242769), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242769, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1242769, _1242771, _1242773)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1242769, _1242775, _1242777)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1242769, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242769), _1242771), _1242775), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1242769), _1242773), _1242777)))], (20425 ^ _779999) ^ [_1151630, _1151632] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1151630, _1151632)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1151632), _1151630)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (3908 ^ _779999) ^ [_838807, _838809, _838811, _838813] : [-(c_List_Otranspose(_838813, _838809) = c_List_Otranspose(_838811, _838807)), _838813 = _838811, _838809 = _838807], (20840 ^ _779999) ^ [_1158295, _1158297] : [class_Rings_Olinordered__idom(_1158295), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), hAPP(c_Groups_Oabs__class_Oabs(_1158295), _1158297)), hAPP(c_Groups_Oabs__class_Oabs(_1158295), _1158297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), _1158297), _1158297))], (44990 ^ _779999) ^ [_1678974, _1678976, _1678978, _1678980] : [_1678976 = _1678980, -(hAPP(hAPP(c_List_Oappend(_1678974), _1678976), _1678978) = hAPP(hAPP(c_List_Oappend(_1678974), _1678980), _1678978))], (34397 ^ _779999) ^ [_1423139, _1423141, _1423143] : [class_Rings_Olinordered__semidom(_1423139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423139), hAPP(hAPP(c_Power_Opower__class_Opower(_1423139), _1423141), 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(_1423139), _1423143), 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(_1423139), c_Groups_Ozero__class_Ozero(_1423139)), _1423143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423139), _1423141), _1423143)))], (30930 ^ _779999) ^ [_1359714, _1359716, _1359718, _1359720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1359716), _1359718)), -(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), _1359718), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359720, _1359714))), _1359716)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359718), _1359714))))], (51746 ^ _779999) ^ [_1827591, _1827593, _1827595, _1827597, _1827599, _1827601, _1827603] : [c_Fun_Obij__betw(_1827591, _1827593, _1827595, _1827597, _1827599), c_Fun_Obij__betw(_1827591, _1827593, _1827595, _1827601, _1827603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1827593, tc_HOL_Obool)), _1827599), _1827603) = c_Orderings_Obot__class_Obot(tc_fun(_1827593, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1827591, _1827593, _1827595, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1827591, tc_HOL_Obool)), _1827597), _1827601), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1827593, tc_HOL_Obool)), _1827599), _1827603)))], (45791 ^ _779999) ^ [_1697139, _1697141] : [class_Complete__Lattice_Ocomplete__lattice(_1697139), -(c_Complete__Lattice_OInf__class_OInf(_1697139, hAPP(c_List_Oset(_1697139), _1697141)) = hAPP(c_List_Ofoldl(_1697139, _1697139, c_Lattices_Osemilattice__inf__class_Oinf(_1697139), c_Orderings_Otop__class_Otop(_1697139)), _1697141))], (35972 ^ _779999) ^ [_1457424, _1457426, _1457428, _1457430, _1457432, _1457434] : [-(hAPP(c_Product__Type_Oapsnd(_1457424, _1457426, _1457428, _1457430), hAPP(hAPP(c_Product__Type_OPair(_1457428, _1457424), _1457432), _1457434)) = hAPP(hAPP(c_Product__Type_OPair(_1457428, _1457426), _1457432), hAPP(_1457430, _1457434)))], (7376 ^ _779999) ^ [_902443, _902445, _902447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902443, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_902443, tc_fun(_902443, tc_HOL_Obool), tc_HOL_Obool), c_member(_902443)), _902445)), hAPP(hAPP(c_COMBC(_902443, tc_fun(_902443, tc_HOL_Obool), tc_HOL_Obool), c_member(_902443)), _902447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902443, tc_HOL_Obool)), _902445), _902447)))], (39997 ^ _779999) ^ [_1555891, _1555893, _1555895, _1555897] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1555891, tc_HOL_Obool), tc_fun(_1555891, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1555891, tc_HOL_Obool), tc_fun(_1555891, tc_HOL_Obool)), _1555893), _1555895)), c_Wellfounded_Omax__ext(_1555891, _1555897)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555891), _1555893)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555891), _1555895)), -(_1555895 = c_Orderings_Obot__class_Obot(tc_fun(_1555891, tc_HOL_Obool))), 40011 ^ _779999 : [(40014 ^ _779999) ^ [_1556296] : [hBOOL(hAPP(hAPP(c_member(_1555891), _1556296), _1555895)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1555891, _1555891)), hAPP(hAPP(c_Product__Type_OPair(_1555891, _1555891), 40010 ^ [_1555891, _1555893, _1555895, _1555897]), _1556296)), _1555897))], (40012 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555891), 40010 ^ [_1555891, _1555893, _1555895, _1555897]), _1555893)))]]], (43255 ^ _779999) ^ [_1634994, _1634996, _1634998, _1635000, _1635002, _1635004] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634994), tc_List_Olist(_1634994))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634994), tc_List_Olist(_1634994)), hAPP(hAPP(c_List_Olist_OCons(_1634994), _1634996), _1634998)), hAPP(hAPP(c_List_Olist_OCons(_1634994), _1635000), _1635002))), c_List_Olex(_1634994, _1635004)))), 43256 ^ _779999 : [(43263 ^ _779999) ^ [] : [_1634996 = _1635000, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634994), tc_List_Olist(_1634994))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634994), tc_List_Olist(_1634994)), _1634998), _1635002)), c_List_Olex(_1634994, _1635004)))], (43257 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634994, _1634994)), hAPP(hAPP(c_Product__Type_OPair(_1634994, _1634994), _1634996), _1635000)), _1635004)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634994)), _1634998) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634994)), _1635002)]]], (36951 ^ _779999) ^ [_1478026, _1478028, _1478030] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1478026, tc_HOL_Obool), tc_fun(_1478026, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1478026, tc_HOL_Obool), tc_fun(_1478026, tc_HOL_Obool)), _1478028), _1478030)), c_Wellfounded_Ofinite__psubset(_1478026)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1478026, tc_HOL_Obool)), _1478028), _1478030)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478026), _1478030))], (19747 ^ _779999) ^ [_1140066, _1140068, _1140070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140066)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1140068), _1140070)), 19754 ^ _779999 : [(19755 ^ _779999) ^ [_1140262] : [19757 ^ _779999 : [(19763 ^ _779999) ^ [] : [-(_1140262 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19759 ^ [_1140066, _1140068, _1140070, _1140262]), 19756 ^ [_1140066, _1140068, _1140070, _1140262]))], (19761 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19759 ^ [_1140066, _1140068, _1140070, _1140262]), _1140070)))], (19758 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 19756 ^ [_1140066, _1140068, _1140070, _1140262]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1140066))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140068), _1140262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140262), _1140066))))]]], (37757 ^ _779999) ^ [_1499613, _1499615, _1499617, _1499619, _1499621] : [c_Typedef_Otype__definition(_1499613, _1499615, _1499617, _1499619, _1499621), -(hAPP(c_Set_Oimage(_1499615, _1499613, _1499619), _1499621) = c_Orderings_Otop__class_Otop(tc_fun(_1499613, tc_HOL_Obool)))], (6223 ^ _779999) ^ [_879482, _879484, _879486] : [_879482 = _879484, 6226 ^ _779999 : [(6229 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879486, tc_HOL_Obool)), _879484), _879482)))], (6227 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879486, tc_HOL_Obool)), _879482), _879484)))]]], (51714 ^ _779999) ^ [_1826839, _1826841, _1826843, _1826845] : [-(c_Product__Type_Ocurry(_1826839, _1826841, _1826843, hAPP(c_Product__Type_Oprod_Oprod__case(_1826839, _1826841, _1826843), _1826845)) = _1826845)], (45610 ^ _779999) ^ [_1693449, _1693451, _1693453] : [-(_1693449 = c_List_Olist_ONil(_1693451)), -(hAPP(c_List_Ohd(_1693451), hAPP(c_List_Orotate(_1693451, _1693453), _1693449)) = hAPP(hAPP(c_List_Onth(_1693451), _1693449), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1693453, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693451)), _1693449))))], (51151 ^ _779999) ^ [_1814695, _1814697] : [51152 ^ _779999 : [(51153 ^ _779999) ^ [_1814751] : [hBOOL(hAPP(hAPP(_1814695, _1814751), _1814751))]], c_Predicate_Osymp(_1814697, _1814695), c_Predicate_Otransp(_1814697, _1814695), -(c_Equiv__Relations_Opart__equivp(_1814697, _1814695))], (16679 ^ _779999) ^ [_1081688, _1081690, _1081692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1081688), _1081690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1081692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081688), _1081692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081690), _1081692))))], (50204 ^ _779999) ^ [_1793538, _1793540, _1793542, _1793544] : [50205 ^ _779999 : [(50208 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1793538), _1793542), _1793544))], (50206 ^ _779999) ^ [] : [_1793540 = _1793544]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1793538), hAPP(hAPP(c_List_Olist_OCons(_1793538), _1793540), _1793542)), _1793544)))], (49870 ^ _779999) ^ [_1787079, _1787081, _1787083] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787079)), c_List_Oreplicate(_1787079, _1787081, _1787083)) = _1787081)], (24780 ^ _779999) ^ [_1244229, _1244231, _1244233] : [class_Orderings_Olinorder(_1244229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244229), _1244231)), -(_1244231 = c_Orderings_Obot__class_Obot(tc_fun(_1244229, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244229), _1244233)), -(_1244233 = c_Orderings_Obot__class_Obot(tc_fun(_1244229, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1244229, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1244229, tc_HOL_Obool)), _1244231), _1244233)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244229), c_Big__Operators_Olinorder__class_OMax(_1244229, _1244231)), c_Big__Operators_Olinorder__class_OMax(_1244229, _1244233)))], (41936 ^ _779999) ^ [_1602373, _1602375, _1602377, _1602379] : [41938 ^ _779999 : [(41941 ^ _779999) ^ [] : [hAPP(_1602379, 41937 ^ [_1602373, _1602375, _1602377, _1602379]) = c_Orderings_Otop__class_Otop(tc_fun(_1602373, tc_HOL_Obool))], (41939 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602375), 41937 ^ [_1602373, _1602375, _1602377, _1602379]), _1602377)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1602373, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602375, tc_fun(_1602373, tc_HOL_Obool)), _1602377), _1602379))], (24326 ^ _779999) ^ [_1235693, _1235695, _1235697, _1235699] : [class_Orderings_Olinorder(_1235693), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235693), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235693), _1235695), _1235697)), _1235699) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235693), _1235695), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1235693), _1235697), _1235699)))], (25056 ^ _779999) ^ [_1250219, _1250221, _1250223] : [class_Orderings_Olinorder(_1250219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250219), _1250221)), -(_1250221 = c_Orderings_Obot__class_Obot(tc_fun(_1250219, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250219), _1250223)), -(_1250223 = c_Orderings_Obot__class_Obot(tc_fun(_1250219, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1250219, c_Orderings_Oord__class_Omax(_1250219), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250219, tc_HOL_Obool)), _1250221), _1250223)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250219), c_Big__Operators_Olattice_OSup__fin(_1250219, c_Orderings_Oord__class_Omax(_1250219), _1250221)), c_Big__Operators_Olattice_OSup__fin(_1250219, c_Orderings_Oord__class_Omax(_1250219), _1250223)))], (1384 ^ _779999) ^ [_800407, _800409] : [-(class_Rings_Oring(_800407)), _800409 = _800407, class_Rings_Oring(_800409)], (31114 ^ _779999) ^ [_1363276, _1363278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363276)), -(c_SMT_Oz3mod(_1363278, _1363276) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363278, _1363276))], (29295 ^ _779999) ^ [_1330341, _1330343, _1330345, _1330347, _1330349] : [class_Fields_Ofield(_1330341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330343), _1330345)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330343), _1330347)), 29309 ^ _779999 : [(29312 ^ _779999) ^ [] : [-(hAPP(_1330349, 29308 ^ [_1330341, _1330343, _1330345, _1330347, _1330349]) = c_Groups_Ozero__class_Ozero(_1330341))], (29310 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330343), 29308 ^ [_1330341, _1330343, _1330345, _1330347, _1330349]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330343, tc_HOL_Obool)), _1330345), _1330347))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330343, _1330341), _1330349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330343, tc_HOL_Obool)), _1330345), _1330347)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330341), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330343, _1330341), _1330349), _1330345)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330343, _1330341), _1330349), _1330347))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330343, _1330341), _1330349), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330343, tc_HOL_Obool)), _1330345), _1330347))))], (43383 ^ _779999) ^ [_1639288, _1639290, _1639292, _1639294, _1639296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639288, _1639288)), hAPP(hAPP(c_Product__Type_OPair(_1639288, _1639288), _1639290), _1639292)), _1639294)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639288), tc_List_Olist(_1639288))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639288), tc_List_Olist(_1639288)), hAPP(hAPP(c_List_Olist_OCons(_1639288), _1639290), _1639296)), hAPP(hAPP(c_List_Olist_OCons(_1639288), _1639292), _1639296))), c_List_Olistrel1(_1639288, _1639294))))], (20369 ^ _779999) ^ [_1150686, _1150688, _1150690] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150686, tc_Nat_Onat), _1150688), _1150690) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150686, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1150686), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1150688)), _1150690)))], (40303 ^ _779999) ^ [_1563855, _1563857] : [-(c_Relation_Orefl__on(_1563855, c_Orderings_Otop__class_Otop(tc_fun(_1563855, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1563855, _1563857)))], (14375 ^ _779999) ^ [_1036731, _1036733, _1036735, _1036737, _1036739, _1036741] : [c_Fun_Oinj__on(_1036731, _1036733, _1036735, _1036737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036733, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1036731, _1036733, _1036735), _1036737)), _1036739)), c_Fun_Oinj__on(_1036733, _1036731, _1036741, _1036739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036731, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1036733, _1036731, _1036741), _1036739)), _1036737)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036731), _1036737)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036733), _1036739)), -(hAPP(c_Finite__Set_Ocard(_1036731), _1036737) = hAPP(c_Finite__Set_Ocard(_1036733), _1036739))], (43487 ^ _779999) ^ [_1642857, _1642859, _1642861, _1642863, _1642865, _1642867] : [c_List_Olistrelp(_1642857, _1642859, hAPP(hAPP(c_List_Olist_OCons(_1642857), _1642861), _1642863), hAPP(hAPP(c_List_Olist_OCons(_1642857), _1642865), _1642867)), 43490 ^ _779999 : [(43493 ^ _779999) ^ [] : [-(c_List_Olistrelp(_1642857, _1642859, _1642863, _1642867))], (43491 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1642859, _1642861), _1642865)))]]], (50446 ^ _779999) ^ [_1799136, _1799138, _1799140] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1799136, _1799138, _1799140, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1799138)], (31265 ^ _779999) ^ [_1365615, _1365617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365615), _1365617)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365617, _1365615) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1365617), _1365615), _1365615))], (48562 ^ _779999) ^ [_1757364, _1757366, _1757368] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1757364), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1757364))), _1757366))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757364))), _1757366))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757364))), hAPP(c_List_Ofilter(tc_List_Olist(_1757364), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1757364)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757368)), c_Nat_Osize__class_Osize(tc_List_Olist(_1757364)))), c_List_Otranspose(_1757364, _1757366))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757364)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1757364)), _1757366), _1757368)))], (35111 ^ _779999) ^ [_1435893, _1435895] : [-(_1435893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435895, _1435893), c_Divides_Odivmod__int(_1435895, _1435893))))], (36495 ^ _779999) ^ [_1467384, _1467386, _1467388, _1467390, _1467392, _1467394] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1467384, _1467386), _1467386, _1467388), hAPP(hAPP(c_COMBB(_1467390, tc_fun(_1467386, _1467388), tc_prod(_1467384, _1467386)), _1467392), hAPP(hAPP(c_COMBB(_1467384, _1467390, tc_prod(_1467384, _1467386)), _1467394), c_Product__Type_Ofst(_1467384, _1467386)))), c_Product__Type_Osnd(_1467384, _1467386)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1467384, _1467386, _1467388), hAPP(hAPP(c_COMBB(_1467390, tc_fun(_1467386, _1467388), _1467384), _1467392), _1467394)))], (34277 ^ _779999) ^ [] : [-(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))))], (33145 ^ _779999) ^ [_1400932, _1400934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1400932)), _1400934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400932), _1400934)))], (30002 ^ _779999) ^ [_1342282, _1342284, _1342286] : [class_Rings_Olinordered__idom(_1342282), 30005 ^ _779999 : [(30012 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342284), _1342286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342282), hAPP(c_Int_Oring__1__class_Oof__int(_1342282), _1342284)), hAPP(c_Int_Oring__1__class_Oof__int(_1342282), _1342286))))], (30006 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342282), hAPP(c_Int_Oring__1__class_Oof__int(_1342282), _1342284)), hAPP(c_Int_Oring__1__class_Oof__int(_1342282), _1342286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342284), _1342286)))]]], (50975 ^ _779999) ^ [_1811658, _1811660] : [c_Relation_Osym(_1811658, _1811660), c_Relation_Otrans(_1811658, _1811660), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1811658, _1811658), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1811658, _1811658, _1811658), hAPP(c_Relation_Oconverse(_1811658, _1811658), _1811660)), _1811660)), _1811660)))], (45520 ^ _779999) ^ [_1691592, _1691594, _1691596, _1691598] : [-(hAPP(c_List_Orotate1(_1691594), hAPP(hAPP(c_List_Olist_OCons(_1691594), _1691596), _1691598)) = hAPP(hAPP(c_List_Oappend(_1691594), _1691598), hAPP(hAPP(c_List_Olist_OCons(_1691594), _1691596), c_List_Olist_ONil(_1691594))))], (38345 ^ _779999) ^ [_1513477, _1513479, _1513481] : [hAPP(c_Relation_ODomain(_1513477, _1513479), _1513481) = c_Orderings_Obot__class_Obot(tc_fun(_1513477, tc_HOL_Obool)), -(_1513481 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513477, _1513479), tc_HOL_Obool)))], (33565 ^ _779999) ^ [_1407657, _1407659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407657), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407657)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407659)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5226 ^ _779999) ^ [_859914, _859916] : [_859916 = _859914, -(c_Groups_Ominus__class_Ominus(_859916) = c_Groups_Ominus__class_Ominus(_859914))], (40241 ^ _779999) ^ [_1561639, _1561641] : [-(c_Transitive__Closure_Otrancl(_1561639, _1561641) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561639, _1561639), tc_HOL_Obool)), _1561641), hAPP(hAPP(c_Relation_Orel__comp(_1561639, _1561639, _1561639), c_Transitive__Closure_Otrancl(_1561639, _1561641)), _1561641)))], (15913 ^ _779999) ^ [_1066844] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1066844) = _1066844)], (36010 ^ _779999) ^ [_1458023, _1458025] : [-(c_Divides_Opdivmod(_1458023, _1458025) = 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), _1458023)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458025))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458023), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458025))))], (9744 ^ _779999) ^ [_945730, _945732, _945734, _945736] : [c_Orderings_Oorder__class_Omono(tc_fun(_945730, tc_HOL_Obool), tc_fun(_945730, tc_HOL_Obool), _945732), hBOOL(hAPP(hAPP(c_member(_945730), _945734), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_945730, tc_HOL_Obool), _945732))), -(hBOOL(hAPP(hAPP(c_member(_945730), _945734), hAPP(_945732, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945730, tc_HOL_Obool)), _945736), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_945730, tc_HOL_Obool), _945732))))))], (24636 ^ _779999) ^ [_1241383, _1241385, _1241387, _1241389] : [class_Orderings_Olinorder(_1241383), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241383), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241383), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1241383), _1241385), _1241387)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1241383), _1241385), _1241389))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1241383), _1241385), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241383), _1241387), _1241389)))))], (7254 ^ _779999) ^ [_900018, _900020, _900022, _900024, _900026, _900028] : [hBOOL(hAPP(hAPP(c_member(_900018), _900020), _900022)), _900024 = hAPP(_900026, _900020), -(hBOOL(hAPP(hAPP(c_member(_900028), _900024), hAPP(c_Set_Oimage(_900018, _900028, _900026), _900022))))], (22912 ^ _779999) ^ [_1206507, _1206509, _1206511, _1206513, _1206515] : [class_Complete__Lattice_Ocomplete__lattice(_1206507), hBOOL(hAPP(hAPP(c_member(_1206509), _1206511), _1206513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206507), hAPP(_1206515, _1206511)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1206509, _1206507), _1206513), _1206515))))], (30451 ^ _779999) ^ [_1350580, _1350582, _1350584, _1350586, _1350588, _1350590] : [class_Divides_Oring__div(_1350580), c_Divides_Odiv__class_Omod(_1350580, _1350582, _1350584) = c_Divides_Odiv__class_Omod(_1350580, _1350586, _1350584), c_Divides_Odiv__class_Omod(_1350580, _1350588, _1350584) = c_Divides_Odiv__class_Omod(_1350580, _1350590, _1350584), -(c_Divides_Odiv__class_Omod(_1350580, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350580), _1350582), _1350588), _1350584) = c_Divides_Odiv__class_Omod(_1350580, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350580), _1350586), _1350590), _1350584))], (15000 ^ _779999) ^ [_1049092, _1049094, _1049096] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049092), _1049094)), -(hAPP(c_Finite__Set_Ocard(_1049092), hAPP(hAPP(c_Set_Oinsert(_1049092), _1049096), _1049094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1049092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049092, tc_HOL_Obool)), _1049094), hAPP(hAPP(c_Set_Oinsert(_1049092), _1049096), c_Orderings_Obot__class_Obot(tc_fun(_1049092, tc_HOL_Obool)))))))], (48578 ^ _779999) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (51786 ^ _779999) ^ [_1828230, _1828232] : [class_Lattices_Olattice(_1828230), -(class_Lattices_Osemilattice__sup(tc_fun(_1828232, _1828230)))], (37545 ^ _779999) ^ [_1492700, _1492702] : [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)), _1492700), _1492702)), 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)), _1492700), 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)), _1492702), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (24138 ^ _779999) ^ [_1230942, _1230944, _1230946] : [class_Orderings_Olinorder(_1230942), hBOOL(hAPP(c_Finite__Set_Ofinite(_1230942), _1230944)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1230942), _1230946)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1230942, tc_HOL_Obool)), _1230944), _1230946) = c_Orderings_Obot__class_Obot(tc_fun(_1230942, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1230942), c_Big__Operators_Olattice_OInf__fin(_1230942, c_Orderings_Oord__class_Omin(_1230942), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230942, tc_HOL_Obool)), _1230944), _1230946))), c_Big__Operators_Olattice_OInf__fin(_1230942, c_Orderings_Oord__class_Omin(_1230942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1230942, tc_HOL_Obool)), _1230944), _1230946))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1230942), c_Big__Operators_Olattice_OInf__fin(_1230942, c_Orderings_Oord__class_Omin(_1230942), _1230944)), c_Big__Operators_Olattice_OInf__fin(_1230942, c_Orderings_Oord__class_Omin(_1230942), _1230946)))], (5084 ^ _779999) ^ [_857705, _857707, _857709, _857711, _857713, _857715, _857717, _857719] : [-(c_Random__Sequence_Omap(_857719, _857715, _857711, _857707) = c_Random__Sequence_Omap(_857717, _857713, _857709, _857705)), _857719 = _857717, _857715 = _857713, _857711 = _857709, _857707 = _857705], (1254 ^ _779999) ^ [_798782, _798784] : [-(class_Rings_Oordered__ring__abs(_798782)), _798784 = _798782, class_Rings_Oordered__ring__abs(_798784)], (38866 ^ _779999) ^ [_1529315, _1529317] : [-(c_Product__Type_Omap__pair(_1529315, _1529315, _1529317, _1529317, c_Fun_Oid(_1529315), c_Fun_Oid(_1529317)) = c_Fun_Oid(tc_prod(_1529315, _1529317)))], (47739 ^ _779999) ^ [_1741246, _1741248, _1741250, _1741252] : [-(c_List_Oupt(_1741246, _1741248) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1741250), _1741252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741246), _1741248)), _1741246 = _1741250, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741246), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1741248) = _1741252], (23471 ^ _779999) ^ [_1218234, _1218236, _1218238, _1218240, _1218242] : [hBOOL(hAPP(hAPP(c_member(_1218234), _1218236), hAPP(c_Set_Ovimage(_1218234, _1218238, _1218240), hAPP(hAPP(c_Set_Oinsert(_1218238), _1218242), c_Orderings_Obot__class_Obot(tc_fun(_1218238, tc_HOL_Obool)))))), -(hAPP(_1218240, _1218236) = _1218242)], (2044 ^ _779999) ^ [_809657, _809659, _809661, _809663, _809665, _809667, _809669, _809671, _809673, _809675] : [-(c_Fun_Ooverride__on(_809675, _809671, _809667, _809663, _809659) = c_Fun_Ooverride__on(_809673, _809669, _809665, _809661, _809657)), _809675 = _809673, _809671 = _809669, _809667 = _809665, _809663 = _809661, _809659 = _809657], (26707 ^ _779999) ^ [_1280602, _1280604] : [class_Groups_Oordered__ab__group__add__abs(_1280602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280602), _1280604), c_Groups_Ozero__class_Ozero(_1280602))), -(hAPP(c_Groups_Oabs__class_Oabs(_1280602), _1280604) = hAPP(c_Groups_Ouminus__class_Ouminus(_1280602), _1280604))], (7960 ^ _779999) ^ [_914258, _914260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914258), _914260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _914260), _914258)), -(_914258 = _914260)], (7633 ^ _779999) ^ [_908273, _908275, _908277] : [class_Orderings_Owellorder(_908273), hBOOL(hAPP(_908275, _908277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908273), c_Orderings_Oord__class_OLeast(_908273, _908275)), _908277)))], (52088 ^ _779999) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (39366 ^ _779999) ^ [_1541248, _1541250] : [hBOOL(hAPP(_1541248, c_Hilbert__Choice_OEps(_1541250, _1541248))), -(hBOOL(hAPP(_1541248, 39369 ^ [_1541248, _1541250])))], (48438 ^ _779999) ^ [_1754756, _1754758, _1754760, _1754762, _1754764] : [c_List_Olist__all2(_1754756, _1754758, _1754760, _1754762, hAPP(c_List_Orev(_1754758), _1754764)), -(c_List_Olist__all2(_1754756, _1754758, _1754760, hAPP(c_List_Orev(_1754756), _1754762), _1754764))], (48590 ^ _779999) ^ [_1758023, _1758025, _1758027] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758023)), c_List_OtakeWhile(_1758023, _1758025, _1758027))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758023)), _1758027))))], (45149 ^ _779999) ^ [_1682240, _1682242, _1682244] : [hAPP(hAPP(c_List_Oappend(_1682240), _1682242), _1682244) = _1682244, -(_1682242 = c_List_Olist_ONil(_1682240))], (18525 ^ _779999) ^ [_1117341, _1117343, _1117345] : [class_Rings_Oring__1(_1117341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117343), _1117345)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117341), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117345), _1117343)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117341), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117341), _1117345)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117341), _1117343)))], (8960 ^ _779999) ^ [_933330, _933332, _933334] : [class_Orderings_Opreorder(_933330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933330), _933332), _933334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933330), _933334), _933332))], (24364 ^ _779999) ^ [_1236428, _1236430, _1236432, _1236434] : [class_Orderings_Olinorder(_1236428), 24367 ^ _779999 : [(24376 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236428), _1236430), _1236432)), _1236434))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), _1236430), _1236434)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), _1236432), _1236434))], (24368 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236428), _1236430), _1236432)), _1236434)), 24371 ^ _779999 : [(24374 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), _1236432), _1236434)))], (24372 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236428), _1236430), _1236434)))]]]]], (37423 ^ _779999) ^ [_1489415, _1489417, _1489419, _1489421] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1489415), _1489417)), 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)), _1489415), _1489419)), 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)), _1489417), _1489421)), 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)), _1489417), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1489419), _1489421))), c_FunDef_Omin__weak)))], (26546 ^ _779999) ^ [_1277265, _1277267] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277265, tc_HOL_Obool)), _1277267), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277265, tc_HOL_Obool)), _1277267)) = c_Orderings_Obot__class_Obot(tc_fun(_1277265, tc_HOL_Obool)))], (10484 ^ _779999) ^ [_960466, _960468] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960466), hAPP(c_Nat_OSuc, _960468)))), 10485 ^ _779999 : [(10488 ^ _779999) ^ [_960554] : [_960466 = hAPP(c_Nat_OSuc, _960554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960554), _960468))], (10486 ^ _779999) ^ [] : [_960466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19543 ^ _779999) ^ [_1136196, _1136198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136198)), -(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), _1136196), _1136198))))], (46394 ^ _779999) ^ [_1710243, _1710245, _1710247, _1710249] : [-(hBOOL(hAPP(c_List_Odistinct(_1710243), hAPP(hAPP(c_List_Omap(_1710245, _1710243), _1710247), _1710249)))), hBOOL(hAPP(c_List_Odistinct(_1710245), _1710249)), c_Fun_Oinj__on(_1710245, _1710243, _1710247, hAPP(c_List_Oset(_1710245), _1710249))], (48971 ^ _779999) ^ [_1765999, _1766001] : [-(c_List_OremoveAll(_1765999, _1766001) = c_List_Ofilter(_1765999, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765999), c_fNot), hAPP(c_fequal, _1766001))))], (39012 ^ _779999) ^ [_1532608, _1532610, _1532612, _1532614, _1532616] : [c_Relation_Orefl__on(_1532608, _1532610, _1532612), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532608, _1532608)), hAPP(hAPP(c_Product__Type_OPair(_1532608, _1532608), _1532614), _1532616)), _1532612)), -(hBOOL(hAPP(hAPP(c_member(_1532608), _1532614), _1532610)))], (18957 ^ _779999) ^ [] : [-(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))))], (33917 ^ _779999) ^ [_1414647, _1414649] : [c_Int_OBit0(_1414647) = c_Int_OBit0(_1414649), -(_1414647 = _1414649)], (37720 ^ _779999) ^ [_1498265, _1498267, _1498269] : [hBOOL(hAPP(hAPP(c_member(_1498265), _1498267), c_Wellfounded_Oacc(_1498265, _1498269))), 37723 ^ _779999 : [(37724 ^ _779999) ^ [_1498379] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498265, _1498265)), hAPP(hAPP(c_Product__Type_OPair(_1498265, _1498265), _1498379), _1498267)), _1498269)), -(hBOOL(hAPP(hAPP(c_member(_1498265), _1498379), c_Wellfounded_Oacc(_1498265, _1498269))))]]], (18784 ^ _779999) ^ [_1122757, _1122759, _1122761, _1122763] : [class_Orderings_Olinorder(_1122757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122757), _1122759), _1122761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122757), _1122761), _1122763)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122757, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1122757, _1122759, _1122761)), c_SetInterval_Oord__class_OatLeastAtMost(_1122757, _1122761, _1122763)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1122757, _1122759, _1122763))], (12083 ^ _779999) ^ [_993037, _993039, _993041, _993043, _993045] : [c_Finite__Set_Ofolding__one(_993037, _993039, _993041), hBOOL(hAPP(c_Finite__Set_Ofinite(_993037), _993043)), 12090 ^ _779999 : [(12097 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993037, tc_HOL_Obool)), _993043), hAPP(hAPP(c_Set_Oinsert(_993037), _993045), c_Orderings_Obot__class_Obot(tc_fun(_993037, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_993037, tc_HOL_Obool))), -(hAPP(_993041, hAPP(hAPP(c_Set_Oinsert(_993037), _993045), _993043)) = hAPP(hAPP(_993039, _993045), hAPP(_993041, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993037, tc_HOL_Obool)), _993043), hAPP(hAPP(c_Set_Oinsert(_993037), _993045), c_Orderings_Obot__class_Obot(tc_fun(_993037, tc_HOL_Obool)))))))], (12091 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993037, tc_HOL_Obool)), _993043), hAPP(hAPP(c_Set_Oinsert(_993037), _993045), c_Orderings_Obot__class_Obot(tc_fun(_993037, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_993037, tc_HOL_Obool)), -(hAPP(_993041, hAPP(hAPP(c_Set_Oinsert(_993037), _993045), _993043)) = _993045)]]], (33295 ^ _779999) ^ [_1403329, _1403331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403329)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403329), _1403331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403329), c_Int_OPls)))], (37085 ^ _779999) ^ [_1481601, _1481603, _1481605, _1481607, _1481609, _1481611, _1481613] : [c_Equiv__Relations_Oequiv(_1481601, _1481603, _1481605), c_Equiv__Relations_Ocongruent(_1481601, tc_fun(_1481607, tc_HOL_Obool), _1481605, _1481609), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481601, tc_HOL_Obool)), _1481611), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481601), _1481603), _1481605))), 37099 ^ _779999 : [(37102 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1481607, tc_HOL_Obool)), hAPP(_1481609, 37098 ^ [_1481601, _1481603, _1481605, _1481607, _1481609, _1481611, _1481613])), _1481613))], (37100 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481601), 37098 ^ [_1481601, _1481603, _1481605, _1481607, _1481609, _1481611, _1481613]), _1481603)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1481607, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481601, tc_fun(_1481607, tc_HOL_Obool)), _1481611), _1481609)), _1481613)))], (16781 ^ _779999) ^ [_1083628, _1083630, _1083632] : [class_Rings_Oring__1(_1083628), hBOOL(hAPP(hAPP(c_member(_1083628), _1083630), c_Int_Oring__1__class_OInts(_1083628))), hBOOL(hAPP(hAPP(c_member(_1083628), _1083632), c_Int_Oring__1__class_OInts(_1083628))), -(hBOOL(hAPP(hAPP(c_member(_1083628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083628), _1083630), _1083632)), c_Int_Oring__1__class_OInts(_1083628))))], (46544 ^ _779999) ^ [_1713493, _1713495, _1713497, _1713499] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713493)), _1713495) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713497)), _1713499), -(hAPP(hAPP(c_List_Omap(tc_prod(_1713493, _1713497), _1713493), c_Product__Type_Ofst(_1713493, _1713497)), hAPP(hAPP(c_List_Ozip(_1713493, _1713497), _1713495), _1713499)) = _1713495)], (11036 ^ _779999) ^ [_970892, _970894, _970896, _970898] : [class_Lattices_Osemilattice__inf(_970892), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970892), _970894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970892), _970896), _970898)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970892), _970896), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970892), _970894), _970898)))], (16069 ^ _779999) ^ [_1070091, _1070093, _1070095] : [class_Rings_Oordered__cancel__semiring(_1070091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070091), _1070093), c_Groups_Ozero__class_Ozero(_1070091))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070091), c_Groups_Ozero__class_Ozero(_1070091)), _1070095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070091), _1070093), _1070095)), c_Groups_Ozero__class_Ozero(_1070091))))], (51934 ^ _779999) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (12695 ^ _779999) ^ [_1004654, _1004656, _1004658] : [class_Lattices_Olattice(_1004654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004654), _1004656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004654), _1004658)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004654, tc_HOL_Obool)), _1004656), _1004658) = c_Orderings_Obot__class_Obot(tc_fun(_1004654, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1004654), c_Big__Operators_Olattice__class_OInf__fin(_1004654, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004654, tc_HOL_Obool)), _1004656), _1004658))), c_Big__Operators_Olattice__class_OInf__fin(_1004654, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004654, tc_HOL_Obool)), _1004656), _1004658))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1004654), c_Big__Operators_Olattice__class_OInf__fin(_1004654, _1004656)), c_Big__Operators_Olattice__class_OInf__fin(_1004654, _1004658)))], (45580 ^ _779999) ^ [_1693115, _1693117, _1693119] : [_1693115 = c_List_Olist_ONil(_1693117), -(hAPP(c_List_Ohd(_1693117), hAPP(hAPP(c_List_Oappend(_1693117), _1693115), _1693119)) = hAPP(c_List_Ohd(_1693117), _1693119))], (37463 ^ _779999) ^ [] : [-(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)))))], (33167 ^ _779999) ^ [_1401259, _1401261] : [class_Int_Onumber__ring(_1401259), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401259), _1401261), hAPP(c_Int_Onumber__class_Onumber__of(_1401259), c_Int_OBit1(c_Int_OPls))) = _1401261)], (14760 ^ _779999) ^ [_1045092, _1045094, _1045096] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045092), _1045094)), _1045096) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045094), _1045096)))], (3068 ^ _779999) ^ [_825691, _825693] : [_825693 = _825691, -(c_HOL_OAll(_825693) = c_HOL_OAll(_825691))], (18059 ^ _779999) ^ [_1108679, _1108681] : [18061 ^ _779999 : [(18064 ^ _779999) ^ [] : [hBOOL(hAPP(_1108681, 18060 ^ [_1108679, _1108681]))], (18062 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18060 ^ [_1108679, _1108681]), _1108679)))]], 18065 ^ _779999 : [(18066 ^ _779999) ^ [_1108829] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1108829), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108679))), -(hBOOL(hAPP(_1108681, _1108829)))]]], (34293 ^ _779999) ^ [_1421306] : [-(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)))), _1421306) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1421306)))], (37483 ^ _779999) ^ [_1490801, _1490803, _1490805, _1490807] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490801, _1490801)), hAPP(hAPP(c_Product__Type_OPair(_1490801, _1490801), _1490803), _1490805)), c_Relation_OId__on(_1490801, _1490807)))), _1490803 = _1490805, hBOOL(hAPP(hAPP(c_member(_1490801), _1490803), _1490807))], (16923 ^ _779999) ^ [_1085986, _1085988, _1085990, _1085992] : [class_Rings_Olinordered__ring__strict(_1085986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085986), _1085988), c_Groups_Ozero__class_Ozero(_1085986))), 16930 ^ _779999 : [(16937 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085986), _1085992), _1085990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085986), _1085988), _1085990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085986), _1085988), _1085992))))], (16931 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085986), _1085988), _1085990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085986), _1085988), _1085992))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085986), _1085992), _1085990)))]]], (3186 ^ _779999) ^ [_827530, _827532, _827534, _827536] : [-(c_Nitpick_Ouminus__frac(_827536, _827532) = c_Nitpick_Ouminus__frac(_827534, _827530)), _827536 = _827534, _827532 = _827530], (242 ^ _779999) ^ [_783712, _783714, _783716, _783718] : [-(c_Nitpick_Orefl_H(_783716, _783712)), c_Nitpick_Orefl_H(_783718, _783714), _783718 = _783716, _783714 = _783712], (1284 ^ _779999) ^ [_799157, _799159] : [-(class_Groups_Oab__group__add(_799157)), _799159 = _799157, class_Groups_Oab__group__add(_799159)], (51760 ^ _779999) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (42171 ^ _779999) ^ [_1609100, _1609102, _1609104, _1609106, _1609108] : [-(_1609100 = c_Orderings_Obot__class_Obot(tc_fun(_1609102, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609104, tc_HOL_Obool)), _1609106), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609102, tc_fun(_1609104, tc_HOL_Obool)), _1609100), _1609108)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609102, tc_fun(_1609104, tc_HOL_Obool)), _1609100), hAPP(hAPP(c_COMBB(tc_fun(_1609104, tc_HOL_Obool), tc_fun(_1609104, tc_HOL_Obool), _1609102), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609104, tc_HOL_Obool)), _1609106)), _1609108)))], (11570 ^ _779999) ^ [_982665, _982667, _982669, _982671] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982665, tc_HOL_Obool)), _982667), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982665, tc_HOL_Obool)), _982669), _982671)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982665, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982665, tc_HOL_Obool)), _982667), _982669)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982665, tc_HOL_Obool)), _982667), _982671)))], (15531 ^ _779999) ^ [_1059961, _1059963, _1059965, _1059967] : [class_Rings_Ocomm__semiring__1(_1059961), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059961), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059961), _1059963), _1059965)), _1059967) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059961), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059961), _1059963), _1059967)), _1059965))], (49872 ^ _779999) ^ [_1787117, _1787119, _1787121, _1787123] : [-(hAPP(hAPP(c_List_Omap(_1787117, _1787119), hAPP(c_COMBK(_1787119, _1787117), _1787121)), _1787123) = c_List_Oreplicate(_1787119, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787117)), _1787123), _1787121))], (51980 ^ _779999) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (4968 ^ _779999) ^ [_855871, _855873, _855875, _855877] : [-(c_List_Oupto(_855877, _855873) = c_List_Oupto(_855875, _855871)), _855877 = _855875, _855873 = _855871], (16649 ^ _779999) ^ [_1081197, _1081199] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1081197, _1081199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1081199)), _1081197))], (35488 ^ _779999) ^ [_1448138, _1448140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448138), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1448140, _1448138) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1448140), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1448138)))], (27154 ^ _779999) ^ [_1291035, _1291037, _1291039] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1291035), _1291037)), _1291039) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1291035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1291037), _1291039)))], (41835 ^ _779999) ^ [_1598893, _1598895, _1598897, _1598899, _1598901, _1598903] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598893, tc_fun(_1598895, tc_HOL_Obool)), _1598897), hAPP(hAPP(c_COMBC(_1598893, tc_fun(_1598899, tc_fun(_1598895, tc_HOL_Obool)), tc_fun(_1598895, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598899, tc_HOL_Obool), tc_fun(tc_fun(_1598899, tc_fun(_1598895, tc_HOL_Obool)), tc_fun(_1598895, tc_HOL_Obool)), _1598893), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598899, tc_fun(_1598895, tc_HOL_Obool))), _1598901)), _1598903)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598899, tc_fun(_1598895, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598893, tc_fun(_1598899, tc_HOL_Obool)), _1598897), _1598901)), _1598903))], (50194 ^ _779999) ^ [_1793404, _1793406, _1793408, _1793410] : [hBOOL(hAPP(hAPP(c_List_Omember(_1793404), hAPP(hAPP(c_List_Olist_OCons(_1793404), _1793406), _1793408)), _1793410)), -(_1793406 = _1793410), -(hBOOL(hAPP(hAPP(c_List_Omember(_1793404), _1793408), _1793410)))], (9684 ^ _779999) ^ [_944605, _944607, _944609] : [class_Groups_Oordered__ab__group__add(_944605), 9687 ^ _779999 : [(9694 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_944605), _944607), _944609)), c_Groups_Ozero__class_Ozero(_944605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944605), _944607), _944609)))], (9688 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944605), _944607), _944609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_944605), _944607), _944609)), c_Groups_Ozero__class_Ozero(_944605))))]]], (17908 ^ _779999) ^ [_1105909, _1105911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105909), _1105911)), -(_1105911 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105909), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 17911 ^ [_1105909, _1105911]))))], (2208 ^ _779999) ^ [_812387, _812389, _812391, _812393, _812395, _812397] : [-(c_SetInterval_Oord_OlessThan(_812397, _812393, _812389) = c_SetInterval_Oord_OlessThan(_812395, _812391, _812387)), _812397 = _812395, _812393 = _812391, _812389 = _812387], (49650 ^ _779999) ^ [_1781396, _1781398, _1781400] : [c_FunDef_Ois__measure(_1781396, _1781398), -(c_FunDef_Ois__measure(tc_prod(_1781396, _1781400), hAPP(hAPP(c_COMBB(_1781396, tc_Nat_Onat, tc_prod(_1781396, _1781400)), _1781398), c_Product__Type_Ofst(_1781396, _1781400))))], (43735 ^ _779999) ^ [_1649324, _1649326, _1649328] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649324)), hAPP(hAPP(c_List_Otake(_1649324), _1649326), _1649328)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649324)), _1649328)), _1649326))], (49988 ^ _779999) ^ [_1789275, _1789277, _1789279, _1789281] : [-(hBOOL(hAPP(_1789275, _1789277))), -(hAPP(c_List_Ofilter(_1789279, _1789275), c_List_Oreplicate(_1789279, _1789281, _1789277)) = c_List_Olist_ONil(_1789279))], (15771 ^ _779999) ^ [_1064467, _1064469, _1064471] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064467), _1064469) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064471), _1064469), -(_1064467 = _1064471), -(_1064469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17707 ^ _779999) ^ [_1101877, _1101879, _1101881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101877)), 17710 ^ _779999 : [(17717 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101879), _1101881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101877), _1101879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101877), _1101881))))], (17711 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101877), _1101879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101877), _1101881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101879), _1101881)))]]], (13612 ^ _779999) ^ [_1022923, _1022925] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022923), _1022925))), -(hAPP(c_Finite__Set_Ocard(_1022923), _1022925) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23463 ^ _779999) ^ [_1217995, _1217997, _1217999, _1218001] : [hAPP(c_Set_Oimage(_1217995, _1217997, _1217999), c_Orderings_Otop__class_Otop(tc_fun(_1217995, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1217997, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1217995, _1217997, _1217999), hAPP(c_Set_Ovimage(_1217995, _1217997, _1217999), _1218001)) = _1218001)], (44558 ^ _779999) ^ [_1669445, _1669447, _1669449] : [-(c_Enum_Oproduct(_1669445, _1669447, c_List_Olist_ONil(_1669445), _1669449) = c_List_Olist_ONil(tc_prod(_1669445, _1669447)))], (12399 ^ _779999) ^ [_999503, _999505, _999507] : [class_Lattices_Olattice(_999503), hBOOL(hAPP(c_Finite__Set_Ofinite(_999503), _999505)), hBOOL(hAPP(hAPP(c_member(_999503), _999507), _999505)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999503), _999507), c_Big__Operators_Olattice__class_OInf__fin(_999503, _999505)) = _999507)], (9320 ^ _779999) ^ [_938817, _938819, _938821] : [class_Orderings_Olinorder(_938817), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938817), _938819), _938821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938817), _938821), _938819)))], (47034 ^ _779999) ^ [_1724586, _1724588, _1724590, _1724592, _1724594, _1724596] : [c_List_Olist__all2(_1724586, _1724588, _1724590, _1724592, _1724594), -(c_List_Olist__all2(_1724586, _1724588, _1724590, hAPP(hAPP(c_List_Otake(_1724586), _1724596), _1724592), hAPP(hAPP(c_List_Otake(_1724588), _1724596), _1724594)))], (1364 ^ _779999) ^ [_800157, _800159] : [-(class_Groups_Oabs__if(_800157)), _800159 = _800157, class_Groups_Oabs__if(_800159)], (22631 ^ _779999) ^ [_1198741, _1198743, _1198745, _1198747, _1198749, _1198751] : [hBOOL(hAPP(hAPP(c_member(_1198741), _1198743), _1198745)), hBOOL(hAPP(hAPP(c_member(_1198747), _1198749), hAPP(_1198751, _1198743))), -(hBOOL(hAPP(hAPP(c_member(_1198747), _1198749), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1198741, tc_fun(_1198747, tc_HOL_Obool)), _1198745), _1198751))))], (17165 ^ _779999) ^ [_1090587, _1090589, _1090591] : [class_Rings_Olinordered__ring(_1090587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090587), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090587), _1090589), _1090589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090587), _1090591), _1090591))), c_Groups_Ozero__class_Ozero(_1090587)))], (13902 ^ _779999) ^ [_1027781, _1027783] : [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), _1027781), _1027783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027783)))], (52306 ^ _779999) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (12948 ^ _779999) ^ [_1009795, _1009797, _1009799, _1009801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009795), _1009797)), -(hAPP(c_Set_Oimage(_1009795, _1009799, _1009801), _1009797) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1009799, tc_HOL_Obool), _1009795, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009799, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1009795, tc_fun(_1009799, tc_HOL_Obool), tc_fun(_1009799, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1009799, tc_fun(tc_fun(_1009799, tc_HOL_Obool), tc_fun(_1009799, tc_HOL_Obool)), _1009795), c_Set_Oinsert(_1009799)), _1009801)), c_Orderings_Obot__class_Obot(tc_fun(_1009799, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1009799, tc_HOL_Obool))), _1009797))], (9568 ^ _779999) ^ [_942590, _942592, _942594, _942596] : [class_Lattices_Osemilattice__sup(_942590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942590), _942592), _942594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942590), _942592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942590), _942596), _942594))))], (318 ^ _779999) ^ [_784912, _784914, _784916, _784918] : [-(c_Nitpick_Owf_H(_784916, _784912)), c_Nitpick_Owf_H(_784918, _784914), _784918 = _784916, _784914 = _784912], (39395 ^ _779999) ^ [_1541863, _1541865, _1541867, _1541869, _1541871, _1541873, _1541875] : [-(hAPP(c_Fun_Ocomp(_1541863, _1541865, _1541867, _1541869), hAPP(c_Fun_Ocomp(_1541871, _1541863, _1541867, _1541873), _1541875)) = hAPP(c_Fun_Ocomp(_1541871, _1541865, _1541867, hAPP(c_Fun_Ocomp(_1541863, _1541865, _1541871, _1541869), _1541873)), _1541875))], (27132 ^ _779999) ^ [_1290612, _1290614] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1290612), _1290614)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1290612)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1290614)))], (8204 ^ _779999) ^ [_919017, _919019, _919021] : [-(hAPP(c_Set_OPow(_919017), hAPP(hAPP(c_Set_Oinsert(_919017), _919019), _919021)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_919017, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_919017), _919021)), hAPP(c_Set_Oimage(tc_fun(_919017, tc_HOL_Obool), tc_fun(_919017, tc_HOL_Obool), hAPP(c_Set_Oinsert(_919017), _919019)), hAPP(c_Set_OPow(_919017), _919021))))], (51426 ^ _779999) ^ [_1820342, _1820344, _1820346] : [c_Fun_Oinj__on(_1820342, _1820344, _1820346, c_Orderings_Otop__class_Otop(tc_fun(_1820342, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1820344, _1820342, c_Hilbert__Choice_Oinv__into(_1820342, _1820344, c_Orderings_Otop__class_Otop(tc_fun(_1820342, tc_HOL_Obool)), _1820346)), c_Orderings_Otop__class_Otop(tc_fun(_1820344, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1820342, tc_HOL_Obool)))], (49878 ^ _779999) ^ [_1787287, _1787289, _1787291] : [-(hAPP(c_List_Orev(_1787287), c_List_Oreplicate(_1787287, _1787289, _1787291)) = c_List_Oreplicate(_1787287, _1787289, _1787291))], (35031 ^ _779999) ^ [_1434394] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1434394)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1434394)))], (11358 ^ _779999) ^ [_977249, _977251, _977253] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977249, tc_HOL_Obool)), _977251), _977253) = c_Orderings_Obot__class_Obot(tc_fun(_977249, tc_HOL_Obool)), 11361 ^ _779999 : [(11362 ^ _779999) ^ [_977373] : [hBOOL(hAPP(hAPP(c_member(_977249), _977373), _977251)), 11365 ^ _779999 : [(11366 ^ _779999) ^ [_977463] : [hBOOL(hAPP(hAPP(c_member(_977249), _977463), _977253)), _977373 = _977463]]]]], (37238 ^ _779999) ^ [_1485479, _1485481] : [c_Equiv__Relations_Oequivp(_1485479, _1485481), 37241 ^ _779999 : [(37248 ^ _779999) ^ [_1485672, _1485674] : [hAPP(_1485481, _1485674) = hAPP(_1485481, _1485672), -(hBOOL(hAPP(hAPP(_1485481, _1485674), _1485672)))], (37242 ^ _779999) ^ [_1485573, _1485575] : [hBOOL(hAPP(hAPP(_1485481, _1485575), _1485573)), -(hAPP(_1485481, _1485575) = hAPP(_1485481, _1485573))]]], (40807 ^ _779999) ^ [_1575569, _1575571, _1575573] : [hAPP(hAPP(c_Relation_Orel__comp(_1575569, _1575569, _1575569), hAPP(c_Relation_Oconverse(_1575569, _1575569), _1575571)), _1575571) = _1575571, hAPP(c_Relation_ODomain(_1575569, _1575569), _1575571) = _1575573, -(c_Equiv__Relations_Oequiv(_1575569, _1575573, _1575571))], (26584 ^ _779999) ^ [_1278130, _1278132, _1278134] : [class_Groups_Oordered__ab__group__add(_1278130), -(hAPP(c_Set_Oimage(_1278130, _1278130, c_Groups_Ouminus__class_Ouminus(_1278130)), c_SetInterval_Oord__class_OatLeastAtMost(_1278130, _1278132, _1278134)) = c_SetInterval_Oord__class_OatLeastAtMost(_1278130, hAPP(c_Groups_Ouminus__class_Ouminus(_1278130), _1278134), hAPP(c_Groups_Ouminus__class_Ouminus(_1278130), _1278132)))], (22082 ^ _779999) ^ [_1187896, _1187898, _1187900, _1187902] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1187896), _1187898))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187900), hAPP(c_Set_Oimage(_1187896, _1187900, _1187902), _1187898))), 22090 ^ _779999 : [(22093 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1187896), hAPP(c_Set_OCollect(_1187896), hAPP(hAPP(c_COMBS(_1187896, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1187896), c_fconj), hAPP(hAPP(c_COMBC(_1187896, tc_fun(_1187896, tc_HOL_Obool), tc_HOL_Obool), c_member(_1187896)), _1187898))), hAPP(hAPP(c_COMBC(_1187896, _1187900, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1187900, tc_fun(_1187900, tc_HOL_Obool), _1187896), c_fequal), _1187902)), hAPP(_1187902, 22089 ^ [_1187896, _1187898, _1187900, _1187902]))))))], (22091 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187896), 22089 ^ [_1187896, _1187898, _1187900, _1187902]), _1187898)))]]], (35412 ^ _779999) ^ [_1446390, _1446392, _1446394, _1446396, _1446398] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446394, _1446390)), hAPP(hAPP(c_Product__Type_OPair(_1446394, _1446390), _1446398), _1446392)), _1446396)), -(hBOOL(hAPP(hAPP(c_member(_1446390), _1446392), hAPP(c_Relation_OImage(_1446394, _1446390, _1446396), hAPP(hAPP(c_Set_Oinsert(_1446394), _1446398), c_Orderings_Obot__class_Obot(tc_fun(_1446394, tc_HOL_Obool)))))))], (17271 ^ _779999) ^ [_1093133, _1093135, _1093137, _1093139] : [class_Groups_Ocomm__monoid__add(_1093133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1093135), _1093137)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1093133), _1093139), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1093135, _1093137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093133), hAPP(_1093139, _1093135)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1093133), _1093139), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1093135), _1093137))))], (37523 ^ _779999) ^ [_1492028, _1492030, _1492032, _1492034] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1492028, tc_HOL_Obool), tc_fun(_1492028, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1492028, tc_HOL_Obool), tc_fun(_1492028, tc_HOL_Obool)), _1492032), _1492034)), c_Wellfounded_Omax__ext(_1492028, _1492030))), -(c_Wellfounded_Omax__extp(_1492028, hAPP(hAPP(c_COMBC(_1492028, tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_fun(_1492028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1492028, tc_fun(tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_fun(_1492028, tc_HOL_Obool)), _1492028), c_COMBC(_1492028, tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1492028, tc_prod(_1492028, _1492028)), tc_fun(_1492028, tc_fun(tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_HOL_Obool)), _1492028), hAPP(c_COMBB(tc_prod(_1492028, _1492028), tc_fun(tc_fun(tc_prod(_1492028, _1492028), tc_HOL_Obool), tc_HOL_Obool), _1492028), c_member(tc_prod(_1492028, _1492028)))), c_Product__Type_OPair(_1492028, _1492028)))), _1492030), _1492032, _1492034))], (13121 ^ _779999) ^ [_1013483, _1013485, _1013487, _1013489] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1013483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013483), _1013485), _1013487)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013483), _1013489), _1013487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013483), _1013485), _1013489)))], (24884 ^ _779999) ^ [_1246110, _1246112, _1246114] : [class_Orderings_Olinorder(_1246110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1246110), _1246112)), -(_1246112 = c_Orderings_Obot__class_Obot(tc_fun(_1246110, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246110), _1246114), c_Big__Operators_Olattice_OSup__fin(_1246110, c_Orderings_Oord__class_Omax(_1246110), _1246112)) = c_Big__Operators_Olattice_OSup__fin(_1246110, c_Orderings_Oord__class_Omax(_1246110), hAPP(c_Set_OCollect(_1246110), hAPP(hAPP(c_COMBB(tc_fun(_1246110, tc_HOL_Obool), tc_HOL_Obool, _1246110), c_HOL_OEx(_1246110)), hAPP(hAPP(c_COMBC(_1246110, tc_fun(_1246110, tc_HOL_Obool), tc_fun(_1246110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246110, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1246110, tc_HOL_Obool), tc_fun(_1246110, tc_HOL_Obool)), _1246110), c_COMBS(_1246110, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246110, tc_HOL_Obool), tc_fun(_1246110, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1246110), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1246110), c_fconj)), hAPP(hAPP(c_COMBC(_1246110, tc_fun(_1246110, _1246110), tc_fun(_1246110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246110, tc_HOL_Obool), tc_fun(tc_fun(_1246110, _1246110), tc_fun(_1246110, tc_HOL_Obool)), _1246110), c_COMBB(_1246110, tc_HOL_Obool, _1246110)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1246110), _1246114))))), hAPP(hAPP(c_COMBC(_1246110, tc_fun(_1246110, tc_HOL_Obool), tc_HOL_Obool), c_member(_1246110)), _1246112))))))], (37136 ^ _779999) ^ [_1482737] : [c_Code__Numeral_OSuc__code__numeral(_1482737) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (25160 ^ _779999) ^ [_1252190, _1252192] : [class_Orderings_Olinorder(_1252190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1252190), _1252192)), -(_1252192 = c_Orderings_Obot__class_Obot(tc_fun(_1252190, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1252190), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1252190), 25173 ^ [_1252190, _1252192]), 25174 ^ [_1252190, _1252192])), hAPP(hAPP(c_Set_Oinsert(_1252190), 25173 ^ [_1252190, _1252192]), hAPP(hAPP(c_Set_Oinsert(_1252190), 25174 ^ [_1252190, _1252192]), c_Orderings_Obot__class_Obot(tc_fun(_1252190, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1252190), c_Big__Operators_Olattice_OSup__fin(_1252190, c_Orderings_Oord__class_Omax(_1252190), _1252192)), _1252192)))], (7980 ^ _779999) ^ [_914622, _914624, _914626, _914628, _914630] : [class_Groups_Ominus(_914622), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914624, _914622)), _914626), _914628), _914630) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_914622), hAPP(_914626, _914630)), hAPP(_914628, _914630)))], (21778 ^ _779999) ^ [_1177310, _1177312, _1177314] : [-(hBOOL(hAPP(_1177310, _1177312))), -(hAPP(c_Set_OCollect(_1177314), hAPP(hAPP(c_COMBS(_1177314, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1177314), c_fconj), hAPP(hAPP(c_COMBC(_1177314, _1177314, tc_HOL_Obool), c_fequal), _1177312))), _1177310)) = c_Orderings_Obot__class_Obot(tc_fun(_1177314, tc_HOL_Obool)))], (49778 ^ _779999) ^ [_1784530, _1784532, _1784534] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1784530, _1784530, hAPP(hAPP(c_COMBB(tc_fun(_1784530, tc_HOL_Obool), tc_fun(_1784530, tc_HOL_Obool), _1784530), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1784530), c_fNot)), c_fequal)), _1784532), _1784534)), _1784532 = _1784534], (45550 ^ _779999) ^ [_1692419, _1692421, _1692423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692419), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692421)), _1692423))), -(_1692423 = hAPP(hAPP(c_List_Oappend(_1692421), hAPP(hAPP(c_List_Otake(_1692421), _1692419), _1692423)), hAPP(hAPP(c_List_Olist_OCons(_1692421), hAPP(hAPP(c_List_Onth(_1692421), _1692423), _1692419)), hAPP(hAPP(c_List_Odrop(_1692421), hAPP(c_Nat_OSuc, _1692419)), _1692423))))], (46568 ^ _779999) ^ [_1714057, _1714059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1714057), _1714059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1714057)), hAPP(c_Code__Numeral_Oof__nat, _1714059))))], (38371 ^ _779999) ^ [_1514045, _1514047, _1514049] : [-(hAPP(c_Set_Oimage(tc_prod(_1514045, _1514047), _1514045, c_Product__Type_Ofst(_1514045, _1514047)), _1514049) = hAPP(c_Relation_ODomain(_1514045, _1514047), _1514049))], (27634 ^ _779999) ^ [_1299718, _1299720, _1299722] : [class_Rings_Oring__1__no__zero__divisors(_1299718), -(_1299720 = c_Groups_Ozero__class_Ozero(_1299718)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299718), _1299720), _1299722) = c_Groups_Ozero__class_Ozero(_1299718)], (10549 ^ _779999) ^ [_961518, _961520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961518), _961520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961518), hAPP(c_Nat_OSuc, _961520))))], (45650 ^ _779999) ^ [_1694227] : [-(hAPP(c_List_Otl(_1694227), c_List_Olist_ONil(_1694227)) = c_List_Olist_ONil(_1694227))], (28708 ^ _779999) ^ [_1319180, _1319182, _1319184] : [class_Fields_Olinordered__field(_1319180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319180), _1319182), c_Groups_Ozero__class_Ozero(_1319180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319180), c_Groups_Ozero__class_Ozero(_1319180)), _1319184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319180), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319180), _1319182), _1319184)), c_Groups_Ozero__class_Ozero(_1319180))))], (11779 ^ _779999) ^ [_986985, _986987, _986989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986985), _986987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986985, tc_HOL_Obool)), _986987), hAPP(c_Set_Oimage(_986985, _986985, _986989), _986987))), -(c_Fun_Oinj__on(_986985, _986985, _986989, _986987))], (5774 ^ _779999) ^ [_871197, _871199] : [hAPP(_871197, 5775 ^ [_871197, _871199]) = hAPP(_871199, 5775 ^ [_871197, _871199]), -(_871197 = _871199)], (11562 ^ _779999) ^ [_982414, _982416, _982418, _982420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982414, tc_HOL_Obool)), _982420), _982416)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982414, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982414, tc_HOL_Obool)), _982416), _982418)), _982420) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982414, tc_HOL_Obool)), _982416), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982414, tc_HOL_Obool)), _982418), _982420)))], (18165 ^ _779999) ^ [_1110663] : [class_Rings_Osemiring__1(_1110663), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110663), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1110663))], (38479 ^ _779999) ^ [_1517368, _1517370, _1517372] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1517368, _1517370), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517368, _1517370), c_Orderings_Otop__class_Otop(tc_fun(_1517368, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1517370, tc_HOL_Obool), _1517368), _1517372))) = hAPP(hAPP(c_Product__Type_OSigma(_1517368, _1517370), c_Orderings_Otop__class_Otop(tc_fun(_1517368, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1517370, tc_HOL_Obool), _1517368), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1517370, tc_HOL_Obool)), _1517372))))], (19417 ^ _779999) ^ [_1134052, _1134054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134052), _1134054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134052)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134054))))], (20331 ^ _779999) ^ [_1149974, _1149976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149976)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1149974)), hAPP(c_Int_Onat, _1149976)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149974), _1149976)))], (6143 ^ _779999) ^ [_878081, _878083, _878085] : [class_Lattices_Osemilattice__sup(_878081), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878081), _878083), _878085) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878081), _878085), _878083))], (44466 ^ _779999) ^ [_1667741, _1667743, _1667745, _1667747] : [-(_1667741 = _1667743), -(c_List_Oremove1(_1667745, _1667741, hAPP(hAPP(c_List_Olist_OCons(_1667745), _1667743), _1667747)) = hAPP(hAPP(c_List_Olist_OCons(_1667745), _1667743), c_List_Oremove1(_1667745, _1667741, _1667747)))], (18355 ^ _779999) ^ [_1114173, _1114175, _1114177, _1114179] : [class_Orderings_Olinorder(_1114173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114173), _1114175), _1114177)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1114173, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1114173, _1114175), _1114179)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1114173, _1114175), _1114177)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1114173, _1114177), _1114179))], (23523 ^ _779999) ^ [_1219301, _1219303, _1219305, _1219307, _1219309] : [hAPP(c_Set_Oimage(_1219301, _1219303, _1219305), c_Orderings_Otop__class_Otop(tc_fun(_1219301, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1219303, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219301, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1219301, _1219303, _1219305), _1219307)), _1219309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219303, tc_HOL_Obool)), _1219307), hAPP(c_Set_Oimage(_1219301, _1219303, _1219305), _1219309))))], (23483 ^ _779999) ^ [_1218518, _1218520, _1218522, _1218524, _1218526] : [-(hAPP(c_Set_Ovimage(_1218518, _1218520, _1218522), hAPP(hAPP(c_Set_Oinsert(_1218520), _1218524), _1218526)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218518, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1218518, _1218520, _1218522), hAPP(hAPP(c_Set_Oinsert(_1218520), _1218524), c_Orderings_Obot__class_Obot(tc_fun(_1218520, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1218518, _1218520, _1218522), _1218526)))], (48460 ^ _779999) ^ [_1755239, _1755241, _1755243] : [-(hAPP(c_List_Orev(_1755239), hAPP(hAPP(c_List_Olist_OCons(_1755239), _1755241), _1755243)) = hAPP(hAPP(c_List_Oappend(_1755239), hAPP(c_List_Orev(_1755239), _1755243)), hAPP(hAPP(c_List_Olist_OCons(_1755239), _1755241), c_List_Olist_ONil(_1755239))))], (15293 ^ _779999) ^ [_1054773] : [class_Rings_Oring__1(_1054773), -(hBOOL(hAPP(hAPP(c_member(_1054773), c_Groups_Ozero__class_Ozero(_1054773)), c_Int_Oring__1__class_OInts(_1054773))))], (43315 ^ _779999) ^ [_1637093, _1637095] : [-(c_List_Olistrel1(_1637093, hAPP(c_Relation_Oconverse(_1637093, _1637093), _1637095)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1637093), tc_List_Olist(_1637093)), c_List_Olistrel1(_1637093, _1637095)))], (25546 ^ _779999) ^ [_1259158, _1259160] : [class_Groups_Ogroup__add(_1259158), 25549 ^ _779999 : [(25556 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_1259158) = _1259160, -(c_Groups_Ozero__class_Ozero(_1259158) = hAPP(c_Groups_Ouminus__class_Ouminus(_1259158), _1259160))], (25550 ^ _779999) ^ [] : [c_Groups_Ozero__class_Ozero(_1259158) = hAPP(c_Groups_Ouminus__class_Ouminus(_1259158), _1259160), -(c_Groups_Ozero__class_Ozero(_1259158) = _1259160)]]], (15205 ^ _779999) ^ [_1053238, _1053240, _1053242] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1053238), 15208 ^ _779999 : [(15215 ^ _779999) ^ [] : [_1053242 = c_Groups_Ozero__class_Ozero(_1053238), -(_1053240 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053238), _1053240), _1053242))], (15209 ^ _779999) ^ [] : [_1053240 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053238), _1053240), _1053242), -(_1053242 = c_Groups_Ozero__class_Ozero(_1053238))]]], (15789 ^ _779999) ^ [_1064740, _1064742, _1064744] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064740), _1064742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064740), _1064744), -(_1064742 = _1064744), -(_1064740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45390 ^ _779999) ^ [_1688464, _1688466, _1688468] : [-(hAPP(hAPP(c_List_Odrop(_1688464), _1688466), c_List_Obutlast(_1688464, _1688468)) = c_List_Obutlast(_1688464, hAPP(hAPP(c_List_Odrop(_1688464), _1688466), _1688468)))], (3140 ^ _779999) ^ [_826841, _826843] : [_826843 = _826841, -(c_Int_Oring__1__class_Oof__int(_826843) = c_Int_Oring__1__class_Oof__int(_826841))], (52012 ^ _779999) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (39691 ^ _779999) ^ [_1548578, _1548580, _1548582, _1548584, _1548586, _1548588, _1548590] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548578, _1548580, _1548582), hAPP(c_Fun_Ocomp(_1548584, tc_fun(_1548580, _1548582), _1548578, _1548586), _1548588)), _1548590) = hAPP(hAPP(_1548586, hAPP(_1548588, hAPP(c_Product__Type_Ofst(_1548578, _1548580), _1548590))), hAPP(c_Product__Type_Osnd(_1548578, _1548580), _1548590)))], (6173 ^ _779999) ^ [_878590, _878592, _878594] : [_878590 = _878592, 6176 ^ _779999 : [(6179 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878594, tc_HOL_Obool)), _878592), _878590)))], (6177 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878594, tc_HOL_Obool)), _878590), _878592)))]]], (34959 ^ _779999) ^ [_1433376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433376)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433376), c_Int_OMin)))], (34335 ^ _779999) ^ [] : [-(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))))], (610 ^ _779999) ^ [_789404, _789406, _789408, _789410, _789412, _789414] : [-(c_Nitpick_Oless__frac(_789412, _789408, _789404)), c_Nitpick_Oless__frac(_789414, _789410, _789406), _789414 = _789412, _789410 = _789408, _789406 = _789404], (18999 ^ _779999) ^ [_1126481, _1126483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126481), _1126483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126483), _1126481)), -(_1126481 = _1126483)], (51930 ^ _779999) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (40848 ^ _779999) ^ [_1576618, _1576620] : [-(c_Relation_Ototal__on(_1576618, c_Orderings_Obot__class_Obot(tc_fun(_1576618, tc_HOL_Obool)), _1576620))], (49776 ^ _779999) ^ [_1784457, _1784459, _1784461, _1784463, _1784465] : [-(c_Predicate_Oconversep(_1784457, _1784459, c_Predicate_Opred__comp(_1784457, _1784461, _1784459, _1784463, _1784465)) = c_Predicate_Opred__comp(_1784459, _1784461, _1784457, c_Predicate_Oconversep(_1784461, _1784459, _1784465), c_Predicate_Oconversep(_1784457, _1784461, _1784463)))], (33507 ^ _779999) ^ [_1406658, _1406660] : [class_Int_Onumber__ring(_1406658), class_Rings_Olinordered__idom(_1406658), 33514 ^ _779999 : [(33521 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406660), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406658), hAPP(c_Int_Onumber__class_Onumber__of(_1406658), _1406660)), c_Groups_Oone__class_Oone(_1406658))))], (33515 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406658), hAPP(c_Int_Onumber__class_Onumber__of(_1406658), _1406660)), c_Groups_Oone__class_Oone(_1406658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406660), c_Int_OBit1(c_Int_OPls))))]]], (30631 ^ _779999) ^ [_1354273, _1354275, _1354277] : [class_Divides_Oring__div(_1354273), -(c_Divides_Odiv__class_Omod(_1354273, hAPP(c_Groups_Ouminus__class_Ouminus(_1354273), _1354275), _1354277) = c_Divides_Odiv__class_Omod(_1354273, hAPP(c_Groups_Ouminus__class_Ouminus(_1354273), c_Divides_Odiv__class_Omod(_1354273, _1354275, _1354277)), _1354277))], (11354 ^ _779999) ^ [_977139, _977141] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977139, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_977139, tc_HOL_Obool))), _977141) = c_Orderings_Obot__class_Obot(tc_fun(_977139, tc_HOL_Obool)))], (8076 ^ _779999) ^ [_916334, _916336, _916338] : [hAPP(c_Set_Oimage(_916336, tc_fun(_916336, tc_HOL_Obool), _916334), _916338) = hAPP(c_Set_OPow(_916336), _916338)], (35560 ^ _779999) ^ [_1449510, _1449512, _1449514, _1449516, _1449518] : [hBOOL(hAPP(hAPP(_1449510, _1449512), _1449514)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1449516, _1449518, tc_HOL_Obool), _1449510), hAPP(hAPP(c_Product__Type_OPair(_1449516, _1449518), _1449512), _1449514))))], (37992 ^ _779999) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (13937 ^ _779999) ^ [_1028358, _1028360] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028358), _1028360)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25568 ^ _779999) ^ [_1259481, _1259483, _1259485] : [class_Groups_Oordered__ab__group__add(_1259481), 25571 ^ _779999 : [(25578 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259481), _1259485), hAPP(c_Groups_Ouminus__class_Ouminus(_1259481), _1259483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259481), _1259483), hAPP(c_Groups_Ouminus__class_Ouminus(_1259481), _1259485))))], (25572 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259481), _1259483), hAPP(c_Groups_Ouminus__class_Ouminus(_1259481), _1259485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259481), _1259485), hAPP(c_Groups_Ouminus__class_Ouminus(_1259481), _1259483))))]]], (48979 ^ _779999) ^ [_1766146, _1766148, _1766150] : [hBOOL(hAPP(c_List_Odistinct(_1766146), _1766148)), -(hBOOL(hAPP(c_List_Odistinct(_1766146), hAPP(c_List_OremoveAll(_1766146, _1766150), _1766148))))], (40359 ^ _779999) ^ [_1565297, _1565299, _1565301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565297, _1565297), tc_HOL_Obool)), _1565299), _1565301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565297, _1565297), tc_HOL_Obool)), _1565301), c_Transitive__Closure_Ortrancl(_1565297, _1565299))), -(c_Transitive__Closure_Ortrancl(_1565297, _1565301) = c_Transitive__Closure_Ortrancl(_1565297, _1565299))], (13407 ^ _779999) ^ [_1018704, _1018706, _1018708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018704), _1018706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018704), _1018708)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018706), _1018708))))], (1554 ^ _779999) ^ [_802532, _802534] : [-(class_Enum_Oenum(_802532)), _802534 = _802532, class_Enum_Oenum(_802534)], (16743 ^ _779999) ^ [_1082880, _1082882, _1082884] : [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, _1082880)), _1082882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1082880)), _1082884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082882), _1082884)))], (47669 ^ _779999) ^ [_1740089, _1740091] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740089), _1740091))), -(c_List_Oupt(_1740089, _1740091) = c_List_Olist_ONil(tc_Nat_Onat))], (30728 ^ _779999) ^ [_1356009, _1356011] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356009, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1356011)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356009, _1356011) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34439 ^ _779999) ^ [_1423845, _1423847, _1423849] : [class_Rings_Olinordered__idom(_1423845), 34442 ^ _779999 : [(34451 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423845), hAPP(hAPP(c_Power_Opower__class_Opower(_1423845), _1423847), 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(_1423845), _1423849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1423845)), _1423847 = c_Groups_Ozero__class_Ozero(_1423845), _1423849 = c_Groups_Ozero__class_Ozero(_1423845)], (34443 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423845), hAPP(hAPP(c_Power_Opower__class_Opower(_1423845), _1423847), 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(_1423845), _1423849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1423845), 34446 ^ _779999 : [(34449 ^ _779999) ^ [] : [-(_1423849 = c_Groups_Ozero__class_Ozero(_1423845))], (34447 ^ _779999) ^ [] : [-(_1423847 = c_Groups_Ozero__class_Ozero(_1423845))]]]]], (34825 ^ _779999) ^ [_1431327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1431327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1431327)))], (1854 ^ _779999) ^ [_806282, _806284] : [-(class_Rings_Osemiring__1(_806282)), _806284 = _806282, class_Rings_Osemiring__1(_806284)], (20675 ^ _779999) ^ [_1155309] : [c_Nat__Transfer_Onat__set(_1155309), 20678 ^ _779999 : [(20685 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155309))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1155309)))], (20679 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1155309)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1155309))))]]], (17951 ^ _779999) ^ [_1106768, _1106770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106768)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106770)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106768), _1106770)))], (21706 ^ _779999) ^ [_1175378, _1175380, _1175382] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1175378), hAPP(c_Set_OCollect(_1175378), hAPP(hAPP(c_COMBS(_1175378, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175378), c_fdisj), _1175380)), _1175382)))), 21709 ^ _779999 : [(21712 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1175378), hAPP(c_Set_OCollect(_1175378), _1175382))))], (21710 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1175378), hAPP(c_Set_OCollect(_1175378), _1175380))))]]], (38531 ^ _779999) ^ [_1519278, _1519280, _1519282, _1519284, _1519286] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519278, _1519280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519278, tc_HOL_Obool)), _1519282), _1519284)), _1519286) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1519278, _1519280), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519278, _1519280), _1519282), _1519286)), hAPP(hAPP(c_Product__Type_OSigma(_1519278, _1519280), _1519284), _1519286)))], (38341 ^ _779999) ^ [_1513381, _1513383] : [-(hAPP(c_Relation_ODomain(_1513381, _1513381), c_Relation_OId__on(_1513381, _1513383)) = _1513383)], (45700 ^ _779999) ^ [_1695250, _1695252, _1695254] : [-(_1695250 = c_List_Olist_ONil(_1695252)), -(hAPP(hAPP(c_List_Otake(_1695252), hAPP(c_Nat_OSuc, _1695254)), _1695250) = hAPP(hAPP(c_List_Olist_OCons(_1695252), hAPP(c_List_Ohd(_1695252), _1695250)), hAPP(hAPP(c_List_Otake(_1695252), _1695254), hAPP(c_List_Otl(_1695252), _1695250))))], (52322 ^ _779999) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (48717 ^ _779999) ^ [_1760698, _1760700, _1760702] : [hBOOL(hAPP(c_List_Odistinct(_1760698), _1760700)), hBOOL(hAPP(hAPP(c_member(_1760698), _1760702), hAPP(c_List_Oset(_1760698), _1760700))), -(c_List_OdropWhile(_1760698, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760698), c_fNot), hAPP(hAPP(c_COMBC(_1760698, _1760698, tc_HOL_Obool), c_fequal), _1760702)), hAPP(c_List_Orev(_1760698), _1760700)) = hAPP(hAPP(c_List_Olist_OCons(_1760698), _1760702), hAPP(c_List_Orev(_1760698), c_List_OtakeWhile(_1760698, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760698), c_fNot), hAPP(hAPP(c_COMBC(_1760698, _1760698, tc_HOL_Obool), c_fequal), _1760702)), _1760700))))], (30286 ^ _779999) ^ [_1347412, _1347414] : [class_Rings_Oring__1(_1347412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347414)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1347412), hAPP(c_Int_Onat, _1347414)) = hAPP(c_Int_Oring__1__class_Oof__int(_1347412), _1347414))], (47536 ^ _779999) ^ [_1736151, _1736153, _1736155] : [hBOOL(hAPP(c_List_Odistinct(_1736151), _1736153)), -(hAPP(c_List_Ofilter(_1736151, hAPP(hAPP(c_COMBC(_1736151, tc_fun(_1736151, tc_HOL_Obool), tc_HOL_Obool), c_member(_1736151)), hAPP(c_List_Oset(_1736151), c_List_Osublist(_1736151, _1736153, _1736155)))), _1736153) = c_List_Osublist(_1736151, _1736153, _1736155))], (23969 ^ _779999) ^ [_1227779, _1227781, _1227783, _1227785, _1227787, _1227789, _1227791] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1227779, tc_fun(_1227781, tc_fun(_1227783, tc_HOL_Obool))), _1227785), _1227787), _1227789), _1227791)), 23973 ^ _779999 : [(23976 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1227787, 23972 ^ [_1227779, _1227781, _1227783, _1227785, _1227787, _1227789, _1227791]), _1227789), _1227791)))], (23974 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1227779), 23972 ^ [_1227779, _1227781, _1227783, _1227785, _1227787, _1227789, _1227791]), _1227785)))]]], (50775 ^ _779999) ^ [_1807882, _1807884] : [c_Equiv__Relations_Oequivp(_1807882, _1807884), 50778 ^ _779999 : [(50783 ^ _779999) ^ [] : [-(c_Predicate_Otransp(_1807882, _1807884))], (50781 ^ _779999) ^ [] : [-(c_Predicate_Osymp(_1807882, _1807884))], (50779 ^ _779999) ^ [] : [-(c_Predicate_Oreflp(_1807882, _1807884))]]], (102 ^ _779999) ^ [_781702, _781704, _781706, _781708, _781710, _781712, _781714, _781716, _781718, _781720] : [-(c_Big__Operators_Ocomm__monoid__big(_781718, _781714, _781710, _781706, _781702)), c_Big__Operators_Ocomm__monoid__big(_781720, _781716, _781712, _781708, _781704), _781720 = _781718, _781716 = _781714, _781712 = _781710, _781708 = _781706, _781704 = _781702], (32779 ^ _779999) ^ [_1394886] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1394886) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1394886))], (30162 ^ _779999) ^ [_1345221, _1345223, _1345225] : [hBOOL(hAPP(_1345221, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1345223), _1345225))), 30165 ^ _779999 : [(30172 ^ _779999) ^ [] : [-(_1345225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30175 ^ _779999 : [(30176 ^ _779999) ^ [_1345473, _1345475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345473), _1345225)), _1345223 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1345225), _1345475)), _1345473), -(hBOOL(hAPP(_1345221, _1345475)))]]], (30166 ^ _779999) ^ [] : [_1345225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1345221, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (46191 ^ _779999) ^ [_1704857, _1704859, _1704861, _1704863] : [hAPP(hAPP(c_List_Omap(_1704857, _1704859), _1704861), _1704863) = c_List_Olist_ONil(_1704859), -(_1704863 = c_List_Olist_ONil(_1704857))], (49347 ^ _779999) ^ [_1775492, _1775494, _1775496, _1775498] : [c_List_Olist__ex(_1775492, _1775494, hAPP(hAPP(c_List_Olist_OCons(_1775492), _1775496), _1775498)), -(hBOOL(hAPP(_1775494, _1775496))), -(c_List_Olist__ex(_1775492, _1775494, _1775498))], (13935 ^ _779999) ^ [_1028319, _1028321] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028319), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028319), _1028321)))))], (1754 ^ _779999) ^ [_805032, _805034] : [-(class_Rings_Ocomm__semiring__1(_805032)), _805034 = _805032, class_Rings_Ocomm__semiring__1(_805034)], (29820 ^ _779999) ^ [_1339158, _1339160, _1339162] : [-(hBOOL(hAPP(_1339158, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1339160), _1339162)))), 29823 ^ _779999 : [(29826 ^ _779999) ^ [] : [hBOOL(hAPP(_1339158, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29824 ^ _779999) ^ [] : [-(_1339162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 29829 ^ _779999 : [(29830 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339162)))], (29836 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29832 ^ [_1339158, _1339160, _1339162]), _1339162)))], (29840 ^ _779999) ^ [] : [hBOOL(hAPP(_1339158, 29831 ^ [_1339158, _1339160, _1339162]))], (29838 ^ _779999) ^ [] : [-(_1339160 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1339162), 29831 ^ [_1339158, _1339160, _1339162])), 29832 ^ [_1339158, _1339160, _1339162]))], (29834 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29832 ^ [_1339158, _1339160, _1339162])))]], 29841 ^ _779999 : [(29842 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29848 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29844 ^ [_1339158, _1339160, _1339162]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29852 ^ _779999) ^ [] : [hBOOL(hAPP(_1339158, 29843 ^ [_1339158, _1339160, _1339162]))], (29850 ^ _779999) ^ [] : [-(_1339160 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1339162), 29843 ^ [_1339158, _1339160, _1339162])), 29844 ^ [_1339158, _1339160, _1339162]))], (29846 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339162), 29844 ^ [_1339158, _1339160, _1339162])))]]], (39675 ^ _779999) ^ [_1548100, _1548102, _1548104, _1548106, _1548108, _1548110] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548100, tc_fun(_1548102, tc_HOL_Obool)), _1548104), hAPP(c_Fun_Ocomp(_1548106, tc_fun(_1548102, tc_HOL_Obool), _1548100, _1548108), _1548110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548106, tc_fun(_1548102, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1548100, _1548106, _1548110), _1548104)), _1548108))], (19922 ^ _779999) ^ [_1143479] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1143479)) = _1143479)], (43851 ^ _779999) ^ [_1652261, _1652263, _1652265] : [43853 ^ _779999 : [(43856 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1652261), 43852 ^ [_1652261, _1652263, _1652265]), _1652265))], (43854 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652261), 43852 ^ [_1652261, _1652263, _1652265]), hAPP(c_List_Oset(_1652261), _1652263))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1652261)), _1652263), c_List_Olists(_1652261, _1652265))))], (11028 ^ _779999) ^ [_970694, _970696, _970698] : [class_Lattices_Osemilattice__inf(_970694), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970694), _970696), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970694), _970696), _970698)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970694), _970696), _970698))], (7894 ^ _779999) ^ [_913320, _913322, _913324] : [-(hBOOL(hAPP(_913320, _913322))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_913320, _913324)), _913322), _913322)))], (44178 ^ _779999) ^ [_1661570, _1661572, _1661574, _1661576, _1661578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661570), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661572)), _1661574))), 44181 ^ _779999 : [(44188 ^ _779999) ^ [] : [-(_1661570 = _1661576), -(hAPP(hAPP(c_List_Onth(_1661572), hAPP(hAPP(c_List_Olist__update(_1661572, _1661574), _1661570), _1661578)), _1661576) = hAPP(hAPP(c_List_Onth(_1661572), _1661574), _1661576))], (44182 ^ _779999) ^ [] : [_1661570 = _1661576, -(hAPP(hAPP(c_List_Onth(_1661572), hAPP(hAPP(c_List_Olist__update(_1661572, _1661574), _1661570), _1661578)), _1661576) = _1661578)]]], (51718 ^ _779999) ^ [_1826921, _1826923, _1826925, _1826927, _1826929, _1826931] : [c_Fun_Obij__betw(_1826921, _1826923, _1826925, c_Orderings_Otop__class_Otop(tc_fun(_1826921, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1826923, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1826921, _1826923, _1826925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1826927, tc_fun(_1826921, tc_HOL_Obool)), _1826929), _1826931)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1826927, tc_fun(_1826923, tc_HOL_Obool)), _1826929), hAPP(hAPP(c_COMBB(tc_fun(_1826921, tc_HOL_Obool), tc_fun(_1826923, tc_HOL_Obool), _1826927), c_Set_Oimage(_1826921, _1826923, _1826925)), _1826931)))], (27140 ^ _779999) ^ [] : [-(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))], (8046 ^ _779999) ^ [_915810, _915812, _915814, _915816, _915818] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_915810, _915812), _915814, _915816, _915818)), 8047 ^ _779999 : [(8054 ^ _779999) ^ [] : [hBOOL(hAPP(_915810, _915814)), 8057 ^ _779999 : [(8058 ^ _779999) ^ [_916020] : [c_Natural_Oevaln(_915812, _915814, _915816, _916020), c_Natural_Oevaln(c_Com_Ocom_OWhile(_915810, _915812), _916020, _915816, _915818)]]], (8048 ^ _779999) ^ [] : [_915818 = _915814, -(hBOOL(hAPP(_915810, _915814)))]]], (21732 ^ _779999) ^ [_1176118, _1176120, _1176122] : [-(hAPP(hAPP(c_Set_Oinsert(_1176118), _1176120), _1176122) = hAPP(c_Set_OCollect(_1176118), hAPP(hAPP(c_COMBS(_1176118, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1176118), c_fdisj), hAPP(hAPP(c_COMBC(_1176118, _1176118, tc_HOL_Obool), c_fequal), _1176120))), hAPP(hAPP(c_COMBC(_1176118, tc_fun(_1176118, tc_HOL_Obool), tc_HOL_Obool), c_member(_1176118)), _1176122))))], (34641 ^ _779999) ^ [_1427621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1427621)), -(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), _1427621), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (26626 ^ _779999) ^ [_1279123, _1279125] : [class_Orderings_Olinorder(_1279123), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279123, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1279123), _1279125)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1279123), _1279125))], (41446 ^ _779999) ^ [_1591089, _1591091, _1591093] : [class_Lattices_Olattice(_1591089), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591089), _1591091)), -(c_Big__Operators_Olattice__class_OInf__fin(_1591089, hAPP(hAPP(c_Set_Oinsert(_1591089), _1591093), _1591091)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591089, _1591089, c_Lattices_Osemilattice__inf__class_Oinf(_1591089)), _1591093), _1591091))], (44554 ^ _779999) ^ [_1669383, _1669385] : [-(c_List_Olistrelp(_1669383, _1669385, c_List_Olist_ONil(_1669383), c_List_Olist_ONil(_1669383)))], (23379 ^ _779999) ^ [_1216204, _1216206, _1216208, _1216210, _1216212] : [hBOOL(hAPP(hAPP(c_member(_1216204), _1216206), hAPP(c_Set_Ovimage(_1216204, _1216208, _1216210), _1216212))), -(hBOOL(hAPP(hAPP(c_member(_1216208), hAPP(_1216210, _1216206)), _1216212)))], (43881 ^ _779999) ^ [_1652951, _1652953, _1652955] : [-(hBOOL(hAPP(hAPP(c_member(_1652951), _1652953), hAPP(c_List_Oset(_1652951), _1652955)))), 43882 ^ _779999 : [(43883 ^ _779999) ^ [_1653025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652951)), _1652955))), hAPP(hAPP(c_List_Onth(_1652951), _1652955), _1653025) = _1652953]]], (22129 ^ _779999) ^ [_1189218, _1189220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189218), c_Orderings_Otop__class_Otop(tc_fun(_1189218, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189220), c_Orderings_Otop__class_Otop(tc_fun(_1189220, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1189218, _1189220)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1189218, _1189220), tc_HOL_Obool)))))], (10447 ^ _779999) ^ [_959859, _959861, _959863] : [class_Complete__Lattice_Ocomplete__lattice(_959859), _959861 = c_Inductive_Ocomplete__lattice__class_Olfp(_959859, _959863), c_Orderings_Oorder__class_Omono(_959859, _959859, _959863), -(_959861 = hAPP(_959863, _959861))], (52102 ^ _779999) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (47561 ^ _779999) ^ [_1736726, _1736728, _1736730] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736726)), hAPP(c_List_Ofilter(_1736726, _1736728), _1736730)) = 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(_1736726)), _1736730)))), hAPP(hAPP(c_COMBB(_1736726, tc_HOL_Obool, tc_Nat_Onat), _1736728), hAPP(c_List_Onth(_1736726), _1736730))))))], (33801 ^ _779999) ^ [_1412472] : [class_Int_Onumber__ring(_1412472), c_Int_Oiszero(_1412472, hAPP(c_Int_Onumber__class_Onumber__of(_1412472), c_Int_OBit1(c_Int_OPls)))], (36679 ^ _779999) ^ [_1471286, _1471288, _1471290, _1471292, _1471294, _1471296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471292, _1471292)), hAPP(hAPP(c_Product__Type_OPair(_1471292, _1471292), hAPP(_1471296, _1471288)), hAPP(_1471296, _1471290))), _1471294)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471286, _1471286)), hAPP(hAPP(c_Product__Type_OPair(_1471286, _1471286), _1471288), _1471290)), hAPP(hAPP(c_Relation_Oinv__image(_1471292, _1471286), _1471294), _1471296))))], (33083 ^ _779999) ^ [_1399982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1399982))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1399982)))], (45452 ^ _779999) ^ [_1689889, _1689891, _1689893, _1689895] : [_1689889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1689891), _1689889), hAPP(hAPP(c_List_Olist_OCons(_1689891), _1689893), _1689895)) = hAPP(hAPP(c_List_Olist_OCons(_1689891), _1689893), _1689895))], (34179 ^ _779999) ^ [_1419165, _1419167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419165), _1419167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1419165)), c_Int_OBit0(_1419167))))], (38951 ^ _779999) ^ [_1531524, _1531526] : [c_Wellfounded_OwfP(_1531524, _1531526), 38954 ^ _779999 : [(38955 ^ _779999) ^ [_1531588] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1531524, _1531526), _1531588)))]]], (28694 ^ _779999) ^ [_1318925, _1318927, _1318929] : [class_Fields_Olinordered__field(_1318925), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318925), _1318927), c_Groups_Ozero__class_Ozero(_1318925))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318925), _1318929), c_Groups_Ozero__class_Ozero(_1318925))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318925), c_Groups_Ozero__class_Ozero(_1318925)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318925), _1318927), _1318929))))], (21832 ^ _779999) ^ [_1179374, _1179376, _1179378, _1179380, _1179382, _1179384] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1179374), _1179376)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179378), _1179380)), 21842 ^ _779999 : [(21845 ^ _779999) ^ [] : [hAPP(c_Finite__Set_Ocard(_1179374), hAPP(c_Set_OCollect(_1179374), hAPP(hAPP(c_COMBS(_1179374, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1179374), c_fconj), hAPP(hAPP(c_COMBC(_1179374, tc_fun(_1179374, tc_HOL_Obool), tc_HOL_Obool), c_member(_1179374)), _1179376))), hAPP(hAPP(c_COMBC(_1179374, _1179378, tc_HOL_Obool), _1179382), 21841 ^ [_1179374, _1179376, _1179378, _1179380, _1179382, _1179384])))) = _1179384], (21843 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1179378), 21841 ^ [_1179374, _1179376, _1179378, _1179380, _1179382, _1179384]), _1179380)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1179374, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1179378, tc_HOL_Obool), tc_Nat_Onat, _1179374), c_Finite__Set_Ocard(_1179378)), hAPP(hAPP(c_COMBB(tc_fun(_1179378, tc_HOL_Obool), tc_fun(_1179378, tc_HOL_Obool), _1179374), c_Set_OCollect(_1179378)), hAPP(hAPP(c_COMBB(tc_fun(_1179378, tc_HOL_Obool), tc_fun(_1179378, tc_HOL_Obool), _1179374), hAPP(c_COMBS(_1179378, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1179378), c_fconj), hAPP(hAPP(c_COMBC(_1179378, tc_fun(_1179378, tc_HOL_Obool), tc_HOL_Obool), c_member(_1179378)), _1179380)))), _1179382)))), _1179376) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179384), hAPP(c_Finite__Set_Ocard(_1179378), _1179380)))], (2484 ^ _779999) ^ [_816637, _816639, _816641, _816643] : [-(c_Divides_Odivmod__int__rel(_816643, _816639) = c_Divides_Odivmod__int__rel(_816641, _816637)), _816643 = _816641, _816639 = _816637], (8716 ^ _779999) ^ [_929222, _929224, _929226, _929228, _929230] : [_929222 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929224, tc_HOL_Obool), _929226), c_Orderings_Oorder__class_Omono(tc_fun(_929224, tc_HOL_Obool), tc_fun(_929224, tc_HOL_Obool), _929226), hBOOL(hAPP(hAPP(c_member(_929224), _929228), _929230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929224, tc_HOL_Obool)), _929230), hAPP(_929226, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929224, tc_HOL_Obool)), _929230), _929222)))), -(hBOOL(hAPP(hAPP(c_member(_929224), _929228), _929222)))], (49127 ^ _779999) ^ [_1770083, _1770085, _1770087, _1770089] : [49129 ^ _779999 : [(49132 ^ _779999) ^ [] : [hBOOL(hAPP(_1770087, 49128 ^ [_1770083, _1770085, _1770087, _1770089]))], (49130 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770083), 49128 ^ [_1770083, _1770085, _1770087, _1770089]), hAPP(c_List_Oset(_1770083), _1770085))))]], -(c_List_OdropWhile(_1770083, _1770087, hAPP(hAPP(c_List_Oappend(_1770083), _1770085), _1770089)) = c_List_OdropWhile(_1770083, _1770087, _1770089))], (34771 ^ _779999) ^ [] : [c_Int_OMin = c_Int_OPls], (33079 ^ _779999) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43225 ^ _779999) ^ [_1634239, _1634241, _1634243, _1634245, _1634247] : [-(hAPP(hAPP(c_List_Olist_OCons(_1634239), _1634241), _1634243) = hAPP(hAPP(c_List_Olist_OCons(_1634239), _1634245), _1634247)), _1634241 = _1634245, _1634243 = _1634247], (40173 ^ _779999) ^ [_1559999] : [-(c_Transitive__Closure_Otrancl(_1559999, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1559999, _1559999), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1559999, _1559999), tc_HOL_Obool)))], (45642 ^ _779999) ^ [_1694054, _1694056, _1694058, _1694060] : [-(hAPP(c_List_Orotate(_1694054, _1694056), hAPP(c_List_Orotate(_1694054, _1694058), _1694060)) = hAPP(c_List_Orotate(_1694054, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1694056), _1694058)), _1694060))], (51978 ^ _779999) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (33753 ^ _779999) ^ [_1411797] : [class_Rings_Osemiring__1(_1411797), -(c_Int_Oiszero(_1411797, c_Groups_Ozero__class_Ozero(_1411797)))], (5146 ^ _779999) ^ [_858690, _858692, _858694, _858696, _858698, _858700] : [-(c_Relation_OImage(_858700, _858696, _858692) = c_Relation_OImage(_858698, _858694, _858690)), _858700 = _858698, _858696 = _858694, _858692 = _858690], (8148 ^ _779999) ^ [_917982, _917984, _917986, _917988] : [c_Natural_Oevaln(_917982, _917984, _917986, _917988), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_917982), _917984), _917988)))], (38678 ^ _779999) ^ [_1523093, _1523095, _1523097, _1523099, _1523101, _1523103, _1523105, _1523107] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1523093, _1523095), tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1523093, _1523095), _1523101), hAPP(c_COMBK(tc_fun(_1523095, tc_HOL_Obool), _1523093), _1523103))), hAPP(c_Product__Type_Oprod_Oprod__case(_1523093, _1523095, tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1523093, tc_fun(_1523095, tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool))), tc_fun(_1523095, tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool)), tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool)), tc_fun(tc_fun(_1523095, tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool))), tc_fun(_1523095, tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool))), _1523093), c_COMBB(tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool)), tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool), _1523095)), hAPP(hAPP(c_COMBB(tc_fun(_1523097, tc_HOL_Obool), tc_fun(tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool)), tc_fun(tc_prod(_1523097, _1523099), tc_HOL_Obool)), _1523093), c_Product__Type_OSigma(_1523097, _1523099)), _1523105))), hAPP(hAPP(c_COMBB(tc_fun(_1523099, tc_HOL_Obool), tc_fun(_1523097, tc_fun(_1523099, tc_HOL_Obool)), _1523095), c_COMBK(tc_fun(_1523099, tc_HOL_Obool), _1523097)), _1523107)))) = hAPP(hAPP(c_Product__Type_OSigma(_1523097, _1523099), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523093, tc_fun(_1523097, tc_HOL_Obool)), _1523101), _1523105)), hAPP(c_COMBK(tc_fun(_1523099, tc_HOL_Obool), _1523097), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523095, tc_fun(_1523099, tc_HOL_Obool)), _1523103), _1523107))))], (33207 ^ _779999) ^ [_1401889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401889), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401889))], (20038 ^ _779999) ^ [_1145287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145287), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1145287) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23149 ^ _779999) ^ [_1212118, _1212120, _1212122] : [class_Orderings_Olinorder(_1212118), 23152 ^ _779999 : [(23159 ^ _779999) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212118), _1212120), _1212122) = _1212120, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212118), _1212120), _1212122)))], (23153 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212118), _1212120), _1212122)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212118), _1212120), _1212122) = _1212120)]]], (45592 ^ _779999) ^ [_1693284, _1693286] : [-(_1693284 = c_List_Olist_ONil(_1693286)), -(hBOOL(hAPP(hAPP(c_member(_1693286), hAPP(c_List_Ohd(_1693286), _1693284)), hAPP(c_List_Oset(_1693286), _1693284))))], (42221 ^ _779999) ^ [_1610169, _1610171] : [class_Complete__Lattice_Ocomplete__lattice(_1610169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610169), _1610171)), -(c_Complete__Lattice_OInf__class_OInf(_1610169, _1610171) = hAPP(hAPP(c_Finite__Set_Ofold(_1610169, _1610169, c_Lattices_Osemilattice__inf__class_Oinf(_1610169)), c_Orderings_Otop__class_Otop(_1610169)), _1610171))], (2624 ^ _779999) ^ [_818771, _818773] : [_818773 = _818771, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_818773) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_818771))], (3624 ^ _779999) ^ [_834327, _834329, _834331, _834333] : [-(c_List_Olistsp(_834333, _834329) = c_List_Olistsp(_834331, _834327)), _834333 = _834331, _834329 = _834327], (16477 ^ _779999) ^ [_1077682, _1077684, _1077686, _1077688] : [class_Rings_Olinordered__semiring__strict(_1077682), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077682), _1077684), _1077686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077682), c_Groups_Ozero__class_Ozero(_1077682)), _1077688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077682), _1077688), _1077684)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077682), _1077688), _1077686))))], (35322 ^ _779999) ^ [_1444487, _1444489, _1444491, _1444493, _1444495, _1444497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1444489, _1444491)), hAPP(hAPP(c_Product__Type_OPair(_1444489, _1444491), _1444495), _1444497)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1444487, tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1444487, tc_HOL_Obool))), _1444493))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1444487, tc_fun(_1444489, tc_fun(_1444491, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1444487, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_fun(_1444489, tc_fun(_1444491, tc_HOL_Obool)), _1444487), hAPP(c_COMBC(_1444489, tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_fun(_1444491, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444491, tc_fun(tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_fun(_1444491, tc_HOL_Obool)), _1444489), c_COMBC(_1444491, tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444491, tc_prod(_1444489, _1444491)), tc_fun(_1444491, tc_fun(tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_HOL_Obool)), _1444489), hAPP(c_COMBB(tc_prod(_1444489, _1444491), tc_fun(tc_fun(tc_prod(_1444489, _1444491), tc_HOL_Obool), tc_HOL_Obool), _1444491), c_member(tc_prod(_1444489, _1444491)))), c_Product__Type_OPair(_1444489, _1444491))))), _1444493)), _1444495), _1444497)))], (3902 ^ _779999) ^ [_838722, _838724] : [_838724 = _838722, -(c_Orderings_Oord__class_Omax(_838724) = c_Orderings_Oord__class_Omax(_838722))], (38707 ^ _779999) ^ [_1525295, _1525297, _1525299, _1525301, _1525303, _1525305] : [class_Groups_Ocomm__monoid__mult(_1525295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525297), _1525299)), 38717 ^ _779999 : [(38720 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525301), hAPP(_1525303, 38716 ^ [_1525295, _1525297, _1525299, _1525301, _1525303, _1525305])))], (38718 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525297), 38716 ^ [_1525295, _1525297, _1525299, _1525301, _1525303, _1525305]), _1525299)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1525295, _1525297, c_Groups_Otimes__class_Otimes(_1525295)), hAPP(hAPP(c_COMBS(_1525297, tc_fun(_1525301, tc_HOL_Obool), _1525295), hAPP(hAPP(c_COMBC(_1525297, _1525295, tc_fun(tc_fun(_1525301, tc_HOL_Obool), _1525295)), hAPP(hAPP(c_COMBB(tc_fun(_1525301, _1525295), tc_fun(_1525295, tc_fun(tc_fun(_1525301, tc_HOL_Obool), _1525295)), _1525297), c_Finite__Set_Ofold__image(_1525295, _1525301, c_Groups_Otimes__class_Otimes(_1525295))), _1525305)), c_Groups_Oone__class_Oone(_1525295))), _1525303)), c_Groups_Oone__class_Oone(_1525295)), _1525299) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1525295, tc_prod(_1525297, _1525301), c_Groups_Otimes__class_Otimes(_1525295)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525297, _1525301, _1525295), _1525305)), c_Groups_Oone__class_Oone(_1525295)), hAPP(hAPP(c_Product__Type_OSigma(_1525297, _1525301), _1525299), _1525303)))], (3776 ^ _779999) ^ [_836669, _836671, _836673, _836675, _836677, _836679] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_836679, _836675, _836671) = c_SetInterval_Oord__class_OgreaterThanLessThan(_836677, _836673, _836669)), _836679 = _836677, _836675 = _836673, _836671 = _836669], (38692 ^ _779999) ^ [_1523880, _1523882, _1523884, _1523886, _1523888, _1523890, _1523892] : [class_Rings_Osemiring__0(_1523880), c_Fun_Oinj__on(tc_prod(_1523882, _1523884), _1523880, hAPP(c_Product__Type_Oprod_Oprod__case(_1523882, _1523884, _1523880), hAPP(hAPP(c_COMBC(_1523882, tc_fun(_1523884, _1523880), tc_fun(_1523884, _1523880)), hAPP(hAPP(c_COMBB(tc_fun(_1523880, _1523880), tc_fun(tc_fun(_1523884, _1523880), tc_fun(_1523884, _1523880)), _1523882), c_COMBB(_1523880, _1523880, _1523884)), hAPP(hAPP(c_COMBB(_1523880, tc_fun(_1523880, _1523880), _1523882), c_Groups_Otimes__class_Otimes(_1523880)), _1523886))), _1523888)), hAPP(hAPP(c_Product__Type_OSigma(_1523882, _1523884), _1523890), hAPP(c_COMBK(tc_fun(_1523884, tc_HOL_Obool), _1523882), _1523892))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1523880), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523882, _1523880), _1523886), _1523890)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523884, _1523880), _1523888), _1523892)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523880, _1523880), c_Fun_Oid(_1523880)), hAPP(c_Set_OCollect(_1523880), hAPP(hAPP(c_COMBB(tc_fun(_1523882, tc_HOL_Obool), tc_HOL_Obool, _1523880), c_HOL_OEx(_1523882)), hAPP(hAPP(c_COMBB(tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool)), tc_fun(_1523882, tc_HOL_Obool), _1523880), hAPP(c_COMBB(tc_fun(_1523884, tc_HOL_Obool), tc_HOL_Obool, _1523882), c_HOL_OEx(_1523884))), hAPP(hAPP(c_COMBC(_1523880, tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool)), tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523882, tc_fun(tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool))), tc_fun(tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool)), tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool))), _1523880), c_COMBS(_1523882, tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523882, tc_fun(_1523884, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1523882, tc_fun(tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool))), _1523880), hAPP(c_COMBB(tc_fun(_1523884, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool)), _1523882), c_COMBS(_1523884, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool)), tc_fun(_1523882, tc_fun(_1523884, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1523880), hAPP(c_COMBB(tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1523882), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523884), c_fconj))), hAPP(hAPP(c_COMBC(_1523880, tc_fun(_1523882, tc_fun(_1523884, _1523880)), tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1523884, _1523880), tc_fun(_1523884, tc_HOL_Obool)), tc_fun(tc_fun(_1523882, tc_fun(_1523884, _1523880)), tc_fun(_1523882, tc_fun(_1523884, tc_HOL_Obool))), _1523880), c_COMBB(tc_fun(_1523884, _1523880), tc_fun(_1523884, tc_HOL_Obool), _1523882)), hAPP(hAPP(c_COMBB(tc_fun(_1523880, tc_HOL_Obool), tc_fun(tc_fun(_1523884, _1523880), tc_fun(_1523884, tc_HOL_Obool)), _1523880), c_COMBB(_1523880, tc_HOL_Obool, _1523884)), c_fequal))), hAPP(hAPP(c_COMBC(_1523882, tc_fun(_1523884, _1523880), tc_fun(_1523884, _1523880)), hAPP(hAPP(c_COMBB(tc_fun(_1523880, _1523880), tc_fun(tc_fun(_1523884, _1523880), tc_fun(_1523884, _1523880)), _1523882), c_COMBB(_1523880, _1523880, _1523884)), hAPP(hAPP(c_COMBB(_1523880, tc_fun(_1523880, _1523880), _1523882), c_Groups_Otimes__class_Otimes(_1523880)), _1523886))), _1523888)))))), hAPP(hAPP(c_COMBC(_1523882, tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1523884, tc_HOL_Obool), tc_fun(_1523884, tc_HOL_Obool)), _1523882), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523884)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523882), c_fconj), hAPP(hAPP(c_COMBC(_1523882, tc_fun(_1523882, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523882)), _1523890)))), hAPP(hAPP(c_COMBC(_1523884, tc_fun(_1523884, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523884)), _1523892))))))))], (42728 ^ _779999) ^ [_1621733, _1621735] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621733, tc_HOL_Obool), _1621735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1621733, tc_HOL_Obool), tc_fun(_1621733, tc_HOL_Obool)), _1621735), c_COMBI(tc_fun(_1621733, tc_HOL_Obool))))], (22227 ^ _779999) ^ [_1191262, _1191264] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1191262, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1191262, tc_HOL_Obool))), _1191264) = _1191264)], (42105 ^ _779999) ^ [_1607266, _1607268, _1607270, _1607272, _1607274] : [class_Complete__Lattice_Ocomplete__lattice(_1607266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607268, tc_HOL_Obool)), _1607270), _1607272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1607266), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607268, _1607266), _1607272), _1607274)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607268, _1607266), _1607270), _1607274))))], (33467 ^ _779999) ^ [_1406039, _1406041] : [class_Int_Onumber__ring(_1406039), class_Rings_Olinordered__idom(_1406039), 33474 ^ _779999 : [(33481 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406041), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406039), hAPP(c_Int_Onumber__class_Onumber__of(_1406039), _1406041)), c_Groups_Oone__class_Oone(_1406039))))], (33475 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406039), hAPP(c_Int_Onumber__class_Onumber__of(_1406039), _1406041)), c_Groups_Oone__class_Oone(_1406039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406041), c_Int_OBit1(c_Int_OPls))))]]], (38236 ^ _779999) ^ [_1510588, _1510590] : [-(hAPP(c_Relation_ORange(_1510588, _1510590), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1510588, _1510590), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1510590, tc_HOL_Obool)))], (732 ^ _779999) ^ [_791259, _791261, _791263, _791265, _791267, _791269] : [-(c_Finite__Set_Ofun__left__comm(_791267, _791263, _791259)), c_Finite__Set_Ofun__left__comm(_791269, _791265, _791261), _791269 = _791267, _791265 = _791263, _791261 = _791259], (20164 ^ _779999) ^ [_1147341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1147341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147341)))], (49694 ^ _779999) ^ [] : [-(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)))], (34795 ^ _779999) ^ [_1430891] : [c_Int_OBit1(_1430891) = c_Int_OMin, -(_1430891 = c_Int_OMin)], (34253 ^ _779999) ^ [_1420700] : [class_Rings_Osemiring__1(_1420700), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1420700), c_Groups_Ozero__class_Ozero(_1420700)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1420700))], (24344 ^ _779999) ^ [_1236070, _1236072, _1236074, _1236076] : [class_Orderings_Olinorder(_1236070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236070), _1236072), _1236074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236070), _1236072), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236070), _1236076), _1236074))))], (12201 ^ _779999) ^ [_995431, _995433, _995435] : [class_Lattices_Olattice(_995431), hBOOL(hAPP(c_Finite__Set_Ofinite(_995431), _995433)), hBOOL(hAPP(hAPP(c_member(_995431), _995435), _995433)), 12212 ^ _779999 : [(12219 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995431, tc_HOL_Obool)), _995433), hAPP(hAPP(c_Set_Oinsert(_995431), _995435), c_Orderings_Obot__class_Obot(tc_fun(_995431, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_995431, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_995431, _995433) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_995431), _995435), c_Big__Operators_Olattice__class_OSup__fin(_995431, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995431, tc_HOL_Obool)), _995433), hAPP(hAPP(c_Set_Oinsert(_995431), _995435), c_Orderings_Obot__class_Obot(tc_fun(_995431, tc_HOL_Obool)))))))], (12213 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995431, tc_HOL_Obool)), _995433), hAPP(hAPP(c_Set_Oinsert(_995431), _995435), c_Orderings_Obot__class_Obot(tc_fun(_995431, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_995431, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_995431, _995433) = _995435)]]], (30589 ^ _779999) ^ [_1353577, _1353579] : [class_Divides_Osemiring__div(_1353577), -(c_Divides_Odiv__class_Omod(_1353577, _1353579, _1353579) = c_Groups_Ozero__class_Ozero(_1353577))], (44035 ^ _779999) ^ [_1658301] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1658301)), -(c_List_Onat__list(_1658301))], (44540 ^ _779999) ^ [_1669140, _1669142, _1669144] : [-(hAPP(hAPP(c_List_Ozip(_1669140, _1669142), c_List_Olist_ONil(_1669140)), _1669144) = c_List_Olist_ONil(tc_prod(_1669140, _1669142)))], (10471 ^ _779999) ^ [_960286, _960288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960286), hAPP(c_Nat_OSuc, _960288))), -(_960286 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10479 ^ _779999 : [(10482 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 10478 ^ [_960286, _960288]), _960288)))], (10480 ^ _779999) ^ [] : [-(_960286 = hAPP(c_Nat_OSuc, 10478 ^ [_960286, _960288]))]]], (23129 ^ _779999) ^ [_1211779, _1211781] : [class_Orderings_Olinorder(_1211779), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211779), _1211781), _1211781) = _1211781)], (21939 ^ _779999) ^ [_1182624, _1182626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182624), _1182626)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1182624, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1182624, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1182624, tc_HOL_Obool), tc_fun(_1182624, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1182624, tc_HOL_Obool))), _1182626)))))], (40053 ^ _779999) ^ [_1557402, _1557404, _1557406, _1557408, _1557410, _1557412] : [c_Com_Ocom_OLocal(_1557402, _1557404, _1557406) = c_Com_Ocom_OLocal(_1557408, _1557410, _1557412), 40056 ^ _779999 : [(40061 ^ _779999) ^ [] : [-(_1557406 = _1557412)], (40059 ^ _779999) ^ [] : [-(_1557404 = _1557410)], (40057 ^ _779999) ^ [] : [-(_1557402 = _1557408)]]], (24644 ^ _779999) ^ [_1241599, _1241601] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1241599)), _1241601) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1241599), 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), _1241599)), _1241601))], (52106 ^ _779999) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (15765 ^ _779999) ^ [_1064354, _1064356] : [class_Rings_Ocomm__semiring__1(_1064354), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064354), _1064356), c_Groups_Oone__class_Oone(_1064354)) = _1064356)], (48999 ^ _779999) ^ [_1766488, _1766490, _1766492] : [hBOOL(hAPP(c_List_Odistinct(_1766488), _1766490)), -(c_List_Oremove1(_1766488, _1766492, _1766490) = hAPP(c_List_OremoveAll(_1766488, _1766492), _1766490))], (40389 ^ _779999) ^ [_1566013, _1566015, _1566017, _1566019] : [40390 ^ _779999 : [(40393 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566013, _1566013)), _1566015), c_Transitive__Closure_Ortrancl(_1566013, _1566019)))], (40391 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566013, _1566013)), _1566015), c_Transitive__Closure_Ortrancl(_1566013, _1566017)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566013, _1566013)), _1566015), c_Transitive__Closure_Ortrancl(_1566013, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566013, _1566013), tc_HOL_Obool)), _1566017), _1566019)))))], (34471 ^ _779999) ^ [_1424407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1424407), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1424407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1424407 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31331 ^ _779999) ^ [_1366782, _1366784, _1366786] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366782), _1366784)), _1366786) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366782), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1366784), _1366786))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366782), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1366784, _1366786))), _1366786)))], (7625 ^ _779999) ^ [_908142, _908144, _908146] : [hAPP(c_Com_Ocom_OBODY, _908142) = c_Com_Ocom_OSemi(_908144, _908146)], (30788 ^ _779999) ^ [_1357251, _1357253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357251), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30791 ^ _779999 : [(30794 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357251), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357253, _1357251))))], (30792 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357253, _1357251)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11508 ^ _779999) ^ [_981182, _981184, _981186, _981188] : [-(hBOOL(hAPP(hAPP(c_member(_981182), _981184), _981186))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981182, tc_HOL_Obool)), _981186), hAPP(hAPP(c_Set_Oinsert(_981182), _981184), _981188)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981182, tc_HOL_Obool)), _981186), _981188))], (51386 ^ _779999) ^ [_1819602, _1819604, _1819606, _1819608, _1819610] : [c_Fun_Oinj__on(_1819602, _1819604, _1819606, c_Orderings_Otop__class_Otop(tc_fun(_1819602, tc_HOL_Obool))), hAPP(_1819606, _1819608) = _1819610, -(hAPP(c_Hilbert__Choice_Oinv__into(_1819602, _1819604, c_Orderings_Otop__class_Otop(tc_fun(_1819602, tc_HOL_Obool)), _1819606), _1819610) = _1819608)], (37710 ^ _779999) ^ [_1498032, _1498034, _1498036, _1498038] : [hBOOL(hAPP(hAPP(c_member(_1498032), _1498034), c_Wellfounded_Oacc(_1498032, _1498036))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1498032, _1498032)), hAPP(hAPP(c_Product__Type_OPair(_1498032, _1498032), _1498038), _1498034)), _1498036)), -(hBOOL(hAPP(hAPP(c_member(_1498032), _1498038), c_Wellfounded_Oacc(_1498032, _1498036))))], (43048 ^ _779999) ^ [_1629107, _1629109, _1629111, _1629113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629107, _1629109)), _1629111), hAPP(c_Relation_Oconverse(_1629109, _1629107), _1629113))), 43053 ^ _779999 : [(43056 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629109, _1629107)), hAPP(hAPP(c_Product__Type_OPair(_1629109, _1629107), 43051 ^ [_1629107, _1629109, _1629111, _1629113]), 43052 ^ [_1629107, _1629109, _1629111, _1629113])), _1629113)))], (43054 ^ _779999) ^ [] : [-(_1629111 = hAPP(hAPP(c_Product__Type_OPair(_1629107, _1629109), 43052 ^ [_1629107, _1629109, _1629111, _1629113]), 43051 ^ [_1629107, _1629109, _1629111, _1629113]))]]], (21351 ^ _779999) ^ [_1168858, _1168860, _1168862] : [class_Groups_Oab__semigroup__mult(_1168858), -(_1168860 = c_Orderings_Obot__class_Obot(tc_fun(_1168858, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168858), _1168860)), -(hBOOL(hAPP(hAPP(c_member(_1168858), _1168862), _1168860))), -(hAPP(c_Finite__Set_Ofold1(_1168858, c_Groups_Otimes__class_Otimes(_1168858)), hAPP(hAPP(c_Set_Oinsert(_1168858), _1168862), _1168860)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168858), _1168862), hAPP(c_Finite__Set_Ofold1(_1168858, c_Groups_Otimes__class_Otimes(_1168858)), _1168860)))], (41011 ^ _779999) ^ [_1580848, _1580850, _1580852, _1580854, _1580856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580848, _1580848)), hAPP(hAPP(c_Product__Type_OPair(_1580848, _1580848), _1580850), _1580852)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580848, _1580848), tc_HOL_Obool), _1580854), _1580856))), 41016 ^ _779999 : [(41019 ^ _779999) ^ [] : [-(_1580850 = _1580852)], (41017 ^ _779999) ^ [] : [-(_1580854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41022 ^ _779999 : [(41027 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580848, _1580848)), hAPP(hAPP(c_Product__Type_OPair(_1580848, _1580848), 41020 ^ [_1580848, _1580850, _1580852, _1580854, _1580856]), _1580852)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580848, _1580848), tc_HOL_Obool), 41021 ^ [_1580848, _1580850, _1580852, _1580854, _1580856]), _1580856))))], (41025 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580848, _1580848)), hAPP(hAPP(c_Product__Type_OPair(_1580848, _1580848), _1580850), 41020 ^ [_1580848, _1580850, _1580852, _1580854, _1580856])), _1580856)))], (41023 ^ _779999) ^ [] : [-(_1580854 = hAPP(c_Nat_OSuc, 41021 ^ [_1580848, _1580850, _1580852, _1580854, _1580856]))]]], (25854 ^ _779999) ^ [_1264571, _1264573] : [class_Groups_Oordered__ab__group__add__abs(_1264571), -(hAPP(c_Groups_Oabs__class_Oabs(_1264571), hAPP(c_Groups_Ouminus__class_Ouminus(_1264571), _1264573)) = hAPP(c_Groups_Oabs__class_Oabs(_1264571), _1264573))], (37666 ^ _779999) ^ [_1496770, _1496772, _1496774, _1496776] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1496770, _1496772, _1496774), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1496770, _1496772), tc_HOL_Obool))), _1496776) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1496770, _1496774), tc_HOL_Obool)))], (6243 ^ _779999) ^ [_879833, _879835, _879837, _879839] : [hBOOL(hAPP(_879833, _879835)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879837, tc_HOL_Obool)), _879839), _879833), _879835)))], (48671 ^ _779999) ^ [_1759659, _1759661, _1759663, _1759665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759659), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759661)), c_List_OtakeWhile(_1759661, _1759663, _1759665)))), -(hAPP(hAPP(c_List_Onth(_1759661), c_List_OtakeWhile(_1759661, _1759663, _1759665)), _1759659) = hAPP(hAPP(c_List_Onth(_1759661), _1759665), _1759659))], (22429 ^ _779999) ^ [_1194978] : [class_Nat_Osemiring__char__0(_1194978), -(c_Fun_Oinj__on(tc_Nat_Onat, _1194978, c_Nat_Osemiring__1__class_Oof__nat(_1194978), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (37596 ^ _779999) ^ [_1493985] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1493985) = 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, _1493985)), 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))))))))], (42177 ^ _779999) ^ [_1609208, _1609210, _1609212, _1609214, _1609216] : [class_Complete__Lattice_Ocomplete__lattice(_1609208), hBOOL(hAPP(hAPP(c_member(_1609210), _1609212), _1609214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609208), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609210, _1609208), _1609214), _1609216)), hAPP(_1609216, _1609212))))], (47012 ^ _779999) ^ [_1724195, _1724197, _1724199, _1724201, _1724203, _1724205, _1724207] : [-(c_List_Olist__all2(_1724195, _1724197, _1724199, hAPP(hAPP(c_List_Olist_OCons(_1724195), _1724201), _1724203), hAPP(hAPP(c_List_Olist_OCons(_1724197), _1724205), _1724207))), hBOOL(hAPP(hAPP(_1724199, _1724201), _1724205)), c_List_Olist__all2(_1724195, _1724197, _1724199, _1724203, _1724207)], (43391 ^ _779999) ^ [_1639561, _1639563, _1639565, _1639567] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1639561), tc_List_Olist(_1639561), c_List_Olistrel(_1639561, _1639563)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639561)), hAPP(hAPP(c_List_Olist_OCons(_1639561), _1639565), _1639567)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639561), tc_HOL_Obool)))) = c_List_Oset__Cons(_1639561, hAPP(c_Relation_OImage(_1639561, _1639561, _1639563), hAPP(hAPP(c_Set_Oinsert(_1639561), _1639565), c_Orderings_Obot__class_Obot(tc_fun(_1639561, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1639561), tc_List_Olist(_1639561), c_List_Olistrel(_1639561, _1639563)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639561)), _1639567), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639561), tc_HOL_Obool))))))], (51486 ^ _779999) ^ [_1821786, _1821788, _1821790] : [hAPP(c_Set_Oimage(_1821786, _1821788, _1821790), c_Orderings_Otop__class_Otop(tc_fun(_1821786, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1821788, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1821786, _1821788, _1821788, _1821790), c_Hilbert__Choice_Oinv__into(_1821786, _1821788, c_Orderings_Otop__class_Otop(tc_fun(_1821786, tc_HOL_Obool)), _1821790)) = c_Fun_Oid(_1821788))], (30832 ^ _779999) ^ [_1357988, _1357990] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357988, _1357990) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357988, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1357990)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357988, _1357990)), _1357990))], (49531 ^ _779999) ^ [_1779167, _1779169, _1779171] : [49533 ^ _779999 : [(49536 ^ _779999) ^ [] : [hBOOL(hAPP(_1779169, 49532 ^ [_1779167, _1779169, _1779171]))], (49534 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779167), 49532 ^ [_1779167, _1779169, _1779171]), hAPP(c_List_Oset(_1779167), _1779171))))]], -(c_List_Olist__all(_1779167, _1779169, _1779171))], (6559 ^ _779999) ^ [_886108, _886110, _886112, _886114, _886116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886108, tc_HOL_Obool)), _886110), hAPP(c_Set_Oimage(_886112, _886108, _886114), _886116)))), 6560 ^ _779999 : [(6561 ^ _779999) ^ [_886188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886112, tc_HOL_Obool)), _886188), _886116)), _886110 = hAPP(c_Set_Oimage(_886112, _886108, _886114), _886188)]]], (8218 ^ _779999) ^ [_919371, _919373, _919375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919371, tc_HOL_Obool)), _919373), _919375)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_919371, tc_HOL_Obool)), _919373), hAPP(c_Set_OPow(_919371), _919375))))], (23053 ^ _779999) ^ [_1210211, _1210213, _1210215, _1210217, _1210219, _1210221] : [hAPP(_1210211, _1210213) = _1210215, hBOOL(hAPP(hAPP(c_member(_1210217), _1210215), _1210219)), -(hBOOL(hAPP(hAPP(c_member(_1210221), _1210213), hAPP(c_Set_Ovimage(_1210221, _1210217, _1210211), _1210219))))], (24682 ^ _779999) ^ [_1242280, _1242282, _1242284, _1242286, _1242288] : [class_Orderings_Olinorder(_1242280), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242280, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1242280, _1242282, _1242284)), c_SetInterval_Oord__class_OatLeastAtMost(_1242280, _1242286, _1242288)) = c_SetInterval_Oord__class_OatLeastAtMost(_1242280, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242280), _1242282), _1242286), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1242280), _1242284), _1242288)))], (43872 ^ _779999) ^ [_1652763, _1652765, _1652767] : [hBOOL(hAPP(hAPP(c_member(_1652763), _1652765), hAPP(c_List_Oset(_1652763), _1652767))), 43876 ^ _779999 : [(43879 ^ _779999) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1652763), _1652767), 43875 ^ [_1652763, _1652765, _1652767]) = _1652765)], (43877 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43875 ^ [_1652763, _1652765, _1652767]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652763)), _1652767))))]]], (34801 ^ _779999) ^ [_1430966] : [_1430966 = c_Int_OMin, -(c_Int_OBit1(_1430966) = c_Int_OMin)], (19530 ^ _779999) ^ [_1135987] : [hBOOL(hAPP(_1135987, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19531 ^ [_1135987]))), 19534 ^ _779999 : [(19535 ^ _779999) ^ [_1136087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136087)), -(hBOOL(hAPP(_1135987, _1136087)))]]], (49724 ^ _779999) ^ [_1783058, _1783060, _1783062, _1783064, _1783066] : [-(_1783058 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1783060, _1783062, _1783064, _1783066), _1783058) = hAPP(c_Lazy__Sequence_Obind(_1783060, _1783062, hAPP(_1783064, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1783058), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1783060, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1783062)), _1783066), _1783058)))], (50599 ^ _779999) ^ [_1802645, _1802647] : [c_Relation_Otrans(_1802645, _1802647), -(c_Relation_Otrans(tc_List_Olist(_1802645), c_List_Olistrel(_1802645, _1802647)))], (40997 ^ _779999) ^ [_1580499, _1580501, _1580503] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580499, _1580499)), _1580501), c_Transitive__Closure_Otrancl(_1580499, _1580503)))), 40998 ^ _779999 : [(40999 ^ _779999) ^ [_1580578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1580578)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580499, _1580499)), _1580501), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580499, _1580499), tc_HOL_Obool), _1580578), _1580503)))]]], (10703 ^ _779999) ^ [_964277, _964279, _964281, _964283] : [-(_964277 = c_Orderings_Obot__class_Obot(tc_fun(_964279, tc_HOL_Obool))), 10706 ^ _779999 : [(10707 ^ _779999) ^ [] : [-(hAPP(c_Set_Oimage(_964281, _964279, 10714 ^ [_964277, _964279, _964281, _964283]), _964283) = _964277), 10708 ^ _779999 : [(10709 ^ _779999) ^ [_964418] : [c_Fun_Oinj__on(_964279, _964281, _964418, _964277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_964281, tc_HOL_Obool)), hAPP(c_Set_Oimage(_964279, _964281, _964418), _964277)), _964283))]]], (10718 ^ _779999) ^ [] : [10719 ^ _779999 : [(10720 ^ _779999) ^ [_964610] : [hAPP(c_Set_Oimage(_964281, _964279, _964610), _964283) = _964277]], 10722 ^ _779999 : [(10725 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_964281, tc_HOL_Obool)), hAPP(c_Set_Oimage(_964279, _964281, 10721 ^ [_964277, _964279, _964281, _964283]), _964277)), _964283)))], (10723 ^ _779999) ^ [] : [-(c_Fun_Oinj__on(_964279, _964281, 10721 ^ [_964277, _964279, _964281, _964283], _964277))]]]]], (39771 ^ _779999) ^ [_1550269, _1550271, _1550273, _1550275, _1550277, _1550279] : [c_Finite__Set_Ofolding(_1550269, _1550271, _1550273, _1550275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550269), _1550277)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550269), _1550279)), -(hAPP(c_Fun_Ocomp(_1550271, _1550271, _1550271, hAPP(_1550275, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1550269, tc_HOL_Obool)), _1550277), _1550279))), hAPP(_1550275, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1550269, tc_HOL_Obool)), _1550277), _1550279))) = hAPP(c_Fun_Ocomp(_1550271, _1550271, _1550271, hAPP(_1550275, _1550277)), hAPP(_1550275, _1550279)))], (48677 ^ _779999) ^ [_1759811, _1759813] : [-(_1759811 = c_List_Olist_ONil(_1759813)), hBOOL(hAPP(c_List_Odistinct(_1759813), _1759811)), -(c_List_OtakeWhile(_1759813, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1759813), c_fNot), hAPP(hAPP(c_COMBC(_1759813, _1759813, tc_HOL_Obool), c_fequal), c_List_Olast(_1759813, _1759811))), _1759811) = c_List_Obutlast(_1759813, _1759811))], (46205 ^ _779999) ^ [_1705130, _1705132, _1705134, _1705136] : [c_List_Olist_ONil(_1705130) = hAPP(hAPP(c_List_Omap(_1705132, _1705130), _1705134), _1705136), -(_1705136 = c_List_Olist_ONil(_1705132))], (33867 ^ _779999) ^ [_1413664, _1413666] : [-(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), _1413664)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1413666)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1413664))) = 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), _1413666)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1413664)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11751 ^ _779999) ^ [_986451, _986453, _986455] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986451), _986453)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_986451), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986451, tc_HOL_Obool)), _986453), _986455))))], (2222 ^ _779999) ^ [_812608, _812610, _812612, _812614, _812616, _812618] : [-(c_SetInterval_Oord_OatLeast(_812618, _812614, _812610) = c_SetInterval_Oord_OatLeast(_812616, _812612, _812608)), _812618 = _812616, _812614 = _812612, _812610 = _812608], (35482 ^ _779999) ^ [_1447944, _1447946, _1447948, _1447950, _1447952, _1447954, _1447956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447944, _1447946)), hAPP(hAPP(c_Product__Type_OPair(_1447944, _1447946), _1447948), _1447950)), _1447952)), -(hBOOL(hAPP(hAPP(c_member(_1447954), hAPP(hAPP(_1447956, _1447948), _1447950)), hAPP(c_Set_Oimage(tc_prod(_1447944, _1447946), _1447954, hAPP(c_Product__Type_Oprod_Oprod__case(_1447944, _1447946, _1447954), _1447956)), _1447952))))], (32633 ^ _779999) ^ [_1392205] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392205))), -(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), _1392205)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4544 ^ _779999) ^ [_849051, _849053] : [_849053 = _849051, -(c_Orderings_Oord__class_Omin(_849053) = c_Orderings_Oord__class_Omin(_849051))], (23249 ^ _779999) ^ [_1213783, _1213785, _1213787, _1213789] : [class_Orderings_Olinorder(_1213783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213783), _1213785), _1213787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213783), _1213785), _1213789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213783), _1213785), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213783), _1213787), _1213789))))], (14547 ^ _779999) ^ [_1040577, _1040579, _1040581, _1040583] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040577), _1040579)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040577), _1040581)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040577, tc_Nat_Onat), _1040583), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040577, tc_HOL_Obool)), _1040579), _1040581)) = 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(_1040577, tc_Nat_Onat), _1040583), _1040579)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040577, tc_Nat_Onat), _1040583), _1040581))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1040577, tc_Nat_Onat), _1040583), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040577, tc_HOL_Obool)), _1040579), _1040581))))], (44572 ^ _779999) ^ [_1669725, _1669727] : [-(hAPP(hAPP(c_List_Otake(_1669725), _1669727), c_List_Olist_ONil(_1669725)) = c_List_Olist_ONil(_1669725))], (47759 ^ _779999) ^ [_1741598, _1741600] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1741598, _1741600)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1741598), hAPP(c_Nat_OSuc, _1741600)))], (46718 ^ _779999) ^ [_1717043] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1717043), 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, _1717043)) = _1717043)], (45562 ^ _779999) ^ [_1692810, _1692812, _1692814] : [-(_1692810 = c_List_Olist_ONil(_1692812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692814), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692812)), _1692810))), -(hAPP(c_List_Ohd(_1692812), hAPP(hAPP(c_List_Odrop(_1692812), _1692814), _1692810)) = hAPP(hAPP(c_List_Onth(_1692812), _1692810), _1692814))], (1524 ^ _779999) ^ [_802157, _802159] : [-(class_Groups_Ouminus(_802157)), _802159 = _802157, class_Groups_Ouminus(_802159)], (13540 ^ _779999) ^ [_1021335, _1021337, _1021339, _1021341, _1021343] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1021335, _1021337, _1021339), _1021341), _1021343), c_Orderings_Obot__class_Obot(tc_fun(_1021337, tc_HOL_Obool))) = _1021343)], (16697 ^ _779999) ^ [_1082036, _1082038, _1082040] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082036), _1082038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082040), _1082038)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082036), _1082040))], (22223 ^ _779999) ^ [_1191170, _1191172] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1191170, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1191170, tc_HOL_Obool))), _1191172) = c_Orderings_Otop__class_Otop(tc_fun(_1191170, tc_HOL_Obool)))], (14778 ^ _779999) ^ [_1045395, _1045397] : [class_Groups_Oone(_1045395), 14781 ^ _779999 : [(14788 ^ _779999) ^ [] : [_1045397 = c_Groups_Oone__class_Oone(_1045395), -(c_Groups_Oone__class_Oone(_1045395) = _1045397)], (14782 ^ _779999) ^ [] : [c_Groups_Oone__class_Oone(_1045395) = _1045397, -(_1045397 = c_Groups_Oone__class_Oone(_1045395))]]], (52136 ^ _779999) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (44029 ^ _779999) ^ [_1658228] : [c_List_Onat__list(_1658228), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1658228)))], (12978 ^ _779999) ^ [_1010622, _1010624, _1010626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010622), _1010624)), hBOOL(hAPP(hAPP(c_member(_1010622), _1010626), _1010624)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1010622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010622, tc_HOL_Obool)), _1010624), hAPP(hAPP(c_Set_Oinsert(_1010622), _1010626), c_Orderings_Obot__class_Obot(tc_fun(_1010622, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1010622), _1010624))], (22886 ^ _779999) ^ [_1205527, _1205529, _1205531, _1205533, _1205535] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205527, tc_HOL_Obool)), _1205529), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205531, tc_fun(_1205527, tc_HOL_Obool)), _1205533), _1205535)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1205531, tc_fun(_1205527, tc_HOL_Obool)), _1205533), hAPP(hAPP(c_COMBB(tc_fun(_1205527, tc_HOL_Obool), tc_fun(_1205527, tc_HOL_Obool), _1205531), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205527, tc_HOL_Obool)), _1205529)), _1205535)))], (39385 ^ _779999) ^ [_1541572, _1541574, _1541576, _1541578, _1541580, _1541582, _1541584] : [-(hAPP(c_Fun_Ocomp(_1541572, _1541574, _1541576, _1541578), c_Fun_Ofun__upd(_1541576, _1541572, _1541580, _1541582, _1541584)) = c_Fun_Ofun__upd(_1541576, _1541574, hAPP(c_Fun_Ocomp(_1541572, _1541574, _1541576, _1541578), _1541580), _1541582, hAPP(_1541578, _1541584)))], (38250 ^ _779999) ^ [_1510882, _1510884, _1510886, _1510888] : [-(hAPP(c_Relation_ORange(_1510882, _1510884), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510882, _1510884), tc_HOL_Obool)), _1510886), _1510888)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510884, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1510882, _1510884), _1510886)), hAPP(c_Relation_ORange(_1510882, _1510884), _1510888)))], (29238 ^ _779999) ^ [_1329192, _1329194, _1329196, _1329198] : [class_Fields_Olinordered__field(_1329192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329192), _1329194), c_Groups_Ozero__class_Ozero(_1329192))), 29245 ^ _779999 : [(29252 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329192), _1329198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329192), _1329196), _1329194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329192), _1329196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329192), _1329198), _1329194))))], (29246 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329192), _1329196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329192), _1329198), _1329194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329192), _1329198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329192), _1329196), _1329194))))]]], (15947 ^ _779999) ^ [_1067874, _1067876, _1067878, _1067880, _1067882] : [class_Rings_Osemiring__0(_1067874), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067874), _1067876), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067878, _1067874), _1067880), _1067882)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1067878, _1067874), hAPP(hAPP(c_COMBB(_1067874, _1067874, _1067878), hAPP(c_Groups_Otimes__class_Otimes(_1067874), _1067876)), _1067880)), _1067882))], (41502 ^ _779999) ^ [_1592293, _1592295, _1592297, _1592299, _1592301] : [c_Finite__Set_Ofolding__one(_1592293, _1592295, _1592297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592293), _1592299)), -(hBOOL(hAPP(hAPP(c_member(_1592293), _1592301), _1592299))), -(hAPP(_1592297, hAPP(hAPP(c_Set_Oinsert(_1592293), _1592301), _1592299)) = hAPP(hAPP(c_Finite__Set_Ofold(_1592293, _1592293, _1592295), _1592301), _1592299))], (48486 ^ _779999) ^ [_1755721, _1755723] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1755721), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1755721))), c_List_Otranspose(_1755721, _1755723)))))], (38451 ^ _779999) ^ [_1516618, _1516620, _1516622, _1516624] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1516618, _1516620)), hAPP(hAPP(c_Product__Type_OSigma(_1516618, _1516620), _1516622), hAPP(c_COMBK(tc_fun(_1516620, tc_HOL_Obool), _1516618), _1516624))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1516618), _1516622)), hAPP(c_Finite__Set_Ocard(_1516620), _1516624)))], (6521 ^ _779999) ^ [_885246, _885248, _885250, _885252] : [class_Orderings_Oord(_885246), 6524 ^ _779999 : [(6531 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885246), hAPP(_885250, 6532 ^ [_885246, _885248, _885250, _885252])), hAPP(_885252, 6532 ^ [_885246, _885248, _885250, _885252]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885248, _885246)), _885250), _885252)))], (6525 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885248, _885246)), _885250), _885252)), 6528 ^ _779999 : [(6529 ^ _779999) ^ [_885403] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885246), hAPP(_885250, _885403)), hAPP(_885252, _885403))))]]]]], (39903 ^ _779999) ^ [_1553539, _1553541, _1553543, _1553545, _1553547, _1553549] : [c_Finite__Set_Ofolding__idem(_1553539, _1553541, _1553543, _1553545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553539), _1553547)), hBOOL(hAPP(hAPP(c_member(_1553539), _1553549), _1553547)), -(hAPP(c_Fun_Ocomp(_1553541, _1553541, _1553541, hAPP(_1553545, _1553547)), hAPP(_1553543, _1553549)) = hAPP(_1553545, _1553547))], (34143 ^ _779999) ^ [_1418458, _1418460] : [class_Int_Onumber__ring(_1418458), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418458), c_Int_OBit0(_1418460)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418458), c_Groups_Ozero__class_Ozero(_1418458)), hAPP(c_Int_Onumber__class_Onumber__of(_1418458), _1418460))), hAPP(c_Int_Onumber__class_Onumber__of(_1418458), _1418460)))], (49868 ^ _779999) ^ [_1787023, _1787025, _1787027] : [-(c_List_Oreplicate(_1787023, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787023)), hAPP(c_List_Ofilter(_1787023, hAPP(c_fequal, _1787025)), _1787027)), _1787025) = hAPP(c_List_Ofilter(_1787023, hAPP(c_fequal, _1787025)), _1787027))], (24176 ^ _779999) ^ [_1231764, _1231766, _1231768] : [class_Orderings_Olinorder(_1231764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1231764), _1231766)), -(_1231766 = c_Orderings_Obot__class_Obot(tc_fun(_1231764, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1231764), _1231768)), -(_1231768 = c_Orderings_Obot__class_Obot(tc_fun(_1231764, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1231764), c_Big__Operators_Olattice_OInf__fin(_1231764, c_Orderings_Oord__class_Omin(_1231764), _1231766)), c_Big__Operators_Olattice_OInf__fin(_1231764, c_Orderings_Oord__class_Omin(_1231764), _1231768)) = c_Big__Operators_Olattice_OInf__fin(_1231764, c_Orderings_Oord__class_Omin(_1231764), hAPP(c_Set_OCollect(_1231764), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_HOL_Obool), tc_HOL_Obool, _1231764), c_HOL_OEx(_1231764)), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool)), tc_fun(_1231764, tc_HOL_Obool), _1231764), hAPP(c_COMBB(tc_fun(_1231764, tc_HOL_Obool), tc_HOL_Obool, _1231764), c_HOL_OEx(_1231764))), hAPP(hAPP(c_COMBC(_1231764, tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool)), tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_fun(tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool))), tc_fun(tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool)), tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool))), _1231764), c_COMBS(_1231764, tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_fun(_1231764, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1231764, tc_fun(tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool))), _1231764), hAPP(c_COMBB(tc_fun(_1231764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool)), _1231764), c_COMBS(_1231764, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool)), tc_fun(_1231764, tc_fun(_1231764, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1231764), hAPP(c_COMBB(tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1231764), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1231764), c_fconj))), hAPP(hAPP(c_COMBC(_1231764, tc_fun(_1231764, tc_fun(_1231764, _1231764)), tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1231764, _1231764), tc_fun(_1231764, tc_HOL_Obool)), tc_fun(tc_fun(_1231764, tc_fun(_1231764, _1231764)), tc_fun(_1231764, tc_fun(_1231764, tc_HOL_Obool))), _1231764), c_COMBB(tc_fun(_1231764, _1231764), tc_fun(_1231764, tc_HOL_Obool), _1231764)), hAPP(hAPP(c_COMBB(tc_fun(_1231764, tc_HOL_Obool), tc_fun(tc_fun(_1231764, _1231764), tc_fun(_1231764, tc_HOL_Obool)), _1231764), c_COMBB(_1231764, tc_HOL_Obool, _1231764)), c_fequal))), c_Orderings_Oord__class_Omax(_1231764)))))), hAPP(hAPP(c_COMBC(_1231764, tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1231764, tc_HOL_Obool), tc_fun(_1231764, tc_HOL_Obool)), _1231764), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1231764)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1231764), c_fconj), hAPP(hAPP(c_COMBC(_1231764, tc_fun(_1231764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1231764)), _1231766)))), hAPP(hAPP(c_COMBC(_1231764, tc_fun(_1231764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1231764)), _1231768))))))))], (7920 ^ _779999) ^ [_913693] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _913693), _913693)))], (40185 ^ _779999) ^ [_1560243, _1560245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560243, _1560243)), _1560245)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560243, _1560243)), c_Transitive__Closure_Otrancl(_1560243, _1560245))))], (23093 ^ _779999) ^ [_1210963, _1210965, _1210967, _1210969] : [class_Orderings_Olinorder(_1210963), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210963), _1210965), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210963), _1210967), _1210969)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210963), _1210967), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210963), _1210965), _1210969)))], (28106 ^ _779999) ^ [_1308369, _1308371, _1308373] : [class_Rings_Olinordered__semidom(_1308369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308369), c_Groups_Ozero__class_Ozero(_1308369)), _1308371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308369), _1308371), c_Groups_Oone__class_Oone(_1308369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308369), hAPP(hAPP(c_Power_Opower__class_Opower(_1308369), _1308371), hAPP(c_Nat_OSuc, _1308373))), c_Groups_Oone__class_Oone(_1308369))))], (39757 ^ _779999) ^ [_1550033, _1550035, _1550037, _1550039, _1550041, _1550043] : [c_Finite__Set_Ofolding(_1550033, _1550035, _1550037, _1550039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550033), _1550041)), -(hBOOL(hAPP(hAPP(c_member(_1550033), _1550043), _1550041))), -(hAPP(_1550039, hAPP(hAPP(c_Set_Oinsert(_1550033), _1550043), _1550041)) = hAPP(c_Fun_Ocomp(_1550035, _1550035, _1550035, hAPP(_1550039, _1550041)), hAPP(_1550037, _1550043)))], (25414 ^ _779999) ^ [_1256984, _1256986, _1256988] : [class_Lattices_Oboolean__algebra(_1256984), 25417 ^ _779999 : [(25424 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256984), _1256988), _1256986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256984), hAPP(c_Groups_Ouminus__class_Ouminus(_1256984), _1256986)), hAPP(c_Groups_Ouminus__class_Ouminus(_1256984), _1256988))))], (25418 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256984), hAPP(c_Groups_Ouminus__class_Ouminus(_1256984), _1256986)), hAPP(c_Groups_Ouminus__class_Ouminus(_1256984), _1256988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256984), _1256988), _1256986)))]]], (46828 ^ _779999) ^ [_1719425, _1719427, _1719429, _1719431] : [-(hBOOL(hAPP(c_List_Olistsp(_1719425, _1719427), hAPP(hAPP(c_List_Olist_OCons(_1719425), _1719429), _1719431)))), hBOOL(hAPP(_1719427, _1719429)), hBOOL(hAPP(c_List_Olistsp(_1719425, _1719427), _1719431))], (43973 ^ _779999) ^ [_1656617, _1656619, _1656621, _1656623, _1656625, _1656627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656617, _1656619)), hAPP(hAPP(c_Product__Type_OPair(_1656617, _1656619), _1656621), _1656623)), hAPP(c_List_Oset(tc_prod(_1656617, _1656619)), hAPP(hAPP(c_List_Ozip(_1656617, _1656619), _1656625), _1656627)))), -(hBOOL(hAPP(hAPP(c_member(_1656617), _1656621), hAPP(c_List_Oset(_1656617), _1656625))))], (51176 ^ _779999) ^ [_1815066, _1815068] : [-(c_Equiv__Relations_Opart__equivp(_1815066, _1815068)), 51179 ^ _779999 : [(51180 ^ _779999) ^ [_1815143] : [hBOOL(hAPP(hAPP(_1815068, _1815143), _1815143))]], c_Predicate_Osymp(_1815066, _1815068), c_Predicate_Otransp(_1815066, _1815068)], (39679 ^ _779999) ^ [_1548246, _1548248, _1548250, _1548252, _1548254, _1548256] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1548246, _1548248), _1548248, tc_prod(_1548250, _1548252), c_Product__Type_Osnd(_1548246, _1548248)), c_Product__Type_Omap__pair(_1548250, _1548246, _1548252, _1548248, _1548254, _1548256)) = hAPP(c_Fun_Ocomp(_1548252, _1548248, tc_prod(_1548250, _1548252), _1548256), c_Product__Type_Osnd(_1548250, _1548252)))], (43523 ^ _779999) ^ [_1643845] : [-(c_List_Olists(_1643845, c_Orderings_Otop__class_Otop(tc_fun(_1643845, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1643845), tc_HOL_Obool)))], (36477 ^ _779999) ^ [_1466982, _1466984, _1466986, _1466988, _1466990] : [hAPP(c_Product__Type_Ofst(_1466982, _1466984), hAPP(hAPP(c_Product__Type_OPair(_1466982, _1466984), _1466986), _1466988)) = _1466990, -(_1466986 = _1466990)], (16415 ^ _779999) ^ [_1076522, _1076524, _1076526, _1076528] : [class_Rings_Olinordered__ring__strict(_1076522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076522), _1076524), c_Groups_Ozero__class_Ozero(_1076522))), 16422 ^ _779999 : [(16429 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076522), _1076528), _1076526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076522), _1076524), _1076526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076522), _1076524), _1076528))))], (16423 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076522), _1076524), _1076526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076522), _1076524), _1076528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076522), _1076528), _1076526)))]]], (2720 ^ _779999) ^ [_820299, _820301] : [_820301 = _820299, -(c_Int_Oint__ge__less__than2(_820301) = c_Int_Oint__ge__less__than2(_820299))], (46880 ^ _779999) ^ [_1720542, _1720544, _1720546] : [hBOOL(hAPP(c_List_Olistsp(_1720542, hAPP(hAPP(c_COMBC(_1720542, tc_fun(_1720542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1720542)), _1720544)), _1720546)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1720542)), _1720546), c_List_Olists(_1720542, _1720544))))], (40543 ^ _779999) ^ [_1569545, _1569547, _1569549, _1569551] : [c_Wellfounded_Owf(_1569545, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1569545, _1569545)), hAPP(hAPP(c_Product__Type_OPair(_1569545, _1569545), _1569547), _1569549)), _1569551)), 40546 ^ _779999 : [(40549 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569545, _1569545)), hAPP(hAPP(c_Product__Type_OPair(_1569545, _1569545), _1569549), _1569547)), c_Transitive__Closure_Ortrancl(_1569545, _1569551)))], (40547 ^ _779999) ^ [] : [-(c_Wellfounded_Owf(_1569545, _1569551))]]], (51511 ^ _779999) ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426] : [class_Groups_Ocomm__monoid__mult(_1822416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1822418), _1822420)), 51521 ^ _779999 : [(51524 ^ _779999) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1822422), hAPP(_1822424, 51520 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426])))], (51522 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822418), 51520 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426]), _1822420)))]], 51528 ^ _779999 : [(51532 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822418), 51530 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426]), _1822420)))], (51534 ^ _779999) ^ [] : [51527 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426] = 51530 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426]], (51536 ^ _779999) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1822422, tc_HOL_Obool)), hAPP(_1822424, 51527 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426])), hAPP(_1822424, 51530 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426])) = c_Orderings_Obot__class_Obot(tc_fun(_1822422, tc_HOL_Obool))], (51529 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822418), 51527 ^ [_1822416, _1822418, _1822420, _1822422, _1822424, _1822426]), _1822420)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1822416, _1822422, c_Groups_Otimes__class_Otimes(_1822416)), _1822426), c_Groups_Oone__class_Oone(_1822416)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1822418, tc_fun(_1822422, tc_HOL_Obool)), _1822420), _1822424)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1822416, _1822418, c_Groups_Otimes__class_Otimes(_1822416)), hAPP(hAPP(c_COMBB(tc_fun(_1822422, tc_HOL_Obool), _1822416, _1822418), hAPP(hAPP(c_Finite__Set_Ofold__image(_1822416, _1822422, c_Groups_Otimes__class_Otimes(_1822416)), _1822426), c_Groups_Oone__class_Oone(_1822416))), _1822424)), c_Groups_Oone__class_Oone(_1822416)), _1822420))], (7312 ^ _779999) ^ [_901212, _901214, _901216, _901218] : [_901218 = c_Orderings_Obot__class_Obot(tc_fun(_901214, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_901212, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_901214, _901212, _901216), _901218))], (6637 ^ _779999) ^ [_888047, _888049, _888051] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _888047)), _888049), _888051)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888047))), _888049), _888051)))], (9062 ^ _779999) ^ [_934956, _934958, _934960, _934962] : [class_Orderings_Oorder(_934956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934956), _934958), _934960)), _934958 = _934962, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934956), _934962), _934960)))], (25472 ^ _779999) ^ [_1258012, _1258014, _1258016] : [class_Groups_Oordered__ab__group__add(_1258012), 25475 ^ _779999 : [(25482 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258012), _1258016), _1258014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258012), hAPP(c_Groups_Ouminus__class_Ouminus(_1258012), _1258014)), hAPP(c_Groups_Ouminus__class_Ouminus(_1258012), _1258016))))], (25476 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258012), hAPP(c_Groups_Ouminus__class_Ouminus(_1258012), _1258014)), hAPP(c_Groups_Ouminus__class_Ouminus(_1258012), _1258016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258012), _1258016), _1258014)))]]], (33155 ^ _779999) ^ [_1401107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401107), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401107)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51768 ^ _779999) ^ [_1827993, _1827995] : [class_Complete__Lattice_Ocomplete__lattice(_1827993), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1827995, _1827993)))], (42323 ^ _779999) ^ [_1612488, _1612490, _1612492, _1612494] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612488, tc_fun(_1612490, tc_HOL_Obool)), _1612492), _1612494) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1612490, tc_HOL_Obool), hAPP(c_Set_Oimage(_1612488, tc_fun(_1612490, tc_HOL_Obool), _1612494), _1612492)))], (38343 ^ _779999) ^ [_1513415, _1513417] : [-(hAPP(c_Relation_ODomain(_1513415, _1513417), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513415, _1513417), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1513415, tc_HOL_Obool)))], (47520 ^ _779999) ^ [_1735752, _1735754, _1735756, _1735758, _1735760] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735752)), hAPP(c_List_Ofilter(_1735752, _1735754), hAPP(hAPP(c_List_Omap(_1735756, _1735752), _1735758), _1735760))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735756)), hAPP(c_List_Ofilter(_1735756, hAPP(c_Fun_Ocomp(_1735752, tc_HOL_Obool, _1735756, _1735754), _1735758)), _1735760)))], (45943 ^ _779999) ^ [_1700563, _1700565, _1700567, _1700569, _1700571] : [class_Orderings_Olinorder(_1700563), 45946 ^ _779999 : [(45955 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1700565), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700565, _1700563, _1700567), _1700569), _1700571)))), -(hBOOL(hAPP(hAPP(c_member(_1700565), _1700569), hAPP(c_List_Oset(_1700565), _1700571)))), hBOOL(hAPP(c_List_Odistinct(_1700565), _1700571))], (45947 ^ _779999) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1700565), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700565, _1700563, _1700567), _1700569), _1700571))), 45950 ^ _779999 : [(45953 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1700565), _1700571)))], (45951 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1700565), _1700569), hAPP(c_List_Oset(_1700565), _1700571)))]]]]], (50137 ^ _779999) ^ [_1791974, _1791976, _1791978, _1791980, _1791982] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1791974, _1791976, _1791978) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1791974, _1791980, _1791982), 50140 ^ _779999 : [(50143 ^ _779999) ^ [] : [-(_1791978 = _1791982)], (50141 ^ _779999) ^ [] : [-(_1791976 = _1791980)]]], (38730 ^ _779999) ^ [_1525953, _1525955] : [-(hAPP(c_Set_Ovimage(_1525953, _1525953, c_Fun_Oid(_1525953)), _1525955) = _1525955)], (30126 ^ _779999) ^ [_1344598, _1344600, _1344602, _1344604] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1344598), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344600, tc_Int_Oint), _1344602), _1344604)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344600, _1344598), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1344598, _1344600), c_Int_Oring__1__class_Oof__int(_1344598)), _1344602)), _1344604)), class_Groups_Ocomm__monoid__mult(_1344598), class_Rings_Oring__1(_1344598)], (3634 ^ _779999) ^ [_834476, _834478, _834480, _834482, _834484, _834486] : [-(c_Finite__Set_Ofold(_834486, _834482, _834478) = c_Finite__Set_Ofold(_834484, _834480, _834476)), _834486 = _834484, _834482 = _834480, _834478 = _834476], (5120 ^ _779999) ^ [_858307, _858309] : [_858309 = _858307, -(c_Random__Sequence_Osingle(_858309) = c_Random__Sequence_Osingle(_858307))], (14630 ^ _779999) ^ [_1042201, _1042203, _1042205, _1042207, _1042209] : [class_Groups_Ocomm__monoid__add(_1042201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042203), _1042205)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042203), _1042207)), 14644 ^ _779999 : [(14647 ^ _779999) ^ [] : [hAPP(_1042209, 14643 ^ [_1042201, _1042203, _1042205, _1042207, _1042209]) = c_Groups_Ozero__class_Ozero(_1042201)], (14645 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042203), 14643 ^ [_1042201, _1042203, _1042205, _1042207, _1042209]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1042203, tc_HOL_Obool)), _1042205), _1042207))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042203, _1042201), _1042209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042203, tc_HOL_Obool)), _1042205), _1042207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042201), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042203, _1042201), _1042209), _1042205)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042203, _1042201), _1042209), _1042207)))], (45540 ^ _779999) ^ [_1692094, _1692096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692094)), _1692096)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1692094), _1692096) = _1692096)], (20518 ^ _779999) ^ [_1153024, _1153026] : [c_Nat__Transfer_Onat__set(_1153024), c_Nat__Transfer_Onat__set(_1153026), 20525 ^ _779999 : [(20532 ^ _779999) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153024) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153026), -(_1153024 = _1153026)], (20526 ^ _779999) ^ [] : [_1153024 = _1153026, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153024) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153026))]]], (1784 ^ _779999) ^ [_805407, _805409] : [-(class_Rings_Ocomm__semiring(_805407)), _805409 = _805407, class_Rings_Ocomm__semiring(_805409)], (27546 ^ _779999) ^ [_1298054, _1298056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298054), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1298054), _1298056)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1298054))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1298056))))], (22809 ^ _779999) ^ [_1203257, _1203259, _1203261, _1203263] : [22811 ^ _779999 : [(22814 ^ _779999) ^ [] : [hAPP(_1203263, 22810 ^ [_1203257, _1203259, _1203261, _1203263]) = c_Orderings_Obot__class_Obot(tc_fun(_1203259, tc_HOL_Obool))], (22812 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1203257), 22810 ^ [_1203257, _1203259, _1203261, _1203263]), _1203261)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1203257, tc_fun(_1203259, tc_HOL_Obool)), _1203261), _1203263) = c_Orderings_Obot__class_Obot(tc_fun(_1203259, tc_HOL_Obool)))], (26422 ^ _779999) ^ [_1275006, _1275008, _1275010] : [class_Lattices_Oboolean__algebra(_1275006), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275006), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1275006), _1275008), _1275010)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275006), hAPP(c_Groups_Ouminus__class_Ouminus(_1275006), _1275008)), hAPP(c_Groups_Ouminus__class_Ouminus(_1275006), _1275010)))], (51049 ^ _779999) ^ [_1813125, _1813127] : [c_Relation_Osym(_1813125, _1813127), -(c_Relation_Osym(tc_List_Olist(_1813125), c_List_Olistrel(_1813125, _1813127)))], (21970 ^ _779999) ^ [_1183488, _1183490, _1183492, _1183494] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1183488), hAPP(c_Set_OCollect(_1183488), _1183490))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1183492), hAPP(c_Set_OCollect(_1183492), hAPP(hAPP(c_COMBB(tc_fun(_1183488, tc_HOL_Obool), tc_HOL_Obool, _1183492), c_HOL_OEx(_1183488)), hAPP(hAPP(c_COMBC(_1183492, tc_fun(_1183488, tc_HOL_Obool), tc_fun(_1183488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183488, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1183488, tc_HOL_Obool), tc_fun(_1183488, tc_HOL_Obool)), _1183492), c_COMBS(_1183488, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183488, tc_HOL_Obool), tc_fun(_1183488, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1183492), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1183488), c_fconj)), hAPP(hAPP(c_COMBC(_1183492, tc_fun(_1183488, _1183492), tc_fun(_1183488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183492, tc_HOL_Obool), tc_fun(tc_fun(_1183488, _1183492), tc_fun(_1183488, tc_HOL_Obool)), _1183492), c_COMBB(_1183492, tc_HOL_Obool, _1183488)), c_fequal)), _1183494)))), _1183490))))))], (600 ^ _779999) ^ [_789279, _789281] : [-(class_Rings_Oinverse(_789279)), _789281 = _789279, class_Rings_Oinverse(_789281)], (48384 ^ _779999) ^ [_1753624, _1753626] : [-(hAPP(c_List_Orev(_1753624), c_List_Oconcat(_1753624, _1753626)) = c_List_Oconcat(_1753624, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753624), tc_List_Olist(_1753624)), c_List_Orev(_1753624)), hAPP(c_List_Orev(tc_List_Olist(_1753624)), _1753626))))], (5572 ^ _779999) ^ [_865319, _865321, _865323, _865325, _865327, _865329] : [-(c_Set_Ovimage(_865329, _865325, _865321) = c_Set_Ovimage(_865327, _865323, _865319)), _865329 = _865327, _865325 = _865323, _865321 = _865319], (11022 ^ _779999) ^ [_970569, _970571, _970573] : [class_Lattices_Olattice(_970569), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970569), _970571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970569), _970571), _970573)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_970569), _970571), _970573))], (52030 ^ _779999) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (2918 ^ _779999) ^ [_823408, _823410, _823412, _823414, _823416, _823418] : [-(c_Com_Ocom_OCond(_823418, _823414, _823410) = c_Com_Ocom_OCond(_823416, _823412, _823408)), _823418 = _823416, _823414 = _823412, _823410 = _823408], (10747 ^ _779999) ^ [_965205, _965207, _965209, _965211, _965213] : [class_Rings_Oring(_965205), hBOOL(hAPP(c_Finite__Set_Ofinite(_965207), _965209)), hBOOL(hAPP(hAPP(c_member(_965207), _965211), _965209)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965207, _965205), _965213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965207, tc_HOL_Obool)), _965209), hAPP(hAPP(c_Set_Oinsert(_965207), _965211), c_Orderings_Obot__class_Obot(tc_fun(_965207, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965205), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965207, _965205), _965213), _965209)), hAPP(_965213, _965211)))], (11390 ^ _779999) ^ [_977895, _977897, _977899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977895, tc_HOL_Obool)), _977897), _977899)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977895, tc_HOL_Obool)), _977897), _977899) = _977897)], (8352 ^ _779999) ^ [_922356, _922358, _922360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922356, tc_HOL_Obool)), _922358), _922360)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922356, tc_HOL_Obool)), _922358), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922356, tc_HOL_Obool)), _922360), _922358)) = _922360)], (37152 ^ _779999) ^ [] : [-(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))], (5688 ^ _779999) ^ [_867037, _867039] : [_867039 = _867037, -(c_Option_Othe(_867039) = c_Option_Othe(_867037))], (49218 ^ _779999) ^ [_1772311, _1772313, _1772315, _1772317, _1772319] : [-(hAPP(hAPP(c_List_Olist_OCons(_1772311), _1772313), _1772315) = hAPP(c_List_Ofilter(_1772311, _1772317), _1772319)), 49219 ^ _779999 : [(49220 ^ _779999) ^ [_1772439, _1772441] : [_1772319 = hAPP(hAPP(c_List_Oappend(_1772311), _1772441), hAPP(hAPP(c_List_Olist_OCons(_1772311), _1772313), _1772439)), 49226 ^ _779999 : [(49229 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1772317, 49225 ^ [_1772311, _1772313, _1772315, _1772317, _1772319, _1772439, _1772441])))], (49227 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772311), 49225 ^ [_1772311, _1772313, _1772315, _1772317, _1772319, _1772439, _1772441]), hAPP(c_List_Oset(_1772311), _1772441))))]], hBOOL(hAPP(_1772317, _1772313)), _1772315 = hAPP(c_List_Ofilter(_1772311, _1772317), _1772439)]]], (47627 ^ _779999) ^ [_1739305, _1739307] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1739305, _1739307)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1739305), _1739307))], (40399 ^ _779999) ^ [_1566295] : [-(c_Transitive__Closure_Ortrancl(_1566295, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1566295, _1566295), tc_HOL_Obool))) = c_Relation_OId(_1566295))], (8518 ^ _779999) ^ [_925710, _925712, _925714, _925716, _925718] : [class_Groups_Oordered__ab__group__add(_925710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925710), _925712), _925714) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_925710), _925716), _925718), 8525 ^ _779999 : [(8532 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925710), _925716), _925718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925710), _925712), _925714)))], (8526 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925710), _925712), _925714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925710), _925716), _925718)))]]], (21149 ^ _779999) ^ [_1164471, _1164473, _1164475, _1164477, _1164479] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1164471, _1164473, hAPP(hAPP(c_Set_Oinsert(_1164471), _1164475), _1164477)), _1164479)), 21154 ^ _779999 : [(21159 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1164471), 21152 ^ [_1164471, _1164473, _1164475, _1164477, _1164479]), 21153 ^ [_1164471, _1164473, _1164475, _1164477, _1164479]))], (21157 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1164471, _1164471, _1164473, 21152 ^ [_1164471, _1164473, _1164475, _1164477, _1164479], 21153 ^ [_1164471, _1164473, _1164475, _1164477, _1164479]), _1164479)))], (21155 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1164471), _1164475), _1164477) = hAPP(hAPP(c_Set_Oinsert(_1164471), 21152 ^ [_1164471, _1164473, _1164475, _1164477, _1164479]), 21153 ^ [_1164471, _1164473, _1164475, _1164477, _1164479]))]]], (15357 ^ _779999) ^ [_1056079, _1056081, _1056083, _1056085] : [class_Rings_Ocomm__semiring__1(_1056079), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056079), _1056081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056079), _1056083), _1056085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056079), _1056083), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056079), _1056081), _1056085)))], (8179 ^ _779999) ^ [_918552, _918554, _918556, _918558, _918560] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_918552, _918554), _918556, _918558, _918560), 8183 ^ _779999 : [(8186 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_918554, 8182 ^ [_918552, _918554, _918556, _918558, _918560], _918558, _918560))], (8184 ^ _779999) ^ [] : [-(c_Natural_Oevaln(_918552, _918556, _918558, 8182 ^ [_918552, _918554, _918556, _918558, _918560]))]]], (24408 ^ _779999) ^ [_1237157, _1237159, _1237161, _1237163] : [class_Orderings_Olinorder(_1237157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237157), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237157), _1237159), _1237161)), _1237163)), 24415 ^ _779999 : [(24418 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237157), _1237161), _1237163)))], (24416 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237157), _1237159), _1237163)))]]], (18387 ^ _779999) ^ [_1114827, _1114829, _1114831] : [class_Orderings_Oorder(_1114827), 18390 ^ _779999 : [(18397 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114827), _1114829), _1114831))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1114827, _1114829, _1114831) = c_Orderings_Obot__class_Obot(tc_fun(_1114827, tc_HOL_Obool)))], (18391 ^ _779999) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1114827, _1114829, _1114831) = c_Orderings_Obot__class_Obot(tc_fun(_1114827, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114827), _1114829), _1114831))]]], (47613 ^ _779999) ^ [_1738766, _1738768, _1738770] : [class_Groups_Omonoid__add(_1738766), -(hAPP(c_List_Ofoldl(_1738766, _1738766, c_Groups_Oplus__class_Oplus(_1738766), _1738768), _1738770) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1738766), _1738768), c_List_Ofoldr(_1738766, _1738766, c_Groups_Oplus__class_Oplus(_1738766), _1738770, c_Groups_Ozero__class_Ozero(_1738766))))], (33049 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (49015 ^ _779999) ^ [_1766796, _1766798, _1766800, _1766802, _1766804] : [c_Fun_Oinj__on(_1766796, _1766798, _1766800, c_Orderings_Otop__class_Otop(tc_fun(_1766796, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1766796, _1766798), _1766800), hAPP(c_List_OremoveAll(_1766796, _1766802), _1766804)) = hAPP(c_List_OremoveAll(_1766798, hAPP(_1766800, _1766802)), hAPP(hAPP(c_List_Omap(_1766796, _1766798), _1766800), _1766804)))], (42319 ^ _779999) ^ [_1612308, _1612310, _1612312, _1612314] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612308, tc_fun(_1612310, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1612308, tc_HOL_Obool), _1612312)), _1612314) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1612308, tc_HOL_Obool), tc_fun(_1612310, tc_HOL_Obool)), _1612312), hAPP(hAPP(c_COMBC(tc_fun(_1612308, tc_HOL_Obool), tc_fun(_1612308, tc_fun(_1612310, tc_HOL_Obool)), tc_fun(_1612310, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612308, tc_fun(_1612310, tc_HOL_Obool))), _1612314)))], (33195 ^ _779999) ^ [_1401703] : [class_Int_Onumber__ring(_1401703), -(hAPP(c_Int_Onumber__class_Onumber__of(_1401703), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1401703))], (36406 ^ _779999) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36374 ^ _779999) ^ [_1464952, _1464954] : [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), _1464952), _1464954))), 36377 ^ _779999 : [(36384 ^ _779999) ^ [] : [-(_1464954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1464952, _1464954) = c_Nitpick_Onat__gcd(_1464954, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1464952, _1464954)))], (36378 ^ _779999) ^ [] : [_1464954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1464952, _1464954) = _1464952)]]], (29200 ^ _779999) ^ [_1328452, _1328454, _1328456, _1328458] : [class_Fields_Olinordered__field(_1328452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328452), _1328454), _1328456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328452), c_Groups_Ozero__class_Ozero(_1328452)), _1328458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328452), c_Groups_Ozero__class_Ozero(_1328452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328452), _1328456), _1328454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328452), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328452), _1328458), _1328456)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328452), _1328458), _1328454))))], (44438 ^ _779999) ^ [_1667203, _1667205, _1667207, _1667209] : [-(hBOOL(hAPP(hAPP(c_member(_1667203), _1667205), hAPP(c_List_Oset(_1667203), _1667207)))), hBOOL(hAPP(hAPP(c_member(_1667203), _1667205), hAPP(c_List_Oset(_1667203), c_List_Oremove1(_1667203, _1667209, _1667207))))], (4392 ^ _779999) ^ [_846747, _846749, _846751, _846753] : [-(c_New__DSequence_Oneg__single(_846753, _846749) = c_New__DSequence_Oneg__single(_846751, _846747)), _846753 = _846751, _846749 = _846747], (38900 ^ _779999) ^ [_1530198, _1530200, _1530202, _1530204, _1530206, _1530208, _1530210, _1530212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530198, _1530200)), _1530202), hAPP(c_Set_Oimage(tc_prod(_1530204, _1530206), tc_prod(_1530198, _1530200), c_Product__Type_Omap__pair(_1530204, _1530198, _1530206, _1530200, _1530208, _1530210)), _1530212))), 38905 ^ _779999 : [(38908 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530204, _1530206)), hAPP(hAPP(c_Product__Type_OPair(_1530204, _1530206), 38903 ^ [_1530198, _1530200, _1530202, _1530204, _1530206, _1530208, _1530210, _1530212]), 38904 ^ [_1530198, _1530200, _1530202, _1530204, _1530206, _1530208, _1530210, _1530212])), _1530212)))], (38906 ^ _779999) ^ [] : [-(_1530202 = hAPP(hAPP(c_Product__Type_OPair(_1530198, _1530200), hAPP(_1530208, 38903 ^ [_1530198, _1530200, _1530202, _1530204, _1530206, _1530208, _1530210, _1530212])), hAPP(_1530210, 38904 ^ [_1530198, _1530200, _1530202, _1530204, _1530206, _1530208, _1530210, _1530212])))]]], (10461 ^ _779999) ^ [_960058, _960060, _960062, _960064, _960066] : [c_Fun_Oinj__on(_960058, _960060, _960062, _960064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960058, tc_HOL_Obool)), _960066), _960064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960060, tc_HOL_Obool)), hAPP(c_Set_Oimage(_960058, _960060, _960062), _960066)), hAPP(c_Set_Oimage(_960058, _960060, _960062), _960064))))], (46846 ^ _779999) ^ [_1719774, _1719776, _1719778, _1719780] : [-(hBOOL(hAPP(c_List_Olistsp(_1719774, _1719776), hAPP(hAPP(c_List_Oappend(_1719774), _1719778), _1719780)))), hBOOL(hAPP(c_List_Olistsp(_1719774, _1719776), _1719778)), hBOOL(hAPP(c_List_Olistsp(_1719774, _1719776), _1719780))], (43279 ^ _779999) ^ [_1636143, _1636145, _1636147, _1636149] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1636143), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1636145), _1636147)))), -(hAPP(c_Random_Opick(_1636145, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1636145)), _1636147), _1636149)), _1636143) = hAPP(c_Random_Opick(_1636145, _1636149), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1636143), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1636145), _1636147))))], (11422 ^ _779999) ^ [_978601, _978603, _978605, _978607] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978601, tc_HOL_Obool)), _978603), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978601, tc_HOL_Obool)), _978605), _978607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978601, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978601, tc_HOL_Obool)), _978603), _978605)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978601, tc_HOL_Obool)), _978603), _978607)))], (36465 ^ _779999) ^ [_1466751, _1466753, _1466755, _1466757] : [-(_1466751 = _1466753), hAPP(c_Product__Type_Ofst(_1466755, _1466757), _1466751) = hAPP(c_Product__Type_Ofst(_1466755, _1466757), _1466753), hAPP(c_Product__Type_Osnd(_1466755, _1466757), _1466751) = hAPP(c_Product__Type_Osnd(_1466755, _1466757), _1466753)], (50301 ^ _779999) ^ [_1795628, _1795630, _1795632] : [-(c_FunDef_OTHE__default(_1795630, _1795632, _1795628) = _1795632), 50303 ^ _779999 : [(50306 ^ _779999) ^ [_1795750] : [hBOOL(hAPP(_1795628, _1795750)), -(_1795750 = 50302 ^ [_1795628, _1795630, _1795632])], (50304 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1795628, 50302 ^ [_1795628, _1795630, _1795632])))]]], (6824 ^ _779999) ^ [_891848, _891850] : [6825 ^ _779999 : [(6826 ^ _779999) ^ [_891901] : [hBOOL(hAPP(hAPP(c_member(_891848), _891901), _891850))]], _891850 = c_Orderings_Obot__class_Obot(tc_fun(_891848, tc_HOL_Obool))], (31586 ^ _779999) ^ [_1372062, _1372064, _1372066] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372062), hAPP(hAPP(c_Set_Oinsert(_1372062), _1372064), c_Orderings_Obot__class_Obot(tc_fun(_1372062, tc_HOL_Obool)))), _1372066) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1372062, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1372062, _1372062, _1372066), hAPP(hAPP(c_Set_Oinsert(_1372062), _1372064), c_Orderings_Obot__class_Obot(tc_fun(_1372062, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1372062, tc_HOL_Obool), tc_HOL_Obool))))], (51932 ^ _779999) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (22743 ^ _779999) ^ [_1201874, _1201876, _1201878, _1201880, _1201882] : [class_Complete__Lattice_Ocomplete__lattice(_1201874), class_Orderings_Olinorder(_1201874), 22750 ^ _779999 : [(22760 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201874), _1201876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201878, _1201874), _1201880), _1201882)))), 22761 ^ _779999 : [(22762 ^ _779999) ^ [_1202222] : [hBOOL(hAPP(hAPP(c_member(_1201878), _1202222), _1201880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201874), _1201876), hAPP(_1201882, _1202222)))]]], (22751 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201874), _1201876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1201878, _1201874), _1201880), _1201882))), 22755 ^ _779999 : [(22758 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201874), _1201876), hAPP(_1201882, 22754 ^ [_1201874, _1201876, _1201878, _1201880, _1201882]))))], (22756 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201878), 22754 ^ [_1201874, _1201876, _1201878, _1201880, _1201882]), _1201880)))]]]]], (10515 ^ _779999) ^ [_960971] : [10516 ^ _779999 : [(10517 ^ _779999) ^ [_961013] : [_960971 = hAPP(c_Nat_OSuc, _961013)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960971)))], (51283 ^ _779999) ^ [_1816999, _1817001] : [c_Equiv__Relations_Opart__equivp(_1816999, _1817001), 51287 ^ _779999 : [(51292 ^ _779999) ^ [] : [-(c_Predicate_Otransp(_1816999, _1817001))], (51290 ^ _779999) ^ [] : [-(c_Predicate_Osymp(_1816999, _1817001))], (51288 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1817001, 51286 ^ [_1816999, _1817001]), 51286 ^ [_1816999, _1817001])))]]], (44730 ^ _779999) ^ [_1672638, _1672640, _1672642] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1672638))), -(c_List_Osublist(_1672640, hAPP(hAPP(c_List_Olist_OCons(_1672640), _1672642), c_List_Olist_ONil(_1672640)), _1672638) = c_List_Olist_ONil(_1672640))], (25010 ^ _779999) ^ [_1249432, _1249434, _1249436] : [class_Orderings_Olinorder(_1249432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249432), _1249434)), -(_1249434 = c_Orderings_Obot__class_Obot(tc_fun(_1249432, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1249432, c_Orderings_Oord__class_Omax(_1249432), hAPP(hAPP(c_Set_Oinsert(_1249432), _1249436), _1249434)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1249432), _1249436), c_Big__Operators_Olattice_OSup__fin(_1249432, c_Orderings_Oord__class_Omax(_1249432), _1249434)))], (19501 ^ _779999) ^ [_1135499] : [-(hBOOL(hAPP(_1135499, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19508 ^ [_1135499])))), 19502 ^ _779999 : [(19503 ^ _779999) ^ [_1135551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135551)), hBOOL(hAPP(_1135499, _1135551))]]], (33979 ^ _779999) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (7475 ^ _779999) ^ [_904664, _904666] : [class_Orderings_Oorder(_904664), 7478 ^ _779999 : [(7485 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904664), hAPP(_904666, 7486 ^ [_904664, _904666])), hAPP(_904666, hAPP(c_Nat_OSuc, 7486 ^ [_904664, _904666])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _904664, _904666))], (7479 ^ _779999) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _904664, _904666), 7482 ^ _779999 : [(7483 ^ _779999) ^ [_904798] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904664), hAPP(_904666, _904798)), hAPP(_904666, hAPP(c_Nat_OSuc, _904798)))))]]]]], (18287 ^ _779999) ^ [_1112815, _1112817, _1112819] : [class_Orderings_Oorder(_1112815), 18290 ^ _779999 : [(18297 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112815), _1112817), _1112819))), -(c_Orderings_Obot__class_Obot(tc_fun(_1112815, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1112815, _1112817), _1112819))], (18291 ^ _779999) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1112815, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1112815, _1112817), _1112819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112815), _1112817), _1112819))]]], (25668 ^ _779999) ^ [_1261247, _1261249, _1261251] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261247, tc_HOL_Obool)), _1261249) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1261247, tc_HOL_Obool)), _1261251), -(_1261249 = _1261251)], (43928 ^ _779999) ^ [_1655327, _1655329, _1655331, _1655333] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1655327, _1655329))), hAPP(hAPP(c_List_Ozip(_1655327, _1655329), _1655331), _1655333)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655327)), _1655331)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655329)), _1655333)))], (22040 ^ _779999) ^ [_1186643, _1186645, _1186647] : [class_Groups_Olinordered__ab__semigroup__add(_1186643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1186643), _1186645)), -(_1186645 = c_Orderings_Obot__class_Obot(tc_fun(_1186643, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186643), _1186647), c_Big__Operators_Olinorder__class_OMin(_1186643, _1186645)) = c_Big__Operators_Olinorder__class_OMin(_1186643, hAPP(c_Set_OCollect(_1186643), hAPP(hAPP(c_COMBB(tc_fun(_1186643, tc_HOL_Obool), tc_HOL_Obool, _1186643), c_HOL_OEx(_1186643)), hAPP(hAPP(c_COMBC(_1186643, tc_fun(_1186643, tc_HOL_Obool), tc_fun(_1186643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1186643, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1186643, tc_HOL_Obool), tc_fun(_1186643, tc_HOL_Obool)), _1186643), c_COMBS(_1186643, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1186643, tc_HOL_Obool), tc_fun(_1186643, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1186643), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1186643), c_fconj)), hAPP(hAPP(c_COMBC(_1186643, tc_fun(_1186643, _1186643), tc_fun(_1186643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1186643, tc_HOL_Obool), tc_fun(tc_fun(_1186643, _1186643), tc_fun(_1186643, tc_HOL_Obool)), _1186643), c_COMBB(_1186643, tc_HOL_Obool, _1186643)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1186643), _1186647))))), hAPP(hAPP(c_COMBC(_1186643, tc_fun(_1186643, tc_HOL_Obool), tc_HOL_Obool), c_member(_1186643)), _1186645))))))], (15875 ^ _779999) ^ [_1066292, _1066294] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066292), _1066294) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15878 ^ _779999 : [(15881 ^ _779999) ^ [] : [-(_1066294 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15879 ^ _779999) ^ [] : [-(_1066292 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10347 ^ _779999) ^ [_957975, _957977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957975), _957977))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957975), _957977)), -(_957975 = _957977)], (38858 ^ _779999) ^ [_1529128, _1529130, _1529132, _1529134, _1529136, _1529138, _1529140] : [-(hAPP(c_Product__Type_Ofst(_1529128, _1529130), hAPP(c_Product__Type_Omap__pair(_1529132, _1529128, _1529134, _1529130, _1529136, _1529138), _1529140)) = hAPP(_1529136, hAPP(c_Product__Type_Ofst(_1529132, _1529134), _1529140)))], (8230 ^ _779999) ^ [_919674, _919676, _919678, _919680] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_919674, _919676)), _919678), _919680)), 8235 ^ _779999 : [(8238 ^ _779999) ^ [] : [hBOOL(hAPP(_919674, _919678))], (8236 ^ _779999) ^ [] : [-(_919680 = _919678)]], 8239 ^ _779999 : [(8245 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_919674, _919676)), 8241 ^ [_919674, _919676, _919678, _919680]), _919680)))], (8243 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_919676), _919678), 8241 ^ [_919674, _919676, _919678, _919680])))], (8240 ^ _779999) ^ [] : [-(hBOOL(hAPP(_919674, _919678)))]]], (16111 ^ _779999) ^ [_1070870, _1070872, _1070874, _1070876] : [class_Rings_Oordered__semiring(_1070870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070870), _1070872), _1070874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070870), c_Groups_Ozero__class_Ozero(_1070870)), _1070876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070870), _1070876), _1070872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070870), _1070876), _1070874))))], (5831 ^ _779999) ^ [_872200, _872202, _872204, _872206, _872208] : [c_Hoare__Mirabelle_Ohoare__derivs(_872200, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_872200), tc_HOL_Obool)), _872202), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_872200), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), hAPP(hAPP(c_COMBB(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_872200)), _872204)), c_Com_Ocom_OBODY)), _872206)), _872208)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_872200), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), hAPP(hAPP(c_COMBB(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_872200)), _872204)), 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))), _872206)), _872208)), -(c_Hoare__Mirabelle_Ohoare__derivs(_872200, _872202, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_872200), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), hAPP(hAPP(c_COMBB(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_872200, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_872200))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_872200)), _872204)), c_Com_Ocom_OBODY)), _872206)), _872208)))], (46646 ^ _779999) ^ [_1715821] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1715821)) = _1715821)], (29570 ^ _779999) ^ [_1334874, _1334876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334876), 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), _1334874), _1334876)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21118 ^ _779999) ^ [_1163841, _1163843] : [class_Orderings_Oorder(_1163841), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1163841, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1163841), _1163843)), hAPP(c_SetInterval_Oord__class_OatLeast(_1163841), _1163843)) = hAPP(hAPP(c_Set_Oinsert(_1163841), _1163843), c_Orderings_Obot__class_Obot(tc_fun(_1163841, tc_HOL_Obool))))], (19107 ^ _779999) ^ [_1128192, _1128194, _1128196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1128192), _1128194)), _1128196) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128192), _1128196)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1128194), _1128196)))], (34647 ^ _779999) ^ [_1427716, _1427718, _1427720] : [class_Int_Onumber__ring(_1427716), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427716), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1427716), _1427718), _1427720)), 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(_1427716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427716), hAPP(hAPP(c_Power_Opower__class_Opower(_1427716), _1427718), 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(_1427716), _1427720), 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(_1427716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427716), hAPP(c_Int_Onumber__class_Onumber__of(_1427716), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1427718)), _1427720)))], (6845 ^ _779999) ^ [_892174, _892176, _892178] : [hBOOL(hAPP(_892178, _892176)), -(hBOOL(hAPP(hAPP(c_member(_892174), _892176), _892178)))], (7332 ^ _779999) ^ [_901622, _901624] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901622, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_901622, tc_HOL_Obool))), _901624) = _901624)], (11318 ^ _779999) ^ [_976327, _976329, _976331, _976333] : [class_Lattices_Odistrib__lattice(_976327), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976327), _976329), _976331)), _976333) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976327), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976327), _976329), _976333)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976327), _976331), _976333)))], (34083 ^ _779999) ^ [_1417435, _1417437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417435), _1417437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1417435)), c_Int_OBit0(_1417437))))], (51902 ^ _779999) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (46698 ^ _779999) ^ [_1716681, _1716683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1716681), _1716683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1716681)), hAPP(c_Code__Numeral_Onat__of, _1716683))))], (51598 ^ _779999) ^ [_1824393, _1824395, _1824397, _1824399, _1824401] : [hBOOL(hAPP(_1824393, hAPP(hAPP(c_Product__Type_OPair(_1824395, _1824397), _1824399), _1824401))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1824395, _1824397, tc_HOL_Obool, _1824393), _1824399), _1824401)))], (48600 ^ _779999) ^ [_1758258, _1758260, _1758262] : [c_List_OtakeWhile(_1758258, _1758260, _1758262) = _1758262, 48603 ^ _779999 : [(48604 ^ _779999) ^ [_1758345] : [hBOOL(hAPP(hAPP(c_member(_1758258), _1758345), hAPP(c_List_Oset(_1758258), _1758262))), -(hBOOL(hAPP(_1758260, _1758345)))]]], (26572 ^ _779999) ^ [_1277852, _1277854, _1277856] : [class_Groups_Olinordered__ab__group__add(_1277852), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1277852), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277852), _1277854), _1277856)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277852), hAPP(c_Groups_Ouminus__class_Ouminus(_1277852), _1277854)), hAPP(c_Groups_Ouminus__class_Ouminus(_1277852), _1277856)))], (32677 ^ _779999) ^ [_1393038, _1393040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393038)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393038), _1393040)))], (43567 ^ _779999) ^ [_1644778, _1644780, _1644782] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644778)), _1644780), c_Wellfounded_Oacc(tc_List_Olist(_1644778), c_List_Olistrel1(_1644778, _1644782)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644778)), _1644780), c_List_Olists(_1644778, c_Wellfounded_Oacc(_1644778, _1644782)))))], (3030 ^ _779999) ^ [_825138, _825140] : [_825140 = _825138, -(c_SetInterval_Oord__class_OgreaterThan(_825140) = c_SetInterval_Oord__class_OgreaterThan(_825138))], (46506 ^ _779999) ^ [_1712938, _1712940] : [hAPP(c_Code__Numeral_Oof__nat, _1712938) = hAPP(c_Code__Numeral_Oof__nat, _1712940), -(_1712938 = _1712940)], (47248 ^ _779999) ^ [_1729003, _1729005] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729003)), c_List_Oremdups(_1729003, c_List_Oconcat(_1729003, _1729005))) = hAPP(c_Finite__Set_Ocard(_1729003), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1729003), tc_fun(_1729003, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1729003)), _1729005)), c_List_Oset(_1729003))))], (35440 ^ _779999) ^ [_1447033, _1447035, _1447037, _1447039] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1447033, _1447035), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1447037), _1447039))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447033), _1447035), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1447039), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447037)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447037)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1447039), 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), _1447035), _1447039))))))], (14491 ^ _779999) ^ [_1039277, _1039279, _1039281, _1039283, _1039285] : [c_Fun_Oinj__on(_1039277, _1039279, _1039281, _1039283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039279, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1039277, _1039279, _1039281), _1039283)), _1039285)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039279), _1039285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1039277), _1039283)), hAPP(c_Finite__Set_Ocard(_1039279), _1039285))))], (32663 ^ _779999) ^ [_1392801, _1392803] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392801))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392801)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1392803)) = 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), _1392803)))], (39445 ^ _779999) ^ [_1542876, _1542878, _1542880, _1542882, _1542884, _1542886, _1542888] : [-(hAPP(c_Product__Type_Oapfst(_1542876, _1542878, _1542880, _1542882), hAPP(c_Product__Type_Oapfst(_1542884, _1542876, _1542880, _1542886), _1542888)) = hAPP(c_Product__Type_Oapfst(_1542884, _1542878, _1542880, hAPP(c_Fun_Ocomp(_1542876, _1542878, _1542884, _1542882), _1542886)), _1542888))], (42045 ^ _779999) ^ [_1605668, _1605670, _1605672, _1605674, _1605676] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605668, tc_HOL_Obool)), _1605670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605672, tc_fun(_1605668, tc_HOL_Obool)), _1605674), _1605676)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605672, tc_fun(_1605668, tc_HOL_Obool)), _1605674), hAPP(hAPP(c_COMBB(tc_fun(_1605668, tc_HOL_Obool), tc_fun(_1605668, tc_HOL_Obool), _1605672), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605668, tc_HOL_Obool)), _1605670)), _1605676)))], (40049 ^ _779999) ^ [_1557278, _1557280, _1557282, _1557284, _1557286] : [c_Com_Ocom_OLocal(_1557278, _1557280, _1557282) = c_Com_Ocom_OWhile(_1557284, _1557286)], (48653 ^ _779999) ^ [_1759305] : [-(c_List_Oreturn__list(_1759305) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1759305))], (10661 ^ _779999) ^ [_963602, _963604, _963606, _963608, _963610, _963612] : [c_Fun_Oinj__on(_963602, _963604, _963606, _963608), -(hBOOL(hAPP(hAPP(c_member(_963604), _963610), hAPP(c_Set_Oimage(_963602, _963604, _963606), _963608)))), -(c_Fun_Oinj__on(_963602, _963604, c_Fun_Ofun__upd(_963602, _963604, _963606, _963612, _963610), _963608))], (52036 ^ _779999) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (17600 ^ _779999) ^ [_1099622, _1099624] : [17602 ^ _779999 : [(17605 ^ _779999) ^ [] : [hBOOL(hAPP(_1099624, 17601 ^ [_1099622, _1099624]))], (17603 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17601 ^ [_1099622, _1099624]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1099622))))]], 17606 ^ _779999 : [(17607 ^ _779999) ^ [_1099777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1099777), _1099622)), -(hBOOL(hAPP(_1099624, _1099777)))]]], (41456 ^ _779999) ^ [_1591274, _1591276, _1591278] : [class_Orderings_Olinorder(_1591274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591274), _1591276)), -(c_Big__Operators_Olinorder__class_OMin(_1591274, hAPP(hAPP(c_Set_Oinsert(_1591274), _1591278), _1591276)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591274, _1591274, c_Orderings_Oord__class_Omin(_1591274)), _1591278), _1591276))], (28300 ^ _779999) ^ [_1311976, _1311978, _1311980, _1311982, _1311984] : [class_Fields_Ofield__inverse__zero(_1311976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311976), _1311978), _1311980)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311976), _1311982), _1311984)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311976), _1311978), _1311982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311976), _1311980), _1311984)))], (8468 ^ _779999) ^ [_924929, _924931, _924933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_924929, tc_HOL_Obool)), _924931), hAPP(hAPP(c_Set_Oinsert(_924929), _924933), c_Orderings_Obot__class_Obot(tc_fun(_924929, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_924929, _924933, _924931) = c_HOL_OThe(_924929, hAPP(hAPP(c_COMBC(_924929, tc_fun(_924929, tc_HOL_Obool), tc_HOL_Obool), c_member(_924929)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924929, tc_HOL_Obool)), _924931), hAPP(hAPP(c_Set_Oinsert(_924929), _924933), c_Orderings_Obot__class_Obot(tc_fun(_924929, tc_HOL_Obool)))))))], (47404 ^ _779999) ^ [_1733214, _1733216, _1733218] : [-(hAPP(c_List_Ofilter(_1733214, _1733216), c_List_Oconcat(_1733214, _1733218)) = c_List_Oconcat(_1733214, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733214), tc_List_Olist(_1733214)), c_List_Ofilter(_1733214, _1733216)), _1733218)))], (34847 ^ _779999) ^ [_1431636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1431636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1431636))))], (2984 ^ _779999) ^ [_824449, _824451, _824453, _824455] : [-(c_Random_Olog(_824455, _824451) = c_Random_Olog(_824453, _824449)), _824455 = _824453, _824451 = _824449], (44556 ^ _779999) ^ [_1669414, _1669416] : [-(c_List_Olistrelp(_1669414, _1669416, c_List_Olist_ONil(_1669414), c_List_Olist_ONil(_1669414)))], (43997 ^ _779999) ^ [_1657253, _1657255, _1657257, _1657259, _1657261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657253), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657255)), _1657257))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657253), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657259)), _1657261))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1657255, _1657259)), hAPP(hAPP(c_List_Ozip(_1657255, _1657259), _1657257), _1657261)), _1657253) = hAPP(hAPP(c_Product__Type_OPair(_1657255, _1657259), hAPP(hAPP(c_List_Onth(_1657255), _1657257), _1657253)), hAPP(hAPP(c_List_Onth(_1657259), _1657261), _1657253)))], (7238 ^ _779999) ^ [_899669, _899671, _899673, _899675, _899677] : [-(hBOOL(hAPP(hAPP(c_member(_899669), _899671), hAPP(c_Set_Oimage(_899673, _899669, _899675), _899677)))), 7239 ^ _779999 : [(7240 ^ _779999) ^ [_899739] : [hBOOL(hAPP(hAPP(c_member(_899673), _899739), _899677)), _899671 = hAPP(_899675, _899739)]]], (13945 ^ _779999) ^ [_1028462, _1028464, _1028466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028464), _1028466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028462), _1028466)), _1028464)))], (8294 ^ _779999) ^ [_920935, _920937, _920939] : [c_Com_Ocom_OWhile(_920935, _920937) = hAPP(c_Com_Ocom_OBODY, _920939)], (6167 ^ _779999) ^ [_878499, _878501] : [class_Lattices_Osemilattice__sup(_878499), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_878499), _878501), _878501) = _878501)], (23605 ^ _779999) ^ [_1220982, _1220984, _1220986] : [class_Orderings_Olinorder(_1220982), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220982), _1220984)), -(_1220984 = c_Orderings_Obot__class_Obot(tc_fun(_1220982, tc_HOL_Obool))), 23616 ^ _779999 : [(23617 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220982), _1220986), hAPP(c_Finite__Set_Ofold1(_1220982, c_Orderings_Oord__class_Omin(_1220982)), _1220984))), 23620 ^ _779999 : [(23621 ^ _779999) ^ [_1221275] : [hBOOL(hAPP(hAPP(c_member(_1220982), _1221275), _1220984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220982), _1220986), _1221275)))]]], (23627 ^ _779999) ^ [] : [23629 ^ _779999 : [(23632 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220982), _1220986), 23628 ^ [_1220982, _1220984, _1220986]))], (23630 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1220982), 23628 ^ [_1220982, _1220984, _1220986]), _1220984)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220982), _1220986), hAPP(c_Finite__Set_Ofold1(_1220982, c_Orderings_Oord__class_Omin(_1220982)), _1220984))))]]], (22545 ^ _779999) ^ [_1197343, _1197345, _1197347] : [class_Orderings_Olinorder(_1197343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197343), _1197345)), hBOOL(hAPP(hAPP(c_member(_1197343), _1197347), _1197345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197343), c_Big__Operators_Olinorder__class_OMin(_1197343, _1197345)), _1197347)))], (42902 ^ _779999) ^ [_1625646, _1625648] : [c_Wellfounded_Owf(_1625646, _1625648), 42905 ^ _779999 : [(42906 ^ _779999) ^ [_1625778] : [42907 ^ _779999 : [(42908 ^ _779999) ^ [_1625883] : [hBOOL(hAPP(hAPP(c_member(_1625646), _1625883), _1625778))]], 42910 ^ _779999 : [(42913 ^ _779999) ^ [_1626005] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625646, _1625646)), hAPP(hAPP(c_Product__Type_OPair(_1625646, _1625646), _1626005), 42909 ^ [_1625646, _1625648, _1625778])), _1625648)), hBOOL(hAPP(hAPP(c_member(_1625646), _1626005), _1625778))], (42911 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625646), 42909 ^ [_1625646, _1625648, _1625778]), _1625778)))]]]]], (34275 ^ _779999) ^ [] : [-(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))))], (14125 ^ _779999) ^ [_1032022, _1032024, _1032026, _1032028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032022), _1032024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1032026), hAPP(c_Set_Oimage(_1032022, _1032026, _1032028), _1032024))), hAPP(c_Finite__Set_Ocard(_1032022), _1032024))))], (50115 ^ _779999) ^ [_1791447, _1791449, _1791451] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1791447), _1791449))), -(hBOOL(hAPP(hAPP(_1791451, _1791447), _1791449))), 50122 ^ _779999 : [(50125 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50120 ^ [_1791447, _1791449, _1791451]), 50121 ^ [_1791447, _1791449, _1791451]))), -(hBOOL(hAPP(hAPP(_1791451, 50120 ^ [_1791447, _1791449, _1791451]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50121 ^ [_1791447, _1791449, _1791451]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50131 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(_1791451, 50120 ^ [_1791447, _1791449, _1791451]), 50121 ^ [_1791447, _1791449, _1791451]))], (50123 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 50120 ^ [_1791447, _1791449, _1791451]), 50121 ^ [_1791447, _1791449, _1791451]))))]]], (26416 ^ _779999) ^ [_1274867, _1274869, _1274871] : [class_Lattices_Oboolean__algebra(_1274867), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1274867), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274867), _1274869), _1274871)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1274867), hAPP(c_Groups_Ouminus__class_Ouminus(_1274867), _1274869)), hAPP(c_Groups_Ouminus__class_Ouminus(_1274867), _1274871)))], (24092 ^ _779999) ^ [_1229959, _1229961, _1229963] : [class_Orderings_Olinorder(_1229959), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229959), _1229961)), 24099 ^ _779999 : [(24106 ^ _779999) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1229959, tc_HOL_Obool)), _1229961), hAPP(hAPP(c_Set_Oinsert(_1229959), _1229963), c_Orderings_Obot__class_Obot(tc_fun(_1229959, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1229959, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1229959, c_Orderings_Oord__class_Omin(_1229959), hAPP(hAPP(c_Set_Oinsert(_1229959), _1229963), _1229961)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229959), _1229963), c_Big__Operators_Olattice_OInf__fin(_1229959, c_Orderings_Oord__class_Omin(_1229959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1229959, tc_HOL_Obool)), _1229961), hAPP(hAPP(c_Set_Oinsert(_1229959), _1229963), c_Orderings_Obot__class_Obot(tc_fun(_1229959, tc_HOL_Obool)))))))], (24100 ^ _779999) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1229959, tc_HOL_Obool)), _1229961), hAPP(hAPP(c_Set_Oinsert(_1229959), _1229963), c_Orderings_Obot__class_Obot(tc_fun(_1229959, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1229959, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1229959, c_Orderings_Oord__class_Omin(_1229959), hAPP(hAPP(c_Set_Oinsert(_1229959), _1229963), _1229961)) = _1229963)]]], (18243 ^ _779999) ^ [_1112109] : [class_Rings_Osemiring__1(_1112109), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1112109), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1112109))], (34837 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (8102 ^ _779999) ^ [_916909, _916911, _916913, _916915] : [hBOOL(hAPP(hAPP(c_member(_916909), _916911), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916909, tc_HOL_Obool)), _916913), _916915))), hBOOL(hAPP(hAPP(c_member(_916909), _916911), _916915))], (8161 ^ _779999) ^ [_918206, _918208, _918210] : [8162 ^ _779999 : [(8163 ^ _779999) ^ [_918256] : [c_Natural_Oevaln(_918206, _918208, _918256, _918210)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_918206), _918208), _918210)))], (47356 ^ _779999) ^ [_1731270, _1731272, _1731274] : [c_List_Oconcat(_1731270, _1731272) = c_List_Oconcat(_1731270, _1731274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731270))), _1731272) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731270))), _1731274), 47366 ^ _779999 : [(47369 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1731270), tc_List_Olist(_1731270), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731270), tc_fun(tc_List_Olist(_1731270), tc_Nat_Onat), tc_fun(tc_List_Olist(_1731270), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1731270), tc_Nat_Onat), tc_fun(tc_List_Olist(_1731270), tc_HOL_Obool)), tc_List_Olist(_1731270)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731270))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1731270)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1731270))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1731270)))), 47365 ^ [_1731270, _1731272, _1731274]))], (47367 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731270), tc_List_Olist(_1731270))), 47365 ^ [_1731270, _1731272, _1731274]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1731270), tc_List_Olist(_1731270))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1731270), tc_List_Olist(_1731270)), _1731272), _1731274)))))]], -(_1731272 = _1731274)], (3162 ^ _779999) ^ [_827160, _827162, _827164, _827166] : [-(c_Nitpick_OAbs__Frac(_827166, _827162) = c_Nitpick_OAbs__Frac(_827164, _827160)), _827166 = _827164, _827162 = _827160], (7109 ^ _779999) ^ [_896911, _896913, _896915, _896917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896911, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_896911), _896913), _896915)), _896917)), 7112 ^ _779999 : [(7115 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896911, tc_HOL_Obool)), _896915), _896917)))], (7113 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896911), _896913), _896917)))]]], (31697 ^ _779999) ^ [_1374544] : [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), _1374544))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374544) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374544)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50165 ^ _779999) ^ [_1792710] : [-(c_Lazy__Sequence_Oyieldn(_1792710) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1792710), _1792710, c_Lazy__Sequence_Oyield(_1792710)))], (41097 ^ _779999) ^ [_1582712, _1582714, _1582716] : [c_Relation_Osingle__valued(_1582712, _1582714, _1582716), 41100 ^ _779999 : [(41101 ^ _779999) ^ [_1582833, _1582835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582712, _1582714)), hAPP(hAPP(c_Product__Type_OPair(_1582712, _1582714), _1582835), _1582833)), _1582716)), 41104 ^ _779999 : [(41105 ^ _779999) ^ [_1582959] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582712, _1582714)), hAPP(hAPP(c_Product__Type_OPair(_1582712, _1582714), _1582835), _1582959)), _1582716)), -(_1582833 = _1582959)]]]]], (49740 ^ _779999) ^ [_1783495, _1783497, _1783499, _1783501] : [-(c_New__Random__Sequence_Oneg__map(_1783495, _1783497, _1783499, _1783501) = c_New__Random__Sequence_Oneg__bind(_1783495, _1783497, _1783501, hAPP(c_Fun_Ocomp(_1783497, 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(_1783497)))))), _1783495, c_New__Random__Sequence_Oneg__single(_1783497)), _1783499)))], (27914 ^ _779999) ^ [_1304774, _1304776, _1304778, _1304780] : [class_Rings_Olinordered__semidom(_1304774), hAPP(hAPP(c_Power_Opower__class_Opower(_1304774), _1304776), hAPP(c_Nat_OSuc, _1304778)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1304774), _1304780), hAPP(c_Nat_OSuc, _1304778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304774), c_Groups_Ozero__class_Ozero(_1304774)), _1304776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304774), c_Groups_Ozero__class_Ozero(_1304774)), _1304780)), -(_1304776 = _1304780)], (50712 ^ _779999) ^ [_1806029, _1806031, _1806033, _1806035] : [class_Complete__Lattice_Ocomplete__lattice(_1806029), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1806031, _1806029), _1806033), _1806035) = c_Complete__Lattice_OInf__class_OInf(_1806029, hAPP(c_Set_OCollect(_1806029), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool), tc_HOL_Obool, _1806029), c_HOL_OEx(tc_fun(_1806031, _1806029))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool), tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool), _1806029), hAPP(c_COMBS(tc_fun(_1806031, _1806029), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1806031, _1806029)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1806031, _1806029), tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1806031, _1806029))), _1806033)))), hAPP(hAPP(c_COMBC(_1806029, tc_fun(tc_fun(_1806031, _1806029), _1806029), tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806029, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1806031, _1806029), _1806029), tc_fun(tc_fun(_1806031, _1806029), tc_HOL_Obool)), _1806029), c_COMBB(_1806029, tc_HOL_Obool, tc_fun(_1806031, _1806029))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1806031, _1806029), _1806031, _1806029), c_COMBI(tc_fun(_1806031, _1806029))), _1806035)))))))], (48508 ^ _779999) ^ [_1756403, _1756405, _1756407, _1756409] : [class_Orderings_Olinorder(_1756403), c_List_Olinorder__class_Osorted(_1756403, hAPP(c_List_Orev(_1756403), _1756405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756407), _1756409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756403)), _1756405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756403), hAPP(hAPP(c_List_Onth(_1756403), _1756405), _1756409)), hAPP(hAPP(c_List_Onth(_1756403), _1756405), _1756407))))], (32153 ^ _779999) ^ [_1382799, _1382801, _1382803] : [class_Int_Onumber__ring(_1382799), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382799), hAPP(c_Int_Onumber__class_Onumber__of(_1382799), _1382801)), hAPP(c_Int_Onumber__class_Onumber__of(_1382799), _1382803)) = hAPP(c_Int_Onumber__class_Onumber__of(_1382799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382801), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1382803))))], (36441 ^ _779999) ^ [_1466261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466261)), 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), _1466261)) = 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), _1466261))))))], (34853 ^ _779999) ^ [_1431737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431737)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431737), c_Int_OMin)))], (13542 ^ _779999) ^ [_1021384, _1021386, _1021388] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1021384), _1021386)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021384), _1021388)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1021384), _1021386)), hAPP(c_Finite__Set_Ocard(_1021384), _1021388)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1021384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1021384, tc_HOL_Obool)), _1021386), _1021388))), hAPP(c_Finite__Set_Ocard(_1021384), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1021384, tc_HOL_Obool)), _1021386), _1021388))))], (45622 ^ _779999) ^ [_1693665, _1693667] : [hBOOL(hAPP(c_List_Odistinct(_1693665), _1693667)), -(hBOOL(hAPP(c_List_Odistinct(_1693665), hAPP(c_List_Otl(_1693665), _1693667))))], (48798 ^ _779999) ^ [_1762331, _1762333, _1762335, _1762337, _1762339] : [c_List_OdropWhile(_1762331, _1762333, _1762335) = hAPP(hAPP(c_List_Olist_OCons(_1762331), _1762337), _1762339), 48801 ^ _779999 : [(48804 ^ _779999) ^ [] : [hBOOL(hAPP(_1762333, _1762337))], (48802 ^ _779999) ^ [] : [-(_1762335 = hAPP(hAPP(c_List_Oappend(_1762331), c_List_OtakeWhile(_1762331, _1762333, _1762335)), hAPP(hAPP(c_List_Olist_OCons(_1762331), _1762337), _1762339)))]]], (40653 ^ _779999) ^ [_1571659, _1571661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1571659)), -(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(_1571659), _1571661))), _1571659)))], (49754 ^ _779999) ^ [_1783851, _1783853, _1783855, _1783857, _1783859] : [-(c_List_Osplice(_1783851, hAPP(hAPP(c_List_Olist_OCons(_1783851), _1783853), _1783855), hAPP(hAPP(c_List_Olist_OCons(_1783851), _1783857), _1783859)) = hAPP(hAPP(c_List_Olist_OCons(_1783851), _1783853), hAPP(hAPP(c_List_Olist_OCons(_1783851), _1783857), c_List_Osplice(_1783851, _1783855, _1783859))))], (29774 ^ _779999) ^ [_1338198, _1338200, _1338202] : [hBOOL(hAPP(_1338198, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1338200), _1338202))), 29777 ^ _779999 : [(29802 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338202), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29805 ^ _779999 : [(29806 ^ _779999) ^ [_1338862] : [-(hBOOL(hAPP(_1338198, _1338862))), 29807 ^ _779999 : [(29808 ^ _779999) ^ [_1338936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338202), _1338936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1338936), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1338200 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1338202), _1338862)), _1338936)]]]]], (29784 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1338202)), 29787 ^ _779999 : [(29788 ^ _779999) ^ [_1338532] : [-(hBOOL(hAPP(_1338198, _1338532))), 29789 ^ _779999 : [(29790 ^ _779999) ^ [_1338603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1338603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338603), _1338202)), _1338200 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1338202), _1338532)), _1338603)]]]]], (29778 ^ _779999) ^ [] : [_1338202 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1338198, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (21786 ^ _779999) ^ [_1177495, _1177497, _1177499] : [-(hAPP(hAPP(c_Set_Oinsert(_1177495), _1177497), _1177499) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1177495, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1177495), hAPP(hAPP(c_COMBC(_1177495, _1177495, tc_HOL_Obool), c_fequal), _1177497))), _1177499))], (6971 ^ _779999) ^ [_894503, _894505, _894507, _894509] : [hBOOL(hAPP(hAPP(c_member(_894503), _894505), _894507)), -(hBOOL(hAPP(hAPP(c_member(_894503), _894505), hAPP(hAPP(c_Set_Oinsert(_894503), _894509), _894507))))], (760 ^ _779999) ^ [_791653, _791655, _791657, _791659] : [-(c_Wellfounded_Owf(_791657, _791653)), c_Wellfounded_Owf(_791659, _791655), _791659 = _791657, _791655 = _791653], (15673 ^ _779999) ^ [_1062572, _1062574, _1062576, _1062578] : [class_Rings_Ocomm__semiring__1(_1062572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062572), _1062574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062572), _1062576), _1062578)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062572), _1062574), _1062576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062572), _1062574), _1062578)))], (41029 ^ _779999) ^ [_1581290, _1581292, _1581294, _1581296, _1581298] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581290, _1581290)), hAPP(hAPP(c_Product__Type_OPair(_1581290, _1581290), _1581292), _1581294)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581290, _1581290), tc_HOL_Obool), _1581296), _1581298))), 41034 ^ _779999 : [(41037 ^ _779999) ^ [] : [-(_1581292 = _1581294)], (41035 ^ _779999) ^ [] : [-(_1581296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41040 ^ _779999 : [(41045 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581290, _1581290)), hAPP(hAPP(c_Product__Type_OPair(_1581290, _1581290), 41038 ^ [_1581290, _1581292, _1581294, _1581296, _1581298]), _1581294)), _1581298)))], (41043 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581290, _1581290)), hAPP(hAPP(c_Product__Type_OPair(_1581290, _1581290), _1581292), 41038 ^ [_1581290, _1581292, _1581294, _1581296, _1581298])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581290, _1581290), tc_HOL_Obool), 41039 ^ [_1581290, _1581292, _1581294, _1581296, _1581298]), _1581298))))], (41041 ^ _779999) ^ [] : [-(_1581296 = hAPP(c_Nat_OSuc, 41039 ^ [_1581290, _1581292, _1581294, _1581296, _1581298]))]]], (46781 ^ _779999) ^ [_1718419, _1718421, _1718423] : [46783 ^ _779999 : [(46786 ^ _779999) ^ [] : [hBOOL(hAPP(_1718421, 46782 ^ [_1718419, _1718421, _1718423]))], (46784 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1718419), 46782 ^ [_1718419, _1718421, _1718423]), hAPP(c_List_Oset(_1718419), _1718423))))]], -(hBOOL(hAPP(c_List_Olistsp(_1718419, _1718421), _1718423)))], (21746 ^ _779999) ^ [_1176577, _1176579, _1176581, _1176583] : [-(hBOOL(hAPP(hAPP(c_member(_1176577), _1176579), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1176577, tc_HOL_Obool)), _1176581), hAPP(c_Set_OCollect(_1176577), _1176583))))), hBOOL(hAPP(hAPP(c_member(_1176577), _1176579), _1176581)), hBOOL(hAPP(_1176583, _1176579))], (39346 ^ _779999) ^ [_1540797, _1540799, _1540801] : [-(hAPP(c_Fun_Ocomp(_1540797, _1540797, _1540799, c_Fun_Oid(_1540797)), _1540801) = _1540801)], (45171 ^ _779999) ^ [_1682661, _1682663, _1682665, _1682667] : [-(hAPP(hAPP(c_List_Otake(_1682661), _1682663), hAPP(hAPP(c_List_Oappend(_1682661), _1682665), _1682667)) = hAPP(hAPP(c_List_Oappend(_1682661), hAPP(hAPP(c_List_Otake(_1682661), _1682663), _1682665)), hAPP(hAPP(c_List_Otake(_1682661), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1682663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682661)), _1682665))), _1682667)))], (48621 ^ _779999) ^ [_1758716, _1758718, _1758720, _1758722, _1758724] : [-(hAPP(hAPP(c_List_Ozip(_1758716, _1758718), _1758720), c_List_OtakeWhile(_1758718, _1758722, _1758724)) = c_List_OtakeWhile(tc_prod(_1758716, _1758718), hAPP(c_Fun_Ocomp(_1758718, tc_HOL_Obool, tc_prod(_1758716, _1758718), _1758722), c_Product__Type_Osnd(_1758716, _1758718)), hAPP(hAPP(c_List_Ozip(_1758716, _1758718), _1758720), _1758724)))], (49718 ^ _779999) ^ [_1782961, _1782963, _1782965, _1782967, _1782969] : [_1782961 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1782963, _1782965, _1782967, _1782969), _1782961) = c_Lazy__Sequence_Oempty(_1782965))], (7594 ^ _779999) ^ [_907517, _907519, _907521] : [class_Orderings_Owellorder(_907517), hBOOL(hAPP(_907519, _907521)), -(hBOOL(hAPP(_907519, c_Orderings_Oord__class_OLeast(_907517, _907519))))], (40041 ^ _779999) ^ [_1557072, _1557074, _1557076] : [c_Com_Ocom_OLocal(_1557072, _1557074, _1557076) = c_Com_Ocom_OSKIP], (22155 ^ _779999) ^ [_1189774, _1189776, _1189778, _1189780, _1189782] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1189774, tc_fun(_1189776, tc_HOL_Obool)), _1189778), _1189780), _1189782)), 22159 ^ _779999 : [(22162 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(_1189780, 22158 ^ [_1189774, _1189776, _1189778, _1189780, _1189782]), _1189782)))], (22160 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189774), 22158 ^ [_1189774, _1189776, _1189778, _1189780, _1189782]), _1189778)))]]], (42327 ^ _779999) ^ [_1612602, _1612604, _1612606] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1612602, tc_HOL_Obool)), _1612604), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1612602, tc_HOL_Obool), _1612606)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1612602, tc_HOL_Obool), tc_fun(_1612602, tc_HOL_Obool)), _1612606), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1612602, tc_HOL_Obool)), _1612604)))], (43647 ^ _779999) ^ [_1647069] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1647069)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1647069), tc_HOL_Obool))))], (42494 ^ _779999) ^ [_1616503] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616503, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1616503, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1616503, tc_HOL_Obool)))], (50967 ^ _779999) ^ [_1811362, _1811364] : [c_Wellfounded_Oacyclic(_1811362, _1811364), -(c_Relation_Oantisym(_1811362, c_Transitive__Closure_Ortrancl(_1811362, _1811364)))], (18653 ^ _779999) ^ [_1120033, _1120035, _1120037, _1120039] : [class_Orderings_Oorder(_1120033), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120033, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1120033, _1120035, _1120037)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1120033, _1120037, _1120039)) = c_Orderings_Obot__class_Obot(tc_fun(_1120033, tc_HOL_Obool)))], (48318 ^ _779999) ^ [_1752328, _1752330] : [-(c_Fun_Oinj__on(tc_List_Olist(_1752328), tc_List_Olist(_1752328), c_List_Orev(_1752328), _1752330))], (30328 ^ _779999) ^ [_1348156, _1348158, _1348160] : [hBOOL(hAPP(_1348156, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1348158), _1348160))), 30333 ^ _779999 : [(30336 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1348156, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30334 ^ _779999) ^ [] : [-(_1348160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 30338 ^ _779999 : [(30343 ^ _779999) ^ [] : [-(hBOOL(hAPP(_1348156, 30337 ^ [_1348156, _1348158, _1348160])))], (30341 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1348158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1348160), hAPP(c_Nat_OSuc, 30337 ^ [_1348156, _1348158, _1348160])))))], (30339 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1348160), 30337 ^ [_1348156, _1348158, _1348160])), _1348158)))]]], (40591 ^ _779999) ^ [_1570745, _1570747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1570745), _1570747)), -(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), _1570745), _1570747)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (17667 ^ _779999) ^ [_1101192, _1101194, _1101196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101192), _1101194)), _1101196) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101194), _1101196)))], (32675 ^ _779999) ^ [_1392988] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1392988)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392988)))], (29364 ^ _779999) ^ [_1331612, _1331614] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331612)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331614)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331612), _1331614))], (46189 ^ _779999) ^ [_1704779, _1704781, _1704783, _1704785] : [-(hAPP(hAPP(c_List_Omap(_1704779, _1704781), _1704783), hAPP(c_List_Otl(_1704779), _1704785)) = hAPP(c_List_Otl(_1704781), hAPP(hAPP(c_List_Omap(_1704779, _1704781), _1704783), _1704785)))], (27370 ^ _779999) ^ [_1294854, _1294856, _1294858] : [class_Rings_Ocomm__semiring__1(_1294854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294854), _1294856), hAPP(hAPP(c_Power_Opower__class_Opower(_1294854), _1294856), _1294858)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1294854), _1294856), hAPP(c_Nat_OSuc, _1294858)))], (31941 ^ _779999) ^ [_1379007, _1379009, _1379011, _1379013] : [class_Int_Onumber__ring(_1379007), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379007), hAPP(c_Int_Onumber__class_Onumber__of(_1379007), _1379009)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379007), hAPP(c_Int_Onumber__class_Onumber__of(_1379007), _1379011)), _1379013)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379007), hAPP(c_Int_Onumber__class_Onumber__of(_1379007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1379009), _1379011))), _1379013))], (13225 ^ _779999) ^ [_1015384, _1015386] : [class_Groups_Omonoid__add(_1015384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015384), _1015386), c_Groups_Ozero__class_Ozero(_1015384)) = _1015386)], (50605 ^ _779999) ^ [_1802747, _1802749] : [c_Relation_Otrans(_1802747, hAPP(c_Relation_Oconverse(_1802747, _1802747), _1802749)), -(c_Relation_Otrans(_1802747, _1802749))], (36673 ^ _779999) ^ [_1471099, _1471101, _1471103, _1471105, _1471107, _1471109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471099, _1471099)), hAPP(hAPP(c_Product__Type_OPair(_1471099, _1471099), _1471101), _1471103)), hAPP(hAPP(c_Relation_Oinv__image(_1471105, _1471099), _1471107), _1471109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471105, _1471105)), hAPP(hAPP(c_Product__Type_OPair(_1471105, _1471105), hAPP(_1471109, _1471101)), hAPP(_1471109, _1471103))), _1471107)))], (49337 ^ _779999) ^ [_1775188, _1775190, _1775192] : [-(hBOOL(hAPP(hAPP(c_member(_1775188), _1775190), hAPP(c_List_Oset(_1775188), _1775192)))), 49338 ^ _779999 : [(49339 ^ _779999) ^ [_1775277] : [49340 ^ _779999 : [(49341 ^ _779999) ^ [_1775350] : [_1775192 = hAPP(hAPP(c_List_Oappend(_1775188), _1775277), hAPP(hAPP(c_List_Olist_OCons(_1775188), _1775190), _1775350))]], -(hBOOL(hAPP(hAPP(c_member(_1775188), _1775190), hAPP(c_List_Oset(_1775188), _1775277))))]]], (29500 ^ _779999) ^ [_1333711, _1333713, _1333715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1333711), _1333713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333711), _1333715)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333713), _1333715))))], (37296 ^ _779999) ^ [_1486882, _1486884, _1486886, _1486888, _1486890, _1486892] : [hAPP(_1486888, hAPP(c_Product__Type_Ofst(_1486882, _1486886), _1486890)) = hAPP(_1486892, hAPP(c_Product__Type_Ofst(_1486882, _1486886), _1486890)), -(hAPP(c_Product__Type_Oapfst(_1486882, _1486884, _1486886, _1486888), _1486890) = hAPP(c_Product__Type_Oapfst(_1486882, _1486884, _1486886, _1486892), _1486890))], (43287 ^ _779999) ^ [_1636284, _1636286, _1636288, _1636290, _1636292, _1636294] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636284, _1636284)), hAPP(hAPP(c_Product__Type_OPair(_1636284, _1636284), _1636286), _1636288)), c_Transitive__Closure_Ortrancl(_1636284, _1636290))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636284), tc_List_Olist(_1636284))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636284), tc_List_Olist(_1636284)), _1636292), _1636294)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636284), c_List_Olistrel1(_1636284, _1636290)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636284), tc_List_Olist(_1636284))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636284), tc_List_Olist(_1636284)), hAPP(hAPP(c_List_Olist_OCons(_1636284), _1636286), _1636292)), hAPP(hAPP(c_List_Olist_OCons(_1636284), _1636288), _1636294))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636284), c_List_Olistrel1(_1636284, _1636290)))))], (11438 ^ _779999) ^ [_979317, _979319, _979321, _979323] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979317, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979317, tc_HOL_Obool)), _979319), _979321)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979317, tc_HOL_Obool)), _979323), _979321)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979317, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979317, tc_HOL_Obool)), _979319), _979321)), _979323))], (9850 ^ _779999) ^ [_949140, _949142, _949144, _949146] : [class_Orderings_Oorder(_949140), class_Enum_Oenum(_949142), 9857 ^ _779999 : [(9866 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_949142, _949140)), _949144), _949146))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949142, _949140)), _949144), _949146)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_949142), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _949142), c_fNot), hAPP(hAPP(c_COMBS(_949142, _949140, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_949140, tc_fun(_949140, tc_HOL_Obool), _949142), c_fequal), _949144)), _949146))))], (9858 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_949142, _949140)), _949144), _949146)), 9861 ^ _779999 : [(9864 ^ _779999) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_949142), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _949142), c_fNot), hAPP(hAPP(c_COMBS(_949142, _949140, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_949140, tc_fun(_949140, tc_HOL_Obool), _949142), c_fequal), _949144)), _949146)))))], (9862 ^ _779999) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949142, _949140)), _949144), _949146)))]]]]], (9428 ^ _779999) ^ [_940367, _940369, _940371] : [class_Orderings_Oorder(_940367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940367), _940369), _940371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940367), _940369), _940371))), -(_940369 = _940371)], (25440 ^ _779999) ^ [_1257446, _1257448, _1257450] : [class_Groups_Oordered__ab__group__add(_1257446), 25443 ^ _779999 : [(25450 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257446), _1257450), hAPP(c_Groups_Ouminus__class_Ouminus(_1257446), _1257448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257446), _1257448), hAPP(c_Groups_Ouminus__class_Ouminus(_1257446), _1257450))))], (25444 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257446), _1257448), hAPP(c_Groups_Ouminus__class_Ouminus(_1257446), _1257450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257446), _1257450), hAPP(c_Groups_Ouminus__class_Ouminus(_1257446), _1257448))))]]], (38724 ^ _779999) ^ [_1525852, _1525854] : [-(hAPP(c_Set_Oimage(_1525852, _1525852, c_Fun_Oid(_1525852)), _1525854) = _1525854)], (33973 ^ _779999) ^ [_1415559] : [c_Int_OPls = _1415559, -(c_Int_OPls = c_Int_OBit0(_1415559))], (26026 ^ _779999) ^ [_1268095, _1268097, _1268099, _1268101] : [c_Com_Ocom_OCond(_1268095, _1268097, _1268099) = hAPP(c_Com_Ocom_OBODY, _1268101)], (21255 ^ _779999) ^ [_1166867, _1166869, _1166871] : [class_Orderings_Olinorder(_1166867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166867), _1166869), _1166871)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166867, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1166867, _1166869), _1166871)), hAPP(c_SetInterval_Oord__class_OatLeast(_1166867), _1166871)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1166867), _1166869))], (52288 ^ _779999) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (9512 ^ _779999) ^ [_941586, _941588, _941590, _941592] : [class_Orderings_Oorder(_941586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941586), _941588), _941590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941586), _941592), _941588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941586), _941592), _941590)))], (44504 ^ _779999) ^ [_1668475, _1668477, _1668479, _1668481] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1668477), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668475)), hAPP(hAPP(c_List_Olist_OCons(_1668477), _1668479), _1668481)) = hAPP(hAPP(c_List_Olist_OCons(_1668477), _1668479), hAPP(hAPP(c_List_Otake(_1668477), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668475)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1668481)))], (16555 ^ _779999) ^ [_1079133, _1079135, _1079137, _1079139, _1079141, _1079143] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1079133), -(_1079135 = c_Groups_Ozero__class_Ozero(_1079133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079133), _1079137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079133), _1079135), _1079141)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079133), _1079139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079133), _1079135), _1079143)), _1079137 = _1079139, -(_1079141 = _1079143)], (43725 ^ _779999) ^ [_1649084, _1649086, _1649088, _1649090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649084), _1649086)), -(hAPP(hAPP(c_List_Onth(_1649088), hAPP(hAPP(c_List_Otake(_1649088), _1649086), _1649090)), _1649084) = hAPP(hAPP(c_List_Onth(_1649088), _1649090), _1649084))], (5034 ^ _779999) ^ [_856928, _856930] : [_856930 = _856928, -(c_DSequence_Ounion(_856930) = c_DSequence_Ounion(_856928))], (11789 ^ _779999) ^ [_987164, _987166, _987168] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987164), _987166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987164, tc_HOL_Obool)), hAPP(c_Set_Oimage(_987164, _987164, _987168), _987166)), _987166)), c_Fun_Oinj__on(_987164, _987164, _987168, _987166), -(hAPP(c_Set_Oimage(_987164, _987164, _987168), _987166) = _987166)], (26312 ^ _779999) ^ [_1273087, _1273089] : [class_Groups_Oab__group__add(_1273087), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273087), hAPP(c_Groups_Ouminus__class_Ouminus(_1273087), _1273089)), _1273089) = c_Groups_Ozero__class_Ozero(_1273087))], (45925 ^ _779999) ^ [_1700185, _1700187, _1700189, _1700191, _1700193] : [class_Orderings_Olinorder(_1700185), -(hAPP(c_List_Oset(_1700187), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700187, _1700185, _1700189), _1700191), _1700193)) = hAPP(hAPP(c_Set_Oinsert(_1700187), _1700191), hAPP(c_List_Oset(_1700187), _1700193)))], (996 ^ _779999) ^ [_795163, _795165, _795167, _795169, _795171, _795173] : [-(c_Equiv__Relations_Oequiv(_795171, _795167, _795163)), c_Equiv__Relations_Oequiv(_795173, _795169, _795165), _795173 = _795171, _795169 = _795167, _795165 = _795163], (44538 ^ _779999) ^ [_1669109, _1669111] : [-(c_List_Osublist(_1669109, _1669111, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1669109))], (34779 ^ _779999) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (47984 ^ _779999) ^ [_1745662, _1745664, _1745666] : [class_Orderings_Olinorder(_1745662), c_List_Olinorder__class_Osorted(_1745662, _1745664), hBOOL(hAPP(c_List_Odistinct(_1745662), _1745664)), c_List_Olinorder__class_Osorted(_1745662, _1745666), hBOOL(hAPP(c_List_Odistinct(_1745662), _1745666)), hAPP(c_List_Oset(_1745662), _1745664) = hAPP(c_List_Oset(_1745662), _1745666), -(_1745664 = _1745666)]], input).
% 48.08/47.16  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs))],start(52442 ^ 0)).
% 48.08/47.16  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs))), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs)), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G)],extension(5821 ^ 1,bind([[_872057, _872059, _872061, _872063], [t_a, v_G, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs), v_Ga]]))).
% 48.08/47.16  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs))), c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), 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))), v_Q)), v_Procs))],extension(5831 ^ 2,bind([[_872200, _872202, _872204, _872206, _872208], [t_a, v_G, v_P, v_Q, v_Procs]]))).
% 48.08/47.16  ncf('1.1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), c_Com_Ocom_OBODY)), v_Q)), v_Procs)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(t_a), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), hAPP(hAPP(c_COMBB(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_a, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_a))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(t_a)), v_P)), 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))), v_Q)), v_Procs)))],extension(52432 ^ 3)).
% 48.08/47.16  ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga))],extension(5805 ^ 2,bind([[_871787, _871789, _871791], [t_a, v_G, v_Ga]]))).
% 48.08/47.16  ncf('1.1.2.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))],extension(52440 ^ 3)).
% 48.08/47.16  %-----------------------------------------------------
% 48.08/47.16  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------