%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW313+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 12:25:55 EDT 2023

% Result   : Theorem 45.17s 44.00s
% Output   : Proof 45.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW313+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 22:14:05 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 45.17/44.00  
% 45.17/44.00  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 45.17/44.00  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.17/44.00  %-----------------------------------------------------
% 45.17/44.00  ncf(matrix, plain, [(52781 ^ _2094755) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)], !, (49526 ^ _782476) ^ [_1781360, _1781362, _1781364] : [c_Fun_Obij__betw(_1781360, _1781362, _1781364, c_Orderings_Otop__class_Otop(tc_fun(_1781360, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781362, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1781362, _1781360, c_Orderings_Otop__class_Otop(tc_fun(_1781362, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1781360, _1781362, c_Orderings_Otop__class_Otop(tc_fun(_1781360, tc_HOL_Obool)), _1781364)) = _1781364)], (44939 ^ _782476) ^ [_1680396, _1680398, _1680400] : [hBOOL(hAPP(c_List_Odistinct(_1680396), hAPP(hAPP(c_List_Oappend(_1680396), _1680398), _1680400))), 44942 ^ _782476 : [(44947 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680396, tc_HOL_Obool)), hAPP(c_List_Oset(_1680396), _1680398)), hAPP(c_List_Oset(_1680396), _1680400)) = c_Orderings_Obot__class_Obot(tc_fun(_1680396, tc_HOL_Obool)))], (44945 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680396), _1680400)))], (44943 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680396), _1680398)))]]], (19274 ^ _782476) ^ [_1145229, _1145231] : [class_Rings_Olinordered__ring(_1145229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145229), _1145231), _1145231)), c_Groups_Ozero__class_Ozero(_1145229)))], (3038 ^ _782476) ^ [_827535, _827537, _827539, _827541] : [-(c_List_Olenlex(_827541, _827537) = c_List_Olenlex(_827539, _827535)), _827541 = _827539, _827537 = _827535], (36559 ^ _782476) ^ [_1476989, _1476991, _1476993, _1476995, _1476997, _1476999] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476991, _1476993)), hAPP(hAPP(c_Product__Type_OPair(_1476991, _1476993), _1476997), _1476999)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476989, tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476989, tc_HOL_Obool))), _1476995))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476989, tc_fun(_1476991, tc_fun(_1476993, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476989, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_fun(_1476991, tc_fun(_1476993, tc_HOL_Obool)), _1476989), hAPP(c_COMBC(_1476991, tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_fun(_1476993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476993, tc_fun(tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_fun(_1476993, tc_HOL_Obool)), _1476991), c_COMBC(_1476993, tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476993, tc_prod(_1476991, _1476993)), tc_fun(_1476993, tc_fun(tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_HOL_Obool)), _1476991), hAPP(c_COMBB(tc_prod(_1476991, _1476993), tc_fun(tc_fun(tc_prod(_1476991, _1476993), tc_HOL_Obool), tc_HOL_Obool), _1476993), c_member(tc_prod(_1476991, _1476993)))), c_Product__Type_OPair(_1476991, _1476993))))), _1476995)), _1476997), _1476999)))], (30887 ^ _782476) ^ [_1367956, _1367958] : [class_Divides_Osemiring__div(_1367956), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367956), _1367958), c_Groups_Oone__class_Oone(_1367956)) = _1367958)], (52011 ^ _782476) ^ [_1835973, _1835975, _1835977] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835973, _1835975) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1835977), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1835973 = _1835975, _1835975 = _1835977], (44284 ^ _782476) ^ [_1665879, _1665881] : [-(hAPP(hAPP(c_List_Otake(_1665879), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1665881) = c_List_Olist_ONil(_1665879))], (42263 ^ _782476) ^ [_1614893, _1614895, _1614897] : [class_Orderings_Olinorder(_1614893), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614893), _1614895)), -(c_Big__Operators_Olattice_OSup__fin(_1614893, c_Orderings_Oord__class_Omax(_1614893), hAPP(hAPP(c_Set_Oinsert(_1614893), _1614897), _1614895)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614893, _1614893, c_Orderings_Oord__class_Omax(_1614893)), _1614897), _1614895))], (50662 ^ _782476) ^ [_1807402, _1807404, _1807406, _1807408] : [class_Complete__Lattice_Ocomplete__lattice(_1807402), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1807404, _1807402), _1807406), _1807408) = c_Complete__Lattice_OSup__class_OSup(_1807402, hAPP(c_Set_OCollect(_1807402), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool), tc_HOL_Obool, _1807402), c_HOL_OEx(tc_fun(_1807404, _1807402))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool), tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool), _1807402), hAPP(c_COMBS(tc_fun(_1807404, _1807402), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1807404, _1807402)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1807404, _1807402), tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1807404, _1807402))), _1807406)))), hAPP(hAPP(c_COMBC(_1807402, tc_fun(tc_fun(_1807404, _1807402), _1807402), tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807402, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1807404, _1807402), _1807402), tc_fun(tc_fun(_1807404, _1807402), tc_HOL_Obool)), _1807402), c_COMBB(_1807402, tc_HOL_Obool, tc_fun(_1807404, _1807402))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1807404, _1807402), _1807404, _1807402), c_COMBI(tc_fun(_1807404, _1807402))), _1807408)))))))], (43644 ^ _782476) ^ [_1651580, _1651582, _1651584, _1651586, _1651588] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1651580, _1651582)), _1651584), hAPP(hAPP(c_List_Ozip(_1651580, _1651582), _1651586), _1651588)) = hAPP(hAPP(c_List_Ozip(_1651580, _1651582), hAPP(hAPP(c_List_Otake(_1651580), _1651584), _1651586)), hAPP(hAPP(c_List_Otake(_1651582), _1651584), _1651588)))], (32940 ^ _782476) ^ [_1407167] : [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), _1407167))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407167) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407167)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (51658 ^ _782476) ^ [_1829333, _1829335, _1829337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1829333), _1829335)), -(_1829335 = c_Orderings_Obot__class_Obot(tc_fun(_1829333, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1829333, _1829337, _1829335), 51665 ^ [_1829333, _1829335, _1829337])))], (46430 ^ _782476) ^ [_1713182, _1713184] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713182), _1713184) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713182)), hAPP(c_Code__Numeral_Onat__of, _1713184))))], (2490 ^ _782476) ^ [_819051, _819053, _819055, _819057] : [-(c_Divides_Odivmod__nat__rel(_819057, _819053) = c_Divides_Odivmod__nat__rel(_819055, _819051)), _819057 = _819055, _819053 = _819051], (34350 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (31468 ^ _782476) ^ [_1377978, _1377980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1377978), _1377980)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377978), _1377980) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4892 ^ _782476) ^ [_857134, _857136, _857138, _857140, _857142, _857144, _857146, _857148] : [-(c_Random__Sequence_Obind(_857148, _857144, _857140, _857136) = c_Random__Sequence_Obind(_857146, _857142, _857138, _857134)), _857148 = _857146, _857144 = _857142, _857140 = _857138, _857136 = _857134], (29166 ^ _782476) ^ [_1336091, _1336093, _1336095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336091), _1336093)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336091), _1336095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336093), _1336095)))], (32223 ^ _782476) ^ [_1392786, _1392788] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392786, _1392788) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392786, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392788)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392786, _1392788)), _1392788))], (41266 ^ _782476) ^ [_1591205, _1591207, _1591209, _1591211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591205, _1591205)), hAPP(hAPP(c_Product__Type_OPair(_1591205, _1591205), _1591207), _1591209)), c_Transitive__Closure_Ortrancl(_1591205, _1591211))), -(_1591207 = _1591209), 41273 ^ _782476 : [(41276 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591205, _1591205)), hAPP(hAPP(c_Product__Type_OPair(_1591205, _1591205), _1591207), _1591209)), c_Transitive__Closure_Otrancl(_1591205, _1591211))))], (41274 ^ _782476) ^ [] : [_1591207 = _1591209]]], (12822 ^ _782476) ^ [_1017344, _1017346, _1017348, _1017350, _1017352] : [c_Fun_Oinj__on(_1017344, _1017346, _1017348, c_Orderings_Otop__class_Otop(tc_fun(_1017344, tc_HOL_Obool))), 12825 ^ _782476 : [(12832 ^ _782476) ^ [] : [_1017350 = _1017352, -(hAPP(c_Set_Oimage(_1017344, _1017346, _1017348), _1017350) = hAPP(c_Set_Oimage(_1017344, _1017346, _1017348), _1017352))], (12826 ^ _782476) ^ [] : [hAPP(c_Set_Oimage(_1017344, _1017346, _1017348), _1017350) = hAPP(c_Set_Oimage(_1017344, _1017346, _1017348), _1017352), -(_1017350 = _1017352)]]], (10899 ^ _782476) ^ [_983269, _983271] : [-(c_Set_Othe__elem(_983269, hAPP(hAPP(c_Set_Oinsert(_983269), _983271), c_Orderings_Obot__class_Obot(tc_fun(_983269, tc_HOL_Obool)))) = _983271)], (43117 ^ _782476) ^ [_1636133, _1636135, _1636137, _1636139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636133), tc_List_Olist(_1636133))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636133), tc_List_Olist(_1636133)), _1636135), _1636137)), c_List_Olistrel(_1636133, _1636139))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636133)), _1636135) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636133)), _1636137))], (52065 ^ _782476) ^ [_1836897, _1836899] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836897, _1836899) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836897), _1836899)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836899), _1836897)))], (40193 ^ _782476) ^ [_1564997, _1564999, _1565001, _1565003] : [c_Wellfounded_Owf(_1564997, _1564999), c_Fun_Oinj__on(_1564997, _1565001, _1565003, c_Orderings_Otop__class_Otop(tc_fun(_1564997, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1565001, hAPP(c_Set_Oimage(tc_prod(_1564997, _1564997), tc_prod(_1565001, _1565001), c_Product__Type_Omap__pair(_1564997, _1565001, _1564997, _1565001, _1565003, _1565003)), _1564999)))], (35428 ^ _782476) ^ [] : [-(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))))], (42985 ^ _782476) ^ [_1631635, _1631637, _1631639] : [-(c_List_Oset__Cons(_1631635, _1631637, _1631639) = hAPP(c_Set_OCollect(tc_List_Olist(_1631635)), hAPP(hAPP(c_COMBB(tc_fun(_1631635, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1631635)), c_HOL_OEx(_1631635)), hAPP(hAPP(c_COMBB(tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_fun(_1631635, tc_HOL_Obool), tc_List_Olist(_1631635)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_HOL_Obool, _1631635), c_HOL_OEx(tc_List_Olist(_1631635)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631635), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631635, tc_fun(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), tc_fun(tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), tc_List_Olist(_1631635)), c_COMBS(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1631635, tc_fun(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), tc_List_Olist(_1631635)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631635), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), _1631635), c_COMBS(tc_List_Olist(_1631635), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1631635)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1631635), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1631635)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631635), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_List_Olist(_1631635))), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1631635), tc_List_Olist(_1631635)), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_fun(tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_List_Olist(_1631635))), tc_fun(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool))), tc_List_Olist(_1631635)), c_COMBB(tc_fun(tc_List_Olist(_1631635), tc_List_Olist(_1631635)), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), _1631635)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631635), tc_List_Olist(_1631635)), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), tc_List_Olist(_1631635)), c_COMBB(tc_List_Olist(_1631635), tc_HOL_Obool, tc_List_Olist(_1631635))), c_fequal))), c_List_Olist_OCons(_1631635)))))), hAPP(hAPP(c_COMBC(_1631635, tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool)), _1631635), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1631635))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631635), c_fconj), hAPP(hAPP(c_COMBC(_1631635, tc_fun(_1631635, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631635)), _1631637)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631635), tc_fun(tc_List_Olist(_1631635), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1631635))), _1631639)))))))], (6865 ^ _782476) ^ [_894831, _894833, _894835, _894837, _894839] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894831, tc_fun(_894833, tc_HOL_Obool)), _894835), _894837), _894839))), 6866 ^ _782476 : [(6867 ^ _782476) ^ [_894903] : [hBOOL(hAPP(hAPP(c_member(_894831), _894903), _894835)), hBOOL(hAPP(hAPP(_894837, _894903), _894839))]]], (52361 ^ _782476) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (35642 ^ _782476) ^ [_1455781, _1455783] : [class_Rings_Olinordered__idom(_1455781), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455781), c_Groups_Ozero__class_Ozero(_1455781)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455781), _1455783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23895 ^ _782476) ^ [_1230591, _1230593] : [-(hAPP(c_Int_Onat, _1230591) = _1230593), 23898 ^ _782476 : [(23901 ^ _782476) ^ [] : [_1230591 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230593)], (23899 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230591)))]], 23902 ^ _782476 : [(23905 ^ _782476) ^ [] : [_1230593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23903 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230591))]]], (11752 ^ _782476) ^ [_996468, _996470, _996472, _996474, _996476] : [class_Groups_Oordered__ab__group__add(_996468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996468), _996470), _996472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996468), _996474), _996476), 11759 ^ _782476 : [(11766 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996468), _996474), _996476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996468), _996470), _996472)))], (11760 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996468), _996470), _996472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996468), _996474), _996476)))]]], (24259 ^ _782476) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (12522 ^ _782476) ^ [_1011316, _1011318] : [-(c_Set_Othe__elem(_1011316, _1011318) = c_HOL_OThe(_1011316, hAPP(hAPP(c_COMBB(tc_fun(_1011316, tc_HOL_Obool), tc_HOL_Obool, _1011316), hAPP(c_fequal, _1011318)), hAPP(hAPP(c_COMBC(_1011316, tc_fun(_1011316, tc_HOL_Obool), tc_fun(_1011316, tc_HOL_Obool)), c_Set_Oinsert(_1011316)), c_Orderings_Obot__class_Obot(tc_fun(_1011316, tc_HOL_Obool))))))], (25678 ^ _782476) ^ [_1263044, _1263046, _1263048, _1263050, _1263052, _1263054, _1263056] : [class_Groups_Ocomm__monoid__add(_1263044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263046), _1263048)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263050), _1263052)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263046, _1263044), hAPP(hAPP(c_COMBS(_1263046, tc_fun(_1263050, tc_HOL_Obool), _1263044), hAPP(hAPP(c_COMBB(tc_fun(_1263050, _1263044), tc_fun(tc_fun(_1263050, tc_HOL_Obool), _1263044), _1263046), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263050, _1263044)), _1263054)), hAPP(hAPP(c_COMBB(tc_fun(_1263050, tc_HOL_Obool), tc_fun(_1263050, tc_HOL_Obool), _1263046), c_Set_OCollect(_1263050)), hAPP(hAPP(c_COMBB(tc_fun(_1263050, tc_HOL_Obool), tc_fun(_1263050, tc_HOL_Obool), _1263046), hAPP(c_COMBS(_1263050, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263050), c_fconj), hAPP(hAPP(c_COMBC(_1263050, tc_fun(_1263050, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263050)), _1263052)))), _1263056)))), _1263048) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263050, _1263044), hAPP(hAPP(c_COMBS(_1263050, tc_fun(_1263046, tc_HOL_Obool), _1263044), hAPP(hAPP(c_COMBB(tc_fun(_1263046, _1263044), tc_fun(tc_fun(_1263046, tc_HOL_Obool), _1263044), _1263050), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263046, _1263044)), hAPP(c_COMBC(_1263046, _1263050, _1263044), _1263054))), hAPP(hAPP(c_COMBB(tc_fun(_1263046, tc_HOL_Obool), tc_fun(_1263046, tc_HOL_Obool), _1263050), c_Set_OCollect(_1263046)), hAPP(hAPP(c_COMBB(tc_fun(_1263046, tc_HOL_Obool), tc_fun(_1263046, tc_HOL_Obool), _1263050), hAPP(c_COMBS(_1263046, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263046), c_fconj), hAPP(hAPP(c_COMBC(_1263046, tc_fun(_1263046, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263046)), _1263048)))), hAPP(c_COMBC(_1263046, _1263050, tc_HOL_Obool), _1263056))))), _1263052))], (35466 ^ _782476) ^ [_1452738, _1452740] : [class_Int_Onumber__ring(_1452738), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452738), _1452740), hAPP(c_Int_Onumber__class_Onumber__of(_1452738), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452738), _1452740), _1452740))], (18344 ^ _782476) ^ [_1128649, _1128651] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128649), _1128651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128651), _1128649) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1128649 = _1128651)], (51881 ^ _782476) ^ [_1833320, _1833322, _1833324] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833320), _1833322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833320), _1833324))), -(_1833320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833322), _1833324)))], (52665 ^ _782476) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (22644 ^ _782476) ^ [_1207181] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207181)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1207181), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1207181)))], (35812 ^ _782476) ^ [_1458664, _1458666, _1458668] : [class_Rings_Olinordered__idom(_1458664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458664), hAPP(hAPP(c_Power_Opower__class_Opower(_1458664), _1458666), 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(_1458664), _1458668), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1458664)))], (33056 ^ _782476) ^ [_1409064, _1409066, _1409068, _1409070] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409064), hAPP(c_Int_Onumber__class_Onumber__of(_1409064), _1409066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409064), _1409068), _1409070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409064), hAPP(c_Int_Onumber__class_Onumber__of(_1409064), _1409066)), _1409068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409064), hAPP(c_Int_Onumber__class_Onumber__of(_1409064), _1409066)), _1409070))), class_Int_Onumber(_1409064), class_Rings_Osemiring(_1409064)], (24881 ^ _782476) ^ [_1247720, _1247722] : [class_Rings_Olinordered__idom(_1247720), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247720), hAPP(c_Groups_Oabs__class_Oabs(_1247720), _1247722)), hAPP(c_Groups_Oabs__class_Oabs(_1247720), _1247722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247720), _1247722), _1247722))], (30634 ^ _782476) ^ [_1363070, _1363072, _1363074, _1363076] : [class_Fields_Ofield(_1363070), -(_1363072 = c_Groups_Ozero__class_Ozero(_1363070)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363070), _1363074), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363070), _1363076), _1363072)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363070), _1363072), _1363074)), _1363076)), _1363072))], (14895 ^ _782476) ^ [_1060581, _1060583, _1060585] : [class_Lattices_Olattice(_1060581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060581), _1060583)), -(_1060583 = c_Orderings_Obot__class_Obot(tc_fun(_1060581, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060581), _1060585)), -(_1060585 = c_Orderings_Obot__class_Obot(tc_fun(_1060581, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060581, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060581, tc_HOL_Obool)), _1060583), _1060585)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060581), c_Big__Operators_Olattice__class_OInf__fin(_1060581, _1060583)), c_Big__Operators_Olattice__class_OInf__fin(_1060581, _1060585)))], (48018 ^ _782476) ^ [_1748090, _1748092, _1748094, _1748096] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1748090), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1748090))), _1748092))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748094), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748090))), c_List_Otranspose(_1748090, _1748092)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748096), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748090))), hAPP(c_List_Ofilter(tc_List_Olist(_1748090), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1748090)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748094)), c_Nat_Osize__class_Osize(tc_List_Olist(_1748090)))), _1748092)))), -(hAPP(hAPP(c_List_Onth(_1748090), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748090)), c_List_Otranspose(_1748090, _1748092)), _1748094)), _1748096) = hAPP(hAPP(c_List_Onth(_1748090), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748090)), _1748092), _1748096)), _1748094))], (28658 ^ _782476) ^ [_1326473, _1326475, _1326477, _1326479, _1326481, _1326483] : [class_Groups_Ocomm__monoid__mult(_1326473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326475), _1326477)), 28665 ^ _782476 : [(28672 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326475), _1326479), _1326477))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326475, _1326473), hAPP(hAPP(c_COMBC(_1326475, _1326473, _1326473), hAPP(hAPP(c_COMBS(_1326475, _1326473, tc_fun(_1326473, _1326473)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326473, tc_fun(_1326473, _1326473)), _1326475), c_If(_1326473)), hAPP(hAPP(c_COMBC(_1326475, _1326475, tc_HOL_Obool), c_fequal), _1326479))), _1326481)), _1326483)), _1326477) = hAPP(hAPP(c_Power_Opower__class_Opower(_1326473), _1326483), hAPP(c_Finite__Set_Ocard(_1326475), _1326477)))], (28666 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1326475), _1326479), _1326477)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326475, _1326473), hAPP(hAPP(c_COMBC(_1326475, _1326473, _1326473), hAPP(hAPP(c_COMBS(_1326475, _1326473, tc_fun(_1326473, _1326473)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326473, tc_fun(_1326473, _1326473)), _1326475), c_If(_1326473)), hAPP(hAPP(c_COMBC(_1326475, _1326475, tc_HOL_Obool), c_fequal), _1326479))), _1326481)), _1326483)), _1326477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326473), hAPP(_1326481, _1326479)), hAPP(hAPP(c_Power_Opower__class_Opower(_1326473), _1326483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1326475), _1326477)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (350 ^ _782476) ^ [_787851, _787853] : [-(c_Nitpick_Ounknown(_787851)), _787853 = _787851, c_Nitpick_Ounknown(_787853)], (4392 ^ _782476) ^ [_849170, _849172] : [_849172 = _849170, -(c_List_Otl(_849172) = c_List_Otl(_849170))], (24911 ^ _782476) ^ [_1248311, _1248313] : [class_Rings_Olinordered__idom(_1248311), -(hAPP(c_Groups_Oabs__class_Oabs(_1248311), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248311), _1248313)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248311), _1248313))], (46542 ^ _782476) ^ [_1715612, _1715614, _1715616, _1715618] : [hBOOL(hAPP(c_List_Olistsp(_1715612, _1715614), hAPP(hAPP(c_List_Olist_OCons(_1715612), _1715616), _1715618))), 46545 ^ _782476 : [(46548 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715612, _1715614), _1715618)))], (46546 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1715614, _1715616)))]]], (36024 ^ _782476) ^ [_1463264] : [c_Int_OMin = c_Int_OBit1(_1463264), -(c_Int_OMin = _1463264)], (25928 ^ _782476) ^ [_1271809, _1271811, _1271813, _1271815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1271809), hAPP(c_Set_OCollect(_1271809), _1271811))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1271813), hAPP(c_Set_OCollect(_1271813), hAPP(hAPP(c_COMBB(tc_fun(_1271809, tc_HOL_Obool), tc_HOL_Obool, _1271813), c_HOL_OEx(_1271809)), hAPP(hAPP(c_COMBC(_1271813, tc_fun(_1271809, tc_HOL_Obool), tc_fun(_1271809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271809, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271809, tc_HOL_Obool), tc_fun(_1271809, tc_HOL_Obool)), _1271813), c_COMBS(_1271809, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271809, tc_HOL_Obool), tc_fun(_1271809, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271813), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271809), c_fconj)), hAPP(hAPP(c_COMBC(_1271813, tc_fun(_1271809, _1271813), tc_fun(_1271809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271813, tc_HOL_Obool), tc_fun(tc_fun(_1271809, _1271813), tc_fun(_1271809, tc_HOL_Obool)), _1271813), c_COMBB(_1271813, tc_HOL_Obool, _1271809)), c_fequal)), _1271815)))), _1271811))))))], (2592 ^ _782476) ^ [_820656, _820658, _820660, _820662, _820664, _820666] : [-(c_Wellfounded_Omlex__prod(_820666, _820662, _820658) = c_Wellfounded_Omlex__prod(_820664, _820660, _820656)), _820666 = _820664, _820662 = _820660, _820658 = _820656], (39312 ^ _782476) ^ [_1539975, _1539977, _1539979] : [c_Wellfounded_Owf(_1539975, _1539977), -(hBOOL(hAPP(hAPP(c_member(_1539975), _1539979), c_Wellfounded_Oacc(_1539975, _1539977))))], (23968 ^ _782476) ^ [_1231836, _1231838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231838)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231836)), hAPP(c_Int_Onat, _1231838)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231836), _1231838)))], (46424 ^ _782476) ^ [_1713082] : [-(hAPP(c_Code__Numeral_Onat__of, _1713082) = c_Code__Numeral_Onat__of__aux(_1713082, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21311 ^ _782476) ^ [_1182639, _1182641, _1182643, _1182645, _1182647] : [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), _1182639), _1182641)), _1182643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182639), _1182645)), _1182647))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182647), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182639), _1182647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182639), _1182643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182645), _1182641)))], (31480 ^ _782476) ^ [_1378198, _1378200, _1378202] : [-(_1378198 = 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), _1378198), _1378200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378198), _1378202)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378200), _1378202))], (5092 ^ _782476) ^ [_860280, _860282, _860284, _860286] : [-(c_List_Olistrel(_860286, _860282) = c_List_Olistrel(_860284, _860280)), _860286 = _860284, _860282 = _860280], (28734 ^ _782476) ^ [_1328251, _1328253] : [class_Rings_Ocomm__semiring__1(_1328251), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1328251), _1328253), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1328253)], (36767 ^ _782476) ^ [_1482123, _1482125, _1482127, _1482129, _1482131, _1482133] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482123, tc_fun(_1482125, tc_HOL_Obool))), _1482127), _1482129), _1482131), _1482133)), -(hBOOL(hAPP(hAPP(_1482127, _1482131), _1482133))), -(hBOOL(hAPP(hAPP(_1482129, _1482131), _1482133)))], (46204 ^ _782476) ^ [_1708725, _1708727, _1708729] : [-(c_Enum_Osublists(_1708725, hAPP(hAPP(c_List_Olist_OCons(_1708725), _1708727), _1708729)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1708725)), tc_List_Olist(tc_List_Olist(_1708725))), c_Enum_Osublists(_1708725, _1708729)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1708725)), tc_List_Olist(tc_List_Olist(_1708725)), tc_List_Olist(tc_List_Olist(_1708725))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1708725)), tc_fun(tc_List_Olist(tc_List_Olist(_1708725)), tc_List_Olist(tc_List_Olist(_1708725))), tc_List_Olist(tc_List_Olist(_1708725))), c_List_Oappend(tc_List_Olist(_1708725))), hAPP(c_List_Omap(tc_List_Olist(_1708725), tc_List_Olist(_1708725)), hAPP(c_List_Olist_OCons(_1708725), _1708727)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1708725))))))], (40007 ^ _782476) ^ [_1560279, _1560281, _1560283] : [c_Fun_Obij__betw(_1560279, _1560279, c_Fun_Oid(_1560279), _1560281, _1560283), -(_1560281 = _1560283)], (21083 ^ _782476) ^ [_1178778, _1178780, _1178782] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178778), _1178780)), _1178782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178780), _1178782)))], (44268 ^ _782476) ^ [_1665568, _1665570] : [-(c_List_Olist_Olist__size(_1665568, _1665570, c_List_Olist_ONil(_1665568)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48417 ^ _782476) ^ [_1756521, _1756523] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1756521), _1756523) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1756521)), c_List_Oembed__list(_1756523))))], (26636 ^ _782476) ^ [_1285507, _1285509, _1285511] : [class_Orderings_Olinorder(_1285507), 26639 ^ _782476 : [(26646 ^ _782476) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285507), _1285509), _1285511) = _1285509, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285507), _1285509), _1285511)))], (26640 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285507), _1285509), _1285511)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285507), _1285509), _1285511) = _1285509)]]], (17694 ^ _782476) ^ [_1117924, _1117926, _1117928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117924), _1117926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117924), _1117928)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117926), _1117924)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117928), _1117924)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117926), _1117928))], (8086 ^ _782476) ^ [_920215, _920217, _920219] : [class_Lattices_Osemilattice__sup(_920215), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920215), _920217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920215), _920217), _920219))))], (43974 ^ _782476) ^ [_1659658, _1659660, _1659662, _1659664] : [hBOOL(hAPP(c_List_Odistinct(_1659658), _1659660)), -(hBOOL(hAPP(hAPP(c_member(_1659658), _1659662), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659658, tc_HOL_Obool)), hAPP(c_List_Oset(_1659658), _1659660)), hAPP(hAPP(c_Set_Oinsert(_1659658), hAPP(hAPP(c_List_Onth(_1659658), _1659660), _1659664)), c_Orderings_Obot__class_Obot(tc_fun(_1659658, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1659658), hAPP(hAPP(c_List_Olist__update(_1659658, _1659660), _1659664), _1659662))))], (28990 ^ _782476) ^ [_1332910, _1332912, _1332914] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332912), _1332914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332910), _1332912)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332910), _1332914)))], (21744 ^ _782476) ^ [_1190734, _1190736, _1190738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190734)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190736), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1190738)), 21754 ^ _782476 : [(21760 ^ _782476) ^ [] : [-(_1190736 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21756 ^ [_1190734, _1190736, _1190738]), 21753 ^ [_1190734, _1190736, _1190738]))], (21758 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21756 ^ [_1190734, _1190736, _1190738]), _1190738)))], (21755 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21753 ^ [_1190734, _1190736, _1190738]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190734))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190736), _1190734) = _1190736)], (52645 ^ _782476) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (18540 ^ _782476) ^ [_1131802, _1131804, _1131806] : [class_Groups_Oordered__comm__monoid__add(_1131802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131802), c_Groups_Ozero__class_Ozero(_1131802)), _1131804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131802), c_Groups_Ozero__class_Ozero(_1131802)), _1131806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131802), c_Groups_Ozero__class_Ozero(_1131802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131802), _1131804), _1131806))))], (37233 ^ _782476) ^ [_1491182, _1491184] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491182), _1491184)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491182), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491184)))], (37044 ^ _782476) ^ [_1487964, _1487966] : [c_Nitpick_Orefl_H(_1487964, _1487966), 37047 ^ _782476 : [(37048 ^ _782476) ^ [_1488042] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487964, _1487964)), hAPP(hAPP(c_Product__Type_OPair(_1487964, _1487964), _1488042), _1488042)), _1487966)))]]], (52677 ^ _782476) ^ [_1843533, _1843535, _1843537, _1843539, _1843541, _1843543] : [-(hAPP(hAPP(hAPP(c_COMBB(_1843533, _1843535, _1843537), _1843539), _1843541), _1843543) = hAPP(_1843539, hAPP(_1843541, _1843543)))], (2990 ^ _782476) ^ [_826825, _826827] : [_826827 = _826825, -(c_Nitpick_Onum(_826827) = c_Nitpick_Onum(_826825))], (15041 ^ _782476) ^ [_1063275, _1063277, _1063279, _1063281, _1063283, _1063285] : [c_Finite__Set_Ofolding(_1063275, _1063277, _1063279, _1063281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063275), _1063283)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063275), _1063285)), -(hAPP(c_Fun_Ocomp(_1063277, _1063277, _1063277, hAPP(_1063281, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063275, tc_HOL_Obool)), _1063283), _1063285))), hAPP(_1063281, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063275, tc_HOL_Obool)), _1063283), _1063285))) = hAPP(c_Fun_Ocomp(_1063277, _1063277, _1063277, hAPP(_1063281, _1063283)), hAPP(_1063281, _1063285)))], (28637 ^ _782476) ^ [_1325978, _1325980, _1325982, _1325984, _1325986] : [class_Groups_Ocomm__monoid__mult(_1325978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325980), _1325982)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325980), _1325984)), 28651 ^ _782476 : [(28654 ^ _782476) ^ [] : [hAPP(_1325986, 28650 ^ [_1325978, _1325980, _1325982, _1325984, _1325986]) = c_Groups_Oone__class_Oone(_1325978)], (28652 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325980), 28650 ^ [_1325978, _1325980, _1325982, _1325984, _1325986]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325980, tc_HOL_Obool)), _1325982), _1325984))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325980, _1325978), _1325986), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325980, tc_HOL_Obool)), _1325982), _1325984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325978), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325980, _1325978), _1325986), _1325982)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325980, _1325978), _1325986), _1325984)))], (42625 ^ _782476) ^ [_1622023, _1622025] : [c_Wellfounded_Owf(_1622023, _1622025), 42628 ^ _782476 : [(42629 ^ _782476) ^ [_1622155] : [42630 ^ _782476 : [(42631 ^ _782476) ^ [_1622260] : [hBOOL(hAPP(hAPP(c_member(_1622023), _1622260), _1622155))]], 42633 ^ _782476 : [(42636 ^ _782476) ^ [_1622382] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622023, _1622023)), hAPP(hAPP(c_Product__Type_OPair(_1622023, _1622023), _1622382), 42632 ^ [_1622023, _1622025, _1622155])), _1622025)), hBOOL(hAPP(hAPP(c_member(_1622023), _1622382), _1622155))], (42634 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622023), 42632 ^ [_1622023, _1622025, _1622155]), _1622155)))]]]]], (47120 ^ _782476) ^ [_1729454, _1729456, _1729458, _1729460, _1729462] : [class_Orderings_Olinorder(_1729454), -(hAPP(c_List_Ofilter(_1729456, _1729458), c_List_Olinorder__class_Osort__key(_1729456, _1729454, _1729460, _1729462)) = c_List_Olinorder__class_Osort__key(_1729456, _1729454, _1729460, hAPP(c_List_Ofilter(_1729456, _1729458), _1729462)))], (1542 ^ _782476) ^ [_804951, _804953] : [-(class_Groups_Ouminus(_804951)), _804953 = _804951, class_Groups_Ouminus(_804953)], (39517 ^ _782476) ^ [_1544901, _1544903, _1544905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544901, _1544903)), _1544905)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544903), hAPP(c_Relation_ORange(_1544901, _1544903), _1544905))))], (28960 ^ _782476) ^ [_1332301, _1332303, _1332305] : [class_Rings_Ocomm__semiring__1(_1332301), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332301), _1332303), hAPP(hAPP(c_Power_Opower__class_Opower(_1332301), _1332303), _1332305)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332301), _1332303), hAPP(c_Nat_OSuc, _1332305)))], (6373 ^ _782476) ^ [_884138, _884140] : [class_Orderings_Owellorder(_884138), 6378 ^ _782476 : [(6379 ^ _782476) ^ [_884232] : [hBOOL(hAPP(_884140, _884232))]], -(hBOOL(hAPP(_884140, c_Orderings_Oord__class_OLeast(_884138, _884140))))], (21421 ^ _782476) ^ [] : [-(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))))], (25590 ^ _782476) ^ [_1260772, _1260774, _1260776] : [-(hAPP(c_Set_OCollect(_1260772), hAPP(hAPP(c_COMBS(_1260772, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260772), c_fconj), _1260774)), _1260776)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1260772, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260772), _1260774)), hAPP(c_Set_OCollect(_1260772), _1260776)))], (34886 ^ _782476) ^ [_1441819, _1441821, _1441823, _1441825] : [-(c_Nat_Onat_Onat__case(_1441819, _1441821, _1441823, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441825)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1441819), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1441825))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1441819, _1441819), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1441819, tc_fun(_1441819, _1441819)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1441819, tc_fun(_1441819, _1441819)), tc_Int_Oint), c_If(_1441819)), c_Nat__Numeral_Oneg)), _1441821)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1441819, tc_Int_Oint), _1441823), c_Int_Onat))))], (41579 ^ _782476) ^ [_1598715, _1598717, _1598719] : [-(hAPP(c_Relation_Oconverse(_1598715, _1598717), _1598719) = hAPP(c_Set_OCollect(tc_prod(_1598717, _1598715)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598717, _1598715, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1598717, tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_fun(_1598715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598715, tc_fun(tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_fun(_1598715, tc_HOL_Obool)), _1598717), c_COMBC(_1598715, tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598715, tc_prod(_1598715, _1598717)), tc_fun(_1598715, tc_fun(tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_HOL_Obool)), _1598717), hAPP(c_COMBB(tc_prod(_1598715, _1598717), tc_fun(tc_fun(tc_prod(_1598715, _1598717), tc_HOL_Obool), tc_HOL_Obool), _1598715), c_member(tc_prod(_1598715, _1598717)))), hAPP(c_COMBC(_1598715, _1598717, tc_prod(_1598715, _1598717)), c_Product__Type_OPair(_1598715, _1598717))))), _1598719))))], (36721 ^ _782476) ^ [_1481223, _1481225, _1481227, _1481229, _1481231] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1481223, _1481225), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1481227), _1481229))), -(_1481225 = 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), _1481231), _1481223), _1481225), 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), _1481231), _1481227)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481231), _1481229)), _1481225))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481231), _1481229), _1481225)))))], (16943 ^ _782476) ^ [_1103118, _1103120, _1103122] : [class_Rings_Ocomm__semiring__1(_1103118), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103118), _1103120), _1103122) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103118), _1103122), _1103120))], (13636 ^ _782476) ^ [_1035162, _1035164, _1035166, _1035168, _1035170, _1035172] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035162, _1035164, _1035166, hAPP(c_COMBK(_1035164, _1035162), _1035168)), _1035170), _1035172) = _1035168)], (46804 ^ _782476) ^ [_1721893, _1721895, _1721897, _1721899, _1721901] : [c_List_Olist__all2(_1721893, _1721895, _1721897, _1721899, _1721901), 46807 ^ _782476 : [(46810 ^ _782476) ^ [_1722056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722056), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721893)), _1721899))), -(hBOOL(hAPP(hAPP(_1721897, hAPP(hAPP(c_List_Onth(_1721893), _1721899), _1722056)), hAPP(hAPP(c_List_Onth(_1721895), _1721901), _1722056))))], (46808 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721893)), _1721899) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721895)), _1721901))]]], (22646 ^ _782476) ^ [_1207219, _1207221] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207219), _1207221)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207219)), hAPP(c_Nat_OSuc, _1207221)))], (6407 ^ _782476) ^ [_884675, _884677, _884679, _884681, _884683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884675, tc_HOL_Obool)), _884677), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884679, tc_fun(_884675, tc_HOL_Obool)), _884681), _884683))), 6410 ^ _782476 : [(6411 ^ _782476) ^ [_884808] : [hBOOL(hAPP(hAPP(c_member(_884679), _884808), _884681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884675, tc_HOL_Obool)), _884677), hAPP(_884683, _884808))))]]], (20853 ^ _782476) ^ [_1174527, _1174529, _1174531, _1174533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174527, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174527, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20854 ^ [_1174527, _1174529, _1174531, _1174533])), _1174529)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174527, 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), 20854 ^ [_1174527, _1174529, _1174531, _1174533]), _1174531))), _1174533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174527, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174527, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174529)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174527, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174533))))], (26966 ^ _782476) ^ [_1291886, _1291888, _1291890, _1291892] : [class_Orderings_Olinorder(_1291886), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291886), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291886), _1291888), _1291890)), _1291892) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291886), _1291888), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291886), _1291890), _1291892)))], (17724 ^ _782476) ^ [_1118478, _1118480, _1118482, _1118484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118478), _1118480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118482), _1118484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118478), _1118482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118480), _1118484))))], (18666 ^ _782476) ^ [_1134041, _1134043, _1134045, _1134047, _1134049] : [class_Rings_Oordered__semiring(_1134041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134041), _1134043), _1134045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134041), _1134047), _1134049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134041), c_Groups_Ozero__class_Ozero(_1134041)), _1134045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134041), c_Groups_Ozero__class_Ozero(_1134041)), _1134047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134041), _1134043), _1134047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134041), _1134045), _1134049))))], (52527 ^ _782476) ^ [_1841956] : [class_Finite__Set_Ofinite(_1841956), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1841956)))], (37744 ^ _782476) ^ [_1500915, _1500917] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1500915), _1500917) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1500915, _1500917)))], (35110 ^ _782476) ^ [_1446248, _1446250, _1446252] : [-(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), _1446248)), 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))), _1446250))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1446252))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1446252)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446248), 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), _1446252), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1446250)))))], (39798 ^ _782476) ^ [_1553319, _1553321] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553319, _1553319), tc_HOL_Obool)), c_Relation_OId__on(_1553319, _1553321)), hAPP(hAPP(c_Product__Type_OSigma(_1553319, _1553319), _1553321), hAPP(c_COMBK(tc_fun(_1553319, tc_HOL_Obool), _1553319), _1553321)))))], (3712 ^ _782476) ^ [_838102, _838104] : [_838104 = _838102, -(c_List_Omonoid__add__class_Olistsum(_838104) = c_List_Omonoid__add__class_Olistsum(_838102))], (51859 ^ _782476) ^ [_1832909, _1832911, _1832913, _1832915] : [class_Rings_Ocomm__semiring__1(_1832909), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832909), _1832911), _1832913)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832909), _1832911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832909), _1832913), _1832915))))], (13908 ^ _782476) ^ [_1040623, _1040625, _1040627, _1040629, _1040631, _1040633, _1040635] : [c_Fun_Obij__betw(_1040623, _1040625, _1040627, _1040629, _1040631), c_Fun_Obij__betw(_1040623, _1040625, _1040627, _1040633, _1040635), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040625, tc_HOL_Obool)), _1040631), _1040635) = c_Orderings_Obot__class_Obot(tc_fun(_1040625, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1040623, _1040625, _1040627, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040623, tc_HOL_Obool)), _1040629), _1040633), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040625, tc_HOL_Obool)), _1040631), _1040635)))], (35432 ^ _782476) ^ [_1451939, _1451941] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1451939)), c_Int_OBit1(_1451941)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1451939)), _1451941)))], (7167 ^ _782476) ^ [_901504, _901506, _901508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901504, tc_HOL_Obool)), _901506), _901508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901504, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901504, tc_fun(_901504, tc_HOL_Obool), tc_HOL_Obool), c_member(_901504)), _901506)), hAPP(hAPP(c_COMBC(_901504, tc_fun(_901504, tc_HOL_Obool), tc_HOL_Obool), c_member(_901504)), _901508))))], (3048 ^ _782476) ^ [_827684, _827686, _827688, _827690, _827692, _827694, _827696, _827698, _827700, _827702, _827704, _827706] : [-(c_Product__Type_Omap__pair(_827706, _827702, _827698, _827694, _827690, _827686) = c_Product__Type_Omap__pair(_827704, _827700, _827696, _827692, _827688, _827684)), _827706 = _827704, _827702 = _827700, _827698 = _827696, _827694 = _827692, _827690 = _827688, _827686 = _827684], (5777 ^ _782476) ^ [_873788, _873790, _873792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873788, tc_HOL_Obool)), _873790), _873792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873788, tc_HOL_Obool)), _873792), _873790)), -(_873790 = _873792)], (17972 ^ _782476) ^ [_1123229, _1123231] : [class_Rings_Olinordered__semidom(_1123229), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123229), c_Groups_Ozero__class_Ozero(_1123229)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123229), _1123231))))], (48324 ^ _782476) ^ [_1754639, _1754641, _1754643] : [48326 ^ _782476 : [(48329 ^ _782476) ^ [] : [hBOOL(hAPP(_1754641, 48325 ^ [_1754639, _1754641, _1754643]))], (48327 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754639), 48325 ^ [_1754639, _1754641, _1754643]), hAPP(c_List_Oset(_1754639), _1754643))))]], -(c_List_OtakeWhile(_1754639, _1754641, _1754643) = _1754643)], (4480 ^ _782476) ^ [_850446, _850448, _850450, _850452] : [-(c_List_Omap(_850452, _850448) = c_List_Omap(_850450, _850446)), _850452 = _850450, _850448 = _850446], (2312 ^ _782476) ^ [_816340, _816342] : [_816342 = _816340, -(c_Int_Opred(_816342) = c_Int_Opred(_816340))], (24917 ^ _782476) ^ [_1248416, _1248418, _1248420] : [class_Groups_Oordered__ab__group__add__abs(_1248416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248416), hAPP(c_Groups_Oabs__class_Oabs(_1248416), _1248418)), _1248420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248416), _1248418), _1248420)))], (36012 ^ _782476) ^ [_1463096] : [c_Int_OBit1(_1463096) = c_Int_OMin, -(_1463096 = c_Int_OMin)], (8627 ^ _782476) ^ [_932459, _932461] : [class_Lattices_Osemilattice__inf(_932459), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932459), _932461), _932461) = _932461)], (40161 ^ _782476) ^ [_1563924, _1563926, _1563928, _1563930, _1563932, _1563934, _1563936] : [-(hAPP(c_Product__Type_Ofst(_1563924, _1563926), hAPP(c_Product__Type_Omap__pair(_1563928, _1563924, _1563930, _1563926, _1563932, _1563934), _1563936)) = hAPP(_1563932, hAPP(c_Product__Type_Ofst(_1563928, _1563930), _1563936)))], (41505 ^ _782476) ^ [_1596834, _1596836, _1596838] : [c_Equiv__Relations_Oequiv(_1596834, _1596836, _1596838), -(hAPP(hAPP(c_Relation_Orel__comp(_1596834, _1596834, _1596834), hAPP(c_Relation_Oconverse(_1596834, _1596834), _1596838)), _1596838) = _1596838)], (21379 ^ _782476) ^ [_1183892, _1183894] : [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)), _1183892)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183892), _1183894)))], (2292 ^ _782476) ^ [_816034, _816036] : [_816036 = _816034, -(c_Int_Oring__1__class_OInts(_816036) = c_Int_Oring__1__class_OInts(_816034))], (7531 ^ _782476) ^ [_908708, _908710, _908712] : [class_Groups_Oordered__ab__group__add(_908708), 7534 ^ _782476 : [(7541 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908708), _908712), hAPP(c_Groups_Ouminus__class_Ouminus(_908708), _908710))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908708), _908710), hAPP(c_Groups_Ouminus__class_Ouminus(_908708), _908712))))], (7535 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908708), _908710), hAPP(c_Groups_Ouminus__class_Ouminus(_908708), _908712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908708), _908712), hAPP(c_Groups_Ouminus__class_Ouminus(_908708), _908710))))]]], (17181 ^ _782476) ^ [_1108845, _1108847, _1108849] : [-(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)), _1108845)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108847, _1108849)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108847), _1108845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108849), _1108845)))], (47297 ^ _782476) ^ [_1734104] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1734104)), c_List_Otranspose__rel(_1734104)), c_List_Olist_ONil(tc_List_Olist(_1734104)))), -(c_List_Otranspose(_1734104, c_List_Olist_ONil(tc_List_Olist(_1734104))) = c_List_Olist_ONil(tc_List_Olist(_1734104)))], (36036 ^ _782476) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (7911 ^ _782476) ^ [_916929, _916931, _916933, _916935] : [7925 ^ _782476 : [(7928 ^ _782476) ^ [] : [-(hBOOL(hAPP(_916935, 7924 ^ [_916929, _916931, _916933, _916935])))], (7926 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916929), 7924 ^ [_916929, _916931, _916933, _916935]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916929, tc_HOL_Obool)), _916931), _916933))))]], 7912 ^ _782476 : [(7919 ^ _782476) ^ [_917138] : [hBOOL(hAPP(hAPP(c_member(_916929), _917138), _916933)), hBOOL(hAPP(_916935, _917138))], (7913 ^ _782476) ^ [_917042] : [hBOOL(hAPP(hAPP(c_member(_916929), _917042), _916931)), hBOOL(hAPP(_916935, _917042))]]], (11772 ^ _782476) ^ [_996823, _996825, _996827, _996829] : [class_Lattices_Osemilattice__sup(_996823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996823), _996825), _996827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996823), _996825), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996823), _996827), _996829))))], (31389 ^ _782476) ^ [_1376370, _1376372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376370))), -(c_SMT_Oz3div(_1376372, _1376370) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376372), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376370))))], (38712 ^ _782476) ^ [_1523924, _1523926] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523924, _1523924)), _1523926)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523924), hAPP(c_Relation_OField(_1523924), _1523926))))], (31614 ^ _782476) ^ [_1380616, _1380618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1380616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380616), _1380618)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380618), _1380616) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1380618), _1380616)), _1380616)))], (42776 ^ _782476) ^ [_1625747, _1625749, _1625751] : [-(c_Nitpick_Oof__frac(_1625749, _1625747, _1625751) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1625747), hAPP(c_Int_Oring__1__class_Oof__int(_1625747), hAPP(c_Nitpick_Onum(_1625749), _1625751))), hAPP(c_Int_Oring__1__class_Oof__int(_1625747), hAPP(c_Nitpick_Odenom(_1625749), _1625751)))), class_Rings_Oinverse(_1625747), class_Rings_Oring__1(_1625747)], (41034 ^ _782476) ^ [_1584634, _1584636] : [-(c_Transitive__Closure_Otrancl(_1584634, _1584636) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584634, _1584634), tc_HOL_Obool)), _1584636), hAPP(hAPP(c_Relation_Orel__comp(_1584634, _1584634, _1584634), c_Transitive__Closure_Otrancl(_1584634, _1584636)), _1584636)))], (50997 ^ _782476) ^ [_1814833, _1814835] : [c_Relation_Osym(_1814833, _1814835), -(c_Relation_Osym(_1814833, c_Transitive__Closure_Otrancl(_1814833, _1814835)))], (16495 ^ _782476) ^ [_1093094, _1093096, _1093098, _1093100] : [class_Rings_Ocomm__semiring__1(_1093094), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093094), _1093096), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093094), _1093098), _1093100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093094), _1093098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093094), _1093096), _1093100)))], (32211 ^ _782476) ^ [_1392591, _1392593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392591)), -(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, _1392593, _1392591))))], (48731 ^ _782476) ^ [_1763100, _1763102, _1763104] : [hBOOL(hAPP(hAPP(c_member(_1763100), _1763102), hAPP(c_List_Oset(_1763100), _1763104))), -(c_List_Oinsert(_1763100, _1763102, _1763104) = _1763104)], (11260 ^ _782476) ^ [_989066, _989068, _989070] : [class_Orderings_Opreorder(_989066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989066), _989068), _989070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989066), _989070), _989068))], (45541 ^ _782476) ^ [_1694090, _1694092, _1694094] : [class_Orderings_Olinorder(_1694090), -(c_Big__Operators_Olattice_OSup__fin(_1694090, c_Orderings_Oord__class_Omax(_1694090), hAPP(c_List_Oset(_1694090), hAPP(hAPP(c_List_Olist_OCons(_1694090), _1694092), _1694094))) = hAPP(c_List_Ofoldl(_1694090, _1694090, c_Orderings_Oord__class_Omax(_1694090), _1694092), _1694094))], (49832 ^ _782476) ^ [_1788927, _1788929, _1788931, _1788933, _1788935] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788929, _1788927)), hAPP(hAPP(c_Product__Type_OPair(_1788929, _1788927), _1788933), _1788935)), hAPP(c_Relation_Oconverse(_1788927, _1788929), _1788931))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788927, _1788929, hAPP(hAPP(c_COMBC(_1788927, tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_fun(_1788929, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788929, tc_fun(tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_fun(_1788929, tc_HOL_Obool)), _1788927), c_COMBC(_1788929, tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788929, tc_prod(_1788927, _1788929)), tc_fun(_1788929, tc_fun(tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_HOL_Obool)), _1788927), hAPP(c_COMBB(tc_prod(_1788927, _1788929), tc_fun(tc_fun(tc_prod(_1788927, _1788929), tc_HOL_Obool), tc_HOL_Obool), _1788929), c_member(tc_prod(_1788927, _1788929)))), c_Product__Type_OPair(_1788927, _1788929)))), _1788931)), _1788933), _1788935)))], (712 ^ _782476) ^ [_793348, _793350, _793352, _793354] : [-(c_FunDef_Ois__measure(_793352, _793348)), c_FunDef_Ois__measure(_793354, _793350), _793354 = _793352, _793350 = _793348], (46892 ^ _782476) ^ [_1723946, _1723948] : [c_List_Olist_ONil(_1723946) = c_List_Oremdups(_1723946, _1723948), -(_1723948 = c_List_Olist_ONil(_1723946))], (37355 ^ _782476) ^ [_1493307, _1493309, _1493311] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493307, _1493309), _1493311)), -(c_Divides_Odivmod__nat(_1493307, _1493309) = _1493311)], (28209 ^ _782476) ^ [_1315834, _1315836, _1315838] : [class_Orderings_Olinorder(_1315834), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315834), _1315836)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315834), _1315838)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315834, tc_HOL_Obool)), _1315836), _1315838) = c_Orderings_Obot__class_Obot(tc_fun(_1315834, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315834), c_Big__Operators_Olattice_OInf__fin(_1315834, c_Orderings_Oord__class_Omin(_1315834), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315834, tc_HOL_Obool)), _1315836), _1315838))), c_Big__Operators_Olattice_OInf__fin(_1315834, c_Orderings_Oord__class_Omin(_1315834), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315834, tc_HOL_Obool)), _1315836), _1315838))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315834), c_Big__Operators_Olattice_OInf__fin(_1315834, c_Orderings_Oord__class_Omin(_1315834), _1315836)), c_Big__Operators_Olattice_OInf__fin(_1315834, c_Orderings_Oord__class_Omin(_1315834), _1315838)))], (19835 ^ _782476) ^ [_1154797, _1154799, _1154801] : [class_Groups_Oordered__comm__monoid__add(_1154797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154797), _1154799), c_Groups_Ozero__class_Ozero(_1154797))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154797), _1154801), c_Groups_Ozero__class_Ozero(_1154797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154797), _1154799), _1154801)), c_Groups_Ozero__class_Ozero(_1154797))))], (36695 ^ _782476) ^ [_1480761, _1480763, _1480765, _1480767] : [_1480761 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1480763), _1480765)), _1480767), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480761, _1480763), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480765), _1480767)))), 36702 ^ _782476 : [(36705 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480767), _1480763))], (36703 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480763)))]], 36710 ^ _782476 : [(36713 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480763), _1480767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480767), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36711 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480763))]]], (34942 ^ _782476) ^ [_1443190] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443190)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443190)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1443190)))], (10445 ^ _782476) ^ [_972556, _972558, _972560, _972562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972556, tc_HOL_Obool)), _972558), hAPP(hAPP(c_Set_Oinsert(_972556), _972560), _972562))), 10448 ^ _782476 : [(10455 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972556), _972560), _972558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972556, tc_HOL_Obool)), _972558), _972562)))], (10449 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972556), _972560), _972558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972556, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972556, tc_HOL_Obool)), _972558), hAPP(hAPP(c_Set_Oinsert(_972556), _972560), c_Orderings_Obot__class_Obot(tc_fun(_972556, tc_HOL_Obool))))), _972562)))]]], (38248 ^ _782476) ^ [_1512597, _1512599, _1512601, _1512603, _1512605, _1512607] : [c_Equiv__Relations_Ocongruent(_1512597, _1512599, _1512601, _1512603), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512597, _1512597)), hAPP(hAPP(c_Product__Type_OPair(_1512597, _1512597), _1512605), _1512607)), _1512601)), -(hAPP(_1512603, _1512605) = hAPP(_1512603, _1512607))], (41469 ^ _782476) ^ [_1596109, _1596111, _1596113] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596109, _1596111)), hAPP(c_Relation_Oconverse(_1596111, _1596109), _1596113))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596111, _1596109)), _1596113)))], (51979 ^ _782476) ^ [_1835434, _1835436, _1835438, _1835440] : [class_Divides_Osemiring__div(_1835434), -(_1835436 = c_Groups_Ozero__class_Ozero(_1835434)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835434), _1835436), _1835438)), 51990 ^ _782476 : [(51997 ^ _782476) ^ [] : [_1835438 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835434), _1835440), _1835436), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1835434), _1835438), _1835436) = _1835440)], (51991 ^ _782476) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1835434), _1835438), _1835436) = _1835440, -(_1835438 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835434), _1835440), _1835436))]]], (39841 ^ _782476) ^ [_1554549, _1554551, _1554553, _1554555, _1554557, _1554559] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554549, _1554551)), hAPP(hAPP(c_Product__Type_OPair(_1554549, _1554551), _1554553), _1554555)), hAPP(hAPP(c_Product__Type_OSigma(_1554549, _1554551), _1554557), _1554559))), 39844 ^ _782476 : [(39847 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554551), _1554555), hAPP(_1554559, _1554553))))], (39845 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554549), _1554553), _1554557)))]]], (51629 ^ _782476) ^ [_1828702, _1828704, _1828706, _1828708, _1828710] : [-(c_New__DSequence_Opos__map(_1828702, _1828704, _1828706, _1828708, _1828710) = c_Lazy__Sequence_Omap(_1828702, _1828704, _1828706, hAPP(_1828708, _1828710)))], (13674 ^ _782476) ^ [_1035950, _1035952, _1035954, _1035956, _1035958, _1035960, _1035962, _1035964, _1035966] : [hAPP(c_Fun_Ocomp(_1035950, _1035952, _1035954, _1035956), _1035958) = hAPP(c_Fun_Ocomp(_1035960, _1035952, _1035954, _1035962), _1035964), -(hAPP(_1035956, hAPP(_1035958, _1035966)) = hAPP(_1035962, hAPP(_1035964, _1035966)))], (35648 ^ _782476) ^ [_1455890, _1455892] : [class_Rings_Olinordered__idom(_1455890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455890), hAPP(hAPP(c_Power_Opower__class_Opower(_1455890), _1455892), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1455890)))], (34338 ^ _782476) ^ [_1432763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432763), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432763)), c_Int_OPls)))], (35416 ^ _782476) ^ [_1451666, _1451668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451666)), c_Int_OBit0(_1451668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451666), _1451668)))], (4696 ^ _782476) ^ [_854006, _854008, _854010, _854012, _854014, _854016] : [-(c_FunDef_OTHE__default(_854016, _854012, _854008) = c_FunDef_OTHE__default(_854014, _854010, _854006)), _854016 = _854014, _854012 = _854010, _854008 = _854006], (22469 ^ _782476) ^ [_1203912, _1203914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203912), _1203914)), -(_1203914 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203912), 22472 ^ [_1203912, _1203914])))], (25892 ^ _782476) ^ [_1270224, _1270226, _1270228] : [class_Lattices_Odistrib__lattice(_1270224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270224), _1270226)), -(_1270226 = c_Orderings_Obot__class_Obot(tc_fun(_1270224, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270224), _1270228)), -(_1270228 = c_Orderings_Obot__class_Obot(tc_fun(_1270224, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270224), c_Big__Operators_Olattice__class_OInf__fin(_1270224, _1270226)), c_Big__Operators_Olattice__class_OInf__fin(_1270224, _1270228)) = c_Big__Operators_Olattice__class_OInf__fin(_1270224, hAPP(c_Set_OCollect(_1270224), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_HOL_Obool), tc_HOL_Obool, _1270224), c_HOL_OEx(_1270224)), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool)), tc_fun(_1270224, tc_HOL_Obool), _1270224), hAPP(c_COMBB(tc_fun(_1270224, tc_HOL_Obool), tc_HOL_Obool, _1270224), c_HOL_OEx(_1270224))), hAPP(hAPP(c_COMBC(_1270224, tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool)), tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_fun(tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool))), tc_fun(tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool)), tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool))), _1270224), c_COMBS(_1270224, tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_fun(_1270224, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1270224, tc_fun(tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool))), _1270224), hAPP(c_COMBB(tc_fun(_1270224, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool)), _1270224), c_COMBS(_1270224, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool)), tc_fun(_1270224, tc_fun(_1270224, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1270224), hAPP(c_COMBB(tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1270224), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270224), c_fconj))), hAPP(hAPP(c_COMBC(_1270224, tc_fun(_1270224, tc_fun(_1270224, _1270224)), tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1270224, _1270224), tc_fun(_1270224, tc_HOL_Obool)), tc_fun(tc_fun(_1270224, tc_fun(_1270224, _1270224)), tc_fun(_1270224, tc_fun(_1270224, tc_HOL_Obool))), _1270224), c_COMBB(tc_fun(_1270224, _1270224), tc_fun(_1270224, tc_HOL_Obool), _1270224)), hAPP(hAPP(c_COMBB(tc_fun(_1270224, tc_HOL_Obool), tc_fun(tc_fun(_1270224, _1270224), tc_fun(_1270224, tc_HOL_Obool)), _1270224), c_COMBB(_1270224, tc_HOL_Obool, _1270224)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1270224)))))), hAPP(hAPP(c_COMBC(_1270224, tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1270224, tc_HOL_Obool), tc_fun(_1270224, tc_HOL_Obool)), _1270224), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1270224)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270224), c_fconj), hAPP(hAPP(c_COMBC(_1270224, tc_fun(_1270224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270224)), _1270226)))), hAPP(hAPP(c_COMBC(_1270224, tc_fun(_1270224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270224)), _1270228))))))))], (23753 ^ _782476) ^ [_1228413, _1228415] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228413) = _1228415), _1228413 = hAPP(c_Int_Onat, _1228415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228415))], (37413 ^ _782476) ^ [_1494392, _1494394] : [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), _1494392), _1494394))), 37416 ^ _782476 : [(37423 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494394), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 37426 ^ _782476 : [(37435 ^ _782476) ^ [] : [-(c_Nitpick_Onorm__frac(_1494392, _1494394) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1494392), _1494394)), 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), _1494392))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1494394)))), -(_1494392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1494394 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37427 ^ _782476) ^ [] : [37428 ^ _782476 : [(37431 ^ _782476) ^ [] : [_1494394 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (37429 ^ _782476) ^ [] : [_1494392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1494392, _1494394) = 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)))]]], (37417 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494394), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1494392, _1494394) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494392), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494394)))]]], (34212 ^ _782476) ^ [_1430865, _1430867] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430865))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430865)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430867)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22302 ^ _782476) ^ [_1201233, _1201235, _1201237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201233), _1201235)), -(hAPP(c_Finite__Set_Ocard(_1201233), hAPP(hAPP(c_Set_Oinsert(_1201233), _1201237), _1201235)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1201233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201233, tc_HOL_Obool)), _1201235), hAPP(hAPP(c_Set_Oinsert(_1201233), _1201237), c_Orderings_Obot__class_Obot(tc_fun(_1201233, tc_HOL_Obool)))))))], (34274 ^ _782476) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (48130 ^ _782476) ^ [_1750531, _1750533, _1750535] : [hAPP(c_List_Orev(_1750531), _1750533) = _1750535, -(_1750533 = hAPP(c_List_Orev(_1750531), _1750535))], (32821 ^ _782476) ^ [_1404833, _1404835, _1404837, _1404839, _1404841] : [-(hAPP(c_Relation_OImage(_1404833, _1404835, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1404833, _1404835), tc_HOL_Obool)), _1404837), _1404839)), _1404841) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404835, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404833, _1404835, _1404837), _1404841)), hAPP(c_Relation_OImage(_1404833, _1404835, _1404839), _1404841)))], (7750 ^ _782476) ^ [_913501, _913503, _913505, _913507] : [class_Lattices_Osemilattice__sup(_913501), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913501), _913503), _913505)), _913507) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913501), _913503), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913501), _913505), _913507)))], (50741 ^ _782476) ^ [_1809829, _1809831] : [c_Predicate_Oreflp(_1809829, _1809831), c_Predicate_Osymp(_1809829, _1809831), c_Predicate_Otransp(_1809829, _1809831), -(c_Equiv__Relations_Oequivp(_1809829, _1809831))], (52401 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (45392 ^ _782476) ^ [_1690918, _1690920, _1690922] : [-(hAPP(hAPP(c_List_Odrop(_1690918), hAPP(c_Nat_OSuc, _1690920)), _1690922) = hAPP(hAPP(c_List_Odrop(_1690918), _1690920), hAPP(c_List_Otl(_1690918), _1690922)))], (34848 ^ _782476) ^ [_1440976, _1440978] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440976)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440978)) = 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)))), _1440976)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440978)))], (17549 ^ _782476) ^ [_1115126, _1115128] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115126), _1115128))))], (50060 ^ _782476) ^ [_1793217, _1793219, _1793221] : [_1793217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1793219), c_List_Oreplicate(_1793219, _1793217, _1793221)) = c_Orderings_Obot__class_Obot(tc_fun(_1793219, tc_HOL_Obool)))], (21495 ^ _782476) ^ [_1185815, _1185817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185815), _1185817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185815)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185817))))], (40067 ^ _782476) ^ [_1561368, _1561370, _1561372, _1561374, _1561376, _1561378] : [class_Groups_Ocomm__monoid__mult(_1561368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561370), _1561372)), 40077 ^ _782476 : [(40080 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561374), hAPP(_1561376, 40076 ^ [_1561368, _1561370, _1561372, _1561374, _1561376, _1561378])))], (40078 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561370), 40076 ^ [_1561368, _1561370, _1561372, _1561374, _1561376, _1561378]), _1561372)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561370, _1561368), hAPP(hAPP(c_COMBS(_1561370, tc_fun(_1561374, tc_HOL_Obool), _1561368), hAPP(hAPP(c_COMBB(tc_fun(_1561374, _1561368), tc_fun(tc_fun(_1561374, tc_HOL_Obool), _1561368), _1561370), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561374, _1561368)), _1561378)), _1561376)), _1561372) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1561370, _1561374), _1561368), hAPP(c_Product__Type_Oprod_Oprod__case(_1561370, _1561374, _1561368), _1561378)), hAPP(hAPP(c_Product__Type_OSigma(_1561370, _1561374), _1561372), _1561376)))], (120 ^ _782476) ^ [_784448, _784450, _784452, _784454, _784456, _784458, _784460, _784462] : [-(c_Finite__Set_Ofolding__idem(_784460, _784456, _784452, _784448)), c_Finite__Set_Ofolding__idem(_784462, _784458, _784454, _784450), _784462 = _784460, _784458 = _784456, _784454 = _784452, _784450 = _784448], (18400 ^ _782476) ^ [_1129478, _1129480, _1129482] : [18401 ^ _782476 : [(18404 ^ _782476) ^ [] : [_1129478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18402 ^ _782476) ^ [] : [_1129480 = _1129482]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129478), _1129480) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129478), _1129482))], (2168 ^ _782476) ^ [_814150, _814152] : [_814152 = _814150, -(c_SetInterval_Oord__class_OgreaterThan(_814152) = c_SetInterval_Oord__class_OgreaterThan(_814150))], (49826 ^ _782476) ^ [_1788544, _1788546, _1788548, _1788550, _1788552] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788544, _1788546, hAPP(hAPP(c_COMBC(_1788544, tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_fun(_1788546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788546, tc_fun(tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_fun(_1788546, tc_HOL_Obool)), _1788544), c_COMBC(_1788546, tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788546, tc_prod(_1788544, _1788546)), tc_fun(_1788546, tc_fun(tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_HOL_Obool)), _1788544), hAPP(c_COMBB(tc_prod(_1788544, _1788546), tc_fun(tc_fun(tc_prod(_1788544, _1788546), tc_HOL_Obool), tc_HOL_Obool), _1788546), c_member(tc_prod(_1788544, _1788546)))), c_Product__Type_OPair(_1788544, _1788546)))), _1788548)), _1788550), _1788552)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788546, _1788544)), hAPP(hAPP(c_Product__Type_OPair(_1788546, _1788544), _1788550), _1788552)), hAPP(c_Relation_Oconverse(_1788544, _1788546), _1788548))))], (50260 ^ _782476) ^ [_1797608, _1797610, _1797612, _1797614, _1797616, _1797618] : [-(c_Nitpick_Opair__box_Opair__box__case(_1797608, _1797610, _1797612, _1797614, c_Nitpick_Opair__box_OPairBox(_1797608, _1797610, _1797616, _1797618)) = hAPP(hAPP(_1797614, _1797616), _1797618))], (40149 ^ _782476) ^ [_1563533, _1563535, _1563537, _1563539, _1563541, _1563543, _1563545, _1563547, _1563549] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563533, _1563535)), hAPP(hAPP(c_Product__Type_OPair(_1563533, _1563535), _1563537), _1563539)), _1563541)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563543, _1563545)), hAPP(hAPP(c_Product__Type_OPair(_1563543, _1563545), hAPP(_1563547, _1563537)), hAPP(_1563549, _1563539))), hAPP(c_Set_Oimage(tc_prod(_1563533, _1563535), tc_prod(_1563543, _1563545), c_Product__Type_Omap__pair(_1563533, _1563543, _1563535, _1563545, _1563547, _1563549)), _1563541))))], (48008 ^ _782476) ^ [_1747763, _1747765, _1747767] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747763), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1747763))), _1747765))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747767), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1747763))), _1747765))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747763), _1747763), hAPP(hAPP(c_COMBC(tc_List_Olist(_1747763), tc_Nat_Onat, _1747763), c_List_Onth(_1747763)), _1747767)), hAPP(c_List_Ofilter(tc_List_Olist(_1747763), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1747763)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747767)), c_Nat_Osize__class_Osize(tc_List_Olist(_1747763)))), c_List_Otranspose(_1747763, _1747765))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1747763)), _1747765), _1747767))], (35714 ^ _782476) ^ [_1456902, _1456904] : [class_Rings_Oring__1__no__zero__divisors(_1456902), 35717 ^ _782476 : [(35718 ^ _782476) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1456902), _1456904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456902), -(_1456904 = c_Groups_Oone__class_Oone(_1456902)), -(_1456904 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456902), c_Groups_Oone__class_Oone(_1456902)))], (35728 ^ _782476) ^ [] : [35729 ^ _782476 : [(35732 ^ _782476) ^ [] : [_1456904 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456902), c_Groups_Oone__class_Oone(_1456902))], (35730 ^ _782476) ^ [] : [_1456904 = c_Groups_Oone__class_Oone(_1456902)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1456902), _1456904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456902))]]], (25470 ^ _782476) ^ [_1258456, _1258458] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258456))), -(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)), _1258456))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258458)))) = 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)), _1258456))), 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, _1258458))))))], (26250 ^ _782476) ^ [_1278602, _1278604, _1278606, _1278608] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278602, tc_Nat_Onat), _1278604), _1278606) = hAPP(c_Nat_OSuc, _1278608), 26254 ^ _782476 : [(26257 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1278604, 26253 ^ [_1278602, _1278604, _1278606, _1278608]))))], (26255 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278602), 26253 ^ [_1278602, _1278604, _1278606, _1278608]), _1278606)))]]], (34108 ^ _782476) ^ [_1429064, _1429066] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429064) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429066), 34111 ^ _782476 : [(34118 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429064)))), 34121 ^ _782476 : [(34128 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429066)))), -(_1429064 = _1429066)], (34122 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429066))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429064) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (34112 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429066)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (38220 ^ _782476) ^ [_1512009, _1512011, _1512013, _1512015, _1512017, _1512019, _1512021, _1512023] : [c_Equiv__Relations_Oequiv(_1512009, _1512011, _1512013), c_Equiv__Relations_Ocongruent2(_1512009, _1512015, _1512017, _1512013, _1512019, _1512021), hBOOL(hAPP(hAPP(c_member(_1512009), _1512023), _1512011)), -(c_Equiv__Relations_Ocongruent(_1512015, _1512017, _1512019, hAPP(_1512021, _1512023)))], (51293 ^ _782476) ^ [_1820401, _1820403] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1820401), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1820403, hAPP(c_Code__Numeral_Onat__of, 51298 ^ [_1820401, _1820403]))), -(hBOOL(hAPP(_1820403, _1820401)))], (41720 ^ _782476) ^ [_1602123, _1602125, _1602127, _1602129, _1602131] : [c_Relation_Osingle__valued(_1602123, _1602123, _1602125), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602123, _1602123)), hAPP(hAPP(c_Product__Type_OPair(_1602123, _1602123), _1602127), _1602129)), c_Transitive__Closure_Ortrancl(_1602123, _1602125))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602123, _1602123)), hAPP(hAPP(c_Product__Type_OPair(_1602123, _1602123), _1602127), _1602131)), c_Transitive__Closure_Ortrancl(_1602123, _1602125))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602123, _1602123)), hAPP(hAPP(c_Product__Type_OPair(_1602123, _1602123), _1602129), _1602131)), c_Transitive__Closure_Ortrancl(_1602123, _1602125)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602123, _1602123)), hAPP(hAPP(c_Product__Type_OPair(_1602123, _1602123), _1602131), _1602129)), c_Transitive__Closure_Ortrancl(_1602123, _1602125))))], (40796 ^ _782476) ^ [_1579692, _1579694, _1579696, _1579698, _1579700] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579692, _1579694, _1579692, _1579696), hAPP(c_Product__Type_OPair(_1579694, _1579692), _1579698)), _1579700) = hAPP(_1579700, _1579698))], (32169 ^ _782476) ^ [_1391892, _1391894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1391892), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391894), _1391892)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391892, _1391894) = _1391892)], (11006 ^ _782476) ^ [_985485, _985487, _985489, _985491] : [-(c_Fun_Ofun__upd(_985485, _985487, _985489, _985491, hAPP(_985489, _985491)) = _985489)], (21367 ^ _782476) ^ [_1183661, _1183663] : [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)), _1183661)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183661), _1183663)))], (16859 ^ _782476) ^ [_1100802, _1100804, _1100806, _1100808, _1100810] : [class_Groups_Ocomm__monoid__add(_1100802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100804), _1100806)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100804, _1100802), hAPP(hAPP(c_COMBS(_1100804, _1100802, _1100802), hAPP(hAPP(c_COMBB(_1100802, tc_fun(_1100802, _1100802), _1100804), c_Groups_Oplus__class_Oplus(_1100802)), _1100808)), _1100810)), _1100806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100802), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100804, _1100802), _1100808), _1100806)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100804, _1100802), _1100810), _1100806)))], (23346 ^ _782476) ^ [_1220750, _1220752, _1220754, _1220756] : [class_Groups_Ocomm__monoid__add(_1220750), 23349 ^ _782476 : [(23356 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220752)), _1220754))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220750), _1220756), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220754, hAPP(c_Nat_OSuc, _1220752))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220750), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220750), _1220756), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220754, _1220752))), hAPP(_1220756, hAPP(c_Nat_OSuc, _1220752))))], (23350 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220752)), _1220754)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220750), _1220756), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220754, hAPP(c_Nat_OSuc, _1220752))) = c_Groups_Ozero__class_Ozero(_1220750))]]], (34184 ^ _782476) ^ [_1430422] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430422)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430422)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430422))], (7891 ^ _782476) ^ [_916530, _916532, _916534, _916536] : [7892 ^ _782476 : [(7893 ^ _782476) ^ [_916640] : [hBOOL(hAPP(hAPP(c_member(_916530), _916640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916530, tc_HOL_Obool)), _916532), _916534))), hBOOL(hAPP(_916536, _916640))]], 7901 ^ _782476 : [(7904 ^ _782476) ^ [] : [-(hBOOL(hAPP(_916536, 7900 ^ [_916530, _916532, _916534, _916536])))], (7902 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916530), 7900 ^ [_916530, _916532, _916534, _916536]), _916532)))]], 7906 ^ _782476 : [(7909 ^ _782476) ^ [] : [-(hBOOL(hAPP(_916536, 7905 ^ [_916530, _916532, _916534, _916536])))], (7907 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916530), 7905 ^ [_916530, _916532, _916534, _916536]), _916534)))]]], (22930 ^ _782476) ^ [_1212472, _1212474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212472), _1212474)), -(_1212474 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212472), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22933 ^ [_1212472, _1212474]))))], (98 ^ _782476) ^ [_784095, _784097, _784099, _784101, _784103, _784105, _784107, _784109] : [-(c_Partial__Function_Omk__less(_784107, _784103, _784099, _784095)), c_Partial__Function_Omk__less(_784109, _784105, _784101, _784097), _784109 = _784107, _784105 = _784103, _784101 = _784099, _784097 = _784095], (24216 ^ _782476) ^ [_1236132, _1236134, _1236136] : [24218 ^ _782476 : [(24221 ^ _782476) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1236136, 24217 ^ [_1236132, _1236134, _1236136]))], (24219 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1236132), 24217 ^ [_1236132, _1236134, _1236136]), _1236134)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236132, tc_Int_Oint), _1236136), _1236134) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236132, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1236132), c_Int_Onat), _1236136)), _1236134)))], (17387 ^ _782476) ^ [_1112392, _1112394] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112392), _1112394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112394), _1112392)))], (35842 ^ _782476) ^ [_1459462, _1459464] : [class_Rings_Oring__1(_1459462), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459462), hAPP(c_Groups_Ouminus__class_Ouminus(_1459462), c_Groups_Oone__class_Oone(_1459462))), 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)))), _1459464)) = c_Groups_Oone__class_Oone(_1459462))], (21029 ^ _782476) ^ [_1177642, _1177644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177642), _1177644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177642), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177644)))], (19544 ^ _782476) ^ [_1149852, _1149854, _1149856] : [class_Groups_Ocomm__monoid__add(_1149852), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149854, _1149852), _1149856), c_Orderings_Obot__class_Obot(tc_fun(_1149854, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149852))], (9792 ^ _782476) ^ [_958005, _958007, _958009] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958005, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_958005, tc_HOL_Obool), _958007)), _958009) = c_Orderings_Obot__class_Obot(tc_fun(_958005, tc_HOL_Obool)), 9795 ^ _782476 : [(9796 ^ _782476) ^ [_958140] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_958005, tc_HOL_Obool)), _958140), _958007)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958005, tc_HOL_Obool)), _958140), _958009) = c_Orderings_Obot__class_Obot(tc_fun(_958005, tc_HOL_Obool)))]]], (2956 ^ _782476) ^ [_826306, _826308, _826310, _826312] : [-(c_Nitpick_OAbs__Frac(_826312, _826308) = c_Nitpick_OAbs__Frac(_826310, _826306)), _826312 = _826310, _826308 = _826306], (1782 ^ _782476) ^ [_807951, _807953] : [-(class_Groups_Osemigroup__add(_807951)), _807953 = _807951, class_Groups_Osemigroup__add(_807953)], (42469 ^ _782476) ^ [_1618835, _1618837, _1618839, _1618841, _1618843, _1618845] : [c_Finite__Set_Ofun__left__comm(_1618835, _1618837, _1618839), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618835, _1618837, _1618839, _1618841, _1618843), _1618845)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618835, _1618837, _1618839), _1618841), _1618843) = _1618845)], (41511 ^ _782476) ^ [_1596947, _1596949, _1596951] : [-(hAPP(c_Relation_ORange(_1596947, _1596949), _1596951) = hAPP(c_Relation_ODomain(_1596949, _1596947), hAPP(c_Relation_Oconverse(_1596947, _1596949), _1596951)))], (49922 ^ _782476) ^ [_1790687, _1790689, _1790691, _1790693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790687), _1790689)), -(hAPP(hAPP(c_List_Onth(_1790691), c_List_Oreplicate(_1790691, _1790689, _1790693)), _1790687) = _1790693)], (47305 ^ _782476) ^ [_1734328, _1734330, _1734332, _1734334] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734328)), _1734330))), c_List_Ofoldr(tc_List_Olist(_1734332), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734332)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734332))), _1734334, 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(_1734328)), _1734330)), c_List_Ofoldr(tc_List_Olist(_1734332), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734332)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734332), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734332)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734332)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1734332), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734332)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734332), tc_List_Olist(_1734332), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734332)))), _1734334), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (40466 ^ _782476) ^ [_1570641, _1570643] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570641), c_Int_OInteg)), hBOOL(hAPP(_1570643, hAPP(c_Int_ORep__Integ, 40471 ^ [_1570641, _1570643]))), -(hBOOL(hAPP(_1570643, _1570641)))], (11246 ^ _782476) ^ [_988833, _988835, _988837, _988839] : [class_Orderings_Oorder(_988833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988833), _988835), _988837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988833), _988839), _988835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988833), _988839), _988837)))], (5458 ^ _782476) ^ [_866005, _866007] : [_866007 = _866005, -(c_Finite__Set_Ofinite(_866007) = c_Finite__Set_Ofinite(_866005))], (20561 ^ _782476) ^ [_1169208] : [_1169208 = 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), _1169208)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32692 ^ _782476) ^ [_1401872, _1401874, _1401876] : [hBOOL(hAPP(_1401872, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401874, _1401876))), 32695 ^ _782476 : [(32702 ^ _782476) ^ [] : [-(_1401876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 32705 ^ _782476 : [(32706 ^ _782476) ^ [_1402120, _1402122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402120), _1401876)), _1401874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401876), _1402122)), _1402120), -(hBOOL(hAPP(_1401872, _1402120)))]]], (32696 ^ _782476) ^ [] : [_1401876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1401872, _1401874)))]]], (27040 ^ _782476) ^ [_1293718] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1293718) = c_Orderings_Oord__class_Omin(_1293718)), class_Lattices_Osemilattice__inf(_1293718), class_Orderings_Olinorder(_1293718)], (51320 ^ _782476) ^ [_1820850, _1820852, _1820854, _1820856, _1820858, _1820860] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820850, _1820852, _1820854, _1820856, c_Lazy__Sequence_Olazy__sequence_OInsert(_1820852, _1820858, _1820860)) = hAPP(hAPP(hAPP(_1820856, _1820858), _1820860), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820850, _1820852, _1820854, _1820856, _1820860)))], (9352 ^ _782476) ^ [_950000, _950002, _950004] : [class_Orderings_Oorder(_950000), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_950000, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_950000, _950002), _950004)), hAPP(c_SetInterval_Oord__class_OatLeast(_950000), _950004)) = c_Orderings_Obot__class_Obot(tc_fun(_950000, tc_HOL_Obool)))], (26306 ^ _782476) ^ [_1279725, _1279727, _1279729, _1279731, _1279733] : [class_Orderings_Olinorder(_1279725), class_Orderings_Olinorder(_1279727), c_Orderings_Oorder__class_Omono(_1279727, _1279725, _1279729), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279725), hAPP(_1279729, _1279731)), hAPP(_1279729, _1279733)) = hAPP(_1279729, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279727), _1279731), _1279733)))], (20963 ^ _782476) ^ [_1176558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176558)))], (22744 ^ _782476) ^ [_1209126, _1209128, _1209130, _1209132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209126), _1209128)), hAPP(c_Finite__Set_Ocard(_1209130), hAPP(c_Set_Oimage(_1209126, _1209130, _1209132), _1209128)) = hAPP(c_Finite__Set_Ocard(_1209126), _1209128), -(c_Fun_Oinj__on(_1209126, _1209130, _1209132, _1209128))], (14787 ^ _782476) ^ [_1058676, _1058678, _1058680, _1058682, _1058684, _1058686] : [c_Finite__Set_Ofolding(_1058676, _1058678, _1058680, _1058682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058676), _1058684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058676), _1058686)), -(hAPP(c_Fun_Ocomp(_1058678, _1058678, _1058678, hAPP(_1058682, _1058686)), hAPP(_1058682, _1058684)) = hAPP(c_Fun_Ocomp(_1058678, _1058678, _1058678, hAPP(_1058682, _1058684)), hAPP(_1058682, _1058686)))], (31506 ^ _782476) ^ [_1378666, _1378668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378666)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378666), _1378668)), _1378666) = _1378668)], (38461 ^ _782476) ^ [_1518416, _1518418] : [c_Equiv__Relations_Oequivp(_1518416, hAPP(hAPP(c_COMBC(_1518416, tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_fun(_1518416, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518416, tc_fun(tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_fun(_1518416, tc_HOL_Obool)), _1518416), c_COMBC(_1518416, tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518416, tc_prod(_1518416, _1518416)), tc_fun(_1518416, tc_fun(tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_HOL_Obool)), _1518416), hAPP(c_COMBB(tc_prod(_1518416, _1518416), tc_fun(tc_fun(tc_prod(_1518416, _1518416), tc_HOL_Obool), tc_HOL_Obool), _1518416), c_member(tc_prod(_1518416, _1518416)))), c_Product__Type_OPair(_1518416, _1518416)))), _1518418)), -(c_Equiv__Relations_Oequiv(_1518416, c_Orderings_Otop__class_Otop(tc_fun(_1518416, tc_HOL_Obool)), _1518418))], (49838 ^ _782476) ^ [_1789316, _1789318, _1789320, _1789322, _1789324, _1789326] : [-(c_New__Random__Sequence_Opos__union(_1789316, _1789318, _1789320, _1789322, _1789324, _1789326) = c_New__DSequence_Opos__union(_1789316, hAPP(hAPP(hAPP(_1789318, _1789322), _1789324), _1789326), hAPP(hAPP(hAPP(_1789320, _1789322), _1789324), _1789326)))], (38455 ^ _782476) ^ [_1518095, _1518097] : [c_Equiv__Relations_Oequiv(_1518095, c_Orderings_Otop__class_Otop(tc_fun(_1518095, tc_HOL_Obool)), _1518097), -(c_Equiv__Relations_Oequivp(_1518095, hAPP(hAPP(c_COMBC(_1518095, tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_fun(_1518095, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518095, tc_fun(tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_fun(_1518095, tc_HOL_Obool)), _1518095), c_COMBC(_1518095, tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518095, tc_prod(_1518095, _1518095)), tc_fun(_1518095, tc_fun(tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_HOL_Obool)), _1518095), hAPP(c_COMBB(tc_prod(_1518095, _1518095), tc_fun(tc_fun(tc_prod(_1518095, _1518095), tc_HOL_Obool), tc_HOL_Obool), _1518095), c_member(tc_prod(_1518095, _1518095)))), c_Product__Type_OPair(_1518095, _1518095)))), _1518097)))], (50074 ^ _782476) ^ [_1793432, _1793434, _1793436] : [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), _1793432), _1793434))), -(hBOOL(hAPP(hAPP(_1793436, _1793432), _1793434))), 50081 ^ _782476 : [(50084 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50079 ^ [_1793432, _1793434, _1793436]), 50080 ^ [_1793432, _1793434, _1793436]))), -(hBOOL(hAPP(hAPP(_1793436, 50079 ^ [_1793432, _1793434, _1793436]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50080 ^ [_1793432, _1793434, _1793436]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50090 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1793436, 50079 ^ [_1793432, _1793434, _1793436]), 50080 ^ [_1793432, _1793434, _1793436]))], (50082 ^ _782476) ^ [] : [-(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), 50079 ^ [_1793432, _1793434, _1793436]), 50080 ^ [_1793432, _1793434, _1793436]))))]]], (446 ^ _782476) ^ [_789253, _789255, _789257, _789259, _789261, _789263] : [-(c_Finite__Set_Ofolding__one__idem(_789261, _789257, _789253)), c_Finite__Set_Ofolding__one__idem(_789263, _789259, _789255), _789263 = _789261, _789259 = _789257, _789255 = _789253], (49022 ^ _782476) ^ [_1770710, _1770712, _1770714] : [c_List_Olist__ex(_1770710, _1770712, _1770714), 49026 ^ _782476 : [(49029 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1770712, hAPP(hAPP(c_List_Onth(_1770710), _1770714), 49025 ^ [_1770710, _1770712, _1770714]))))], (49027 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49025 ^ [_1770710, _1770712, _1770714]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770710)), _1770714))))]]], (49303 ^ _782476) ^ [_1776467, _1776469, _1776471] : [49305 ^ _782476 : [(49308 ^ _782476) ^ [] : [hBOOL(hAPP(_1776469, 49304 ^ [_1776467, _1776469, _1776471]))], (49306 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776467), 49304 ^ [_1776467, _1776469, _1776471]), hAPP(c_List_Oset(_1776467), _1776471))))]], -(c_List_Olist__all(_1776467, _1776469, _1776471))], (48367 ^ _782476) ^ [_1755490] : [-(c_List_Oreturn__list(_1755490) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1755490))], (49389 ^ _782476) ^ [_1778149, _1778151, _1778153] : [-(c_List_Olist__ex1(_1778149, _1778151, _1778153)), 49390 ^ _782476 : [(49391 ^ _782476) ^ [_1778243] : [hBOOL(hAPP(hAPP(c_member(_1778149), _1778243), hAPP(c_List_Oset(_1778149), _1778153))), hBOOL(hAPP(_1778151, _1778243)), 49399 ^ _782476 : [(49404 ^ _782476) ^ [] : [49398 ^ [_1778149, _1778151, _1778153, _1778243] = _1778243], (49402 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1778151, 49398 ^ [_1778149, _1778151, _1778153, _1778243])))], (49400 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778149), 49398 ^ [_1778149, _1778151, _1778153, _1778243]), hAPP(c_List_Oset(_1778149), _1778153))))]]]]], (17291 ^ _782476) ^ [_1110953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110953), _1110953))], (37203 ^ _782476) ^ [_1490547, _1490549] : [-(_1490547 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37206 ^ _782476 : [(37213 ^ _782476) ^ [] : [-(_1490549 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1490547, _1490549) = 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, _1490549))), 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)), _1490549)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490547))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490549), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490547), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1490547, _1490549)), 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), _1490549))))), c_Divides_Opdivmod(_1490547, _1490549)))))], (37207 ^ _782476) ^ [] : [_1490549 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490547, _1490549) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490547))]]], (47238 ^ _782476) ^ [_1732075, _1732077, _1732079, _1732081] : [hBOOL(hAPP(hAPP(c_member(_1732075), _1732077), hAPP(c_List_Oset(_1732075), _1732079))), -(hBOOL(hAPP(_1732081, _1732077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732075)), hAPP(c_List_Ofilter(_1732075, _1732081), _1732079))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732075)), _1732079))))], (37782 ^ _782476) ^ [_1501772, _1501774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501774), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501772), _1501774) = 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), _1501772), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501774)))))], (6536 ^ _782476) ^ [_887563, _887565, _887567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887563, tc_HOL_Obool), tc_HOL_Obool)), _887565), _887567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887563, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887563, tc_HOL_Obool), _887567)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887563, tc_HOL_Obool), _887565))))], (27387 ^ _782476) ^ [_1300391, _1300393, _1300395, _1300397] : [class_Orderings_Olinorder(_1300391), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300391, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1300391), _1300393)), c_SetInterval_Oord__class_OatLeastAtMost(_1300391, _1300395, _1300397)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300391, _1300395, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300391), _1300393), _1300397)))], (44008 ^ _782476) ^ [_1660328, _1660330, _1660332, _1660334] : [hBOOL(hAPP(c_List_Odistinct(_1660328), _1660330)), hBOOL(hAPP(c_List_Odistinct(_1660332), _1660334)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660328, _1660332)), c_Enum_Oproduct(_1660328, _1660332, _1660330, _1660334))))], (39610 ^ _782476) ^ [_1547424, _1547426, _1547428] : [hAPP(c_Relation_ODomain(_1547424, _1547426), _1547428) = c_Orderings_Obot__class_Obot(tc_fun(_1547424, tc_HOL_Obool)), -(_1547428 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547424, _1547426), tc_HOL_Obool)))], (49870 ^ _782476) ^ [_1789820, _1789822, _1789824] : [-(_1789820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1789822), c_List_Oreplicate(_1789822, _1789820, _1789824)) = c_List_Oreplicate(_1789822, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1789820), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1789824))], (27787 ^ _782476) ^ [_1307835, _1307837, _1307839, _1307841, _1307843] : [class_Groups_Ocomm__monoid__mult(_1307835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307837), _1307839)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307837), _1307841)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307837, tc_HOL_Obool)), _1307839), _1307841) = c_Orderings_Obot__class_Obot(tc_fun(_1307837, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307837, _1307835), _1307843), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307837, tc_HOL_Obool)), _1307839), _1307841)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307835), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307837, _1307835), _1307843), _1307839)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307837, _1307835), _1307843), _1307841)))], (22530 ^ _782476) ^ [_1205008, _1205010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205008), _1205010)), 22533 ^ _782476 : [(22540 ^ _782476) ^ [] : [_1205010 = _1205008, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205010), hAPP(c_Nat_OSuc, _1205008))))], (22534 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205010), hAPP(c_Nat_OSuc, _1205008))), -(_1205010 = _1205008)]]], (18062 ^ _782476) ^ [_1124609, _1124611] : [class_Groups_Ocomm__monoid__add(_1124609), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124609), _1124611), c_Groups_Ozero__class_Ozero(_1124609)) = _1124611)], (21929 ^ _782476) ^ [_1195014, _1195016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195014), _1195016)), -(c_Nat__Transfer_Otsub(_1195016, _1195014) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195016), _1195014))], (26330 ^ _782476) ^ [_1280177, _1280179, _1280181] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280177, tc_Nat_Onat), _1280179), _1280181) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280177, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1280177), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1280179)), _1280181)))], (52041 ^ _782476) ^ [_1836461, _1836463] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836461), _1836463)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836463, _1836461) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (16757 ^ _782476) ^ [_1098549, _1098551] : [class_Rings_Ocomm__semiring__1(_1098549), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098549), _1098551), _1098551) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098549), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098549), c_Groups_Oone__class_Oone(_1098549)), c_Groups_Oone__class_Oone(_1098549))), _1098551))], (52251 ^ _782476) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (4436 ^ _782476) ^ [_849808, _849810] : [_849810 = _849808, -(c_List_Otake(_849810) = c_List_Otake(_849808))], (44160 ^ _782476) ^ [_1663560, _1663562, _1663564] : [-(hBOOL(hAPP(hAPP(c_member(_1663560), _1663562), hAPP(c_List_Oset(_1663560), _1663564)))), -(c_List_Oremove1(_1663560, _1663562, _1663564) = _1663564)], (50493 ^ _782476) ^ [_1803428, _1803430, _1803432, _1803434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803428, tc_fun(_1803430, tc_HOL_Obool)), _1803432), _1803434) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803430, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1803430, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1803428, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1803430, tc_HOL_Obool)), c_HOL_OEx(_1803428)), hAPP(hAPP(c_COMBB(tc_fun(_1803428, tc_HOL_Obool), tc_fun(_1803428, tc_HOL_Obool), tc_fun(_1803430, tc_HOL_Obool)), hAPP(c_COMBS(_1803428, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803428), c_fconj), hAPP(hAPP(c_COMBC(_1803428, tc_fun(_1803428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1803428)), _1803432)))), hAPP(hAPP(c_COMBC(tc_fun(_1803430, tc_HOL_Obool), tc_fun(_1803428, tc_fun(_1803430, tc_HOL_Obool)), tc_fun(_1803428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803430, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803428, tc_fun(_1803430, tc_HOL_Obool)), tc_fun(_1803428, tc_HOL_Obool)), tc_fun(_1803430, tc_HOL_Obool)), c_COMBB(tc_fun(_1803430, tc_HOL_Obool), tc_HOL_Obool, _1803428)), c_fequal)), _1803434))))))], (7407 ^ _782476) ^ [_906337, _906339, _906341] : [class_Groups_Oordered__ab__group__add(_906337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906337), _906339), _906341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906337), hAPP(c_Groups_Ouminus__class_Ouminus(_906337), _906341)), hAPP(c_Groups_Ouminus__class_Ouminus(_906337), _906339))))], (33302 ^ _782476) ^ [_1413782, _1413784, _1413786, _1413788] : [class_Fields_Ofield__inverse__zero(_1413782), class_Int_Onumber(_1413782), 33309 ^ _782476 : [(33310 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413782), _1413786), _1413788), 33313 ^ _782476 : [(33320 ^ _782476) ^ [] : [_1413788 = c_Groups_Ozero__class_Ozero(_1413782), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784) = c_Groups_Ozero__class_Ozero(_1413782))], (33314 ^ _782476) ^ [] : [-(_1413788 = c_Groups_Ozero__class_Ozero(_1413782)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413782), hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784)), _1413788) = _1413786)]]], (33326 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413782), _1413786), _1413788)), 33329 ^ _782476 : [(33332 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413782), hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784)), _1413788) = _1413786], (33330 ^ _782476) ^ [] : [_1413788 = c_Groups_Ozero__class_Ozero(_1413782)]], 33333 ^ _782476 : [(33336 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413782), _1413784) = c_Groups_Ozero__class_Ozero(_1413782)], (33334 ^ _782476) ^ [] : [-(_1413788 = c_Groups_Ozero__class_Ozero(_1413782))]]]]], (34868 ^ _782476) ^ [_1441423, _1441425] : [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(_1441425))), 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)), _1441423))))), -(hAPP(c_Nat_OSuc, _1441423) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441425))], (50054 ^ _782476) ^ [_1793145, _1793147, _1793149] : [-(_1793145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793147), c_List_Oreplicate(_1793147, _1793145, _1793149)) = hAPP(hAPP(c_Set_Oinsert(_1793147), _1793149), c_Orderings_Obot__class_Obot(tc_fun(_1793147, tc_HOL_Obool))))], (36108 ^ _782476) ^ [_1464544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464544)))], (24098 ^ _782476) ^ [_1234205, _1234207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234205), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234205), _1234207)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234205))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234207))))], (30716 ^ _782476) ^ [_1364663, _1364665, _1364667, _1364669] : [class_Fields_Olinordered__field(_1364663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364663), _1364665), _1364667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364663), c_Groups_Ozero__class_Ozero(_1364663)), _1364669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364663), c_Groups_Ozero__class_Ozero(_1364663)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364663), _1364667), _1364665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364663), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364663), _1364669), _1364667)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364663), _1364669), _1364665))))], (16703 ^ _782476) ^ [_1097366, _1097368, _1097370, _1097372] : [class_Rings_Ocomm__semiring(_1097366), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097366), _1097368), _1097370)), _1097372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097366), _1097368), _1097372)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097366), _1097370), _1097372)))], (49346 ^ _782476) ^ [_1777312, _1777314] : [-(c_FunDef_Ois__measure(_1777312, _1777314))], (21385 ^ _782476) ^ [_1184018, _1184020] : [_1184018 = _1184020, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184018) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184020))], (49426 ^ _782476) ^ [_1778827, _1778829, _1778831, _1778833, _1778835, _1778837, _1778839] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1778827, _1778829, _1778831, _1778833, _1778835, _1778837, _1778839) = c_New__DSequence_Oneg__decr__bind(_1778827, _1778829, hAPP(hAPP(hAPP(_1778831, _1778835), _1778837), _1778839), hAPP(hAPP(c_COMBC(_1778827, 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(_1778829)))), hAPP(hAPP(c_COMBC(_1778827, 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(_1778829))))), hAPP(hAPP(c_COMBC(_1778827, 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(_1778829)))))), _1778833), _1778835)), _1778837)), _1778839)))], (38008 ^ _782476) ^ [_1507186, _1507188, _1507190, _1507192, _1507194, _1507196, _1507198] : [c_Equiv__Relations_Oequiv(_1507186, _1507188, _1507190), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507186, tc_HOL_Obool)), _1507192), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507186), _1507188), _1507190))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507186, tc_HOL_Obool)), _1507194), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507186), _1507188), _1507190))), hBOOL(hAPP(hAPP(c_member(_1507186), _1507196), _1507192)), hBOOL(hAPP(hAPP(c_member(_1507186), _1507198), _1507194)), 38027 ^ _782476 : [(38034 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507186, _1507186)), hAPP(hAPP(c_Product__Type_OPair(_1507186, _1507186), _1507196), _1507198)), _1507190)), -(_1507192 = _1507194)], (38028 ^ _782476) ^ [] : [_1507192 = _1507194, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507186, _1507186)), hAPP(hAPP(c_Product__Type_OPair(_1507186, _1507186), _1507196), _1507198)), _1507190)))]]], (9879 ^ _782476) ^ [_960268, _960270, _960272, _960274, _960276] : [_960268 = c_Orderings_Obot__class_Obot(tc_fun(_960270, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960272, tc_HOL_Obool)), _960274), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960270, tc_fun(_960272, tc_HOL_Obool)), _960268), _960276)) = _960274)], (1172 ^ _782476) ^ [_800326, _800328] : [-(class_Lattices_Obounded__lattice(_800326)), _800328 = _800326, class_Lattices_Obounded__lattice(_800328)], (18170 ^ _782476) ^ [_1126221, _1126223, _1126225] : [class_Groups_Ogroup__add(_1126221), 18173 ^ _782476 : [(18180 ^ _782476) ^ [] : [_1126223 = _1126225, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126221), _1126223), _1126225) = c_Groups_Ozero__class_Ozero(_1126221))], (18174 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126221), _1126223), _1126225) = c_Groups_Ozero__class_Ozero(_1126221), -(_1126223 = _1126225)]]], (1982 ^ _782476) ^ [_810451, _810453] : [-(class_Rings_Odvd(_810451)), _810453 = _810451, class_Rings_Odvd(_810453)], (47668 ^ _782476) ^ [_1741420, _1741422, _1741424] : [class_Orderings_Olinorder(_1741420), c_List_Olinorder__class_Osorted(_1741420, _1741422), -(c_List_Olinorder__class_Osorted(_1741420, hAPP(hAPP(c_List_Odrop(_1741420), _1741424), _1741422)))], (40035 ^ _782476) ^ [_1560754] : [-(hAPP(c_Set_Oimage(_1560754, _1560754, c_Fun_Oid(_1560754)), c_Orderings_Otop__class_Otop(tc_fun(_1560754, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560754, tc_HOL_Obool)))], (34764 ^ _782476) ^ [_1439474, _1439476] : [class_Int_Onumber__ring(_1439474), class_Rings_Olinordered__idom(_1439474), 34771 ^ _782476 : [(34778 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439474), c_Groups_Oone__class_Oone(_1439474)), hAPP(c_Int_Onumber__class_Onumber__of(_1439474), _1439476))))], (34772 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439474), c_Groups_Oone__class_Oone(_1439474)), hAPP(c_Int_Onumber__class_Onumber__of(_1439474), _1439476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439476)))]]], (48333 ^ _782476) ^ [_1754827, _1754829, _1754831, _1754833, _1754835] : [-(hAPP(hAPP(c_List_Ozip(_1754827, _1754829), c_List_OtakeWhile(_1754827, _1754831, _1754833)), _1754835) = c_List_OtakeWhile(tc_prod(_1754827, _1754829), hAPP(c_Fun_Ocomp(_1754827, tc_HOL_Obool, tc_prod(_1754827, _1754829), _1754831), c_Product__Type_Ofst(_1754827, _1754829)), hAPP(hAPP(c_List_Ozip(_1754827, _1754829), _1754833), _1754835)))], (42913 ^ _782476) ^ [_1629754, _1629756, _1629758, _1629760, _1629762, _1629764] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629754), tc_List_Olist(_1629754))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629754), tc_List_Olist(_1629754)), hAPP(hAPP(c_List_Olist_OCons(_1629754), _1629756), _1629758)), hAPP(hAPP(c_List_Olist_OCons(_1629754), _1629760), _1629762))), c_List_Olexord(_1629754, _1629764)))), 42914 ^ _782476 : [(42917 ^ _782476) ^ [] : [_1629756 = _1629760, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629754), tc_List_Olist(_1629754))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629754), tc_List_Olist(_1629754)), _1629758), _1629762)), c_List_Olexord(_1629754, _1629764)))], (42915 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629754, _1629754)), hAPP(hAPP(c_Product__Type_OPair(_1629754, _1629754), _1629756), _1629760)), _1629764))]]], (1562 ^ _782476) ^ [_805201, _805203] : [-(class_Finite__Set_Ofinite(_805201)), _805203 = _805201, class_Finite__Set_Ofinite(_805203)], (46164 ^ _782476) ^ [_1707688, _1707690, _1707692, _1707694, _1707696] : [-(c_Enum_Oproduct(_1707688, _1707690, hAPP(hAPP(c_List_Olist_OCons(_1707688), _1707692), _1707694), _1707696) = hAPP(hAPP(c_List_Oappend(tc_prod(_1707688, _1707690)), hAPP(hAPP(c_List_Omap(_1707690, tc_prod(_1707688, _1707690)), hAPP(c_Product__Type_OPair(_1707688, _1707690), _1707692)), _1707696)), c_Enum_Oproduct(_1707688, _1707690, _1707694, _1707696)))], (13595 ^ _782476) ^ [_1034190, _1034192, _1034194, _1034196, _1034198, _1034200, _1034202] : [c_Fun_Oinj__on(_1034190, _1034192, _1034194, hAPP(c_Set_Oimage(_1034196, _1034190, _1034198), _1034200)), c_Fun_Oinj__on(_1034196, _1034190, _1034198, _1034200), hBOOL(hAPP(hAPP(c_member(_1034192), _1034202), hAPP(c_Set_Oimage(_1034190, _1034192, _1034194), hAPP(c_Set_Oimage(_1034196, _1034190, _1034198), _1034200)))), -(hAPP(c_Fun_Othe__inv__into(_1034196, _1034192, _1034200, hAPP(c_Fun_Ocomp(_1034190, _1034192, _1034196, _1034194), _1034198)), _1034202) = hAPP(hAPP(c_Fun_Ocomp(_1034190, _1034196, _1034192, c_Fun_Othe__inv__into(_1034196, _1034190, _1034200, _1034198)), c_Fun_Othe__inv__into(_1034190, _1034192, hAPP(c_Set_Oimage(_1034196, _1034190, _1034198), _1034200), _1034194)), _1034202))], (3894 ^ _782476) ^ [_840961, _840963] : [_840963 = _840961, -(c_Groups_Oabs__class_Oabs(_840963) = c_Groups_Oabs__class_Oabs(_840961))], (45505 ^ _782476) ^ [_1693324, _1693326] : [class_Complete__Lattice_Ocomplete__lattice(_1693324), -(c_Complete__Lattice_OInf__class_OInf(_1693324, hAPP(c_List_Oset(_1693324), _1693326)) = hAPP(c_List_Ofoldl(_1693324, _1693324, c_Lattices_Osemilattice__inf__class_Oinf(_1693324), c_Orderings_Otop__class_Otop(_1693324)), _1693326))], (49554 ^ _782476) ^ [_1781958, _1781960, _1781962, _1781964, _1781966, _1781968] : [hAPP(c_Set_Oimage(_1781958, _1781960, _1781962), _1781964) = _1781966, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781960, tc_HOL_Obool)), _1781968), _1781966)), -(hAPP(c_Set_Oimage(_1781958, _1781960, _1781962), hAPP(c_Set_Oimage(_1781960, _1781958, c_Hilbert__Choice_Oinv__into(_1781958, _1781960, _1781964, _1781962)), _1781968)) = _1781968)], (38843 ^ _782476) ^ [] : [-(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))))))], (5188 ^ _782476) ^ [_861762, _861764, _861766, _861768] : [-(c_Quickcheck_Obeyond(_861768, _861764) = c_Quickcheck_Obeyond(_861766, _861762)), _861768 = _861766, _861764 = _861762], (1382 ^ _782476) ^ [_802951, _802953] : [-(class_Groups_Oabs__if(_802951)), _802953 = _802951, class_Groups_Oabs__if(_802953)], (49508 ^ _782476) ^ [_1780946, _1780948, _1780950, _1780952] : [c_Fun_Oinj__on(_1780946, _1780948, _1780950, c_Orderings_Otop__class_Otop(tc_fun(_1780946, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780946, _1780948, c_Orderings_Otop__class_Otop(tc_fun(_1780946, tc_HOL_Obool)), _1780950), hAPP(_1780950, _1780952)) = _1780952)], (17704 ^ _782476) ^ [_1118125, _1118127, _1118129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118125), _1118127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118125), _1118129)), 17711 ^ _782476 : [(17718 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118127), _1118129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118127), _1118125)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118129), _1118125))))], (17712 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118127), _1118125)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118129), _1118125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118127), _1118129)))]]], (36220 ^ _782476) ^ [_1466225, _1466227] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466225), _1466227) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1466225 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1466225 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (7936 ^ _782476) ^ [_917538, _917540, _917542] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917538, tc_HOL_Obool)), _917540), _917542) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917538, tc_HOL_Obool)), _917542), _917540))], (9399 ^ _782476) ^ [_950814, _950816] : [9400 ^ _782476 : [(9401 ^ _782476) ^ [_950867] : [hBOOL(hAPP(hAPP(c_member(_950814), _950867), _950816))]], _950816 = c_Orderings_Obot__class_Obot(tc_fun(_950814, tc_HOL_Obool))], (50192 ^ _782476) ^ [_1796134, _1796136, _1796138] : [hBOOL(hAPP(hAPP(c_member(_1796134), _1796138), hAPP(c_List_Oset(_1796134), _1796136))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1796134), _1796136), _1796138)))], (31888 ^ _782476) ^ [_1386333, _1386335, _1386337, _1386339] : [class_Divides_Osemiring__div(_1386333), -(c_Divides_Odiv__class_Omod(_1386333, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386333), _1386335), _1386337), _1386339) = c_Divides_Odiv__class_Omod(_1386333, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386333), c_Divides_Odiv__class_Omod(_1386333, _1386335, _1386339)), _1386337), _1386339))], (21343 ^ _782476) ^ [] : [-(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)))], (7828 ^ _782476) ^ [_915198, _915200] : [class_Lattices_Osemilattice__sup(_915198), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915198), _915200), _915200) = _915200)], (49762 ^ _782476) ^ [_1787180, _1787182] : [c_Wellfounded_Oacyclic(_1787180, hAPP(c_Set_OCollect(tc_prod(_1787180, _1787180)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787180, _1787180, tc_HOL_Obool), _1787182))), -(c_Wellfounded_Oacyclic(_1787180, hAPP(c_Set_OCollect(tc_prod(_1787180, _1787180)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787180, _1787180, tc_HOL_Obool), c_Predicate_Oconversep(_1787180, _1787180, _1787182)))))], (3198 ^ _782476) ^ [_830053, _830055, _830057, _830059] : [-(c_Big__Operators_Olattice__class_OSup__fin(_830059, _830055) = c_Big__Operators_Olattice__class_OSup__fin(_830057, _830053)), _830059 = _830057, _830055 = _830053], (10859 ^ _782476) ^ [_982310, _982312, _982314, _982316] : [-(hAPP(c_Set_Oimage(_982310, _982312, _982314), _982316) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982310, tc_fun(_982312, tc_HOL_Obool)), _982316), hAPP(hAPP(c_COMBC(_982310, tc_fun(_982312, tc_HOL_Obool), tc_fun(_982312, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_982312, tc_fun(tc_fun(_982312, tc_HOL_Obool), tc_fun(_982312, tc_HOL_Obool)), _982310), c_Set_Oinsert(_982312)), _982314)), c_Orderings_Obot__class_Obot(tc_fun(_982312, tc_HOL_Obool)))))], (41956 ^ _782476) ^ [_1608641, _1608643, _1608645, _1608647] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608641, _1608641)), hAPP(hAPP(c_Product__Type_OPair(_1608641, _1608641), _1608643), _1608645)), c_Transitive__Closure_Otrancl(_1608641, _1608647))), 41960 ^ _782476 : [(41963 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608641, _1608641)), hAPP(hAPP(c_Product__Type_OPair(_1608641, _1608641), 41959 ^ [_1608641, _1608643, _1608645, _1608647]), _1608645)), _1608647)))], (41961 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608641, _1608641)), hAPP(hAPP(c_Product__Type_OPair(_1608641, _1608641), _1608643), 41959 ^ [_1608641, _1608643, _1608645, _1608647])), c_Transitive__Closure_Ortrancl(_1608641, _1608647))))]]], (23829 ^ _782476) ^ [_1229638, _1229640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229640)), 23836 ^ _782476 : [(23843 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229638), _1229640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229638)), hAPP(c_Int_Onat, _1229640))))], (23837 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229638)), hAPP(c_Int_Onat, _1229640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229638), _1229640)))]]], (48669 ^ _782476) ^ [_1761993, _1761995, _1761997, _1761999] : [-(hBOOL(hAPP(_1761993, _1761995))), -(hAPP(c_List_OremoveAll(_1761997, _1761995), hAPP(c_List_Ofilter(_1761997, _1761993), _1761999)) = hAPP(c_List_Ofilter(_1761997, _1761993), _1761999))], (46362 ^ _782476) ^ [_1712035] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1712035)) = _1712035)], (37615 ^ _782476) ^ [_1498333, _1498335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498333), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1498335), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498333, _1498335) = 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), _1498333), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498335)))))], (29146 ^ _782476) ^ [_1335823] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1335823) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22790 ^ _782476) ^ [_1209978, _1209980, _1209982] : [class_Rings_Oring__1(_1209978), hBOOL(hAPP(hAPP(c_member(_1209978), _1209980), c_Int_Oring__1__class_OInts(_1209978))), hBOOL(hAPP(hAPP(c_member(_1209978), _1209982), c_Int_Oring__1__class_OInts(_1209978))), -(hBOOL(hAPP(hAPP(c_member(_1209978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209978), _1209980), _1209982)), c_Int_Oring__1__class_OInts(_1209978))))], (30668 ^ _782476) ^ [_1363673, _1363675, _1363677] : [class_Fields_Olinordered__field(_1363673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363673), _1363675), _1363677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363673), _1363675), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363673), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363673), _1363675), _1363677)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363673), c_Groups_Oone__class_Oone(_1363673)), c_Groups_Oone__class_Oone(_1363673))))))], (15230 ^ _782476) ^ [_1067168, _1067170] : [class_Complete__Lattice_Ocomplete__lattice(_1067168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067168), _1067170)), -(_1067170 = c_Orderings_Obot__class_Obot(tc_fun(_1067168, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067168, _1067170) = c_Complete__Lattice_OSup__class_OSup(_1067168, _1067170))], (22009 ^ _782476) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (5600 ^ _782476) ^ [_868286, _868288] : [_868288 = _868286, -(c_Rings_Odvd__class_Odvd(_868288) = c_Rings_Odvd__class_Odvd(_868286))], (16665 ^ _782476) ^ [_1096559, _1096561, _1096563, _1096565] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096559), 16668 ^ _782476 : [(16675 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096559), _1096563), _1096565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096559), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096559), _1096561), _1096563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096559), _1096561), _1096565))))], (16669 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096559), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096559), _1096561), _1096563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096559), _1096561), _1096565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096559), _1096563), _1096565)))]]], (43037 ^ _782476) ^ [_1633580, _1633582, _1633584, _1633586, _1633588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633580), tc_List_Olist(_1633580))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633580), tc_List_Olist(_1633580)), _1633582), _1633584)), c_List_Olistrel1(_1633580, _1633586))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633580), tc_List_Olist(_1633580))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633580), tc_List_Olist(_1633580)), hAPP(hAPP(c_List_Olist_OCons(_1633580), _1633588), _1633582)), hAPP(hAPP(c_List_Olist_OCons(_1633580), _1633588), _1633584))), c_List_Olistrel1(_1633580, _1633586))))], (48804 ^ _782476) ^ [_1764948, _1764950, _1764952, _1764954, _1764956] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764948, _1764948)), hAPP(hAPP(c_Product__Type_OPair(_1764948, _1764948), _1764950), _1764952)), c_List_Omeasures(_1764948, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764948, tc_Nat_Onat)), _1764954), _1764956))))), 48805 ^ _782476 : [(48808 ^ _782476) ^ [] : [hAPP(_1764954, _1764950) = hAPP(_1764954, _1764952), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764948, _1764948)), hAPP(hAPP(c_Product__Type_OPair(_1764948, _1764948), _1764950), _1764952)), c_List_Omeasures(_1764948, _1764956)))], (48806 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764954, _1764950)), hAPP(_1764954, _1764952)))]]], (17848 ^ _782476) ^ [_1120702, _1120704, _1120706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120702), _1120704)), _1120706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120706), _1120704))))], (32163 ^ _782476) ^ [_1391725, _1391727, _1391729, _1391731] : [class_Divides_Osemiring__div(_1391725), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391725), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391725), _1391727), _1391729)), _1391729)), c_Divides_Odiv__class_Omod(_1391725, _1391727, _1391729))), _1391731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391725), _1391727), _1391731))], (14459 ^ _782476) ^ [_1051779, _1051781, _1051783] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051779), _1051781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051779, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1051779, _1051779, _1051783), _1051781)), _1051781)), c_Fun_Oinj__on(_1051779, _1051779, _1051783, _1051781), -(hAPP(c_Set_Oimage(_1051779, _1051779, _1051783), _1051781) = _1051781)], (23001 ^ _782476) ^ [_1213896, _1213898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213896), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213898), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213896))))), -(_1213896 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213898), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213896))))], (38401 ^ _782476) ^ [_1516581] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516581)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1516581)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23801 ^ _782476) ^ [_1229203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229203)))], (32038 ^ _782476) ^ [_1389362, _1389364, _1389366] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389362), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389364, _1389366)), _1389366) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389362), _1389364), _1389366))], (23017 ^ _782476) ^ [_1214237, _1214239] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214237), _1214239)))), -(_1214239 = c_Orderings_Obot__class_Obot(tc_fun(_1214237, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214237), _1214239))], (37251 ^ _782476) ^ [_1491526, _1491528] : [-(c_Divides_Odivmod__nat(_1491528, _1491526) = 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), _1491528), _1491526), _1491526))), -(_1491526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491528), _1491526)))], (26810 ^ _782476) ^ [_1288628, _1288630, _1288632, _1288634] : [class_Groups_Oordered__ab__group__add(_1288628), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288628), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288628), _1288630), _1288632)), _1288634) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288628), _1288630), _1288634)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288628), _1288632), _1288634)))], (15630 ^ _782476) ^ [_1074803, _1074805, _1074807, _1074809, _1074811, _1074813, _1074815, _1074817] : [c_Finite__Set_Ofolding__image__simple(_1074803, _1074805, _1074807, _1074809, _1074811, _1074813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074805), _1074815)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074805), _1074817)), 15644 ^ _782476 : [(15647 ^ _782476) ^ [] : [hAPP(_1074811, 15643 ^ [_1074803, _1074805, _1074807, _1074809, _1074811, _1074813, _1074815, _1074817]) = _1074809], (15645 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1074805), 15643 ^ [_1074803, _1074805, _1074807, _1074809, _1074811, _1074813, _1074815, _1074817]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074805, tc_HOL_Obool)), _1074815), _1074817))))]], -(hAPP(_1074813, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074805, tc_HOL_Obool)), _1074815), _1074817)) = hAPP(hAPP(_1074807, hAPP(_1074813, _1074815)), hAPP(_1074813, _1074817)))], (10 ^ _782476) ^ [_782599, _782601, _782603] : [-(_782603 = _782599), _782603 = _782601, _782601 = _782599], (40248 ^ _782476) ^ [_1566447, _1566449] : [c_Wellfounded_OwfP(_1566447, _1566449), -(c_Wellfounded_Owf(_1566447, hAPP(c_Set_OCollect(tc_prod(_1566447, _1566447)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566447, _1566447, tc_HOL_Obool), _1566449))))], (52395 ^ _782476) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (21189 ^ _782476) ^ [_1180435, _1180437, _1180439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180435)), _1180435 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180435), _1180439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180439), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35444 ^ _782476) ^ [_1452251, _1452253] : [class_Int_Onumber__ring(_1452251), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452251), c_Groups_Oone__class_Oone(_1452251)), c_Groups_Oone__class_Oone(_1452251))), hAPP(c_Int_Onumber__class_Onumber__of(_1452251), _1452253)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452251), c_Int_OBit0(_1452253)))], (32881 ^ _782476) ^ [_1406018, _1406020, _1406022, _1406024, _1406026, _1406028] : [class_Groups_Oab__semigroup__mult(_1406018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406020), _1406022)), 32891 ^ _782476 : [(32894 ^ _782476) ^ [] : [hAPP(_1406024, 32890 ^ [_1406018, _1406020, _1406022, _1406024, _1406026, _1406028]) = hAPP(_1406026, 32890 ^ [_1406018, _1406020, _1406022, _1406024, _1406026, _1406028])], (32892 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406020), 32890 ^ [_1406018, _1406020, _1406022, _1406024, _1406026, _1406028]), _1406022)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406018, _1406020, c_Groups_Otimes__class_Otimes(_1406018)), _1406024), _1406028), _1406022) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406018, _1406020, c_Groups_Otimes__class_Otimes(_1406018)), _1406026), _1406028), _1406022))], (26876 ^ _782476) ^ [_1289917, _1289919, _1289921] : [class_Orderings_Olinorder(_1289917), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289917), _1289919), _1289921) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289917), _1289921), _1289919))], (6590 ^ _782476) ^ [_888597, _888599, _888601, _888603, _888605] : [class_Orderings_Oorder(_888597), 6593 ^ _782476 : [(6606 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888597, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888597, _888599, _888601)), c_SetInterval_Oord__class_OatLeastAtMost(_888597, _888603, _888605)))), 6607 ^ _782476 : [(6610 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888603), _888599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888601), _888605))], (6608 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888599), _888601)))]]], (6594 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888597, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888597, _888599, _888601)), c_SetInterval_Oord__class_OatLeastAtMost(_888597, _888603, _888605))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888599), _888601)), 6601 ^ _782476 : [(6604 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888601), _888605)))], (6602 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888597), _888603), _888599)))]]]]], (38375 ^ _782476) ^ [_1516113] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1516113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1516113)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2612 ^ _782476) ^ [_820962, _820964] : [_820964 = _820962, -(c_Int_Oint__ge__less__than2(_820964) = c_Int_Oint__ge__less__than2(_820962))], (1252 ^ _782476) ^ [_801326, _801328] : [-(class_Groups_Oordered__ab__group__add(_801326)), _801328 = _801326, class_Groups_Oordered__ab__group__add(_801328)], (45511 ^ _782476) ^ [_1693439, _1693441, _1693443] : [class_Lattices_Olattice(_1693439), -(c_Big__Operators_Olattice__class_OSup__fin(_1693439, hAPP(c_List_Oset(_1693439), hAPP(hAPP(c_List_Olist_OCons(_1693439), _1693441), _1693443))) = hAPP(c_List_Ofoldl(_1693439, _1693439, c_Lattices_Osemilattice__sup__class_Osup(_1693439), _1693441), _1693443))], (618 ^ _782476) ^ [_791871, _791873, _791875, _791877, _791879, _791881, _791883, _791885, _791887, _791889] : [-(c_Typedef_Otype__definition(_791887, _791883, _791879, _791875, _791871)), c_Typedef_Otype__definition(_791889, _791885, _791881, _791877, _791873), _791889 = _791887, _791885 = _791883, _791881 = _791879, _791877 = _791875, _791873 = _791871], (6084 ^ _782476) ^ [_878787, _878789, _878791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878787, tc_HOL_Obool)), _878789), _878791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878787, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_878787, _878789)), c_Predicate_OPowp(_878787, _878791))))], (26834 ^ _782476) ^ [_1289162, _1289164, _1289166, _1289168] : [class_Orderings_Olinorder(_1289162), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289162), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289162), _1289164), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289162), _1289166), _1289168))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289162), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289162), _1289164), _1289166)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289162), _1289164), _1289168)))))], (25596 ^ _782476) ^ [_1260954, _1260956, _1260958] : [-(hAPP(hAPP(c_Set_Oinsert(_1260954), _1260956), _1260958) = hAPP(c_Set_OCollect(_1260954), hAPP(hAPP(c_COMBS(_1260954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260954), c_fdisj), hAPP(hAPP(c_COMBC(_1260954, _1260954, tc_HOL_Obool), c_fequal), _1260956))), hAPP(hAPP(c_COMBC(_1260954, tc_fun(_1260954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1260954)), _1260958))))], (37926 ^ _782476) ^ [_1504744, _1504746, _1504748, _1504750, _1504752, _1504754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504744, _1504744)), hAPP(hAPP(c_Product__Type_OPair(_1504744, _1504744), _1504746), _1504748)), hAPP(hAPP(c_Relation_Oinv__image(_1504750, _1504744), _1504752), _1504754))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504750, _1504750)), hAPP(hAPP(c_Product__Type_OPair(_1504750, _1504750), hAPP(_1504754, _1504746)), hAPP(_1504754, _1504748))), _1504752)))], (27078 ^ _782476) ^ [_1294451, _1294453, _1294455, _1294457] : [class_Fields_Olinordered__field(_1294451), -(hAPP(c_Groups_Oabs__class_Oabs(_1294451), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294453, _1294451), _1294455), _1294457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294453, _1294451), hAPP(hAPP(c_COMBB(_1294451, _1294451, _1294453), c_Groups_Oabs__class_Oabs(_1294451)), _1294455)), _1294457))], (44789 ^ _782476) ^ [_1677128, _1677130, _1677132] : [c_List_Olist_ONil(_1677128) = hAPP(hAPP(c_List_Oappend(_1677128), _1677130), _1677132), 44792 ^ _782476 : [(44795 ^ _782476) ^ [] : [-(_1677132 = c_List_Olist_ONil(_1677128))], (44793 ^ _782476) ^ [] : [-(_1677130 = c_List_Olist_ONil(_1677128))]]], (48034 ^ _782476) ^ [_1748561, _1748563] : [hAPP(c_List_Orev(_1748561), _1748563) = c_List_Olist_ONil(_1748561), -(_1748563 = c_List_Olist_ONil(_1748561))], (11190 ^ _782476) ^ [_987943, _987945, _987947, _987949] : [class_Orderings_Oorder(_987943), _987945 = _987947, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987943), _987949), _987947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987943), _987949), _987945)))], (41360 ^ _782476) ^ [_1593245, _1593247, _1593249, _1593251] : [-(c_Wellfounded_Oacyclic(_1593245, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593245, _1593245)), hAPP(hAPP(c_Product__Type_OPair(_1593245, _1593245), _1593247), _1593249)), _1593251))), c_Wellfounded_Oacyclic(_1593245, _1593251), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593245, _1593245)), hAPP(hAPP(c_Product__Type_OPair(_1593245, _1593245), _1593249), _1593247)), c_Transitive__Closure_Ortrancl(_1593245, _1593251))))], (50246 ^ _782476) ^ [_1797349, _1797351, _1797353, _1797355, _1797357, _1797359] : [-(c_Nitpick_Opair__box_OPairBox(_1797349, _1797351, _1797353, _1797355) = c_Nitpick_Opair__box_OPairBox(_1797349, _1797351, _1797357, _1797359)), _1797353 = _1797357, _1797355 = _1797359], (47610 ^ _782476) ^ [_1740467, _1740469, _1740471] : [class_Orderings_Olinorder(_1740467), c_List_Olinorder__class_Osorted(_1740467, _1740469), -(c_List_Olinorder__class_Osorted(_1740467, hAPP(hAPP(c_List_Otake(_1740467), _1740471), _1740469)))], (43087 ^ _782476) ^ [_1635258, _1635260, _1635262, _1635264, _1635266, _1635268] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635258), tc_List_Olist(_1635258))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635258), tc_List_Olist(_1635258)), hAPP(hAPP(c_List_Olist_OCons(_1635258), _1635260), _1635262)), hAPP(hAPP(c_List_Olist_OCons(_1635258), _1635264), _1635266))), c_List_Olistrel1(_1635258, _1635268)))), 43088 ^ _782476 : [(43095 ^ _782476) ^ [] : [_1635260 = _1635264, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635258), tc_List_Olist(_1635258))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635258), tc_List_Olist(_1635258)), _1635262), _1635266)), c_List_Olistrel1(_1635258, _1635268)))], (43089 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635258, _1635258)), hAPP(hAPP(c_Product__Type_OPair(_1635258, _1635258), _1635260), _1635264)), _1635268)), _1635262 = _1635266]]], (2826 ^ _782476) ^ [_824305, _824307, _824309, _824311] : [-(c_Random_Oinc__shift(_824311, _824307) = c_Random_Oinc__shift(_824309, _824305)), _824311 = _824309, _824307 = _824305], (28778 ^ _782476) ^ [_1329211, _1329213] : [class_Rings_Odivision__ring(_1329211), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329211), _1329213), c_Groups_Oone__class_Oone(_1329211)) = _1329213)], (16177 ^ _782476) ^ [_1086210, _1086212, _1086214, _1086216, _1086218] : [class_Groups_Ocomm__monoid__mult(_1086210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086212), _1086214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086212), _1086216)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086210), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086210, _1086212, c_Groups_Otimes__class_Otimes(_1086210)), _1086218), c_Groups_Oone__class_Oone(_1086210)), _1086214)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086210, _1086212, c_Groups_Otimes__class_Otimes(_1086210)), _1086218), c_Groups_Oone__class_Oone(_1086210)), _1086216)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086210), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086210, _1086212, c_Groups_Otimes__class_Otimes(_1086210)), _1086218), c_Groups_Oone__class_Oone(_1086210)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086212, tc_HOL_Obool)), _1086214), _1086216))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086210, _1086212, c_Groups_Otimes__class_Otimes(_1086210)), _1086218), c_Groups_Oone__class_Oone(_1086210)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086212, tc_HOL_Obool)), _1086214), _1086216))))], (28984 ^ _782476) ^ [_1332813, _1332815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332813)), -(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), _1332813), _1332815))))], (38847 ^ _782476) ^ [_1527561] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1527561)) = _1527561)], (48901 ^ _782476) ^ [_1767635, _1767637, _1767639, _1767641, _1767643] : [class_Orderings_Olinorder(_1767635), 48907 ^ _782476 : [(48910 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767635), hAPP(_1767641, _1767643)), hAPP(_1767641, 48906 ^ [_1767635, _1767637, _1767639, _1767641, _1767643])))], (48908 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767637), 48906 ^ [_1767635, _1767637, _1767639, _1767641, _1767643]), hAPP(c_List_Oset(_1767637), _1767639))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1767637, _1767635, _1767641), _1767643), _1767639) = hAPP(hAPP(c_List_Olist_OCons(_1767637), _1767643), _1767639))], (2086 ^ _782476) ^ [_812789, _812791, _812793, _812795] : [-(c_Enum_Oenum__the(_812795, _812791) = c_Enum_Oenum__the(_812793, _812789)), _812795 = _812793, _812791 = _812789], (45420 ^ _782476) ^ [_1691512, _1691514, _1691516] : [-(hAPP(c_List_Orotate(_1691512, _1691514), _1691516) = hAPP(hAPP(c_List_Oappend(_1691512), hAPP(hAPP(c_List_Odrop(_1691512), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691514, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691512)), _1691516))), _1691516)), hAPP(hAPP(c_List_Otake(_1691512), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691514, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691512)), _1691516))), _1691516)))], (38931 ^ _782476) ^ [_1530709, _1530711, _1530713, _1530715, _1530717, _1530719] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530709, _1530711, _1530713), _1530715), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530711, _1530713), tc_HOL_Obool)), _1530717), _1530719)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530709, _1530713), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530709, _1530711, _1530713), _1530715), _1530717)), hAPP(hAPP(c_Relation_Orel__comp(_1530709, _1530711, _1530713), _1530715), _1530719)))], (25650 ^ _782476) ^ [_1262313, _1262315, _1262317] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262313, tc_HOL_Obool)), _1262315), _1262317) = hAPP(c_Set_OCollect(_1262313), hAPP(hAPP(c_COMBS(_1262313, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262313), c_fconj), hAPP(hAPP(c_COMBC(_1262313, tc_fun(_1262313, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262313)), _1262315))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262313), c_fNot), hAPP(hAPP(c_COMBC(_1262313, tc_fun(_1262313, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262313)), _1262317)))))], (39525 ^ _782476) ^ [_1545081, _1545083, _1545085, _1545087] : [hBOOL(hAPP(hAPP(c_member(_1545081), _1545083), hAPP(c_Relation_ORange(_1545085, _1545081), _1545087))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545085, _1545081)), hAPP(hAPP(c_Product__Type_OPair(_1545085, _1545081), 39528 ^ [_1545081, _1545083, _1545085, _1545087]), _1545083)), _1545087)))], (38814 ^ _782476) ^ [_1526742, _1526744, _1526746, _1526748] : [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), _1526742), _1526744)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526746), _1526748))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526742), _1526748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526746), _1526744))], (52387 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (22076 ^ _782476) ^ [_1197521, _1197523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197521)), hAPP(c_Nat_OSuc, _1197523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197521), _1197523)))], (17061 ^ _782476) ^ [_1105855, _1105857, _1105859, _1105861, _1105863] : [class_Groups_Oab__group__add(_1105855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105857), _1105859)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105857), _1105861)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105857, _1105855), _1105863), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1105857, tc_HOL_Obool)), _1105859), _1105861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1105855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105855), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105857, _1105855), _1105863), _1105859)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105857, _1105855), _1105863), _1105861))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105857, _1105855), _1105863), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105857, tc_HOL_Obool)), _1105859), _1105861))))], (34988 ^ _782476) ^ [_1444168, _1444170, _1444172, _1444174] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444168, _1444170, _1444172), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1444174)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1444168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1444174))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444168, _1444168), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1444168, tc_fun(_1444168, _1444168)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1444168, tc_fun(_1444168, _1444168)), tc_Int_Oint), c_If(_1444168)), c_Nat__Numeral_Oneg)), _1444170)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444168, _1444168), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1444168, _1444168), tc_Int_Oint), _1444172), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1444168, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1444168, _1444170, _1444172)), c_Int_Onat)))))], (20555 ^ _782476) ^ [_1169121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169121)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1169121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4276 ^ _782476) ^ [_847304, _847306] : [_847306 = _847304, -(c_If(_847306) = c_If(_847304))], (14246 ^ _782476) ^ [_1047859] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047859), c_Orderings_Obot__class_Obot(tc_fun(_1047859, tc_HOL_Obool)))))], (4068 ^ _782476) ^ [_843984, _843986, _843988, _843990, _843992, _843994, _843996, _843998] : [-(c_New__DSequence_Opos__bind(_843998, _843994, _843990, _843986) = c_New__DSequence_Opos__bind(_843996, _843992, _843988, _843984)), _843998 = _843996, _843994 = _843992, _843990 = _843988, _843986 = _843984], (23461 ^ _782476) ^ [_1223272, _1223274, _1223276, _1223278, _1223280] : [class_Groups_Oordered__ab__semigroup__add(_1223272), class_Rings_Osemiring__1(_1223272), 23471 ^ _782476 : [(23474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223272), hAPP(_1223278, 23470 ^ [_1223272, _1223274, _1223276, _1223278, _1223280])), _1223280))], (23472 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1223274), 23470 ^ [_1223272, _1223274, _1223276, _1223278, _1223280]), _1223276)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223272), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223274, _1223272), _1223278), _1223276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223272), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223272), hAPP(c_Finite__Set_Ocard(_1223274), _1223276))), _1223280))))], (48971 ^ _782476) ^ [_1769564, _1769566, _1769568, _1769570, _1769572] : [-(hAPP(c_List_Ofilter(_1769564, _1769566), _1769568) = hAPP(hAPP(c_List_Olist_OCons(_1769564), _1769570), _1769572)), 48972 ^ _782476 : [(48973 ^ _782476) ^ [_1769692, _1769694] : [_1769568 = hAPP(hAPP(c_List_Oappend(_1769564), _1769694), hAPP(hAPP(c_List_Olist_OCons(_1769564), _1769570), _1769692)), 48979 ^ _782476 : [(48982 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1769566, 48978 ^ [_1769564, _1769566, _1769568, _1769570, _1769572, _1769692, _1769694])))], (48980 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769564), 48978 ^ [_1769564, _1769566, _1769568, _1769570, _1769572, _1769692, _1769694]), hAPP(c_List_Oset(_1769564), _1769694))))]], hBOOL(hAPP(_1769566, _1769570)), _1769572 = hAPP(c_List_Ofilter(_1769564, _1769566), _1769692)]]], (1922 ^ _782476) ^ [_809701, _809703] : [-(class_Orderings_Oord(_809701)), _809703 = _809701, class_Orderings_Oord(_809703)], (45396 ^ _782476) ^ [_1691016, _1691018, _1691020] : [-(hAPP(c_List_Otl(_1691016), hAPP(hAPP(c_List_Oappend(_1691016), _1691018), _1691020)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1691016), _1691016, hAPP(c_List_Otl(_1691016), _1691020), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1691016), tc_List_Olist(_1691016)), _1691016), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691016), tc_List_Olist(_1691016), tc_List_Olist(_1691016)), c_List_Oappend(_1691016)), _1691020))), _1691018))], (1912 ^ _782476) ^ [_809576, _809578] : [-(class_Rings_Osemiring(_809576)), _809578 = _809576, class_Rings_Osemiring(_809578)], (40500 ^ _782476) ^ [_1571565, _1571567, _1571569] : [-(c_Relation_Orefl__on(_1571565, _1571567, _1571569)), 40504 ^ _782476 : [(40507 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1571565, _1571565, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571565, tc_fun(_1571565, tc_HOL_Obool), tc_fun(_1571565, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571565, tc_HOL_Obool), tc_fun(_1571565, tc_HOL_Obool)), _1571565), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571565)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571565), c_fconj), hAPP(hAPP(c_COMBC(_1571565, tc_fun(_1571565, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571565)), _1571567)))), hAPP(hAPP(c_COMBC(_1571565, tc_fun(_1571565, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571565)), _1571567))), 40503 ^ [_1571565, _1571567, _1571569]))], (40505 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571565, _1571565)), 40503 ^ [_1571565, _1571567, _1571569]), _1571569)))]], 40509 ^ _782476 : [(40512 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571565, _1571565)), hAPP(hAPP(c_Product__Type_OPair(_1571565, _1571565), 40508 ^ [_1571565, _1571567, _1571569]), 40508 ^ [_1571565, _1571567, _1571569])), _1571569))], (40510 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571565), 40508 ^ [_1571565, _1571567, _1571569]), _1571567)))]]], (52597 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (47431 ^ _782476) ^ [_1737026, _1737028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737026)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737028))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737026), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737028)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737026)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737026)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737028))))], (45595 ^ _782476) ^ [_1695423, _1695425, _1695427, _1695429, _1695431, _1695433] : [class_Orderings_Olinorder(_1695423), 45598 ^ _782476 : [(45605 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695423), hAPP(_1695425, _1695427)), hAPP(_1695425, _1695429)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695431, _1695423, _1695425), _1695427), hAPP(hAPP(c_List_Olist_OCons(_1695431), _1695429), _1695433)) = hAPP(hAPP(c_List_Olist_OCons(_1695431), _1695429), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695431, _1695423, _1695425), _1695427), _1695433)))], (45599 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695423), hAPP(_1695425, _1695427)), hAPP(_1695425, _1695429))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695431, _1695423, _1695425), _1695427), hAPP(hAPP(c_List_Olist_OCons(_1695431), _1695429), _1695433)) = hAPP(hAPP(c_List_Olist_OCons(_1695431), _1695427), hAPP(hAPP(c_List_Olist_OCons(_1695431), _1695429), _1695433)))]]], (52635 ^ _782476) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (44895 ^ _782476) ^ [_1679197, _1679199, _1679201, _1679203] : [hBOOL(hAPP(hAPP(c_member(_1679197), _1679199), hAPP(c_List_Oset(_1679197), _1679201))), -(c_List_Oremove1(_1679197, _1679199, hAPP(hAPP(c_List_Oappend(_1679197), _1679201), _1679203)) = hAPP(hAPP(c_List_Oappend(_1679197), c_List_Oremove1(_1679197, _1679199, _1679201)), _1679203))], (42951 ^ _782476) ^ [_1630664, _1630666, _1630668] : [_1630664 = hAPP(hAPP(c_List_Olist_OCons(_1630666), _1630668), _1630664)], (14224 ^ _782476) ^ [_1047414, _1047416] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047414, _1047416)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047414, _1047416), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047414), c_Orderings_Otop__class_Otop(tc_fun(_1047414, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047416), c_Orderings_Otop__class_Otop(tc_fun(_1047416, tc_HOL_Obool))))], (52311 ^ _782476) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (7547 ^ _782476) ^ [_908991, _908993, _908995] : [class_Groups_Oordered__ab__group__add(_908991), 7550 ^ _782476 : [(7557 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), hAPP(c_Groups_Ouminus__class_Ouminus(_908991), _908995)), _908993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), hAPP(c_Groups_Ouminus__class_Ouminus(_908991), _908993)), _908995)))], (7551 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), hAPP(c_Groups_Ouminus__class_Ouminus(_908991), _908993)), _908995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), hAPP(c_Groups_Ouminus__class_Ouminus(_908991), _908995)), _908993)))]]], (35534 ^ _782476) ^ [_1453849, _1453851] : [class_Rings_Oring__1(_1453849), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453849), hAPP(c_Groups_Ouminus__class_Ouminus(_1453849), _1453851)), 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(_1453849), _1453851), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (6215 ^ _782476) ^ [_881238, _881240, _881242] : [class_Orderings_Oorder(_881238), 6218 ^ _782476 : [(6225 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881238), _881240), _881242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881238, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881238), _881240)), hAPP(c_SetInterval_Oord__class_OatMost(_881238), _881242))))], (6219 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881238, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881238), _881240)), hAPP(c_SetInterval_Oord__class_OatMost(_881238), _881242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881238), _881240), _881242)))]]], (46940 ^ _782476) ^ [_1724761, _1724763, _1724765, _1724767] : [-(c_List_Oremdups(_1724761, hAPP(hAPP(c_List_Omap(_1724763, _1724761), _1724765), c_List_Oremdups(_1724763, _1724767))) = c_List_Oremdups(_1724761, hAPP(hAPP(c_List_Omap(_1724763, _1724761), _1724765), _1724767)))], (1672 ^ _782476) ^ [_806576, _806578] : [-(class_Rings_Oordered__comm__semiring(_806576)), _806578 = _806576, class_Rings_Oordered__comm__semiring(_806578)], (43191 ^ _782476) ^ [_1638820, _1638822, _1638824, _1638826, _1638828, _1638830] : [hBOOL(hAPP(hAPP(_1638820, _1638822), _1638824)), c_List_Olistrelp(_1638826, _1638820, _1638828, _1638830), -(c_List_Olistrelp(_1638826, _1638820, hAPP(hAPP(c_List_Olist_OCons(_1638826), _1638822), _1638828), hAPP(hAPP(c_List_Olist_OCons(_1638826), _1638824), _1638830)))], (38889 ^ _782476) ^ [] : [-(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))], (37776 ^ _782476) ^ [_1501657] : [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), _1501657))), -(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), _1501657)) = 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), _1501657))))], (10125 ^ _782476) ^ [_965570, _965572, _965574, _965576] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965570, tc_HOL_Obool)), _965572), hAPP(hAPP(c_Set_Oinsert(_965570), _965574), _965576)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965570, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965570, tc_HOL_Obool)), _965572), _965576)), hAPP(hAPP(c_Set_Oinsert(_965570), _965574), c_Orderings_Obot__class_Obot(tc_fun(_965570, tc_HOL_Obool)))))], (14066 ^ _782476) ^ [_1043870, _1043872, _1043874, _1043876, _1043878] : [c_Finite__Set_Ofolding__one(_1043870, _1043872, _1043874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043870), _1043876)), hBOOL(hAPP(hAPP(c_member(_1043870), _1043878), _1043876)), 14077 ^ _782476 : [(14084 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043870, tc_HOL_Obool)), _1043876), hAPP(hAPP(c_Set_Oinsert(_1043870), _1043878), c_Orderings_Obot__class_Obot(tc_fun(_1043870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043870, tc_HOL_Obool))), -(hAPP(_1043874, _1043876) = hAPP(hAPP(_1043872, _1043878), hAPP(_1043874, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043870, tc_HOL_Obool)), _1043876), hAPP(hAPP(c_Set_Oinsert(_1043870), _1043878), c_Orderings_Obot__class_Obot(tc_fun(_1043870, tc_HOL_Obool)))))))], (14078 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043870, tc_HOL_Obool)), _1043876), hAPP(hAPP(c_Set_Oinsert(_1043870), _1043878), c_Orderings_Obot__class_Obot(tc_fun(_1043870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043870, tc_HOL_Obool)), -(hAPP(_1043874, _1043876) = _1043878)]]], (27187 ^ _782476) ^ [_1296278, _1296280, _1296282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296278), _1296280)), 27190 ^ _782476 : [(27191 ^ _782476) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296278, tc_Nat_Onat), _1296282), _1296280) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 27194 ^ _782476 : [(27195 ^ _782476) ^ [_1296440] : [hBOOL(hAPP(hAPP(c_member(_1296278), _1296440), _1296280)), -(hAPP(_1296282, _1296440) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (27201 ^ _782476) ^ [] : [27203 ^ _782476 : [(27206 ^ _782476) ^ [] : [hAPP(_1296282, 27202 ^ [_1296278, _1296280, _1296282]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (27204 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1296278), 27202 ^ [_1296278, _1296280, _1296282]), _1296280)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296278, tc_Nat_Onat), _1296282), _1296280) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (45639 ^ _782476) ^ [_1696370, _1696372, _1696374, _1696376, _1696378] : [class_Orderings_Olinorder(_1696370), -(hAPP(c_List_Oset(_1696372), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696372, _1696370, _1696374), _1696376), _1696378)) = hAPP(hAPP(c_Set_Oinsert(_1696372), _1696376), hAPP(c_List_Oset(_1696372), _1696378)))], (52593 ^ _782476) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27359 ^ _782476) ^ [_1299865, _1299867, _1299869, _1299871, _1299873] : [class_Lattices_Osemilattice__sup(_1299865), class_Orderings_Olinorder(_1299867), c_Orderings_Oorder__class_Omono(_1299867, _1299865, _1299869), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299865), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299865), hAPP(_1299869, _1299871)), hAPP(_1299869, _1299873))), hAPP(_1299869, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299867), _1299871), _1299873)))))], (37225 ^ _782476) ^ [_1491054] : [-(c_Divides_Odivmod__nat(_1491054, 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)), _1491054))], (3522 ^ _782476) ^ [_835105, _835107] : [_835107 = _835105, -(c_Int_Onumber__class_Onumber__of(_835107) = c_Int_Onumber__class_Onumber__of(_835105))], (10397 ^ _782476) ^ [_971153, _971155, _971157] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971153, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971153, tc_HOL_Obool)), _971155), _971157)), _971155)))], (49754 ^ _782476) ^ [_1786978, _1786980, _1786982, _1786984] : [-(hAPP(c_New__DSequence_Opos__union(_1786978, _1786980, _1786982), _1786984) = c_Lazy__Sequence_Oappend(_1786978, hAPP(_1786980, _1786984), hAPP(_1786982, _1786984)))], (52599 ^ _782476) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (49774 ^ _782476) ^ [_1787482, _1787484, _1787486, _1787488, _1787490] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787482, _1787484, _1787486), _1787488), _1787490)), -(hBOOL(hAPP(hAPP(_1787486, _1787490), _1787488)))], (10205 ^ _782476) ^ [_967248, _967250, _967252] : [hBOOL(hAPP(hAPP(c_member(_967248), _967250), _967252)), -(hAPP(hAPP(c_Set_Oinsert(_967248), _967250), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967248, tc_HOL_Obool)), _967252), hAPP(hAPP(c_Set_Oinsert(_967248), _967250), c_Orderings_Obot__class_Obot(tc_fun(_967248, tc_HOL_Obool))))) = _967252)], (41382 ^ _782476) ^ [_1593808, _1593810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593808), _1593810)), -(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), _1593808), _1593810)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (20611 ^ _782476) ^ [_1170015] : [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), _1170015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170015)))], (24899 ^ _782476) ^ [_1248115] : [class_Rings_Olinordered__idom(_1248115), -(hAPP(c_Groups_Oabs__class_Oabs(_1248115), c_Groups_Oone__class_Oone(_1248115)) = c_Groups_Oone__class_Oone(_1248115))], (11860 ^ _782476) ^ [_998406, _998408, _998410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998406, tc_HOL_Obool)), _998408), _998410)), 11863 ^ _782476 : [(11866 ^ _782476) ^ [] : [_998408 = _998410], (11864 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998406, tc_HOL_Obool)), _998408), _998410)))]]], (30688 ^ _782476) ^ [_1364103, _1364105, _1364107] : [class_Fields_Olinordered__field__inverse__zero(_1364103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364103), c_Groups_Ozero__class_Ozero(_1364103)), _1364105)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364103), hAPP(c_Groups_Oabs__class_Oabs(_1364103), _1364107)), _1364105) = hAPP(c_Groups_Oabs__class_Oabs(_1364103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364103), _1364107), _1364105)))], (43281 ^ _782476) ^ [_1640963, _1640965, _1640967] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640963)), _1640965), c_List_Olists(_1640963, c_Wellfounded_Oacc(_1640963, _1640967)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640963)), _1640965), c_Wellfounded_Oacc(tc_List_Olist(_1640963), c_List_Olistrel1(_1640963, _1640967)))))], (50442 ^ _782476) ^ [_1802085, _1802087, _1802089, _1802091] : [c_Relation_Otrans(_1802085, _1802087), c_Relation_Otrans(_1802089, _1802091), -(c_Relation_Otrans(tc_prod(_1802085, _1802089), c_Wellfounded_Olex__prod(_1802085, _1802089, _1802087, _1802091)))], (17329 ^ _782476) ^ [_1111351, _1111353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111351), _1111353)), _1111351 = _1111353], (41553 ^ _782476) ^ [_1598242, _1598244, _1598246] : [c_Relation_Orefl__on(_1598242, _1598244, _1598246), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598242, _1598242), tc_HOL_Obool)), _1598246), hAPP(hAPP(c_Relation_Orel__comp(_1598242, _1598242, _1598242), hAPP(c_Relation_Oconverse(_1598242, _1598242), _1598246)), _1598246))))], (5130 ^ _782476) ^ [_860833, _860835] : [_860835 = _860833, -(c_Lattices_Osemilattice__inf__class_Oinf(_860835) = c_Lattices_Osemilattice__inf__class_Oinf(_860833))], (51805 ^ _782476) ^ [_1831936, _1831938, _1831940, _1831942] : [class_Rings_Ocomm__semiring__1(_1831936), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831936), _1831938), _1831940)), _1831942)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831936), _1831940), _1831942)))], (14611 ^ _782476) ^ [_1054672, _1054674, _1054676, _1054678, _1054680, _1054682] : [c_Finite__Set_Ofolding(_1054672, _1054674, _1054676, _1054678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054672), _1054680)), hBOOL(hAPP(hAPP(c_member(_1054672), _1054682), _1054680)), -(hAPP(_1054678, _1054680) = hAPP(c_Fun_Ocomp(_1054674, _1054674, _1054674, hAPP(_1054678, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054672, tc_HOL_Obool)), _1054680), hAPP(hAPP(c_Set_Oinsert(_1054672), _1054682), c_Orderings_Obot__class_Obot(tc_fun(_1054672, tc_HOL_Obool)))))), hAPP(_1054676, _1054682)))], (45977 ^ _782476) ^ [_1702706, _1702708, _1702710, _1702712, _1702714] : [class_Rings_Osemiring__0(_1702706), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702706), hAPP(hAPP(c_List_Omap(_1702708, _1702706), hAPP(hAPP(c_COMBB(_1702706, _1702706, _1702708), hAPP(c_Groups_Otimes__class_Otimes(_1702706), _1702710)), _1702712)), _1702714)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702706), _1702710), hAPP(c_List_Omonoid__add__class_Olistsum(_1702706), hAPP(hAPP(c_List_Omap(_1702708, _1702706), _1702712), _1702714))))], (38925 ^ _782476) ^ [_1530495, _1530497, _1530499, _1530501, _1530503, _1530505, _1530507] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530495, _1530497, _1530499), _1530501), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530503, tc_fun(tc_prod(_1530497, _1530499), tc_HOL_Obool)), _1530505), _1530507)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530503, tc_fun(tc_prod(_1530495, _1530499), tc_HOL_Obool)), _1530505), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530497, _1530499), tc_HOL_Obool), tc_fun(tc_prod(_1530495, _1530499), tc_HOL_Obool), _1530503), hAPP(c_Relation_Orel__comp(_1530495, _1530497, _1530499), _1530501)), _1530507)))], (31221 ^ _782476) ^ [_1373193, _1373195, _1373197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373193)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373195), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1373197), _1373193)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373195), _1373197)), _1373193))], (47116 ^ _782476) ^ [_1729256, _1729258] : [-(c_List_Oconcat(_1729256, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729256), tc_List_Olist(_1729256)), c_List_Olist_Olist__case(tc_List_Olist(_1729256), _1729256, c_List_Olist_ONil(_1729256), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729256), tc_fun(tc_List_Olist(_1729256), tc_List_Olist(_1729256)), _1729256), c_COMBK(tc_List_Olist(_1729256), tc_List_Olist(_1729256))), hAPP(hAPP(c_COMBC(_1729256, tc_List_Olist(_1729256), tc_List_Olist(_1729256)), c_List_Olist_OCons(_1729256)), c_List_Olist_ONil(_1729256))))), _1729258)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729256), _1729256), c_List_Ohd(_1729256)), hAPP(c_List_Ofilter(tc_List_Olist(_1729256), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1729256)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729256), tc_List_Olist(_1729256), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1729256)))), _1729258)))], (8250 ^ _782476) ^ [_924435, _924437, _924439] : [class_Orderings_Olinorder(_924435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924435), _924437), _924439)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924435, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924435, _924437), _924439)), hAPP(c_SetInterval_Oord__class_OatLeast(_924435), _924439)) = hAPP(c_SetInterval_Oord__class_OatLeast(_924435), _924437))], (40617 ^ _782476) ^ [_1575200, _1575202, _1575204, _1575206, _1575208, _1575210] : [40620 ^ _782476 : [(40623 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1575206), _1575208), hAPP(hAPP(_1575210, 40618 ^ [_1575200, _1575202, _1575204, _1575206, _1575208, _1575210]), 40619 ^ [_1575200, _1575202, _1575204, _1575206, _1575208, _1575210])))], (40621 ^ _782476) ^ [] : [-(_1575200 = hAPP(hAPP(c_Product__Type_OPair(_1575202, _1575204), 40618 ^ [_1575200, _1575202, _1575204, _1575206, _1575208, _1575210]), 40619 ^ [_1575200, _1575202, _1575204, _1575206, _1575208, _1575210]))]], -(hBOOL(hAPP(hAPP(c_member(_1575206), _1575208), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1575202, _1575204, tc_fun(_1575206, tc_HOL_Obool)), _1575210), _1575200))))], (35570 ^ _782476) ^ [_1454489] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454489))), 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), _1454489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (18268 ^ _782476) ^ [_1127642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127642), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51592 ^ _782476) ^ [_1828084, _1828086, _1828088] : [51594 ^ _782476 : [(51597 ^ _782476) ^ [] : [hBOOL(hAPP(_1828084, 51593 ^ [_1828084, _1828086, _1828088]))], (51595 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51593 ^ [_1828084, _1828086, _1828088]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1828086), _1828088))))]], -(c_List_Oall__interval__nat(_1828084, _1828086, _1828088))], (6501 ^ _782476) ^ [_886901, _886903, _886905, _886907, _886909, _886911] : [c_Predicate_Oinv__imagep(_886901, _886903, _886905, _886907, _886909, _886911), -(hBOOL(hAPP(hAPP(_886905, hAPP(_886907, _886909)), hAPP(_886907, _886911))))], (39380 ^ _782476) ^ [_1541488, _1541490] : [c_FunDef_Oreduction__pair(_1541488, _1541490), 39383 ^ _782476 : [(39386 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541488, _1541488, _1541488), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool), tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool)), _1541490)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool), tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool)), _1541490))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool), tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool)), _1541490))))], (39384 ^ _782476) ^ [] : [-(c_Wellfounded_Owf(_1541488, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool), tc_fun(tc_prod(_1541488, _1541488), tc_HOL_Obool)), _1541490)))]]], (40039 ^ _782476) ^ [_1560834, _1560836, _1560838, _1560840] : [c_Finite__Set_Ofolding(_1560834, _1560836, _1560838, _1560840), -(hAPP(_1560840, c_Orderings_Obot__class_Obot(tc_fun(_1560834, tc_HOL_Obool))) = c_Fun_Oid(_1560836))], (16579 ^ _782476) ^ [_1094894, _1094896, _1094898, _1094900] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094894), 16582 ^ _782476 : [(16589 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094894), _1094898), _1094900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094894), _1094896), _1094898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094894), _1094896), _1094900))))], (16583 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094894), _1094896), _1094898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094894), _1094896), _1094900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094894), _1094898), _1094900)))]]], (43660 ^ _782476) ^ [_1652072, _1652074, _1652076] : [-(_1652072 = _1652074), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652076)), _1652072) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652076)), _1652074), 43666 ^ _782476 : [(43669 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1652076, _1652076, tc_HOL_Obool), c_fequal), 43665 ^ [_1652072, _1652074, _1652076]))], (43667 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652076, _1652076)), 43665 ^ [_1652072, _1652074, _1652076]), hAPP(c_List_Oset(tc_prod(_1652076, _1652076)), hAPP(hAPP(c_List_Ozip(_1652076, _1652076), _1652072), _1652074)))))]]], (31251 ^ _782476) ^ [_1373779, _1373781, _1373783] : [class_Divides_Osemiring__div(_1373779), -(_1373781 = c_Groups_Ozero__class_Ozero(_1373779)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373779), _1373781), _1373783)), _1373781) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373779), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373779), _1373783), _1373781)), c_Groups_Oone__class_Oone(_1373779)))], (47724 ^ _782476) ^ [_1742230, _1742232, _1742234, _1742236] : [class_Orderings_Olinorder(_1742230), -(c_List_Olinorder__class_Osorted(_1742230, hAPP(hAPP(c_List_Omap(_1742232, _1742230), _1742234), c_List_Olinorder__class_Osort__key(_1742232, _1742230, _1742234, _1742236))))], (21135 ^ _782476) ^ [_1179619] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179619), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1179619)], (22850 ^ _782476) ^ [_1211050, _1211052] : [class_Rings_Osemiring__1(_1211050), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211050), hAPP(c_Nat_OSuc, _1211052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211050), c_Groups_Oone__class_Oone(_1211050)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211050), _1211052)))], (52237 ^ _782476) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (6650 ^ _782476) ^ [_889734, _889736, _889738, _889740, _889742, _889744, _889746, _889748] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889734, tc_fun(_889736, tc_fun(_889738, tc_HOL_Obool))), _889740), _889742), _889744), _889746)), -(hBOOL(hAPP(hAPP(hAPP(_889742, _889748), _889744), _889746))), hBOOL(hAPP(hAPP(c_member(_889734), _889748), _889740))], (46182 ^ _782476) ^ [_1708164, _1708166, _1708168, _1708170] : [class_Groups_Ocomm__monoid__add(_1708164), 46185 ^ _782476 : [(46192 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1708166), _1708168))), -(c_Nitpick_Osetsum_H(_1708166, _1708164, _1708170, _1708168) = c_Groups_Ozero__class_Ozero(_1708164))], (46186 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1708166), _1708168)), -(c_Nitpick_Osetsum_H(_1708166, _1708164, _1708170, _1708168) = hAPP(c_List_Omonoid__add__class_Olistsum(_1708164), hAPP(hAPP(c_List_Omap(_1708166, _1708164), _1708170), c_Hilbert__Choice_OEps(tc_List_Olist(_1708166), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708166), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708166)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708166), tc_fun(_1708166, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1708166, tc_HOL_Obool), tc_fun(tc_fun(_1708166, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1708166)), c_fequal), c_List_Oset(_1708166))), _1708168))), c_List_Odistinct(_1708166))))))]]], (20573 ^ _782476) ^ [_1169390] : [_1169390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169390) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22182 ^ _782476) ^ [_1199187, _1199189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199187), hAPP(c_Nat_OSuc, _1199189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199187), _1199189))), -(_1199187 = hAPP(c_Nat_OSuc, _1199189))], (45054 ^ _782476) ^ [_1683498, _1683500, _1683502, _1683504, _1683506] : [hAPP(hAPP(c_List_Odrop(_1683498), _1683500), _1683502) = hAPP(hAPP(c_List_Olist_OCons(_1683498), _1683504), _1683506), -(hAPP(hAPP(c_List_Onth(_1683498), _1683502), _1683500) = _1683504)], (33998 ^ _782476) ^ [_1427058, _1427060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427058), _1427060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427058)), c_Int_OBit1(_1427060))))], (12732 ^ _782476) ^ [_1015806, _1015808, _1015810, _1015812, _1015814] : [c_Fun_Oinj__on(_1015806, _1015808, _1015810, _1015812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015806, tc_HOL_Obool)), _1015814), _1015812)), -(c_Fun_Oinj__on(_1015806, _1015808, _1015810, _1015814))], (10405 ^ _782476) ^ [_971405, _971407, _971409, _971411] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971405, tc_HOL_Obool)), _971407), _971409)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971405, tc_HOL_Obool)), _971411), _971409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971405, tc_HOL_Obool)), _971407), _971409)), _971411))], (29022 ^ _782476) ^ [_1333619, _1333621] : [-(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), _1333619)), _1333621))))], (2774 ^ _782476) ^ [_823485, _823487, _823489, _823491] : [-(c_Wellfounded_Omax__ext(_823491, _823487) = c_Wellfounded_Omax__ext(_823489, _823485)), _823491 = _823489, _823487 = _823485], (15476 ^ _782476) ^ [_1071704, _1071706, _1071708, _1071710, _1071712] : [c_Finite__Set_Ofolding__one__idem(_1071704, _1071706, _1071708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071704), _1071710)), -(_1071710 = c_Orderings_Obot__class_Obot(tc_fun(_1071704, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071704), _1071712)), -(_1071712 = c_Orderings_Obot__class_Obot(tc_fun(_1071704, tc_HOL_Obool))), -(hAPP(_1071708, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071704, tc_HOL_Obool)), _1071710), _1071712)) = hAPP(hAPP(_1071706, hAPP(_1071708, _1071710)), hAPP(_1071708, _1071712)))], (21437 ^ _782476) ^ [_1184845] : [-(hBOOL(hAPP(_1184845, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21444 ^ [_1184845])))), 21438 ^ _782476 : [(21439 ^ _782476) ^ [_1184897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184897)), hBOOL(hAPP(_1184845, _1184897))]]], (16224 ^ _782476) ^ [_1087388, _1087390] : [class_Rings_Ocomm__semiring__1(_1087388), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087388), _1087390), c_Groups_Oone__class_Oone(_1087388)) = _1087390)], (45234 ^ _782476) ^ [_1687777, _1687779, _1687781, _1687783] : [-(hAPP(c_List_Orotate1(_1687779), hAPP(hAPP(c_List_Olist_OCons(_1687779), _1687781), _1687783)) = hAPP(hAPP(c_List_Oappend(_1687779), _1687783), hAPP(hAPP(c_List_Olist_OCons(_1687779), _1687781), c_List_Olist_ONil(_1687779))))], (42925 ^ _782476) ^ [_1630127, _1630129, _1630131, _1630133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630127)), _1630129)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630127)), _1630131))), _1630129 = hAPP(hAPP(c_List_Olist_OCons(_1630127), _1630133), _1630131)], (17662 ^ _782476) ^ [_1117367, _1117369, _1117371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117367), _1117369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117367), _1117371)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117369), _1117371))))], (36924 ^ _782476) ^ [_1485530, _1485532, _1485534, _1485536, _1485538, _1485540] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485530, _1485532, _1485534), _1485536), hAPP(hAPP(c_Product__Type_OPair(_1485530, _1485532), _1485538), _1485540)) = hAPP(hAPP(_1485536, _1485538), _1485540))], (32563 ^ _782476) ^ [_1399266, _1399268, _1399270] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399266, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399266), _1399268), _1399270), -(_1399268 = c_Orderings_Obot__class_Obot(tc_fun(_1399266, tc_HOL_Obool)))], (11136 ^ _782476) ^ [_987112, _987114, _987116] : [class_Orderings_Oorder(_987112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987112), _987114), _987116)), _987114 = _987116], (34004 ^ _782476) ^ [_1427180, _1427182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427180)), c_Int_OBit1(_1427182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427180), _1427182)))], (48294 ^ _782476) ^ [_1754069, _1754071, _1754073] : [class_Orderings_Olinorder(_1754069), c_List_Olinorder__class_Osorted(_1754069, _1754071), -(c_List_Olinorder__class_Osorted(_1754069, c_List_OtakeWhile(_1754069, _1754073, _1754071)))], (10887 ^ _782476) ^ [_982995, _982997] : [class_Orderings_Olinorder(_982995), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982995, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_982995), _982997)), hAPP(hAPP(c_Set_Oinsert(_982995), _982997), c_Orderings_Obot__class_Obot(tc_fun(_982995, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_982995), _982997))], (37269 ^ _782476) ^ [_1491745, _1491747] : [-(_1491745 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1491747, _1491745) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491747), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491745)))], (8750 ^ _782476) ^ [_935058, _935060, _935062, _935064] : [class_Lattices_Osemilattice__inf(_935058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935058), _935060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935058), _935062), _935064))), 8757 ^ _782476 : [(8760 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935058), _935060), _935064)))], (8758 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935058), _935060), _935062)))]]], (49432 ^ _782476) ^ [_1779146, _1779148, _1779150, _1779152, _1779154] : [_1779146 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779148, _1779150, _1779152, _1779154), _1779146) = c_Lazy__Sequence_Oempty(_1779150))], (37672 ^ _782476) ^ [_1499356, _1499358, _1499360] : [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), _1499356), _1499358))), -(hBOOL(hAPP(hAPP(_1499360, _1499356), _1499358))), 37679 ^ _782476 : [(37682 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37678 ^ [_1499356, _1499358, _1499360]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1499360, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37677 ^ [_1499356, _1499358, _1499360])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37678 ^ [_1499356, _1499358, _1499360]))))], (37688 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1499360, 37677 ^ [_1499356, _1499358, _1499360]), 37678 ^ [_1499356, _1499358, _1499360]))], (37680 ^ _782476) ^ [] : [-(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), 37677 ^ [_1499356, _1499358, _1499360]), 37678 ^ [_1499356, _1499358, _1499360]))))]]], (47291 ^ _782476) ^ [_1733835, _1733837, _1733839, _1733841] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1733835, tc_Nat_Onat), _1733835), c_Product__Type_Ofst(_1733835, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733835, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733835, tc_Nat_Onat)), _1733837), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1733835, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1733835, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1733835, tc_Nat_Onat), _1733839), _1733841))) = hAPP(hAPP(c_List_Omap(tc_prod(_1733835, tc_Nat_Onat), _1733835), c_Product__Type_Ofst(_1733835, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733835, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733835, tc_Nat_Onat)), _1733837), c_Product__Type_Osnd(_1733835, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1733835, tc_Nat_Onat), _1733839), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1733841)))))], (14310 ^ _782476) ^ [_1049029, _1049031, _1049033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049029), _1049031)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049029), _1049033)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049029), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1049029, tc_HOL_Obool)), _1049031), _1049033))))], (3784 ^ _782476) ^ [_839228, _839230, _839232, _839234] : [-(c_List_Olex(_839234, _839230) = c_List_Olex(_839232, _839228)), _839234 = _839232, _839230 = _839228], (40173 ^ _782476) ^ [_1564405, _1564407] : [-(c_Product__Type_Omap__pair(_1564405, _1564405, _1564407, _1564407, c_COMBI(_1564405), c_COMBI(_1564407)) = c_Fun_Oid(tc_prod(_1564405, _1564407)))], (6965 ^ _782476) ^ [_896658, _896660, _896662] : [hBOOL(hAPP(hAPP(c_member(_896658), _896660), _896662)), -(hBOOL(hAPP(_896662, _896660)))], (38899 ^ _782476) ^ [_1528940, _1528942, _1528944] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1528940, hAPP(hAPP(c_COMBC(_1528940, tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_fun(_1528940, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528940, tc_fun(tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_fun(_1528940, tc_HOL_Obool)), _1528940), c_COMBC(_1528940, tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528940, tc_prod(_1528940, _1528940)), tc_fun(_1528940, tc_fun(tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_HOL_Obool)), _1528940), hAPP(c_COMBB(tc_prod(_1528940, _1528940), tc_fun(tc_fun(tc_prod(_1528940, _1528940), tc_HOL_Obool), tc_HOL_Obool), _1528940), c_member(tc_prod(_1528940, _1528940)))), c_Product__Type_OPair(_1528940, _1528940)))), _1528942)), _1528944)), -(hBOOL(hAPP(hAPP(c_member(_1528940), _1528944), c_Wellfounded_Oacc(_1528940, _1528942))))], (21231 ^ _782476) ^ [_1181136, _1181138, _1181140, _1181142, _1181144] : [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), _1181136), _1181138)), _1181140)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181136), _1181142)), _1181144))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181140), _1181136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181144), _1181136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181138), _1181142)))], (18884 ^ _782476) ^ [_1138097, _1138099, _1138101] : [class_Rings_Olinordered__ring__strict(_1138097), 18887 ^ _782476 : [(18902 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138097), _1138099), _1138101)))), 18903 ^ _782476 : [(18910 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), _1138099), c_Groups_Ozero__class_Ozero(_1138097))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), _1138101), c_Groups_Ozero__class_Ozero(_1138097)))], (18904 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), _1138099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), _1138101))]]], (18888 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138097), _1138099), _1138101))), 18893 ^ _782476 : [(18896 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), _1138101)))], (18894 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), c_Groups_Ozero__class_Ozero(_1138097)), _1138099)))]], 18897 ^ _782476 : [(18900 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), _1138101), c_Groups_Ozero__class_Ozero(_1138097))))], (18898 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138097), _1138099), c_Groups_Ozero__class_Ozero(_1138097))))]]]]], (49460 ^ _782476) ^ [_1779856, _1779858, _1779860] : [-(hAPP(c_New__DSequence_Oneg__single(_1779856, _1779858), _1779860) = c_Lazy__Sequence_Ohb__single(_1779856, _1779858))], (10907 ^ _782476) ^ [_983528, _983530, _983532, _983534, _983536, _983538] : [-(hBOOL(hAPP(hAPP(c_member(_983528), _983530), _983532))), -(hAPP(c_Set_Oimage(_983528, _983534, c_Fun_Ofun__upd(_983528, _983534, _983536, _983530, _983538)), _983532) = hAPP(c_Set_Oimage(_983528, _983534, _983536), _983532))], (21648 ^ _782476) ^ [_1188890, _1188892, _1188894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188890)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188892), _1188894)), 21655 ^ _782476 : [(21656 ^ _782476) ^ [_1189080] : [21658 ^ _782476 : [(21664 ^ _782476) ^ [] : [-(_1189080 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21660 ^ [_1188890, _1188892, _1188894, _1189080]), 21657 ^ [_1188890, _1188892, _1188894, _1189080]))], (21662 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21660 ^ [_1188890, _1188892, _1188894, _1189080]), _1188894)))], (21659 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21657 ^ [_1188890, _1188892, _1188894, _1189080]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188890))))]], -(_1189080 = _1188892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1189080), _1188890) = _1188892]]], (12798 ^ _782476) ^ [_1016976, _1016978, _1016980, _1016982] : [class_Orderings_Oorder(_1016976), class_Orderings_Olinorder(_1016978), c_Orderings_Oorder__class_Ostrict__mono(_1016978, _1016976, _1016980), -(c_Fun_Oinj__on(_1016978, _1016976, _1016980, _1016982))], (37391 ^ _782476) ^ [_1494069, _1494071] : [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), _1494069), _1494071))), 37394 ^ _782476 : [(37403 ^ _782476) ^ [] : [-(c_Divides_OposDivAlg(_1494069, _1494071) = hAPP(c_Divides_Oadjust(_1494071), c_Divides_OposDivAlg(_1494069, 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)))), _1494071)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494069), _1494071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494071), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37395 ^ _782476) ^ [] : [37396 ^ _782476 : [(37399 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494071), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37397 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494069), _1494071))]], -(c_Divides_OposDivAlg(_1494069, _1494071) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494069))]]], (44506 ^ _782476) ^ [_1670106, _1670108, _1670110, _1670112, _1670114, _1670116] : [-(hAPP(c_List_Olist_Olist__case(_1670106, _1670108, _1670110, _1670112), hAPP(hAPP(c_List_Olist_OCons(_1670108), _1670114), _1670116)) = hAPP(hAPP(_1670112, _1670114), _1670116))], (50575 ^ _782476) ^ [_1805033, _1805035] : [c_Relation_Otrans(_1805033, _1805035), -(c_Relation_Otrans(tc_List_Olist(_1805033), c_List_Olistrel(_1805033, _1805035)))], (18270 ^ _782476) ^ [_1127676] : [-(_1127676 = 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)), _1127676)))], (52223 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (48276 ^ _782476) ^ [_1753549, _1753551, _1753553] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753549), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753549))), _1753551))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753553), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753549))), _1753551))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753549))), hAPP(c_List_Ofilter(tc_List_Olist(_1753549), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1753549)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753553)), c_Nat_Osize__class_Osize(tc_List_Olist(_1753549)))), c_List_Otranspose(_1753549, _1753551))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753549)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753549)), _1753551), _1753553)))], (5728 ^ _782476) ^ [_870204, _870206, _870208, _870210] : [-(tc_fun(_870210, _870206) = tc_fun(_870208, _870204)), _870210 = _870208, _870206 = _870204], (25321 ^ _782476) ^ [_1255683, _1255685] : [class_Rings_Olinordered__idom(_1255683), 25324 ^ _782476 : [(25331 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255683), c_Groups_Ozero__class_Ozero(_1255683)), _1255685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255683), c_Groups_Ozero__class_Ozero(_1255683)), c_Groups_Osgn__class_Osgn(_1255683, _1255685))))], (25325 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255683), c_Groups_Ozero__class_Ozero(_1255683)), c_Groups_Osgn__class_Osgn(_1255683, _1255685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255683), c_Groups_Ozero__class_Ozero(_1255683)), _1255685)))]]], (22776 ^ _782476) ^ [_1209723, _1209725, _1209727] : [class_Rings_Oring__1(_1209723), hBOOL(hAPP(hAPP(c_member(_1209723), _1209725), c_Int_Oring__1__class_OInts(_1209723))), hBOOL(hAPP(hAPP(c_member(_1209723), _1209727), c_Int_Oring__1__class_OInts(_1209723))), -(hBOOL(hAPP(hAPP(c_member(_1209723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209723), _1209725), _1209727)), c_Int_Oring__1__class_OInts(_1209723))))], (37377 ^ _782476) ^ [_1493708, _1493710, _1493712, _1493714, _1493716, _1493718, _1493720] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493708, _1493710), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493712), _1493714))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493716, _1493710), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493718), _1493720))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1493710)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493708), _1493716), _1493710), 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), _1493712), _1493718)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493714), _1493720)), _1493710))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493714), _1493720), _1493710)))))], (13068 ^ _782476) ^ [_1022406, _1022408, _1022410] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022406, tc_HOL_Obool)), _1022408), hAPP(hAPP(c_Set_Oinsert(_1022406), _1022410), c_Orderings_Obot__class_Obot(tc_fun(_1022406, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1022406, _1022410, _1022408) = c_HOL_OThe(_1022406, hAPP(hAPP(c_COMBC(_1022406, tc_fun(_1022406, tc_HOL_Obool), tc_HOL_Obool), c_member(_1022406)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022406, tc_HOL_Obool)), _1022408), hAPP(hAPP(c_Set_Oinsert(_1022406), _1022410), c_Orderings_Obot__class_Obot(tc_fun(_1022406, tc_HOL_Obool)))))))], (45432 ^ _782476) ^ [_1691751, _1691753, _1691755, _1691757] : [45433 ^ _782476 : [(45434 ^ _782476) ^ [_1691848, _1691850] : [_1691751 = hAPP(hAPP(c_List_Olist_OCons(_1691753), _1691850), _1691848)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691753), tc_List_Olist(_1691753))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691753), tc_List_Olist(_1691753)), _1691755), hAPP(hAPP(c_List_Oappend(_1691753), _1691755), _1691751))), c_List_Olexord(_1691753, _1691757))))], (39577 ^ _782476) ^ [_1546704, _1546706, _1546708] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1546704), _1546706), _1546708) = c_Nitpick_OAbs__Frac(_1546704, c_Nitpick_Onorm__frac(_1546706, _1546708)))], (3324 ^ _782476) ^ [_832082, _832084, _832086, _832088] : [-(c_HOL_OLet(_832088, _832084) = c_HOL_OLet(_832086, _832082)), _832088 = _832086, _832084 = _832082], (51504 ^ _782476) ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748)), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), _1824750), _1824752)), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), _1824754), _1824756))), c_Transitive__Closure_Ortrancl(tc_prod(_1824746, _1824748), _1824758))), hBOOL(hAPP(hAPP(_1824760, _1824754), _1824756)), 51517 ^ _782476 : [(51520 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748)), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), 51515 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]), 51516 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760])), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), _1824754), _1824756))), c_Transitive__Closure_Ortrancl(tc_prod(_1824746, _1824748), _1824758))))], (51522 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1824760, 51515 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]), 51516 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760])))], (51524 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1824760, 51513 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]), 51514 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]))], (51518 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824746, _1824748), tc_prod(_1824746, _1824748)), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), 51513 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]), 51514 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760])), hAPP(hAPP(c_Product__Type_OPair(_1824746, _1824748), 51515 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]), 51516 ^ [_1824746, _1824748, _1824750, _1824752, _1824754, _1824756, _1824758, _1824760]))), _1824758)))]], -(hBOOL(hAPP(hAPP(_1824760, _1824750), _1824752)))], (24344 ^ _782476) ^ [_1238116, _1238118] : [c_Nat__Transfer_Onat__set(_1238116), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1238118), _1238116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238118)))], (5376 ^ _782476) ^ [_864674, _864676, _864678, _864680, _864682, _864684, _864686, _864688] : [-(c_Fun_Ocomp(_864688, _864684, _864680, _864676) = c_Fun_Ocomp(_864686, _864682, _864678, _864674)), _864688 = _864686, _864684 = _864682, _864680 = _864678, _864676 = _864674], (34048 ^ _782476) ^ [_1427873, _1427875] : [class_Int_Onumber__ring(_1427873), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427873), c_Int_OBit1(_1427875)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427873), c_Groups_Oone__class_Oone(_1427873)), hAPP(c_Int_Onumber__class_Onumber__of(_1427873), _1427875))), hAPP(c_Int_Onumber__class_Onumber__of(_1427873), _1427875)))], (12069 ^ _782476) ^ [_1002084, _1002086, _1002088, _1002090, _1002092] : [class_Complete__Lattice_Ocomplete__lattice(_1002084), class_Orderings_Olinorder(_1002084), 12076 ^ _782476 : [(12086 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002084), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002086, _1002084), _1002088), _1002090)), _1002092))), 12087 ^ _782476 : [(12088 ^ _782476) ^ [_1002432] : [hBOOL(hAPP(hAPP(c_member(_1002086), _1002432), _1002088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002084), hAPP(_1002090, _1002432)), _1002092))]]], (12077 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002084), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002086, _1002084), _1002088), _1002090)), _1002092)), 12081 ^ _782476 : [(12084 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002084), hAPP(_1002090, 12080 ^ [_1002084, _1002086, _1002088, _1002090, _1002092])), _1002092)))], (12082 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002086), 12080 ^ [_1002084, _1002086, _1002088, _1002090, _1002092]), _1002088)))]]]]], (39919 ^ _782476) ^ [_1556498, _1556500, _1556502, _1556504] : [_1556498 = c_Orderings_Obot__class_Obot(tc_fun(_1556500, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556500, _1556502), _1556502, c_Product__Type_Osnd(_1556500, _1556502)), hAPP(hAPP(c_Product__Type_OSigma(_1556500, _1556502), _1556498), hAPP(c_COMBK(tc_fun(_1556502, tc_HOL_Obool), _1556500), _1556504))) = c_Orderings_Obot__class_Obot(tc_fun(_1556502, tc_HOL_Obool)))], (49615 ^ _782476) ^ [_1783420] : [-(c_Hilbert__Choice_Oinv__into(_1783420, _1783420, c_Orderings_Otop__class_Otop(tc_fun(_1783420, tc_HOL_Obool)), c_Fun_Oid(_1783420)) = c_Fun_Oid(_1783420))], (24010 ^ _782476) ^ [_1232653] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1232653) = 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), _1232653))))], (19206 ^ _782476) ^ [_1144017, _1144019, _1144021, _1144023] : [class_Rings_Olinordered__ring__strict(_1144017), 19209 ^ _782476 : [(19224 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144017), _1144019), _1144021)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144017), _1144019), _1144023)))), 19225 ^ _782476 : [(19232 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144019), c_Groups_Ozero__class_Ozero(_1144017))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144023), _1144021))], (19226 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), c_Groups_Ozero__class_Ozero(_1144017)), _1144019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144021), _1144023))]]], (19210 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144017), _1144019), _1144021)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144017), _1144019), _1144023))), 19215 ^ _782476 : [(19218 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144021), _1144023)))], (19216 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), c_Groups_Ozero__class_Ozero(_1144017)), _1144019)))]], 19219 ^ _782476 : [(19222 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144023), _1144021)))], (19220 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144017), _1144019), c_Groups_Ozero__class_Ozero(_1144017))))]]]]], (26060 ^ _782476) ^ [_1275479, _1275481] : [class_Orderings_Olinorder(_1275479), -(c_Big__Operators_Olinorder__class_OMin(_1275479, hAPP(hAPP(c_Set_Oinsert(_1275479), _1275481), c_Orderings_Obot__class_Obot(tc_fun(_1275479, tc_HOL_Obool)))) = _1275481)], (33640 ^ _782476) ^ [_1420160, _1420162, _1420164, _1420166] : [class_Int_Onumber__ring(_1420160), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420160), hAPP(c_Int_Onumber__class_Onumber__of(_1420160), _1420162)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1420160), _1420164), hAPP(c_Int_Onumber__class_Onumber__of(_1420160), _1420166))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420160), hAPP(c_Int_Onumber__class_Onumber__of(_1420160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1420162), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1420166)))), _1420164))], (48699 ^ _782476) ^ [_1762463, _1762465] : [-(hAPP(c_List_OremoveAll(_1762463, _1762465), c_List_Olist_ONil(_1762463)) = c_List_Olist_ONil(_1762463))], (52295 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (8900 ^ _782476) ^ [_937687, _937689, _937691] : [class_Lattices_Olattice(_937687), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937687), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937687), _937689), _937691)), _937689)))], (40416 ^ _782476) ^ [_1569965, _1569967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569965, _1569965)), _1569967)), 40419 ^ _782476 : [(40426 ^ _782476) ^ [] : [c_Wellfounded_Oacyclic(_1569965, _1569967), -(c_Wellfounded_Owf(_1569965, _1569967))], (40420 ^ _782476) ^ [] : [c_Wellfounded_Owf(_1569965, _1569967), -(c_Wellfounded_Oacyclic(_1569965, _1569967))]]], (12742 ^ _782476) ^ [_1015975, _1015977, _1015979, _1015981, _1015983] : [c_Fun_Oinj__on(_1015975, _1015977, _1015979, c_Orderings_Otop__class_Otop(tc_fun(_1015975, tc_HOL_Obool))), hAPP(_1015979, _1015981) = hAPP(_1015979, _1015983), -(_1015981 = _1015983)], (32638 ^ _782476) ^ [_1400495, _1400497, _1400499] : [-(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), _1400495), _1400497)), _1400499), _1400497) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400499, _1400497))], (4062 ^ _782476) ^ [_843899, _843901] : [_843901 = _843899, -(c_New__DSequence_Opos__empty(_843901) = c_New__DSequence_Opos__empty(_843899))], (25626 ^ _782476) ^ [_1261812, _1261814, _1261816] : [hBOOL(hAPP(_1261812, _1261814)), -(hAPP(c_Set_OCollect(_1261816), hAPP(hAPP(c_COMBS(_1261816, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261816), c_fconj), hAPP(c_fequal, _1261814))), _1261812)) = hAPP(hAPP(c_Set_Oinsert(_1261816), _1261814), c_Orderings_Obot__class_Obot(tc_fun(_1261816, tc_HOL_Obool))))], (44548 ^ _782476) ^ [_1671489, _1671491, _1671493, _1671495, _1671497, _1671499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671489), tc_List_Olist(_1671489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671489), tc_List_Olist(_1671489)), hAPP(hAPP(c_List_Oappend(_1671489), _1671491), hAPP(hAPP(c_List_Olist_OCons(_1671489), _1671493), c_List_Olist_ONil(_1671489)))), hAPP(hAPP(c_List_Oappend(_1671489), _1671495), hAPP(hAPP(c_List_Olist_OCons(_1671489), _1671497), c_List_Olist_ONil(_1671489))))), c_List_Olistrel1(_1671489, _1671499))), 44553 ^ _782476 : [(44556 ^ _782476) ^ [] : [-(_1671493 = _1671497)], (44554 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671489), tc_List_Olist(_1671489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671489), tc_List_Olist(_1671489)), _1671491), _1671495)), c_List_Olistrel1(_1671489, _1671499))))]], 44557 ^ _782476 : [(44560 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1671489, _1671489)), hAPP(hAPP(c_Product__Type_OPair(_1671489, _1671489), _1671493), _1671497)), _1671499)))], (44558 ^ _782476) ^ [] : [-(_1671491 = _1671495)]]], (47224 ^ _782476) ^ [_1731588, _1731590, _1731592] : [-(c_List_Oremdups(_1731588, hAPP(c_List_Ofilter(_1731588, _1731590), _1731592)) = hAPP(c_List_Ofilter(_1731588, _1731590), c_List_Oremdups(_1731588, _1731592)))], (39552 ^ _782476) ^ [_1545988, _1545990, _1545992, _1545994] : [hBOOL(hAPP(hAPP(c_member(_1545990), _1545994), hAPP(c_Relation_ORange(_1545988, _1545990), _1545992))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1545988, _1545990, hAPP(hAPP(c_COMBC(_1545988, tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_fun(_1545990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545990, tc_fun(tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_fun(_1545990, tc_HOL_Obool)), _1545988), c_COMBC(_1545990, tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545990, tc_prod(_1545988, _1545990)), tc_fun(_1545990, tc_fun(tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_HOL_Obool)), _1545988), hAPP(c_COMBB(tc_prod(_1545988, _1545990), tc_fun(tc_fun(tc_prod(_1545988, _1545990), tc_HOL_Obool), tc_HOL_Obool), _1545990), c_member(tc_prod(_1545988, _1545990)))), c_Product__Type_OPair(_1545988, _1545990)))), _1545992)), _1545994)))], (38796 ^ _782476) ^ [_1526339, _1526341, _1526343, _1526345] : [c_FunDef_Oreduction__pair(_1526339, _1526341), -(c_FunDef_Oreduction__pair(_1526343, hAPP(hAPP(c_FunDef_Orp__inv__image(_1526339, _1526343), _1526341), _1526345)))], (20653 ^ _782476) ^ [] : [-(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))], (16809 ^ _782476) ^ [_1099651, _1099653, _1099655, _1099657, _1099659, _1099661] : [class_Rings_Oring(_1099651), 16812 ^ _782476 : [(16819 ^ _782476) ^ [] : [_1099657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099651), _1099659), _1099653)), _1099655)), _1099661), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), _1099653), _1099655)), _1099657) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), _1099659), _1099655)), _1099661))], (16813 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), _1099653), _1099655)), _1099657) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), _1099659), _1099655)), _1099661), -(_1099657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099651), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099651), _1099659), _1099653)), _1099655)), _1099661))]]], (4984 ^ _782476) ^ [_858574, _858576] : [_858576 = _858574, -(c_Wellfounded_Ofinite__psubset(_858576) = c_Wellfounded_Ofinite__psubset(_858574))], (45565 ^ _782476) ^ [_1694676, _1694678, _1694680] : [class_Orderings_Olinorder(_1694676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1694676), _1694678)), -(c_List_Olinorder__class_Osorted__list__of__set(_1694676, hAPP(hAPP(c_Set_Oinsert(_1694676), _1694680), _1694678)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694676, _1694676, c_COMBI(_1694676)), _1694680), c_List_Olinorder__class_Osorted__list__of__set(_1694676, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1694676, tc_HOL_Obool)), _1694678), hAPP(hAPP(c_Set_Oinsert(_1694676), _1694680), c_Orderings_Obot__class_Obot(tc_fun(_1694676, tc_HOL_Obool)))))))], (48723 ^ _782476) ^ [_1762858, _1762860, _1762862, _1762864, _1762866] : [c_Fun_Oinj__on(_1762858, _1762860, _1762862, c_Orderings_Otop__class_Otop(tc_fun(_1762858, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1762858, _1762860), _1762862), hAPP(c_List_OremoveAll(_1762858, _1762864), _1762866)) = hAPP(c_List_OremoveAll(_1762860, hAPP(_1762862, _1762864)), hAPP(hAPP(c_List_Omap(_1762858, _1762860), _1762862), _1762866)))], (42720 ^ _782476) ^ [_1624231, _1624233, _1624235, _1624237, _1624239, _1624241, _1624243, _1624245] : [c_Finite__Set_Ofolding__image__simple__idem(_1624231, _1624233, _1624235, _1624237, _1624239, _1624241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624233), _1624243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624233, tc_HOL_Obool)), _1624245), _1624243)), -(hAPP(hAPP(_1624235, hAPP(_1624241, _1624245)), hAPP(_1624241, _1624243)) = hAPP(_1624241, _1624243))], (38405 ^ _782476) ^ [_1516656, _1516658, _1516660, _1516662, _1516664, _1516666] : [-(c_Product__Type_Oprod_Oprod__rec(_1516656, _1516658, _1516660, _1516662, hAPP(hAPP(c_Product__Type_OPair(_1516656, _1516658), _1516664), _1516666)) = hAPP(hAPP(_1516662, _1516664), _1516666))], (5820 ^ _782476) ^ [_874581, _874583, _874585, _874587, _874589] : [class_Orderings_Oord(_874581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874583, _874581)), _874585), _874587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874581), hAPP(_874585, _874589)), hAPP(_874587, _874589))))], (39388 ^ _782476) ^ [_1541777, _1541779] : [-(c_FunDef_Oreduction__pair(_1541777, _1541779)), c_Wellfounded_Owf(_1541777, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool), tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool)), _1541779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541777, _1541777, _1541777), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool), tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool)), _1541779)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool), tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool)), _1541779))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool), tc_fun(tc_prod(_1541777, _1541777), tc_HOL_Obool)), _1541779)))], (40442 ^ _782476) ^ [_1570344, _1570346] : [c_Nitpick_Owf_H(_1570344, _1570346), 40445 ^ _782476 : [(40448 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570344, _1570344)), _1570346))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (40446 ^ _782476) ^ [] : [-(c_Wellfounded_Oacyclic(_1570344, _1570346))]]], (44414 ^ _782476) ^ [_1668085, _1668087, _1668089] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668085), tc_List_Olist(_1668085))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668085), tc_List_Olist(_1668085)), _1668087), c_List_Olist_ONil(_1668085))), c_List_Olistrel1(_1668085, _1668089)))], (11126 ^ _782476) ^ [_986952, _986954, _986956] : [class_Orderings_Opreorder(_986952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986952), _986954), _986956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986952), _986956), _986954))], (37353 ^ _782476) ^ [_1493274, _1493276] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493274, _1493276), c_Divides_Odivmod__nat(_1493274, _1493276))))], (46076 ^ _782476) ^ [_1705669, _1705671, _1705673, _1705675, _1705677] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705669), tc_List_Olist(_1705671), tc_List_Olist(_1705673), hAPP(c_List_Omap(_1705669, _1705671), _1705675)), hAPP(c_List_Omap(_1705673, _1705669), _1705677)) = hAPP(c_List_Omap(_1705673, _1705671), hAPP(c_Fun_Ocomp(_1705669, _1705671, _1705673, _1705675), _1705677)))], (35186 ^ _782476) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (23388 ^ _782476) ^ [_1221692, _1221694] : [class_Int_Oring__char__0(_1221692), hBOOL(hAPP(hAPP(c_member(_1221692), _1221694), c_Int_Oring__1__class_OInts(_1221692))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221692), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221692), c_Groups_Oone__class_Oone(_1221692)), _1221694)), _1221694) = c_Groups_Ozero__class_Ozero(_1221692)], (52273 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (8422 ^ _782476) ^ [_928274, _928276] : [class_Groups_Oordered__ab__group__add(_928274), -(hAPP(c_Set_Oimage(_928274, _928274, c_Groups_Ouminus__class_Ouminus(_928274)), hAPP(c_SetInterval_Oord__class_OatLeast(_928274), _928276)) = hAPP(c_SetInterval_Oord__class_OatMost(_928274), hAPP(c_Groups_Ouminus__class_Ouminus(_928274), _928276)))], (20655 ^ _782476) ^ [] : [-(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))))], (24360 ^ _782476) ^ [_1238342] : [c_Nat__Transfer_Onat__set(_1238342), 24363 ^ _782476 : [(24370 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238342))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1238342)))], (24364 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1238342)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238342))))]]], (2558 ^ _782476) ^ [_820121, _820123, _820125, _820127, _820129, _820131, _820133, _820135] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820135, _820131, _820127, _820123) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820133, _820129, _820125, _820121)), _820135 = _820133, _820131 = _820129, _820127 = _820125, _820123 = _820121], (43821 ^ _782476) ^ [_1656009, _1656011] : [-(c_List_Obutlast(_1656009, _1656011) = hAPP(hAPP(c_List_Otake(_1656009), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656009)), _1656011)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1656011))], (46662 ^ _782476) ^ [_1718862, _1718864, _1718866, _1718868, _1718870, _1718872, _1718874] : [c_List_Olist__all2(_1718868, _1718864, hAPP(hAPP(c_COMBB(_1718862, tc_fun(_1718864, tc_HOL_Obool), _1718868), _1718866), _1718870), _1718872, _1718874), -(c_List_Olist__all2(_1718862, _1718864, _1718866, hAPP(hAPP(c_List_Omap(_1718868, _1718862), _1718870), _1718872), _1718874))], (34190 ^ _782476) ^ [_1430481, _1430483] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430481))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430481), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430483)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21021 ^ _782476) ^ [_1177493, _1177495] : [21022 ^ _782476 : [(21025 ^ _782476) ^ [] : [_1177493 = _1177495], (21023 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177493), _1177495))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177495), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21119 ^ _782476) ^ [_1179435, _1179437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179435), _1179437))), -(_1179435 = _1179437), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179437), _1179435)))], (25525 ^ _782476) ^ [_1259440, _1259442] : [hAPP(c_Set_OCollect(_1259440), _1259442) = c_Orderings_Obot__class_Obot(tc_fun(_1259440, tc_HOL_Obool)), 25528 ^ _782476 : [(25529 ^ _782476) ^ [_1259525] : [hBOOL(hAPP(_1259442, _1259525))]]], (39651 ^ _782476) ^ [_1548376, _1548378, _1548380, _1548382, _1548384] : [-(hAPP(c_Relation_ODomain(_1548376, _1548378), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1548376, _1548378)), hAPP(hAPP(c_Product__Type_OPair(_1548376, _1548378), _1548380), _1548382)), _1548384)) = hAPP(hAPP(c_Set_Oinsert(_1548376), _1548380), hAPP(c_Relation_ODomain(_1548376, _1548378), _1548384)))], (23775 ^ _782476) ^ [_1228710, _1228712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228710), hAPP(c_Int_Onat, _1228712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228710)), _1228712)))], (36434 ^ _782476) ^ [_1473648, _1473650, _1473652, _1473654, _1473656, _1473658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473648, _1473650)), hAPP(hAPP(c_Product__Type_OPair(_1473648, _1473650), _1473656), _1473658)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool)), _1473652), _1473654))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473648, tc_fun(_1473650, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1473648, tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_fun(_1473650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473650, tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_fun(_1473650, tc_HOL_Obool)), _1473648), c_COMBC(_1473650, tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473650, tc_prod(_1473648, _1473650)), tc_fun(_1473650, tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), _1473648), hAPP(c_COMBB(tc_prod(_1473648, _1473650), tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool), _1473650), c_member(tc_prod(_1473648, _1473650)))), c_Product__Type_OPair(_1473648, _1473650)))), _1473652)), hAPP(hAPP(c_COMBC(_1473648, tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_fun(_1473650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473650, tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_fun(_1473650, tc_HOL_Obool)), _1473648), c_COMBC(_1473650, tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473650, tc_prod(_1473648, _1473650)), tc_fun(_1473650, tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool)), _1473648), hAPP(c_COMBB(tc_prod(_1473648, _1473650), tc_fun(tc_fun(tc_prod(_1473648, _1473650), tc_HOL_Obool), tc_HOL_Obool), _1473650), c_member(tc_prod(_1473648, _1473650)))), c_Product__Type_OPair(_1473648, _1473650)))), _1473654)), _1473656), _1473658)))], (11574 ^ _782476) ^ [_993772, _993774, _993776] : [class_Orderings_Oorder(_993772), -(_993774 = _993776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993772), _993774), _993776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993772), _993774), _993776)))], (38861 ^ _782476) ^ [_1527928, _1527930, _1527932, _1527934] : [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), _1527928), _1527930)), 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), _1527932), _1527934)), 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), _1527928), _1527934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527932), _1527930))))], (50369 ^ _782476) ^ [_1800023, _1800025, _1800027] : [c_List_Oall__interval__int(_1800023, _1800025, _1800027), 50372 ^ _782476 : [(50373 ^ _782476) ^ [_1800101] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1800101), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1800025, _1800027))), -(hBOOL(hAPP(_1800023, _1800101)))]]], (37297 ^ _782476) ^ [_1492194, _1492196, _1492198, _1492200, _1492202] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492194, _1492196), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492198), _1492200))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492196)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492202), _1492194), _1492196), 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), _1492202), _1492198)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492202), _1492200)), _1492196))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492202), _1492200), _1492196)))))], (29136 ^ _782476) ^ [_1335664, _1335666, _1335668] : [class_Rings_Oring__1__no__zero__divisors(_1335664), -(_1335666 = c_Groups_Ozero__class_Ozero(_1335664)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335664), _1335666), _1335668) = c_Groups_Ozero__class_Ozero(_1335664)], (45945 ^ _782476) ^ [_1701863, _1701865, _1701867, _1701869] : [c_List_Olist_ONil(_1701863) = hAPP(hAPP(c_List_Omap(_1701865, _1701863), _1701867), _1701869), -(_1701869 = c_List_Olist_ONil(_1701865))], (9223 ^ _782476) ^ [_946740, _946742, _946744, _946746] : [hBOOL(hAPP(hAPP(c_member(_946742), _946746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946740, tc_fun(_946742, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946740, tc_HOL_Obool))), _946744))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946740, tc_fun(_946742, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946740, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946742, tc_HOL_Obool), tc_fun(_946742, tc_HOL_Obool), _946740), hAPP(c_COMBC(_946742, tc_fun(_946742, tc_HOL_Obool), tc_HOL_Obool), c_member(_946742))), _946744)), _946746)))], (22878 ^ _782476) ^ [_1211530, _1211532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211530), _1211532))))], (34558 ^ _782476) ^ [_1436194] : [-(c_Int_Osucc(_1436194) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436194), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37932 ^ _782476) ^ [_1504931, _1504933, _1504935, _1504937, _1504939, _1504941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504937, _1504937)), hAPP(hAPP(c_Product__Type_OPair(_1504937, _1504937), hAPP(_1504941, _1504933)), hAPP(_1504941, _1504935))), _1504939)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504931, _1504931)), hAPP(hAPP(c_Product__Type_OPair(_1504931, _1504931), _1504933), _1504935)), hAPP(hAPP(c_Relation_Oinv__image(_1504937, _1504931), _1504939), _1504941))))], (25959 ^ _782476) ^ [_1273098, _1273100, _1273102] : [class_Groups_Olinordered__ab__semigroup__add(_1273098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273098), _1273100)), -(_1273100 = c_Orderings_Obot__class_Obot(tc_fun(_1273098, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273098), _1273102), c_Big__Operators_Olinorder__class_OMin(_1273098, _1273100)) = c_Big__Operators_Olinorder__class_OMin(_1273098, hAPP(c_Set_OCollect(_1273098), hAPP(hAPP(c_COMBB(tc_fun(_1273098, tc_HOL_Obool), tc_HOL_Obool, _1273098), c_HOL_OEx(_1273098)), hAPP(hAPP(c_COMBC(_1273098, tc_fun(_1273098, tc_HOL_Obool), tc_fun(_1273098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273098, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273098, tc_HOL_Obool), tc_fun(_1273098, tc_HOL_Obool)), _1273098), c_COMBS(_1273098, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273098, tc_HOL_Obool), tc_fun(_1273098, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273098), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273098), c_fconj)), hAPP(hAPP(c_COMBC(_1273098, tc_fun(_1273098, _1273098), tc_fun(_1273098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273098, tc_HOL_Obool), tc_fun(tc_fun(_1273098, _1273098), tc_fun(_1273098, tc_HOL_Obool)), _1273098), c_COMBB(_1273098, tc_HOL_Obool, _1273098)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273098), _1273102))))), hAPP(hAPP(c_COMBC(_1273098, tc_fun(_1273098, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273098)), _1273100))))))], (11058 ^ _782476) ^ [_986121, _986123, _986125] : [class_Orderings_Olinorder(_986121), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986121), _986123), _986125))), -(_986123 = _986125), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986121), _986125), _986123)))], (10535 ^ _782476) ^ [_974787, _974789, _974791, _974793] : [-(hBOOL(hAPP(hAPP(c_member(_974787), _974789), _974791))), 10538 ^ _782476 : [(10545 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974787, tc_HOL_Obool)), _974791), _974793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974787, tc_HOL_Obool)), _974791), hAPP(hAPP(c_Set_Oinsert(_974787), _974789), _974793))))], (10539 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974787, tc_HOL_Obool)), _974791), hAPP(hAPP(c_Set_Oinsert(_974787), _974789), _974793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974787, tc_HOL_Obool)), _974791), _974793)))]]], (46618 ^ _782476) ^ [_1717731, _1717733, _1717735, _1717737, _1717739] : [c_List_Olist__all2(_1717731, _1717733, _1717735, _1717737, _1717739), 46621 ^ _782476 : [(46624 ^ _782476) ^ [_1717897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717731, _1717733)), _1717897), hAPP(c_List_Oset(tc_prod(_1717731, _1717733)), hAPP(hAPP(c_List_Ozip(_1717731, _1717733), _1717737), _1717739)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1717731, _1717733, tc_HOL_Obool), _1717735), _1717897)))], (46622 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717731)), _1717737) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717733)), _1717739))]]], (25973 ^ _782476) ^ [_1273584, _1273586, _1273588] : [class_Groups_Olinordered__ab__semigroup__add(_1273584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273584), _1273586)), -(_1273586 = c_Orderings_Obot__class_Obot(tc_fun(_1273584, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273584), _1273588), c_Big__Operators_Olinorder__class_OMax(_1273584, _1273586)) = c_Big__Operators_Olinorder__class_OMax(_1273584, hAPP(c_Set_OCollect(_1273584), hAPP(hAPP(c_COMBB(tc_fun(_1273584, tc_HOL_Obool), tc_HOL_Obool, _1273584), c_HOL_OEx(_1273584)), hAPP(hAPP(c_COMBC(_1273584, tc_fun(_1273584, tc_HOL_Obool), tc_fun(_1273584, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273584, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273584, tc_HOL_Obool), tc_fun(_1273584, tc_HOL_Obool)), _1273584), c_COMBS(_1273584, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273584, tc_HOL_Obool), tc_fun(_1273584, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273584), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273584), c_fconj)), hAPP(hAPP(c_COMBC(_1273584, tc_fun(_1273584, _1273584), tc_fun(_1273584, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273584, tc_HOL_Obool), tc_fun(tc_fun(_1273584, _1273584), tc_fun(_1273584, tc_HOL_Obool)), _1273584), c_COMBB(_1273584, tc_HOL_Obool, _1273584)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273584), _1273588))))), hAPP(hAPP(c_COMBC(_1273584, tc_fun(_1273584, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273584)), _1273586))))))], (51923 ^ _782476) ^ [_1834228, _1834230, _1834232, _1834234] : [class_Rings_Ocomm__ring(_1834228), class_Rings_Odvd(_1834228), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834228), _1834230), _1834232)), 51934 ^ _782476 : [(51941 ^ _782476) ^ [_1834654, _1834656] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834228), _1834230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1834228), _1834656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834228), _1834654), _1834232))), _1834234))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834228), _1834230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834228), _1834656), _1834234))))], (51935 ^ _782476) ^ [_1834481, _1834483] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834228), _1834230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834228), _1834483), _1834234))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834228), _1834230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1834228), _1834483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834228), _1834481), _1834232))), _1834234))))]]], (50139 ^ _782476) ^ [_1795010] : [-(c_Lazy__Sequence_Oyieldn(_1795010) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1795010), _1795010, c_Lazy__Sequence_Oyield(_1795010)))], (24893 ^ _782476) ^ [_1247986, _1247988, _1247990] : [class_Groups_Oordered__ab__group__add__abs(_1247986), -(hAPP(c_Groups_Oabs__class_Oabs(_1247986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247986), _1247988), _1247990)) = hAPP(c_Groups_Oabs__class_Oabs(_1247986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247986), _1247990), _1247988)))], (17776 ^ _782476) ^ [_1119442, _1119444] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119442), _1119444) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17779 ^ _782476 : [(17782 ^ _782476) ^ [] : [-(_1119444 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17780 ^ _782476) ^ [] : [-(_1119442 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (40586 ^ _782476) ^ [_1574250, _1574252] : [class_Complete__Lattice_Ocomplete__lattice(_1574250), -(c_Complete__Lattice_OSup__class_OSup(_1574250, _1574252) = c_Complete__Lattice_OInf__class_OInf(_1574250, hAPP(c_Set_OCollect(_1574250), hAPP(hAPP(c_COMBB(tc_fun(_1574250, tc_HOL_Obool), tc_HOL_Obool, _1574250), c_HOL_OAll(_1574250)), hAPP(hAPP(c_COMBB(tc_fun(_1574250, tc_HOL_Obool), tc_fun(_1574250, tc_HOL_Obool), _1574250), hAPP(c_COMBS(_1574250, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574250), c_fimplies), hAPP(hAPP(c_COMBC(_1574250, tc_fun(_1574250, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574250)), _1574252)))), hAPP(c_COMBC(_1574250, _1574250, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1574250)))))))], (44901 ^ _782476) ^ [_1679344, _1679346, _1679348, _1679350] : [-(hBOOL(hAPP(hAPP(c_member(_1679344), _1679346), hAPP(c_List_Oset(_1679344), _1679348)))), -(c_List_Oremove1(_1679344, _1679346, hAPP(hAPP(c_List_Oappend(_1679344), _1679348), _1679350)) = hAPP(hAPP(c_List_Oappend(_1679344), _1679348), c_List_Oremove1(_1679344, _1679346, _1679350)))], (51107 ^ _782476) ^ [_1816511, _1816513] : [51108 ^ _782476 : [(51109 ^ _782476) ^ [_1816567] : [hBOOL(hAPP(hAPP(_1816511, _1816567), _1816567))]], c_Predicate_Osymp(_1816513, _1816511), c_Predicate_Otransp(_1816513, _1816511), -(c_Equiv__Relations_Opart__equivp(_1816513, _1816511))], (18426 ^ _782476) ^ [_1129863] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129863), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41445 ^ _782476) ^ [_1595397, _1595399, _1595401, _1595403, _1595405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595397, _1595399)), hAPP(hAPP(c_Product__Type_OPair(_1595397, _1595399), _1595401), _1595403)), hAPP(c_Relation_Oconverse(_1595399, _1595397), _1595405))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595399, _1595397)), hAPP(hAPP(c_Product__Type_OPair(_1595399, _1595397), _1595403), _1595401)), _1595405)))], (31854 ^ _782476) ^ [_1385595, _1385597] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385595, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385597)) = 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), _1385595), _1385597)))], (21345 ^ _782476) ^ [_1183218, _1183220] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183218)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183220)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183218), _1183220)))], (36460 ^ _782476) ^ [_1474750, _1474752, _1474754] : [class_Enum_Oenum(_1474750), class_Enum_Oenum(_1474752), 36467 ^ _782476 : [(36474 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474752), hAPP(hAPP(c_COMBB(tc_fun(_1474750, tc_HOL_Obool), tc_HOL_Obool, _1474752), c_Enum_Oenum__class_Oenum__all(_1474750)), hAPP(hAPP(c_COMBB(tc_fun(_1474750, tc_prod(_1474752, _1474750)), tc_fun(_1474750, tc_HOL_Obool), _1474752), hAPP(c_COMBB(tc_prod(_1474752, _1474750), tc_HOL_Obool, _1474750), _1474754)), c_Product__Type_OPair(_1474752, _1474750))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474752, _1474750)), _1474754)))], (36468 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474752, _1474750)), _1474754)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474752), hAPP(hAPP(c_COMBB(tc_fun(_1474750, tc_HOL_Obool), tc_HOL_Obool, _1474752), c_Enum_Oenum__class_Oenum__all(_1474750)), hAPP(hAPP(c_COMBB(tc_fun(_1474750, tc_prod(_1474752, _1474750)), tc_fun(_1474750, tc_HOL_Obool), _1474752), hAPP(c_COMBB(tc_prod(_1474752, _1474750), tc_HOL_Obool, _1474750), _1474754)), c_Product__Type_OPair(_1474752, _1474750))))))]]], (26870 ^ _782476) ^ [_1289808, _1289810, _1289812] : [class_Orderings_Olinorder(_1289808), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289808), _1289810), _1289812) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289808), _1289812), _1289810))], (52633 ^ _782476) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (27527 ^ _782476) ^ [_1303241, _1303243] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303241)), _1303243) = 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), _1303241)), _1303243))], (8981 ^ _782476) ^ [_939629, _939631, _939633, _939635] : [hBOOL(hAPP(hAPP(c_member(_939629), _939631), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939629, tc_HOL_Obool)), _939633), _939635))), 8984 ^ _782476 : [(8987 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939629), _939631), _939635)))], (8985 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939629), _939631), _939633)))]]], (17311 ^ _782476) ^ [_1111173, _1111175] : [-(_1111173 = _1111175), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111173), _1111175))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111175), _1111173)))], (13844 ^ _782476) ^ [_1039395, _1039397, _1039399, _1039401, _1039403, _1039405, _1039407] : [c_Fun_Obij__betw(_1039395, _1039397, _1039399, _1039401, _1039403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039395, tc_HOL_Obool)), _1039405), _1039401)), hAPP(c_Set_Oimage(_1039395, _1039397, _1039399), _1039405) = _1039407, -(c_Fun_Obij__betw(_1039395, _1039397, _1039399, _1039405, _1039407))], (9774 ^ _782476) ^ [_957682, _957684] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957682, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957682, tc_HOL_Obool)), _957684)), _957684) = c_Orderings_Obot__class_Obot(tc_fun(_957682, tc_HOL_Obool)))], (39849 ^ _782476) ^ [_1554746, _1554748, _1554750, _1554752, _1554754, _1554756] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1554746, _1554748)), hAPP(hAPP(c_Product__Type_OPair(_1554746, _1554748), _1554750), _1554752)), hAPP(hAPP(c_Product__Type_OSigma(_1554746, _1554748), _1554754), _1554756)))), hBOOL(hAPP(hAPP(c_member(_1554746), _1554750), _1554754)), hBOOL(hAPP(hAPP(c_member(_1554748), _1554752), hAPP(_1554756, _1554750)))], (17806 ^ _782476) ^ [_1119882, _1119884, _1119886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119882), _1119886)), _1119884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119884), _1119886))))], (9247 ^ _782476) ^ [_947644, _947646, _947648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947644, tc_HOL_Obool)), _947646), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947644, tc_HOL_Obool), _947648)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947644, tc_HOL_Obool), tc_fun(_947644, tc_HOL_Obool)), _947648), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947644, tc_HOL_Obool)), _947646)))], (26486 ^ _782476) ^ [_1282892, _1282894, _1282896] : [class_Orderings_Olinorder(_1282892), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282892), _1282894), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282892), _1282896), _1282894))))], (46964 ^ _782476) ^ [_1725254, _1725256] : [class_Orderings_Olinorder(_1725254), -(c_List_Olinorder__class_Osorted__list__of__set(_1725254, hAPP(c_List_Oset(_1725254), _1725256)) = c_List_Olinorder__class_Osort__key(_1725254, _1725254, c_COMBI(_1725254), c_List_Oremdups(_1725254, _1725256)))], (33076 ^ _782476) ^ [_1409550, _1409552, _1409554, _1409556] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409550), _1409552), _1409554)), hAPP(c_Int_Onumber__class_Onumber__of(_1409550), _1409556)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409550), _1409552), hAPP(c_Int_Onumber__class_Onumber__of(_1409550), _1409556))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409550), _1409554), hAPP(c_Int_Onumber__class_Onumber__of(_1409550), _1409556)))), class_Int_Onumber(_1409550), class_Rings_Oring(_1409550)], (39546 ^ _782476) ^ [_1545637, _1545639, _1545641, _1545643] : [hBOOL(hAPP(c_Predicate_ORangeP(_1545637, _1545639, hAPP(hAPP(c_COMBC(_1545637, tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_fun(_1545639, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545639, tc_fun(tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_fun(_1545639, tc_HOL_Obool)), _1545637), c_COMBC(_1545639, tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545639, tc_prod(_1545637, _1545639)), tc_fun(_1545639, tc_fun(tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_HOL_Obool)), _1545637), hAPP(c_COMBB(tc_prod(_1545637, _1545639), tc_fun(tc_fun(tc_prod(_1545637, _1545639), tc_HOL_Obool), tc_HOL_Obool), _1545639), c_member(tc_prod(_1545637, _1545639)))), c_Product__Type_OPair(_1545637, _1545639)))), _1545641)), _1545643)), -(hBOOL(hAPP(hAPP(c_member(_1545639), _1545643), hAPP(c_Relation_ORange(_1545637, _1545639), _1545641))))], (37914 ^ _782476) ^ [_1504541, _1504543] : [hAPP(c_Int_ORep__Integ, _1504541) = hAPP(c_Int_ORep__Integ, _1504543), -(_1504541 = _1504543)], (46176 ^ _782476) ^ [_1708015, _1708017, _1708019, _1708021] : [c_Fun_Oinj__on(_1708015, _1708017, _1708019, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1708015, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1708015), tc_fun(_1708015, tc_HOL_Obool), c_List_Oset(_1708015)), _1708021))), -(c_Fun_Oinj__on(tc_List_Olist(_1708015), tc_List_Olist(_1708017), hAPP(c_List_Omap(_1708015, _1708017), _1708019), _1708021))], (39638 ^ _782476) ^ [_1548059, _1548061, _1548063, _1548065] : [hBOOL(hAPP(hAPP(c_member(_1548059), _1548061), hAPP(c_Relation_ODomain(_1548059, _1548063), _1548065))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548059, _1548063)), hAPP(hAPP(c_Product__Type_OPair(_1548059, _1548063), _1548061), 39641 ^ [_1548059, _1548061, _1548063, _1548065])), _1548065)))], (1372 ^ _782476) ^ [_802826, _802828] : [-(class_Groups_Osgn__if(_802826)), _802828 = _802826, class_Groups_Osgn__if(_802828)], (45270 ^ _782476) ^ [_1688793, _1688795, _1688797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688793), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688795)), _1688797))), -(hAPP(hAPP(c_List_Oappend(_1688795), hAPP(hAPP(c_List_Otake(_1688795), _1688793), _1688797)), hAPP(hAPP(c_List_Olist_OCons(_1688795), hAPP(c_List_Ohd(_1688795), hAPP(hAPP(c_List_Odrop(_1688795), _1688793), _1688797))), c_List_Olist_ONil(_1688795))) = hAPP(hAPP(c_List_Otake(_1688795), hAPP(c_Nat_OSuc, _1688793)), _1688797))], (38720 ^ _782476) ^ [_1524067] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1524067)), -(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))), _1524067)), c_FunDef_Omax__weak)))], (36629 ^ _782476) ^ [_1479243, _1479245, _1479247] : [class_Rings_Osemiring__1(_1479243), hBOOL(hAPP(hAPP(c_member(_1479243), _1479245), c_Nat_Osemiring__1__class_ONats(_1479243))), hBOOL(hAPP(hAPP(c_member(_1479243), _1479247), c_Nat_Osemiring__1__class_ONats(_1479243))), -(hBOOL(hAPP(hAPP(c_member(_1479243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1479243), _1479245), _1479247)), c_Nat_Osemiring__1__class_ONats(_1479243))))], (7938 ^ _782476) ^ [_917587, _917589] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917587, tc_HOL_Obool)), _917589), _917589) = _917589)], (16379 ^ _782476) ^ [_1090853, _1090855, _1090857, _1090859] : [class_Rings_Ocomm__semiring__1(_1090853), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090853), _1090855), _1090857)), _1090859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090853), _1090855), _1090859)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090853), _1090857), _1090859)))], (43031 ^ _782476) ^ [_1633325, _1633327, _1633329, _1633331, _1633333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633325), tc_List_Olist(_1633325))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633325), tc_List_Olist(_1633325)), _1633327), _1633329)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633325), c_List_Olistrel1(_1633325, _1633331)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633325), tc_List_Olist(_1633325))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633325), tc_List_Olist(_1633325)), hAPP(hAPP(c_List_Olist_OCons(_1633325), _1633333), _1633327)), hAPP(hAPP(c_List_Olist_OCons(_1633325), _1633333), _1633329))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633325), c_List_Olistrel1(_1633325, _1633331)))))], (39600 ^ _782476) ^ [_1547181, _1547183, _1547185, _1547187, _1547189] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547181, _1547183)), hAPP(hAPP(c_Product__Type_OPair(_1547181, _1547183), _1547185), _1547187)), _1547189)), -(hBOOL(hAPP(hAPP(c_member(_1547181), _1547185), hAPP(c_Relation_ODomain(_1547181, _1547183), _1547189))))], (3508 ^ _782476) ^ [_834884, _834886, _834888, _834890, _834892, _834894] : [-(c_List_Osublist(_834894, _834890, _834886) = c_List_Osublist(_834892, _834888, _834884)), _834894 = _834892, _834890 = _834888, _834886 = _834884], (40003 ^ _782476) ^ [_1560197, _1560199] : [-(hAPP(c_Fun_Oid(_1560197), _1560199) = _1560199)], (20033 ^ _782476) ^ [_1158568, _1158570, _1158572, _1158574] : [class_Rings_Olinordered__semiring__strict(_1158568), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158568), _1158570), _1158572)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158568), _1158570), _1158574))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158568), c_Groups_Ozero__class_Ozero(_1158568)), _1158570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158568), _1158572), _1158574)))], (2 ^ _782476) ^ [_782503] : [-(_782503 = _782503)], (9393 ^ _782476) ^ [_950683, _950685] : [_950685 = c_Orderings_Obot__class_Obot(tc_fun(_950683, tc_HOL_Obool)), 9396 ^ _782476 : [(9397 ^ _782476) ^ [_950763] : [hBOOL(hAPP(hAPP(c_member(_950683), _950763), _950685))]]], (49049 ^ _782476) ^ [_1771277, _1771279, _1771281] : [49050 ^ _782476 : [(49051 ^ _782476) ^ [_1771354, _1771356] : [_1771281 = hAPP(hAPP(c_List_Oappend(_1771277), _1771356), hAPP(hAPP(c_List_Olist_OCons(_1771277), _1771279), _1771354))]], -(hBOOL(hAPP(hAPP(c_member(_1771277), _1771279), hAPP(c_List_Oset(_1771277), _1771281))))], (46578 ^ _782476) ^ [_1716289, _1716291, _1716293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1716289, tc_HOL_Obool)), _1716291), _1716293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1716289), tc_HOL_Obool)), c_List_Olistsp(_1716289, _1716291)), c_List_Olistsp(_1716289, _1716293))))], (8220 ^ _782476) ^ [_923794, _923796, _923798, _923800, _923802] : [hBOOL(hAPP(hAPP(c_member(_923794), _923796), _923798)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923800, tc_HOL_Obool)), hAPP(_923802, _923796)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923794, tc_fun(_923800, tc_HOL_Obool)), _923798), _923802)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923794, tc_fun(_923800, tc_HOL_Obool)), _923798), _923802))], (41150 ^ _782476) ^ [_1588294, _1588296] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588294, _1588294, _1588294), c_Transitive__Closure_Ortrancl(_1588294, _1588296)), c_Transitive__Closure_Ortrancl(_1588294, _1588296)) = c_Transitive__Closure_Ortrancl(_1588294, _1588296))], (12182 ^ _782476) ^ [_1003973, _1003975, _1003977] : [class_Orderings_Oorder(_1003973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003973), _1003975), _1003977)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1003973, _1003977, _1003975) = c_Orderings_Obot__class_Obot(tc_fun(_1003973, tc_HOL_Obool)))], (29218 ^ _782476) ^ [_1337054, _1337056, _1337058, _1337060] : [class_Groups_Omonoid__mult(_1337054), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337054), _1337056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337058), _1337060)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337054), hAPP(hAPP(c_Power_Opower__class_Opower(_1337054), _1337056), _1337058)), _1337060))], (31301 ^ _782476) ^ [_1374594, _1374596, _1374598] : [hBOOL(hAPP(_1374594, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374596), _1374598))), 31304 ^ _782476 : [(31329 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374598), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31332 ^ _782476 : [(31333 ^ _782476) ^ [_1375258] : [-(hBOOL(hAPP(_1374594, _1375258))), 31334 ^ _782476 : [(31335 ^ _782476) ^ [_1375332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374598), _1375332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375332), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1374596 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374598), _1375258)), _1375332)]]]]], (31311 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374598)), 31314 ^ _782476 : [(31315 ^ _782476) ^ [_1374928] : [-(hBOOL(hAPP(_1374594, _1374928))), 31316 ^ _782476 : [(31317 ^ _782476) ^ [_1374999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374999), _1374598)), _1374596 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374598), _1374928)), _1374999)]]]]], (31305 ^ _782476) ^ [] : [_1374598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1374594, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19793 ^ _782476) ^ [_1154036, _1154038, _1154040] : [class_Groups_Oordered__comm__monoid__add(_1154036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154036), c_Groups_Ozero__class_Ozero(_1154036)), _1154038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154036), c_Groups_Ozero__class_Ozero(_1154036)), _1154040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154036), c_Groups_Ozero__class_Ozero(_1154036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154036), _1154038), _1154040))))], (42355 ^ _782476) ^ [_1616655, _1616657, _1616659] : [class_Orderings_Olinorder(_1616655), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616655), _1616657)), -(hBOOL(hAPP(hAPP(c_member(_1616655), _1616659), _1616657))), -(c_Big__Operators_Olinorder__class_OMin(_1616655, hAPP(hAPP(c_Set_Oinsert(_1616655), _1616659), _1616657)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616655, _1616655, c_Orderings_Oord__class_Omin(_1616655)), _1616659), _1616657))], (33190 ^ _782476) ^ [_1411813, _1411815, _1411817] : [class_Int_Onumber__ring(_1411813), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411813), hAPP(c_Int_Onumber__class_Onumber__of(_1411813), _1411815)), hAPP(c_Int_Onumber__class_Onumber__of(_1411813), _1411817)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411815), _1411817)))], (44698 ^ _782476) ^ [_1675050, _1675052, _1675054, _1675056] : [hAPP(hAPP(c_List_Oappend(_1675050), _1675052), _1675054) = hAPP(hAPP(c_List_Oappend(_1675050), _1675056), _1675054), -(_1675052 = _1675056)], (44578 ^ _782476) ^ [_1672391, _1672393, _1672395, _1672397, _1672399] : [hAPP(hAPP(c_List_Oappend(_1672391), _1672393), _1672395) = hAPP(hAPP(c_List_Olist_OCons(_1672391), _1672397), _1672399), 44583 ^ _782476 : [(44586 ^ _782476) ^ [] : [-(_1672395 = hAPP(hAPP(c_List_Olist_OCons(_1672391), _1672397), _1672399))], (44584 ^ _782476) ^ [] : [-(_1672393 = c_List_Olist_ONil(_1672391))]], 44588 ^ _782476 : [(44591 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1672391), 44587 ^ [_1672391, _1672393, _1672395, _1672397, _1672399]), _1672395) = _1672399)], (44589 ^ _782476) ^ [] : [-(_1672393 = hAPP(hAPP(c_List_Olist_OCons(_1672391), _1672397), 44587 ^ [_1672391, _1672393, _1672395, _1672397, _1672399]))]]], (30332 ^ _782476) ^ [_1357425, _1357427, _1357429, _1357431] : [class_Fields_Olinordered__field(_1357425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357425), _1357427), _1357429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357425), _1357431), c_Groups_Ozero__class_Ozero(_1357425))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357425), c_Groups_Ozero__class_Ozero(_1357425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357425), _1357427), _1357429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357425), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357425), _1357431), _1357427)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357425), _1357431), _1357429))))], (52417 ^ _782476) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (40410 ^ _782476) ^ [_1569888, _1569890] : [c_Wellfounded_Owf(_1569888, _1569890), -(c_Wellfounded_Oacyclic(_1569888, _1569890))], (10059 ^ _782476) ^ [_964218, _964220, _964222, _964224] : [class_Orderings_Oorder(_964218), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964218, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_964218, _964220, _964222)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964218, _964222, _964224)) = c_Orderings_Obot__class_Obot(tc_fun(_964218, tc_HOL_Obool)))], (36216 ^ _782476) ^ [_1466174] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1466174)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466174)))], (40484 ^ _782476) ^ [_1570946, _1570948, _1570950] : [c_Relation_Orefl__on(_1570946, _1570948, _1570950), 40487 ^ _782476 : [(40494 ^ _782476) ^ [_1571430] : [hBOOL(hAPP(hAPP(c_member(_1570946), _1571430), _1570948)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570946, _1570946)), hAPP(hAPP(c_Product__Type_OPair(_1570946, _1570946), _1571430), _1571430)), _1570950)))], (40488 ^ _782476) ^ [_1571157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570946, _1570946)), _1571157), _1570950)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1570946, _1570946, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1570946, tc_fun(_1570946, tc_HOL_Obool), tc_fun(_1570946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570946, tc_HOL_Obool), tc_fun(_1570946, tc_HOL_Obool)), _1570946), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570946)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570946), c_fconj), hAPP(hAPP(c_COMBC(_1570946, tc_fun(_1570946, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570946)), _1570948)))), hAPP(hAPP(c_COMBC(_1570946, tc_fun(_1570946, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570946)), _1570948))), _1571157)))]]], (19632 ^ _782476) ^ [_1151215, _1151217, _1151219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151215)), 19635 ^ _782476 : [(19642 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151217), _1151219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151215), _1151217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151215), _1151219))))], (19636 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151215), _1151217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151215), _1151219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151217), _1151219)))]]], (10269 ^ _782476) ^ [_968570, _968572, _968574, _968576] : [-(hBOOL(hAPP(hAPP(c_member(_968570), _968572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968570, tc_HOL_Obool)), _968574), _968576)))), hBOOL(hAPP(hAPP(c_member(_968570), _968572), _968574)), -(hBOOL(hAPP(hAPP(c_member(_968570), _968572), _968576)))], (7231 ^ _782476) ^ [_902847, _902849, _902851, _902853] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_902847, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902849, tc_fun(tc_fun(_902847, tc_HOL_Obool), tc_HOL_Obool)), _902851), hAPP(hAPP(c_COMBB(tc_fun(_902847, tc_HOL_Obool), tc_fun(tc_fun(_902847, tc_HOL_Obool), tc_HOL_Obool), _902849), c_Set_OPow(_902847)), _902853))), hAPP(c_Set_OPow(_902847), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902849, tc_fun(_902847, tc_HOL_Obool)), _902851), _902853)))))], (558 ^ _782476) ^ [_790999, _791001] : [-(c_Nat__Transfer_Onat__set(_790999)), _791001 = _790999, c_Nat__Transfer_Onat__set(_791001)], (36050 ^ _782476) ^ [_1463593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463593))))], (18230 ^ _782476) ^ [_1127084, _1127086] : [class_Groups_Olinordered__ab__group__add(_1127084), 18233 ^ _782476 : [(18240 ^ _782476) ^ [] : [_1127086 = c_Groups_Ozero__class_Ozero(_1127084), -(_1127086 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127084), _1127086))], (18234 ^ _782476) ^ [] : [_1127086 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127084), _1127086), -(_1127086 = c_Groups_Ozero__class_Ozero(_1127084))]]], (10727 ^ _782476) ^ [_978906, _978908, _978910] : [class_Complete__Lattice_Ocomplete__lattice(_978906), -(c_Complete__Lattice_OInf__class_OInf(_978906, hAPP(hAPP(c_Set_Oinsert(_978906), _978908), _978910)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978906), _978908), c_Complete__Lattice_OInf__class_OInf(_978906, _978910)))], (45553 ^ _782476) ^ [_1694396, _1694398, _1694400, _1694402] : [class_Complete__Lattice_Ocomplete__lattice(_1694396), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1694398, _1694396), hAPP(c_List_Oset(_1694398), _1694400)), _1694402) = hAPP(c_List_Ofoldl(_1694396, _1694398, hAPP(c_COMBC(_1694398, _1694396, _1694396), hAPP(hAPP(c_COMBB(_1694396, tc_fun(_1694396, _1694396), _1694398), c_Lattices_Osemilattice__inf__class_Oinf(_1694396)), _1694402)), c_Orderings_Otop__class_Otop(_1694396)), _1694400))], (9632 ^ _782476) ^ [_955368, _955370, _955372] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955368, tc_fun(_955370, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_955368, tc_HOL_Obool))), _955372) = c_Orderings_Otop__class_Otop(tc_fun(_955370, tc_HOL_Obool)))], (47620 ^ _782476) ^ [_1740614, _1740616] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1740614, _1740616)))], (43179 ^ _782476) ^ [_1638431, _1638433, _1638435, _1638437, _1638439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638431), tc_List_Olist(_1638431))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638431), tc_List_Olist(_1638431)), _1638433), hAPP(hAPP(c_List_Olist_OCons(_1638431), _1638435), _1638437))), c_List_Olistrel(_1638431, _1638439))), 43184 ^ _782476 : [(43189 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638431), tc_List_Olist(_1638431))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638431), tc_List_Olist(_1638431)), 43183 ^ [_1638431, _1638433, _1638435, _1638437, _1638439]), _1638437)), c_List_Olistrel(_1638431, _1638439))))], (43187 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638431, _1638431)), hAPP(hAPP(c_Product__Type_OPair(_1638431, _1638431), 43182 ^ [_1638431, _1638433, _1638435, _1638437, _1638439]), _1638435)), _1638439)))], (43185 ^ _782476) ^ [] : [-(_1638433 = hAPP(hAPP(c_List_Olist_OCons(_1638431), 43182 ^ [_1638431, _1638433, _1638435, _1638437, _1638439]), 43183 ^ [_1638431, _1638433, _1638435, _1638437, _1638439]))]]], (35654 ^ _782476) ^ [_1456000, _1456002] : [class_Rings_Olinordered__idom(_1456000), 35657 ^ _782476 : [(35664 ^ _782476) ^ [] : [-(_1456002 = c_Groups_Ozero__class_Ozero(_1456000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456000), c_Groups_Ozero__class_Ozero(_1456000)), hAPP(hAPP(c_Power_Opower__class_Opower(_1456000), _1456002), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35658 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456000), c_Groups_Ozero__class_Ozero(_1456000)), hAPP(hAPP(c_Power_Opower__class_Opower(_1456000), _1456002), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1456002 = c_Groups_Ozero__class_Ozero(_1456000)]]], (10243 ^ _782476) ^ [_967992, _967994, _967996] : [class_Groups_Oab__group__add(_967992), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967992), _967994), _967996)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967992), _967996), _967994))], (22038 ^ _782476) ^ [_1196945] : [hAPP(c_Nat_OSuc, _1196945) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (52681 ^ _782476) ^ [_1843637, _1843639, _1843641, _1843643, _1843645, _1843647] : [-(hAPP(hAPP(hAPP(c_COMBS(_1843637, _1843639, _1843641), _1843643), _1843645), _1843647) = hAPP(hAPP(_1843643, _1843647), hAPP(_1843645, _1843647)))], (44887 ^ _782476) ^ [_1678928, _1678930, _1678932, _1678934, _1678936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678928), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678930)), _1678932))), -(hAPP(hAPP(c_List_Olist__update(_1678930, hAPP(hAPP(c_List_Oappend(_1678930), _1678932), _1678934)), _1678928), _1678936) = hAPP(hAPP(c_List_Oappend(_1678930), hAPP(hAPP(c_List_Olist__update(_1678930, _1678932), _1678928), _1678936)), _1678934))], (36084 ^ _782476) ^ [_1464152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464152)))], (49484 ^ _782476) ^ [_1780520, _1780522, _1780524, _1780526, _1780528, _1780530] : [c_Fun_Oinj__on(_1780520, _1780522, _1780524, _1780526), hBOOL(hAPP(hAPP(c_member(_1780520), _1780528), _1780526)), hAPP(_1780524, _1780528) = _1780530, -(hAPP(c_Hilbert__Choice_Oinv__into(_1780520, _1780522, _1780526, _1780524), _1780530) = _1780528)], (14877 ^ _782476) ^ [_1060267, _1060269, _1060271] : [class_Lattices_Olattice(_1060267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060267), _1060269)), -(_1060271 = c_Orderings_Obot__class_Obot(tc_fun(_1060267, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060267, tc_HOL_Obool)), _1060271), _1060269)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060267), c_Big__Operators_Olattice__class_OInf__fin(_1060267, _1060271)), c_Big__Operators_Olattice__class_OInf__fin(_1060267, _1060269)) = c_Big__Operators_Olattice__class_OInf__fin(_1060267, _1060269))], (22648 ^ _782476) ^ [_1207265] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207265)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207265)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207265)))], (41529 ^ _782476) ^ [_1597444, _1597446, _1597448, _1597450] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597444, _1597444)), hAPP(hAPP(c_Product__Type_OPair(_1597444, _1597444), _1597446), _1597448)), hAPP(c_Relation_Oconverse(_1597444, _1597444), c_Transitive__Closure_Otrancl(_1597444, _1597450)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597444, _1597444)), hAPP(hAPP(c_Product__Type_OPair(_1597444, _1597444), _1597446), _1597448)), c_Transitive__Closure_Otrancl(_1597444, hAPP(c_Relation_Oconverse(_1597444, _1597444), _1597450)))))], (23145 ^ _782476) ^ [_1216975, _1216977] : [-(_1216975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216975), _1216977) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216975), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1216977)))], (52671 ^ _782476) ^ [_1843441] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1843441)))], (13686 ^ _782476) ^ [_1036251, _1036253, _1036255, _1036257, _1036259, _1036261, _1036263, _1036265] : [c_Fun_Obij__betw(_1036251, _1036253, _1036255, _1036257, _1036259), 13689 ^ _782476 : [(13696 ^ _782476) ^ [] : [c_Fun_Obij__betw(_1036251, _1036261, hAPP(c_Fun_Ocomp(_1036253, _1036261, _1036251, _1036263), _1036255), _1036257, _1036265), -(c_Fun_Obij__betw(_1036253, _1036261, _1036263, _1036259, _1036265))], (13690 ^ _782476) ^ [] : [c_Fun_Obij__betw(_1036253, _1036261, _1036263, _1036259, _1036265), -(c_Fun_Obij__betw(_1036251, _1036261, hAPP(c_Fun_Ocomp(_1036253, _1036261, _1036251, _1036263), _1036255), _1036257, _1036265))]]], (34900 ^ _782476) ^ [_1442211, _1442213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442211)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442213))), -(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(_1442213))), 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), _1442211)), c_Int_Onat))))))], (47311 ^ _782476) ^ [_1734593, _1734595, _1734597, _1734599, _1734601, _1734603] : [-(c_List_Ofoldr(_1734593, _1734595, _1734597, hAPP(hAPP(c_List_Oappend(_1734593), _1734599), _1734601), _1734603) = c_List_Ofoldr(_1734593, _1734595, _1734597, _1734599, c_List_Ofoldr(_1734593, _1734595, _1734597, _1734601, _1734603)))], (50497 ^ _782476) ^ [_1803740, _1803742, _1803744, _1803746] : [c_Relation_Otrans(_1803740, _1803742), -(c_Relation_Otrans(_1803744, hAPP(hAPP(c_Relation_Oinv__image(_1803740, _1803744), _1803742), _1803746)))], (23653 ^ _782476) ^ [_1226791] : [-(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)), _1226791)) = _1226791)], (38837 ^ _782476) ^ [_1527259, _1527261, _1527263] : [class_Rings_Oring__1(_1527259), -(hAPP(c_Int_Oring__1__class_Oof__int(_1527259), 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), _1527261), _1527263)), 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(_1527259), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527259), _1527261)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527259), _1527263)))], (45458 ^ _782476) ^ [_1692389, _1692391, _1692393, _1692395, _1692397, _1692399] : [-(hAPP(c_List_Ofoldl(_1692389, _1692391, _1692393, _1692395), hAPP(hAPP(c_List_Olist_OCons(_1692391), _1692397), _1692399)) = hAPP(c_List_Ofoldl(_1692389, _1692391, _1692393, hAPP(hAPP(_1692393, _1692395), _1692397)), _1692399))], (50111 ^ _782476) ^ [_1794250, _1794252, _1794254, _1794256] : [-(c_Lazy__Sequence_Oappend(_1794250, c_Lazy__Sequence_Olazy__sequence_OInsert(_1794250, _1794252, _1794254), _1794256) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794250, _1794252, c_Lazy__Sequence_Oappend(_1794250, _1794254, _1794256)))], (9766 ^ _782476) ^ [_957508, _957510] : [_957510 = c_Orderings_Obot__class_Obot(tc_fun(_957508, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957508, tc_HOL_Obool)), _957510), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957508, tc_HOL_Obool)), _957510))))], (13212 ^ _782476) ^ [_1025833, _1025835, _1025837, _1025839, _1025841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025833, tc_HOL_Obool)), _1025835), _1025837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025839, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1025839, _1025833, _1025841), _1025835)), hAPP(c_Set_Ovimage(_1025839, _1025833, _1025841), _1025837))))], (26078 ^ _782476) ^ [_1275733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275733)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275733))], (49744 ^ _782476) ^ [_1786815, _1786817, _1786819] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1786815, _1786817), _1786819) = c_Lazy__Sequence_Oproduct(_1786815, _1786817, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786815, _1786819), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786817, _1786819))), class_Lazy__Sequence_Osmall__lazy(_1786815), class_Lazy__Sequence_Osmall__lazy(_1786817)], (23683 ^ _782476) ^ [_1227298, _1227300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227298)), hAPP(c_Int_Onat, _1227300))), 23686 ^ _782476 : [(23689 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227298), _1227300)))], (23687 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227300)))]]], (52373 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (14547 ^ _782476) ^ [_1053333, _1053335, _1053337, _1053339, _1053341] : [c_Finite__Set_Ofolding__one(_1053333, _1053335, _1053337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053333), _1053339)), 14554 ^ _782476 : [(14561 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053333, tc_HOL_Obool)), _1053339), hAPP(hAPP(c_Set_Oinsert(_1053333), _1053341), c_Orderings_Obot__class_Obot(tc_fun(_1053333, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053333, tc_HOL_Obool))), -(hAPP(_1053337, hAPP(hAPP(c_Set_Oinsert(_1053333), _1053341), _1053339)) = hAPP(hAPP(_1053335, _1053341), hAPP(_1053337, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053333, tc_HOL_Obool)), _1053339), hAPP(hAPP(c_Set_Oinsert(_1053333), _1053341), c_Orderings_Obot__class_Obot(tc_fun(_1053333, tc_HOL_Obool)))))))], (14555 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053333, tc_HOL_Obool)), _1053339), hAPP(hAPP(c_Set_Oinsert(_1053333), _1053341), c_Orderings_Obot__class_Obot(tc_fun(_1053333, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053333, tc_HOL_Obool)), -(hAPP(_1053337, hAPP(hAPP(c_Set_Oinsert(_1053333), _1053341), _1053339)) = _1053341)]]], (48863 ^ _782476) ^ [_1766844, _1766846] : [class_Orderings_Olinorder(_1766844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1766844), _1766846)), 48871 ^ _782476 : [(48874 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766844, 48870 ^ [_1766844, _1766846]))], (48876 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1766844), 48870 ^ [_1766844, _1766846])))], (48878 ^ _782476) ^ [_1767170] : [-(_1767170 = 48870 ^ [_1766844, _1766846]), hAPP(c_List_Oset(_1766844), _1767170) = _1766846, c_List_Olinorder__class_Osorted(_1766844, _1767170), hBOOL(hAPP(c_List_Odistinct(_1766844), _1767170))], (48872 ^ _782476) ^ [] : [-(hAPP(c_List_Oset(_1766844), 48870 ^ [_1766844, _1766846]) = _1766846)]]], (35998 ^ _782476) ^ [_1462917] : [c_Int_OBit0(_1462917) = c_Int_OMin], (11670 ^ _782476) ^ [_995125, _995127, _995129] : [class_Orderings_Oorder(_995125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995125), _995127), _995129)), -(_995129 = _995127), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995125), _995127), _995129)))], (16739 ^ _782476) ^ [_1098140, _1098142, _1098144] : [class_Groups_Ogroup__add(_1098140), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098140), hAPP(c_Groups_Ouminus__class_Ouminus(_1098140), _1098142)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098140), _1098142), _1098144)) = _1098144)], (21961 ^ _782476) ^ [_1195542, _1195544, _1195546] : [-(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), _1195542)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1195544))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195546))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195546), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1195544)))))], (13224 ^ _782476) ^ [_1026176, _1026178, _1026180, _1026182, _1026184] : [-(hAPP(c_Set_Ovimage(_1026176, _1026178, _1026180), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026178, tc_HOL_Obool)), _1026182), _1026184)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026176, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026176, _1026178, _1026180), _1026182)), hAPP(c_Set_Ovimage(_1026176, _1026178, _1026180), _1026184)))], (27161 ^ _782476) ^ [_1295921, _1295923, _1295925] : [class_Groups_Ocomm__monoid__mult(_1295921), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295923, _1295921), _1295925), c_Orderings_Obot__class_Obot(tc_fun(_1295923, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295921))], (34262 ^ _782476) ^ [_1431654, _1431656] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431654)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431656)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431656))), 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), _1431654)), c_Int_Onat)))))], (28754 ^ _782476) ^ [_1328591, _1328593, _1328595, _1328597] : [class_Rings_Odivision__ring(_1328591), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328591), _1328593), _1328595)), _1328597) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328591), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328591), _1328593), _1328597)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328591), _1328595), _1328597)))], (30350 ^ _782476) ^ [_1357784, _1357786, _1357788, _1357790] : [class_Fields_Olinordered__field(_1357784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357784), _1357786), _1357788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357784), c_Groups_Ozero__class_Ozero(_1357784)), _1357790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357784), c_Groups_Ozero__class_Ozero(_1357784)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357784), _1357788), _1357786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357784), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357784), _1357790), _1357788)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357784), _1357790), _1357786))))], (40540 ^ _782476) ^ [_1572637, _1572639, _1572641] : [40542 ^ _782476 : [(40545 ^ _782476) ^ [] : [hBOOL(hAPP(_1572639, 40541 ^ [_1572637, _1572639, _1572641]))], (40543 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572637), 40541 ^ [_1572637, _1572639, _1572641]), _1572641)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1572637, _1572639), _1572641)))], (16407 ^ _782476) ^ [_1091430, _1091432, _1091434, _1091436] : [class_Rings_Ocomm__semiring__1(_1091430), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091430), _1091432), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091430), _1091434), _1091436)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091430), _1091432), _1091434)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091430), _1091432), _1091436)))], (29102 ^ _782476) ^ [_1335048, _1335050, _1335052] : [class_Rings_Olinordered__semidom(_1335048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335048), c_Groups_Oone__class_Oone(_1335048)), _1335050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1335052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335048), c_Groups_Oone__class_Oone(_1335048)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335048), _1335050), _1335052))))], (36386 ^ _782476) ^ [_1469100, _1469102, _1469104, _1469106] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469100, _1469102)), hAPP(hAPP(c_Product__Type_OPair(_1469100, _1469102), _1469104), _1469106)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1469100, _1469102), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1469100, tc_fun(_1469102, tc_HOL_Obool))), _1469104), _1469106)))], (15564 ^ _782476) ^ [_1073375, _1073377, _1073379, _1073381, _1073383] : [c_Finite__Set_Ofolding__one__idem(_1073375, _1073377, _1073379), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073375), _1073381)), hBOOL(hAPP(hAPP(c_member(_1073375), _1073383), _1073381)), -(hAPP(hAPP(_1073377, _1073383), hAPP(_1073379, _1073381)) = hAPP(_1073379, _1073381))], (14681 ^ _782476) ^ [_1056227, _1056229, _1056231, _1056233, _1056235, _1056237, _1056239, _1056241] : [c_Finite__Set_Ofolding__image__simple(_1056227, _1056229, _1056231, _1056233, _1056235, _1056237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056229), _1056239)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056229), _1056241)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056229, tc_HOL_Obool)), _1056239), _1056241) = c_Orderings_Obot__class_Obot(tc_fun(_1056229, tc_HOL_Obool)), -(hAPP(_1056237, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056229, tc_HOL_Obool)), _1056239), _1056241)) = hAPP(hAPP(_1056231, hAPP(_1056237, _1056239)), hAPP(_1056237, _1056241)))], (44188 ^ _782476) ^ [_1664037, _1664039, _1664041] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664037, tc_HOL_Obool)), hAPP(c_List_Oset(_1664037), c_List_Oremove1(_1664037, _1664039, _1664041))), hAPP(c_List_Oset(_1664037), _1664041))))], (10169 ^ _782476) ^ [_966522, _966524, _966526, _966528, _966530] : [class_Groups_Ominus(_966522), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966524, _966522)), _966526), _966528), _966530) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966522), hAPP(_966526, _966530)), hAPP(_966528, _966530)))], (39422 ^ _782476) ^ [_1542586, _1542588, _1542590, _1542592] : [39424 ^ _782476 : [(39427 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1542588, hAPP(_1542590, 39423 ^ [_1542586, _1542588, _1542590, _1542592]))), hAPP(_1542588, 39423 ^ [_1542586, _1542588, _1542590, _1542592])))], (39425 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1542586, 39423 ^ [_1542586, _1542588, _1542590, _1542592])))]], -(c_Wellfounded_Owf(_1542592, hAPP(c_Set_OCollect(tc_prod(_1542592, _1542592)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542592, _1542592, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1542592, tc_HOL_Obool), tc_fun(_1542592, tc_HOL_Obool), _1542592), hAPP(c_COMBS(_1542592, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542592), c_fconj), _1542586))), hAPP(hAPP(c_COMBC(_1542592, tc_fun(_1542592, _1542592), tc_fun(_1542592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542592, tc_HOL_Obool), tc_fun(tc_fun(_1542592, _1542592), tc_fun(_1542592, tc_HOL_Obool)), _1542592), c_COMBB(_1542592, tc_HOL_Obool, _1542592)), c_fequal)), _1542590))))))], (20517 ^ _782476) ^ [_1168427, _1168429, _1168431, _1168433] : [class_Rings_Osemiring__1(_1168427), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168427), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168429, tc_Nat_Onat), _1168431), _1168433)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168429, _1168427), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1168427, _1168429), c_Nat_Osemiring__1__class_Oof__nat(_1168427)), _1168431)), _1168433))], (8931 ^ _782476) ^ [_938418, _938420, _938422, _938424, _938426] : [-(hAPP(c_Set_Oimage(_938418, _938420, _938422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938418, tc_HOL_Obool)), _938424), _938426)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938420, tc_HOL_Obool)), hAPP(c_Set_Oimage(_938418, _938420, _938422), _938424)), hAPP(c_Set_Oimage(_938418, _938420, _938422), _938426)))], (47337 ^ _782476) ^ [_1735248, _1735250, _1735252, _1735254] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1735248, tc_Nat_Onat), _1735248), c_Product__Type_Ofst(_1735248, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735248, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735248, 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(_1735248, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735248, tc_Nat_Onat))), _1735250)), hAPP(hAPP(c_List_Ozip(_1735248, tc_Nat_Onat), _1735252), c_List_Oupt(_1735254, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735254), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735248)), _1735252)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1735248, tc_Nat_Onat), _1735248), c_Product__Type_Ofst(_1735248, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735248, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735248, 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(_1735248, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1735248, 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(_1735248, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1735248, tc_Nat_Onat))), _1735254))), _1735250)), hAPP(hAPP(c_List_Ozip(_1735248, tc_Nat_Onat), _1735252), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735248)), _1735252))))))], (966 ^ _782476) ^ [_797135, _797137, _797139, _797141] : [-(c_Predicate_Otransp(_797139, _797135)), c_Predicate_Otransp(_797141, _797137), _797141 = _797139, _797137 = _797135], (52315 ^ _782476) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (36649 ^ _782476) ^ [_1479593, _1479595] : [class_Rings_Osemiring__1(_1479593), -(hBOOL(hAPP(hAPP(c_member(_1479593), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1479593), _1479595)), c_Nat_Osemiring__1__class_ONats(_1479593))))], (35150 ^ _782476) ^ [_1447063, _1447065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447063), _1447065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447063)), c_Int_OBit0(_1447065))))], (47333 ^ _782476) ^ [_1735084, _1735086] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735084))), c_List_Otranspose(_1735084, _1735086)) = c_List_Ofoldr(tc_List_Olist(_1735084), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1735084)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735084))), _1735086, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46784 ^ _782476) ^ [_1721435, _1721437, _1721439, _1721441, _1721443, _1721445] : [c_List_Olist__all2(_1721435, _1721437, _1721439, _1721441, _1721443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721445), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721437)), _1721443))), -(hBOOL(hAPP(hAPP(_1721439, hAPP(hAPP(c_List_Onth(_1721435), _1721441), _1721445)), hAPP(hAPP(c_List_Onth(_1721437), _1721443), _1721445))))], (2692 ^ _782476) ^ [_822202, _822204, _822206, _822208, _822210, _822212, _822214, _822216] : [-(c_Product__Type_Oapfst(_822216, _822212, _822208, _822204) = c_Product__Type_Oapfst(_822214, _822210, _822206, _822202)), _822216 = _822214, _822212 = _822210, _822208 = _822206, _822204 = _822202], (7940 ^ _782476) ^ [_917623, _917625, _917627] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_917623, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_917623, tc_HOL_Obool), tc_HOL_Obool)), _917625), _917627)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917623, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917623, tc_HOL_Obool), _917625)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917623, tc_HOL_Obool), _917627)))], (50288 ^ _782476) ^ [_1798189, _1798191, _1798193, _1798195] : [class_Groups_Ocomm__monoid__add(_1798189), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1798191, tc_HOL_Obool)), _1798193)), 50298 ^ _782476 : [(50301 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1798191), 50297 ^ [_1798189, _1798191, _1798193, _1798195]))], (50299 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798191, tc_HOL_Obool)), 50297 ^ [_1798189, _1798191, _1798193, _1798195]), _1798193)))]], 50305 ^ _782476 : [(50309 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798191, tc_HOL_Obool)), 50307 ^ [_1798189, _1798191, _1798193, _1798195]), _1798193)))], (50306 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798191, tc_HOL_Obool)), 50304 ^ [_1798189, _1798191, _1798193, _1798195]), _1798193)))], (50318 ^ _782476) ^ [] : [hAPP(_1798195, 50312 ^ [_1798189, _1798191, _1798193, _1798195]) = c_Groups_Ozero__class_Ozero(_1798189)], (50314 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798191), 50312 ^ [_1798189, _1798191, _1798193, _1798195]), 50304 ^ [_1798189, _1798191, _1798193, _1798195])))], (50316 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798191), 50312 ^ [_1798189, _1798191, _1798193, _1798195]), 50307 ^ [_1798189, _1798191, _1798193, _1798195])))], (50311 ^ _782476) ^ [] : [50304 ^ [_1798189, _1798191, _1798193, _1798195] = 50307 ^ [_1798189, _1798191, _1798193, _1798195]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798191, _1798189), _1798195), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1798191, tc_HOL_Obool), _1798193)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1798191, tc_HOL_Obool), _1798189), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798191, _1798189), _1798195)), _1798193))], (52377 ^ _782476) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (41834 ^ _782476) ^ [_1605036, _1605038, _1605040, _1605042] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605036, _1605036), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1605038), _1605040)), _1605042) = hAPP(c_Fun_Ocomp(_1605036, _1605036, _1605036, hAPP(hAPP(c_Nat_Ocompow(_1605036, _1605036), _1605038), _1605042)), hAPP(hAPP(c_Nat_Ocompow(_1605036, _1605036), _1605040), _1605042)))], (8989 ^ _782476) ^ [_939796, _939798, _939800, _939802] : [-(hBOOL(hAPP(hAPP(c_member(_939796), _939798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939796, tc_HOL_Obool)), _939800), _939802)))), hBOOL(hAPP(hAPP(c_member(_939796), _939798), _939800)), hBOOL(hAPP(hAPP(c_member(_939796), _939798), _939802))], (51947 ^ _782476) ^ [_1834841, _1834843, _1834845, _1834847, _1834849] : [class_Divides_Osemiring__div(_1834841), -(_1834843 = c_Groups_Ozero__class_Ozero(_1834841)), -(_1834845 = c_Groups_Ozero__class_Ozero(_1834841)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834841), _1834843), _1834847)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834841), _1834845), _1834849)), 51966 ^ _782476 : [(51973 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834841), _1834847), _1834845) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834841), _1834843), _1834849), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834841), _1834847), _1834843) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834841), _1834849), _1834845))], (51967 ^ _782476) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834841), _1834847), _1834843) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834841), _1834849), _1834845), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834841), _1834847), _1834845) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834841), _1834843), _1834849))]]], (52683 ^ _782476) ^ [_1843692, _1843694] : [hBOOL(hAPP(hAPP(c_fequal, _1843692), _1843694)), -(_1843692 = _1843694)], (18068 ^ _782476) ^ [_1124704, _1124706] : [class_Rings_Omult__zero(_1124704), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124704), c_Groups_Ozero__class_Ozero(_1124704)), _1124706) = c_Groups_Ozero__class_Ozero(_1124704))], (50152 ^ _782476) ^ [_1795378, _1795380, _1795382] : [hBOOL(hAPP(hAPP(c_member(_1795378), _1795380), hAPP(c_List_Oset(_1795378), _1795382))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795378), _1795382), _1795380)))], (50198 ^ _782476) ^ [_1796253, _1796255, _1796257, _1796259, _1796261, _1796263] : [-(c_Nitpick_Opair__box_Opair__box__size(_1796253, _1796255, _1796257, _1796259, c_Nitpick_Opair__box_OPairBox(_1796253, _1796255, _1796261, _1796263)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1796257, _1796261)), hAPP(_1796259, _1796263))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52721 ^ _782476) ^ [_1844162, _1844164] : [hBOOL(hAPP(hAPP(c_fconj, _1844162), _1844164)), -(hBOOL(_1844162))], (9516 ^ _782476) ^ [_953062, _953064] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_953062, _953064, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_953062), tc_HOL_Obool))))], (23569 ^ _782476) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26492 ^ _782476) ^ [_1282999, _1283001, _1283003] : [class_Orderings_Olinorder(_1282999), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282999), _1283001), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282999), _1283001), _1283003))))], (41763 ^ _782476) ^ [_1603082, _1603084, _1603086] : [c_Wellfounded_Owf(_1603082, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603082, _1603082), tc_HOL_Obool), _1603084), _1603086)), -(c_Wellfounded_Owf(_1603082, _1603086))], (52029 ^ _782476) ^ [_1836263, _1836265] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836263), _1836265)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836265, _1836263) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52285 ^ _782476) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (23171 ^ _782476) ^ [_1217474, _1217476] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1217474), _1217476))), -(hAPP(c_Finite__Set_Ocard(_1217474), _1217476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52253 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (6742 ^ _782476) ^ [_891585, _891587, _891589, _891591, _891593, _891595] : [hBOOL(hAPP(hAPP(c_member(_891585), _891587), _891589)), hBOOL(hAPP(hAPP(_891591, _891587), _891593)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891585, tc_fun(_891595, tc_HOL_Obool)), _891589), _891591), _891593)))], (10499 ^ _782476) ^ [_974012, _974014, _974016] : [hBOOL(hAPP(hAPP(c_member(_974012), _974014), hAPP(hAPP(c_Set_Oinsert(_974012), _974016), c_Orderings_Obot__class_Obot(tc_fun(_974012, tc_HOL_Obool))))), -(_974014 = _974016)], (19610 ^ _782476) ^ [_1150857, _1150859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150859), _1150857)), -(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), _1150857), _1150859))))], (2642 ^ _782476) ^ [_821433, _821435] : [_821435 = _821433, -(c_Nitpick_Oone__frac(_821435) = c_Nitpick_Oone__frac(_821433))], (43529 ^ _782476) ^ [_1647640, _1647642, _1647644, _1647646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647640), _1647642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647644, tc_HOL_Obool)), hAPP(c_List_Oset(_1647644), hAPP(hAPP(c_List_Otake(_1647644), _1647640), _1647646))), hAPP(c_List_Oset(_1647644), hAPP(hAPP(c_List_Otake(_1647644), _1647642), _1647646)))))], (44002 ^ _782476) ^ [_1660225, _1660227, _1660229] : [hBOOL(hAPP(c_List_Odistinct(_1660225), _1660227)), -(hBOOL(hAPP(c_List_Odistinct(_1660225), c_List_Osublist(_1660225, _1660227, _1660229))))], (16025 ^ _782476) ^ [_1082720, _1082722] : [class_Groups_Ocomm__monoid__mult(_1082720), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082720), _1082722), c_Groups_Oone__class_Oone(_1082720)) = _1082722)], (41431 ^ _782476) ^ [_1594939, _1594941, _1594943, _1594945, _1594947] : [-(hAPP(c_Relation_Oconverse(_1594939, _1594941), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594943, tc_fun(tc_prod(_1594939, _1594941), tc_HOL_Obool)), _1594945), _1594947)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594943, tc_fun(tc_prod(_1594941, _1594939), tc_HOL_Obool)), _1594945), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1594939, _1594941), tc_HOL_Obool), tc_fun(tc_prod(_1594941, _1594939), tc_HOL_Obool), _1594943), c_Relation_Oconverse(_1594939, _1594941)), _1594947)))], (51869 ^ _782476) ^ [_1833088, _1833090, _1833092] : [class_Rings_Ocomm__semiring__1(_1833088), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833088), _1833090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833088), _1833092), _1833090))))], (16745 ^ _782476) ^ [_1098259, _1098261, _1098263] : [class_Rings_Ocomm__semiring__1(_1098259), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098259), _1098261), _1098263)), _1098263) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098259), _1098261), c_Groups_Oone__class_Oone(_1098259))), _1098263))], (19656 ^ _782476) ^ [_1151636, _1151638] : [-(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), _1151636), _1151638)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151638))], (43123 ^ _782476) ^ [_1636302, _1636304, _1636306, _1636308, _1636310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636302), tc_List_Olist(_1636302))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636302), tc_List_Olist(_1636302)), _1636304), _1636306)), c_List_Olistrel(_1636302, c_Transitive__Closure_Ortrancl(_1636302, _1636308)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636302), tc_List_Olist(_1636302))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636302), tc_List_Olist(_1636302)), _1636306), _1636310)), c_List_Olistrel(_1636302, c_Transitive__Closure_Ortrancl(_1636302, _1636308)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636302), tc_List_Olist(_1636302))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636302), tc_List_Olist(_1636302)), _1636304), _1636310)), c_List_Olistrel(_1636302, c_Transitive__Closure_Ortrancl(_1636302, _1636308)))))], (50333 ^ _782476) ^ [_1799426] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1799426)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799426)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31167 ^ _782476) ^ [_1372260, _1372262, _1372264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372260), 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)), _1372262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372262), _1372264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372260), _1372262)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372260), _1372264))))], (46336 ^ _782476) ^ [_1711305, _1711307, _1711309, _1711311] : [class_Groups_Ocomm__monoid__add(_1711305), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711305), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711305), _1711307), c_List_Oupto(_1711309, _1711311))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711305), _1711307), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711309, _1711311))))], (44502 ^ _782476) ^ [_1669829] : [-(c_List_Olistset(_1669829, c_List_Olist_ONil(tc_fun(_1669829, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669829)), c_List_Olist_ONil(_1669829)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669829), tc_HOL_Obool))))], (48453 ^ _782476) ^ [_1757361, _1757363, _1757365] : [-(c_List_OdropWhile(_1757361, _1757363, _1757365) = c_List_Olist_ONil(_1757361)), hBOOL(hAPP(_1757363, hAPP(c_List_Ohd(_1757361), c_List_OdropWhile(_1757361, _1757363, _1757365))))], (26532 ^ _782476) ^ [_1283678, _1283680, _1283682, _1283684, _1283686] : [class_Orderings_Olinorder(_1283678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283678), _1283680), _1283682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283678), _1283684), _1283686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283678), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283678), _1283680), _1283684)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283678), _1283682), _1283686))))], (33956 ^ _782476) ^ [_1426328, _1426330] : [c_Int_OBit1(_1426328) = c_Int_OBit1(_1426330), -(_1426328 = _1426330)], (35398 ^ _782476) ^ [_1451321, _1451323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451321), _1451323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451321)), c_Int_OBit1(_1451323))))], (49350 ^ _782476) ^ [_1777362, _1777364] : [-(c_FunDef_Ois__measure(_1777362, _1777364))], (42774 ^ _782476) ^ [_1625676, _1625678, _1625680] : [-(c_Nitpick_Otimes__frac(_1625676, _1625678, _1625680) = hAPP(hAPP(c_Nitpick_Ofrac(_1625676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1625676), _1625678)), hAPP(c_Nitpick_Onum(_1625676), _1625680))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1625676), _1625678)), hAPP(c_Nitpick_Odenom(_1625676), _1625680))))], (36422 ^ _782476) ^ [_1472357, _1472359, _1472361, _1472363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool)), _1472361), _1472363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472357, tc_fun(_1472359, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472357, tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_fun(_1472359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472359, tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_fun(_1472359, tc_HOL_Obool)), _1472357), c_COMBC(_1472359, tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472359, tc_prod(_1472357, _1472359)), tc_fun(_1472359, tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), _1472357), hAPP(c_COMBB(tc_prod(_1472357, _1472359), tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool), _1472359), c_member(tc_prod(_1472357, _1472359)))), c_Product__Type_OPair(_1472357, _1472359)))), _1472361)), hAPP(hAPP(c_COMBC(_1472357, tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_fun(_1472359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472359, tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_fun(_1472359, tc_HOL_Obool)), _1472357), c_COMBC(_1472359, tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472359, tc_prod(_1472357, _1472359)), tc_fun(_1472359, tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool)), _1472357), hAPP(c_COMBB(tc_prod(_1472357, _1472359), tc_fun(tc_fun(tc_prod(_1472357, _1472359), tc_HOL_Obool), tc_HOL_Obool), _1472359), c_member(tc_prod(_1472357, _1472359)))), c_Product__Type_OPair(_1472357, _1472359)))), _1472363))))], (3548 ^ _782476) ^ [_835496, _835498, _835500, _835502, _835504, _835506] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_835506, _835502, _835498) = c_SetInterval_Oord__class_OgreaterThanLessThan(_835504, _835500, _835496)), _835506 = _835504, _835502 = _835500, _835498 = _835496], (172 ^ _782476) ^ [_785346, _785348, _785350, _785352, _785354, _785356] : [-(c_Big__Operators_Osemilattice__big(_785354, _785350, _785346)), c_Big__Operators_Osemilattice__big(_785356, _785352, _785348), _785356 = _785354, _785352 = _785350, _785348 = _785346], (29658 ^ _782476) ^ [_1345254, _1345256, _1345258, _1345260] : [class_Rings_Olinordered__semidom(_1345254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345254), c_Groups_Oone__class_Oone(_1345254)), _1345256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345254), hAPP(hAPP(c_Power_Opower__class_Opower(_1345254), _1345256), _1345258)), hAPP(hAPP(c_Power_Opower__class_Opower(_1345254), _1345256), _1345260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1345258), _1345260)))], (36230 ^ _782476) ^ [_1466342, _1466344] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466342), _1466344) = c_Groups_Oone__class_Oone(tc_Int_Oint), 36235 ^ _782476 : [(36238 ^ _782476) ^ [] : [-(_1466344 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36236 ^ _782476) ^ [] : [-(_1466342 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 36239 ^ _782476 : [(36242 ^ _782476) ^ [] : [-(_1466344 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36240 ^ _782476) ^ [] : [-(_1466342 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (39485 ^ _782476) ^ [_1544106] : [-(c_Nitpick_Ozero__frac(_1544106) = c_Nitpick_OAbs__Frac(_1544106, 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))))], (5502 ^ _782476) ^ [_866651, _866653] : [_866653 = _866651, -(c_Groups_Otimes__class_Otimes(_866653) = c_Groups_Otimes__class_Otimes(_866651))], (39748 ^ _782476) ^ [_1551468, _1551470, _1551472] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551468, _1551470), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551468, _1551470), _1551472), hAPP(c_COMBK(tc_fun(_1551470, tc_HOL_Obool), _1551468), c_Orderings_Otop__class_Otop(tc_fun(_1551470, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1551468, _1551470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551468, tc_HOL_Obool)), _1551472)), hAPP(c_COMBK(tc_fun(_1551470, tc_HOL_Obool), _1551468), c_Orderings_Otop__class_Otop(tc_fun(_1551470, tc_HOL_Obool)))))], (47236 ^ _782476) ^ [_1731992, _1731994, _1731996] : [-(hAPP(c_List_Oset(_1731992), hAPP(c_List_Ofilter(_1731992, _1731994), _1731996)) = hAPP(c_Set_OCollect(_1731992), hAPP(hAPP(c_COMBS(_1731992, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1731992), c_fconj), hAPP(hAPP(c_COMBC(_1731992, tc_fun(_1731992, tc_HOL_Obool), tc_HOL_Obool), c_member(_1731992)), hAPP(c_List_Oset(_1731992), _1731996)))), _1731994)))], (38180 ^ _782476) ^ [_1510984, _1510986, _1510988, _1510990, _1510992, _1510994, _1510996, _1510998, _1511000, _1511002] : [c_Equiv__Relations_Oequiv(_1510984, _1510986, _1510988), c_Equiv__Relations_Oequiv(_1510990, _1510992, _1510994), c_Equiv__Relations_Ocongruent2(_1510984, _1510990, tc_fun(_1510996, tc_HOL_Obool), _1510988, _1510994, _1510998), hBOOL(hAPP(hAPP(c_member(_1510984), _1511000), _1510986)), hBOOL(hAPP(hAPP(c_member(_1510990), _1511002), _1510992)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510984, tc_fun(_1510996, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510984, _1510984, _1510988), hAPP(hAPP(c_Set_Oinsert(_1510984), _1511000), c_Orderings_Obot__class_Obot(tc_fun(_1510984, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1510990, tc_fun(_1510996, tc_HOL_Obool)), tc_fun(_1510996, tc_HOL_Obool), _1510984), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510990, tc_fun(_1510996, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510990, _1510990, _1510994), hAPP(hAPP(c_Set_Oinsert(_1510990), _1511002), c_Orderings_Obot__class_Obot(tc_fun(_1510990, tc_HOL_Obool)))))), _1510998)) = hAPP(hAPP(_1510998, _1511000), _1511002))], (50971 ^ _782476) ^ [_1814417, _1814419, _1814421, _1814423] : [c_Relation_Osym(_1814417, _1814419), -(c_Relation_Osym(_1814421, hAPP(hAPP(c_Relation_Oinv__image(_1814417, _1814421), _1814419), _1814423)))], (25720 ^ _782476) ^ [_1264820, _1264822, _1264824, _1264826, _1264828, _1264830] : [class_Groups_Ocomm__monoid__add(_1264820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264822), _1264824)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264822, _1264820), hAPP(hAPP(c_COMBS(_1264822, _1264820, _1264820), hAPP(hAPP(c_COMBS(_1264822, _1264820, tc_fun(_1264820, _1264820)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1264820, tc_fun(_1264820, _1264820)), _1264822), c_If(_1264820)), _1264826)), _1264828)), _1264830)), _1264824) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264820), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264822, _1264820), _1264828), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264822, tc_HOL_Obool)), _1264824), hAPP(c_Set_OCollect(_1264822), _1264826)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264822, _1264820), _1264830), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264822, tc_HOL_Obool)), _1264824), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264822, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264822), _1264826))))))], (33184 ^ _782476) ^ [_1411678, _1411680, _1411682] : [class_Int_Onumber__ring(_1411678), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411680), _1411682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411678), hAPP(c_Int_Onumber__class_Onumber__of(_1411678), _1411680)), hAPP(c_Int_Onumber__class_Onumber__of(_1411678), _1411682)))], (31944 ^ _782476) ^ [_1387525, _1387527, _1387529, _1387531] : [class_Divides_Osemiring__div(_1387525), -(c_Divides_Odiv__class_Omod(_1387525, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387525), _1387527), _1387529), _1387531) = c_Divides_Odiv__class_Omod(_1387525, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387525), c_Divides_Odiv__class_Omod(_1387525, _1387527, _1387531)), c_Divides_Odiv__class_Omod(_1387525, _1387529, _1387531)), _1387531))], (19742 ^ _782476) ^ [_1153200, _1153202] : [_1153200 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153200), _1153202), -(_1153202 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1153200 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33944 ^ _782476) ^ [_1426117] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426117)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426117))))], (50440 ^ _782476) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (8894 ^ _782476) ^ [_937580, _937582, _937584] : [class_Lattices_Osemilattice__inf(_937580), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937580), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937580), _937582), _937584)), _937582)))], (10191 ^ _782476) ^ [_966931, _966933, _966935, _966937] : [10192 ^ _782476 : [(10195 ^ _782476) ^ [] : [hBOOL(hAPP(_966935, _966937))], (10193 ^ _782476) ^ [] : [_966933 = _966937]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966931), _966933), _966935), _966937)))], (7151 ^ _782476) ^ [_901126, _901128, _901130, _901132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901126, tc_HOL_Obool)), _901128), _901130)), hBOOL(hAPP(hAPP(c_member(_901126), _901132), _901128)), -(hBOOL(hAPP(hAPP(c_member(_901126), _901132), _901130)))], (45184 ^ _782476) ^ [_1686470, _1686472, _1686474, _1686476, _1686478] : [hAPP(hAPP(c_List_Oappend(_1686470), _1686472), _1686474) = hAPP(hAPP(c_List_Oappend(_1686470), _1686476), _1686478), 45187 ^ _782476 : [(45196 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686472)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686476)))), 45199 ^ _782476 : [(45202 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1686470), hAPP(hAPP(c_List_Odrop(_1686470), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686476)), _1686472)), _1686474) = _1686478)], (45200 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1686470), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686476)), _1686472) = _1686476)]]], (45188 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686472)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686476))), 45191 ^ _782476 : [(45194 ^ _782476) ^ [] : [-(_1686474 = hAPP(hAPP(c_List_Oappend(_1686470), hAPP(hAPP(c_List_Odrop(_1686470), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686472)), _1686476)), _1686478))], (45192 ^ _782476) ^ [] : [-(_1686472 = hAPP(hAPP(c_List_Otake(_1686470), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686470)), _1686472)), _1686476))]]]]], (48385 ^ _782476) ^ [_1755829, _1755831, _1755833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755829)), c_List_OtakeWhile(_1755829, _1755831, _1755833))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755829)), _1755833))), hBOOL(hAPP(_1755831, hAPP(hAPP(c_List_Onth(_1755829), _1755833), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755829)), c_List_OtakeWhile(_1755829, _1755831, _1755833)))))], (44304 ^ _782476) ^ [_1666187, _1666189] : [-(hAPP(hAPP(c_List_Otake(_1666187), _1666189), c_List_Olist_ONil(_1666187)) = c_List_Olist_ONil(_1666187))], (17832 ^ _782476) ^ [_1120360, _1120362, _1120364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120360), _1120362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120364), _1120360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120360), _1120364)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120362), _1120364))))], (51679 ^ _782476) ^ [_1829617, _1829619, _1829621] : [class_Rings_Odvd(_1829617), class_Rings_Osemiring__0(_1829617), 51686 ^ _782476 : [(51696 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1829619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829617), _1829621), 51703 ^ [_1829617, _1829619, _1829621])))), 51697 ^ _782476 : [(51698 ^ _782476) ^ [_1829946] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829617), _1829621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829617), _1829946), c_Groups_Ozero__class_Ozero(_1829617)))), hBOOL(hAPP(_1829619, _1829946))]]], (51687 ^ _782476) ^ [] : [51688 ^ _782476 : [(51689 ^ _782476) ^ [_1829809] : [hBOOL(hAPP(_1829619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829617), _1829621), _1829809)))]], 51691 ^ _782476 : [(51694 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1829619, 51690 ^ [_1829617, _1829619, _1829621])))], (51692 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829617), _1829621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829617), 51690 ^ [_1829617, _1829619, _1829621]), c_Groups_Ozero__class_Ozero(_1829617)))))]]]]], (1552 ^ _782476) ^ [_805076, _805078] : [-(class_Lazy__Sequence_Osmall__lazy(_805076)), _805078 = _805076, class_Lazy__Sequence_Osmall__lazy(_805078)], (49878 ^ _782476) ^ [_1789928, _1789930] : [-(c_List_Oreplicate(_1789928, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1789930) = c_List_Olist_ONil(_1789928))], (11656 ^ _782476) ^ [_994951, _994953, _994955] : [class_Orderings_Oorder(_994951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994951), _994953), _994955)), -(_994953 = _994955), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994951), _994953), _994955)))], (26072 ^ _782476) ^ [_1275699] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275699)))], (18598 ^ _782476) ^ [_1132781, _1132783, _1132785, _1132787] : [class_Groups_Oordered__comm__monoid__add(_1132781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132781), c_Groups_Ozero__class_Ozero(_1132781)), _1132783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132781), _1132785), _1132787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132781), _1132785), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132781), _1132787), _1132783))))], (34270 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (27529 ^ _782476) ^ [_1303286, _1303288] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1303286), hAPP(c_Nat_OSuc, _1303288)) = 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)), _1303288)), _1303286))], (50705 ^ _782476) ^ [_1809257, _1809259] : [c_Predicate_Otransp(_1809257, _1809259), -(c_Relation_Otrans(_1809257, hAPP(c_Set_OCollect(tc_prod(_1809257, _1809257)), hAPP(c_Product__Type_Oprod_Oprod__case(_1809257, _1809257, tc_HOL_Obool), _1809259))))], (41162 ^ _782476) ^ [_1588584, _1588586, _1588588, _1588590, _1588592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588584, _1588584)), hAPP(hAPP(c_Product__Type_OPair(_1588584, _1588584), _1588586), _1588588)), c_Transitive__Closure_Ortrancl(_1588584, _1588590))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588584, _1588584)), hAPP(hAPP(c_Product__Type_OPair(_1588584, _1588584), _1588588), _1588592)), c_Transitive__Closure_Ortrancl(_1588584, _1588590))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588584, _1588584)), hAPP(hAPP(c_Product__Type_OPair(_1588584, _1588584), _1588586), _1588592)), c_Transitive__Closure_Ortrancl(_1588584, _1588590))))], (19736 ^ _782476) ^ [_1153099, _1153101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153099), _1153101)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153099), _1153101) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39032 ^ _782476) ^ [_1533721, _1533723, _1533725, _1533727, _1533729, _1533731] : [c_Typedef_Otype__definition(_1533721, _1533723, _1533725, _1533727, _1533729), -(hAPP(_1533727, hAPP(_1533725, _1533731)) = _1533731)], (1852 ^ _782476) ^ [_808826, _808828] : [-(class_Groups_Omonoid__mult(_808826)), _808828 = _808826, class_Groups_Omonoid__mult(_808828)], (6987 ^ _782476) ^ [_897062, _897064, _897066] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897062, tc_HOL_Obool)), _897064), _897066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897062, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_897062, tc_HOL_Obool), _897066)), _897064)))], (45248 ^ _782476) ^ [_1688070, _1688072, _1688074, _1688076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688070), _1688072)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688074)), _1688076))), -(hAPP(hAPP(c_List_Otake(_1688074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688070), _1688072)), _1688076) = hAPP(hAPP(c_List_Oappend(_1688074), hAPP(hAPP(c_List_Otake(_1688074), _1688070), _1688076)), hAPP(hAPP(c_List_Otake(_1688074), _1688072), hAPP(hAPP(c_List_Odrop(_1688074), _1688070), _1688076))))], (45100 ^ _782476) ^ [_1684556, _1684558] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684556)), hAPP(c_List_Orotate1(_1684556), _1684558)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684556)), _1684558))], (41836 ^ _782476) ^ [_1605106, _1605108] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605106, _1605106), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605108) = c_Fun_Oid(_1605106))], (31466 ^ _782476) ^ [_1377949] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377949), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1377949)], (22088 ^ _782476) ^ [_1197736, _1197738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197736), _1197738))), 22091 ^ _782476 : [(22098 ^ _782476) ^ [] : [_1197736 = _1197738, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197736), hAPP(c_Nat_OSuc, _1197738))))], (22092 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197736), hAPP(c_Nat_OSuc, _1197738))), -(_1197736 = _1197738)]]], (52489 ^ _782476) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (5016 ^ _782476) ^ [_859042, _859044, _859046, _859048] : [-(c_Complete__Lattice_OInf__class_OInf(_859048, _859044) = c_Complete__Lattice_OInf__class_OInf(_859046, _859042)), _859048 = _859046, _859044 = _859042], (52319 ^ _782476) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (48314 ^ _782476) ^ [_1754443, _1754445, _1754447] : [c_List_OtakeWhile(_1754443, _1754445, _1754447) = _1754447, 48317 ^ _782476 : [(48318 ^ _782476) ^ [_1754530] : [hBOOL(hAPP(hAPP(c_member(_1754443), _1754530), hAPP(c_List_Oset(_1754443), _1754447))), -(hBOOL(hAPP(_1754445, _1754530)))]]], (21151 ^ _782476) ^ [_1179852, _1179854, _1179856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179852), _1179854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179854), _1179856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179852), _1179856)))], (7085 ^ _782476) ^ [_899626, _899628, _899630] : [class_Complete__Lattice_Ocomplete__lattice(_899626), hBOOL(hAPP(hAPP(c_member(_899626), _899628), _899630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899626), c_Complete__Lattice_OInf__class_OInf(_899626, _899630)), _899628)))], (15758 ^ _782476) ^ [_1077332, _1077334, _1077336, _1077338, _1077340, _1077342] : [class_Groups_Oab__semigroup__mult(_1077332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077334), _1077336)), -(hBOOL(hAPP(hAPP(c_member(_1077334), _1077338), _1077336))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077332, _1077334, c_Groups_Otimes__class_Otimes(_1077332)), _1077340), _1077342), hAPP(hAPP(c_Set_Oinsert(_1077334), _1077338), _1077336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077332), hAPP(_1077340, _1077338)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077332, _1077334, c_Groups_Otimes__class_Otimes(_1077332)), _1077340), _1077342), _1077336)))], (9249 ^ _782476) ^ [_947711, _947713, _947715] : [class_Groups_Oordered__ab__group__add(_947711), -(hAPP(c_Set_Oimage(_947711, _947711, c_Groups_Ouminus__class_Ouminus(_947711)), c_SetInterval_Oord__class_OgreaterThanAtMost(_947711, _947713, _947715)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947711, hAPP(c_Groups_Ouminus__class_Ouminus(_947711), _947715)), hAPP(c_Groups_Ouminus__class_Ouminus(_947711), _947713)))], (38794 ^ _782476) ^ [] : [-(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)))], (41052 ^ _782476) ^ [_1585169, _1585171, _1585173, _1585175] : [-(c_Transitive__Closure_Otrancl(_1585169, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1585169, _1585169)), hAPP(hAPP(c_Product__Type_OPair(_1585169, _1585169), _1585171), _1585173)), _1585175)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585169, _1585169), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585169, _1585175)), hAPP(c_Set_OCollect(tc_prod(_1585169, _1585169)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585169, _1585169, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585169, tc_fun(_1585169, tc_HOL_Obool), tc_fun(_1585169, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1585169, tc_HOL_Obool), tc_fun(_1585169, tc_HOL_Obool)), _1585169), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1585169)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585169), c_fconj), hAPP(hAPP(c_COMBC(_1585169, tc_fun(tc_prod(_1585169, _1585169), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585169, _1585169), tc_fun(tc_fun(tc_prod(_1585169, _1585169), tc_HOL_Obool), tc_HOL_Obool), _1585169), c_member(tc_prod(_1585169, _1585169))), hAPP(hAPP(c_COMBC(_1585169, _1585169, tc_prod(_1585169, _1585169)), c_Product__Type_OPair(_1585169, _1585169)), _1585171))), c_Transitive__Closure_Ortrancl(_1585169, _1585175))))), hAPP(hAPP(c_COMBC(_1585169, tc_fun(tc_prod(_1585169, _1585169), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585169, _1585169), tc_fun(tc_fun(tc_prod(_1585169, _1585169), tc_HOL_Obool), tc_HOL_Obool), _1585169), c_member(tc_prod(_1585169, _1585169))), hAPP(c_Product__Type_OPair(_1585169, _1585169), _1585173))), c_Transitive__Closure_Ortrancl(_1585169, _1585175)))))))], (36078 ^ _782476) ^ [_1464039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464039), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1464039)), c_Int_OMin)))], (44444 ^ _782476) ^ [_1668823, _1668825, _1668827] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668823))), -(c_List_Osublist(_1668825, hAPP(hAPP(c_List_Olist_OCons(_1668825), _1668827), c_List_Olist_ONil(_1668825)), _1668823) = c_List_Olist_ONil(_1668825))], (41060 ^ _782476) ^ [_1585858, _1585860, _1585862, _1585864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585858, _1585858)), hAPP(hAPP(c_Product__Type_OPair(_1585858, _1585858), _1585862), _1585864)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool)), _1585860), c_Relation_OId(_1585858)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585858, tc_fun(_1585858, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585858, tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_fun(_1585858, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585858, tc_fun(tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_fun(_1585858, tc_HOL_Obool)), _1585858), c_COMBC(_1585858, tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585858, tc_prod(_1585858, _1585858)), tc_fun(_1585858, tc_fun(tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_HOL_Obool)), _1585858), hAPP(c_COMBB(tc_prod(_1585858, _1585858), tc_fun(tc_fun(tc_prod(_1585858, _1585858), tc_HOL_Obool), tc_HOL_Obool), _1585858), c_member(tc_prod(_1585858, _1585858)))), c_Product__Type_OPair(_1585858, _1585858)))), _1585860)), c_fequal), _1585862), _1585864)))], (15957 ^ _782476) ^ [_1081297, _1081299, _1081301, _1081303, _1081305] : [class_Rings_Oring(_1081297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081299), _1081301)), hBOOL(hAPP(hAPP(c_member(_1081299), _1081303), _1081301)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081299, _1081297), _1081305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081299, tc_HOL_Obool)), _1081301), hAPP(hAPP(c_Set_Oinsert(_1081299), _1081303), c_Orderings_Obot__class_Obot(tc_fun(_1081299, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1081297), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081299, _1081297), _1081305), _1081301)), hAPP(_1081305, _1081303)))], (46934 ^ _782476) ^ [_1724668, _1724670] : [hBOOL(hAPP(c_List_Odistinct(_1724668), _1724670)), -(c_List_Oremdups(_1724668, _1724670) = _1724670)], (40179 ^ _782476) ^ [_1564532, _1564534] : [-(c_Product__Type_Omap__pair(_1564532, _1564532, _1564534, _1564534, c_Fun_Oid(_1564532), c_Fun_Oid(_1564534)) = c_Fun_Oid(tc_prod(_1564532, _1564534)))], (52679 ^ _782476) ^ [_1843585, _1843587, _1843589, _1843591, _1843593, _1843595] : [-(hAPP(hAPP(hAPP(c_COMBC(_1843585, _1843587, _1843589), _1843591), _1843593), _1843595) = hAPP(hAPP(_1843591, _1843595), _1843593))], (11622 ^ _782476) ^ [_994523, _994525, _994527] : [class_Orderings_Olinorder(_994523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994523), _994525), _994527)), 11629 ^ _782476 : [(11636 ^ _782476) ^ [] : [_994525 = _994527, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994523), _994525), _994527))], (11630 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994523), _994525), _994527))), -(_994525 = _994527)]]], (5452 ^ _782476) ^ [_865920, _865922] : [_865922 = _865920, -(c_Groups_Oone__class_Oone(_865922) = c_Groups_Oone__class_Oone(_865920))], (49410 ^ _782476) ^ [_1778614, _1778616, _1778618, _1778620, _1778622] : [_1778614 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778616, _1778618, _1778620, _1778622), _1778614) = c_Lazy__Sequence_Ohit__bound(_1778618))], (36643 ^ _782476) ^ [_1479498] : [class_Rings_Osemiring__1(_1479498), -(hBOOL(hAPP(hAPP(c_member(_1479498), c_Groups_Oone__class_Oone(_1479498)), c_Nat_Osemiring__1__class_ONats(_1479498))))], (45983 ^ _782476) ^ [_1702889, _1702891, _1702893, _1702895, _1702897] : [class_Groups_Oab__group__add(_1702889), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702889), hAPP(hAPP(c_List_Omap(_1702891, _1702889), hAPP(hAPP(c_COMBS(_1702891, _1702889, _1702889), hAPP(hAPP(c_COMBB(_1702889, tc_fun(_1702889, _1702889), _1702891), c_Groups_Ominus__class_Ominus(_1702889)), _1702893)), _1702895)), _1702897)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1702889), hAPP(c_List_Omonoid__add__class_Olistsum(_1702889), hAPP(hAPP(c_List_Omap(_1702891, _1702889), _1702893), _1702897))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702889), hAPP(hAPP(c_List_Omap(_1702891, _1702889), _1702895), _1702897))))], (34264 ^ _782476) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (48216 ^ _782476) ^ [_1752389, _1752391, _1752393, _1752395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752391)), _1752393))), -(hAPP(c_List_Orev(_1752391), hAPP(hAPP(c_List_Olist__update(_1752391, _1752393), _1752389), _1752395)) = hAPP(hAPP(c_List_Olist__update(_1752391, hAPP(c_List_Orev(_1752391), _1752393)), 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(_1752391)), _1752393)), _1752389)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1752395))], (26864 ^ _782476) ^ [_1289699, _1289701, _1289703] : [class_Orderings_Olinorder(_1289699), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289699), _1289701), _1289703) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289699), _1289703), _1289701))], (32898 ^ _782476) ^ [_1406423, _1406425, _1406427] : [class_Orderings_Olinorder(_1406423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406423), _1406425)), 32908 ^ _782476 : [(32911 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406423), 32907 ^ [_1406423, _1406425, _1406427]), _1406427))], (32909 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406423), 32907 ^ [_1406423, _1406425, _1406427]), _1406425)))]], hBOOL(hAPP(hAPP(c_member(_1406423), _1406427), _1406425)), -(c_Big__Operators_Olinorder__class_OMax(_1406423, _1406425) = _1406427)], (40952 ^ _782476) ^ [_1582637, _1582639, _1582641, _1582643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582637, _1582637)), hAPP(hAPP(c_Product__Type_OPair(_1582637, _1582637), _1582639), _1582641)), _1582643)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582637, _1582637)), hAPP(hAPP(c_Product__Type_OPair(_1582637, _1582637), _1582639), _1582641)), c_Transitive__Closure_Otrancl(_1582637, _1582643))))], (32559 ^ _782476) ^ [_1399168, _1399170] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399168, _1399170)), _1399168)))], (34266 ^ _782476) ^ [_1431744] : [c_Int_OPls = c_Int_OBit1(_1431744)], (6995 ^ _782476) ^ [_897275, _897277, _897279, _897281] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897275, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897277, tc_fun(_897275, tc_HOL_Obool)), _897279), _897281)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897277, tc_fun(_897275, tc_HOL_Obool)), _897279), hAPP(hAPP(c_COMBB(tc_fun(_897275, tc_HOL_Obool), tc_fun(_897275, tc_HOL_Obool), _897277), c_Groups_Ouminus__class_Ouminus(tc_fun(_897275, tc_HOL_Obool))), _897281)))], (49144 ^ _782476) ^ [_1773177, _1773179, _1773181] : [hBOOL(hAPP(hAPP(c_member(_1773177), _1773179), hAPP(c_List_Oset(_1773177), _1773181))), 49149 ^ _782476 : [(49152 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1773177), _1773179), hAPP(c_List_Oset(_1773177), 49148 ^ [_1773177, _1773179, _1773181])))], (49150 ^ _782476) ^ [] : [-(_1773181 = hAPP(hAPP(c_List_Oappend(_1773177), 49147 ^ [_1773177, _1773179, _1773181]), hAPP(hAPP(c_List_Olist_OCons(_1773177), _1773179), 49148 ^ [_1773177, _1773179, _1773181])))]]], (43501 ^ _782476) ^ [_1646945, _1646947] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1646945), hAPP(c_List_Oset(_1646945), _1646947))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646945)), _1646947))))], (42057 ^ _782476) ^ [_1610890, _1610892, _1610894] : [class_Complete__Lattice_Ocomplete__lattice(_1610890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610890), _1610892)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1610890), _1610894), c_Complete__Lattice_OSup__class_OSup(_1610890, _1610892)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610890, _1610890, c_Lattices_Osemilattice__sup__class_Osup(_1610890)), _1610894), _1610892))], (16043 ^ _782476) ^ [_1083161, _1083163, _1083165, _1083167, _1083169, _1083171, _1083173] : [class_Rings_Osemiring__0(_1083161), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083161), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083163, _1083161), _1083165), _1083167)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083169, _1083161), _1083171), _1083173)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083163, _1083161), hAPP(hAPP(c_COMBC(_1083163, tc_fun(_1083169, tc_HOL_Obool), _1083161), hAPP(hAPP(c_COMBB(tc_fun(_1083169, _1083161), tc_fun(tc_fun(_1083169, tc_HOL_Obool), _1083161), _1083163), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083169, _1083161)), hAPP(hAPP(c_COMBC(_1083163, tc_fun(_1083169, _1083161), tc_fun(_1083169, _1083161)), hAPP(hAPP(c_COMBB(tc_fun(_1083161, _1083161), tc_fun(tc_fun(_1083169, _1083161), tc_fun(_1083169, _1083161)), _1083163), c_COMBB(_1083161, _1083161, _1083169)), hAPP(hAPP(c_COMBB(_1083161, tc_fun(_1083161, _1083161), _1083163), c_Groups_Otimes__class_Otimes(_1083161)), _1083165))), _1083171))), _1083173)), _1083167))], (52619 ^ _782476) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (32919 ^ _782476) ^ [_1406795, _1406797, _1406799] : [class_Orderings_Olinorder(_1406795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406795), _1406797)), 32929 ^ _782476 : [(32932 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406795), _1406799), 32928 ^ [_1406795, _1406797, _1406799]))], (32930 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406795), 32928 ^ [_1406795, _1406797, _1406799]), _1406797)))]], hBOOL(hAPP(hAPP(c_member(_1406795), _1406799), _1406797)), -(c_Big__Operators_Olinorder__class_OMin(_1406795, _1406797) = _1406799)], (52093 ^ _782476) ^ [_1837382, _1837384] : [52094 ^ _782476 : [(52097 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837384), _1837382))], (52095 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837382), _1837384)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1837382, _1837384))], (17261 ^ _782476) ^ [_1110446, _1110448, _1110450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110446), _1110448)), 17264 ^ _782476 : [(17271 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110450), _1110446)), _1110448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110450), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110448), _1110446))))], (17265 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110450), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110448), _1110446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110450), _1110446)), _1110448)))]]], (33620 ^ _782476) ^ [_1419808, _1419810] : [class_Int_Onumber__ring(_1419808), class_Rings_Olinordered__idom(_1419808), 33627 ^ _782476 : [(33634 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419808), hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810)), c_Groups_Ozero__class_Ozero(_1419808)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419808), hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810)) = hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810))], (33628 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419808), hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810)), c_Groups_Ozero__class_Ozero(_1419808))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419808), hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1419808), hAPP(c_Int_Onumber__class_Onumber__of(_1419808), _1419810)))]]], (29828 ^ _782476) ^ [_1348493, _1348495, _1348497] : [class_Fields_Ofield__inverse__zero(_1348493), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348493), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348493), _1348495), _1348497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348493), _1348495), hAPP(c_Groups_Ouminus__class_Ouminus(_1348493), _1348497)))], (26804 ^ _782476) ^ [_1288469, _1288471, _1288473, _1288475] : [class_Groups_Oordered__ab__group__add(_1288469), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288469), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288469), _1288471), _1288473)), _1288475) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288469), _1288471), _1288475)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288469), _1288473), _1288475)))], (12714 ^ _782476) ^ [_1015497, _1015499, _1015501, _1015503, _1015505, _1015507] : [c_Fun_Oinj__on(_1015497, _1015499, _1015501, _1015503), hAPP(_1015501, _1015505) = hAPP(_1015501, _1015507), hBOOL(hAPP(hAPP(c_member(_1015497), _1015505), _1015503)), hBOOL(hAPP(hAPP(c_member(_1015497), _1015507), _1015503)), -(_1015505 = _1015507)], (26332 ^ _782476) ^ [_1280235, _1280237, _1280239, _1280241] : [class_Orderings_Olinorder(_1280235), 26335 ^ _782476 : [(26336 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280235), _1280239), _1280241))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), _1280239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), _1280241)))], (26346 ^ _782476) ^ [] : [26347 ^ _782476 : [(26350 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), _1280241))], (26348 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), _1280239))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280235), _1280237), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280235), _1280239), _1280241))))]]], (52413 ^ _782476) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (31604 ^ _782476) ^ [_1380437, _1380439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380439)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380437)), hAPP(c_Int_Onat, _1380439)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380437), _1380439)))], (9267 ^ _782476) ^ [_948086, _948088, _948090, _948092] : [hAPP(c_Set_Oimage(_948086, _948088, _948090), c_Orderings_Otop__class_Otop(tc_fun(_948086, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_948088, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948088, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948088, tc_HOL_Obool)), hAPP(c_Set_Oimage(_948086, _948088, _948090), _948092))), hAPP(c_Set_Oimage(_948086, _948088, _948090), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948086, tc_HOL_Obool)), _948092)))))], (49456 ^ _782476) ^ [_1779745, _1779747, _1779749, _1779751, _1779753] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1779745), _1779747), _1779749), _1779751), _1779753) = c_New__DSequence_Oneg__single(_1779745, _1779747))], (12298 ^ _782476) ^ [_1005763, _1005765] : [class_Complete__Lattice_Ocomplete__lattice(_1005763), c_Orderings_Oorder__class_Omono(_1005763, _1005763, _1005765), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005763), hAPP(_1005765, c_Inductive_Ocomplete__lattice__class_Ogfp(_1005763, _1005765))), c_Inductive_Ocomplete__lattice__class_Ogfp(_1005763, _1005765))))], (28772 ^ _782476) ^ [_1329052, _1329054, _1329056, _1329058] : [class_Rings_Ocomm__semiring__1(_1329052), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329052), _1329054), _1329056)), _1329058) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329052), hAPP(hAPP(c_Power_Opower__class_Opower(_1329052), _1329054), _1329058)), hAPP(hAPP(c_Power_Opower__class_Opower(_1329052), _1329056), _1329058)))], (5416 ^ _782476) ^ [_865364, _865366, _865368, _865370, _865372, _865374, _865376, _865378] : [-(c_Lazy__Sequence_Omap(_865378, _865374, _865370, _865366) = c_Lazy__Sequence_Omap(_865376, _865372, _865368, _865364)), _865378 = _865376, _865374 = _865372, _865370 = _865368, _865366 = _865364], (7695 ^ _782476) ^ [_912438, _912440, _912442, _912444, _912446] : [class_Complete__Lattice_Ocomplete__lattice(_912438), 7701 ^ _782476 : [(7704 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912438), _912444), hAPP(_912446, 7700 ^ [_912438, _912440, _912442, _912444, _912446])))], (7702 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912440), 7700 ^ [_912438, _912440, _912442, _912444, _912446]), _912442)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912438), _912444), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_912440, _912438), _912442), _912446))))], (22296 ^ _782476) ^ [_1201122, _1201124, _1201126, _1201128] : [class_Rings_Osemiring__1(_1201122), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1201122, _1201124, hAPP(c_Nat_OSuc, _1201126), _1201128) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1201122, _1201124, _1201126, hAPP(_1201124, _1201128)))], (7932 ^ _782476) ^ [_917405, _917407, _917409, _917411] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917405, tc_HOL_Obool)), _917407), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917405, tc_HOL_Obool)), _917409), _917411)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917405, tc_HOL_Obool)), _917409), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917405, tc_HOL_Obool)), _917407), _917411)))], (24875 ^ _782476) ^ [_1247561, _1247563, _1247565] : [class_Groups_Oordered__ab__group__add__abs(_1247561), -(hAPP(c_Groups_Oabs__class_Oabs(_1247561), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247561), hAPP(c_Groups_Oabs__class_Oabs(_1247561), _1247563)), hAPP(c_Groups_Oabs__class_Oabs(_1247561), _1247565))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247561), hAPP(c_Groups_Oabs__class_Oabs(_1247561), _1247563)), hAPP(c_Groups_Oabs__class_Oabs(_1247561), _1247565)))], (32648 ^ _782476) ^ [_1400699, _1400701] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400699, _1400701)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400699), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400701)))], (35508 ^ _782476) ^ [] : [-(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))))], (44338 ^ _782476) ^ [_1666768, _1666770] : [_1666770 = c_List_Olist_ONil(_1666768), -(c_Orderings_Obot__class_Obot(tc_fun(_1666768, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666768), _1666770))], (30734 ^ _782476) ^ [_1365022, _1365024, _1365026, _1365028] : [class_Fields_Olinordered__field(_1365022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365022), _1365024), c_Groups_Ozero__class_Ozero(_1365022))), 30741 ^ _782476 : [(30748 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365022), _1365028), _1365024)), _1365026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365022), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365022), _1365026), _1365024)), _1365028)))], (30742 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365022), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365022), _1365026), _1365024)), _1365028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365022), _1365028), _1365024)), _1365026)))]]], (43673 ^ _782476) ^ [_1652407, _1652409, _1652411, _1652413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652407, _1652407)), hAPP(hAPP(c_Product__Type_OPair(_1652407, _1652407), _1652409), _1652411)), hAPP(c_List_Oset(tc_prod(_1652407, _1652407)), hAPP(hAPP(c_List_Ozip(_1652407, _1652407), _1652413), _1652413)))), 43676 ^ _782476 : [(43679 ^ _782476) ^ [] : [-(_1652409 = _1652411)], (43677 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652407), _1652409), hAPP(c_List_Oset(_1652407), _1652413))))]]], (17642 ^ _782476) ^ [_1116904, _1116906] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116904), _1116906)), _1116904) = _1116906)], (5712 ^ _782476) ^ [_869970, _869972, _869974, _869976] : [-(hAPP(_869976, _869972) = hAPP(_869974, _869970)), _869976 = _869974, _869972 = _869970], (24498 ^ _782476) ^ [_1240799, _1240801, _1240803] : [class_Int_Oring__char__0(_1240799), 24501 ^ _782476 : [(24508 ^ _782476) ^ [] : [_1240801 = _1240803, -(hAPP(c_Int_Oring__1__class_Oof__int(_1240799), _1240801) = hAPP(c_Int_Oring__1__class_Oof__int(_1240799), _1240803))], (24502 ^ _782476) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1240799), _1240801) = hAPP(c_Int_Oring__1__class_Oof__int(_1240799), _1240803), -(_1240801 = _1240803)]]], (29532 ^ _782476) ^ [_1342841, _1342843, _1342845, _1342847] : [class_Rings_Olinordered__semidom(_1342841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342843), _1342845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342841), c_Groups_Oone__class_Oone(_1342841)), _1342847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342841), hAPP(hAPP(c_Power_Opower__class_Opower(_1342841), _1342847), _1342843)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342841), _1342847), _1342845))))], (30945 ^ _782476) ^ [_1368880] : [-(_1368880 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368880), _1368880) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27008 ^ _782476) ^ [_1292911, _1292913, _1292915, _1292917] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1292911), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292913, tc_Nat_Onat), _1292915), _1292917)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292913, _1292911), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1292911, _1292913), c_Nat_Osemiring__1__class_Oof__nat(_1292911)), _1292915)), _1292917)), class_Groups_Ocomm__monoid__mult(_1292911), class_Rings_Osemiring__1(_1292911)], (9686 ^ _782476) ^ [_956253, _956255] : [class_Lattices_Obounded__lattice__bot(_956253), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956253), _956255), c_Orderings_Obot__class_Obot(_956253)) = c_Orderings_Obot__class_Obot(_956253))], (40165 ^ _782476) ^ [_1564055, _1564057, _1564059, _1564061, _1564063, _1564065] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564055, _1564057), _1564057, tc_prod(_1564059, _1564061), c_Product__Type_Osnd(_1564055, _1564057)), c_Product__Type_Omap__pair(_1564059, _1564055, _1564061, _1564057, _1564063, _1564065)) = hAPP(c_Fun_Ocomp(_1564061, _1564057, tc_prod(_1564059, _1564061), _1564065), c_Product__Type_Osnd(_1564059, _1564061)))], (28273 ^ _782476) ^ [_1317847, _1317849, _1317851] : [28275 ^ _782476 : [(28278 ^ _782476) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1317851, 28274 ^ [_1317847, _1317849, _1317851]))], (28276 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317847), 28274 ^ [_1317847, _1317849, _1317851]), _1317849)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317847, tc_Int_Oint), _1317851), _1317849) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317847, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1317847), c_Int_Onat), _1317851)), _1317849)))], (2128 ^ _782476) ^ [_813460, _813462, _813464, _813466, _813468, _813470, _813472, _813474, _813476, _813478] : [-(c_Fun_Ooverride__on(_813478, _813474, _813470, _813466, _813462) = c_Fun_Ooverride__on(_813476, _813472, _813468, _813464, _813460)), _813478 = _813476, _813474 = _813472, _813470 = _813468, _813466 = _813464, _813462 = _813460], (46503 ^ _782476) ^ [_1714749, _1714751, _1714753] : [46505 ^ _782476 : [(46508 ^ _782476) ^ [] : [hBOOL(hAPP(_1714751, 46504 ^ [_1714749, _1714751, _1714753]))], (46506 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1714749), 46504 ^ [_1714749, _1714751, _1714753]), hAPP(c_List_Oset(_1714749), _1714753))))]], -(hBOOL(hAPP(c_List_Olistsp(_1714749, _1714751), _1714753)))], (32125 ^ _782476) ^ [_1390897, _1390899] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390897, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390899)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390897, _1390899) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7095 ^ _782476) ^ [_899791, _899793] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_899791, tc_HOL_Obool), _899793) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_899791, tc_HOL_Obool), tc_fun(_899791, tc_HOL_Obool)), _899793), c_COMBI(tc_fun(_899791, tc_HOL_Obool))))], (18186 ^ _782476) ^ [_1126462] : [class_Rings_Ozero__neq__one(_1126462), c_Groups_Oone__class_Oone(_1126462) = c_Groups_Ozero__class_Ozero(_1126462)], (33026 ^ _782476) ^ [_1408494, _1408496, _1408498] : [class_Int_Onumber(_1408494), class_Orderings_Olinorder(_1408494), 33033 ^ _782476 : [(33040 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408494), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408498)), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408496)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408494), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408496)), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408498))))], (33034 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408494), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408496)), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408498))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408494), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408498)), hAPP(c_Int_Onumber__class_Onumber__of(_1408494), _1408496)))]]], (10571 ^ _782476) ^ [_975626, _975628, _975630, _975632] : [-(hBOOL(hAPP(hAPP(c_member(_975626), _975628), _975630))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975626, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975626), _975628), _975632)), _975630) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975626, tc_HOL_Obool)), _975632), _975630))], (45633 ^ _782476) ^ [_1696279] : [class_Orderings_Olinorder(_1696279), -(c_Finite__Set_Ofun__left__comm(_1696279, tc_List_Olist(_1696279), c_List_Olinorder__class_Oinsort__key(_1696279, _1696279, c_COMBI(_1696279))))], (38855 ^ _782476) ^ [_1527716, _1527718, _1527720, _1527722] : [-(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), _1527716), _1527718)), 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), _1527720), _1527722)), 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), _1527716), _1527720)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527718), _1527722))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (14002 ^ _782476) ^ [_1042565, _1042567, _1042569, _1042571, _1042573, _1042575] : [c_Fun_Obij__betw(_1042565, _1042567, _1042569, c_Orderings_Otop__class_Otop(tc_fun(_1042565, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042567, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042565, _1042567, _1042569), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042571, tc_fun(_1042565, tc_HOL_Obool)), _1042573), _1042575)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042571, tc_fun(_1042567, tc_HOL_Obool)), _1042573), hAPP(hAPP(c_COMBB(tc_fun(_1042565, tc_HOL_Obool), tc_fun(_1042567, tc_HOL_Obool), _1042571), c_Set_Oimage(_1042565, _1042567, _1042569)), _1042575)))], (10071 ^ _782476) ^ [_964506, _964508, _964510, _964512, _964514] : [_964506 = c_Orderings_Obot__class_Obot(tc_fun(_964508, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964508, tc_fun(_964510, tc_HOL_Obool)), _964506), hAPP(hAPP(c_COMBB(tc_fun(_964510, tc_HOL_Obool), tc_fun(_964510, tc_HOL_Obool), _964508), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964510, tc_HOL_Obool)), _964512)), _964514)) = c_Orderings_Otop__class_Otop(tc_fun(_964510, tc_HOL_Obool)))], (19556 ^ _782476) ^ [_1150070, _1150072, _1150074, _1150076] : [class_Groups_Ocomm__monoid__add(_1150070), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150072), _1150074))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150072, _1150070), _1150076), _1150074) = c_Groups_Ozero__class_Ozero(_1150070))], (46998 ^ _782476) ^ [_1725858, _1725860, _1725862, _1725864] : [class_Orderings_Olinorder(_1725858), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725860)), c_List_Olinorder__class_Osort__key(_1725860, _1725858, _1725862, _1725864)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725860)), _1725864))], (23253 ^ _782476) ^ [_1218962, _1218964, _1218966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218962), _1218964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1218962, tc_HOL_Obool)), _1218964), hAPP(hAPP(c_Set_Oinsert(_1218962), _1218966), c_Orderings_Obot__class_Obot(tc_fun(_1218962, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1218962), _1218964))))], (38517 ^ _782476) ^ [_1519654, _1519656, _1519658, _1519660, _1519662] : [c_Equiv__Relations_Oequivp(_1519654, _1519656), hBOOL(hAPP(hAPP(_1519656, _1519658), _1519660)), hBOOL(hAPP(hAPP(_1519656, _1519660), _1519662)), -(hBOOL(hAPP(hAPP(_1519656, _1519658), _1519662)))], (28227 ^ _782476) ^ [_1316206, _1316208, _1316210] : [class_Orderings_Olinorder(_1316206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316206), _1316208)), hBOOL(hAPP(hAPP(c_member(_1316206), _1316210), _1316208)), 28238 ^ _782476 : [(28245 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316206, tc_HOL_Obool)), _1316208), hAPP(hAPP(c_Set_Oinsert(_1316206), _1316210), c_Orderings_Obot__class_Obot(tc_fun(_1316206, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316206, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1316206, c_Orderings_Oord__class_Omin(_1316206), _1316208) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316206), _1316210), c_Big__Operators_Olattice_OInf__fin(_1316206, c_Orderings_Oord__class_Omin(_1316206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316206, tc_HOL_Obool)), _1316208), hAPP(hAPP(c_Set_Oinsert(_1316206), _1316210), c_Orderings_Obot__class_Obot(tc_fun(_1316206, tc_HOL_Obool)))))))], (28239 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316206, tc_HOL_Obool)), _1316208), hAPP(hAPP(c_Set_Oinsert(_1316206), _1316210), c_Orderings_Obot__class_Obot(tc_fun(_1316206, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316206, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1316206, c_Orderings_Oord__class_Omin(_1316206), _1316208) = _1316210)]]], (10175 ^ _782476) ^ [_966659, _966661, _966663, _966665, _966667] : [class_Groups_Ominus(_966659), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966661, _966659)), _966663), _966665), _966667) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966659), hAPP(_966663, _966667)), hAPP(_966665, _966667)))], (20920 ^ _782476) ^ [_1175797, _1175799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175797), _1175799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175797), _1175799)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8403 ^ _782476) ^ [_927770, _927772] : [class_Lattices_Olattice(_927770), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927770), _927772), _927772) = _927772)], (20425 ^ _782476) ^ [_1166673, _1166675, _1166677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166673), _1166675))), 20428 ^ _782476 : [(20435 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166677), _1166675))), -(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)), _1166673)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166677), _1166675)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (20429 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166677), _1166675)), -(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)), _1166673)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166677), _1166675)) = 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))))]]], (31538 ^ _782476) ^ [_1379183, _1379185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1379183)), 31541 ^ _782476 : [(31548 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379185), _1379183))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379185), _1379183) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379185), _1379183)), _1379183)))], (31542 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379185), _1379183)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379185), _1379183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13756 ^ _782476) ^ [_1037631, _1037633, _1037635, _1037637] : [c_Fun_Obij__betw(_1037631, _1037633, _1037635, c_Orderings_Obot__class_Obot(tc_fun(_1037631, tc_HOL_Obool)), _1037637), -(_1037637 = c_Orderings_Obot__class_Obot(tc_fun(_1037633, tc_HOL_Obool)))], (29186 ^ _782476) ^ [_1336393, _1336395] : [29187 ^ _782476 : [(29190 ^ _782476) ^ [] : [_1336395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29188 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336393))]], -(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), _1336393), _1336395))))], (49424 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15558 ^ _782476) ^ [_1073280, _1073282, _1073284, _1073286] : [c_Finite__Set_Ofolding__one__idem(_1073280, _1073282, _1073284), -(hAPP(hAPP(_1073282, _1073286), _1073286) = _1073286)], (44112 ^ _782476) ^ [_1662605, _1662607] : [class_Groups_Ocomm__monoid__add(_1662605), hBOOL(hAPP(c_List_Odistinct(_1662605), _1662607)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1662605), _1662607) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1662605, _1662605), c_COMBI(_1662605)), hAPP(c_List_Oset(_1662605), _1662607)))], (24052 ^ _782476) ^ [_1233429, _1233431, _1233433, _1233435] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1233429, _1233431)), c_Sum__Type_OPlus(_1233429, _1233431, _1233433, _1233435)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1233429), _1233433)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1233431), _1233435))], (47776 ^ _782476) ^ [_1743201, _1743203, _1743205, _1743207, _1743209] : [class_Orderings_Olinorder(_1743201), -(c_List_Olinorder__class_Osorted(_1743201, hAPP(hAPP(c_List_Omap(_1743203, _1743201), _1743205), hAPP(c_List_Ofilter(_1743203, hAPP(hAPP(c_COMBC(_1743203, _1743201, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1743201, tc_fun(_1743201, tc_HOL_Obool), _1743203), c_fequal), _1743205)), hAPP(_1743207, _1743209))), _1743209))))], (44412 ^ _782476) ^ [_1668011, _1668013, _1668015] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668011), tc_List_Olist(_1668011))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668011), tc_List_Olist(_1668011)), c_List_Olist_ONil(_1668011)), _1668013)), c_List_Olistrel1(_1668011, _1668015)))], (40655 ^ _782476) ^ [_1576353, _1576355] : [-(c_Hilbert__Choice_OEps(_1576353, hAPP(hAPP(c_COMBC(_1576353, _1576353, tc_HOL_Obool), c_fequal), _1576355)) = _1576355)], (43721 ^ _782476) ^ [_1653717, _1653719, _1653721, _1653723] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653717)), _1653719), hAPP(c_List_Oset(tc_List_Olist(_1653717)), c_Enum_On__lists(_1653717, _1653721, _1653723)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653717)), _1653719) = _1653721)], (39168 ^ _782476) ^ [_1537380, _1537382, _1537384, _1537386] : [c_Wellfounded_Owf(_1537380, _1537382), -(c_Wellfounded_Owf(_1537384, hAPP(hAPP(c_Relation_Oinv__image(_1537380, _1537384), _1537382), _1537386)))], (32626 ^ _782476) ^ [_1400387, _1400389] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400387), _1400389))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400387, _1400389) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400387), _1400389), _1400389))], (7846 ^ _782476) ^ [_915491, _915493, _915495, _915497] : [hBOOL(hAPP(_915491, _915493)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915495, tc_HOL_Obool)), _915491), _915497), _915493)))], (35224 ^ _782476) ^ [_1448257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448257)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448257), c_Int_OPls)))], (51101 ^ _782476) ^ [_1816402, _1816404] : [c_Relation_Osym(_1816402, hAPP(c_Set_OCollect(tc_prod(_1816402, _1816402)), hAPP(c_Product__Type_Oprod_Oprod__case(_1816402, _1816402, tc_HOL_Obool), _1816404))), -(c_Predicate_Osymp(_1816402, _1816404))], (8912 ^ _782476) ^ [_937969, _937971, _937973, _937975, _937977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937969, tc_HOL_Obool)), _937971), hAPP(c_Set_Oimage(_937973, _937969, _937975), _937977))), 8916 ^ _782476 : [(8919 ^ _782476) ^ [] : [-(_937971 = hAPP(c_Set_Oimage(_937973, _937969, _937975), 8915 ^ [_937969, _937971, _937973, _937975, _937977]))], (8917 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937973, tc_HOL_Obool)), 8915 ^ [_937969, _937971, _937973, _937975, _937977]), _937977)))]]], (4224 ^ _782476) ^ [_846476, _846478] : [_846478 = _846476, -(c_Fun_Oid(_846478) = c_Fun_Oid(_846476))], (31131 ^ _782476) ^ [_1371684, _1371686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371684), _1371686)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371684), _1371686) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13742 ^ _782476) ^ [_1037353, _1037355, _1037357, _1037359, _1037361, _1037363] : [-(hAPP(c_Set_Oimage(_1037353, _1037355, hAPP(c_Fun_Ocomp(_1037357, _1037355, _1037353, _1037359), _1037361)), _1037363) = hAPP(c_Set_Oimage(_1037357, _1037355, _1037359), hAPP(c_Set_Oimage(_1037353, _1037357, _1037361), _1037363)))], (48665 ^ _782476) ^ [_1761912, _1761914, _1761916] : [-(c_List_Oinsert(_1761912, _1761914, c_List_Oremdups(_1761912, _1761916)) = c_List_Oremdups(_1761912, c_List_Oinsert(_1761912, _1761914, _1761916)))], (20934 ^ _782476) ^ [_1176042] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176042) = _1176042)], (52363 ^ _782476) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (26824 ^ _782476) ^ [_1288897, _1288899] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288897)), hAPP(c_Nat_OSuc, _1288899)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288897), _1288899)))], (10663 ^ _782476) ^ [_977725, _977727, _977729] : [class_Orderings_Oorder(_977725), _977727 = _977729, -(c_SetInterval_Oord__class_OatLeastAtMost(_977725, _977727, _977729) = hAPP(hAPP(c_Set_Oinsert(_977725), _977727), c_Orderings_Obot__class_Obot(tc_fun(_977725, tc_HOL_Obool))))], (29276 ^ _782476) ^ [_1338207, _1338209, _1338211] : [class_Power_Opower(_1338207), class_Rings_Omult__zero(_1338207), class_Rings_Ono__zero__divisors(_1338207), class_Rings_Ozero__neq__one(_1338207), 29291 ^ _782476 : [(29300 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338207), _1338209), _1338211) = c_Groups_Ozero__class_Ozero(_1338207)), _1338209 = c_Groups_Ozero__class_Ozero(_1338207), -(_1338211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29292 ^ _782476) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1338207), _1338209), _1338211) = c_Groups_Ozero__class_Ozero(_1338207), 29295 ^ _782476 : [(29298 ^ _782476) ^ [] : [_1338211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29296 ^ _782476) ^ [] : [-(_1338209 = c_Groups_Ozero__class_Ozero(_1338207))]]]]], (36875 ^ _782476) ^ [_1484452, _1484454, _1484456, _1484458, _1484460, _1484462] : [hAPP(hAPP(c_Product__Type_OPair(_1484452, _1484454), _1484456), _1484458) = hAPP(hAPP(c_Product__Type_OPair(_1484452, _1484454), _1484460), _1484462), 36878 ^ _782476 : [(36881 ^ _782476) ^ [] : [-(_1484458 = _1484462)], (36879 ^ _782476) ^ [] : [-(_1484456 = _1484460)]]], (20093 ^ _782476) ^ [_1159698, _1159700, _1159702] : [class_Rings_Olinordered__idom(_1159698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159698), c_Groups_Ozero__class_Ozero(_1159698)), _1159700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159698), c_Groups_Ozero__class_Ozero(_1159698)), _1159702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159698), _1159702), c_Groups_Oone__class_Oone(_1159698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159698), _1159702), _1159700)), _1159700)))], (540 ^ _782476) ^ [_790730, _790732, _790734, _790736, _790738, _790740] : [-(c_Nitpick_Oless__eq__frac(_790738, _790734, _790730)), c_Nitpick_Oless__eq__frac(_790740, _790736, _790732), _790740 = _790738, _790736 = _790734, _790732 = _790730], (26972 ^ _782476) ^ [_1292029, _1292031, _1292033, _1292035] : [class_Orderings_Olinorder(_1292029), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292029), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292029), _1292031), _1292033)), _1292035) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292029), _1292031), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292029), _1292033), _1292035)))], (50345 ^ _782476) ^ [_1799673, _1799675, _1799677] : [c_List_Olist__all(tc_Int_Oint, _1799673, c_List_Oupto(_1799675, _1799677)), -(c_List_Oall__interval__int(_1799673, _1799675, _1799677))], (9518 ^ _782476) ^ [_953107, _953109] : [hAPP(c_Set_OPow(_953107), _953109) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953107, tc_HOL_Obool), tc_HOL_Obool))], (39558 ^ _782476) ^ [_1546345, _1546347, _1546349, _1546351, _1546353] : [hBOOL(hAPP(hAPP(_1546345, _1546347), _1546349)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1546351, _1546353, _1546345), _1546349)))], (15368 ^ _782476) ^ [_1069452, _1069454, _1069456] : [class_Lattices_Olattice(_1069452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069452), _1069454)), -(_1069454 = c_Orderings_Obot__class_Obot(tc_fun(_1069452, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069452), _1069456)), -(_1069456 = c_Orderings_Obot__class_Obot(tc_fun(_1069452, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069452, tc_HOL_Obool)), _1069454), _1069456) = c_Orderings_Obot__class_Obot(tc_fun(_1069452, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1069452, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069452, tc_HOL_Obool)), _1069454), _1069456)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069452), c_Big__Operators_Olattice__class_OSup__fin(_1069452, _1069454)), c_Big__Operators_Olattice__class_OSup__fin(_1069452, _1069456)))], (17453 ^ _782476) ^ [_1113489, _1113491, _1113493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113489), _1113491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113489), _1113493)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113491), _1113493))))], (46080 ^ _782476) ^ [_1705811, _1705813, _1705815, _1705817, _1705819, _1705821] : [-(hAPP(hAPP(c_List_Omap(_1705811, _1705813), _1705815), hAPP(hAPP(c_List_Omap(_1705817, _1705811), _1705819), _1705821)) = hAPP(hAPP(c_List_Omap(_1705817, _1705813), hAPP(c_Fun_Ocomp(_1705811, _1705813, _1705817, _1705815), _1705819)), _1705821))], (23091 ^ _782476) ^ [_1215843, _1215845, _1215847] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1215843), _1215845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215843, tc_HOL_Obool)), _1215845), _1215847)), -(hAPP(c_Finite__Set_Ocard(_1215843), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1215843, tc_HOL_Obool)), _1215847), _1215845)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1215843), _1215847)), hAPP(c_Finite__Set_Ocard(_1215843), _1215845)))], (25638 ^ _782476) ^ [_1262058, _1262060, _1262062] : [hBOOL(hAPP(_1262058, _1262060)), -(hAPP(c_Set_OCollect(_1262062), hAPP(hAPP(c_COMBS(_1262062, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262062), c_fconj), hAPP(hAPP(c_COMBC(_1262062, _1262062, tc_HOL_Obool), c_fequal), _1262060))), _1262058)) = hAPP(hAPP(c_Set_Oinsert(_1262062), _1262060), c_Orderings_Obot__class_Obot(tc_fun(_1262062, tc_HOL_Obool))))], (52247 ^ _782476) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52341 ^ _782476) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (14206 ^ _782476) ^ [_1047039, _1047041] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047039), c_Orderings_Otop__class_Otop(tc_fun(_1047039, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047041), c_Orderings_Otop__class_Otop(tc_fun(_1047041, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1047039, _1047041)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1047039, _1047041), tc_HOL_Obool)))))], (8354 ^ _782476) ^ [_926777, _926779, _926781, _926783, _926785] : [hBOOL(hAPP(hAPP(c_member(_926777), _926779), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926781, tc_fun(_926777, tc_HOL_Obool)), _926783), _926785))), 8358 ^ _782476 : [(8361 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926777), _926779), hAPP(_926785, 8357 ^ [_926777, _926779, _926781, _926783, _926785]))))], (8359 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926781), 8357 ^ [_926777, _926779, _926781, _926783, _926785]), _926783)))]]], (46236 ^ _782476) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7682 ^ _782476) ^ [_912041, _912043, _912045, _912047, _912049, _912051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912041, tc_HOL_Obool)), _912043), _912045)), 7688 ^ _782476 : [(7691 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912047, tc_HOL_Obool)), hAPP(_912049, 7687 ^ [_912041, _912043, _912045, _912047, _912049, _912051])), hAPP(_912051, 7687 ^ [_912041, _912043, _912045, _912047, _912049, _912051])))], (7689 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912041), 7687 ^ [_912041, _912043, _912045, _912047, _912049, _912051]), _912043)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912047, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912041, tc_fun(_912047, tc_HOL_Obool)), _912043), _912049)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912041, tc_fun(_912047, tc_HOL_Obool)), _912045), _912051))))], (37625 ^ _782476) ^ [_1498520, _1498522] : [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), _1498520), _1498522))), 37628 ^ _782476 : [(37635 ^ _782476) ^ [] : [-(_1498522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1498520, _1498522) = c_Nitpick_Onat__gcd(_1498522, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1498520, _1498522)))], (37629 ^ _782476) ^ [] : [_1498522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1498520, _1498522) = _1498520)]]], (35916 ^ _782476) ^ [_1460938, _1460940] : [class_Rings_Osemiring__1(_1460938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460940)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460938), 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)))), _1460940))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460938), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460938), hAPP(c_Int_Onat, _1460940))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460938), hAPP(c_Int_Onat, _1460940))))], (51349 ^ _782476) ^ [_1821410, _1821412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1821410), _1821412)), -(c_Quickcheck_Obeyond(_1821410, _1821412) = _1821412)], (32782 ^ _782476) ^ [_1403782, _1403784, _1403786, _1403788] : [class_Groups_Ocomm__monoid__mult(_1403782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403784), _1403786)), 32792 ^ _782476 : [(32795 ^ _782476) ^ [] : [hAPP(_1403788, 32791 ^ [_1403782, _1403784, _1403786, _1403788]) = c_Groups_Oone__class_Oone(_1403782)], (32793 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403784), 32791 ^ [_1403782, _1403784, _1403786, _1403788]), _1403786)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403782, _1403784, c_Groups_Otimes__class_Otimes(_1403782)), _1403788), c_Groups_Oone__class_Oone(_1403782)), _1403786) = c_Groups_Oone__class_Oone(_1403782))], (39129 ^ _782476) ^ [_1536623, _1536625, _1536627, _1536629] : [-(c_Wellfounded_Omax__extp(_1536623, _1536625, _1536627, _1536629)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536623), _1536627)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536623), _1536629)), -(_1536629 = c_Orderings_Obot__class_Obot(tc_fun(_1536623, tc_HOL_Obool))), 39143 ^ _782476 : [(39146 ^ _782476) ^ [_1536968] : [hBOOL(hAPP(hAPP(c_member(_1536623), _1536968), _1536629)), hBOOL(hAPP(hAPP(_1536625, 39142 ^ [_1536623, _1536625, _1536627, _1536629]), _1536968))], (39144 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536623), 39142 ^ [_1536623, _1536625, _1536627, _1536629]), _1536627)))]]], (7455 ^ _782476) ^ [_907554, _907556, _907558] : [class_Lattices_Oboolean__algebra(_907554), 7458 ^ _782476 : [(7465 ^ _782476) ^ [] : [_907556 = _907558, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907554), _907556) = hAPP(c_Groups_Ouminus__class_Ouminus(_907554), _907558))], (7459 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907554), _907556) = hAPP(c_Groups_Ouminus__class_Ouminus(_907554), _907558), -(_907556 = _907558)]]], (44648 ^ _782476) ^ [_1673896, _1673898, _1673900, _1673902, _1673904] : [-(hAPP(hAPP(c_List_Oappend(_1673896), _1673898), hAPP(hAPP(c_List_Olist_OCons(_1673896), _1673900), c_List_Olist_ONil(_1673896))) = hAPP(hAPP(c_List_Oappend(_1673896), _1673902), hAPP(hAPP(c_List_Olist_OCons(_1673896), _1673904), c_List_Olist_ONil(_1673896)))), _1673898 = _1673902, _1673900 = _1673904], (42303 ^ _782476) ^ [_1615788, _1615790, _1615792, _1615794] : [class_Complete__Lattice_Ocomplete__lattice(_1615788), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615790), _1615792)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615790, _1615788), _1615792), _1615794) = hAPP(hAPP(c_Finite__Set_Ofold(_1615790, _1615788, hAPP(hAPP(c_COMBB(_1615788, tc_fun(_1615788, _1615788), _1615790), c_Lattices_Osemilattice__inf__class_Oinf(_1615788)), _1615794)), c_Orderings_Otop__class_Otop(_1615788)), _1615792))], (41024 ^ _782476) ^ [_1584419, _1584421, _1584423, _1584425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584419, _1584419)), _1584421), c_Transitive__Closure_Otrancl(_1584419, _1584423))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584419, _1584419), tc_HOL_Obool)), _1584423), _1584425)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584419, _1584419)), _1584421), c_Transitive__Closure_Otrancl(_1584419, _1584425))))], (9426 ^ _782476) ^ [_951261, _951263] : [_951263 = c_Orderings_Obot__class_Obot(tc_fun(_951261, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951261, tc_HOL_Obool)), _951263), c_Orderings_Obot__class_Obot(tc_fun(_951261, tc_HOL_Obool)))))], (40375 ^ _782476) ^ [_1569186, _1569188, _1569190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569186, _1569186), tc_HOL_Obool)), _1569188), hAPP(hAPP(c_Product__Type_OSigma(_1569186, _1569186), _1569190), hAPP(c_COMBK(tc_fun(_1569186, tc_HOL_Obool), _1569186), _1569190)))), 40381 ^ _782476 : [(40384 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569186, _1569186)), hAPP(hAPP(c_Product__Type_OPair(_1569186, _1569186), 40380 ^ [_1569186, _1569188, _1569190]), 40380 ^ [_1569186, _1569188, _1569190])), _1569188))], (40382 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1569186), 40380 ^ [_1569186, _1569188, _1569190]), _1569190)))]], -(c_Relation_Orefl__on(_1569186, _1569190, _1569188))], (5240 ^ _782476) ^ [_862582, _862584, _862586, _862588] : [-(c_Transitive__Closure_Otrancl(_862588, _862584) = c_Transitive__Closure_Otrancl(_862586, _862582)), _862588 = _862586, _862584 = _862582], (46400 ^ _782476) ^ [_1712659, _1712661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712659)), hAPP(c_Code__Numeral_Onat__of, _1712661))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712659), _1712661)))], (10715 ^ _782476) ^ [_978620, _978622, _978624] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978620, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978620, tc_HOL_Obool)), _978622), _978624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978620, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978620, tc_HOL_Obool)), _978622)), _978624))], (34850 ^ _782476) ^ [_1441031, _1441033] : [class_Int_Onumber__ring(_1441031), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1441031), c_Groups_Oone__class_Oone(_1441031)), hAPP(c_Int_Onumber__class_Onumber__of(_1441031), _1441033)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441031), 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), _1441033))))], (45438 ^ _782476) ^ [_1691947, _1691949, _1691951, _1691953] : [-(hAPP(c_List_Ofoldl(_1691947, _1691949, _1691951, _1691953), c_List_Olist_ONil(_1691949)) = _1691953)], (45382 ^ _782476) ^ [_1690746, _1690748, _1690750] : [-(_1690746 = c_List_Olist_ONil(_1690748)), -(hAPP(c_List_Otl(_1690748), hAPP(hAPP(c_List_Oappend(_1690748), _1690746), _1690750)) = hAPP(hAPP(c_List_Oappend(_1690748), hAPP(c_List_Otl(_1690748), _1690746)), _1690750))], (37237 ^ _782476) ^ [_1491269, _1491271, _1491273] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491269), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491271)), _1491273)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1491269, _1491271), hAPP(c_Divides_OnegateSnd, _1491273))))], (42011 ^ _782476) ^ [_1609859, _1609861, _1609863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609859), _1609861)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609859, tc_HOL_Obool)), _1609861), _1609863) = hAPP(hAPP(c_Finite__Set_Ofold(_1609859, tc_fun(_1609859, tc_HOL_Obool), c_Set_Oinsert(_1609859)), _1609863), _1609861))], (34364 ^ _782476) ^ [_1433179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433179), 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), _1433179)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (13514 ^ _782476) ^ [_1032679, _1032681, _1032683, _1032685, _1032687] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032679, _1032681, _1032683, _1032685, c_Orderings_Obot__class_Obot(tc_fun(_1032679, tc_HOL_Obool))), _1032687)), -(_1032687 = _1032685)], (9802 ^ _782476) ^ [_958273, _958275, _958277] : [9804 ^ _782476 : [(9807 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958273, tc_HOL_Obool)), 9803 ^ [_958273, _958275, _958277]), _958277) = c_Orderings_Obot__class_Obot(tc_fun(_958273, tc_HOL_Obool))], (9805 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958273, tc_HOL_Obool)), 9803 ^ [_958273, _958275, _958277]), _958275)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958273, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_958273, tc_HOL_Obool), _958275)), _958277) = c_Orderings_Obot__class_Obot(tc_fun(_958273, tc_HOL_Obool)))], (48092 ^ _782476) ^ [_1749704, _1749706] : [hBOOL(hAPP(c_List_Odistinct(_1749704), _1749706)), -(hBOOL(hAPP(c_List_Odistinct(_1749704), hAPP(c_List_Orev(_1749704), _1749706))))], (42816 ^ _782476) ^ [_1626563] : [-(c_Nitpick_Odenom(_1626563) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626563, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626563)))], (8282 ^ _782476) ^ [_925091, _925093, _925095, _925097, _925099] : [class_Complete__Lattice_Ocomplete__lattice(_925091), 8288 ^ _782476 : [(8291 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925091), hAPP(_925097, 8287 ^ [_925091, _925093, _925095, _925097, _925099])), _925099))], (8289 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925093), 8287 ^ [_925091, _925093, _925095, _925097, _925099]), _925095)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925091), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_925093, _925091), _925095), _925097)), _925099)))], (21249 ^ _782476) ^ [_1181485, _1181487, _1181489, _1181491, _1181493, _1181495] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181485), _1181487)), _1181489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181491), _1181493)), _1181495), 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), _1181491), _1181493)), _1181495))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181495), _1181491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181491), _1181485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181487), _1181493)))], (3134 ^ _782476) ^ [_829071, _829073, _829075, _829077] : [-(c_List_Olistset(_829077, _829073) = c_List_Olistset(_829075, _829071)), _829077 = _829075, _829073 = _829071], (27236 ^ _782476) ^ [_1297253, _1297255, _1297257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297253), _1297255)), 27239 ^ _782476 : [(27240 ^ _782476) ^ [] : [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(_1297253, tc_Nat_Onat), _1297257), _1297255))), 27243 ^ _782476 : [(27244 ^ _782476) ^ [_1297421] : [hBOOL(hAPP(hAPP(c_member(_1297253), _1297421), _1297255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297257, _1297421))))]]], (27250 ^ _782476) ^ [] : [27252 ^ _782476 : [(27255 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297257, 27251 ^ [_1297253, _1297255, _1297257])))], (27253 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1297253), 27251 ^ [_1297253, _1297255, _1297257]), _1297255)))]], -(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(_1297253, tc_Nat_Onat), _1297257), _1297255))))]]], (10337 ^ _782476) ^ [_969844, _969846, _969848] : [hAPP(hAPP(c_Set_Oinsert(_969844), _969846), c_Orderings_Obot__class_Obot(tc_fun(_969844, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_969844), _969848), c_Orderings_Obot__class_Obot(tc_fun(_969844, tc_HOL_Obool))), -(_969846 = _969848)], (10343 ^ _782476) ^ [_969999, _970001, _970003, _970005, _970007] : [hAPP(hAPP(c_Set_Oinsert(_969999), _970001), hAPP(hAPP(c_Set_Oinsert(_969999), _970003), c_Orderings_Obot__class_Obot(tc_fun(_969999, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_969999), _970005), hAPP(hAPP(c_Set_Oinsert(_969999), _970007), c_Orderings_Obot__class_Obot(tc_fun(_969999, tc_HOL_Obool)))), 10348 ^ _782476 : [(10351 ^ _782476) ^ [] : [-(_970003 = _970007)], (10349 ^ _782476) ^ [] : [-(_970001 = _970005)]], 10352 ^ _782476 : [(10355 ^ _782476) ^ [] : [-(_970003 = _970005)], (10353 ^ _782476) ^ [] : [-(_970001 = _970007)]]], (13174 ^ _782476) ^ [_1025023, _1025025, _1025027, _1025029, _1025031] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1025023, _1025025, _1025027), _1025029), _1025031)), -(hBOOL(hAPP(_1025029, hAPP(_1025027, _1025031))))], (41256 ^ _782476) ^ [_1590917, _1590919, _1590921, _1590923, _1590925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590917, _1590917)), hAPP(hAPP(c_Product__Type_OPair(_1590917, _1590917), _1590919), _1590921)), _1590923)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590917, _1590917)), hAPP(hAPP(c_Product__Type_OPair(_1590917, _1590917), _1590921), _1590925)), c_Transitive__Closure_Ortrancl(_1590917, _1590923))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590917, _1590917)), hAPP(hAPP(c_Product__Type_OPair(_1590917, _1590917), _1590919), _1590925)), c_Transitive__Closure_Otrancl(_1590917, _1590923))))], (1040 ^ _782476) ^ [_798176, _798178, _798180, _798182, _798184, _798186, _798188, _798190, _798192, _798194, _798196, _798198] : [-(c_Equiv__Relations_Ocongruent2(_798196, _798192, _798188, _798184, _798180, _798176)), c_Equiv__Relations_Ocongruent2(_798198, _798194, _798190, _798186, _798182, _798178), _798198 = _798196, _798194 = _798192, _798190 = _798188, _798186 = _798184, _798182 = _798180, _798178 = _798176], (36823 ^ _782476) ^ [_1483329, _1483331, _1483333] : [-(c_Fun_Oinj__on(tc_prod(_1483329, _1483331), tc_prod(_1483331, _1483329), hAPP(c_Product__Type_Oprod_Oprod__case(_1483329, _1483331, tc_prod(_1483331, _1483329)), hAPP(c_COMBC(_1483331, _1483329, tc_prod(_1483331, _1483329)), c_Product__Type_OPair(_1483331, _1483329))), _1483333))], (25783 ^ _782476) ^ [_1266622, _1266624, _1266626, _1266628, _1266630] : [_1266622 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266624, tc_HOL_Obool), _1266626), c_Orderings_Oorder__class_Omono(tc_fun(_1266624, tc_HOL_Obool), tc_fun(_1266624, tc_HOL_Obool), _1266626), hBOOL(hAPP(hAPP(c_member(_1266624), _1266628), _1266622)), 25797 ^ _782476 : [(25800 ^ _782476) ^ [] : [hBOOL(hAPP(_1266630, 25796 ^ [_1266622, _1266624, _1266626, _1266628, _1266630]))], (25798 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266624), 25796 ^ [_1266622, _1266624, _1266626, _1266628, _1266630]), hAPP(_1266626, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266624, tc_HOL_Obool)), _1266622), hAPP(c_Set_OCollect(_1266624), _1266630))))))]], -(hBOOL(hAPP(_1266630, _1266628)))], (49478 ^ _782476) ^ [_1780339, _1780341, _1780343, _1780345] : [c_Fun_Obij__betw(_1780339, _1780341, _1780343, c_Orderings_Otop__class_Otop(tc_fun(_1780339, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1780341, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1780339, _1780341, _1780343), hAPP(c_Set_OCollect(_1780339), _1780345)) = hAPP(c_Set_OCollect(_1780341), hAPP(hAPP(c_COMBB(_1780339, tc_HOL_Obool, _1780341), _1780345), c_Hilbert__Choice_Oinv__into(_1780339, _1780341, c_Orderings_Otop__class_Otop(tc_fun(_1780339, tc_HOL_Obool)), _1780343))))], (52197 ^ _782476) ^ [_1838783, _1838785] : [class_Groups_Ouminus(_1838783), -(class_Groups_Ouminus(tc_fun(_1838785, _1838783)))], (17515 ^ _782476) ^ [_1114609, _1114611] : [17516 ^ _782476 : [(17519 ^ _782476) ^ [] : [_1114609 = _1114611], (17517 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114609), _1114611))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114609), _1114611)))], (42203 ^ _782476) ^ [_1613767, _1613769, _1613771] : [class_Lattices_Oab__semigroup__idem__mult(_1613767), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613767), _1613769)), -(hAPP(c_Finite__Set_Ofold1(_1613767, c_Groups_Otimes__class_Otimes(_1613767)), hAPP(hAPP(c_Set_Oinsert(_1613767), _1613771), _1613769)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613767, _1613767, c_Groups_Otimes__class_Otimes(_1613767)), _1613771), _1613769))], (35144 ^ _782476) ^ [_1446962, _1446964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1446962)), c_Int_OBit0(_1446964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446962), _1446964)))], (48098 ^ _782476) ^ [_1749809, _1749811] : [-(hAPP(c_List_Orev(_1749809), c_List_Oconcat(_1749809, _1749811)) = c_List_Oconcat(_1749809, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1749809), tc_List_Olist(_1749809)), c_List_Orev(_1749809)), hAPP(c_List_Orev(tc_List_Olist(_1749809)), _1749811))))], (43287 ^ _782476) ^ [_1641127, _1641129, _1641131, _1641133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641127), tc_List_Olist(_1641127))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641127), tc_List_Olist(_1641127)), _1641129), _1641131)), c_List_Olistrel(_1641127, _1641133))), 43290 ^ _782476 : [(43293 ^ _782476) ^ [_1641356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641356), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641127)), _1641129))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641127, _1641127)), hAPP(hAPP(c_Product__Type_OPair(_1641127, _1641127), hAPP(hAPP(c_List_Onth(_1641127), _1641129), _1641356)), hAPP(hAPP(c_List_Onth(_1641127), _1641131), _1641356))), _1641133)))], (43291 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641127)), _1641129) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641127)), _1641131))]]], (9199 ^ _782476) ^ [_945961, _945963] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945961, tc_HOL_Obool)), _945963), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945961, tc_HOL_Obool)), _945963)) = c_Orderings_Otop__class_Otop(tc_fun(_945961, tc_HOL_Obool)))], (4164 ^ _782476) ^ [_845574, _845576, _845578, _845580] : [-(c_New__DSequence_Oneg__single(_845580, _845576) = c_New__DSequence_Oneg__single(_845578, _845574)), _845580 = _845578, _845576 = _845574], (42999 ^ _782476) ^ [_1632416, _1632418, _1632420] : [-(c_Random_Oselect__weight(_1632416, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632416)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1632416), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1632418)), _1632420)) = c_Random_Oselect__weight(_1632416, _1632420))], (8671 ^ _782476) ^ [_933217, _933219, _933221, _933223, _933225] : [-(hAPP(c_Set_Oimage(_933217, _933219, hAPP(hAPP(c_COMBB(_933221, _933219, _933217), _933223), _933225)), c_Orderings_Otop__class_Otop(tc_fun(_933217, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_933221, _933219, _933223), hAPP(c_Set_Oimage(_933217, _933221, _933225), c_Orderings_Otop__class_Otop(tc_fun(_933217, tc_HOL_Obool)))))], (46608 ^ _782476) ^ [_1717011, _1717013, _1717015] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1717011)), _1717015), c_List_Olists(_1717011, _1717013))), -(hBOOL(hAPP(c_List_Olistsp(_1717011, hAPP(hAPP(c_COMBC(_1717011, tc_fun(_1717011, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717011)), _1717013)), _1717015)))], (36018 ^ _782476) ^ [_1463171] : [_1463171 = c_Int_OMin, -(c_Int_OBit1(_1463171) = c_Int_OMin)], (12366 ^ _782476) ^ [_1007095, _1007097, _1007099, _1007101] : [class_Complete__Lattice_Ocomplete__lattice(_1007095), _1007097 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1007095, _1007099), c_Orderings_Oorder__class_Omono(_1007095, _1007095, _1007099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007095), _1007101), hAPP(_1007099, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007095), _1007101), _1007097)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007095), _1007101), _1007097)))], (36655 ^ _782476) ^ [_1479720, _1479722, _1479724, _1479726, _1479728] : [hBOOL(hAPP(hAPP(c_member(_1479720), _1479722), hAPP(c_Relation_OImage(_1479724, _1479720, _1479726), hAPP(hAPP(c_Set_Oinsert(_1479724), _1479728), c_Orderings_Obot__class_Obot(tc_fun(_1479724, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1479724, _1479720)), hAPP(hAPP(c_Product__Type_OPair(_1479724, _1479720), _1479728), _1479722)), _1479726)))], (796 ^ _782476) ^ [_794692, _794694] : [-(class_Fields_Olinordered__field(_794692)), _794694 = _794692, class_Fields_Olinordered__field(_794694)], (20215 ^ _782476) ^ [_1162003, _1162005, _1162007] : [20216 ^ _782476 : [(20219 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162003), _1162007))], (20217 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162005)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162003), _1162005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162007), _1162005))))], (17381 ^ _782476) ^ [_1112280, _1112282, _1112284] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112282), _1112284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112282), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112280), _1112284)))], (38344 ^ _782476) ^ [_1515355, _1515357, _1515359, _1515361, _1515363, _1515365, _1515367] : [c_Equiv__Relations_Oequiv(_1515355, _1515357, _1515359), c_Equiv__Relations_Ocongruent(_1515355, tc_fun(_1515361, tc_HOL_Obool), _1515359, _1515363), hBOOL(hAPP(hAPP(c_member(tc_fun(_1515355, tc_HOL_Obool)), _1515365), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515355), _1515357), _1515359))), 38358 ^ _782476 : [(38361 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1515361, tc_HOL_Obool)), hAPP(_1515363, 38357 ^ [_1515355, _1515357, _1515359, _1515361, _1515363, _1515365, _1515367])), _1515367))], (38359 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515355), 38357 ^ [_1515355, _1515357, _1515359, _1515361, _1515363, _1515365, _1515367]), _1515357)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1515361, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1515355, tc_fun(_1515361, tc_HOL_Obool)), _1515365), _1515363)), _1515367)))], (9243 ^ _782476) ^ [_947491, _947493, _947495] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_947491, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_947491, tc_HOL_Obool), tc_HOL_Obool)), _947493), _947495)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947491, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947491, tc_HOL_Obool), _947493)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947491, tc_HOL_Obool), _947495)))], (9151 ^ _782476) ^ [_944614, _944616, _944618, _944620] : [class_Lattices_Olattice(_944614), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944614), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944614), _944616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944614), _944618), _944620))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944614), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944614), _944616), _944618)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944614), _944616), _944620)))))], (23478 ^ _782476) ^ [_1223680, _1223682, _1223684] : [hAPP(c_Finite__Set_Ocard(_1223680), _1223682) = hAPP(c_Nat_OSuc, _1223684), 23483 ^ _782476 : [(23486 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1223680), 23481 ^ [_1223680, _1223682, _1223684]), 23482 ^ [_1223680, _1223682, _1223684]))], (23488 ^ _782476) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1223680), 23482 ^ [_1223680, _1223682, _1223684]) = _1223684)], (23490 ^ _782476) ^ [] : [_1223684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(23482 ^ [_1223680, _1223682, _1223684] = c_Orderings_Obot__class_Obot(tc_fun(_1223680, tc_HOL_Obool)))], (23484 ^ _782476) ^ [] : [-(_1223682 = hAPP(hAPP(c_Set_Oinsert(_1223680), 23481 ^ [_1223680, _1223682, _1223684]), 23482 ^ [_1223680, _1223682, _1223684]))]]], (13870 ^ _782476) ^ [_1039922, _1039924, _1039926] : [c_Fun_Obij__betw(_1039922, _1039924, _1039926, c_Orderings_Otop__class_Otop(tc_fun(_1039922, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039924, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1039922, _1039924, _1039926, c_Orderings_Otop__class_Otop(tc_fun(_1039922, tc_HOL_Obool))))], (26428 ^ _782476) ^ [_1281898, _1281900, _1281902, _1281904] : [class_Orderings_Olinorder(_1281898), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281898), _1281900), _1281902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281898), _1281900), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281898), _1281904), _1281902))))], (3860 ^ _782476) ^ [_840434, _840436] : [_840436 = _840434, -(c_List_Odistinct(_840436) = c_List_Odistinct(_840434))], (50363 ^ _782476) ^ [_1799957, _1799959, _1799961] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799957), _1799959, _1799961)), -(c_List_Olist__ex(tc_Int_Oint, _1799957, c_List_Oupto(_1799959, _1799961)))], (41136 ^ _782476) ^ [_1587937, _1587939] : [-(hAPP(c_Relation_ORange(_1587937, _1587937), c_Transitive__Closure_Ortrancl(_1587937, _1587939)) = c_Orderings_Otop__class_Otop(tc_fun(_1587937, tc_HOL_Obool)))], (43115 ^ _782476) ^ [_1636080, _1636082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636080), tc_List_Olist(_1636080)), tc_HOL_Obool)), c_List_Olistrel(_1636080, _1636082)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636080), c_List_Olistrel1(_1636080, _1636082)))))], (48553 ^ _782476) ^ [_1759539, _1759541] : [class_Orderings_Olinorder(_1759539), 48560 ^ _782476 : [(48565 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759539), hAPP(hAPP(c_List_Onth(_1759539), _1759541), 48558 ^ [_1759539, _1759541])), hAPP(hAPP(c_List_Onth(_1759539), _1759541), 48559 ^ [_1759539, _1759541])))], (48563 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48559 ^ [_1759539, _1759541]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759539)), _1759541))))], (48561 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48558 ^ [_1759539, _1759541]), 48559 ^ [_1759539, _1759541])))]], -(c_List_Olinorder__class_Osorted(_1759539, _1759541))], (41054 ^ _782476) ^ [_1585437, _1585439, _1585441, _1585443] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585437, tc_fun(_1585437, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585437, tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_fun(_1585437, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585437, tc_fun(tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_fun(_1585437, tc_HOL_Obool)), _1585437), c_COMBC(_1585437, tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585437, tc_prod(_1585437, _1585437)), tc_fun(_1585437, tc_fun(tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_HOL_Obool)), _1585437), hAPP(c_COMBB(tc_prod(_1585437, _1585437), tc_fun(tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool), tc_HOL_Obool), _1585437), c_member(tc_prod(_1585437, _1585437)))), c_Product__Type_OPair(_1585437, _1585437)))), _1585439)), c_fequal), _1585441), _1585443)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585437, _1585437)), hAPP(hAPP(c_Product__Type_OPair(_1585437, _1585437), _1585441), _1585443)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585437, _1585437), tc_HOL_Obool)), _1585439), c_Relation_OId(_1585437)))))], (38670 ^ _782476) ^ [_1522955, _1522957, _1522959, _1522961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522955), _1522957)), 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)), _1522959), _1522955)), 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)), _1522961), _1522957)), 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)), _1522959), _1522961)), _1522957)), c_FunDef_Omax__weak)))], (36380 ^ _782476) ^ [_1468943, _1468945, _1468947, _1468949] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1468943, tc_fun(_1468945, tc_HOL_Obool))), _1468947), _1468949)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1468943, _1468945)), hAPP(hAPP(c_Product__Type_OPair(_1468943, _1468945), _1468947), _1468949)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1468943, _1468945), tc_HOL_Obool)))))], (21824 ^ _782476) ^ [_1192228, _1192230, _1192232, _1192234, _1192236] : [class_Groups_Ocomm__monoid__add(_1192228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192230), _1192232)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192230), _1192234)), 21838 ^ _782476 : [(21841 ^ _782476) ^ [] : [hAPP(_1192236, 21837 ^ [_1192228, _1192230, _1192232, _1192234, _1192236]) = c_Groups_Ozero__class_Ozero(_1192228)], (21839 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192230), 21837 ^ [_1192228, _1192230, _1192232, _1192234, _1192236]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192230, tc_HOL_Obool)), _1192232), _1192234))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192230, _1192228), _1192236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192230, tc_HOL_Obool)), _1192232), _1192234)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192228), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192230, _1192228), _1192236), _1192232)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192230, _1192228), _1192236), _1192234)))], (46234 ^ _782476) ^ [_1709317, _1709319] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1709317)), hAPP(c_Code__Numeral_Oof__nat, _1709319)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1709317), _1709319)))], (18390 ^ _782476) ^ [_1129366, _1129368, _1129370] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129366), _1129368) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129366), _1129370), -(_1129368 = _1129370), -(_1129366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24164 ^ _782476) ^ [_1235370, _1235372] : [c_Nat__Transfer_Ois__nat(_1235370), c_Nat__Transfer_Ois__nat(_1235372), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235370), _1235372)))], (24028 ^ _782476) ^ [_1232975, _1232977, _1232979, _1232981] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1232975, _1232977)), c_Sum__Type_OPlus(_1232975, _1232977, _1232979, _1232981))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1232975), _1232979)))], (36042 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (34178 ^ _782476) ^ [_1430331] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430331))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430331)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37073 ^ _782476) ^ [_1488520, _1488522] : [37074 ^ _782476 : [(37077 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488522), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37075 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488520), _1488522))]], -(c_Divides_OposDivAlg(_1488520, _1488522) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488520))], (34398 ^ _782476) ^ [_1433706] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433706), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433706)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1433706)))], (25957 ^ _782476) ^ [_1272818, _1272820] : [-(hAPP(c_Set_OPow(_1272818), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272818, tc_HOL_Obool)), _1272820)) = hAPP(c_Set_OCollect(tc_fun(_1272818, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272818, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1272818, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1272818, tc_HOL_Obool), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272818, tc_HOL_Obool)), c_COMBS(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1272818, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1272818, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1272818, tc_HOL_Obool), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_fun(_1272818, tc_HOL_Obool)), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_fun(_1272818, tc_HOL_Obool)), tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272818, tc_HOL_Obool)), c_COMBB(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272818, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1272818, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272818, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272818, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1272818, tc_HOL_Obool)), _1272820)), c_Set_OPow(_1272818))))))], (43157 ^ _782476) ^ [_1637315, _1637317, _1637319, _1637321, _1637323, _1637325] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637315, _1637315)), hAPP(hAPP(c_Product__Type_OPair(_1637315, _1637315), _1637317), _1637319)), _1637321)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637315), tc_List_Olist(_1637315))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637315), tc_List_Olist(_1637315)), _1637323), _1637325)), c_List_Olistrel(_1637315, _1637321))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637315), tc_List_Olist(_1637315))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637315), tc_List_Olist(_1637315)), hAPP(hAPP(c_List_Olist_OCons(_1637315), _1637317), _1637323)), hAPP(hAPP(c_List_Olist_OCons(_1637315), _1637319), _1637325))), c_List_Olistrel(_1637315, _1637321))))], (10181 ^ _782476) ^ [_966817, _966819, _966821, _966823] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966817), _966819), _966821), _966823)), -(_966819 = _966823), -(hBOOL(hAPP(_966821, _966823)))], (45811 ^ _782476) ^ [_1699192, _1699194, _1699196] : [-(c_List_Olast(_1699192, hAPP(hAPP(c_List_Oappend(_1699192), _1699194), hAPP(hAPP(c_List_Olist_OCons(_1699192), _1699196), c_List_Olist_ONil(_1699192)))) = _1699196)], (13427 ^ _782476) ^ [_1031122, _1031124] : [-(c_HOL_OThe(_1031122, hAPP(c_fequal, _1031124)) = _1031124)], (2342 ^ _782476) ^ [_816811, _816813] : [_816813 = _816811, -(c_Enum_Oenum__class_Oenum__ex(_816813) = c_Enum_Oenum__class_Oenum__ex(_816811))], (7660 ^ _782476) ^ [_911383, _911385, _911387, _911389, _911391, _911393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911383, tc_HOL_Obool)), _911385), _911387)), 7666 ^ _782476 : [(7669 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911389, tc_HOL_Obool)), hAPP(_911391, 7665 ^ [_911383, _911385, _911387, _911389, _911391, _911393])), hAPP(_911393, 7665 ^ [_911383, _911385, _911387, _911389, _911391, _911393])))], (7667 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911383), 7665 ^ [_911383, _911385, _911387, _911389, _911391, _911393]), _911387)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911389, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911383, tc_fun(_911389, tc_HOL_Obool)), _911387), _911391)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911383, tc_fun(_911389, tc_HOL_Obool)), _911387), _911393))))], (38383 ^ _782476) ^ [_1516314, _1516316] : [c_Code__Numeral_OSuc__code__numeral(_1516314) = c_Code__Numeral_OSuc__code__numeral(_1516316), -(_1516314 = _1516316)], (9979 ^ _782476) ^ [_962370, _962372, _962374] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962370, tc_HOL_Obool)), _962372), _962374) = c_Orderings_Obot__class_Obot(tc_fun(_962370, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962370, tc_HOL_Obool)), _962372), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962370, tc_HOL_Obool)), _962374))))], (29024 ^ _782476) ^ [_1333655, _1333657, _1333659, _1333661] : [class_Groups_Ocomm__monoid__mult(_1333655), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333657), _1333659)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333657, _1333655), hAPP(c_COMBK(_1333655, _1333657), _1333661)), _1333659) = hAPP(hAPP(c_Power_Opower__class_Opower(_1333655), _1333661), hAPP(c_Finite__Set_Ocard(_1333657), _1333659)))], (27034 ^ _782476) ^ [_1293559, _1293561, _1293563, _1293565, _1293567] : [class_Orderings_Olinorder(_1293559), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293559, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293559, _1293561, _1293563)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293559, _1293565, _1293567)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1293559, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293559), _1293561), _1293565), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293559), _1293563), _1293567)))], (9819 ^ _782476) ^ [_958708, _958710, _958712, _958714, _958716] : [c_Orderings_Oorder__class_Omono(tc_fun(_958708, tc_HOL_Obool), tc_fun(_958710, tc_HOL_Obool), _958712), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958710, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958710, tc_HOL_Obool)), hAPP(_958712, _958714)), hAPP(_958712, _958716))), hAPP(_958712, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958708, tc_HOL_Obool)), _958714), _958716)))))], (15738 ^ _782476) ^ [_1077018, _1077020] : [class_Lattices_Olattice(_1077018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077018), _1077020)), -(c_Big__Operators_Olattice__class_OSup__fin(_1077018, _1077020) = hAPP(c_Finite__Set_Ofold1(_1077018, c_Lattices_Osemilattice__sup__class_Osup(_1077018)), _1077020))], (52405 ^ _782476) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (34918 ^ _782476) ^ [_1442667, _1442669] : [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(_1442669))), 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), _1442667)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442667)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442669))))], (20880 ^ _782476) ^ [] : [-(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))))], (44128 ^ _782476) ^ [_1663028, _1663030] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1663028), _1663030))), -(c_Nitpick_Ocard_H(_1663028, _1663030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34404 ^ _782476) ^ [_1433761, _1433763] : [class_Int_Onumber__ring(_1433761), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433761), hAPP(c_Int_Onumber__class_Onumber__of(_1433761), c_Int_OBit1(c_Int_OPls))), _1433763) = _1433763)], (45462 ^ _782476) ^ [_1692517] : [class_Groups_Omonoid__add(_1692517), -(c_List_Omonoid__add__class_Olistsum(_1692517) = c_List_Ofoldl(_1692517, _1692517, c_Groups_Oplus__class_Oplus(_1692517), c_Groups_Ozero__class_Ozero(_1692517)))], (52477 ^ _782476) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (18460 ^ _782476) ^ [_1130372, _1130374, _1130376] : [class_Rings_Olinordered__semidom(_1130372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130374), _1130376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130372), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130372), _1130374)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130372), _1130376))))], (44280 ^ _782476) ^ [_1665798, _1665800, _1665802] : [hAPP(hAPP(c_List_Olist_OCons(_1665798), _1665800), _1665802) = c_List_Olist_ONil(_1665798)], (49768 ^ _782476) ^ [_1787327, _1787329, _1787331, _1787333] : [-(c_Predicate_Oconversep(_1787327, _1787329, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787327, tc_fun(_1787329, tc_HOL_Obool))), _1787331), _1787333)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787329, tc_fun(_1787327, tc_HOL_Obool))), c_Predicate_Oconversep(_1787327, _1787329, _1787331)), c_Predicate_Oconversep(_1787327, _1787329, _1787333)))], (6090 ^ _782476) ^ [_878924, _878926, _878928, _878930] : [class_Orderings_Oorder(_878924), class_Enum_Oenum(_878926), 6097 ^ _782476 : [(6104 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878926), hAPP(hAPP(c_COMBS(_878926, _878924, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878924, tc_fun(_878924, tc_HOL_Obool), _878926), c_Orderings_Oord__class_Oless__eq(_878924)), _878928)), _878930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878926, _878924)), _878928), _878930)))], (6098 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878926, _878924)), _878928), _878930)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878926), hAPP(hAPP(c_COMBS(_878926, _878924, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878924, tc_fun(_878924, tc_HOL_Obool), _878926), c_Orderings_Oord__class_Oless__eq(_878924)), _878928)), _878930))))]]], (52745 ^ _782476) ^ [_1844510, _1844512] : [hBOOL(hAPP(hAPP(c_fdisj, _1844510), _1844512)), -(hBOOL(_1844510)), -(hBOOL(_1844512))], (40994 ^ _782476) ^ [_1583624, _1583626, _1583628, _1583630, _1583632] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583624, _1583624)), hAPP(hAPP(c_Product__Type_OPair(_1583624, _1583624), _1583626), _1583628)), c_Transitive__Closure_Otrancl(_1583624, _1583630))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583624, _1583624)), hAPP(hAPP(c_Product__Type_OPair(_1583624, _1583624), _1583628), _1583632)), _1583630)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583624, _1583624)), hAPP(hAPP(c_Product__Type_OPair(_1583624, _1583624), _1583626), _1583632)), c_Transitive__Closure_Otrancl(_1583624, _1583630))))], (39690 ^ _782476) ^ [_1549991, _1549993, _1549995, _1549997, _1549999, _1550001] : [hBOOL(hAPP(hAPP(c_member(_1549991), _1549993), _1549995)), hBOOL(hAPP(hAPP(c_member(_1549997), _1549999), hAPP(_1550001, _1549993))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549991, _1549997)), hAPP(hAPP(c_Product__Type_OPair(_1549991, _1549997), _1549993), _1549999)), hAPP(hAPP(c_Product__Type_OSigma(_1549991, _1549997), _1549995), _1550001))))], (17924 ^ _782476) ^ [_1122491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122491), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52605 ^ _782476) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52483 ^ _782476) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (50109 ^ _782476) ^ [_1794199, _1794201, _1794203] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794199)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794199, _1794201, _1794203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794199)), _1794203)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12130 ^ _782476) ^ [_1003174, _1003176, _1003178, _1003180, _1003182] : [class_Orderings_Oorder(_1003174), class_Orderings_Oorder(_1003176), c_Orderings_Oorder__class_Ostrict__mono(_1003176, _1003174, _1003178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003176), _1003180), _1003182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003174), hAPP(_1003178, _1003180)), hAPP(_1003178, _1003182))))], (39299 ^ _782476) ^ [_1539740, _1539742] : [c_Wellfounded_Owf(_1539740, _1539742), 39302 ^ _782476 : [(39303 ^ _782476) ^ [_1539809] : [-(hBOOL(hAPP(hAPP(c_member(_1539740), _1539809), c_Wellfounded_Oacc(_1539740, _1539742))))]]], (48822 ^ _782476) ^ [_1765442, _1765444, _1765446, _1765448, _1765450, _1765452, _1765454, _1765456] : [48824 ^ _782476 : [(48827 ^ _782476) ^ [] : [hAPP(c_Fun_Ocomp(_1765446, _1765446, _1765448, hAPP(_1765450, 48823 ^ [_1765442, _1765444, _1765446, _1765448, _1765450, _1765452, _1765454, _1765456])), _1765452) = hAPP(c_Fun_Ocomp(_1765448, _1765446, _1765448, _1765452), hAPP(_1765454, 48823 ^ [_1765442, _1765444, _1765446, _1765448, _1765450, _1765452, _1765454, _1765456]))], (48825 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765442), 48823 ^ [_1765442, _1765444, _1765446, _1765448, _1765450, _1765452, _1765454, _1765456]), hAPP(c_List_Oset(_1765442), _1765444))))]], -(hAPP(c_List_Ofoldl(_1765446, _1765442, hAPP(c_COMBC(_1765442, _1765446, _1765446), _1765450), hAPP(_1765452, _1765456)), _1765444) = hAPP(_1765452, hAPP(c_List_Ofoldl(_1765448, _1765442, hAPP(c_COMBC(_1765442, _1765448, _1765448), _1765454), _1765456), _1765444)))], (17179 ^ _782476) ^ [_1108763, _1108765, _1108767, _1108769] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108763, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108765)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1108763, tc_HOL_Obool), tc_Nat_Onat), _1108767), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1108769))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108763, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108769, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108765), _1108769))), _1108767))], (44282 ^ _782476) ^ [_1665835] : [-(c_Enum_Osublists(_1665835, c_List_Olist_ONil(_1665835)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1665835)), c_List_Olist_ONil(_1665835)), c_List_Olist_ONil(tc_List_Olist(_1665835))))], (21423 ^ _782476) ^ [] : [-(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)))], (16631 ^ _782476) ^ [_1095898, _1095900, _1095902, _1095904, _1095906] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1095898), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095898), _1095900), _1095902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095898), _1095904), _1095906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095898), _1095900), _1095904)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095898), _1095902), _1095906))))], (14671 ^ _782476) ^ [_1055972, _1055974, _1055976, _1055978, _1055980, _1055982] : [c_Finite__Set_Ofolding(_1055972, _1055974, _1055976, _1055978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055972), _1055980)), -(hAPP(_1055978, hAPP(hAPP(c_Set_Oinsert(_1055972), _1055982), _1055980)) = hAPP(c_Fun_Ocomp(_1055974, _1055974, _1055974, hAPP(_1055978, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055972, tc_HOL_Obool)), _1055980), hAPP(hAPP(c_Set_Oinsert(_1055972), _1055982), c_Orderings_Obot__class_Obot(tc_fun(_1055972, tc_HOL_Obool)))))), hAPP(_1055976, _1055982)))], (50929 ^ _782476) ^ [_1813261, _1813263, _1813265, _1813267, _1813269, _1813271] : [-(c_Partial__Function_Ofun__lub(_1813261, _1813263, _1813265, _1813267, _1813269, _1813271) = hAPP(_1813267, hAPP(c_Set_OCollect(_1813261), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool), tc_HOL_Obool, _1813261), c_HOL_OEx(tc_fun(_1813265, _1813261))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool), tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool), _1813261), hAPP(c_COMBS(tc_fun(_1813265, _1813261), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1813265, _1813261)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1813265, _1813261), tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1813265, _1813261))), _1813269)))), hAPP(hAPP(c_COMBC(_1813261, tc_fun(tc_fun(_1813265, _1813261), _1813261), tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1813261, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1813265, _1813261), _1813261), tc_fun(tc_fun(_1813265, _1813261), tc_HOL_Obool)), _1813261), c_COMBB(_1813261, tc_HOL_Obool, tc_fun(_1813265, _1813261))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1813265, _1813261), _1813265, _1813261), c_COMBI(tc_fun(_1813265, _1813261))), _1813271)))))))], (49448 ^ _782476) ^ [_1779466, _1779468, _1779470, _1779472] : [-(c_New__Random__Sequence_Opos__empty(_1779466, _1779468, _1779470, _1779472) = c_New__DSequence_Opos__empty(_1779466))], (49122 ^ _782476) ^ [_1772575, _1772577] : [c_List_Olist__ex(_1772575, _1772577, c_List_Olist_ONil(_1772575))], (37716 ^ _782476) ^ [_1500321, _1500323, _1500325, _1500327] : [hAPP(c_Product__Type_Ofst(_1500321, _1500323), _1500325) = hAPP(c_Product__Type_Ofst(_1500321, _1500323), _1500327), hAPP(c_Product__Type_Osnd(_1500321, _1500323), _1500325) = hAPP(c_Product__Type_Osnd(_1500321, _1500323), _1500327), -(_1500325 = _1500327)], (9554 ^ _782476) ^ [_953769, _953771] : [class_Orderings_Obot(_953769), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953769), c_Orderings_Obot__class_Obot(_953769)), _953771)))], (44883 ^ _782476) ^ [_1678780, _1678782, _1678784, _1678786] : [-(hAPP(hAPP(c_List_Onth(_1678780), hAPP(hAPP(c_List_Oappend(_1678780), _1678782), _1678784)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678780)), _1678782)), _1678786)) = hAPP(hAPP(c_List_Onth(_1678780), _1678784), _1678786))], (22634 ^ _782476) ^ [_1206996, _1206998] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206996), hAPP(c_Nat_OSuc, _1206998)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1206996, _1206998))], (46282 ^ _782476) ^ [_1710242, _1710244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710242), _1710244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710242)), hAPP(c_Code__Numeral_Oof__nat, _1710244))))], (32179 ^ _782476) ^ [_1392049, _1392051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392049), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32182 ^ _782476 : [(32185 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392049), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392051, _1392049))))], (32183 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392051, _1392049)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5086 ^ _782476) ^ [_860195, _860197] : [_860197 = _860195, -(c_Relation_OId(_860197) = c_Relation_OId(_860195))], (52235 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (16489 ^ _782476) ^ [_1092985, _1092987, _1092989] : [class_Rings_Ocomm__semiring__1(_1092985), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092985), _1092987), _1092989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092985), _1092989), _1092987))], (31852 ^ _782476) ^ [_1385553, _1385555] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385553), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385555)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385553, _1385555)))], (39606 ^ _782476) ^ [_1547328, _1547330] : [-(hAPP(c_Relation_ODomain(_1547328, _1547328), c_Relation_OId__on(_1547328, _1547330)) = _1547330)], (48172 ^ _782476) ^ [_1751367, _1751369, _1751371, _1751373, _1751375] : [-(c_List_Ofoldr(_1751367, _1751369, _1751371, _1751373, _1751375) = hAPP(c_List_Ofoldl(_1751369, _1751367, hAPP(c_COMBC(_1751367, _1751369, _1751369), _1751371), _1751375), hAPP(c_List_Orev(_1751367), _1751373)))], (24322 ^ _782476) ^ [_1237813, _1237815] : [c_Nat__Transfer_Ois__nat(_1237813), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1237813, _1237815)))], (5124 ^ _782476) ^ [_860748, _860750] : [_860750 = _860748, -(c_HOL_OEx(_860750) = c_HOL_OEx(_860748))], (47234 ^ _782476) ^ [_1731919, _1731921, _1731923, _1731925] : [-(c_List_Otranspose(_1731919, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731921), tc_List_Olist(_1731919)), hAPP(c_List_Omap(_1731921, _1731919), _1731923)), _1731925)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731921), tc_List_Olist(_1731919)), hAPP(c_List_Omap(_1731921, _1731919), _1731923)), c_List_Otranspose(_1731921, _1731925)))], (15434 ^ _782476) ^ [_1070776, _1070778, _1070780] : [class_Lattices_Olattice(_1070776), hAPP(_1070778, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070776), 15439 ^ [_1070776, _1070778, _1070780]), 15440 ^ [_1070776, _1070778, _1070780])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070776), hAPP(_1070778, 15439 ^ [_1070776, _1070778, _1070780])), hAPP(_1070778, 15440 ^ [_1070776, _1070778, _1070780])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070776), _1070780)), -(_1070780 = c_Orderings_Obot__class_Obot(tc_fun(_1070776, tc_HOL_Obool))), -(hAPP(_1070778, c_Big__Operators_Olattice__class_OSup__fin(_1070776, _1070780)) = c_Big__Operators_Olattice__class_OSup__fin(_1070776, hAPP(c_Set_Oimage(_1070776, _1070776, _1070778), _1070780)))], (50052 ^ _782476) ^ [_1793100, _1793102, _1793104] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1793100), hAPP(c_COMBK(_1793100, tc_Nat_Onat), _1793102)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1793104)) = c_List_Oreplicate(_1793100, _1793104, _1793102))], (12616 ^ _782476) ^ [_1013519, _1013521, _1013523, _1013525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013519, tc_HOL_Obool)), _1013521), _1013523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013519, tc_HOL_Obool)), _1013523), _1013525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013519, tc_HOL_Obool)), _1013521), _1013525)))], (10841 ^ _782476) ^ [_981873, _981875, _981877, _981879, _981881] : [-(_981873 = c_Orderings_Obot__class_Obot(tc_fun(_981875, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981875, tc_fun(_981877, tc_HOL_Obool)), _981873), hAPP(hAPP(c_COMBC(_981875, tc_fun(_981877, tc_HOL_Obool), tc_fun(_981877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981877, tc_HOL_Obool), tc_fun(tc_fun(_981877, tc_HOL_Obool), tc_fun(_981877, tc_HOL_Obool)), _981875), c_Groups_Ominus__class_Ominus(tc_fun(_981877, tc_HOL_Obool))), _981879)), _981881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981877, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981875, tc_fun(_981877, tc_HOL_Obool)), _981873), _981879)), _981881))], (38397 ^ _782476) ^ [_1516525] : [c_Code__Numeral_OSuc__code__numeral(_1516525) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (16269 ^ _782476) ^ [_1088339, _1088341, _1088343, _1088345, _1088347] : [class_Groups_Ocomm__monoid__add(_1088339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088341), _1088343)), hBOOL(hAPP(hAPP(c_member(_1088341), _1088345), _1088343)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088341, _1088339), _1088347), _1088343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088339), hAPP(_1088347, _1088345)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088341, _1088339), _1088347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088341, tc_HOL_Obool)), _1088343), hAPP(hAPP(c_Set_Oinsert(_1088341), _1088345), c_Orderings_Obot__class_Obot(tc_fun(_1088341, tc_HOL_Obool)))))))], (48419 ^ _782476) ^ [_1756564] : [-(c_List_Oembed__list(_1756564) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1756564))], (38132 ^ _782476) ^ [_1509848, _1509850, _1509852, _1509854, _1509856] : [c_Equiv__Relations_Oequiv(_1509848, _1509850, _1509852), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509848, _1509848)), hAPP(hAPP(c_Product__Type_OPair(_1509848, _1509848), _1509854), _1509856)), _1509852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509848, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1509848, _1509848, _1509852), hAPP(hAPP(c_Set_Oinsert(_1509848), _1509854), c_Orderings_Obot__class_Obot(tc_fun(_1509848, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1509848, _1509848, _1509852), hAPP(hAPP(c_Set_Oinsert(_1509848), _1509856), c_Orderings_Obot__class_Obot(tc_fun(_1509848, tc_HOL_Obool)))))))], (50141 ^ _782476) ^ [_1795043, _1795045, _1795047, _1795049, _1795051, _1795053] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1795043, _1795045, _1795047, _1795049, c_Lazy__Sequence_Olazy__sequence_OInsert(_1795045, _1795051, _1795053)) = hAPP(hAPP(_1795049, _1795051), _1795053))], (25622 ^ _782476) ^ [_1261701, _1261703] : [-(hAPP(c_Set_OCollect(_1261701), hAPP(c_fequal, _1261703)) = hAPP(hAPP(c_Set_Oinsert(_1261701), _1261703), c_Orderings_Obot__class_Obot(tc_fun(_1261701, tc_HOL_Obool))))], (5654 ^ _782476) ^ [_869073, _869075] : [_869075 = _869073, -(c_COMBI(_869075) = c_COMBI(_869073))], (12158 ^ _782476) ^ [_1003627, _1003629, _1003631] : [class_Complete__Lattice_Ocomplete__lattice(_1003627), _1003629 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1003627, _1003631), c_Orderings_Oorder__class_Omono(_1003627, _1003627, _1003631), -(_1003629 = hAPP(_1003631, _1003629))], (52643 ^ _782476) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (16697 ^ _782476) ^ [_1097173, _1097175, _1097177, _1097179, _1097181] : [class_Rings_Osemiring(_1097173), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097173), _1097175), _1097177)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097173), _1097179), _1097177)), _1097181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097173), _1097175), _1097179)), _1097177)), _1097181))], (7065 ^ _782476) ^ [_899212, _899214, _899216, _899218, _899220] : [-(hBOOL(hAPP(hAPP(c_member(_899212), _899214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_899216, tc_fun(_899212, tc_HOL_Obool)), _899218), _899220)))), 7066 ^ _782476 : [(7067 ^ _782476) ^ [_899294] : [hBOOL(hAPP(hAPP(c_member(_899216), _899294), _899218)), hBOOL(hAPP(hAPP(c_member(_899212), _899214), hAPP(_899220, _899294)))]]], (30654 ^ _782476) ^ [_1363426, _1363428, _1363430, _1363432, _1363434] : [class_Fields_Ofield(_1363426), -(_1363428 = c_Groups_Ozero__class_Ozero(_1363426)), -(_1363430 = c_Groups_Ozero__class_Ozero(_1363426)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363426), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363426), _1363432), _1363428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363426), _1363434), _1363430)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363426), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363426), _1363432), _1363430)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363426), _1363434), _1363428))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363426), _1363428), _1363430)))], (4122 ^ _782476) ^ [_844887, _844889] : [_844889 = _844887, -(c_New__Random__Sequence_Oneg__single(_844889) = c_New__Random__Sequence_Oneg__single(_844887))], (6339 ^ _782476) ^ [_883632, _883634] : [class_Enum_Oenum(_883632), 6342 ^ _782476 : [(6350 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883632), _883634)), 6353 ^ _782476 : [(6354 ^ _782476) ^ [_883850] : [-(hBOOL(hAPP(_883634, _883850)))]]], (6343 ^ _782476) ^ [] : [hBOOL(hAPP(_883634, 6344 ^ [_883632, _883634])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883632), _883634)))]]], (22674 ^ _782476) ^ [_1207857, _1207859] : [hAPP(c_Finite__Set_Ocard(_1207857), _1207859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1207859 = c_Orderings_Obot__class_Obot(tc_fun(_1207857, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207857), _1207859))], (13800 ^ _782476) ^ [_1038519, _1038521, _1038523, _1038525, _1038527, _1038529] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038519, tc_fun(_1038521, tc_HOL_Obool)), _1038523), hAPP(c_Fun_Ocomp(_1038525, tc_fun(_1038521, tc_HOL_Obool), _1038519, _1038527), _1038529)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038525, tc_fun(_1038521, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038519, _1038525, _1038529), _1038523)), _1038527))], (17505 ^ _782476) ^ [_1114503, _1114505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114503), _1114505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114503), _1114505))), -(_1114503 = _1114505)], (28077 ^ _782476) ^ [_1313448, _1313450, _1313452] : [class_Orderings_Olinorder(_1313448), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313448), _1313450)), -(_1313450 = c_Orderings_Obot__class_Obot(tc_fun(_1313448, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1313448, c_Orderings_Oord__class_Omin(_1313448), hAPP(hAPP(c_Set_Oinsert(_1313448), _1313452), _1313450)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313448), _1313452), c_Big__Operators_Olattice_OInf__fin(_1313448, c_Orderings_Oord__class_Omin(_1313448), _1313450)))], (41773 ^ _782476) ^ [_1603306, _1603308, _1603310, _1603312] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1603306, _1603308), tc_fun(_1603306, _1603308)), _1603310), c_Fun_Ocomp(_1603308, _1603308, _1603306, _1603312)) = c_Fun_Ocomp(_1603308, _1603308, _1603306, hAPP(hAPP(c_Nat_Ocompow(_1603308, _1603308), _1603310), _1603312)))], (52279 ^ _782476) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (8327 ^ _782476) ^ [_926114, _926116, _926118, _926120, _926122] : [8329 ^ _782476 : [(8332 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_926118, 8328 ^ [_926114, _926116, _926118, _926120, _926122]), _926120))], (8330 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926114), 8328 ^ [_926114, _926116, _926118, _926120, _926122]), _926116)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926114, tc_fun(_926122, tc_HOL_Obool)), _926116), _926118), _926120)))], (13922 ^ _782476) ^ [_1040928, _1040930, _1040932, _1040934, _1040936, _1040938, _1040940] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040928, tc_HOL_Obool)), _1040930), _1040932) = c_Orderings_Obot__class_Obot(tc_fun(_1040928, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040934, tc_HOL_Obool)), _1040936), _1040938) = c_Orderings_Obot__class_Obot(tc_fun(_1040934, tc_HOL_Obool)), c_Fun_Obij__betw(_1040928, _1040934, _1040940, _1040930, _1040936), c_Fun_Obij__betw(_1040928, _1040934, _1040940, _1040932, _1040938), -(c_Fun_Obij__betw(_1040928, _1040934, _1040940, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040928, tc_HOL_Obool)), _1040930), _1040932), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040934, tc_HOL_Obool)), _1040936), _1040938)))], (38879 ^ _782476) ^ [_1528534, _1528536, _1528538, _1528540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528534), _1528540)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528538), _1528536))), -(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), _1528534), _1528536)), 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), _1528538), _1528540)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (52491 ^ _782476) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (50625 ^ _782476) ^ [_1806211, _1806213, _1806215] : [-(c_List_Olist__ex(_1806211, _1806213, _1806215)), 50626 ^ _782476 : [(50627 ^ _782476) ^ [_1806268] : [hBOOL(hAPP(hAPP(c_member(_1806211), _1806268), hAPP(c_List_Oset(_1806211), _1806215))), hBOOL(hAPP(_1806213, _1806268))]]], (17171 ^ _782476) ^ [_1108602] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1108602))))], (17425 ^ _782476) ^ [_1112976, _1112978] : [-(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)), _1112976), _1112978))], (47031 ^ _782476) ^ [_1726548, _1726550] : [c_List_Olist_ONil(_1726548) = c_List_Oconcat(_1726548, _1726550), 47034 ^ _782476 : [(47035 ^ _782476) ^ [_1726639] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726548)), _1726639), hAPP(c_List_Oset(tc_List_Olist(_1726548)), _1726550))), -(_1726639 = c_List_Olist_ONil(_1726548))]]], (43275 ^ _782476) ^ [_1640820, _1640822, _1640824] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640820)), _1640822), c_Wellfounded_Oacc(tc_List_Olist(_1640820), c_List_Olistrel1(_1640820, _1640824)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640820)), _1640822), c_List_Olists(_1640820, c_Wellfounded_Oacc(_1640820, _1640824)))))], (28304 ^ _782476) ^ [_1319194, _1319196, _1319198] : [class_Orderings_Olinorder(_1319194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319194), _1319196)), -(_1319196 = c_Orderings_Obot__class_Obot(tc_fun(_1319194, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319194), _1319198), c_Big__Operators_Olattice_OSup__fin(_1319194, c_Orderings_Oord__class_Omax(_1319194), _1319196)) = c_Big__Operators_Olattice_OSup__fin(_1319194, c_Orderings_Oord__class_Omax(_1319194), hAPP(c_Set_OCollect(_1319194), hAPP(hAPP(c_COMBB(tc_fun(_1319194, tc_HOL_Obool), tc_HOL_Obool, _1319194), c_HOL_OEx(_1319194)), hAPP(hAPP(c_COMBC(_1319194, tc_fun(_1319194, tc_HOL_Obool), tc_fun(_1319194, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319194, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1319194, tc_HOL_Obool), tc_fun(_1319194, tc_HOL_Obool)), _1319194), c_COMBS(_1319194, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319194, tc_HOL_Obool), tc_fun(_1319194, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1319194), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1319194), c_fconj)), hAPP(hAPP(c_COMBC(_1319194, tc_fun(_1319194, _1319194), tc_fun(_1319194, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319194, tc_HOL_Obool), tc_fun(tc_fun(_1319194, _1319194), tc_fun(_1319194, tc_HOL_Obool)), _1319194), c_COMBB(_1319194, tc_HOL_Obool, _1319194)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1319194), _1319198))))), hAPP(hAPP(c_COMBC(_1319194, tc_fun(_1319194, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319194)), _1319196))))))], (23737 ^ _782476) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6959 ^ _782476) ^ [_896578, _896580, _896582] : [-(hBOOL(hAPP(hAPP(c_member(_896578), _896580), _896582))), -(hBOOL(hAPP(hAPP(c_member(_896578), _896580), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896578, tc_HOL_Obool)), _896582))))], (388 ^ _782476) ^ [_788362, _788364, _788366, _788368, _788370, _788372] : [-(c_Relation_Ototal__on(_788370, _788366, _788362)), c_Relation_Ototal__on(_788372, _788368, _788364), _788372 = _788370, _788368 = _788366, _788364 = _788362], (22052 ^ _782476) ^ [_1197130, _1197132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197132), hAPP(c_Nat_OSuc, _1197130))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197130), _1197132))], (41374 ^ _782476) ^ [_1593647, _1593649] : [-(c_Relation_Oirrefl(_1593647, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1593647, _1593647), tc_HOL_Obool)), _1593649), c_Relation_OId(_1593647))))], (46270 ^ _782476) ^ [] : [-(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))], (34972 ^ _782476) ^ [_1443909, _1443911] : [class_Int_Onumber__ring(_1443909), 34975 ^ _782476 : [(34982 ^ _782476) ^ [] : [c_Int_Oiszero(_1443909, hAPP(c_Int_Onumber__class_Onumber__of(_1443909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443911), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1443909), _1443911) = c_Groups_Oone__class_Oone(_1443909))], (34976 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1443909), _1443911) = c_Groups_Oone__class_Oone(_1443909), -(c_Int_Oiszero(_1443909, hAPP(c_Int_Onumber__class_Onumber__of(_1443909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443911), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (42327 ^ _782476) ^ [_1616227, _1616229, _1616231] : [class_Lattices_Olattice(_1616227), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616227), _1616229)), -(hBOOL(hAPP(hAPP(c_member(_1616227), _1616231), _1616229))), -(c_Big__Operators_Olattice__class_OSup__fin(_1616227, hAPP(hAPP(c_Set_Oinsert(_1616227), _1616231), _1616229)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616227, _1616227, c_Lattices_Osemilattice__sup__class_Osup(_1616227)), _1616231), _1616229))], (9241 ^ _782476) ^ [_947430, _947432, _947434, _947436] : [-(hAPP(c_Set_Oimage(_947430, _947432, _947434), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947430, tc_HOL_Obool), _947436)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947430, tc_HOL_Obool), tc_fun(_947432, tc_HOL_Obool)), _947436), c_Set_Oimage(_947430, _947432, _947434)))], (2928 ^ _782476) ^ [_825902, _825904] : [_825904 = _825902, -(c_Rings_Oinverse__class_Odivide(_825904) = c_Rings_Oinverse__class_Odivide(_825902))], (48839 ^ _782476) ^ [_1766223, _1766225, _1766227, _1766229] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1766223, _1766225, _1766227, _1766229) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1766223, _1766225), _1766227), _1766229)))], (27224 ^ _782476) ^ [_1296943, _1296945] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1296943), _1296945)), _1296945) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1296943), _1296945))], (32716 ^ _782476) ^ [_1402305, _1402307, _1402309] : [-(hBOOL(hAPP(_1402305, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402307, _1402309)))), 32719 ^ _782476 : [(32722 ^ _782476) ^ [] : [hBOOL(hAPP(_1402305, _1402307))], (32720 ^ _782476) ^ [] : [-(_1402309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 32723 ^ _782476 : [(32728 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32726 ^ [_1402305, _1402307, _1402309]), _1402309)))], (32730 ^ _782476) ^ [] : [-(_1402307 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402309), 32725 ^ [_1402305, _1402307, _1402309])), 32726 ^ [_1402305, _1402307, _1402309]))], (32732 ^ _782476) ^ [] : [hBOOL(hAPP(_1402305, 32726 ^ [_1402305, _1402307, _1402309]))], (32724 ^ _782476) ^ [] : [_1402309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (37940 ^ _782476) ^ [_1505637, _1505639, _1505641, _1505643, _1505645, _1505647] : [c_Equiv__Relations_Oequiv(_1505637, _1505639, _1505641), hBOOL(hAPP(hAPP(c_member(_1505637), _1505643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505637, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505637, _1505637, _1505641), hAPP(hAPP(c_Set_Oinsert(_1505637), _1505645), c_Orderings_Obot__class_Obot(tc_fun(_1505637, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505637, _1505637, _1505641), hAPP(hAPP(c_Set_Oinsert(_1505637), _1505647), c_Orderings_Obot__class_Obot(tc_fun(_1505637, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505637, _1505637)), hAPP(hAPP(c_Product__Type_OPair(_1505637, _1505637), _1505645), _1505647)), _1505641)))], (24064 ^ _782476) ^ [_1233667] : [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, _1233667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233667)))], (28748 ^ _782476) ^ [_1328492, _1328494] : [class_Rings_Odivision__ring(_1328492), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328492), c_Groups_Ozero__class_Ozero(_1328492)), _1328494) = c_Groups_Ozero__class_Ozero(_1328492))], (37643 ^ _782476) ^ [_1498795, _1498797, _1498799, _1498801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498795, _1498795)), hAPP(hAPP(c_Product__Type_OPair(_1498795, _1498795), _1498797), _1498799)), hAPP(c_Wellfounded_Omeasure(_1498795), _1498801))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498801, _1498797)), hAPP(_1498801, _1498799))))], (10787 ^ _782476) ^ [_980384, _980386, _980388, _980390, _980392, _980394] : [hBOOL(hAPP(hAPP(c_member(_980384), _980386), _980388)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980384, tc_fun(_980390, tc_HOL_Obool)), _980388), hAPP(hAPP(c_COMBB(tc_fun(_980390, tc_HOL_Obool), tc_fun(_980390, tc_HOL_Obool), _980384), hAPP(c_Set_Oinsert(_980390), _980392)), _980394)) = hAPP(hAPP(c_Set_Oinsert(_980390), _980392), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980384, tc_fun(_980390, tc_HOL_Obool)), _980388), _980394)))], (20839 ^ _782476) ^ [_1174252, _1174254, _1174256] : [-(hBOOL(hAPP(_1174252, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174254), _1174256))))), 20842 ^ _782476 : [(20845 ^ _782476) ^ [] : [hBOOL(hAPP(_1174252, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174254)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174256))))], (20843 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174256), _1174254)))]], 20846 ^ _782476 : [(20849 ^ _782476) ^ [] : [hBOOL(hAPP(_1174252, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20847 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174254), _1174256)))]]], (20495 ^ _782476) ^ [_1168031, _1168033, _1168035] : [class_Rings_Olinordered__ring__strict(_1168031), 20498 ^ _782476 : [(20507 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168031), _1168033), _1168033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168031), _1168035), _1168035))), c_Groups_Ozero__class_Ozero(_1168031)))), _1168033 = c_Groups_Ozero__class_Ozero(_1168031), _1168035 = c_Groups_Ozero__class_Ozero(_1168031)], (20499 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168031), _1168033), _1168033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168031), _1168035), _1168035))), c_Groups_Ozero__class_Ozero(_1168031))), 20502 ^ _782476 : [(20505 ^ _782476) ^ [] : [-(_1168035 = c_Groups_Ozero__class_Ozero(_1168031))], (20503 ^ _782476) ^ [] : [-(_1168033 = c_Groups_Ozero__class_Ozero(_1168031))]]]]], (49772 ^ _782476) ^ [_1787423, _1787425, _1787427] : [-(c_Predicate_Oconversep(_1787423, _1787425, c_Predicate_Oconversep(_1787425, _1787423, _1787427)) = _1787427)], (25624 ^ _782476) ^ [_1261747, _1261749] : [-(hAPP(c_Set_OCollect(_1261747), hAPP(hAPP(c_COMBC(_1261747, _1261747, tc_HOL_Obool), c_fequal), _1261749)) = hAPP(hAPP(c_Set_Oinsert(_1261747), _1261749), c_Orderings_Obot__class_Obot(tc_fun(_1261747, tc_HOL_Obool))))], (51528 ^ _782476) ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808)), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), _1825810), _1825812)), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), _1825814), _1825816))), c_Transitive__Closure_Ortrancl(tc_prod(_1825806, _1825808), _1825818))), hBOOL(hAPP(hAPP(_1825820, _1825810), _1825812)), 51539 ^ _782476 : [(51544 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808)), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), 51537 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]), 51538 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820])), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), 51541 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]), 51542 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]))), _1825818)))], (51546 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1825820, 51537 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]), 51538 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820])))], (51548 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1825820, 51541 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]), 51542 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]))], (51540 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825806, _1825808), tc_prod(_1825806, _1825808)), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), _1825810), _1825812)), hAPP(hAPP(c_Product__Type_OPair(_1825806, _1825808), 51537 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]), 51538 ^ [_1825806, _1825808, _1825810, _1825812, _1825814, _1825816, _1825818, _1825820]))), c_Transitive__Closure_Ortrancl(tc_prod(_1825806, _1825808), _1825818))))]], -(hBOOL(hAPP(hAPP(_1825820, _1825814), _1825816)))], (19903 ^ _782476) ^ [_1156069, _1156071, _1156073, _1156075, _1156077] : [class_Rings_Olinordered__semiring__strict(_1156069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156069), _1156071), _1156073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156069), _1156075), _1156077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156069), c_Groups_Ozero__class_Ozero(_1156069)), _1156073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156069), c_Groups_Ozero__class_Ozero(_1156069)), _1156075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156069), _1156071), _1156075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156069), _1156073), _1156077))))], (32678 ^ _782476) ^ [_1401293, _1401295] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401293), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401295), _1401293)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401295), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401295, _1401293)))], (48292 ^ _782476) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (37938 ^ _782476) ^ [_1505124, _1505126] : [-(c_FunDef_Orp__inv__image(_1505124, _1505126) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))))), tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))), tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)), tc_fun(tc_fun(_1505126, _1505124), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool)), c_COMBS(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)), tc_fun(tc_fun(_1505126, _1505124), tc_fun(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), tc_fun(tc_prod(_1505124, _1505124), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool))), tc_fun(_1505126, _1505124)), c_Product__Type_OPair(tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool), tc_fun(tc_prod(_1505126, _1505126), tc_HOL_Obool)))), c_Relation_Oinv__image(_1505124, _1505126))))), c_Relation_Oinv__image(_1505124, _1505126))))], (22700 ^ _782476) ^ [_1208291, _1208293, _1208295] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208291), _1208293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208291), _1208293)), hAPP(c_Finite__Set_Ocard(_1208291), hAPP(hAPP(c_Set_Oinsert(_1208291), _1208295), _1208293)))))], (18148 ^ _782476) ^ [_1125885, _1125887] : [class_Groups_Ogroup__add(_1125885), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125885), _1125887), _1125887) = c_Groups_Ozero__class_Ozero(_1125885))], (9378 ^ _782476) ^ [_950488] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_950488, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_950488, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_950488, tc_HOL_Obool)))], (3406 ^ _782476) ^ [_833303, _833305, _833307, _833309] : [-(c_List_Olists(_833309, _833305) = c_List_Olists(_833307, _833303)), _833309 = _833307, _833305 = _833303], (13988 ^ _782476) ^ [_1042325, _1042327, _1042329, _1042331, _1042333] : [class_Groups_Oab__semigroup__mult(_1042325), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042325, _1042325, c_Groups_Otimes__class_Otimes(_1042325), _1042327, _1042329), _1042331)), -(hBOOL(hAPP(hAPP(c_member(_1042325), _1042327), _1042329))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042325, _1042325, c_Groups_Otimes__class_Otimes(_1042325), _1042333, hAPP(hAPP(c_Set_Oinsert(_1042325), _1042327), _1042329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042325), _1042333), _1042331))))], (21983 ^ _782476) ^ [_1196026, _1196028] : [-(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, _1196026)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1196028))))], (28474 ^ _782476) ^ [_1322556, _1322558, _1322560] : [class_Orderings_Olinorder(_1322556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322556), _1322558)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322556), _1322560)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322556, tc_HOL_Obool)), _1322558), _1322560) = c_Orderings_Obot__class_Obot(tc_fun(_1322556, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322556), c_Big__Operators_Olattice_OSup__fin(_1322556, c_Orderings_Oord__class_Omax(_1322556), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322556, tc_HOL_Obool)), _1322558), _1322560))), c_Big__Operators_Olattice_OSup__fin(_1322556, c_Orderings_Oord__class_Omax(_1322556), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322556, tc_HOL_Obool)), _1322558), _1322560))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322556), c_Big__Operators_Olattice_OSup__fin(_1322556, c_Orderings_Oord__class_Omax(_1322556), _1322558)), c_Big__Operators_Olattice_OSup__fin(_1322556, c_Orderings_Oord__class_Omax(_1322556), _1322560)))], (41535 ^ _782476) ^ [_1597637, _1597639, _1597641, _1597643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597637, _1597637)), hAPP(hAPP(c_Product__Type_OPair(_1597637, _1597637), _1597639), _1597641)), c_Transitive__Closure_Otrancl(_1597637, hAPP(c_Relation_Oconverse(_1597637, _1597637), _1597643)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597637, _1597637)), hAPP(hAPP(c_Product__Type_OPair(_1597637, _1597637), _1597639), _1597641)), hAPP(c_Relation_Oconverse(_1597637, _1597637), c_Transitive__Closure_Otrancl(_1597637, _1597643)))))], (35692 ^ _782476) ^ [_1456599, _1456601] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1456599), hAPP(c_Int_Onumber__class_Onumber__of(_1456599), _1456601)), 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(_1456599), hAPP(c_Int_Onumber__class_Onumber__of(_1456599), _1456601)), hAPP(c_Int_Onumber__class_Onumber__of(_1456599), _1456601))), class_Groups_Omonoid__mult(_1456599), class_Int_Onumber(_1456599)], (35422 ^ _782476) ^ [_1451767, _1451769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451767), _1451769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451767)), c_Int_OBit0(_1451769))))], (36440 ^ _782476) ^ [_1474311, _1474313, _1474315] : [class_Enum_Oenum(_1474311), class_Enum_Oenum(_1474313), 36447 ^ _782476 : [(36454 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474313), hAPP(hAPP(c_COMBB(tc_fun(_1474311, tc_HOL_Obool), tc_HOL_Obool, _1474313), c_Enum_Oenum__class_Oenum__ex(_1474311)), hAPP(hAPP(c_COMBB(tc_fun(_1474311, tc_prod(_1474313, _1474311)), tc_fun(_1474311, tc_HOL_Obool), _1474313), hAPP(c_COMBB(tc_prod(_1474313, _1474311), tc_HOL_Obool, _1474311), _1474315)), c_Product__Type_OPair(_1474313, _1474311))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474313, _1474311)), _1474315)))], (36448 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474313, _1474311)), _1474315)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474313), hAPP(hAPP(c_COMBB(tc_fun(_1474311, tc_HOL_Obool), tc_HOL_Obool, _1474313), c_Enum_Oenum__class_Oenum__ex(_1474311)), hAPP(hAPP(c_COMBB(tc_fun(_1474311, tc_prod(_1474313, _1474311)), tc_fun(_1474311, tc_HOL_Obool), _1474313), hAPP(c_COMBB(tc_prod(_1474313, _1474311), tc_HOL_Obool, _1474311), _1474315)), c_Product__Type_OPair(_1474313, _1474311))))))]]], (34950 ^ _782476) ^ [_1443308, _1443310] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1443308)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443310)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443310))), 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, _1443308))), 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), _1443308)), c_Int_Onat)))))], (6690 ^ _782476) ^ [_890588, _890590, _890592] : [-(hBOOL(hAPP(hAPP(c_member(_890588), _890590), _890592))), -(hBOOL(hAPP(hAPP(c_member(_890588), _890590), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_890588, tc_HOL_Obool)), _890592))))], (28596 ^ _782476) ^ [_1325039, _1325041] : [class_Orderings_Olinorder(_1325039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325039), _1325041)), -(_1325041 = c_Orderings_Obot__class_Obot(tc_fun(_1325039, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1325039), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325039), 28609 ^ [_1325039, _1325041]), 28610 ^ [_1325039, _1325041])), hAPP(hAPP(c_Set_Oinsert(_1325039), 28609 ^ [_1325039, _1325041]), hAPP(hAPP(c_Set_Oinsert(_1325039), 28610 ^ [_1325039, _1325041]), c_Orderings_Obot__class_Obot(tc_fun(_1325039, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1325039), c_Big__Operators_Olinorder__class_OMin(_1325039, _1325041)), _1325041)))], (20949 ^ _782476) ^ [_1176316] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176316)), _1176316) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13218 ^ _782476) ^ [_1025984, _1025986, _1025988] : [-(hAPP(c_Set_Ovimage(_1025984, _1025986, _1025988), c_Orderings_Otop__class_Otop(tc_fun(_1025986, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1025984, tc_HOL_Obool)))], (40021 ^ _782476) ^ [_1560484, _1560486, _1560488] : [-(hAPP(c_Fun_Ocomp(_1560484, _1560486, _1560484, _1560488), c_Fun_Oid(_1560484)) = _1560488)], (45332 ^ _782476) ^ [_1689757, _1689759, _1689761] : [-(hAPP(c_List_Otl(_1689757), hAPP(hAPP(c_List_Odrop(_1689757), _1689759), _1689761)) = hAPP(hAPP(c_List_Odrop(_1689757), _1689759), hAPP(c_List_Otl(_1689757), _1689761)))], (5532 ^ _782476) ^ [_867122, _867124, _867126, _867128, _867130, _867132, _867134, _867136] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_867136, _867132, _867128, _867124) = c_SetInterval_Oord_OgreaterThanLessThan(_867134, _867130, _867126, _867122)), _867136 = _867134, _867132 = _867130, _867128 = _867126, _867124 = _867122], (46602 ^ _782476) ^ [_1716872, _1716874, _1716876] : [hBOOL(hAPP(c_List_Olistsp(_1716872, hAPP(hAPP(c_COMBC(_1716872, tc_fun(_1716872, tc_HOL_Obool), tc_HOL_Obool), c_member(_1716872)), _1716874)), _1716876)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1716872)), _1716876), c_List_Olists(_1716872, _1716874))))], (31956 ^ _782476) ^ [_1387803, _1387805, _1387807, _1387809] : [class_Divides_Osemiring__div(_1387803), -(c_Divides_Odiv__class_Omod(_1387803, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387803), _1387805), _1387807), _1387809) = c_Divides_Odiv__class_Omod(_1387803, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387803), _1387805), c_Divides_Odiv__class_Omod(_1387803, _1387807, _1387809)), _1387809))], (34236 ^ _782476) ^ [_1431227, _1431229] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431227))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431227)), _1431229)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1431229))], (14931 ^ _782476) ^ [_1061174, _1061176, _1061178, _1061180, _1061182, _1061184, _1061186, _1061188] : [c_Finite__Set_Ofolding__image__simple(_1061174, _1061176, _1061178, _1061180, _1061182, _1061184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061176), _1061186)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061176), _1061188)), -(hAPP(hAPP(_1061178, hAPP(_1061184, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061176, tc_HOL_Obool)), _1061186), _1061188))), hAPP(_1061184, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061176, tc_HOL_Obool)), _1061186), _1061188))) = hAPP(hAPP(_1061178, hAPP(_1061184, _1061186)), hAPP(_1061184, _1061188)))], (8888 ^ _782476) ^ [_937473, _937475, _937477] : [class_Lattices_Olattice(_937473), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937473), _937475), _937477)), _937477)))], (52437 ^ _782476) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (22906 ^ _782476) ^ [_1211986, _1211988] : [-(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), _1211986), _1211988)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211988))], (8110 ^ _782476) ^ [_920712, _920714, _920716, _920718] : [hBOOL(hAPP(hAPP(c_member(_920712), _920714), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920712, tc_HOL_Obool)), _920716), _920718))), -(hBOOL(hAPP(hAPP(c_member(_920712), _920714), _920716))), -(hBOOL(hAPP(hAPP(c_member(_920712), _920714), _920718)))], (43516 ^ _782476) ^ [_1647321, _1647323, _1647325] : [43518 ^ _782476 : [(43521 ^ _782476) ^ [] : [hBOOL(hAPP(_1647325, hAPP(hAPP(c_List_Onth(_1647321), _1647323), 43517 ^ [_1647321, _1647323, _1647325])))], (43519 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43517 ^ [_1647321, _1647323, _1647325]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647321)), _1647323))))]], 43522 ^ _782476 : [(43523 ^ _782476) ^ [_1647523] : [hBOOL(hAPP(hAPP(c_member(_1647321), _1647523), hAPP(c_List_Oset(_1647321), _1647323))), -(hBOOL(hAPP(_1647325, _1647523)))]]], (46206 ^ _782476) ^ [_1708874, _1708876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708874)), hAPP(c_Code__Numeral_Oof__nat, _1708876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708874), _1708876)))], (45390 ^ _782476) ^ [_1690868, _1690870, _1690872] : [-(hAPP(c_List_Orotate(_1690868, _1690870), _1690872) = hAPP(c_List_Orotate(_1690868, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1690870, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690868)), _1690872))), _1690872))], (32620 ^ _782476) ^ [_1400298, _1400300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400298), _1400300)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400298, _1400300) = _1400298)], (17145 ^ _782476) ^ [_1107951, _1107953, _1107955, _1107957, _1107959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107951), _1107953)), 17148 ^ _782476 : [(17155 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107957), 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), _1107953), _1107951)), _1107955)), _1107959))), -(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), _1107951), _1107955)), _1107957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107953), _1107955)), _1107959))))], (17149 ^ _782476) ^ [] : [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), _1107951), _1107955)), _1107957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107953), _1107955)), _1107959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107957), 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), _1107953), _1107951)), _1107955)), _1107959))))]]], (26418 ^ _782476) ^ [_1281737, _1281739, _1281741] : [class_Orderings_Olinorder(_1281737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281737), _1281739), _1281741)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281737), _1281739), _1281741) = _1281741)], (21349 ^ _782476) ^ [_1183325, _1183327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183325)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183325), _1183327)))], (52443 ^ _782476) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (35910 ^ _782476) ^ [_1460831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1460831)), -(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), _1460831), 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)))))))], (49055 ^ _782476) ^ [_1771458, _1771460, _1771462, _1771464] : [c_List_Olist__ex(_1771458, _1771460, hAPP(hAPP(c_List_Olist_OCons(_1771458), _1771462), _1771464)), -(hBOOL(hAPP(_1771460, _1771462))), -(c_List_Olist__ex(_1771458, _1771460, _1771464))], (47293 ^ _782476) ^ [_1733978, _1733980] : [-(c_Random_Oselect__weight(_1733978, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1733978), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1733978, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1733978, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1733978)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1733980)) = c_Random_Oselect__weight(_1733978, _1733980))], (10137 ^ _782476) ^ [_965967, _965969, _965971, _965973] : [-(hBOOL(hAPP(hAPP(c_member(_965967), _965969), _965971))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965967, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965967), _965969), _965973)), _965971) = hAPP(hAPP(c_Set_Oinsert(_965967), _965969), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965967, tc_HOL_Obool)), _965973), _965971)))], (46368 ^ _782476) ^ [_1712154, _1712156] : [hAPP(c_Code__Numeral_Onat__of, _1712154) = hAPP(c_Code__Numeral_Onat__of, _1712156), -(_1712154 = _1712156)], (13638 ^ _782476) ^ [_1035212, _1035214, _1035216, _1035218, _1035220, _1035222, _1035224] : [hAPP(c_Fun_Ocomp(_1035212, _1035214, _1035216, _1035218), _1035220) = _1035222, -(hAPP(_1035218, hAPP(_1035220, _1035224)) = hAPP(_1035222, _1035224))], (46054 ^ _782476) ^ [_1704673, _1704675, _1704677, _1704679, _1704681, _1704683, _1704685, _1704687] : [-(hAPP(hAPP(c_List_Ozip(_1704673, _1704675), hAPP(hAPP(c_List_Omap(_1704677, _1704673), _1704679), _1704681)), hAPP(hAPP(c_List_Omap(_1704683, _1704675), _1704685), _1704687)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704677, _1704683), tc_prod(_1704673, _1704675)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704677, _1704683, tc_prod(_1704673, _1704675)), hAPP(hAPP(c_COMBC(_1704677, tc_fun(_1704683, _1704675), tc_fun(_1704683, tc_prod(_1704673, _1704675))), hAPP(hAPP(c_COMBB(tc_fun(_1704675, tc_prod(_1704673, _1704675)), tc_fun(tc_fun(_1704683, _1704675), tc_fun(_1704683, tc_prod(_1704673, _1704675))), _1704677), c_COMBB(_1704675, tc_prod(_1704673, _1704675), _1704683)), hAPP(hAPP(c_COMBB(_1704673, tc_fun(_1704675, tc_prod(_1704673, _1704675)), _1704677), c_Product__Type_OPair(_1704673, _1704675)), _1704679))), _1704685))), hAPP(hAPP(c_List_Ozip(_1704677, _1704683), _1704681), _1704687)))], (6120 ^ _782476) ^ [_879469, _879471, _879473, _879475] : [class_Orderings_Oord(_879469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879469), hAPP(_879471, 6125 ^ [_879469, _879471, _879473, _879475])), hAPP(_879473, 6125 ^ [_879469, _879471, _879473, _879475]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879475, _879469)), _879471), _879473)))], (36689 ^ _782476) ^ [_1480534, _1480536, _1480538, _1480540] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480534, _1480536), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480538), _1480540))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480534), _1480536), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480540), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480538)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480538)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480540), 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), _1480536), _1480540))))))], (43473 ^ _782476) ^ [_1646362, _1646364, _1646366, _1646368] : [hBOOL(hAPP(hAPP(c_member(_1646362), _1646364), hAPP(c_List_Oset(_1646362), hAPP(hAPP(c_List_Olist_OCons(_1646362), _1646366), _1646368)))), -(_1646364 = _1646366), -(hBOOL(hAPP(hAPP(c_member(_1646362), _1646364), hAPP(c_List_Oset(_1646362), _1646368))))], (39499 ^ _782476) ^ [_1544472, _1544474, _1544476] : [-(hAPP(c_Relation_ORange(_1544472, _1544474), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1544472, _1544474), tc_HOL_Obool), _1544476)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1544472, _1544474), tc_HOL_Obool), tc_fun(_1544474, tc_HOL_Obool)), _1544476), c_Relation_ORange(_1544472, _1544474)))], (39532 ^ _782476) ^ [_1545238, _1545240, _1545242, _1545244] : [39533 ^ _782476 : [(39534 ^ _782476) ^ [_1545313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545242, _1545238)), hAPP(hAPP(c_Product__Type_OPair(_1545242, _1545238), _1545313), _1545240)), _1545244))]], -(hBOOL(hAPP(hAPP(c_member(_1545238), _1545240), hAPP(c_Relation_ORange(_1545242, _1545238), _1545244))))], (43483 ^ _782476) ^ [_1646519, _1646521, _1646523, _1646525] : [-(hBOOL(hAPP(hAPP(c_member(_1646519), _1646521), hAPP(c_List_Oset(_1646519), _1646523)))), hBOOL(hAPP(hAPP(c_member(_1646519), _1646521), hAPP(c_List_Oset(_1646519), c_List_Osublist(_1646519, _1646523, _1646525))))], (10053 ^ _782476) ^ [_964091, _964093, _964095] : [class_Orderings_Oorder(_964091), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964091, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964091), _964093)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964091, _964093, _964095)) = c_Orderings_Obot__class_Obot(tc_fun(_964091, tc_HOL_Obool)))], (36916 ^ _782476) ^ [_1485299, _1485301, _1485303, _1485305, _1485307, _1485309] : [_1485299 = _1485301, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485303, _1485305, _1485307), _1485309), _1485299) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485303, _1485305, _1485307), _1485309), _1485301))], (4364 ^ _782476) ^ [_848766, _848768] : [_848768 = _848766, -(c_Groups_Ouminus__class_Ouminus(_848768) = c_Groups_Ouminus__class_Ouminus(_848766))], (18282 ^ _782476) ^ [_1127799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127799), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47345 ^ _782476) ^ [_1735557, _1735559, _1735561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735557), _1735559)), -(c_List_Oupt(_1735557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735559), _1735561)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735557, _1735559)), c_List_Oupt(_1735559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735559), _1735561))))], (28678 ^ _782476) ^ [_1327085, _1327087, _1327089, _1327091, _1327093] : [class_Fields_Ofield(_1327085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327087), _1327089)), -(hAPP(_1327091, _1327093) = c_Groups_Ozero__class_Ozero(_1327085)), 28689 ^ _782476 : [(28696 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327087), _1327093), _1327089))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327087, _1327085), _1327091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327087, tc_HOL_Obool)), _1327089), hAPP(hAPP(c_Set_Oinsert(_1327087), _1327093), c_Orderings_Obot__class_Obot(tc_fun(_1327087, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327087, _1327085), _1327091), _1327089))], (28690 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327087), _1327093), _1327089)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327087, _1327085), _1327091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327087, tc_HOL_Obool)), _1327089), hAPP(hAPP(c_Set_Oinsert(_1327087), _1327093), c_Orderings_Obot__class_Obot(tc_fun(_1327087, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327085), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327087, _1327085), _1327091), _1327089)), hAPP(_1327091, _1327093)))]]], (18508 ^ _782476) ^ [_1131236, _1131238] : [class_Groups_Olinordered__ab__group__add(_1131236), 18511 ^ _782476 : [(18518 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131236), c_Groups_Ozero__class_Ozero(_1131236)), _1131238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131236), c_Groups_Ozero__class_Ozero(_1131236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131236), _1131238), _1131238))))], (18512 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131236), c_Groups_Ozero__class_Ozero(_1131236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131236), _1131238), _1131238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131236), c_Groups_Ozero__class_Ozero(_1131236)), _1131238)))]]], (2072 ^ _782476) ^ [_812568, _812570, _812572, _812574, _812576, _812578] : [-(c_SetInterval_Oord_OatMost(_812578, _812574, _812570) = c_SetInterval_Oord_OatMost(_812576, _812572, _812568)), _812578 = _812576, _812574 = _812572, _812570 = _812568], (43878 ^ _782476) ^ [_1657364, _1657366, _1657368, _1657370, _1657372, _1657374, _1657376] : [-(hAPP(hAPP(c_List_Ozip(_1657364, _1657366), hAPP(hAPP(c_List_Olist__update(_1657364, _1657368), _1657370), _1657372)), hAPP(hAPP(c_List_Olist__update(_1657366, _1657374), _1657370), _1657376)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1657364, _1657366), hAPP(hAPP(c_List_Ozip(_1657364, _1657366), _1657368), _1657374)), _1657370), hAPP(hAPP(c_Product__Type_OPair(_1657364, _1657366), _1657372), _1657376)))], (31229 ^ _782476) ^ [_1373363, _1373365, _1373367, _1373369, _1373371] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373363, _1373365, _1373367), _1373369), hAPP(c_Nat_OSuc, _1373371)) = hAPP(hAPP(_1373367, _1373369), hAPP(hAPP(c_Power_Opower_Opower(_1373363, _1373365, _1373367), _1373369), _1373371)))], (51783 ^ _782476) ^ [_1831578, _1831580, _1831582, _1831584] : [class_Rings_Oidom(_1831578), 51786 ^ _782476 : [(51787 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831578), _1831580), _1831582)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831578), _1831584), _1831582))), -(_1831582 = c_Groups_Ozero__class_Ozero(_1831578)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831578), _1831580), _1831584)))], (51797 ^ _782476) ^ [] : [51798 ^ _782476 : [(51801 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831578), _1831580), _1831584))], (51799 ^ _782476) ^ [] : [_1831582 = c_Groups_Ozero__class_Ozero(_1831578)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831578), _1831580), _1831582)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831578), _1831584), _1831582))))]]], (2966 ^ _782476) ^ [_826455, _826457, _826459, _826461, _826463, _826465] : [-(c_Nitpick_Oplus__frac(_826465, _826461, _826457) = c_Nitpick_Oplus__frac(_826463, _826459, _826455)), _826465 = _826463, _826461 = _826459, _826457 = _826455], (12432 ^ _782476) ^ [_1008353, _1008355, _1008357, _1008359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008353, tc_HOL_Obool)), _1008355), hAPP(hAPP(c_Set_Oinsert(_1008353), _1008357), _1008359))), 12435 ^ _782476 : [(12442 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008353), _1008357), _1008359))), 12445 ^ _782476 : [(12452 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008353), _1008357), _1008355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008353, tc_HOL_Obool)), _1008355), _1008359)))], (12446 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008353), _1008357), _1008355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008353, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008353, tc_HOL_Obool)), _1008355), hAPP(hAPP(c_Set_Oinsert(_1008353), _1008357), c_Orderings_Obot__class_Obot(tc_fun(_1008353, tc_HOL_Obool))))), _1008359)))]]], (12436 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008353), _1008357), _1008359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008353, tc_HOL_Obool)), _1008355), _1008359)))]]], (34416 ^ _782476) ^ [_1433963, _1433965] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433963), _1433965), hAPP(c_Int_Onumber__class_Onumber__of(_1433963), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1433963)), class_Fields_Ofield__inverse__zero(_1433963), class_Int_Onumber__ring(_1433963)], (48345 ^ _782476) ^ [_1755139, _1755141, _1755143, _1755145, _1755147] : [-(hBOOL(hAPP(_1755139, _1755141))), -(c_List_OtakeWhile(_1755143, _1755139, hAPP(hAPP(c_List_Oappend(_1755143), _1755145), hAPP(hAPP(c_List_Olist_OCons(_1755143), _1755141), _1755147))) = c_List_OtakeWhile(_1755143, _1755139, _1755145))], (25692 ^ _782476) ^ [_1263737, _1263739, _1263741, _1263743, _1263745, _1263747] : [-(hAPP(c_Set_Oimage(_1263737, _1263739, hAPP(hAPP(c_COMBS(_1263737, _1263739, _1263739), hAPP(hAPP(c_COMBS(_1263737, _1263739, tc_fun(_1263739, _1263739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1263739, tc_fun(_1263739, _1263739)), _1263737), c_If(_1263739)), _1263741)), _1263743)), _1263745)), _1263747) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263739, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1263737, _1263739, _1263743), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263737, tc_HOL_Obool)), _1263747), hAPP(c_Set_OCollect(_1263737), _1263741)))), hAPP(c_Set_Oimage(_1263737, _1263739, _1263745), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263737, tc_HOL_Obool)), _1263747), hAPP(c_Set_OCollect(_1263737), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1263737), c_fNot), _1263741))))))], (32823 ^ _782476) ^ [_1404910, _1404912, _1404914, _1404916] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1404910, tc_HOL_Obool)), _1404912), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1404910), _1404914), _1404916))), 32827 ^ _782476 : [(32830 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404910), 32826 ^ [_1404910, _1404912, _1404914, _1404916]), _1404914)))], (32828 ^ _782476) ^ [] : [-(_1404912 = hAPP(c_Relation_OImage(_1404910, _1404910, _1404916), hAPP(hAPP(c_Set_Oinsert(_1404910), 32826 ^ [_1404910, _1404912, _1404914, _1404916]), c_Orderings_Obot__class_Obot(tc_fun(_1404910, tc_HOL_Obool)))))]]], (52281 ^ _782476) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (41463 ^ _782476) ^ [_1595918, _1595920, _1595922, _1595924] : [-(hAPP(c_Relation_Oconverse(_1595918, _1595918), hAPP(hAPP(c_Relation_Oinv__image(_1595920, _1595918), _1595922), _1595924)) = hAPP(hAPP(c_Relation_Oinv__image(_1595920, _1595918), hAPP(c_Relation_Oconverse(_1595920, _1595920), _1595922)), _1595924))], (12584 ^ _782476) ^ [_1012796, _1012798, _1012800, _1012802, _1012804] : [c_Fun_Oinj__on(_1012796, _1012798, _1012800, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012796, tc_HOL_Obool)), _1012802), _1012804)), 12587 ^ _782476 : [(12592 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012798, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1012796, _1012798, _1012800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012796, tc_HOL_Obool)), _1012802), _1012804))), hAPP(c_Set_Oimage(_1012796, _1012798, _1012800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012796, tc_HOL_Obool)), _1012804), _1012802))) = c_Orderings_Obot__class_Obot(tc_fun(_1012798, tc_HOL_Obool)))], (12590 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1012796, _1012798, _1012800, _1012804))], (12588 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1012796, _1012798, _1012800, _1012802))]]], (46226 ^ _782476) ^ [_1709208, _1709210] : [_1709208 = _1709210, -(hAPP(c_Code__Numeral_Oof__nat, _1709208) = hAPP(c_Code__Numeral_Oof__nat, _1709210))], (7379 ^ _782476) ^ [_905798, _905800, _905802, _905804] : [hBOOL(hAPP(hAPP(_905802, _905804), _905800)), -(hBOOL(hAPP(hAPP(c_member(_905798), _905800), c_SetInterval_Oord_OatLeast(_905798, _905802, _905804))))], (8804 ^ _782476) ^ [_936050, _936052, _936054] : [class_Lattices_Osemilattice__inf(_936050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936050), _936052), _936054)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936050), _936054), _936052) = _936052)], (17393 ^ _782476) ^ [_1112438, _1112440] : [_1112438 = _1112440, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112438), _1112440)))], (45066 ^ _782476) ^ [_1683755, _1683757] : [hBOOL(hAPP(c_List_Odistinct(_1683755), hAPP(c_List_Orotate1(_1683755), _1683757))), -(hBOOL(hAPP(c_List_Odistinct(_1683755), _1683757)))], (16331 ^ _782476) ^ [_1089916] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1089916)), 16335 ^ _782476 : [(16336 ^ _782476) ^ [_1089996] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1089996), _1089916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089996), 16334 ^ [_1089916])))]]], (20233 ^ _782476) ^ [_1162360, _1162362, _1162364] : [20234 ^ _782476 : [(20237 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162362), _1162364))], (20235 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162360)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162360), _1162362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162360), _1162364))))], (17303 ^ _782476) ^ [_1111039, _1111041] : [17304 ^ _782476 : [(17307 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111041), _1111039))], (17305 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111039), _1111041))]], _1111039 = _1111041], (9915 ^ _782476) ^ [_961157, _961159, _961161, _961163, _961165] : [_961157 = c_Orderings_Obot__class_Obot(tc_fun(_961159, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961159, tc_fun(_961161, tc_HOL_Obool)), _961157), hAPP(hAPP(c_COMBB(tc_fun(_961161, tc_HOL_Obool), tc_fun(_961161, tc_HOL_Obool), _961159), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961161, tc_HOL_Obool)), _961163)), _961165)) = c_Orderings_Otop__class_Otop(tc_fun(_961161, tc_HOL_Obool)))], (17495 ^ _782476) ^ [_1114334, _1114336] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114334), _1114336))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114334), _1114336)), -(_1114334 = _1114336)], (39458 ^ _782476) ^ [_1543628, _1543630] : [c_Wellfounded_Owf(_1543628, _1543630), -(c_Wellfounded_Owf(tc_List_Olist(_1543628), c_List_Olex(_1543628, _1543630)))], (17205 ^ _782476) ^ [_1109304, _1109306, _1109308, _1109310, _1109312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109304), _1109306)), 17208 ^ _782476 : [(17215 ^ _782476) ^ [] : [_1109310 = 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), _1109306), _1109304)), _1109308)), _1109312), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109304), _1109308)), _1109310) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109306), _1109308)), _1109312))], (17209 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109304), _1109308)), _1109310) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109306), _1109308)), _1109312), -(_1109310 = 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), _1109306), _1109304)), _1109308)), _1109312))]]], (44256 ^ _782476) ^ [_1665380] : [class_Orderings_Olinorder(_1665380), -(c_List_Olinorder__class_Osorted__list__of__set(_1665380, c_Orderings_Obot__class_Obot(tc_fun(_1665380, tc_HOL_Obool))) = c_List_Olist_ONil(_1665380))], (17285 ^ _782476) ^ [] : [-(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)))], (9601 ^ _782476) ^ [_954696, _954698, _954700] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954696, tc_fun(_954698, tc_HOL_Obool)), _954700), hAPP(c_COMBK(tc_fun(_954698, tc_HOL_Obool), _954696), c_Orderings_Obot__class_Obot(tc_fun(_954698, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_954698, tc_HOL_Obool)))], (11270 ^ _782476) ^ [_989226, _989228, _989230] : [class_Orderings_Olinorder(_989226), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989226), _989228), _989230))), -(_989228 = _989230), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989226), _989230), _989228)))], (44250 ^ _782476) ^ [_1665261, _1665263] : [-(c_List_Oremove1(_1665261, _1665263, c_List_Olist_ONil(_1665261)) = c_List_Olist_ONil(_1665261))], (28454 ^ _782476) ^ [_1322068, _1322070, _1322072] : [class_Orderings_Olinorder(_1322068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322068), _1322070)), 28461 ^ _782476 : [(28468 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322068, tc_HOL_Obool)), _1322070), hAPP(hAPP(c_Set_Oinsert(_1322068), _1322072), c_Orderings_Obot__class_Obot(tc_fun(_1322068, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322068, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1322068, c_Orderings_Oord__class_Omax(_1322068), hAPP(hAPP(c_Set_Oinsert(_1322068), _1322072), _1322070)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322068), _1322072), c_Big__Operators_Olattice_OSup__fin(_1322068, c_Orderings_Oord__class_Omax(_1322068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322068, tc_HOL_Obool)), _1322070), hAPP(hAPP(c_Set_Oinsert(_1322068), _1322072), c_Orderings_Obot__class_Obot(tc_fun(_1322068, tc_HOL_Obool)))))))], (28462 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322068, tc_HOL_Obool)), _1322070), hAPP(hAPP(c_Set_Oinsert(_1322068), _1322072), c_Orderings_Obot__class_Obot(tc_fun(_1322068, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322068, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322068, c_Orderings_Oord__class_Omax(_1322068), hAPP(hAPP(c_Set_Oinsert(_1322068), _1322072), _1322070)) = _1322072)]]], (4950 ^ _782476) ^ [_858039, _858041, _858043, _858045, _858047, _858049, _858051, _858053] : [-(c_Wellfounded_Olex__prod(_858053, _858049, _858045, _858041) = c_Wellfounded_Olex__prod(_858051, _858047, _858043, _858039)), _858053 = _858051, _858049 = _858047, _858045 = _858043, _858041 = _858039], (19186 ^ _782476) ^ [_1143636, _1143638, _1143640, _1143642] : [class_Rings_Olinordered__ring__strict(_1143636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143636), c_Groups_Ozero__class_Ozero(_1143636)), _1143638)), 19193 ^ _782476 : [(19200 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143636), _1143640), _1143642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143636), _1143638), _1143640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143636), _1143638), _1143642))))], (19194 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143636), _1143638), _1143640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143636), _1143638), _1143642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143636), _1143640), _1143642)))]]], (41769 ^ _782476) ^ [_1603185, _1603187, _1603189, _1603191] : [-(hAPP(hAPP(c_Nat_Ocompow(_1603185, _1603185), _1603187), hAPP(hAPP(c_Nat_Ocompow(_1603185, _1603185), _1603189), _1603191)) = hAPP(hAPP(c_Nat_Ocompow(_1603185, _1603185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1603189), _1603187)), _1603191))], (10950 ^ _782476) ^ [_984337, _984339, _984341, _984343] : [class_Orderings_Olinorder(_984337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984337), _984339), _984341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984337), _984341), _984343)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984337, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_984337, _984339, _984341)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984337, _984341, _984343)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984337, _984339), _984343))], (35230 ^ _782476) ^ [_1448352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448352), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448352)), c_Int_OPls)))], (47004 ^ _782476) ^ [_1725975, _1725977, _1725979] : [class_Orderings_Olinorder(_1725975), -(c_List_Olinorder__class_Osort__key(_1725977, _1725975, _1725979, c_List_Olist_ONil(_1725977)) = c_List_Olist_ONil(_1725977))], (9867 ^ _782476) ^ [_959990, _959992, _959994, _959996, _959998] : [_959990 = c_Orderings_Obot__class_Obot(tc_fun(_959992, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959994, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959992, tc_fun(_959994, tc_HOL_Obool)), _959990), _959996)), _959998) = _959998)], (35836 ^ _782476) ^ [_1459293, _1459295, _1459297] : [class_Rings_Ocomm__semiring__1(_1459293), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459293), _1459295), 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)))), _1459297))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459293), _1459295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459293), hAPP(hAPP(c_Power_Opower__class_Opower(_1459293), _1459295), _1459297)), hAPP(hAPP(c_Power_Opower__class_Opower(_1459293), _1459295), _1459297))))], (46136 ^ _782476) ^ [_1707066, _1707068, _1707070] : [c_Fun_Oinj__on(_1707066, _1707068, _1707070, c_Orderings_Otop__class_Otop(tc_fun(_1707066, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1707066), tc_List_Olist(_1707068), hAPP(c_List_Omap(_1707066, _1707068), _1707070), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707066), tc_HOL_Obool))))], (39544 ^ _782476) ^ [_1545579, _1545581] : [-(c_Nitpick_Onumber__of__frac(_1545579, _1545581) = c_Nitpick_OAbs__Frac(_1545579, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1545581), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (15190 ^ _782476) ^ [_1066426, _1066428, _1066430, _1066432, _1066434, _1066436, _1066438] : [c_Finite__Set_Ofolding__idem(_1066426, _1066428, _1066430, _1066432), -(hAPP(c_Fun_Ocomp(_1066428, _1066428, _1066434, hAPP(_1066430, _1066436)), hAPP(c_Fun_Ocomp(_1066428, _1066428, _1066434, hAPP(_1066430, _1066436)), _1066438)) = hAPP(c_Fun_Ocomp(_1066428, _1066428, _1066434, hAPP(_1066430, _1066436)), _1066438))], (51452 ^ _782476) ^ [_1823476, _1823478, _1823480] : [hBOOL(hAPP(hAPP(_1823478, _1823480), _1823480)), -(hBOOL(hAPP(c_Quotient_ORespects(_1823476, _1823478), _1823480)))], (8603 ^ _782476) ^ [_931995, _931997, _931999] : [class_Lattices_Osemilattice__inf(_931995), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931995), _931997), _931999) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931995), _931999), _931997))], (41200 ^ _782476) ^ [_1589545, _1589547, _1589549] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589545, _1589545, _1589547), c_Relation_OId(_1589545)), _1589549) = _1589549)], (16841 ^ _782476) ^ [_1100445, _1100447, _1100449] : [class_Groups_Ogroup__add(_1100445), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100445), _1100447), _1100449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100445), _1100447), hAPP(c_Groups_Ouminus__class_Ouminus(_1100445), _1100449)))], (26960 ^ _782476) ^ [_1291743, _1291745, _1291747, _1291749] : [class_Orderings_Olinorder(_1291743), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291743), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291743), _1291745), _1291747)), _1291749) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291743), _1291745), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291743), _1291747), _1291749)))], (32670 ^ _782476) ^ [_1401057, _1401059, _1401061] : [-(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), _1401057), _1401059)), _1401061)), _1401059) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1401061), _1401059))], (1952 ^ _782476) ^ [_810076, _810078] : [-(class_Groups_Ozero(_810076)), _810078 = _810076, class_Groups_Ozero(_810078)], (48992 ^ _782476) ^ [_1770090, _1770092, _1770094, _1770096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770092)), _1770094))), 48998 ^ _782476 : [(49001 ^ _782476) ^ [] : [hBOOL(hAPP(_1770096, 48997 ^ [_1770090, _1770092, _1770094, _1770096]))], (48999 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770092), 48997 ^ [_1770090, _1770092, _1770094, _1770096]), hAPP(c_List_Oset(_1770092), _1770094))))]], -(hBOOL(hAPP(_1770096, hAPP(hAPP(c_List_Onth(_1770092), _1770094), _1770090))))], (36284 ^ _782476) ^ [_1467142, _1467144] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1467142), hAPP(hAPP(c_Power_Opower__class_Opower(_1467142), hAPP(c_Int_Onumber__class_Onumber__of(_1467142), c_Int_OMin)), _1467144)) = c_Groups_Oone__class_Oone(_1467142)), class_Int_Onumber__ring(_1467142), class_Rings_Olinordered__idom(_1467142)], (25369 ^ _782476) ^ [_1256435] : [-(_1256435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25372 ^ _782476 : [(25379 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256435))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256435) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25373 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256435)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256435) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (50006 ^ _782476) ^ [_1792258, _1792260, _1792262] : [-(_1792258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1792260), c_List_Oreplicate(_1792260, _1792258, _1792262)) = _1792262)], (19702 ^ _782476) ^ [_1152491, _1152493, _1152495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152491), _1152493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152491), _1152495)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152493), _1152495))))], (50012 ^ _782476) ^ [_1792305, _1792307, _1792309, _1792311] : [-(hAPP(hAPP(c_List_Otake(_1792305), _1792307), c_List_Oreplicate(_1792305, _1792309, _1792311)) = c_List_Oreplicate(_1792305, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792307), _1792309), _1792311))], (14733 ^ _782476) ^ [_1057385, _1057387, _1057389, _1057391, _1057393, _1057395, _1057397, _1057399, _1057401, _1057403, _1057405] : [c_Finite__Set_Ofolding(_1057385, _1057387, _1057389, _1057391), -(hAPP(c_Fun_Ocomp(_1057393, _1057395, _1057397, _1057399), hAPP(c_Fun_Ocomp(_1057401, _1057393, _1057397, _1057403), _1057405)) = hAPP(c_Fun_Ocomp(_1057401, _1057395, _1057397, hAPP(c_Fun_Ocomp(_1057393, _1057395, _1057401, _1057399), _1057403)), _1057405))], (49904 ^ _782476) ^ [_1790355, _1790357] : [-(c_List_Oconcat(_1790355, c_List_Oreplicate(tc_List_Olist(_1790355), _1790357, c_List_Olist_ONil(_1790355))) = c_List_Olist_ONil(_1790355))], (2058 ^ _782476) ^ [_812347, _812349, _812351, _812353, _812355, _812357] : [-(c_SetInterval_Oord_OatLeast(_812357, _812353, _812349) = c_SetInterval_Oord_OatLeast(_812355, _812351, _812347)), _812357 = _812355, _812353 = _812351, _812349 = _812347], (21941 ^ _782476) ^ [_1195159, _1195161] : [class_Rings_Olinordered__idom(_1195159), hBOOL(hAPP(hAPP(c_member(_1195159), _1195161), c_Int_Oring__1__class_OInts(_1195159))), 21948 ^ _782476 : [(21955 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195159), _1195161), c_Groups_Ozero__class_Ozero(_1195159))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195159), c_Groups_Oone__class_Oone(_1195159)), _1195161)), _1195161)), c_Groups_Ozero__class_Ozero(_1195159))))], (21949 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195159), c_Groups_Oone__class_Oone(_1195159)), _1195161)), _1195161)), c_Groups_Ozero__class_Ozero(_1195159))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195159), _1195161), c_Groups_Ozero__class_Ozero(_1195159))))]]], (51355 ^ _782476) ^ [_1821497, _1821499] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1821497), _1821499))), -(c_Quickcheck_Obeyond(_1821497, _1821499) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (20545 ^ _782476) ^ [_1168950, _1168952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168950)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168952))))), _1168950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168952 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16283 ^ _782476) ^ [_1088664, _1088666] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088664), _1088666))))], (9157 ^ _782476) ^ [_944787, _944789, _944791, _944793] : [class_Lattices_Olattice(_944787), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944787), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944787), _944789), _944791)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944787), _944789), _944793))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944787), _944789), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944787), _944791), _944793)))))], (37890 ^ _782476) ^ [_1503825] : [-(hAPP(c_Int_Onat, _1503825) = 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, _1503825)), 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)))))))], (21989 ^ _782476) ^ [_1196144] : [hAPP(c_Nat_OSuc, _1196144) = _1196144], (31554 ^ _782476) ^ [_1379455, _1379457, _1379459] : [hBOOL(hAPP(_1379455, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379457), _1379459))), 31557 ^ _782476 : [(31564 ^ _782476) ^ [] : [-(_1379459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31567 ^ _782476 : [(31568 ^ _782476) ^ [_1379707, _1379709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379707), _1379459)), _1379457 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379459), _1379709)), _1379707), -(hBOOL(hAPP(_1379455, _1379709)))]]], (31558 ^ _782476) ^ [] : [_1379459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1379455, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (30156 ^ _782476) ^ [_1354205, _1354207, _1354209, _1354211] : [class_Fields_Ofield__inverse__zero(_1354205), -(_1354207 = c_Groups_Ozero__class_Ozero(_1354205)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354205), _1354209), _1354207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354205), _1354211), _1354207)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354205), _1354209), _1354211))], (48060 ^ _782476) ^ [_1749002, _1749004, _1749006] : [hAPP(hAPP(c_List_Olist_OCons(_1749002), _1749004), c_List_Olist_ONil(_1749002)) = hAPP(c_List_Orev(_1749002), _1749006), -(_1749006 = hAPP(hAPP(c_List_Olist_OCons(_1749002), _1749004), c_List_Olist_ONil(_1749002)))], (39883 ^ _782476) ^ [_1555659, _1555661, _1555663, _1555665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555659, _1555661)), hAPP(hAPP(c_Product__Type_OSigma(_1555659, _1555661), _1555663), hAPP(c_COMBK(tc_fun(_1555661, tc_HOL_Obool), _1555659), _1555665)))), -(_1555663 = c_Orderings_Obot__class_Obot(tc_fun(_1555659, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555661), _1555665)))], (1202 ^ _782476) ^ [_800701, _800703] : [-(class_Groups_Olinordered__ab__group__add(_800701)), _800703 = _800701, class_Groups_Olinordered__ab__group__add(_800703)], (20771 ^ _782476) ^ [_1172960, _1172962] : [20779 ^ _782476 : [(20782 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1172962, 20778 ^ [_1172960, _1172962])))], (20780 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20778 ^ [_1172960, _1172962]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172960))))]], 20772 ^ _782476 : [(20773 ^ _782476) ^ [_1173028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173028), _1172960)), hBOOL(hAPP(_1172962, _1173028))]]], (43535 ^ _782476) ^ [_1647803, _1647805, _1647807, _1647809, _1647811] : [hBOOL(hAPP(hAPP(c_member(_1647803), _1647805), hAPP(c_List_Oset(_1647803), _1647807))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647809), hAPP(_1647811, _1647805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647809), c_List_Olist_Olist__size(_1647803, _1647811, _1647807))))], (21005 ^ _782476) ^ [_1177249, _1177251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177249), _1177251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177251), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (41792 ^ _782476) ^ [_1603805, _1603807, _1603809] : [41793 ^ _782476 : [(41794 ^ _782476) ^ [_1603881] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603805, _1603805)), _1603807), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603805, _1603805), tc_HOL_Obool), _1603881), _1603809)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603805, _1603805)), _1603807), c_Transitive__Closure_Ortrancl(_1603805, _1603809))))], (45048 ^ _782476) ^ [_1683348, _1683350, _1683352] : [-(hAPP(hAPP(c_List_Oappend(_1683348), hAPP(hAPP(c_List_Otake(_1683348), _1683350), _1683352)), hAPP(hAPP(c_List_Odrop(_1683348), _1683350), _1683352)) = _1683352)], (46288 ^ _782476) ^ [_1710353, _1710355] : [hBOOL(hAPP(c_List_Odistinct(_1710353), _1710355)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1710353, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710353), tc_fun(_1710353, tc_HOL_Obool)), c_List_Oset(_1710353)), c_Enum_Osublists(_1710353, _1710355)))))], (50184 ^ _782476) ^ [_1795969, _1795971] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795969), c_List_Olist_ONil(_1795969)), _1795971))], (10199 ^ _782476) ^ [_967076, _967078, _967080] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967076, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967076, tc_HOL_Obool)), _967078), _967080)), _967080) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967076, tc_HOL_Obool)), _967078), _967080))], (11642 ^ _782476) ^ [_994779, _994781, _994783] : [class_Orderings_Oorder(_994779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994779), _994781), _994783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994779), _994781), _994783))), -(_994781 = _994783)], (26954 ^ _782476) ^ [_1291584, _1291586, _1291588, _1291590] : [class_Orderings_Olinorder(_1291584), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291584), _1291586), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291584), _1291588), _1291590)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291584), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291584), _1291586), _1291588)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291584), _1291586), _1291590)))], (20537 ^ _782476) ^ [_1168823, _1168825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168823)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168825)))), 20540 ^ _782476 : [(20543 ^ _782476) ^ [] : [-(_1168825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20541 ^ _782476) ^ [] : [-(_1168823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (30610 ^ _782476) ^ [_1362645, _1362647, _1362649, _1362651] : [class_Fields_Ofield(_1362645), -(_1362647 = c_Groups_Ozero__class_Ozero(_1362645)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362645), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362645), _1362649), _1362647)), _1362651) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362645), _1362649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362645), _1362647), _1362651))), _1362647))], (1312 ^ _782476) ^ [_802076, _802078] : [-(class_Rings_Ocomm__ring__1(_802076)), _802078 = _802076, class_Rings_Ocomm__ring__1(_802078)], (3374 ^ _782476) ^ [_832835, _832837, _832839, _832841] : [-(c_Code__Numeral_Onat__of__aux(_832841, _832837) = c_Code__Numeral_Onat__of__aux(_832839, _832835)), _832841 = _832839, _832837 = _832835], (4414 ^ _782476) ^ [_849489, _849491, _849493, _849495] : [-(c_List_Ozip(_849495, _849491) = c_List_Ozip(_849493, _849489)), _849495 = _849493, _849491 = _849489], (19538 ^ _782476) ^ [_1149747, _1149749] : [class_Groups_Ogroup__add(_1149747), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149747), c_Groups_Ozero__class_Ozero(_1149747)), _1149749) = hAPP(c_Groups_Ouminus__class_Ouminus(_1149747), _1149749))], (13906 ^ _782476) ^ [_1040585, _1040587, _1040589] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040585, _1040587, c_Orderings_Obot__class_Obot(tc_fun(_1040585, tc_HOL_Obool))), _1040589))], (4926 ^ _782476) ^ [_857669, _857671, _857673, _857675] : [-(c_Product__Type_Ofst(_857675, _857671) = c_Product__Type_Ofst(_857673, _857669)), _857675 = _857673, _857671 = _857669], (52075 ^ _782476) ^ [_1837058, _1837060] : [52076 ^ _782476 : [(52079 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837060), _1837058))], (52077 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837058), _1837060)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1837058, _1837060) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (47859 ^ _782476) ^ [_1744852, _1744854, _1744856, _1744858, _1744860, _1744862] : [class_Orderings_Olinorder(_1744852), c_List_Olinorder__class_Osorted(_1744852, hAPP(hAPP(c_List_Omap(_1744854, _1744852), _1744856), _1744858)), hBOOL(hAPP(_1744860, _1744862)), -(hAPP(c_List_Ofilter(_1744854, _1744860), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744854, _1744852, _1744856), _1744862), _1744858)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744854, _1744852, _1744856), _1744862), hAPP(c_List_Ofilter(_1744854, _1744860), _1744858)))], (28091 ^ _782476) ^ [_1313668, _1313670, _1313672] : [class_Orderings_Olinorder(_1313668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313668), _1313670)), -(_1313672 = c_Orderings_Obot__class_Obot(tc_fun(_1313668, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313668, tc_HOL_Obool)), _1313672), _1313670)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313668), c_Big__Operators_Olattice_OInf__fin(_1313668, c_Orderings_Oord__class_Omin(_1313668), _1313672)), c_Big__Operators_Olattice_OInf__fin(_1313668, c_Orderings_Oord__class_Omin(_1313668), _1313670)) = c_Big__Operators_Olattice_OInf__fin(_1313668, c_Orderings_Oord__class_Omin(_1313668), _1313670))], (13828 ^ _782476) ^ [_1039103, _1039105, _1039107, _1039109, _1039111, _1039113] : [c_Fun_Oinj__on(_1039103, _1039105, _1039107, _1039109), 13831 ^ _782476 : [(13838 ^ _782476) ^ [] : [c_Fun_Oinj__on(_1039103, _1039111, hAPP(c_Fun_Ocomp(_1039105, _1039111, _1039103, _1039113), _1039107), _1039109), -(c_Fun_Oinj__on(_1039105, _1039111, _1039113, hAPP(c_Set_Oimage(_1039103, _1039105, _1039107), _1039109)))], (13832 ^ _782476) ^ [] : [c_Fun_Oinj__on(_1039105, _1039111, _1039113, hAPP(c_Set_Oimage(_1039103, _1039105, _1039107), _1039109)), -(c_Fun_Oinj__on(_1039103, _1039111, hAPP(c_Fun_Ocomp(_1039105, _1039111, _1039103, _1039113), _1039107), _1039109))]]], (40607 ^ _782476) ^ [_1574931, _1574933, _1574935, _1574937, _1574939, _1574941] : [hBOOL(hAPP(hAPP(c_member(_1574931), _1574933), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1574935, _1574937, tc_fun(_1574931, tc_HOL_Obool)), _1574939), _1574941))), 40612 ^ _782476 : [(40615 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574931), _1574933), hAPP(hAPP(_1574939, 40610 ^ [_1574931, _1574933, _1574935, _1574937, _1574939, _1574941]), 40611 ^ [_1574931, _1574933, _1574935, _1574937, _1574939, _1574941]))))], (40613 ^ _782476) ^ [] : [-(_1574941 = hAPP(hAPP(c_Product__Type_OPair(_1574935, _1574937), 40610 ^ [_1574931, _1574933, _1574935, _1574937, _1574939, _1574941]), 40611 ^ [_1574931, _1574933, _1574935, _1574937, _1574939, _1574941]))]]], (3182 ^ _782476) ^ [_829819, _829821] : [_829821 = _829819, -(c_List_Orotate1(_829821) = c_List_Orotate1(_829819))], (43471 ^ _782476) ^ [_1646309, _1646311, _1646313] : [-(hAPP(c_List_Oset(_1646309), hAPP(hAPP(c_List_Olist_OCons(_1646309), _1646311), _1646313)) = hAPP(hAPP(c_Set_Oinsert(_1646309), _1646311), hAPP(c_List_Oset(_1646309), _1646313)))], (31900 ^ _782476) ^ [_1386603, _1386605, _1386607] : [class_Divides_Osemiring__div(_1386603), -(c_Divides_Odiv__class_Omod(_1386603, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386603), _1386605), _1386607), _1386605) = c_Divides_Odiv__class_Omod(_1386603, _1386607, _1386605))], (32614 ^ _782476) ^ [_1400177, _1400179] : [32615 ^ _782476 : [(32616 ^ _782476) ^ [_1400226] : [_1400177 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400179), _1400226)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400177, _1400179) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40260 ^ _782476) ^ [_1566659] : [-(c_Wellfounded_OwfP(_1566659, hAPP(c_COMBK(tc_fun(_1566659, tc_HOL_Obool), _1566659), hAPP(c_COMBK(tc_HOL_Obool, _1566659), c_fFalse))))], (38577 ^ _782476) ^ [_1521179, _1521181, _1521183, _1521185, _1521187] : [hBOOL(hAPP(hAPP(c_member(_1521179), _1521181), hAPP(c_Relation_OImage(_1521183, _1521179, _1521185), _1521187))), 38581 ^ _782476 : [(38584 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521183), 38580 ^ [_1521179, _1521181, _1521183, _1521185, _1521187]), _1521187)))], (38582 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521183, _1521179)), hAPP(hAPP(c_Product__Type_OPair(_1521183, _1521179), 38580 ^ [_1521179, _1521181, _1521183, _1521185, _1521187]), _1521181)), _1521185)))]]], (8762 ^ _782476) ^ [_935281, _935283, _935285, _935287, _935289] : [class_Lattices_Osemilattice__inf(_935281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935281), _935283), _935285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935281), _935287), _935289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935281), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935281), _935283), _935287)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935281), _935285), _935289))))], (22228 ^ _782476) ^ [_1199912, _1199914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199912)), _1199914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199912), _1199914)))], (50979 ^ _782476) ^ [_1814561, _1814563, _1814565] : [c_Relation_Osym(_1814561, _1814563), c_Relation_Osym(_1814561, _1814565), -(c_Relation_Osym(_1814561, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1814561, _1814561), tc_HOL_Obool)), _1814563), _1814565)))], (36262 ^ _782476) ^ [_1466785] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466785)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466785)))], (3154 ^ _782476) ^ [_829369, _829371, _829373, _829375, _829377, _829379, _829381, _829383] : [-(c_Nat_Onat_Onat__case(_829383, _829379, _829375, _829371) = c_Nat_Onat_Onat__case(_829381, _829377, _829373, _829369)), _829383 = _829381, _829379 = _829377, _829375 = _829373, _829371 = _829369], (9997 ^ _782476) ^ [_962793, _962795, _962797] : [class_Orderings_Oorder(_962793), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962793, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962793), _962795)), c_SetInterval_Oord__class_OatLeastAtMost(_962793, _962795, _962797)) = c_Orderings_Obot__class_Obot(tc_fun(_962793, tc_HOL_Obool)))], (16415 ^ _782476) ^ [_1091650, _1091652, _1091654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091650), _1091652)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091652), _1091654)) = 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, _1091650), _1091652)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091652), _1091654))))], (35450 ^ _782476) ^ [_1452390] : [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), _1452390))), 35453 ^ _782476 : [(35456 ^ _782476) ^ [] : [-(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(_1452390)))))], (35454 ^ _782476) ^ [] : [-(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(_1452390)))))]]], (10799 ^ _782476) ^ [_980846, _980848, _980850, _980852, _980854] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980846, tc_fun(_980848, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980846), _980850), _980852)), _980854) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980848, tc_HOL_Obool)), hAPP(_980854, _980850)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980846, tc_fun(_980848, tc_HOL_Obool)), _980852), _980854)))], (36404 ^ _782476) ^ [_1470415, _1470417, _1470419, _1470421, _1470423, _1470425] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470415, tc_fun(_1470417, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1470415, tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_fun(_1470417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470417, tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_fun(_1470417, tc_HOL_Obool)), _1470415), c_COMBC(_1470417, tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470417, tc_prod(_1470415, _1470417)), tc_fun(_1470417, tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), _1470415), hAPP(c_COMBB(tc_prod(_1470415, _1470417), tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool), _1470417), c_member(tc_prod(_1470415, _1470417)))), c_Product__Type_OPair(_1470415, _1470417)))), _1470419)), hAPP(hAPP(c_COMBC(_1470415, tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_fun(_1470417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470417, tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_fun(_1470417, tc_HOL_Obool)), _1470415), c_COMBC(_1470417, tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470417, tc_prod(_1470415, _1470417)), tc_fun(_1470417, tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool)), _1470415), hAPP(c_COMBB(tc_prod(_1470415, _1470417), tc_fun(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool), tc_HOL_Obool), _1470417), c_member(tc_prod(_1470415, _1470417)))), c_Product__Type_OPair(_1470415, _1470417)))), _1470421)), _1470423), _1470425)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470415, _1470417)), hAPP(hAPP(c_Product__Type_OPair(_1470415, _1470417), _1470423), _1470425)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1470415, _1470417), tc_HOL_Obool)), _1470419), _1470421))))], (47564 ^ _782476) ^ [_1739814, _1739816, _1739818] : [class_Orderings_Olinorder(_1739814), 47567 ^ _782476 : [(47574 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1739814, _1739818), -(c_List_Olinorder__class_Osorted(_1739814, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739814, _1739814, c_COMBI(_1739814)), _1739816), _1739818)))], (47568 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1739814, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739814, _1739814, c_COMBI(_1739814)), _1739816), _1739818)), -(c_List_Olinorder__class_Osorted(_1739814, _1739818))]]], (41559 ^ _782476) ^ [_1598381, _1598383, _1598385] : [hAPP(hAPP(c_Relation_Orel__comp(_1598381, _1598381, _1598381), hAPP(c_Relation_Oconverse(_1598381, _1598381), _1598383)), _1598383) = _1598383, hAPP(c_Relation_ODomain(_1598381, _1598381), _1598383) = _1598385, -(c_Equiv__Relations_Oequiv(_1598381, _1598385, _1598383))], (28029 ^ _782476) ^ [_1312391, _1312393, _1312395] : [class_Orderings_Olinorder(_1312391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312391), _1312393)), -(_1312393 = c_Orderings_Obot__class_Obot(tc_fun(_1312391, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312391), _1312395), c_Big__Operators_Olattice_OInf__fin(_1312391, c_Orderings_Oord__class_Omin(_1312391), _1312393)) = c_Big__Operators_Olattice_OInf__fin(_1312391, c_Orderings_Oord__class_Omin(_1312391), hAPP(c_Set_OCollect(_1312391), hAPP(hAPP(c_COMBB(tc_fun(_1312391, tc_HOL_Obool), tc_HOL_Obool, _1312391), c_HOL_OEx(_1312391)), hAPP(hAPP(c_COMBC(_1312391, tc_fun(_1312391, tc_HOL_Obool), tc_fun(_1312391, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312391, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1312391, tc_HOL_Obool), tc_fun(_1312391, tc_HOL_Obool)), _1312391), c_COMBS(_1312391, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312391, tc_HOL_Obool), tc_fun(_1312391, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1312391), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1312391), c_fconj)), hAPP(hAPP(c_COMBC(_1312391, tc_fun(_1312391, _1312391), tc_fun(_1312391, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312391, tc_HOL_Obool), tc_fun(tc_fun(_1312391, _1312391), tc_fun(_1312391, tc_HOL_Obool)), _1312391), c_COMBB(_1312391, tc_HOL_Obool, _1312391)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1312391), _1312395))))), hAPP(hAPP(c_COMBC(_1312391, tc_fun(_1312391, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312391)), _1312393))))))], (12042 ^ _782476) ^ [_1001566, _1001568, _1001570, _1001572, _1001574] : [class_Complete__Lattice_Ocomplete__lattice(_1001566), class_Orderings_Olinorder(_1001566), 12049 ^ _782476 : [(12059 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001566), _1001568), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001570, _1001566), _1001572), _1001574)))), 12060 ^ _782476 : [(12061 ^ _782476) ^ [_1001914] : [hBOOL(hAPP(hAPP(c_member(_1001570), _1001914), _1001572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001566), _1001568), hAPP(_1001574, _1001914)))]]], (12050 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001566), _1001568), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001570, _1001566), _1001572), _1001574))), 12054 ^ _782476 : [(12057 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001566), _1001568), hAPP(_1001574, 12053 ^ [_1001566, _1001568, _1001570, _1001572, _1001574]))))], (12055 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001570), 12053 ^ [_1001566, _1001568, _1001570, _1001572, _1001574]), _1001572)))]]]]], (4448 ^ _782476) ^ [_849978, _849980, _849982, _849984] : [-(c_List_Olast(_849984, _849980) = c_List_Olast(_849982, _849978)), _849984 = _849982, _849980 = _849978], (40276 ^ _782476) ^ [_1566922, _1566924] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1566922, _1566924), 40277 ^ [_1566922, _1566924])), -(c_Wellfounded_OwfP(_1566922, _1566924))], (1432 ^ _782476) ^ [_803576, _803578] : [-(class_Orderings_Owellorder(_803576)), _803578 = _803576, class_Orderings_Owellorder(_803578)], (6913 ^ _782476) ^ [_895729, _895731, _895733, _895735] : [_895729 = _895731, 6916 ^ _782476 : [(6923 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895733), _895735), _895731)), -(hBOOL(hAPP(hAPP(c_member(_895733), _895735), _895729)))], (6917 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895733), _895735), _895729)), -(hBOOL(hAPP(hAPP(c_member(_895733), _895735), _895731)))]]], (26438 ^ _782476) ^ [_1282077, _1282079, _1282081, _1282083] : [class_Orderings_Olinorder(_1282077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282077), _1282079), _1282081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282077), _1282079), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282077), _1282081), _1282083))))], (6513 ^ _782476) ^ [_887129, _887131, _887133] : [class_Orderings_Oorder(_887129), hBOOL(hAPP(_887131, _887133)), 6523 ^ _782476 : [(6526 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887129), _887133), 6522 ^ [_887129, _887131, _887133]))], (6524 ^ _782476) ^ [] : [-(hBOOL(hAPP(_887131, 6522 ^ [_887129, _887131, _887133])))]], -(c_Orderings_Oord__class_OLeast(_887129, _887131) = _887133)], (14336 ^ _782476) ^ [_1049486, _1049488, _1049490, _1049492] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049486), _1049488)), 14339 ^ _782476 : [(14340 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049490), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049486, tc_fun(_1049490, tc_HOL_Obool)), _1049488), _1049492))), 14343 ^ _782476 : [(14344 ^ _782476) ^ [_1049670] : [hBOOL(hAPP(hAPP(c_member(_1049486), _1049670), _1049488)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049490), hAPP(_1049492, _1049670))))]]], (14350 ^ _782476) ^ [] : [14352 ^ _782476 : [(14355 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049490), hAPP(_1049492, 14351 ^ [_1049486, _1049488, _1049490, _1049492])))], (14353 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049486), 14351 ^ [_1049486, _1049488, _1049490, _1049492]), _1049488)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049490), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049486, tc_fun(_1049490, tc_HOL_Obool)), _1049488), _1049492))))]]], (17227 ^ _782476) ^ [_1109802, _1109804, _1109806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109802), _1109804)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109804), _1109802)), _1109806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109804), _1109806)), _1109802))], (40114 ^ _782476) ^ [_1562659, _1562661, _1562663, _1562665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562659), _1562661)), 40120 ^ _782476 : [(40123 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562663), hAPP(_1562665, 40119 ^ [_1562659, _1562661, _1562663, _1562665])))], (40121 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562659), 40119 ^ [_1562659, _1562661, _1562663, _1562665]), _1562661)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562659, _1562663)), hAPP(hAPP(c_Product__Type_OSigma(_1562659, _1562663), _1562661), _1562665))))], (37243 ^ _782476) ^ [_1491395, _1491397] : [37244 ^ _782476 : [(37247 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491397), _1491395))], (37245 ^ _782476) ^ [] : [_1491395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1491397, _1491395) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491397))], (50402 ^ _782476) ^ [_1800952, _1800954, _1800956] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800952, _1800954, _1800956, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1800954)], (49792 ^ _782476) ^ [_1787833, _1787835, _1787837, _1787839, _1787841] : [hBOOL(hAPP(hAPP(_1787837, _1787841), _1787839)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787833, _1787835, _1787837), _1787839), _1787841)))], (13818 ^ _782476) ^ [_1038916, _1038918, _1038920, _1038922, _1038924, _1038926] : [c_Fun_Oinj__on(_1038916, _1038918, _1038920, _1038922), c_Fun_Oinj__on(_1038918, _1038924, _1038926, hAPP(c_Set_Oimage(_1038916, _1038918, _1038920), _1038922)), -(c_Fun_Oinj__on(_1038916, _1038924, hAPP(c_Fun_Ocomp(_1038918, _1038924, _1038916, _1038926), _1038920), _1038922))], (8190 ^ _782476) ^ [_922616, _922618, _922620, _922622, _922624] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922616, tc_fun(_922618, tc_HOL_Obool)), _922620), hAPP(hAPP(c_COMBS(_922616, tc_fun(_922618, tc_HOL_Obool), tc_fun(_922618, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922618, tc_HOL_Obool), tc_fun(tc_fun(_922618, tc_HOL_Obool), tc_fun(_922618, tc_HOL_Obool)), _922616), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922618, tc_HOL_Obool))), _922622)), _922624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922618, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922616, tc_fun(_922618, tc_HOL_Obool)), _922620), _922622)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922616, tc_fun(_922618, tc_HOL_Obool)), _922620), _922624)))], (13784 ^ _782476) ^ [_1038181] : [class_Lattices_Oab__semigroup__idem__mult(_1038181), -(c_Finite__Set_Ofun__left__comm__idem(_1038181, _1038181, c_Groups_Otimes__class_Otimes(_1038181)))], (23984 ^ _782476) ^ [_1232138, _1232140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232140)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232138)), hAPP(c_Int_Onat, _1232140)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232138), _1232140)))], (22011 ^ _782476) ^ [_1196468] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1196468) = 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)), _1196468)))], (13940 ^ _782476) ^ [_1041345, _1041347, _1041349] : [c_Fun_Obij__betw(_1041345, _1041347, _1041349, c_Orderings_Otop__class_Otop(tc_fun(_1041345, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041347, tc_HOL_Obool))), 13943 ^ _782476 : [(13946 ^ _782476) ^ [] : [-(hAPP(c_Set_Oimage(_1041345, _1041347, _1041349), c_Orderings_Otop__class_Otop(tc_fun(_1041345, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041347, tc_HOL_Obool)))], (13944 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1041345, _1041347, _1041349, c_Orderings_Otop__class_Otop(tc_fun(_1041345, tc_HOL_Obool))))]]], (14176 ^ _782476) ^ [_1046546, _1046548] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046546, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046546), _1046548))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046546), _1046548)))], (9813 ^ _782476) ^ [_958581, _958583, _958585, _958587] : [class_Orderings_Oorder(_958581), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958581, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958581, _958583, _958585)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958581, _958585, _958587)) = c_Orderings_Obot__class_Obot(tc_fun(_958581, tc_HOL_Obool)))], (38234 ^ _782476) ^ [_1512260, _1512262, _1512264, _1512266, _1512268, _1512270, _1512272, _1512274, _1512276, _1512278] : [c_Equiv__Relations_Ocongruent2(_1512260, _1512262, _1512264, _1512266, _1512268, _1512270), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512260, _1512260)), hAPP(hAPP(c_Product__Type_OPair(_1512260, _1512260), _1512272), _1512274)), _1512266)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512262, _1512262)), hAPP(hAPP(c_Product__Type_OPair(_1512262, _1512262), _1512276), _1512278)), _1512268)), -(hAPP(hAPP(_1512270, _1512272), _1512276) = hAPP(hAPP(_1512270, _1512274), _1512278))], (14449 ^ _782476) ^ [_1051600, _1051602, _1051604] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051600), _1051602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051600, tc_HOL_Obool)), _1051602), hAPP(c_Set_Oimage(_1051600, _1051600, _1051604), _1051602))), -(c_Fun_Oinj__on(_1051600, _1051600, _1051604, _1051602))], (33452 ^ _782476) ^ [_1416556, _1416558, _1416560, _1416562] : [class_Fields_Olinordered__field__inverse__zero(_1416556), class_Int_Onumber(_1416556), 33459 ^ _782476 : [(33460 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416556), _1416558), _1416560)), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562))), 33463 ^ _782476 : [(33470 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), _1416560))), 33473 ^ _782476 : [(33480 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416560), c_Groups_Ozero__class_Ozero(_1416556)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562))))], (33474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416560), c_Groups_Ozero__class_Ozero(_1416556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416556), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)), _1416560)), _1416558)))]]], (33464 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), _1416560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416556), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)), _1416560))))]]], (33486 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416556), _1416558), _1416560)), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)))), 33489 ^ _782476 : [(33492 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416556), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)), _1416560)))], (33490 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), _1416560)))]], 33493 ^ _782476 : [(33496 ^ _782476) ^ [] : [33497 ^ _782476 : [(33500 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416556), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)), _1416560)), _1416558))], (33498 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416560), c_Groups_Ozero__class_Ozero(_1416556))))]], 33501 ^ _782476 : [(33504 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), hAPP(c_Int_Onumber__class_Onumber__of(_1416556), _1416562)))], (33502 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), _1416560), c_Groups_Ozero__class_Ozero(_1416556)))]]], (33494 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416556), c_Groups_Ozero__class_Ozero(_1416556)), _1416560))]]]]], (17409 ^ _782476) ^ [_1112688, _1112690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112688), _1112690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112690), _1112688)), -(_1112688 = _1112690)], (52479 ^ _782476) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (25458 ^ _782476) ^ [_1258153, _1258155] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258153)), -(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)), _1258153))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258155))))) = 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)), _1258153))), 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, _1258155))))))], (2380 ^ _782476) ^ [_817364, _817366, _817368, _817370] : [-(c_Groups_Osgn__class_Osgn(_817370, _817366) = c_Groups_Osgn__class_Osgn(_817368, _817364)), _817370 = _817368, _817366 = _817364], (51250 ^ _782476) ^ [_1818975, _1818977] : [c_Equiv__Relations_Opart__equivp(_1818975, _1818977), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1818975, tc_HOL_Obool)), 51253 ^ [_1818975, _1818977]), hAPP(hAPP(c_COMBB(tc_fun(_1818975, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1818975, tc_HOL_Obool)), c_HOL_OEx(_1818975)), hAPP(hAPP(c_COMBB(tc_fun(_1818975, tc_HOL_Obool), tc_fun(_1818975, tc_HOL_Obool), tc_fun(_1818975, tc_HOL_Obool)), hAPP(c_COMBS(_1818975, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1818975), c_fconj), hAPP(hAPP(c_COMBS(_1818975, _1818975, tc_HOL_Obool), _1818977), c_COMBI(_1818975))))), hAPP(hAPP(c_COMBC(tc_fun(_1818975, tc_HOL_Obool), tc_fun(_1818975, tc_fun(_1818975, tc_HOL_Obool)), tc_fun(_1818975, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1818975, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1818975, tc_fun(_1818975, tc_HOL_Obool)), tc_fun(_1818975, tc_HOL_Obool)), tc_fun(_1818975, tc_HOL_Obool)), c_COMBB(tc_fun(_1818975, tc_HOL_Obool), tc_HOL_Obool, _1818975)), c_fequal)), _1818977))))))], (34640 ^ _782476) ^ [_1437475] : [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), _1437475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437475)))], (24757 ^ _782476) ^ [_1245239, _1245241, _1245243, _1245245, _1245247] : [class_Groups_Ocomm__monoid__add(_1245239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245241), _1245243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245241, tc_HOL_Obool)), _1245245), _1245243)), 24771 ^ _782476 : [(24774 ^ _782476) ^ [] : [hAPP(_1245247, 24770 ^ [_1245239, _1245241, _1245243, _1245245, _1245247]) = c_Groups_Ozero__class_Ozero(_1245239)], (24772 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245241), 24770 ^ [_1245239, _1245241, _1245243, _1245245, _1245247]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245241, tc_HOL_Obool)), _1245243), _1245245))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245241, _1245239), _1245247), _1245245) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245241, _1245239), _1245247), _1245243))], (17594 ^ _782476) ^ [_1116005, _1116007, _1116009, _1116011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116005), _1116007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116009), _1116011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116005), _1116009)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116007), _1116011))))], (30176 ^ _782476) ^ [_1354529, _1354531, _1354533, _1354535, _1354537] : [class_Fields_Ofield(_1354529), -(_1354531 = c_Groups_Ozero__class_Ozero(_1354529)), -(_1354533 = c_Groups_Ozero__class_Ozero(_1354529)), 30187 ^ _782476 : [(30194 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354529), _1354535), _1354533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354529), _1354537), _1354531), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354529), _1354535), _1354531) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354529), _1354537), _1354533))], (30188 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354529), _1354535), _1354531) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354529), _1354537), _1354533), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354529), _1354535), _1354533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354529), _1354537), _1354531))]]], (39416 ^ _782476) ^ [_1542499, _1542501] : [c_Wellfounded_Owf(_1542499, _1542501), -(c_Wellfounded_Owf(tc_List_Olist(_1542499), c_List_Olenlex(_1542499, _1542501)))], (51815 ^ _782476) ^ [_1832115, _1832117, _1832119, _1832121] : [class_Rings_Ocomm__semiring__1(_1832115), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832115), _1832117), _1832119)), _1832121)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832115), _1832117), _1832121)))], (33010 ^ _782476) ^ [_1408254, _1408256] : [class_Int_Onumber__ring(_1408254), 33013 ^ _782476 : [(33020 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408256)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408256)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408254), _1408256))], (33014 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408256))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408256)) = c_Groups_Ozero__class_Ozero(_1408254))]]], (17443 ^ _782476) ^ [_1113298, _1113300, _1113302, _1113304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113298), _1113300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113302), _1113304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113298), _1113302)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113300), _1113304))))], (27473 ^ _782476) ^ [_1302138, _1302140, _1302142, _1302144, _1302146] : [class_Groups_Ocomm__monoid__mult(_1302138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302140), _1302142)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302140), _1302144)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302138), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302140, _1302138), _1302146), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302140, tc_HOL_Obool)), _1302142), _1302144))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302140, _1302138), _1302146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302140, tc_HOL_Obool)), _1302142), _1302144))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302138), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302140, _1302138), _1302146), _1302142)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302140, _1302138), _1302146), _1302144)))], (20926 ^ _782476) ^ [_1175902, _1175904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175902), _1175904)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175902), _1175904)))], (878 ^ _782476) ^ [_795901, _795903, _795905, _795907] : [-(c_Wellfounded_Oacyclic(_795905, _795901)), c_Wellfounded_Oacyclic(_795907, _795903), _795907 = _795905, _795903 = _795901], (51033 ^ _782476) ^ [_1815393, _1815395] : [c_Relation_Osym(_1815393, _1815395), -(c_Relation_Osym(_1815393, hAPP(c_Relation_Oconverse(_1815393, _1815393), _1815395)))], (42969 ^ _782476) ^ [_1631179, _1631181, _1631183, _1631185, _1631187, _1631189] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631179), tc_List_Olist(_1631179))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631179), tc_List_Olist(_1631179)), hAPP(hAPP(c_List_Olist_OCons(_1631179), _1631181), _1631183)), hAPP(hAPP(c_List_Olist_OCons(_1631179), _1631185), _1631187))), c_List_Olex(_1631179, _1631189)))), 42970 ^ _782476 : [(42977 ^ _782476) ^ [] : [_1631181 = _1631185, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631179), tc_List_Olist(_1631179))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631179), tc_List_Olist(_1631179)), _1631183), _1631187)), c_List_Olex(_1631179, _1631189)))], (42971 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631179, _1631179)), hAPP(hAPP(c_Product__Type_OPair(_1631179, _1631179), _1631181), _1631185)), _1631189)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631179)), _1631183) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631179)), _1631187)]]], (41641 ^ _782476) ^ [_1600007, _1600009, _1600011] : [c_Relation_Osingle__valued(_1600007, _1600009, _1600011), 41644 ^ _782476 : [(41645 ^ _782476) ^ [_1600128, _1600130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600007, _1600009)), hAPP(hAPP(c_Product__Type_OPair(_1600007, _1600009), _1600130), _1600128)), _1600011)), 41648 ^ _782476 : [(41649 ^ _782476) ^ [_1600254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600007, _1600009)), hAPP(hAPP(c_Product__Type_OPair(_1600007, _1600009), _1600130), _1600254)), _1600011)), -(_1600128 = _1600254)]]]]], (34554 ^ _782476) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (41929 ^ _782476) ^ [_1607709, _1607711, _1607713, _1607715, _1607717] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607709, _1607709)), hAPP(hAPP(c_Product__Type_OPair(_1607709, _1607709), _1607711), _1607713)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607709, _1607709), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1607715)), _1607717))), 41933 ^ _782476 : [(41936 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607709, _1607709)), hAPP(hAPP(c_Product__Type_OPair(_1607709, _1607709), 41932 ^ [_1607709, _1607711, _1607713, _1607715, _1607717]), _1607713)), _1607717)))], (41934 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607709, _1607709)), hAPP(hAPP(c_Product__Type_OPair(_1607709, _1607709), _1607711), 41932 ^ [_1607709, _1607711, _1607713, _1607715, _1607717])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607709, _1607709), tc_HOL_Obool), _1607715), _1607717))))]]], (39995 ^ _782476) ^ [_1560066, _1560068] : [-(c_Fun_Obij__betw(_1560066, _1560066, c_Fun_Oid(_1560066), _1560068, _1560068))], (46088 ^ _782476) ^ [_1706017, _1706019, _1706021, _1706023, _1706025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706017), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706019)), _1706021))), -(hAPP(hAPP(c_List_Onth(_1706023), hAPP(hAPP(c_List_Omap(_1706019, _1706023), _1706025), _1706021)), _1706017) = hAPP(_1706025, hAPP(hAPP(c_List_Onth(_1706019), _1706021), _1706017)))], (49524 ^ _782476) ^ [_1781260, _1781262, _1781264, _1781266, _1781268] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781260, _1781262, _1781264, _1781266), _1781268) = c_Hilbert__Choice_OEps(_1781260, hAPP(hAPP(c_COMBS(_1781260, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781260), c_fconj), hAPP(hAPP(c_COMBC(_1781260, tc_fun(_1781260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1781260)), _1781264))), hAPP(hAPP(c_COMBC(_1781260, _1781262, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781262, tc_fun(_1781262, tc_HOL_Obool), _1781260), c_fequal), _1781266)), _1781268))))], (39297 ^ _782476) ^ [_1539700] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1539700)))], (20223 ^ _782476) ^ [_1162183, _1162185, _1162187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162183), _1162185)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162183), _1162187))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162185), _1162187)))], (45166 ^ _782476) ^ [_1686074, _1686076, _1686078, _1686080] : [_1686074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1686076), _1686074), hAPP(hAPP(c_List_Olist_OCons(_1686076), _1686078), _1686080)) = hAPP(hAPP(c_List_Olist_OCons(_1686076), _1686078), _1686080))], (9035 ^ _782476) ^ [_940801, _940803, _940805, _940807] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940801, tc_HOL_Obool)), _940803), _940805)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940801, tc_HOL_Obool)), _940805), _940807))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940801, tc_HOL_Obool)), _940807), _940803)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940801, tc_HOL_Obool)), _940803), _940805)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940801, tc_HOL_Obool)), _940805), _940807))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940801, tc_HOL_Obool)), _940807), _940803)))], (39752 ^ _782476) ^ [_1551652, _1551654, _1551656, _1551658, _1551660, _1551662] : [class_Groups_Ocomm__monoid__mult(_1551652), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551654, _1551652), hAPP(hAPP(c_COMBC(_1551654, tc_fun(_1551656, tc_HOL_Obool), _1551652), hAPP(hAPP(c_COMBB(tc_fun(_1551656, _1551652), tc_fun(tc_fun(_1551656, tc_HOL_Obool), _1551652), _1551654), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551656, _1551652)), _1551658)), _1551660)), _1551662) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1551654, _1551656), _1551652), hAPP(c_Product__Type_Oprod_Oprod__case(_1551654, _1551656, _1551652), _1551658)), hAPP(hAPP(c_Product__Type_OSigma(_1551654, _1551656), _1551662), hAPP(c_COMBK(tc_fun(_1551656, tc_HOL_Obool), _1551654), _1551660))))], (1402 ^ _782476) ^ [_803201, _803203] : [-(class_Rings_Oring(_803201)), _803203 = _803201, class_Rings_Oring(_803203)], (9760 ^ _782476) ^ [_957389, _957391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957389, tc_HOL_Obool)), _957391), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957389, tc_HOL_Obool)), _957391))), -(_957391 = c_Orderings_Obot__class_Obot(tc_fun(_957389, tc_HOL_Obool)))], (41278 ^ _782476) ^ [_1591463, _1591465, _1591467, _1591469] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591463, _1591463)), hAPP(hAPP(c_Product__Type_OPair(_1591463, _1591463), _1591465), _1591467)), c_Transitive__Closure_Ortrancl(_1591463, _1591469)))), 41279 ^ _782476 : [(41282 ^ _782476) ^ [] : [-(_1591465 = _1591467), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591463, _1591463)), hAPP(hAPP(c_Product__Type_OPair(_1591463, _1591463), _1591465), _1591467)), c_Transitive__Closure_Otrancl(_1591463, _1591469)))], (41280 ^ _782476) ^ [] : [_1591465 = _1591467]]], (26354 ^ _782476) ^ [_1280584, _1280586, _1280588, _1280590] : [class_Orderings_Olinorder(_1280584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280584), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280584), _1280586), _1280588)), _1280590)), 26361 ^ _782476 : [(26364 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280584), _1280588), _1280590)))], (26362 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280584), _1280586), _1280590)))]]], (51318 ^ _782476) ^ [_1820813, _1820815, _1820817, _1820819] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820813, _1820815, _1820817, _1820819, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1820815)) = _1820817)], (43870 ^ _782476) ^ [_1657191, _1657193, _1657195, _1657197, _1657199, _1657201] : [-(_1657191 = _1657193), -(hAPP(hAPP(c_List_Olist__update(_1657195, hAPP(hAPP(c_List_Olist__update(_1657195, _1657197), _1657191), _1657199)), _1657193), _1657201) = hAPP(hAPP(c_List_Olist__update(_1657195, hAPP(hAPP(c_List_Olist__update(_1657195, _1657197), _1657193), _1657201)), _1657191), _1657199))], (41152 ^ _782476) ^ [_1588338, _1588340] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588338, _1588338, _1588338), _1588340), c_Transitive__Closure_Ortrancl(_1588338, _1588340)) = hAPP(hAPP(c_Relation_Orel__comp(_1588338, _1588338, _1588338), c_Transitive__Closure_Ortrancl(_1588338, _1588340)), _1588340))], (17385 ^ _782476) ^ [_1112368] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112368), _1112368)))], (40270 ^ _782476) ^ [_1566830, _1566832] : [c_Wellfounded_OwfP(_1566830, _1566832), 40273 ^ _782476 : [(40274 ^ _782476) ^ [_1566894] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566830, _1566832), _1566894)))]]], (34388 ^ _782476) ^ [_1433537] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1433537)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1433537))))], (29776 ^ _782476) ^ [_1347425, _1347427, _1347429, _1347431] : [class_Fields_Olinordered__field(_1347425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347425), c_Groups_Ozero__class_Ozero(_1347425)), _1347427)), 29783 ^ _782476 : [(29790 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347425), _1347429), _1347427)), _1347431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347425), _1347429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347425), _1347431), _1347427))))], (29784 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347425), _1347429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347425), _1347431), _1347427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347425), _1347429), _1347427)), _1347431)))]]], (48441 ^ _782476) ^ [_1757180, _1757182, _1757184] : [-(hAPP(hAPP(c_List_Oappend(_1757180), c_List_OtakeWhile(_1757180, _1757182, _1757184)), c_List_OdropWhile(_1757180, _1757182, _1757184)) = _1757184)], (3690 ^ _782476) ^ [_837783, _837785, _837787, _837789] : [-(c_List_Obutlast(_837789, _837785) = c_List_Obutlast(_837787, _837783)), _837789 = _837787, _837785 = _837783], (39257 ^ _782476) ^ [_1538922, _1538924] : [c_Wellfounded_Owf(_1538922, _1538924), -(c_Wellfounded_Owf(tc_fun(_1538922, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1538922, _1538924)))], (39336 ^ _782476) ^ [_1540624, _1540626] : [c_Wellfounded_Owf(_1540624, _1540626), 39340 ^ _782476 : [(39341 ^ _782476) ^ [_1540760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540624, _1540624)), hAPP(hAPP(c_Product__Type_OPair(_1540624, _1540624), hAPP(_1540760, hAPP(c_Nat_OSuc, 39339 ^ [_1540624, _1540626, _1540760]))), hAPP(_1540760, 39339 ^ [_1540624, _1540626, _1540760]))), _1540626))]]], (33340 ^ _782476) ^ [_1414377, _1414379, _1414381, _1414383] : [class_Fields_Ofield__inverse__zero(_1414377), class_Int_Onumber(_1414377), 33347 ^ _782476 : [(33348 ^ _782476) ^ [] : [_1414379 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414377), _1414381), hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383)), 33351 ^ _782476 : [(33358 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383) = c_Groups_Ozero__class_Ozero(_1414377), -(_1414379 = c_Groups_Ozero__class_Ozero(_1414377))], (33352 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383) = c_Groups_Ozero__class_Ozero(_1414377)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414377), _1414379), hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383)) = _1414381)]]], (33364 ^ _782476) ^ [] : [-(_1414379 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414377), _1414381), hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383))), 33367 ^ _782476 : [(33370 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414377), _1414379), hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383)) = _1414381], (33368 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383) = c_Groups_Ozero__class_Ozero(_1414377)]], 33371 ^ _782476 : [(33374 ^ _782476) ^ [] : [_1414379 = c_Groups_Ozero__class_Ozero(_1414377)], (33372 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414377), _1414383) = c_Groups_Ozero__class_Ozero(_1414377))]]]]], (46272 ^ _782476) ^ [_1710010, _1710012, _1710014] : [-(hAPP(hAPP(c_List_Ozip(_1710010, _1710012), hAPP(hAPP(c_List_Omap(tc_prod(_1710010, _1710012), _1710010), c_Product__Type_Ofst(_1710010, _1710012)), _1710014)), hAPP(hAPP(c_List_Omap(tc_prod(_1710010, _1710012), _1710012), c_Product__Type_Osnd(_1710010, _1710012)), _1710014)) = _1710014)], (4408 ^ _782476) ^ [_849404, _849406] : [_849406 = _849404, -(c_List_Onth(_849406) = c_List_Onth(_849404))], (32094 ^ _782476) ^ [_1390372, _1390374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390374, _1390372)), _1390372)))], (35472 ^ _782476) ^ [_1452855, _1452857] : [class_Int_Onumber__ring(_1452855), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452855), hAPP(c_Int_Onumber__class_Onumber__of(_1452855), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1452857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452855), _1452857), _1452857))], (40960 ^ _782476) ^ [_1582869, _1582871, _1582873] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582869, _1582869)), _1582871), _1582873)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582869, _1582869)), _1582871), c_Transitive__Closure_Otrancl(_1582869, _1582873))))], (15987 ^ _782476) ^ [_1081839, _1081841, _1081843, _1081845, _1081847, _1081849] : [class_Groups_Ocomm__monoid__add(_1081839), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081841, _1081839), hAPP(hAPP(c_COMBC(_1081841, tc_fun(_1081843, tc_HOL_Obool), _1081839), hAPP(hAPP(c_COMBB(tc_fun(_1081843, _1081839), tc_fun(tc_fun(_1081843, tc_HOL_Obool), _1081839), _1081841), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081843, _1081839)), _1081845)), _1081847)), _1081849) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081843, _1081839), hAPP(hAPP(c_COMBC(_1081843, tc_fun(_1081841, tc_HOL_Obool), _1081839), hAPP(hAPP(c_COMBB(tc_fun(_1081841, _1081839), tc_fun(tc_fun(_1081841, tc_HOL_Obool), _1081839), _1081843), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081841, _1081839)), hAPP(c_COMBC(_1081841, _1081843, _1081839), _1081845))), _1081849)), _1081847))], (13384 ^ _782476) ^ [_1030180, _1030182, _1030184, _1030186] : [class_Orderings_Oorder(_1030180), class_Enum_Oenum(_1030182), 13391 ^ _782476 : [(13400 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030182, _1030180)), _1030184), _1030186))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030182, _1030180)), _1030184), _1030186)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030182), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030182), c_fNot), hAPP(hAPP(c_COMBS(_1030182, _1030180, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030180, tc_fun(_1030180, tc_HOL_Obool), _1030182), c_fequal), _1030184)), _1030186))))], (13392 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030182, _1030180)), _1030184), _1030186)), 13395 ^ _782476 : [(13398 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030182), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030182), c_fNot), hAPP(hAPP(c_COMBS(_1030182, _1030180, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030180, tc_fun(_1030180, tc_HOL_Obool), _1030182), c_fequal), _1030184)), _1030186)))))], (13396 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030182, _1030180)), _1030184), _1030186)))]]]]], (3430 ^ _782476) ^ [_833673, _833675, _833677, _833679, _833681, _833683] : [-(c_Enum_On__lists(_833683, _833679, _833675) = c_Enum_On__lists(_833681, _833677, _833673)), _833683 = _833681, _833679 = _833677, _833675 = _833673], (39657 ^ _782476) ^ [_1548611, _1548613] : [-(hAPP(c_Relation_OField(_1548611), _1548613) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1548611, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548611, _1548611), _1548613)), hAPP(c_Relation_ORange(_1548611, _1548611), _1548613)))], (6131 ^ _782476) ^ [_879733, _879735, _879737, _879739, _879741, _879743] : [c_Predicate_Oinv__imagep(_879733, _879735, _879737, _879739, _879741, _879743), -(hBOOL(hAPP(hAPP(_879737, hAPP(_879739, _879741)), hAPP(_879739, _879743))))], (5832 ^ _782476) ^ [_874819, _874821, _874823] : [_874819 = _874821, 5835 ^ _782476 : [(5838 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874823, tc_HOL_Obool)), _874821), _874819)))], (5836 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874823, tc_HOL_Obool)), _874819), _874821)))]]], (18766 ^ _782476) ^ [_1135963, _1135965, _1135967, _1135969] : [class_Rings_Oordered__semiring(_1135963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135963), _1135965), _1135967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135963), c_Groups_Ozero__class_Ozero(_1135963)), _1135969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135963), _1135965), _1135969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135963), _1135967), _1135969))))], (36310 ^ _782476) ^ [_1467559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467559)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1467559) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1467559), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (46760 ^ _782476) ^ [_1721038, _1721040, _1721042, _1721044] : [c_List_Olist__all2(_1721038, _1721040, _1721042, c_List_Olist_ONil(_1721038), _1721044), -(_1721044 = c_List_Olist_ONil(_1721040))], (44562 ^ _782476) ^ [_1671899, _1671901, _1671903, _1671905, _1671907, _1671909] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671899), tc_List_Olist(_1671899))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671899), tc_List_Olist(_1671899)), hAPP(hAPP(c_List_Oappend(_1671899), _1671901), hAPP(hAPP(c_List_Olist_OCons(_1671899), _1671903), c_List_Olist_ONil(_1671899)))), hAPP(hAPP(c_List_Oappend(_1671899), _1671905), hAPP(hAPP(c_List_Olist_OCons(_1671899), _1671907), c_List_Olist_ONil(_1671899))))), c_List_Olistrel1(_1671899, _1671909)))), 44563 ^ _782476 : [(44570 ^ _782476) ^ [] : [_1671901 = _1671905, hBOOL(hAPP(hAPP(c_member(tc_prod(_1671899, _1671899)), hAPP(hAPP(c_Product__Type_OPair(_1671899, _1671899), _1671903), _1671907)), _1671909))], (44564 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671899), tc_List_Olist(_1671899))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671899), tc_List_Olist(_1671899)), _1671901), _1671905)), c_List_Olistrel1(_1671899, _1671909))), _1671903 = _1671907]]], (44034 ^ _782476) ^ [_1660831, _1660833, _1660835] : [-(hBOOL(hAPP(c_List_Odistinct(_1660831), hAPP(hAPP(c_List_Olist_OCons(_1660831), _1660833), _1660835)))), -(hBOOL(hAPP(hAPP(c_member(_1660831), _1660833), hAPP(c_List_Oset(_1660831), _1660835)))), hBOOL(hAPP(c_List_Odistinct(_1660831), _1660835))], (50388 ^ _782476) ^ [_1800380, _1800382, _1800384, _1800386] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800380, _1800382, _1800384, c_Code__Numeral_OSuc__code__numeral(_1800386)) = hAPP(hAPP(_1800384, _1800386), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800380, _1800382, _1800384, _1800386)))], (7003 ^ _782476) ^ [_897588, _897590, _897592, _897594] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897588, tc_fun(_897590, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897588, tc_HOL_Obool), _897592)), _897594) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897588, tc_HOL_Obool), tc_fun(_897590, tc_HOL_Obool)), _897592), hAPP(hAPP(c_COMBC(tc_fun(_897588, tc_HOL_Obool), tc_fun(_897588, tc_fun(_897590, tc_HOL_Obool)), tc_fun(_897590, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897588, tc_fun(_897590, tc_HOL_Obool))), _897594)))], (22114 ^ _782476) ^ [_1198117, _1198119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198117), _1198119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198117), hAPP(c_Nat_OSuc, _1198119))))], (42772 ^ _782476) ^ [_1625545, _1625547, _1625549] : [-(c_Nitpick_Oplus__frac(_1625545, _1625547, _1625549) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1625545), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1625545), _1625547), hAPP(c_Nitpick_Odenom(_1625545), _1625549))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1625545), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1625545), tc_Int_Oint), c_Nitpick_Ofrac(_1625545)), 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(_1625545), _1625547))), 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(_1625545), _1625547))))), 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(_1625545), _1625549))), 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(_1625545), _1625549)))))), c_COMBI(tc_Int_Oint))))], (30054 ^ _782476) ^ [_1352627, _1352629, _1352631] : [class_Fields_Olinordered__field__inverse__zero(_1352627), 30057 ^ _782476 : [(30072 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352627), _1352629), _1352631)))), 30073 ^ _782476 : [(30080 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), _1352629), c_Groups_Ozero__class_Ozero(_1352627))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), _1352631), c_Groups_Ozero__class_Ozero(_1352627)))], (30074 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), _1352629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), _1352631))]]], (30058 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352627), _1352629), _1352631))), 30063 ^ _782476 : [(30066 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), _1352631)))], (30064 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), c_Groups_Ozero__class_Ozero(_1352627)), _1352629)))]], 30067 ^ _782476 : [(30070 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), _1352631), c_Groups_Ozero__class_Ozero(_1352627))))], (30068 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352627), _1352629), c_Groups_Ozero__class_Ozero(_1352627))))]]]]], (51707 ^ _782476) ^ [_1830119, _1830121, _1830123] : [class_Divides_Osemiring__div(_1830119), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830119), _1830121), _1830123)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830119), _1830121), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830119), _1830123), _1830121)) = _1830123)], (9211 ^ _782476) ^ [_946297, _946299, _946301, _946303] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946297, tc_fun(_946299, tc_HOL_Obool)), _946301), _946303) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_946299, tc_HOL_Obool), hAPP(c_Set_Oimage(_946297, tc_fun(_946299, tc_HOL_Obool), _946303), _946301)))], (19342 ^ _782476) ^ [_1146474] : [class_Rings_Olinordered__semidom(_1146474), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146474), c_Groups_Ozero__class_Ozero(_1146474)), c_Groups_Oone__class_Oone(_1146474))))], (36208 ^ _782476) ^ [_1466058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1466058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466058))))], (52607 ^ _782476) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (39760 ^ _782476) ^ [_1552012, _1552014, _1552016, _1552018, _1552020] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552012, _1552014), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552012, tc_HOL_Obool)), _1552016), _1552018)), hAPP(c_COMBK(tc_fun(_1552014, tc_HOL_Obool), _1552012), _1552020)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552012, _1552014), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552012, _1552014), _1552016), hAPP(c_COMBK(tc_fun(_1552014, tc_HOL_Obool), _1552012), _1552020))), hAPP(hAPP(c_Product__Type_OSigma(_1552012, _1552014), _1552018), hAPP(c_COMBK(tc_fun(_1552014, tc_HOL_Obool), _1552012), _1552020))))], (31578 ^ _782476) ^ [_1379892, _1379894, _1379896] : [-(hBOOL(hAPP(_1379892, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379894), _1379896)))), 31581 ^ _782476 : [(31584 ^ _782476) ^ [] : [hBOOL(hAPP(_1379892, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31582 ^ _782476) ^ [] : [-(_1379896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 31585 ^ _782476 : [(31590 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31588 ^ [_1379892, _1379894, _1379896]), _1379896)))], (31592 ^ _782476) ^ [] : [-(_1379894 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379896), 31587 ^ [_1379892, _1379894, _1379896])), 31588 ^ [_1379892, _1379894, _1379896]))], (31594 ^ _782476) ^ [] : [hBOOL(hAPP(_1379892, 31587 ^ [_1379892, _1379894, _1379896]))], (31586 ^ _782476) ^ [] : [_1379896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43876 ^ _782476) ^ [_1657271, _1657273, _1657275, _1657277, _1657279, _1657281] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1657271, _1657273), hAPP(hAPP(c_List_Ozip(_1657271, _1657273), _1657275), _1657277)), _1657279), _1657281) = hAPP(hAPP(c_List_Ozip(_1657271, _1657273), hAPP(hAPP(c_List_Olist__update(_1657271, _1657275), _1657279), hAPP(c_Product__Type_Ofst(_1657271, _1657273), _1657281))), hAPP(hAPP(c_List_Olist__update(_1657273, _1657277), _1657279), hAPP(c_Product__Type_Osnd(_1657271, _1657273), _1657281))))], (42949 ^ _782476) ^ [_1630614, _1630616, _1630618] : [hAPP(hAPP(c_List_Olist_OCons(_1630614), _1630616), _1630618) = _1630618], (36803 ^ _782476) ^ [_1482840, _1482842, _1482844, _1482846, _1482848, _1482850, _1482852] : [hBOOL(hAPP(hAPP(c_member(_1482840), _1482842), hAPP(hAPP(_1482844, _1482846), _1482848))), -(hBOOL(hAPP(hAPP(c_member(_1482840), _1482842), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1482850, _1482852, tc_fun(_1482840, tc_HOL_Obool)), _1482844), hAPP(hAPP(c_Product__Type_OPair(_1482850, _1482852), _1482846), _1482848)))))], (25117 ^ _782476) ^ [_1251982, _1251984, _1251986] : [class_Groups_Oordered__ab__group__add__abs(_1251982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251982), hAPP(c_Groups_Oabs__class_Oabs(_1251982), _1251984)), _1251986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251982), hAPP(c_Groups_Ouminus__class_Ouminus(_1251982), _1251984)), _1251986)))], (52317 ^ _782476) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (13226 ^ _782476) ^ [_1026250, _1026252, _1026254, _1026256] : [-(hAPP(c_Set_Ovimage(_1026250, _1026252, _1026254), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026252, tc_HOL_Obool)), _1026256)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026250, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026250, _1026252, _1026254), _1026256)))], (40559 ^ _782476) ^ [_1573107, _1573109, _1573111, _1573113] : [c_Equiv__Relations_Ocongruent(_1573107, _1573109, _1573111, _1573113), 40562 ^ _782476 : [(40563 ^ _782476) ^ [_1573252] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573107, _1573107)), _1573252), _1573111)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573107, _1573107, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573107, tc_fun(_1573107, _1573109), tc_fun(_1573107, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573109, tc_HOL_Obool), tc_fun(tc_fun(_1573107, _1573109), tc_fun(_1573107, tc_HOL_Obool)), _1573107), c_COMBB(_1573109, tc_HOL_Obool, _1573107)), hAPP(hAPP(c_COMBB(_1573109, tc_fun(_1573109, tc_HOL_Obool), _1573107), c_fequal), _1573113))), _1573113)), _1573252)))]]], (34580 ^ _782476) ^ [_1436539, _1436541] : [class_Int_Onumber__ring(_1436539), class_Rings_Olinordered__idom(_1436539), 34587 ^ _782476 : [(34594 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436539), c_Groups_Ozero__class_Ozero(_1436539)), hAPP(c_Int_Onumber__class_Onumber__of(_1436539), _1436541))))], (34588 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436539), c_Groups_Ozero__class_Ozero(_1436539)), hAPP(c_Int_Onumber__class_Onumber__of(_1436539), _1436541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436541)))]]], (52325 ^ _782476) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (28109 ^ _782476) ^ [_1314000, _1314002, _1314004] : [class_Orderings_Olinorder(_1314000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314000), _1314002)), hBOOL(hAPP(hAPP(c_member(_1314000), _1314004), _1314002)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1314000), _1314004), c_Big__Operators_Olattice_OInf__fin(_1314000, c_Orderings_Oord__class_Omin(_1314000), _1314002)) = _1314004)], (10717 ^ _782476) ^ [_978685, _978687, _978689] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978685, tc_HOL_Obool)), _978687), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978685, tc_HOL_Obool)), _978689)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978685, tc_HOL_Obool)), _978687), _978689))], (9047 ^ _782476) ^ [_941316, _941318] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941316, tc_HOL_Obool)), _941318), c_Orderings_Otop__class_Otop(tc_fun(_941316, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_941316, tc_HOL_Obool)))], (17950 ^ _782476) ^ [_1122901] : [class_Rings_Osemiring__1(_1122901), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122901), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1122901))], (39078 ^ _782476) ^ [_1534498, _1534500, _1534502, _1534504, _1534506, _1534508] : [c_Typedef_Otype__definition(_1534498, _1534500, _1534502, _1534504, _1534506), hBOOL(hAPP(hAPP(c_member(_1534500), _1534508), _1534506)), -(hAPP(_1534502, hAPP(_1534504, _1534508)) = _1534508)], (44374 ^ _782476) ^ [_1667350] : [class_Groups_Omonoid__add(_1667350), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667350), c_List_Olist_ONil(_1667350)) = c_Groups_Ozero__class_Ozero(_1667350))], (10525 ^ _782476) ^ [_974579, _974581, _974583, _974585] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974579, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974579), _974581), _974583)), _974585))), hBOOL(hAPP(hAPP(c_member(_974579), _974581), _974585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974579, tc_HOL_Obool)), _974583), _974585))], (49428 ^ _782476) ^ [_1778944, _1778946, _1778948, _1778950, _1778952] : [-(hAPP(c_New__DSequence_Oneg__bind(_1778944, _1778946, _1778948, _1778950), _1778952) = c_Lazy__Sequence_Ohb__bind(_1778944, _1778946, hAPP(_1778948, _1778952), hAPP(hAPP(c_COMBC(_1778944, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778946))), _1778950), _1778952)))], (14130 ^ _782476) ^ [_1045593, _1045595, _1045597] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045593), _1045595)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045593), hAPP(hAPP(c_Set_Oinsert(_1045593), _1045597), _1045595))))], (13672 ^ _782476) ^ [_1035900, _1035902, _1035904, _1035906, _1035908, _1035910] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035900, _1035902, _1035904, _1035906), _1035908), _1035910) = hAPP(_1035906, hAPP(_1035908, _1035910)))], (3094 ^ _782476) ^ [_828467, _828469] : [_828469 = _828467, -(c_Set_OPow(_828469) = c_Set_OPow(_828467))], (35348 ^ _782476) ^ [_1450447, _1450449] : [class_Int_Onumber__ring(_1450447), class_Int_Oring__char__0(_1450447), 35355 ^ _782476 : [(35362 ^ _782476) ^ [] : [c_Int_Oiszero(_1450447, hAPP(c_Int_Onumber__class_Onumber__of(_1450447), _1450449)), -(c_Int_Oiszero(_1450447, hAPP(c_Int_Onumber__class_Onumber__of(_1450447), c_Int_OBit0(_1450449))))], (35356 ^ _782476) ^ [] : [c_Int_Oiszero(_1450447, hAPP(c_Int_Onumber__class_Onumber__of(_1450447), c_Int_OBit0(_1450449))), -(c_Int_Oiszero(_1450447, hAPP(c_Int_Onumber__class_Onumber__of(_1450447), _1450449)))]]], (11346 ^ _782476) ^ [_990384, _990386, _990388, _990390, _990392, _990394] : [_990384 = _990386, -(hAPP(c_Fun_Ofun__upd(_990388, _990390, _990392, _990386, _990394), _990384) = _990394)], (4768 ^ _782476) ^ [_855148, _855150, _855152, _855154, _855156, _855158] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855158, _855154, _855150) = c_SetInterval_Oord__class_OatLeastAtMost(_855156, _855152, _855148)), _855158 = _855156, _855154 = _855152, _855150 = _855148], (29356 ^ _782476) ^ [_1339507, _1339509, _1339511] : [class_Groups_Omonoid__mult(_1339507), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339507), _1339509), hAPP(c_Nat_OSuc, _1339511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339507), hAPP(hAPP(c_Power_Opower__class_Opower(_1339507), _1339509), _1339511)), _1339509))], (45120 ^ _782476) ^ [_1684938, _1684940, _1684942, _1684944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1684938), _1684940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684942, tc_HOL_Obool)), hAPP(c_List_Oset(_1684942), hAPP(hAPP(c_List_Odrop(_1684942), _1684940), _1684944))), hAPP(c_List_Oset(_1684942), hAPP(hAPP(c_List_Odrop(_1684942), _1684938), _1684944)))))], (13423 ^ _782476) ^ [_1030991] : [-(c_Finite__Set_Ofun__left__comm__idem(_1030991, tc_fun(_1030991, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1030991, tc_HOL_Obool), tc_fun(tc_fun(_1030991, tc_HOL_Obool), tc_fun(_1030991, tc_HOL_Obool)), _1030991), hAPP(c_COMBC(tc_fun(_1030991, tc_HOL_Obool), tc_fun(_1030991, tc_HOL_Obool), tc_fun(_1030991, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1030991, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1030991, tc_fun(_1030991, tc_HOL_Obool), tc_fun(_1030991, tc_HOL_Obool)), c_Set_Oinsert(_1030991)), c_Orderings_Obot__class_Obot(tc_fun(_1030991, tc_HOL_Obool))))))], (49462 ^ _782476) ^ [_1779892, _1779894, _1779896, _1779898, _1779900] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1779892), _1779894), _1779896), _1779898), _1779900) = c_New__DSequence_Opos__single(_1779892, _1779894))], (48751 ^ _782476) ^ [_1763461, _1763463] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1763461)), _1763463)), 48757 ^ _782476 : [(48760 ^ _782476) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1763461), 48756 ^ [_1763461, _1763463]))], (48758 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763461)), 48756 ^ [_1763461, _1763463]), hAPP(c_List_Oset(tc_List_Olist(_1763461)), _1763463))))]], 48764 ^ _782476 : [(48768 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763461)), 48766 ^ [_1763461, _1763463]), hAPP(c_List_Oset(tc_List_Olist(_1763461)), _1763463))))], (48770 ^ _782476) ^ [] : [48763 ^ [_1763461, _1763463] = 48766 ^ [_1763461, _1763463]], (48772 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1763461, tc_HOL_Obool)), hAPP(c_List_Oset(_1763461), 48763 ^ [_1763461, _1763463])), hAPP(c_List_Oset(_1763461), 48766 ^ [_1763461, _1763463])) = c_Orderings_Obot__class_Obot(tc_fun(_1763461, tc_HOL_Obool))], (48765 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763461)), 48763 ^ [_1763461, _1763463]), hAPP(c_List_Oset(tc_List_Olist(_1763461)), _1763463))))]], -(hBOOL(hAPP(c_List_Odistinct(_1763461), c_List_Oconcat(_1763461, _1763463))))], (48086 ^ _782476) ^ [_1749605, _1749607] : [hBOOL(hAPP(c_List_Odistinct(_1749605), hAPP(c_List_Orev(_1749605), _1749607))), -(hBOOL(hAPP(c_List_Odistinct(_1749605), _1749607)))], (52563 ^ _782476) ^ [_1842415, _1842417] : [-(class_Enum_Oenum(tc_prod(_1842415, _1842417))), class_Enum_Oenum(_1842415), class_Enum_Oenum(_1842417)], (44769 ^ _782476) ^ [_1676755, _1676757, _1676759] : [class_Groups_Omonoid__add(_1676755), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676755), hAPP(hAPP(c_List_Oappend(_1676755), _1676757), _1676759)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676755), hAPP(c_List_Omonoid__add__class_Olistsum(_1676755), _1676757)), hAPP(c_List_Omonoid__add__class_Olistsum(_1676755), _1676759)))], (42107 ^ _782476) ^ [_1611937, _1611939, _1611941, _1611943, _1611945] : [class_Complete__Lattice_Ocomplete__lattice(_1611937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611939), _1611941)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611937), _1611943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611939, _1611937), _1611941), _1611945)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611939, _1611937, hAPP(hAPP(c_COMBB(_1611937, tc_fun(_1611937, _1611937), _1611939), c_Lattices_Osemilattice__inf__class_Oinf(_1611937)), _1611945)), _1611943), _1611941))], (36865 ^ _782476) ^ [_1484261, _1484263, _1484265, _1484267, _1484269, _1484271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484261, tc_fun(_1484263, tc_HOL_Obool))), _1484265), _1484267)), hBOOL(hAPP(hAPP(_1484265, _1484269), _1484271)), -(hBOOL(hAPP(hAPP(_1484267, _1484269), _1484271)))], (40019 ^ _782476) ^ [_1560455, _1560457] : [-(c_Fun_Oinj__on(_1560455, _1560455, c_Fun_Oid(_1560455), _1560457))], (9843 ^ _782476) ^ [_959379, _959381, _959383, _959385, _959387] : [_959379 = c_Orderings_Obot__class_Obot(tc_fun(_959381, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959381, tc_fun(_959383, tc_HOL_Obool)), _959379), hAPP(hAPP(c_COMBC(_959381, tc_fun(_959383, tc_HOL_Obool), tc_fun(_959383, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959383, tc_HOL_Obool), tc_fun(tc_fun(_959383, tc_HOL_Obool), tc_fun(_959383, tc_HOL_Obool)), _959381), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959383, tc_HOL_Obool))), _959385)), _959387)) = c_Orderings_Obot__class_Obot(tc_fun(_959383, tc_HOL_Obool)))], (35434 ^ _782476) ^ [_1451984, _1451986] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1451984)), c_Int_OBit1(_1451986)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451984), c_Int_Osucc(_1451986))))], (52409 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (17794 ^ _782476) ^ [_1119692, _1119694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119692), _1119694))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119692), _1119694)) = _1119692)], (52265 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (5638 ^ _782476) ^ [_868839, _868841, _868843, _868845] : [-(tc_prod(_868845, _868841) = tc_prod(_868843, _868839)), _868845 = _868843, _868841 = _868839], (45899 ^ _782476) ^ [_1700801, _1700803, _1700805, _1700807, _1700809] : [c_Fun_Oinj__on(_1700801, _1700803, _1700805, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1700801, tc_HOL_Obool)), hAPP(c_List_Oset(_1700801), _1700807)), hAPP(c_List_Oset(_1700801), _1700809))), 45902 ^ _782476 : [(45909 ^ _782476) ^ [] : [_1700807 = _1700809, -(hAPP(hAPP(c_List_Omap(_1700801, _1700803), _1700805), _1700807) = hAPP(hAPP(c_List_Omap(_1700801, _1700803), _1700805), _1700809))], (45903 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Omap(_1700801, _1700803), _1700805), _1700807) = hAPP(hAPP(c_List_Omap(_1700801, _1700803), _1700805), _1700809), -(_1700807 = _1700809)]]], (52339 ^ _782476) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52761 ^ _782476) ^ [_1844644, _1844646] : [hBOOL(_1844644), -(hBOOL(hAPP(hAPP(c_fimplies, _1844646), _1844644)))], (45849 ^ _782476) ^ [_1699907, _1699909, _1699911] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699907)), _1699909), c_List_Olists(_1699907, _1699911))), -(_1699909 = c_List_Olist_ONil(_1699907)), 45858 ^ _782476 : [(45863 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699907)), 45857 ^ [_1699907, _1699909, _1699911]), c_List_Olists(_1699907, _1699911))))], (45861 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699907), 45856 ^ [_1699907, _1699909, _1699911]), _1699911)))], (45859 ^ _782476) ^ [] : [-(_1699909 = hAPP(hAPP(c_List_Olist_OCons(_1699907), 45856 ^ [_1699907, _1699909, _1699911]), 45857 ^ [_1699907, _1699909, _1699911]))]]], (51899 ^ _782476) ^ [_1833615, _1833617, _1833619, _1833621] : [class_Rings_Ocomm__ring(_1833615), class_Rings_Odvd(_1833615), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833615), _1833617), _1833619)), 51910 ^ _782476 : [(51917 ^ _782476) ^ [_1834041, _1834043] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833615), _1833617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1833615), _1834043), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833615), _1834041), _1833619))), _1833621))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833615), _1833617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833615), _1834043), _1833621))))], (51911 ^ _782476) ^ [_1833868, _1833870] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833615), _1833617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833615), _1833870), _1833621))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833615), _1833617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1833615), _1833870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833615), _1833868), _1833619))), _1833621))))]]], (39700 ^ _782476) ^ [_1550226, _1550228, _1550230] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550226, _1550228), c_Orderings_Obot__class_Obot(tc_fun(_1550226, tc_HOL_Obool))), _1550230) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1550226, _1550228), tc_HOL_Obool)))], (50219 ^ _782476) ^ [_1796766, _1796768, _1796770] : [-(c_List_Olist__ex1(_1796766, _1796768, _1796770)), 50220 ^ _782476 : [(50221 ^ _782476) ^ [_1796860] : [hBOOL(hAPP(hAPP(c_member(_1796766), _1796860), hAPP(c_List_Oset(_1796766), _1796770))), hBOOL(hAPP(_1796768, _1796860)), 50229 ^ _782476 : [(50234 ^ _782476) ^ [] : [50228 ^ [_1796766, _1796768, _1796770, _1796860] = _1796860], (50232 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1796768, 50228 ^ [_1796766, _1796768, _1796770, _1796860])))], (50230 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796766), 50228 ^ [_1796766, _1796768, _1796770, _1796860]), hAPP(c_List_Oset(_1796766), _1796770))))]]]]], (36537 ^ _782476) ^ [_1476328, _1476330, _1476332] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476328, _1476328), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476330), _1476332))), -(_1476328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476332 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12650 ^ _782476) ^ [_1014269, _1014271, _1014273, _1014275] : [12652 ^ _782476 : [(12656 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014269), 12654 ^ [_1014269, _1014271, _1014273, _1014275]), _1014275)))], (12658 ^ _782476) ^ [] : [-(hAPP(_1014273, 12651 ^ [_1014269, _1014271, _1014273, _1014275]) = hAPP(_1014273, 12654 ^ [_1014269, _1014271, _1014273, _1014275]))], (12660 ^ _782476) ^ [] : [12651 ^ [_1014269, _1014271, _1014273, _1014275] = 12654 ^ [_1014269, _1014271, _1014273, _1014275]], (12653 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014269), 12651 ^ [_1014269, _1014271, _1014273, _1014275]), _1014275)))]], -(c_Fun_Oinj__on(_1014269, _1014271, _1014273, _1014275))], (6833 ^ _782476) ^ [_893999, _894001, _894003, _894005, _894007, _894009] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893999, tc_fun(_894001, tc_HOL_Obool)), _894003), hAPP(hAPP(c_COMBC(_893999, tc_fun(_894005, tc_fun(_894001, tc_HOL_Obool)), tc_fun(_894001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_894005, tc_HOL_Obool), tc_fun(tc_fun(_894005, tc_fun(_894001, tc_HOL_Obool)), tc_fun(_894001, tc_HOL_Obool)), _893999), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894005, tc_fun(_894001, tc_HOL_Obool))), _894007)), _894009)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894005, tc_fun(_894001, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893999, tc_fun(_894005, tc_HOL_Obool)), _894003), _894007)), _894009))], (36571 ^ _782476) ^ [_1477988, _1477990, _1477992, _1477994, _1477996, _1477998] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477990, _1477992)), hAPP(hAPP(c_Product__Type_OPair(_1477990, _1477992), _1477996), _1477998)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477988, tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477988, tc_HOL_Obool))), _1477994))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477988, tc_fun(_1477990, tc_fun(_1477992, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477988, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_fun(_1477990, tc_fun(_1477992, tc_HOL_Obool)), _1477988), hAPP(c_COMBC(_1477990, tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_fun(_1477992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477992, tc_fun(tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_fun(_1477992, tc_HOL_Obool)), _1477990), c_COMBC(_1477992, tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477992, tc_prod(_1477990, _1477992)), tc_fun(_1477992, tc_fun(tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_HOL_Obool)), _1477990), hAPP(c_COMBB(tc_prod(_1477990, _1477992), tc_fun(tc_fun(tc_prod(_1477990, _1477992), tc_HOL_Obool), tc_HOL_Obool), _1477992), c_member(tc_prod(_1477990, _1477992)))), c_Product__Type_OPair(_1477990, _1477992))))), _1477994)), _1477996), _1477998)))], (1602 ^ _782476) ^ [_805701, _805703] : [-(class_Rings_Olinordered__comm__semiring__strict(_805701)), _805703 = _805701, class_Rings_Olinordered__comm__semiring__strict(_805703)], (15088 ^ _782476) ^ [_1064303, _1064305, _1064307] : [class_Lattices_Olattice(_1064303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064303), _1064305)), hBOOL(hAPP(hAPP(c_member(_1064303), _1064307), _1064305)), 15099 ^ _782476 : [(15106 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064303, tc_HOL_Obool)), _1064305), hAPP(hAPP(c_Set_Oinsert(_1064303), _1064307), c_Orderings_Obot__class_Obot(tc_fun(_1064303, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064303, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1064303, _1064305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064303), _1064307), c_Big__Operators_Olattice__class_OSup__fin(_1064303, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064303, tc_HOL_Obool)), _1064305), hAPP(hAPP(c_Set_Oinsert(_1064303), _1064307), c_Orderings_Obot__class_Obot(tc_fun(_1064303, tc_HOL_Obool)))))))], (15100 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064303, tc_HOL_Obool)), _1064305), hAPP(hAPP(c_Set_Oinsert(_1064303), _1064307), c_Orderings_Obot__class_Obot(tc_fun(_1064303, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064303, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1064303, _1064305) = _1064307)]]], (22612 ^ _782476) ^ [_1206537] : [-(hAPP(c_Nat_OSuc, _1206537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1206537))], (30774 ^ _782476) ^ [_1365784, _1365786, _1365788, _1365790] : [class_Fields_Olinordered__field(_1365784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365784), c_Groups_Ozero__class_Ozero(_1365784)), _1365786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365784), _1365788), _1365786)), _1365790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365784), _1365788), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365784), _1365790), _1365786))))], (52457 ^ _782476) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (38732 ^ _782476) ^ [_1524322, _1524324] : [-(c_Relation_OId__on(_1524322, _1524324) = hAPP(c_Product__Type_Oprod_Oprod__case(_1524322, _1524322, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1524322, tc_HOL_Obool, tc_fun(_1524322, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524322, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1524322, tc_HOL_Obool)), _1524322), c_COMBC(_1524322, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524322, tc_HOL_Obool), tc_fun(_1524322, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1524322), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524322), c_fconj)), c_fequal))), _1524324)))], (47130 ^ _782476) ^ [_1729722, _1729724, _1729726, _1729728, _1729730, _1729732] : [class_Orderings_Olinorder(_1729722), -(hBOOL(hAPP(_1729724, _1729726))), -(hAPP(c_List_Ofilter(_1729728, _1729724), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1729728, _1729722, _1729730), _1729726), _1729732)) = hAPP(c_List_Ofilter(_1729728, _1729724), _1729732))], (19116 ^ _782476) ^ [_1142361, _1142363, _1142365] : [class_Rings_Olinordered__semiring__strict(_1142361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142361), c_Groups_Ozero__class_Ozero(_1142361)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142361), _1142363), _1142365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142361), c_Groups_Ozero__class_Ozero(_1142361)), _1142365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142361), c_Groups_Ozero__class_Ozero(_1142361)), _1142363)))], (13680 ^ _782476) ^ [_1036097, _1036099, _1036101, _1036103, _1036105, _1036107, _1036109, _1036111] : [hAPP(c_Fun_Ocomp(_1036097, _1036099, _1036101, _1036103), _1036105) = hAPP(c_Fun_Ocomp(_1036107, _1036099, _1036101, _1036109), _1036111), 13683 ^ _782476 : [(13684 ^ _782476) ^ [_1036212] : [-(hAPP(_1036103, hAPP(_1036105, _1036212)) = hAPP(_1036109, hAPP(_1036111, _1036212)))]]], (50549 ^ _782476) ^ [_1804650] : [-(c_Relation_Otrans(tc_fun(_1804650, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1804650)))], (48816 ^ _782476) ^ [_1765271, _1765273, _1765275, _1765277, _1765279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1765271, _1765273)), hAPP(_1765271, _1765275))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765277, _1765277)), hAPP(hAPP(c_Product__Type_OPair(_1765277, _1765277), _1765273), _1765275)), c_List_Omeasures(_1765277, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1765277, tc_Nat_Onat)), _1765271), _1765279)))))], (19526 ^ _782476) ^ [_1149555, _1149557] : [class_Groups_Ogroup__add(_1149555), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149555), _1149557), hAPP(c_Groups_Ouminus__class_Ouminus(_1149555), _1149557)) = c_Groups_Ozero__class_Ozero(_1149555))], (26924 ^ _782476) ^ [_1290853, _1290855, _1290857, _1290859] : [class_Orderings_Olinorder(_1290853), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290853), _1290855), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290853), _1290857), _1290859)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290853), _1290857), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290853), _1290855), _1290859)))], (32658 ^ _782476) ^ [_1400910, _1400912] : [-(_1400910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1400912, _1400910) = c_Nitpick_Onat__gcd(_1400910, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400912, _1400910)))], (32373 ^ _782476) ^ [_1395636, _1395638, _1395640, _1395642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395638), _1395640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395640), 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), _1395638), _1395636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395638), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395642, _1395636))), _1395640))))], (22168 ^ _782476) ^ [_1198981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198981)), _1198981))], (40005 ^ _782476) ^ [_1560227, _1560229] : [-(hAPP(c_Set_Ovimage(_1560227, _1560227, c_Fun_Oid(_1560227)), _1560229) = _1560229)], (47622 ^ _782476) ^ [_1740642, _1740644, _1740646] : [class_Orderings_Olinorder(_1740642), c_List_Olinorder__class_Osorted(_1740642, _1740644), -(c_List_Olinorder__class_Osorted(_1740642, c_List_Oremove1(_1740642, _1740646, _1740644)))], (45410 ^ _782476) ^ [_1691330, _1691332] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691330)), hAPP(c_List_Otl(_1691330), _1691332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691330)), _1691332)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (20651 ^ _782476) ^ [_1170767, _1170769] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170767)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170769)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170767), _1170769)))], (36294 ^ _782476) ^ [_1467307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467307)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1467307) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (33974 ^ _782476) ^ [_1426612, _1426614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426612), _1426614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426612)), c_Int_OBit1(_1426614))))], (16373 ^ _782476) ^ [_1090694, _1090696, _1090698, _1090700] : [class_Rings_Ocomm__semiring__1(_1090694), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090694), _1090696), _1090698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090694), _1090700), _1090698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090694), _1090696), _1090700)), _1090698))], (23133 ^ _782476) ^ [_1216786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216786)), -(_1216786 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216786), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (23157 ^ _782476) ^ [_1217168] : [-(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, _1217168)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37742 ^ _782476) ^ [_1500856, _1500858, _1500860, _1500862, _1500864] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500856, _1500858, _1500860), _1500862), _1500864) = hAPP(hAPP(_1500862, hAPP(c_Product__Type_Ofst(_1500856, _1500858), _1500864)), hAPP(c_Product__Type_Osnd(_1500856, _1500858), _1500864)))], (27072 ^ _782476) ^ [_1294336, _1294338, _1294340] : [class_Groups_Ocomm__monoid__mult(_1294336), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294338, _1294336), hAPP(c_COMBK(_1294336, _1294338), c_Groups_Oone__class_Oone(_1294336))), _1294340) = c_Groups_Oone__class_Oone(_1294336))], (39997 ^ _782476) ^ [_1560096, _1560098] : [-(hAPP(c_Set_Oimage(_1560096, _1560096, c_Fun_Oid(_1560096)), _1560098) = _1560098)], (23159 ^ _782476) ^ [_1217205, _1217207] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217205), _1217207)), -(hAPP(c_Finite__Set_Ocard(_1217205), _1217207) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217205, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217205), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217207))], (32946 ^ _782476) ^ [_1407282, _1407284] : [class_Int_Onumber__ring(_1407282), 32949 ^ _782476 : [(32956 ^ _782476) ^ [] : [-(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), _1407284)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407282), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407284)) = c_Groups_Ozero__class_Ozero(_1407282))], (32950 ^ _782476) ^ [] : [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), _1407284))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407282), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407284)) = hAPP(c_Int_Onumber__class_Onumber__of(_1407282), _1407284))]]], (36523 ^ _782476) ^ [_1476124, _1476126, _1476128, _1476130, _1476132, _1476134] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476124, _1476126), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476128), _1476130))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476124, _1476126), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476132), _1476134))), -(_1476126 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476128 = _1476132)], (49635 ^ _782476) ^ [_1783859, _1783861, _1783863] : [c_Fun_Oinj__on(_1783859, _1783861, _1783863, c_Orderings_Otop__class_Otop(tc_fun(_1783859, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1783861, _1783859, c_Hilbert__Choice_Oinv__into(_1783859, _1783861, c_Orderings_Otop__class_Otop(tc_fun(_1783859, tc_HOL_Obool)), _1783863)), c_Orderings_Otop__class_Otop(tc_fun(_1783861, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783859, tc_HOL_Obool)))], (42439 ^ _782476) ^ [_1618236, _1618238, _1618240, _1618242, _1618244, _1618246] : [c_Finite__Set_Ofun__left__comm(_1618236, _1618238, _1618240), -(hAPP(hAPP(_1618240, _1618242), hAPP(hAPP(_1618240, _1618244), _1618246)) = hAPP(hAPP(_1618240, _1618244), hAPP(hAPP(_1618240, _1618242), _1618246)))], (35894 ^ _782476) ^ [_1460505, _1460507, _1460509] : [class_Rings_Olinordered__idom(_1460505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460505), _1460507), c_Groups_Ozero__class_Ozero(_1460505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460505), hAPP(hAPP(c_Power_Opower__class_Opower(_1460505), _1460507), 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)))), _1460509)))), c_Groups_Ozero__class_Ozero(_1460505))))], (47167 ^ _782476) ^ [_1730405, _1730407, _1730409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730405, tc_HOL_Obool)), hAPP(c_List_Oset(_1730405), hAPP(c_List_Ofilter(_1730405, _1730407), _1730409))), hAPP(c_List_Oset(_1730405), _1730409))))], (39489 ^ _782476) ^ [_1544209, _1544211, _1544213, _1544215, _1544217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544209, _1544211)), hAPP(hAPP(c_Product__Type_OPair(_1544209, _1544211), _1544213), _1544215)), _1544217)), -(hBOOL(hAPP(hAPP(c_member(_1544211), _1544215), hAPP(c_Relation_ORange(_1544209, _1544211), _1544217))))], (36936 ^ _782476) ^ [_1485843, _1485845, _1485847, _1485849] : [-(c_HOL_OThe(tc_prod(_1485843, _1485845), hAPP(c_Product__Type_Oprod_Oprod__case(_1485843, _1485845, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1485843, tc_fun(_1485845, tc_HOL_Obool), tc_fun(_1485845, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1485845, tc_HOL_Obool), tc_fun(_1485845, tc_HOL_Obool)), _1485843), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1485845)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1485843), c_fconj), hAPP(c_fequal, _1485847)))), hAPP(c_fequal, _1485849)))) = hAPP(hAPP(c_Product__Type_OPair(_1485843, _1485845), _1485847), _1485849))], (8939 ^ _782476) ^ [_938651, _938653, _938655, _938657] : [class_Lattices_Odistrib__lattice(_938651), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938651), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938651), _938653), _938655)), _938657) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938651), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938651), _938653), _938657)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938651), _938655), _938657)))], (44722 ^ _782476) ^ [_1675543, _1675545, _1675547, _1675549, _1675551] : [hAPP(hAPP(c_List_Oappend(_1675543), _1675545), _1675547) = hAPP(hAPP(c_List_Oappend(_1675543), _1675549), _1675551), 44728 ^ _782476 : [(44731 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675543), 44725 ^ [_1675543, _1675545, _1675547, _1675549, _1675551]), _1675547) = _1675551)], (44729 ^ _782476) ^ [] : [-(_1675545 = hAPP(hAPP(c_List_Oappend(_1675543), _1675549), 44725 ^ [_1675543, _1675545, _1675547, _1675549, _1675551]))]], 44732 ^ _782476 : [(44735 ^ _782476) ^ [] : [-(_1675547 = hAPP(hAPP(c_List_Oappend(_1675543), 44725 ^ [_1675543, _1675545, _1675547, _1675549, _1675551]), _1675551))], (44733 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675543), _1675545), 44725 ^ [_1675543, _1675545, _1675547, _1675549, _1675551]) = _1675549)]]], (17423 ^ _782476) ^ [_1112939, _1112941] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112939), _1112941) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112941), _1112939))], (17668 ^ _782476) ^ [_1117490, _1117492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117490), _1117492)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117492), _1117490)) = _1117490)], (37002 ^ _782476) ^ [_1487265, _1487267] : [-(c_Divides_OnegDivAlg(_1487265, _1487267) = hAPP(c_Divides_Oadjust(_1487267), c_Divides_OnegDivAlg(_1487265, 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)))), _1487267)))), -(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), _1487265), _1487267)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487267), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10589 ^ _782476) ^ [_975956, _975958, _975960, _975962] : [-(hBOOL(hAPP(hAPP(c_member(_975956), _975958), _975960))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975956, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975956), _975958), _975962)), _975960) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975956, tc_HOL_Obool)), _975962), _975960))], (14150 ^ _782476) ^ [_1045978, _1045980, _1045982] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045978), _1045980)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045978), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045978, tc_HOL_Obool)), _1045980), _1045982))))], (6875 ^ _782476) ^ [_895055, _895057, _895059] : [hBOOL(hAPP(hAPP(c_member(_895055), _895057), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895055, tc_HOL_Obool)), _895059))), hBOOL(hAPP(hAPP(c_member(_895055), _895057), _895059))], (41138 ^ _782476) ^ [_1587976] : [-(c_Transitive__Closure_Ortrancl(_1587976, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587976, _1587976), tc_HOL_Obool))) = c_Relation_OId(_1587976))], (26822 ^ _782476) ^ [_1288868] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288868), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48459 ^ _782476) ^ [_1757467, _1757469, _1757471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757467)), c_List_OdropWhile(_1757467, _1757469, _1757471))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757467)), _1757471))))], (22706 ^ _782476) ^ [_1208424, _1208426, _1208428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208424), _1208426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208424, tc_HOL_Obool)), _1208428), _1208426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208424), _1208428)), hAPP(c_Finite__Set_Ocard(_1208424), _1208426))))], (13510 ^ _782476) ^ [_1032595, _1032597, _1032599, _1032601] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032595, _1032597, _1032599, _1032601, c_Orderings_Obot__class_Obot(tc_fun(_1032595, tc_HOL_Obool))), _1032601)))], (50509 ^ _782476) ^ [_1803962] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803962, tc_HOL_Obool) = c_Set_OBex(_1803962))], (36218 ^ _782476) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (13812 ^ _782476) ^ [_1038793, _1038795, _1038797, _1038799, _1038801, _1038803] : [c_Fun_Oinj__on(_1038793, _1038795, hAPP(c_Fun_Ocomp(_1038797, _1038795, _1038793, _1038799), _1038801), _1038803), -(c_Fun_Oinj__on(_1038797, _1038795, _1038799, hAPP(c_Set_Oimage(_1038793, _1038797, _1038801), _1038803)))], (22310 ^ _782476) ^ [_1201439, _1201441] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1201439), _1201441))), -(hAPP(c_Finite__Set_Ocard(_1201439), _1201441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50137 ^ _782476) ^ [_1794948, _1794950, _1794952, _1794954, _1794956] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1794948, _1794950, _1794952, _1794954, _1794956) = c_Option_Ooption_Ooption__case(_1794948, tc_prod(_1794950, tc_Lazy__Sequence_Olazy__sequence(_1794950)), _1794952, hAPP(c_Product__Type_Oprod_Oprod__case(_1794950, tc_Lazy__Sequence_Olazy__sequence(_1794950), _1794948), _1794954), hAPP(c_Lazy__Sequence_Oyield(_1794950), _1794956)))], (30913 ^ _782476) ^ [_1368369, _1368371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368369), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30916 ^ _782476 : [(30923 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368371), _1368369)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30917 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368371), _1368369)), 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)), _1368371)))]]], (26408 ^ _782476) ^ [_1281576, _1281578, _1281580] : [class_Orderings_Olinorder(_1281576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281576), _1281578), _1281580)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281576), _1281580), _1281578) = _1281580)], (43151 ^ _782476) ^ [_1637104, _1637106, _1637108, _1637110] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637104), tc_List_Olist(_1637104))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637104), tc_List_Olist(_1637104)), _1637106), _1637108)), c_List_Olistrel(_1637104, _1637110))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637104), tc_List_Olist(_1637104))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637104), tc_List_Olist(_1637104)), _1637106), _1637108)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637104), c_List_Olistrel1(_1637104, _1637110)))))], (3942 ^ _782476) ^ [_841805, _841807, _841809, _841811, _841813, _841815, _841817, _841819] : [-(c_New__DSequence_Oneg__decr__bind(_841819, _841815, _841811, _841807) = c_New__DSequence_Oneg__decr__bind(_841817, _841813, _841809, _841805)), _841819 = _841817, _841815 = _841813, _841811 = _841809, _841807 = _841805], (42883 ^ _782476) ^ [_1628862, _1628864, _1628866, _1628868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628862), tc_List_Olist(_1628862))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628862), tc_List_Olist(_1628862)), _1628864), _1628866)), c_List_Olex(_1628862, _1628868))), 42886 ^ _782476 : [(42889 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628862)), _1628864) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628862)), _1628866))], (42887 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628862), tc_List_Olist(_1628862))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628862), tc_List_Olist(_1628862)), _1628864), _1628866)), c_List_Olexord(_1628862, _1628868))))]]], (41629 ^ _782476) ^ [_1599801, _1599803, _1599805] : [c_Relation_Ototal__on(_1599801, _1599803, hAPP(c_Relation_Oconverse(_1599801, _1599801), _1599805)), -(c_Relation_Ototal__on(_1599801, _1599803, _1599805))], (37517 ^ _782476) ^ [_1496429, _1496431, _1496433, _1496435, _1496437, _1496439] : [hAPP(c_Product__Type_Oapsnd(_1496429, _1496431, _1496433, _1496435), _1496437) = hAPP(c_Product__Type_Oapsnd(_1496429, _1496431, _1496433, _1496439), _1496437), -(hAPP(_1496435, hAPP(c_Product__Type_Osnd(_1496433, _1496429), _1496437)) = hAPP(_1496439, hAPP(c_Product__Type_Osnd(_1496433, _1496429), _1496437)))], (2222 ^ _782476) ^ [_814983, _814985] : [_814985 = _814983, -(c_SetInterval_Oord__class_OatLeast(_814985) = c_SetInterval_Oord__class_OatLeast(_814983))], (45547 ^ _782476) ^ [_1694225, _1694227, _1694229, _1694231] : [class_Complete__Lattice_Ocomplete__lattice(_1694225), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694227, _1694225), hAPP(c_List_Oset(_1694227), _1694229)), _1694231) = hAPP(c_List_Ofoldl(_1694225, _1694227, hAPP(c_COMBC(_1694227, _1694225, _1694225), hAPP(hAPP(c_COMBB(_1694225, tc_fun(_1694225, _1694225), _1694227), c_Lattices_Osemilattice__sup__class_Osup(_1694225)), _1694231)), c_Orderings_Obot__class_Obot(_1694225)), _1694229))], (43697 ^ _782476) ^ [_1653022, _1653024, _1653026, _1653028, _1653030, _1653032] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653022, _1653024)), hAPP(hAPP(c_Product__Type_OPair(_1653022, _1653024), _1653026), _1653028)), hAPP(c_List_Oset(tc_prod(_1653022, _1653024)), hAPP(hAPP(c_List_Ozip(_1653022, _1653024), _1653030), _1653032)))), -(hBOOL(hAPP(hAPP(c_member(_1653024), _1653028), hAPP(c_List_Oset(_1653024), _1653032))))], (47590 ^ _782476) ^ [_1740198] : [class_Orderings_Olinorder(_1740198), -(c_List_Olinorder__class_Osorted(_1740198, c_List_Olist_ONil(_1740198)))], (8409 ^ _782476) ^ [_927861, _927863, _927865, _927867, _927869] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_927861, tc_fun(_927863, tc_HOL_Obool)), _927865), hAPP(hAPP(c_COMBS(_927861, tc_fun(_927863, tc_HOL_Obool), tc_fun(_927863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_927863, tc_HOL_Obool), tc_fun(tc_fun(_927863, tc_HOL_Obool), tc_fun(_927863, tc_HOL_Obool)), _927861), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927863, tc_HOL_Obool))), _927867)), _927869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927863, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927863, tc_HOL_Obool), hAPP(c_Set_Oimage(_927861, tc_fun(_927863, tc_HOL_Obool), _927867), _927865))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927863, tc_HOL_Obool), hAPP(c_Set_Oimage(_927861, tc_fun(_927863, tc_HOL_Obool), _927869), _927865))))], (35818 ^ _782476) ^ [_1458808, _1458810, _1458812] : [class_Int_Onumber__ring(_1458808), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1458808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458808), _1458810), _1458812)), 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(_1458808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458808), hAPP(hAPP(c_Power_Opower__class_Opower(_1458808), _1458810), 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(_1458808), _1458812), 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(_1458808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458808), hAPP(c_Int_Onumber__class_Onumber__of(_1458808), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1458810)), _1458812)))], (21079 ^ _782476) ^ [_1178690, _1178692] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178690), _1178692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178692), _1178690))], (27287 ^ _782476) ^ [_1298251, _1298253] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298251)), _1298253) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298251), 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), _1298251)), _1298253))], (20581 ^ _782476) ^ [_1169506, _1169508] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169506)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169508), 20584 ^ _782476 : [(20587 ^ _782476) ^ [] : [-(_1169508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20585 ^ _782476) ^ [] : [-(_1169506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7822 ^ _782476) ^ [_915061, _915063, _915065, _915067, _915069] : [class_Lattices_Olattice(_915061), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915063, _915061)), _915065), _915067), _915069) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915061), hAPP(_915065, _915069)), hAPP(_915067, _915069)))], (568 ^ _782476) ^ [_791124, _791126, _791128, _791130, _791132, _791134, _791136, _791138] : [-(c_List_Olistrelp(_791136, _791132, _791128, _791124)), c_List_Olistrelp(_791138, _791134, _791130, _791126), _791138 = _791136, _791134 = _791132, _791130 = _791128, _791126 = _791124], (41603 ^ _782476) ^ [_1599363] : [-(c_Relation_Osingle__valued(_1599363, _1599363, c_Relation_OId(_1599363)))], (34224 ^ _782476) ^ [_1431049, _1431051] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431049))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431049)), _1431051) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1431051))], (51578 ^ _782476) ^ [_1827801] : [-(c_Lazy__Sequence_Oflat(_1827801, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1827801))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1827801))], (40698 ^ _782476) ^ [_1577072, _1577074, _1577076] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577072, _1577074), _1577076) = c_Hilbert__Choice_OEps(tc_prod(_1577072, _1577074), hAPP(c_Product__Type_Oprod_Oprod__case(_1577072, _1577074, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1577074, tc_prod(_1577072, _1577074)), tc_fun(_1577074, tc_HOL_Obool), _1577072), hAPP(c_COMBB(tc_prod(_1577072, _1577074), tc_HOL_Obool, _1577074), _1577076)), c_Product__Type_OPair(_1577072, _1577074)))))], (16535 ^ _782476) ^ [_1094038, _1094040, _1094042, _1094044] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094038), _1094040), _1094042)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094038), _1094044), _1094042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094038), _1094040), _1094044)))], (31906 ^ _782476) ^ [_1386712, _1386714, _1386716] : [class_Divides_Osemiring__div(_1386712), -(c_Divides_Odiv__class_Omod(_1386712, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386712), _1386714), _1386716), _1386716) = c_Divides_Odiv__class_Omod(_1386712, _1386714, _1386716))], (21991 ^ _782476) ^ [_1196185, _1196187] : [hAPP(c_Nat_OSuc, _1196185) = hAPP(c_Nat_OSuc, _1196187), -(_1196185 = _1196187)], (12788 ^ _782476) ^ [_1016787, _1016789, _1016791, _1016793, _1016795] : [c_Fun_Oinj__on(_1016787, _1016789, _1016791, _1016793), -(c_Fun_Oinj__on(_1016787, _1016789, _1016791, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016787, tc_HOL_Obool)), _1016793), _1016795)))], (45354 ^ _782476) ^ [_1690183, _1690185, _1690187] : [-(c_List_Orotate(_1690183, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690185), _1690187)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1690183), tc_List_Olist(_1690183), tc_List_Olist(_1690183), c_List_Orotate(_1690183, _1690185)), c_List_Orotate(_1690183, _1690187)))], (26584 ^ _782476) ^ [_1284608, _1284610, _1284612] : [class_Orderings_Olinorder(_1284608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284608), _1284610), _1284612)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284608), _1284610), _1284612) = _1284610)], (44480 ^ _782476) ^ [_1669515, _1669517] : [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), _1669515), _1669517))), 44483 ^ _782476 : [(44490 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669515), _1669517))), -(c_List_Oupto(_1669515, _1669517) = c_List_Olist_ONil(tc_Int_Oint))], (44484 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669515), _1669517)), -(c_List_Oupto(_1669515, _1669517) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1669515), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1669515), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1669517)))]]], (15736 ^ _782476) ^ [_1076978, _1076980, _1076982] : [-(hAPP(c_Finite__Set_Ofold1(_1076978, _1076980), _1076982) = c_HOL_OThe(_1076978, c_Finite__Set_Ofold1Set(_1076978, _1076980, _1076982)))], (38929 ^ _782476) ^ [_1530654, _1530656, _1530658, _1530660] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530654, _1530656, _1530658), _1530660), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530656, _1530658), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530654, _1530658), tc_HOL_Obool)))], (44775 ^ _782476) ^ [_1676906, _1676908, _1676910] : [_1676906 = c_List_Olist_ONil(_1676908), -(c_List_Obutlast(_1676908, hAPP(hAPP(c_List_Oappend(_1676908), _1676910), _1676906)) = c_List_Obutlast(_1676908, _1676910))], (2606 ^ _782476) ^ [_820877, _820879] : [_820879 = _820877, -(c_Int_Oint__ge__less__than(_820879) = c_Int_Oint__ge__less__than(_820877))], (10701 ^ _782476) ^ [_978343, _978345] : [class_Complete__Lattice_Ocomplete__lattice(_978343), -(c_Complete__Lattice_OSup__class_OSup(_978343, hAPP(hAPP(c_Set_Oinsert(_978343), _978345), c_Orderings_Obot__class_Obot(tc_fun(_978343, tc_HOL_Obool)))) = _978345)], (28814 ^ _782476) ^ [_1329937, _1329939, _1329941, _1329943, _1329945] : [class_Fields_Ofield(_1329937), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329937), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329939, _1329937), _1329941), _1329943)), _1329945) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329939, _1329937), hAPP(hAPP(c_COMBC(_1329939, _1329937, _1329937), hAPP(hAPP(c_COMBB(_1329937, tc_fun(_1329937, _1329937), _1329939), c_Rings_Oinverse__class_Odivide(_1329937)), _1329941)), _1329945)), _1329943))], (48084 ^ _782476) ^ [_1749532, _1749534, _1749536] : [-(hAPP(c_List_Orev(_1749532), hAPP(hAPP(c_List_Oappend(_1749532), _1749534), _1749536)) = hAPP(hAPP(c_List_Oappend(_1749532), hAPP(c_List_Orev(_1749532), _1749536)), hAPP(c_List_Orev(_1749532), _1749534)))], (47114 ^ _782476) ^ [_1729030, _1729032, _1729034, _1729036] : [-(c_List_Otranspose(_1729030, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729030)), hAPP(hAPP(c_List_Olist_OCons(_1729030), _1729032), _1729034)), _1729036)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729030)), hAPP(hAPP(c_List_Olist_OCons(_1729030), _1729032), c_List_Oconcat(_1729030, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729030), tc_List_Olist(_1729030)), c_List_Olist_Olist__case(tc_List_Olist(_1729030), _1729030, c_List_Olist_ONil(_1729030), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729030), tc_fun(tc_List_Olist(_1729030), tc_List_Olist(_1729030)), _1729030), c_COMBK(tc_List_Olist(_1729030), tc_List_Olist(_1729030))), hAPP(hAPP(c_COMBC(_1729030, tc_List_Olist(_1729030), tc_List_Olist(_1729030)), c_List_Olist_OCons(_1729030)), c_List_Olist_ONil(_1729030))))), _1729036)))), c_List_Otranspose(_1729030, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729030)), _1729034), c_List_Oconcat(tc_List_Olist(_1729030), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729030), tc_List_Olist(tc_List_Olist(_1729030))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1729030)), _1729030, c_List_Olist_ONil(tc_List_Olist(_1729030)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1729030), tc_List_Olist(tc_List_Olist(_1729030))), _1729030), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729030), tc_List_Olist(tc_List_Olist(_1729030)), tc_List_Olist(tc_List_Olist(_1729030))), c_List_Olist_OCons(tc_List_Olist(_1729030))), c_List_Olist_ONil(tc_List_Olist(_1729030)))))), _1729036))))))], (20872 ^ _782476) ^ [_1175058, _1175060] : [_1175058 = _1175060, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175058) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175060))], (6076 ^ _782476) ^ [_878638, _878640, _878642] : [_878638 = _878640, 6079 ^ _782476 : [(6082 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878642, tc_HOL_Obool)), _878640), _878638)))], (6080 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878642, tc_HOL_Obool)), _878638), _878640)))]]], (50859 ^ _782476) ^ [_1811830, _1811832] : [-(c_Relation_Oantisym(_1811830, c_Relation_OId__on(_1811830, _1811832)))], (44787 ^ _782476) ^ [_1677075, _1677077] : [-(hAPP(hAPP(c_List_Oappend(_1677075), c_List_Olist_ONil(_1677075)), _1677077) = _1677077)], (46772 ^ _782476) ^ [_1721247, _1721249, _1721251, _1721253] : [c_List_Olist__all2(_1721247, _1721249, _1721251, _1721253, c_List_Olist_ONil(_1721249)), -(_1721253 = c_List_Olist_ONil(_1721247))], (17740 ^ _782476) ^ [_1118792, _1118794, _1118796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118792), _1118794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118792), _1118796)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118794), _1118796))))], (37560 ^ _782476) ^ [_1497343, _1497345, _1497347] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497343, _1497345), _1497347)), 37563 ^ _782476 : [(37564 ^ _782476) ^ [_1497428] : [hBOOL(hAPP(hAPP(_1497345, _1497428), _1497347)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497343, _1497345), _1497428)))]]], (47212 ^ _782476) ^ [_1731315, _1731317, _1731319] : [hBOOL(hAPP(c_List_Odistinct(_1731315), _1731317)), -(hBOOL(hAPP(c_List_Odistinct(_1731315), hAPP(c_List_Ofilter(_1731315, _1731319), _1731317))))], (40516 ^ _782476) ^ [_1572206, _1572208] : [40518 ^ _782476 : [(40521 ^ _782476) ^ [] : [hBOOL(hAPP(_1572206, hAPP(c_Int_OAbs__Integ, 40517 ^ [_1572206, _1572208])))], (40519 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40517 ^ [_1572206, _1572208]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1572206, _1572208)))], (16133 ^ _782476) ^ [_1085399, _1085401, _1085403, _1085405] : [-(hBOOL(hAPP(hAPP(c_member(_1085399), _1085401), _1085403))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085399, tc_Nat_Onat), _1085405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085399, tc_HOL_Obool)), _1085403), hAPP(hAPP(c_Set_Oinsert(_1085399), _1085401), c_Orderings_Obot__class_Obot(tc_fun(_1085399, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085399, tc_Nat_Onat), _1085405), _1085403))], (26102 ^ _782476) ^ [_1276088] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1276088))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1276088)) = _1276088)], (32752 ^ _782476) ^ [_1403026, _1403028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403028)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1403026), hAPP(c_Int_Onat, _1403028)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1403026, _1403028)))], (14375 ^ _782476) ^ [_1050216, _1050218, _1050220, _1050222, _1050224, _1050226] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1050216, _1050218, _1050220, _1050222, _1050224), _1050226)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050216), _1050224)))], (32106 ^ _782476) ^ [_1390591, _1390593] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390591, _1390593) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1390591 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390593), 32109 ^ [_1390591, _1390593]))], (12796 ^ _782476) ^ [_1016938, _1016940, _1016942, _1016944] : [-(c_Nitpick_Ofold__graph_H(_1016938, _1016940, _1016942, _1016944, c_Orderings_Obot__class_Obot(tc_fun(_1016938, tc_HOL_Obool)), _1016944))], (30754 ^ _782476) ^ [_1365403, _1365405, _1365407, _1365409] : [class_Fields_Olinordered__field(_1365403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365403), _1365405), c_Groups_Ozero__class_Ozero(_1365403))), 30761 ^ _782476 : [(30768 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365403), _1365409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365403), _1365407), _1365405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365403), _1365407), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365403), _1365409), _1365405))))], (30762 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365403), _1365407), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365403), _1365409), _1365405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365403), _1365409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365403), _1365407), _1365405))))]]], (52541 ^ _782476) ^ [_1842130, _1842132] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1842130, _1842132)))], (42087 ^ _782476) ^ [_1611483, _1611485, _1611487, _1611489, _1611491, _1611493] : [c_Finite__Set_Ofun__left__comm__idem(_1611483, _1611485, _1611487), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611483), _1611489)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611483, _1611485, _1611487), _1611491), hAPP(hAPP(c_Set_Oinsert(_1611483), _1611493), _1611489)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611483, _1611485, _1611487), hAPP(hAPP(_1611487, _1611493), _1611491)), _1611489))], (48713 ^ _782476) ^ [_1762657, _1762659, _1762661] : [hBOOL(hAPP(hAPP(c_member(_1762657), _1762659), hAPP(c_List_Oset(_1762657), _1762661))), -(c_List_Oinsert(_1762657, _1762659, _1762661) = _1762661)], (45793 ^ _782476) ^ [_1698988, _1698990, _1698992] : [_1698988 = c_List_Olist_ONil(_1698990), -(c_List_Olast(_1698990, hAPP(hAPP(c_List_Olist_OCons(_1698990), _1698992), _1698988)) = _1698992)], (52257 ^ _782476) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (43133 ^ _782476) ^ [_1636641, _1636643] : [-(c_List_Olistrel(_1636641, c_Transitive__Closure_Ortrancl(_1636641, _1636643)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636641), c_List_Olistrel1(_1636641, _1636643)))], (22928 ^ _782476) ^ [] : [-(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))], (8411 ^ _782476) ^ [_927990, _927992, _927994] : [8413 ^ _782476 : [(8416 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_927990), 8412 ^ [_927990, _927992, _927994]), _927994))], (8414 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927990), 8412 ^ [_927990, _927992, _927994]), _927992)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927990, tc_HOL_Obool)), _927992), _927994)))], (5882 ^ _782476) ^ [_875663, _875665, _875667, _875669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875663, tc_HOL_Obool)), _875665), _875667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875663, tc_HOL_Obool)), _875667), _875669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875663, tc_HOL_Obool)), _875665), _875669)))], (50561 ^ _782476) ^ [_1804817] : [-(c_Relation_Otrans(_1804817, c_Relation_OId(_1804817)))], (37499 ^ _782476) ^ [_1496002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1496002)), 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), _1496002)) = 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), _1496002))))))], (9412 ^ _782476) ^ [_950992, _950994] : [hBOOL(hAPP(hAPP(c_member(_950992), _950994), c_Orderings_Obot__class_Obot(tc_fun(_950992, tc_HOL_Obool))))], (36675 ^ _782476) ^ [_1480224, _1480226, _1480228, _1480230, _1480232, _1480234, _1480236] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480224, _1480226), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480228), _1480230))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480232, _1480226), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480234), _1480236))), -(_1480226 = 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), _1480224), _1480232), _1480226), 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), _1480228), _1480234)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480230), _1480236)), _1480226))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480230), _1480236), _1480226)))))], (16107 ^ _782476) ^ [_1084665, _1084667, _1084669, _1084671, _1084673, _1084675] : [class_Groups_Ocomm__monoid__add(_1084665), c_Fun_Oinj__on(_1084667, _1084669, _1084671, _1084673), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084669, _1084665), _1084675), hAPP(c_Set_Oimage(_1084667, _1084669, _1084671), _1084673)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084667, _1084665), hAPP(c_Fun_Ocomp(_1084669, _1084665, _1084667, _1084675), _1084671)), _1084673))], (20383 ^ _782476) ^ [_1165659, _1165661, _1165663, _1165665, _1165667] : [class_Groups_Ocomm__monoid__add(_1165659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165661), _1165663)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165661, _1165659), _1165665), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1165661, tc_HOL_Obool)), _1165663), _1165667)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165661, _1165659), hAPP(hAPP(c_COMBC(_1165661, _1165659, _1165659), hAPP(hAPP(c_COMBS(_1165661, _1165659, tc_fun(_1165659, _1165659)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165659, tc_fun(_1165659, _1165659)), _1165661), c_If(_1165659)), hAPP(hAPP(c_COMBC(_1165661, tc_fun(_1165661, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165661)), _1165667))), _1165665)), c_Groups_Ozero__class_Ozero(_1165659))), _1165663))], (10767 ^ _782476) ^ [_979939, _979941, _979943, _979945, _979947] : [-(_979939 = c_Orderings_Obot__class_Obot(tc_fun(_979941, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_979943), _979945), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979941, tc_fun(_979943, tc_HOL_Obool)), _979939), _979947)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979941, tc_fun(_979943, tc_HOL_Obool)), _979939), hAPP(hAPP(c_COMBB(tc_fun(_979943, tc_HOL_Obool), tc_fun(_979943, tc_HOL_Obool), _979941), hAPP(c_Set_Oinsert(_979943), _979945)), _979947)))], (12384 ^ _782476) ^ [_1007400, _1007402, _1007404] : [class_Complete__Lattice_Ocomplete__lattice(_1007400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007400), _1007402), hAPP(_1007404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007400), _1007402), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007400, _1007404))))), c_Orderings_Oorder__class_Omono(_1007400, _1007400, _1007404), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007400), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007400), _1007402), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007400, _1007404))), hAPP(_1007404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007400), _1007402), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007400, _1007404))))))], (17379 ^ _782476) ^ [_1112229, _1112231, _1112233] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112229), _1112231)), _1112233) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112231), _1112233)))], (40084 ^ _782476) ^ [_1561845, _1561847, _1561849, _1561851, _1561853, _1561855] : [class_Groups_Ocomm__monoid__add(_1561845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561847), _1561849)), 40094 ^ _782476 : [(40097 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561851), hAPP(_1561853, 40093 ^ [_1561845, _1561847, _1561849, _1561851, _1561853, _1561855])))], (40095 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561847), 40093 ^ [_1561845, _1561847, _1561849, _1561851, _1561853, _1561855]), _1561849)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561847, _1561845), hAPP(hAPP(c_COMBS(_1561847, tc_fun(_1561851, tc_HOL_Obool), _1561845), hAPP(hAPP(c_COMBB(tc_fun(_1561851, _1561845), tc_fun(tc_fun(_1561851, tc_HOL_Obool), _1561845), _1561847), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561851, _1561845)), _1561855)), _1561853)), _1561849) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1561847, _1561851), _1561845), hAPP(c_Product__Type_Oprod_Oprod__case(_1561847, _1561851, _1561845), _1561855)), hAPP(hAPP(c_Product__Type_OSigma(_1561847, _1561851), _1561849), _1561853)))], (34032 ^ _782476) ^ [_1427659] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427659)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427659))], (14260 ^ _782476) ^ [_1048129, _1048131] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1048129, _1048131)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1048129, _1048131), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048131), c_Orderings_Otop__class_Otop(tc_fun(_1048131, tc_HOL_Obool)))))], (37732 ^ _782476) ^ [_1500619, _1500621, _1500623, _1500625] : [-(hAPP(c_Product__Type_Ofst(_1500619, _1500621), hAPP(hAPP(c_Product__Type_OPair(_1500619, _1500621), _1500623), _1500625)) = _1500623)], (8824 ^ _782476) ^ [_936372, _936374, _936376, _936378] : [class_Lattices_Osemilattice__inf(_936372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936372), _936374), _936376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936372), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936372), _936378), _936374)), _936376)))], (22258 ^ _782476) ^ [_1200511] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1200511)) = _1200511)], (48240 ^ _782476) ^ [_1752925, _1752927, _1752929] : [class_Orderings_Olinorder(_1752925), c_List_Olinorder__class_Osorted(_1752925, hAPP(c_List_Orev(_1752925), _1752927)), 48247 ^ _782476 : [(48254 ^ _782476) ^ [] : [-(_1752927 = c_List_Olist_ONil(_1752925)), -(c_List_Ofoldr(_1752925, _1752925, c_Orderings_Oord__class_Omax(_1752925), _1752927, _1752929) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1752925), hAPP(hAPP(c_List_Onth(_1752925), _1752927), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1752929))], (48248 ^ _782476) ^ [] : [_1752927 = c_List_Olist_ONil(_1752925), -(c_List_Ofoldr(_1752925, _1752925, c_Orderings_Oord__class_Omax(_1752925), _1752927, _1752929) = _1752929)]]], (30871 ^ _782476) ^ [_1367722, _1367724] : [class_Divides_Osemiring__div(_1367722), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367722), _1367724), c_Groups_Ozero__class_Ozero(_1367722)) = c_Groups_Ozero__class_Ozero(_1367722))], (10129 ^ _782476) ^ [_965736, _965738, _965740] : [-(hAPP(hAPP(c_Set_Oinsert(_965736), _965738), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965736, tc_HOL_Obool)), _965740), hAPP(hAPP(c_Set_Oinsert(_965736), _965738), c_Orderings_Obot__class_Obot(tc_fun(_965736, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_965736), _965738), _965740))], (44458 ^ _782476) ^ [_1669057, _1669059, _1669061, _1669063] : [-(_1669057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1669059), _1669057), hAPP(hAPP(c_List_Olist_OCons(_1669059), _1669061), _1669063)) = hAPP(hAPP(c_List_Olist_OCons(_1669059), _1669061), hAPP(hAPP(c_List_Otake(_1669059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1669057), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1669063)))], (7436 ^ _782476) ^ [_907047, _907049, _907051, _907053, _907055, _907057, _907059] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907047, tc_fun(_907049, tc_fun(_907051, tc_HOL_Obool))), _907053), _907055), _907057), _907059)), 7439 ^ _782476 : [(7440 ^ _782476) ^ [_907175] : [hBOOL(hAPP(hAPP(c_member(_907047), _907175), _907053)), -(hBOOL(hAPP(hAPP(hAPP(_907055, _907175), _907057), _907059)))]]], (23958 ^ _782476) ^ [_1231657, _1231659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231659)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231657), _1231659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231657)), hAPP(c_Int_Onat, _1231659)))], (26320 ^ _782476) ^ [_1279974, _1279976, _1279978, _1279980] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1279974), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279976, tc_Int_Oint), _1279978), _1279980)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279976, _1279974), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1279974, _1279976), c_Int_Oring__1__class_Oof__int(_1279974)), _1279978)), _1279980)), class_Groups_Ocomm__monoid__mult(_1279974), class_Rings_Oring__1(_1279974)], (24239 ^ _782476) ^ [_1236607, _1236609] : [c_Nat__Transfer_Onat__set(_1236607), c_Nat__Transfer_Onat__set(_1236609), 24246 ^ _782476 : [(24253 ^ _782476) ^ [] : [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), _1236607)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1236609))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1236607), _1236609)))], (24247 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1236607), _1236609)), -(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), _1236607)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1236609))))]]], (7631 ^ _782476) ^ [_910732, _910734, _910736] : [class_Orderings_Olinorder(_910732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910732), _910734), _910736)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910732, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910732, _910734, _910736)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_910732), _910736)) = hAPP(c_SetInterval_Oord__class_OatLeast(_910732), _910734))], (9903 ^ _782476) ^ [_960805, _960807, _960809, _960811, _960813] : [_960805 = c_Orderings_Obot__class_Obot(tc_fun(_960807, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960807, tc_fun(_960809, tc_HOL_Obool)), _960805), hAPP(hAPP(c_COMBC(_960807, tc_fun(_960809, tc_HOL_Obool), tc_fun(_960809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960809, tc_HOL_Obool), tc_fun(tc_fun(_960809, tc_HOL_Obool), tc_fun(_960809, tc_HOL_Obool)), _960807), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960809, tc_HOL_Obool))), _960811)), _960813)) = c_Orderings_Otop__class_Otop(tc_fun(_960809, tc_HOL_Obool)))], (40254 ^ _782476) ^ [_1566550, _1566552] : [c_Wellfounded_Owf(_1566550, hAPP(c_Set_OCollect(tc_prod(_1566550, _1566550)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566550, _1566550, tc_HOL_Obool), _1566552))), -(c_Wellfounded_OwfP(_1566550, _1566552))], (27345 ^ _782476) ^ [_1299630, _1299632, _1299634] : [class_Orderings_Olinorder(_1299630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299630), _1299632)), hBOOL(hAPP(hAPP(c_member(_1299630), _1299634), _1299632)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299630), _1299634), c_Big__Operators_Olinorder__class_OMin(_1299630, _1299632)) = c_Big__Operators_Olinorder__class_OMin(_1299630, _1299632))], (41208 ^ _782476) ^ [_1589719, _1589721, _1589723] : [_1589721 = _1589723, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589719, _1589719)), hAPP(hAPP(c_Product__Type_OPair(_1589719, _1589719), _1589721), _1589723)), c_Relation_OId(_1589719))))], (2262 ^ _782476) ^ [_815587, _815589, _815591, _815593] : [-(c_SMT_Oz3div(_815593, _815589) = c_SMT_Oz3div(_815591, _815587)), _815593 = _815591, _815589 = _815587], (4558 ^ _782476) ^ [_851743, _851745] : [_851745 = _851743, -(c_Lazy__Sequence_Oyieldn(_851745) = c_Lazy__Sequence_Oyieldn(_851743))], (44678 ^ _782476) ^ [_1674593, _1674595, _1674597, _1674599] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674593)), hAPP(hAPP(c_List_Oappend(_1674593), _1674595), _1674597)), c_List_Olists(_1674593, _1674599)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674593)), _1674595), c_List_Olists(_1674593, _1674599))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674593)), _1674597), c_List_Olists(_1674593, _1674599)))], (51015 ^ _782476) ^ [_1815117, _1815119] : [c_Relation_Osym(_1815117, _1815119), -(hAPP(c_Relation_Oconverse(_1815117, _1815117), _1815119) = _1815119)], (46489 ^ _782476) ^ [_1714469, _1714471] : [-(hBOOL(hAPP(c_List_Olistsp(_1714469, _1714471), c_List_Olist_ONil(_1714469))))], (29448 ^ _782476) ^ [_1341328, _1341330, _1341332] : [class_Rings_Olinordered__semidom(_1341328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341328), c_Groups_Oone__class_Oone(_1341328)), _1341330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341328), hAPP(hAPP(c_Power_Opower__class_Opower(_1341328), _1341330), _1341332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341328), _1341330), hAPP(hAPP(c_Power_Opower__class_Opower(_1341328), _1341330), _1341332)))))], (48663 ^ _782476) ^ [_1761849, _1761851, _1761853, _1761855] : [-(hAPP(c_List_OremoveAll(_1761849, _1761851), hAPP(hAPP(c_List_Oappend(_1761849), _1761853), _1761855)) = hAPP(hAPP(c_List_Oappend(_1761849), hAPP(c_List_OremoveAll(_1761849, _1761851), _1761853)), hAPP(c_List_OremoveAll(_1761849, _1761851), _1761855)))], (9314 ^ _782476) ^ [_949151, _949153] : [-(hAPP(c_Set_Oimage(_949151, _949151, c_COMBI(_949151)), _949153) = _949153)], (6241 ^ _782476) ^ [_881739, _881741, _881743, _881745, _881747] : [class_Complete__Lattice_Ocomplete__lattice(_881739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881741, tc_HOL_Obool)), _881743), _881745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881739), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881741, _881739), _881745), _881747)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881741, _881739), _881743), _881747))))], (38935 ^ _782476) ^ [_1530891, _1530893, _1530895, _1530897, _1530899, _1530901, _1530903] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530891, _1530893, _1530895), hAPP(hAPP(c_Relation_Orel__comp(_1530891, _1530897, _1530893), _1530899), _1530901)), _1530903) = hAPP(hAPP(c_Relation_Orel__comp(_1530891, _1530897, _1530895), _1530899), hAPP(hAPP(c_Relation_Orel__comp(_1530897, _1530893, _1530895), _1530901), _1530903)))], (49348 ^ _782476) ^ [_1777337, _1777339] : [-(c_FunDef_Ois__measure(_1777337, _1777339))], (38399 ^ _782476) ^ [_1516550] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516550)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1516550)], (14745 ^ _782476) ^ [_1057693, _1057695, _1057697, _1057699, _1057701, _1057703, _1057705, _1057707] : [c_Finite__Set_Ofolding(_1057693, _1057695, _1057697, _1057699), -(hAPP(c_Fun_Ocomp(_1057695, _1057695, _1057701, hAPP(_1057697, _1057703)), hAPP(c_Fun_Ocomp(_1057695, _1057695, _1057701, hAPP(_1057697, _1057705)), _1057707)) = hAPP(c_Fun_Ocomp(_1057695, _1057695, _1057701, hAPP(_1057697, _1057705)), hAPP(c_Fun_Ocomp(_1057695, _1057695, _1057701, hAPP(_1057697, _1057703)), _1057707)))], (44809 ^ _782476) ^ [_1677473, _1677475, _1677477] : [_1677473 = hAPP(hAPP(c_List_Oappend(_1677475), _1677473), _1677477), -(_1677477 = c_List_Olist_ONil(_1677475))], (25363 ^ _782476) ^ [_1256359] : [_1256359 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256359) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19991 ^ _782476) ^ [_1157761, _1157763, _1157765, _1157767] : [class_Rings_Olinordered__semiring(_1157761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157761), _1157763), _1157765)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157761), _1157767), _1157765))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157761), c_Groups_Ozero__class_Ozero(_1157761)), _1157765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157761), _1157763), _1157767)))], (48208 ^ _782476) ^ [_1752139, _1752141, _1752143] : [-(hAPP(c_List_Orotate(_1752139, _1752141), hAPP(c_List_Orev(_1752139), _1752143)) = hAPP(c_List_Orev(_1752139), hAPP(c_List_Orotate(_1752139, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752139)), _1752143)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1752141, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752139)), _1752143)))), _1752143)))], (26658 ^ _782476) ^ [_1285870, _1285872, _1285874] : [class_Orderings_Olinorder(_1285870), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285870), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285870), _1285872), _1285874)), _1285872)))], (40972 ^ _782476) ^ [_1583131, _1583133] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583131, _1583131)), c_Transitive__Closure_Otrancl(_1583131, _1583133))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583131, _1583131)), _1583133)))], (32243 ^ _782476) ^ [_1393053, _1393055, _1393057] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393053), _1393055)), _1393057) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393053), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393055), _1393057))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393053), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393055, _1393057))), _1393057)))], (41704 ^ _782476) ^ [_1601541, _1601543, _1601545] : [41706 ^ _782476 : [(41707 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601541), 41705 ^ [_1601541, _1601543, _1601545]), _1601543)))], (41712 ^ _782476) ^ [] : [41705 ^ [_1601541, _1601543, _1601545] = 41708 ^ [_1601541, _1601543, _1601545]], (41716 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601541, _1601541)), hAPP(hAPP(c_Product__Type_OPair(_1601541, _1601541), 41708 ^ [_1601541, _1601543, _1601545]), 41705 ^ [_1601541, _1601543, _1601545])), _1601545))], (41714 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601541, _1601541)), hAPP(hAPP(c_Product__Type_OPair(_1601541, _1601541), 41705 ^ [_1601541, _1601543, _1601545]), 41708 ^ [_1601541, _1601543, _1601545])), _1601545))], (41710 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601541), 41708 ^ [_1601541, _1601543, _1601545]), _1601543)))]], -(c_Relation_Ototal__on(_1601541, _1601543, _1601545))], (34784 ^ _782476) ^ [_1439779, _1439781] : [class_Int_Onumber__ring(_1439779), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439779), hAPP(c_Int_Onumber__class_Onumber__of(_1439779), _1439781)), c_Groups_Oone__class_Oone(_1439779)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1439781), c_Int_OBit1(c_Int_OPls))))], (19172 ^ _782476) ^ [_1143381, _1143383, _1143385] : [class_Rings_Olinordered__semiring__strict(_1143381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143381), c_Groups_Ozero__class_Ozero(_1143381)), _1143383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143381), c_Groups_Ozero__class_Ozero(_1143381)), _1143385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143381), c_Groups_Ozero__class_Ozero(_1143381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143381), _1143383), _1143385))))], (33146 ^ _782476) ^ [_1410847, _1410849, _1410851] : [class_Int_Onumber(_1410847), class_Orderings_Oord(_1410847), 33153 ^ _782476 : [(33160 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410847), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410849)), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410851)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410847), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410849)), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410851)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410849))], (33154 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410847), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410849)), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410851))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410847), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410849)), hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410851)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410847), _1410851))]]], (2842 ^ _782476) ^ [_824539, _824541, _824543, _824545] : [-(c_Relation_ORange(_824545, _824541) = c_Relation_ORange(_824543, _824539)), _824545 = _824543, _824541 = _824539], (10853 ^ _782476) ^ [_982183, _982185, _982187, _982189, _982191] : [-(_982183 = c_Orderings_Obot__class_Obot(tc_fun(_982185, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982187, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982185, tc_fun(_982187, tc_HOL_Obool)), _982183), _982189)), _982191) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982185, tc_fun(_982187, tc_HOL_Obool)), _982183), hAPP(hAPP(c_COMBC(_982185, tc_fun(_982187, tc_HOL_Obool), tc_fun(_982187, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_982187, tc_HOL_Obool), tc_fun(tc_fun(_982187, tc_HOL_Obool), tc_fun(_982187, tc_HOL_Obool)), _982185), c_Groups_Ominus__class_Ominus(tc_fun(_982187, tc_HOL_Obool))), _982189)), _982191)))], (39999 ^ _782476) ^ [_1560130, _1560132] : [-(c_Product__Type_Oapsnd(_1560130, _1560130, _1560132, c_Fun_Oid(_1560130)) = c_Fun_Oid(tc_prod(_1560132, _1560130)))], (256 ^ _782476) ^ [_786560, _786562] : [-(class_Fields_Olinordered__field__inverse__zero(_786560)), _786562 = _786560, class_Fields_Olinordered__field__inverse__zero(_786562)], (42987 ^ _782476) ^ [_1632185, _1632187, _1632189, _1632191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632185), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632187), _1632189))), -(hAPP(c_Random_Opick(_1632187, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632187)), _1632189), _1632191)), _1632185) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1632187), _1632189))], (20567 ^ _782476) ^ [_1169313] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169313) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1169313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50020 ^ _782476) ^ [_1792397, _1792399, _1792401] : [-(hAPP(c_List_Orev(_1792397), c_List_Oreplicate(_1792397, _1792399, _1792401)) = c_List_Oreplicate(_1792397, _1792399, _1792401))], (23310 ^ _782476) ^ [_1220087, _1220089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1220087, _1220089))))], (2458 ^ _782476) ^ [_818513, _818515, _818517, _818519, _818521, _818523, _818525, _818527, _818529, _818531] : [-(c_Product__Type_Oprod_Oprod__size(_818531, _818527, _818523, _818519, _818515) = c_Product__Type_Oprod_Oprod__size(_818529, _818525, _818521, _818517, _818513)), _818531 = _818529, _818527 = _818525, _818523 = _818521, _818519 = _818517, _818515 = _818513], (34432 ^ _782476) ^ [_1434205] : [class_Int_Onumber__ring(_1434205), -(c_Groups_Oone__class_Oone(_1434205) = hAPP(c_Int_Onumber__class_Onumber__of(_1434205), c_Int_OBit1(c_Int_OPls)))], (5052 ^ _782476) ^ [_859676, _859678, _859680, _859682, _859684, _859686] : [-(c_Relation_Orel__comp(_859686, _859682, _859678) = c_Relation_Orel__comp(_859684, _859680, _859676)), _859686 = _859684, _859682 = _859680, _859678 = _859676], (24382 ^ _782476) ^ [_1238653, _1238655] : [c_Nat__Transfer_Ois__nat(_1238653), c_Nat__Transfer_Onat__set(_1238655), 24389 ^ _782476 : [(24396 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1238653)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238655))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1238653), _1238655)))], (24390 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1238653), _1238655)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1238653)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238655))))]]], (45931 ^ _782476) ^ [_1701590, _1701592, _1701594, _1701596] : [hAPP(hAPP(c_List_Omap(_1701590, _1701592), _1701594), _1701596) = c_List_Olist_ONil(_1701592), -(_1701596 = c_List_Olist_ONil(_1701590))], (5972 ^ _782476) ^ [_877091, _877093, _877095, _877097] : [class_Orderings_Oord(_877091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877091), _877093), _877095)), _877095 = _877097, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877091), _877093), _877097)))], (25207 ^ _782476) ^ [_1253575, _1253577, _1253579] : [class_Rings_Oordered__ring__abs(_1253575), -(hAPP(c_Groups_Oabs__class_Oabs(_1253575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253575), _1253577), _1253579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253575), hAPP(c_Groups_Oabs__class_Oabs(_1253575), _1253577)), hAPP(c_Groups_Oabs__class_Oabs(_1253575), _1253579))), 25214 ^ _782476 : [(25217 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253575), _1253577), c_Groups_Ozero__class_Ozero(_1253575)))], (25215 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253575), c_Groups_Ozero__class_Ozero(_1253575)), _1253577))]], 25218 ^ _782476 : [(25221 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253575), _1253579), c_Groups_Ozero__class_Ozero(_1253575)))], (25219 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253575), c_Groups_Ozero__class_Ozero(_1253575)), _1253579))]]], (45262 ^ _782476) ^ [_1688497, _1688499, _1688501, _1688503, _1688505] : [-(hAPP(hAPP(c_List_Ozip(_1688497, _1688499), hAPP(hAPP(c_List_Oappend(_1688497), _1688501), _1688503)), _1688505) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688497, _1688499)), hAPP(hAPP(c_List_Ozip(_1688497, _1688499), _1688501), hAPP(hAPP(c_List_Otake(_1688499), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688497)), _1688501)), _1688505))), hAPP(hAPP(c_List_Ozip(_1688497, _1688499), _1688503), hAPP(hAPP(c_List_Odrop(_1688499), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688497)), _1688501)), _1688505))))], (22120 ^ _782476) ^ [_1198220, _1198222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198220), _1198222)), -(hAPP(c_Nat_OSuc, _1198220) = _1198222), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198220)), _1198222)))], (45757 ^ _782476) ^ [_1698487, _1698489, _1698491] : [_1698487 = c_List_Olist_ONil(_1698489), -(c_List_Olast(_1698489, hAPP(hAPP(c_List_Oappend(_1698489), _1698491), _1698487)) = c_List_Olast(_1698489, _1698491))], (33004 ^ _782476) ^ [_1408153, _1408155] : [class_Int_Onumber__ring(_1408153), -(hAPP(c_Int_Oring__1__class_Oof__int(_1408153), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408155)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408153), _1408155))], (38893 ^ _782476) ^ [_1528841] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1528841)), c_Int_OInteg)))], (36547 ^ _782476) ^ [_1476440] : [-(_1476440 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1476440), 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)))))], (32807 ^ _782476) ^ [_1404476, _1404478, _1404480] : [-(hAPP(c_Relation_OImage(_1404476, _1404478, _1404480), c_Orderings_Obot__class_Obot(tc_fun(_1404476, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1404478, tc_HOL_Obool)))], (22494 ^ _782476) ^ [_1204379, _1204381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204379), hAPP(c_Nat_OSuc, _1204381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204379), _1204381)))], (43312 ^ _782476) ^ [_1641978, _1641980, _1641982] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641978, _1641978)), hAPP(hAPP(c_Product__Type_OPair(_1641978, _1641978), 43313 ^ [_1641978, _1641980, _1641982]), 43313 ^ [_1641978, _1641980, _1641982])), _1641980))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641978), tc_List_Olist(_1641978))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641978), tc_List_Olist(_1641978)), _1641982), _1641982)), c_List_Olexord(_1641978, _1641980)))], (22068 ^ _782476) ^ [_1197363, _1197365] : [22069 ^ _782476 : [(22072 ^ _782476) ^ [] : [_1197363 = _1197365], (22070 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197363), _1197365))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197363), hAPP(c_Nat_OSuc, _1197365))))], (14014 ^ _782476) ^ [_1042914, _1042916, _1042918, _1042920] : [_1042918 = _1042920, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042914, _1042916, hAPP(hAPP(c_Set_Oinsert(_1042914), _1042918), c_Orderings_Obot__class_Obot(tc_fun(_1042914, tc_HOL_Obool)))), _1042920)))], (38853 ^ _782476) ^ [_1527672] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1527672) = 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), _1527672), 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))))))], (20461 ^ _782476) ^ [_1167369, _1167371, _1167373] : [class_Rings_Olinordered__ring(_1167369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167369), _1167371), _1167371)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167369), _1167373), _1167373))), c_Groups_Ozero__class_Ozero(_1167369)))], (5484 ^ _782476) ^ [_866396, _866398] : [_866398 = _866396, -(c_Groups_Ominus__class_Ominus(_866398) = c_Groups_Ominus__class_Ominus(_866396))], (41800 ^ _782476) ^ [_1604033, _1604035, _1604037, _1604039] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604033, _1604033), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1604035), _1604037)), _1604039) = hAPP(hAPP(c_Relation_Orel__comp(_1604033, _1604033, _1604033), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604033, _1604033), tc_HOL_Obool), _1604035), _1604039)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604033, _1604033), tc_HOL_Obool), _1604037), _1604039)))], (19336 ^ _782476) ^ [_1146378] : [class_Rings_Olinordered__semidom(_1146378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146378), c_Groups_Oone__class_Oone(_1146378)), c_Groups_Ozero__class_Ozero(_1146378)))], (23039 ^ _782476) ^ [_1214673, _1214675, _1214677] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214673), _1214675)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214673), _1214677)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214673), _1214675)), hAPP(c_Finite__Set_Ocard(_1214673), _1214677)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214673, tc_HOL_Obool)), _1214675), _1214677))), hAPP(c_Finite__Set_Ocard(_1214673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214673, tc_HOL_Obool)), _1214675), _1214677))))], (35790 ^ _782476) ^ [_1458289, _1458291, _1458293] : [class_Rings_Olinordered__idom(_1458289), 35793 ^ _782476 : [(35794 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458289), c_Groups_Ozero__class_Ozero(_1458289)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458289), hAPP(hAPP(c_Power_Opower__class_Opower(_1458289), _1458291), 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(_1458289), _1458293), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1458291 = c_Groups_Ozero__class_Ozero(_1458289), _1458293 = c_Groups_Ozero__class_Ozero(_1458289)], (35804 ^ _782476) ^ [] : [35805 ^ _782476 : [(35808 ^ _782476) ^ [] : [-(_1458293 = c_Groups_Ozero__class_Ozero(_1458289))], (35806 ^ _782476) ^ [] : [-(_1458291 = c_Groups_Ozero__class_Ozero(_1458289))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458289), c_Groups_Ozero__class_Ozero(_1458289)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458289), hAPP(hAPP(c_Power_Opower__class_Opower(_1458289), _1458291), 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(_1458289), _1458293), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (52021 ^ _782476) ^ [_1836130] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836130, _1836130) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1836130), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (3444 ^ _782476) ^ [_833894, _833896, _833898, _833900, _833902, _833904] : [-(c_List_Opartition(_833904, _833900, _833896) = c_List_Opartition(_833902, _833898, _833894)), _833904 = _833902, _833900 = _833898, _833896 = _833894], (35314 ^ _782476) ^ [_1449814, _1449816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449814), _1449816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449814)), c_Int_OBit0(_1449816))))], (9652 ^ _782476) ^ [_955732, _955734] : [class_Lattices_Obounded__lattice__bot(_955732), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955732), _955734), c_Orderings_Obot__class_Obot(_955732)) = _955734)], (41334 ^ _782476) ^ [_1592608, _1592610, _1592612, _1592614] : [c_Wellfounded_Owf(_1592608, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592608, _1592608)), hAPP(hAPP(c_Product__Type_OPair(_1592608, _1592608), _1592610), _1592612)), _1592614)), 41337 ^ _782476 : [(41340 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592608, _1592608)), hAPP(hAPP(c_Product__Type_OPair(_1592608, _1592608), _1592612), _1592610)), c_Transitive__Closure_Ortrancl(_1592608, _1592614)))], (41338 ^ _782476) ^ [] : [-(c_Wellfounded_Owf(_1592608, _1592614))]]], (5150 ^ _782476) ^ [_861139, _861141] : [_861141 = _861139, -(c_Orderings_Otop__class_Otop(_861141) = c_Orderings_Otop__class_Otop(_861139))], (2370 ^ _782476) ^ [_817215, _817217, _817219, _817221] : [-(c_Divides_Odivmod__int__rel(_817221, _817217) = c_Divides_Odivmod__int__rel(_817219, _817215)), _817221 = _817219, _817217 = _817215], (51727 ^ _782476) ^ [_1830509, _1830511, _1830513] : [class_Divides_Osemiring__div(_1830509), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830509), _1830511), _1830513)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830509), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830509), _1830513), _1830511)), _1830511) = _1830513)], (8707 ^ _782476) ^ [_934135] : [class_Complete__Lattice_Ocomplete__lattice(_934135), -(c_Complete__Lattice_OSup__class_OSup(_934135, c_Orderings_Otop__class_Otop(tc_fun(_934135, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_934135))], (22636 ^ _782476) ^ [_1207034] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207034) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207034)))], (34268 ^ _782476) ^ [_1431778] : [c_Int_OBit1(_1431778) = c_Int_OPls], (1322 ^ _782476) ^ [_802201, _802203] : [-(class_Groups_Ogroup__add(_802201)), _802203 = _802201, class_Groups_Ogroup__add(_802203)], (18214 ^ _782476) ^ [_1126852, _1126854] : [class_Groups_Ogroup__add(_1126852), 18217 ^ _782476 : [(18224 ^ _782476) ^ [] : [_1126854 = c_Groups_Ozero__class_Ozero(_1126852), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126852), _1126854) = c_Groups_Ozero__class_Ozero(_1126852))], (18218 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126852), _1126854) = c_Groups_Ozero__class_Ozero(_1126852), -(_1126854 = c_Groups_Ozero__class_Ozero(_1126852))]]], (46816 ^ _782476) ^ [_1722209, _1722211, _1722213, _1722215, _1722217] : [-(c_List_Olist__all2(_1722209, _1722211, _1722213, _1722215, _1722217)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722209)), _1722215) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722211)), _1722217), 46822 ^ _782476 : [(46825 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1722213, hAPP(hAPP(c_List_Onth(_1722209), _1722215), 46821 ^ [_1722209, _1722211, _1722213, _1722215, _1722217])), hAPP(hAPP(c_List_Onth(_1722211), _1722217), 46821 ^ [_1722209, _1722211, _1722213, _1722215, _1722217])))], (46823 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46821 ^ [_1722209, _1722211, _1722213, _1722215, _1722217]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722209)), _1722215))))]]], (42141 ^ _782476) ^ [_1612628, _1612630, _1612632, _1612634] : [class_Lattices_Osemilattice__inf(_1612628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612628), _1612630)), hBOOL(hAPP(hAPP(c_member(_1612628), _1612632), _1612630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612628), hAPP(hAPP(c_Finite__Set_Ofold(_1612628, _1612628, c_Lattices_Osemilattice__inf__class_Oinf(_1612628)), _1612634), _1612630)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1612628), _1612632), _1612634))))], (42421 ^ _782476) ^ [_1617903, _1617905, _1617907, _1617909, _1617911] : [c_Finite__Set_Ofun__left__comm(_1617903, _1617905, _1617907), -(hAPP(c_Fun_Ocomp(_1617905, _1617905, _1617905, hAPP(_1617907, _1617909)), hAPP(_1617907, _1617911)) = hAPP(c_Fun_Ocomp(_1617905, _1617905, _1617905, hAPP(_1617907, _1617911)), hAPP(_1617907, _1617909)))], (13312 ^ _782476) ^ [_1028282, _1028284, _1028286, _1028288] : [c_Fun_Oinj__on(_1028282, _1028284, _1028286, c_Orderings_Otop__class_Otop(tc_fun(_1028282, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1028282, _1028284, c_Orderings_Otop__class_Otop(tc_fun(_1028282, tc_HOL_Obool)), _1028286), hAPP(_1028286, _1028288)) = _1028288)], (216 ^ _782476) ^ [_786060, _786062] : [-(class_Rings_Odivision__ring__inverse__zero(_786060)), _786062 = _786060, class_Rings_Odivision__ring__inverse__zero(_786062)], (52573 ^ _782476) ^ [_1842544, _1842546] : [-(class_Nat_Osize(tc_prod(_1842544, _1842546)))], (38202 ^ _782476) ^ [_1511585, _1511587, _1511589] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511585, tc_HOL_Obool), tc_fun(_1511585, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511585, tc_HOL_Obool), tc_fun(_1511585, tc_HOL_Obool)), _1511587), _1511589)), c_Wellfounded_Ofinite__psubset(_1511585))), 38205 ^ _782476 : [(38208 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1511585), _1511589)))], (38206 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511585, tc_HOL_Obool)), _1511587), _1511589)))]]], (38586 ^ _782476) ^ [_1521403, _1521405, _1521407] : [-(c_Wellfounded_Omlex__prod(_1521403, _1521405, _1521407) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1521403), _1521403), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1521403, c_Wellfounded_Oless__than, _1521407)), hAPP(hAPP(c_COMBS(_1521403, _1521403, tc_prod(tc_Nat_Onat, _1521403)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1521403, tc_prod(tc_Nat_Onat, _1521403)), _1521403), c_Product__Type_OPair(tc_Nat_Onat, _1521403)), _1521405)), c_COMBI(_1521403))))], (50113 ^ _782476) ^ [_1794319, _1794321, _1794323, _1794325, _1794327] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1794319, _1794321, _1794323) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794319, _1794325, _1794327), 50116 ^ _782476 : [(50119 ^ _782476) ^ [] : [-(_1794323 = _1794327)], (50117 ^ _782476) ^ [] : [-(_1794321 = _1794325)]]], (52209 ^ _782476) ^ [_1838941, _1838943] : [-(class_Enum_Oenum(tc_fun(_1838941, _1838943))), class_Enum_Oenum(_1838941), class_Enum_Oenum(_1838943)], (40764 ^ _782476) ^ [_1578880, _1578882, _1578884] : [c_Wellfounded_Owf(_1578880, _1578882), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578880, _1578880)), hAPP(hAPP(c_Product__Type_OPair(_1578880, _1578880), hAPP(_1578884, hAPP(c_Nat_OSuc, 40767 ^ [_1578880, _1578882, _1578884]))), hAPP(_1578884, 40767 ^ [_1578880, _1578882, _1578884]))), _1578882))], (16961 ^ _782476) ^ [_1103513, _1103515, _1103517, _1103519] : [class_Rings_Ocomm__semiring__1(_1103513), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103513), _1103515), _1103517)), _1103519) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103513), _1103515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103513), _1103517), _1103519)))], (33912 ^ _782476) ^ [_1425505, _1425507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425505)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425505), _1425507)))], (47544 ^ _782476) ^ [_1739525] : [class_Orderings_Olinorder(_1739525), -(c_List_Olinorder__class_Osorted(_1739525, c_List_Olist_ONil(_1739525)))], (22212 ^ _782476) ^ [_1199685, _1199687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199685), _1199687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199685), hAPP(c_Nat_OSuc, _1199687))))], (5440 ^ _782476) ^ [_865750, _865752] : [_865752 = _865750, -(c_Power_Opower__class_Opower(_865752) = c_Power_Opower__class_Opower(_865750))], (322 ^ _782476) ^ [_787465, _787467, _787469, _787471] : [-(c_FunDef_Oreduction__pair(_787469, _787465)), c_FunDef_Oreduction__pair(_787471, _787467), _787471 = _787469, _787467 = _787465], (5986 ^ _782476) ^ [_877310, _877312, _877314, _877316] : [class_Orderings_Oorder(_877310), _877312 = _877314, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877310), _877316), _877314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877310), _877316), _877312)))], (6636 ^ _782476) ^ [_889471, _889473, _889475, _889477] : [_889471 = _889473, 6641 ^ _782476 : [(6644 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889475), _889477), _889473)))], (6642 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889475), _889477), _889471)))]], 6645 ^ _782476 : [(6648 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889475), _889477), _889473))], (6646 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889475), _889477), _889471))]]], (12458 ^ _782476) ^ [_1008880, _1008882, _1008884, _1008886] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008880, tc_HOL_Obool)), _1008882), hAPP(hAPP(c_Set_Oinsert(_1008880), _1008884), _1008886)))), 12461 ^ _782476 : [(12464 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008880, tc_HOL_Obool)), _1008882), _1008886))], (12462 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008880), _1008884), _1008886)))]], 12465 ^ _782476 : [(12468 ^ _782476) ^ [] : [12469 ^ _782476 : [(12472 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008880, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008880, tc_HOL_Obool)), _1008882), hAPP(hAPP(c_Set_Oinsert(_1008880), _1008884), c_Orderings_Obot__class_Obot(tc_fun(_1008880, tc_HOL_Obool))))), _1008886))], (12470 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008880), _1008884), _1008882)))]], 12473 ^ _782476 : [(12476 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008880, tc_HOL_Obool)), _1008882), _1008886))], (12474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008880), _1008884), _1008882))]]], (12466 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008880), _1008884), _1008886))]]], (17582 ^ _782476) ^ [_1115771, _1115773, _1115775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115771), _1115773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115775), _1115773))))], (40557 ^ _782476) ^ [_1572952, _1572954, _1572956, _1572958] : [-(hAPP(c_Set_OCollect(_1572952), hAPP(hAPP(c_COMBB(tc_fun(_1572954, tc_HOL_Obool), tc_HOL_Obool, _1572952), c_HOL_OAll(_1572954)), hAPP(hAPP(c_COMBB(tc_fun(_1572954, tc_HOL_Obool), tc_fun(_1572954, tc_HOL_Obool), _1572952), hAPP(c_COMBS(_1572954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572954), c_fimplies), hAPP(hAPP(c_COMBC(_1572954, tc_fun(_1572954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572954)), _1572956)))), _1572958))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572954, tc_fun(_1572952, tc_HOL_Obool)), _1572956), hAPP(hAPP(c_COMBB(tc_fun(_1572952, tc_HOL_Obool), tc_fun(_1572952, tc_HOL_Obool), _1572954), c_Set_OCollect(_1572952)), hAPP(c_COMBC(_1572952, _1572954, tc_HOL_Obool), _1572958))))], (36070 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (45709 ^ _782476) ^ [_1697645, _1697647, _1697649] : [class_Orderings_Olinorder(_1697645), hBOOL(hAPP(hAPP(c_member(_1697645), _1697647), hAPP(c_List_Oset(_1697645), _1697649))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697645, _1697645, c_COMBI(_1697645), _1697647, _1697649) = _1697649)], (18486 ^ _782476) ^ [_1130824, _1130826, _1130828] : [class_Rings_Olinordered__semidom(_1130824), 18489 ^ _782476 : [(18496 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130826), _1130828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130824), _1130826)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130824), _1130828))))], (18490 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130824), _1130826)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130824), _1130828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130826), _1130828)))]]], (35938 ^ _782476) ^ [_1461389, _1461391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1461389), 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)))), _1461391))), 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)))), _1461389)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461391), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1461389))], (47250 ^ _782476) ^ [_1732336, _1732338, _1732340] : [hBOOL(hAPP(c_List_Odistinct(_1732336), _1732338)), -(hAPP(c_List_Ofilter(_1732336, hAPP(hAPP(c_COMBC(_1732336, tc_fun(_1732336, tc_HOL_Obool), tc_HOL_Obool), c_member(_1732336)), hAPP(c_List_Oset(_1732336), c_List_Osublist(_1732336, _1732338, _1732340)))), _1732338) = c_List_Osublist(_1732336, _1732338, _1732340))], (7005 ^ _782476) ^ [_897678, _897680, _897682, _897684] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897678, tc_fun(_897680, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897678, tc_HOL_Obool), _897682)), _897684) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897678, tc_HOL_Obool), tc_fun(_897680, tc_HOL_Obool)), _897682), hAPP(hAPP(c_COMBC(tc_fun(_897678, tc_HOL_Obool), tc_fun(_897678, tc_fun(_897680, tc_HOL_Obool)), tc_fun(_897680, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897678, tc_fun(_897680, tc_HOL_Obool))), _897684)))], (7942 ^ _782476) ^ [_917693, _917695, _917697, _917699] : [class_Lattices_Osemilattice__sup(_917693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917693), _917695), _917697)), _917699)), 7949 ^ _782476 : [(7952 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917693), _917697), _917699)))], (7950 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917693), _917695), _917699)))]]], (11290 ^ _782476) ^ [_989482, _989484, _989486, _989488, _989490] : [hAPP(_989486, _989488) = _989490, -(c_Fun_Ofun__upd(_989482, _989484, _989486, _989488, _989490) = _989486)], (46870 ^ _782476) ^ [_1723506, _1723508, _1723510, _1723512, _1723514] : [c_Finite__Set_Ofun__left__comm(_1723506, _1723508, _1723510), -(hAPP(hAPP(c_Finite__Set_Ofold(_1723506, _1723508, _1723510), _1723512), hAPP(c_List_Oset(_1723506), _1723514)) = hAPP(c_List_Ofoldl(_1723508, _1723506, hAPP(c_COMBC(_1723506, _1723508, _1723508), _1723510), _1723512), c_List_Oremdups(_1723506, _1723514)))], (52267 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (17129 ^ _782476) ^ [_1107590, _1107592, _1107594, _1107596, _1107598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107590), _1107592)), 17132 ^ _782476 : [(17139 ^ _782476) ^ [] : [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), _1107592), _1107590)), _1107594)), _1107596) = _1107598, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107592), _1107594)), _1107596) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107590), _1107594)), _1107598))], (17133 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107592), _1107594)), _1107596) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107590), _1107594)), _1107598), -(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), _1107592), _1107590)), _1107594)), _1107596) = _1107598)]]], (42875 ^ _782476) ^ [_1627881, _1627883] : [-(c_List_Olenlex(_1627881, _1627883) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1627881), tc_List_Olist(_1627881), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627881), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), tc_List_Olist(_1627881)), c_COMBS(tc_List_Olist(_1627881), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627881)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627881)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627881), tc_fun(tc_List_Olist(_1627881), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627881), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), tc_List_Olist(_1627881)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627881))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627881)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1627881))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627881)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627881), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), tc_List_Olist(_1627881)), c_COMBS(tc_List_Olist(_1627881), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627881)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627881)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627881), tc_fun(tc_List_Olist(_1627881), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627881), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), tc_List_Olist(_1627881)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627881))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627881)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1627881))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627881)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627881), tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627881), tc_HOL_Obool)), tc_List_Olist(_1627881)), c_COMBC(tc_List_Olist(_1627881), tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627881), tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881))), tc_fun(tc_List_Olist(_1627881), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1627881)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1627881)), c_member(tc_prod(tc_List_Olist(_1627881), tc_List_Olist(_1627881))))), c_Product__Type_OPair(tc_List_Olist(_1627881), tc_List_Olist(_1627881))))), c_List_Olex(_1627881, _1627883)))))))], (23177 ^ _782476) ^ [_1217521, _1217523] : [class_Int_Oring__char__0(_1217521), hBOOL(hAPP(hAPP(c_member(_1217521), _1217523), c_Int_Oring__1__class_OInts(_1217521))), 23184 ^ _782476 : [(23191 ^ _782476) ^ [] : [_1217523 = c_Groups_Ozero__class_Ozero(_1217521), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217521), _1217523), _1217523) = c_Groups_Ozero__class_Ozero(_1217521))], (23185 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217521), _1217523), _1217523) = c_Groups_Ozero__class_Ozero(_1217521), -(_1217523 = c_Groups_Ozero__class_Ozero(_1217521))]]], (18738 ^ _782476) ^ [_1135425, _1135427, _1135429, _1135431] : [class_Rings_Oordered__comm__semiring(_1135425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135425), _1135427), _1135429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135425), c_Groups_Ozero__class_Ozero(_1135425)), _1135431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135431), _1135427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135431), _1135429))))], (47248 ^ _782476) ^ [_1732249, _1732251, _1732253] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1732249, tc_HOL_Obool)), hAPP(c_List_Oset(_1732249), _1732251)), hAPP(hAPP(c_Set_Oinsert(_1732249), _1732253), c_Orderings_Obot__class_Obot(tc_fun(_1732249, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1732249), hAPP(c_List_Ofilter(_1732249, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732249), c_fNot), hAPP(hAPP(c_COMBC(_1732249, _1732249, tc_HOL_Obool), c_fequal), _1732253))), _1732251)))], (36843 ^ _782476) ^ [_1483804, _1483806, _1483808, _1483810, _1483812, _1483814] : [hBOOL(hAPP(hAPP(_1483804, _1483806), _1483808)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483810, tc_fun(_1483812, tc_HOL_Obool))), _1483804), _1483814), _1483806), _1483808)))], (11878 ^ _782476) ^ [_998751, _998753, _998755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998751, tc_HOL_Obool)), _998753), _998755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998751, tc_HOL_Obool)), _998753), _998755))), -(_998753 = _998755)], (1522 ^ _782476) ^ [_804701, _804703] : [-(class_Orderings_Otop(_804701)), _804703 = _804701, class_Orderings_Otop(_804703)], (748 ^ _782476) ^ [_793894, _793896, _793898, _793900, _793902, _793904, _793906, _793908, _793910, _793912] : [-(c_Fun_Obij__betw(_793910, _793906, _793902, _793898, _793894)), c_Fun_Obij__betw(_793912, _793908, _793904, _793900, _793896), _793912 = _793910, _793908 = _793906, _793904 = _793902, _793900 = _793898, _793896 = _793894], (39538 ^ _782476) ^ [_1545398, _1545400, _1545402, _1545404, _1545406] : [-(hAPP(c_Relation_ORange(_1545398, _1545400), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1545398, _1545400)), hAPP(hAPP(c_Product__Type_OPair(_1545398, _1545400), _1545402), _1545404)), _1545406)) = hAPP(hAPP(c_Set_Oinsert(_1545400), _1545404), hAPP(c_Relation_ORange(_1545398, _1545400), _1545406)))], (23671 ^ _782476) ^ [_1227099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227099), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227099) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31870 ^ _782476) ^ [_1385920, _1385922, _1385924, _1385926] : [class_Divides_Osemiring__div(_1385920), -(c_Divides_Odiv__class_Omod(_1385920, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385920), c_Divides_Odiv__class_Omod(_1385920, _1385922, _1385924)), _1385926), _1385924) = c_Divides_Odiv__class_Omod(_1385920, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385920), _1385922), _1385926), _1385924))], (49564 ^ _782476) ^ [_1782193, _1782195, _1782197] : [hAPP(c_Set_Oimage(_1782193, _1782195, _1782197), c_Orderings_Otop__class_Otop(tc_fun(_1782193, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782195, tc_HOL_Obool)), 49567 ^ _782476 : [(49568 ^ _782476) ^ [_1782304] : [-(hAPP(_1782197, hAPP(c_Hilbert__Choice_Oinv__into(_1782193, _1782195, c_Orderings_Otop__class_Otop(tc_fun(_1782193, tc_HOL_Obool)), _1782197), _1782304)) = _1782304)]]], (36038 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25833 ^ _782476) ^ [_1267819] : [-(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)))), _1267819))))], (33882 ^ _782476) ^ [_1424858] : [-(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), _1424858)) = 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), _1424858))))], (52047 ^ _782476) ^ [_1836573, _1836575] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836573, _1836575) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836573), _1836575)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836575), _1836573)))], (16230 ^ _782476) ^ [_1087483, _1087485, _1087487, _1087489, _1087491] : [class_Groups_Ocomm__monoid__add(_1087483), class_Groups_Oordered__cancel__ab__semigroup__add(_1087483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087485), _1087487)), -(_1087487 = c_Orderings_Obot__class_Obot(tc_fun(_1087485, tc_HOL_Obool))), 16248 ^ _782476 : [(16251 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087483), hAPP(_1087489, 16247 ^ [_1087483, _1087485, _1087487, _1087489, _1087491])), hAPP(_1087491, 16247 ^ [_1087483, _1087485, _1087487, _1087489, _1087491])))], (16249 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087485), 16247 ^ [_1087483, _1087485, _1087487, _1087489, _1087491]), _1087487)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087483), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087485, _1087483), _1087489), _1087487)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087485, _1087483), _1087491), _1087487))))], (28790 ^ _782476) ^ [_1329435, _1329437] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329435), _1329437)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329435)), _1329437))], (38588 ^ _782476) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (24120 ^ _782476) ^ [_1234681, _1234683, _1234685, _1234687] : [c_Sum__Type_OPlus(_1234681, _1234683, _1234685, _1234687) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1234681, _1234683), tc_HOL_Obool)), 24123 ^ _782476 : [(24126 ^ _782476) ^ [] : [-(_1234687 = c_Orderings_Obot__class_Obot(tc_fun(_1234683, tc_HOL_Obool)))], (24124 ^ _782476) ^ [] : [-(_1234685 = c_Orderings_Obot__class_Obot(tc_fun(_1234681, tc_HOL_Obool)))]]], (22476 ^ _782476) ^ [_1204025, _1204027] : [22477 ^ _782476 : [(22478 ^ _782476) ^ [_1204078] : [_1204027 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204025), _1204078))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204025), _1204027)))], (1572 ^ _782476) ^ [_805326, _805328] : [-(class_Enum_Oenum(_805326)), _805328 = _805326, class_Enum_Oenum(_805328)], (17173 ^ _782476) ^ [_1108630, _1108632] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108630, _1108632))))], (7285 ^ _782476) ^ [_903892, _903894, _903896, _903898, _903900, _903902] : [-(hBOOL(hAPP(hAPP(c_member(_903892), _903894), c_SetInterval_Oord_OgreaterThanAtMost(_903892, _903896, _903898, _903900, _903902)))), hBOOL(hAPP(hAPP(_903898, _903900), _903894)), hBOOL(hAPP(hAPP(_903896, _903894), _903902))], (51305 ^ _782476) ^ [_1820581] : [-(_1820581 = hAPP(c_Code__Numeral_Oof__nat, 51303 ^ [_1820581]))], (17610 ^ _782476) ^ [_1116307, _1116309, _1116311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116307), _1116309)), _1116311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116307), _1116311)))], (39295 ^ _782476) ^ [_1539675] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1539675)))], (46158 ^ _782476) ^ [_1707529, _1707531, _1707533, _1707535] : [class_Rings_Osemiring__1(_1707529), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707529), hAPP(hAPP(c_List_Omap(_1707531, _1707529), hAPP(c_COMBK(_1707529, _1707531), _1707533)), _1707535)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1707529), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1707529), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707531)), _1707535))), _1707533))], (22082 ^ _782476) ^ [_1197626, _1197628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197626), _1197628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197626)), hAPP(c_Nat_OSuc, _1197628))))], (5738 ^ _782476) ^ [_870349, _870351] : [_870351 = _870349, -(tc_Hoare__Mirabelle_Otriple(_870351) = tc_Hoare__Mirabelle_Otriple(_870349))], (10401 ^ _782476) ^ [_971285, _971287, _971289] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971285, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971285, tc_HOL_Obool)), _971287), _971289)), _971289) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971285, tc_HOL_Obool)), _971287), _971289))], (20309 ^ _782476) ^ [_1164029, _1164031, _1164033, _1164035, _1164037] : [class_Groups_Ocomm__monoid__add(_1164029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1164031), _1164033)), 20316 ^ _782476 : [(20323 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164031), _1164035), _1164033))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1164031, _1164029), hAPP(hAPP(c_COMBC(_1164031, _1164029, _1164029), hAPP(hAPP(c_COMBS(_1164031, _1164029, tc_fun(_1164029, _1164029)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164029, tc_fun(_1164029, _1164029)), _1164031), c_If(_1164029)), hAPP(hAPP(c_COMBC(_1164031, _1164031, tc_HOL_Obool), c_fequal), _1164035))), _1164037)), c_Groups_Ozero__class_Ozero(_1164029))), _1164033) = c_Groups_Ozero__class_Ozero(_1164029))], (20317 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1164031), _1164035), _1164033)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1164031, _1164029), hAPP(hAPP(c_COMBC(_1164031, _1164029, _1164029), hAPP(hAPP(c_COMBS(_1164031, _1164029, tc_fun(_1164029, _1164029)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164029, tc_fun(_1164029, _1164029)), _1164031), c_If(_1164029)), hAPP(hAPP(c_COMBC(_1164031, _1164031, tc_HOL_Obool), c_fequal), _1164035))), _1164037)), c_Groups_Ozero__class_Ozero(_1164029))), _1164033) = hAPP(_1164037, _1164035))]]], (48032 ^ _782476) ^ [_1748513, _1748515] : [-(c_Fun_Oinj__on(tc_List_Olist(_1748513), tc_List_Olist(_1748513), c_List_Orev(_1748513), _1748515))], (20 ^ _782476) ^ [_782736, _782738, _782740, _782742, _782744, _782746, _782748, _782750, _782752, _782754, _782756, _782758] : [-(c_Predicate_Oinv__imagep(_782756, _782752, _782748, _782744, _782740, _782736)), c_Predicate_Oinv__imagep(_782758, _782754, _782750, _782746, _782742, _782738), _782758 = _782756, _782754 = _782752, _782750 = _782748, _782746 = _782744, _782742 = _782740, _782738 = _782736], (43251 ^ _782476) ^ [_1640302, _1640304, _1640306] : [c_Relation_Orefl__on(_1640302, _1640304, _1640306), -(c_Relation_Orefl__on(tc_List_Olist(_1640302), c_List_Olists(_1640302, _1640304), c_List_Olistrel(_1640302, _1640306)))], (19666 ^ _782476) ^ [_1151809, _1151811, _1151813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151809), _1151811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151809), _1151813))), 19669 ^ _782476 : [(19672 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151811), _1151813)))], (19670 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151809)))]]], (9640 ^ _782476) ^ [_955569, _955571, _955573, _955575] : [-(_955569 = c_Orderings_Obot__class_Obot(tc_fun(_955571, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955571, tc_fun(_955573, tc_HOL_Obool)), _955569), hAPP(c_COMBK(tc_fun(_955573, tc_HOL_Obool), _955571), _955575)) = _955575)], (35392 ^ _782476) ^ [_1451220, _1451222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451220)), c_Int_OBit1(_1451222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451220), _1451222)))], (42891 ^ _782476) ^ [_1629113, _1629115, _1629117, _1629119] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629113), tc_List_Olist(_1629113))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629113), tc_List_Olist(_1629113)), _1629115), _1629117)), c_List_Olex(_1629113, _1629119)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629113), tc_List_Olist(_1629113))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629113), tc_List_Olist(_1629113)), _1629115), _1629117)), c_List_Olexord(_1629113, _1629119))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629113)), _1629115) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629113)), _1629117)], (4868 ^ _782476) ^ [_856748, _856750] : [_856750 = _856748, -(c_DSequence_Osingle(_856750) = c_DSequence_Osingle(_856748))], (28017 ^ _782476) ^ [_1312217] : [class_Orderings_Oord(_1312217), -(c_Orderings_Oord__class_Omax(_1312217) = c_Orderings_Oord_Omax(_1312217, c_Orderings_Oord__class_Oless__eq(_1312217)))], (45825 ^ _782476) ^ [_1699450, _1699452, _1699454, _1699456] : [hAPP(hAPP(c_List_Oappend(_1699450), _1699452), hAPP(hAPP(c_List_Olist_OCons(_1699450), _1699454), c_List_Olist_ONil(_1699450))) = _1699456, 45828 ^ _782476 : [(45833 ^ _782476) ^ [] : [-(c_List_Olast(_1699450, _1699456) = _1699454)], (45831 ^ _782476) ^ [] : [-(c_List_Obutlast(_1699450, _1699456) = _1699452)], (45829 ^ _782476) ^ [] : [_1699456 = c_List_Olist_ONil(_1699450)]]], (47285 ^ _782476) ^ [_1733676, _1733678] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733676)), c_List_Otranspose__rel(_1733676)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733676)), c_List_Olist_ONil(_1733676)), _1733678))), -(c_List_Otranspose(_1733676, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733676)), c_List_Olist_ONil(_1733676)), _1733678)) = c_List_Otranspose(_1733676, _1733678))], (2044 ^ _782476) ^ [_812126, _812128, _812130, _812132, _812134, _812136] : [-(c_SetInterval_Oord_OlessThan(_812136, _812132, _812128) = c_SetInterval_Oord_OlessThan(_812134, _812130, _812126)), _812136 = _812134, _812132 = _812130, _812128 = _812126], (16595 ^ _782476) ^ [_1095201, _1095203, _1095205, _1095207] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095201), 16598 ^ _782476 : [(16605 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095201), _1095203), _1095207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095201), _1095203), _1095205)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095201), _1095207), _1095205))))], (16599 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095201), _1095203), _1095205)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095201), _1095207), _1095205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095201), _1095203), _1095207)))]]], (21610 ^ _782476) ^ [_1188196, _1188198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188196)), 21619 ^ _782476 : [(21622 ^ _782476) ^ [] : [hBOOL(hAPP(_1188198, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188196, _1188198]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188196, _1188198]), _1188196))))], (21620 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1188198, 21615 ^ [_1188196, _1188198])))]], 21623 ^ _782476 : [(21626 ^ _782476) ^ [] : [hBOOL(hAPP(_1188198, 21615 ^ [_1188196, _1188198]))], (21624 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1188198, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188196, _1188198]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188196, _1188198]), _1188196)))))]], 21627 ^ _782476 : [(21637 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1188198, 21644 ^ [_1188196, _1188198]))), 21638 ^ _782476 : [(21639 ^ _782476) ^ [_1188743] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188743), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188196))), hBOOL(hAPP(_1188198, _1188743))]]], (21628 ^ _782476) ^ [] : [21629 ^ _782476 : [(21630 ^ _782476) ^ [_1188628] : [hBOOL(hAPP(_1188198, _1188628))]], 21632 ^ _782476 : [(21635 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1188198, 21631 ^ [_1188196, _1188198])))], (21633 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21631 ^ [_1188196, _1188198]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188196))))]]]]], (7367 ^ _782476) ^ [_905553, _905555, _905557, _905559] : [hBOOL(hAPP(hAPP(_905557, _905555), _905559)), -(hBOOL(hAPP(hAPP(c_member(_905553), _905555), c_SetInterval_Oord_OlessThan(_905553, _905557, _905559))))], (13668 ^ _782476) ^ [_1035783, _1035785, _1035787, _1035789, _1035791, _1035793] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035783, _1035785, _1035787, _1035789), _1035791), _1035793) = hAPP(_1035789, hAPP(_1035791, _1035793)))], (8651 ^ _782476) ^ [_932831, _932833] : [class_Lattices_Olattice(_932831), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932831), _932833), _932833) = _932833)], (39976 ^ _782476) ^ [_1559423, _1559425, _1559427, _1559429] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559425, _1559423), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1559423, tc_prod(_1559425, _1559423), 39972 ^ [_1559423, _1559425, _1559427, _1559429]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559425, tc_fun(_1559423, tc_HOL_Obool)), _1559427), _1559429))), hAPP(hAPP(c_Product__Type_OSigma(_1559425, _1559423), _1559427), _1559429))))], (44218 ^ _782476) ^ [_1664660, _1664662, _1664664, _1664666] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664660) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1664662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664660)), hAPP(hAPP(c_List_Olist_OCons(_1664662), _1664664), _1664666)) = hAPP(hAPP(c_List_Olist_OCons(_1664662), _1664664), hAPP(hAPP(c_List_Otake(_1664662), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664660)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1664666)))], (20649 ^ _782476) ^ [_1170721, _1170723] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170721), _1170723)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170721)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170723)))], (36132 ^ _782476) ^ [_1464854] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1464854) = c_Int_Opred(_1464854))], (28740 ^ _782476) ^ [_1328342, _1328344, _1328346] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328342), _1328344)), _1328346) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328344), _1328346)))], (31488 ^ _782476) ^ [_1378308, _1378310] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378308)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378310)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378308), _1378310)))], (52695 ^ _782476) ^ [] : [hBOOL(c_fFalse)], (35326 ^ _782476) ^ [_1450040, _1450042] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450040)), c_Int_OBit1(_1450042)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450040), _1450042)))], (20467 ^ _782476) ^ [_1167513, _1167515, _1167517] : [class_Rings_Olinordered__ring__strict(_1167513), 20470 ^ _782476 : [(20471 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167513), c_Groups_Ozero__class_Ozero(_1167513)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167513), _1167515), _1167515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167513), _1167517), _1167517)))), _1167515 = c_Groups_Ozero__class_Ozero(_1167513), _1167517 = c_Groups_Ozero__class_Ozero(_1167513)], (20481 ^ _782476) ^ [] : [20482 ^ _782476 : [(20485 ^ _782476) ^ [] : [-(_1167517 = c_Groups_Ozero__class_Ozero(_1167513))], (20483 ^ _782476) ^ [] : [-(_1167515 = c_Groups_Ozero__class_Ozero(_1167513))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167513), c_Groups_Ozero__class_Ozero(_1167513)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167513), _1167515), _1167515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167513), _1167517), _1167517)))))]]], (49452 ^ _782476) ^ [_1779563, _1779565, _1779567, _1779569, _1779571, _1779573, _1779575] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1779563, _1779565, _1779567, _1779569), _1779571), _1779573), _1779575) = c_New__DSequence_Opos__bind(_1779563, _1779565, hAPP(hAPP(hAPP(_1779567, _1779571), _1779573), _1779575), hAPP(hAPP(c_COMBC(_1779563, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779565))), hAPP(hAPP(c_COMBC(_1779563, 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(_1779565)))), hAPP(hAPP(c_COMBC(_1779563, 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(_1779565))))), _1779569), _1779571)), _1779573)), _1779575)))], (10461 ^ _782476) ^ [_972888, _972890, _972892, _972894] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972888, tc_HOL_Obool)), _972890), hAPP(hAPP(c_Set_Oinsert(_972888), _972892), _972894)))), 10464 ^ _782476 : [(10467 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972888, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972888, tc_HOL_Obool)), _972890), hAPP(hAPP(c_Set_Oinsert(_972888), _972892), c_Orderings_Obot__class_Obot(tc_fun(_972888, tc_HOL_Obool))))), _972894))], (10465 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972888), _972892), _972890)))]], 10468 ^ _782476 : [(10471 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972888, tc_HOL_Obool)), _972890), _972894))], (10469 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972888), _972892), _972890))]]], (42901 ^ _782476) ^ [_1629427, _1629429, _1629431, _1629433, _1629435, _1629437] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629427), tc_List_Olist(_1629427))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629427), tc_List_Olist(_1629427)), hAPP(hAPP(c_List_Olist_OCons(_1629427), _1629429), _1629431)), hAPP(hAPP(c_List_Olist_OCons(_1629427), _1629433), _1629435))), c_List_Olexord(_1629427, _1629437))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629427, _1629427)), hAPP(hAPP(c_Product__Type_OPair(_1629427, _1629427), _1629429), _1629433)), _1629437))), 42908 ^ _782476 : [(42911 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629427), tc_List_Olist(_1629427))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629427), tc_List_Olist(_1629427)), _1629431), _1629435)), c_List_Olexord(_1629427, _1629437))))], (42909 ^ _782476) ^ [] : [-(_1629429 = _1629433)]]], (37012 ^ _782476) ^ [_1487337, _1487339] : [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), _1487337))), 37015 ^ _782476 : [(37022 ^ _782476) ^ [] : [-(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), _1487339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487339), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487339), 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), _1487337)))))], (37016 ^ _782476) ^ [] : [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), _1487339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487339), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337)) = 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), _1487339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487337))))]]], (13143 ^ _782476) ^ [_1024279, _1024281, _1024283, _1024285] : [c_Fun_Oinj__on(_1024279, _1024281, _1024283, c_Orderings_Otop__class_Otop(tc_fun(_1024279, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024279, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1024279, _1024281, _1024283), hAPP(hAPP(c_Set_Oinsert(_1024281), _1024285), c_Orderings_Obot__class_Obot(tc_fun(_1024281, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1024279), c_HOL_OThe(_1024279, hAPP(hAPP(c_COMBC(_1024279, _1024281, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1024281, tc_fun(_1024281, tc_HOL_Obool), _1024279), c_fequal), _1024283)), _1024285))), c_Orderings_Obot__class_Obot(tc_fun(_1024279, tc_HOL_Obool))))))], (38276 ^ _782476) ^ [_1513223] : [-(c_Wellfounded_Ofinite__psubset(_1513223) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1513223, tc_HOL_Obool), tc_fun(_1513223, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1513223, tc_HOL_Obool), tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1513223, tc_HOL_Obool), tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1513223, tc_HOL_Obool)), c_COMBS(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513223, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1513223, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1513223, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1513223, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1513223)))))], (41108 ^ _782476) ^ [_1587271, _1587273, _1587275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587271, _1587271), tc_HOL_Obool)), _1587273), _1587275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587271, _1587271), tc_HOL_Obool)), _1587275), c_Transitive__Closure_Ortrancl(_1587271, _1587273))), -(c_Transitive__Closure_Ortrancl(_1587271, _1587275) = c_Transitive__Closure_Ortrancl(_1587271, _1587273))], (50256 ^ _782476) ^ [_1797516, _1797518, _1797520, _1797522] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1797516, _1797518)), c_Nitpick_Opair__box_OPairBox(_1797516, _1797518, _1797520, _1797522)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46084 ^ _782476) ^ [_1705947] : [-(hAPP(c_List_Omap(_1705947, _1705947), c_COMBI(_1705947)) = c_Fun_Oid(tc_List_Olist(_1705947)))], (19821 ^ _782476) ^ [_1154544, _1154546, _1154548, _1154550] : [class_Groups_Oordered__comm__monoid__add(_1154544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154544), c_Groups_Ozero__class_Ozero(_1154544)), _1154546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154544), _1154548), _1154550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154544), _1154548), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154544), _1154546), _1154550))))], (26448 ^ _782476) ^ [_1282256, _1282258, _1282260, _1282262] : [class_Orderings_Olinorder(_1282256), 26451 ^ _782476 : [(26460 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282256), _1282258), _1282260)), _1282262))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), _1282258), _1282262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), _1282260), _1282262))], (26452 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282256), _1282258), _1282260)), _1282262)), 26455 ^ _782476 : [(26458 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), _1282260), _1282262)))], (26456 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282256), _1282258), _1282262)))]]]]], (52675 ^ _782476) ^ [_1843495, _1843497, _1843499, _1843501] : [-(hAPP(hAPP(c_COMBK(_1843495, _1843497), _1843499), _1843501) = _1843499)], (51021 ^ _782476) ^ [_1815202, _1815204] : [hAPP(c_Relation_Oconverse(_1815202, _1815202), _1815204) = _1815204, -(c_Relation_Osym(_1815202, _1815204))], (34556 ^ _782476) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (34156 ^ _782476) ^ [_1429862, _1429864, _1429866] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429862))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429862)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429864)), _1429866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429864)), _1429866))], (52581 ^ _782476) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (49466 ^ _782476) ^ [_1779978, _1779980, _1779982] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779978)), c_List_Osplice(_1779978, _1779980, _1779982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779978)), _1779980)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779978)), _1779982)))], (30210 ^ _782476) ^ [_1355136, _1355138, _1355140] : [class_Fields_Olinordered__field(_1355136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355136), c_Groups_Ozero__class_Ozero(_1355136)), _1355138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355136), c_Groups_Ozero__class_Ozero(_1355136)), _1355140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355136), c_Groups_Ozero__class_Ozero(_1355136)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355136), _1355138), _1355140))))], (33226 ^ _782476) ^ [_1412577, _1412579, _1412581, _1412583] : [class_Fields_Ofield__inverse__zero(_1412577), class_Int_Onumber(_1412577), 33233 ^ _782476 : [(33234 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412577), _1412579), hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581)) = _1412583, 33237 ^ _782476 : [(33244 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581) = c_Groups_Ozero__class_Ozero(_1412577), -(_1412583 = c_Groups_Ozero__class_Ozero(_1412577))], (33238 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581) = c_Groups_Ozero__class_Ozero(_1412577)), -(_1412579 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412577), _1412583), hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581)))]]], (33250 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412577), _1412579), hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581)) = _1412583), 33253 ^ _782476 : [(33256 ^ _782476) ^ [] : [_1412579 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412577), _1412583), hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581))], (33254 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581) = c_Groups_Ozero__class_Ozero(_1412577)]], 33257 ^ _782476 : [(33260 ^ _782476) ^ [] : [_1412583 = c_Groups_Ozero__class_Ozero(_1412577)], (33258 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412577), _1412581) = c_Groups_Ozero__class_Ozero(_1412577))]]]]], (6941 ^ _782476) ^ [_896246, _896248, _896250] : [hBOOL(hAPP(hAPP(c_member(_896246), _896248), hAPP(c_fequal, _896250))), -(_896248 = _896250)], (41196 ^ _782476) ^ [_1589472, _1589474] : [-(hAPP(c_Relation_OImage(_1589472, _1589472, c_Relation_OId(_1589472)), _1589474) = _1589474)], (46048 ^ _782476) ^ [_1704486, _1704488, _1704490, _1704492] : [-(hAPP(c_List_Oset(_1704486), hAPP(hAPP(c_List_Omap(_1704488, _1704486), _1704490), _1704492)) = hAPP(c_Set_Oimage(_1704488, _1704486, _1704490), hAPP(c_List_Oset(_1704488), _1704492)))], (38835 ^ _782476) ^ [] : [-(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))], (6716 ^ _782476) ^ [_891042, _891044, _891046, _891048] : [hBOOL(hAPP(hAPP(c_member(_891042), _891044), c_Complete__Lattice_OInf__class_OInf(tc_fun(_891042, tc_HOL_Obool), _891046))), hBOOL(hAPP(hAPP(c_member(tc_fun(_891042, tc_HOL_Obool)), _891048), _891046)), -(hBOOL(hAPP(hAPP(c_member(_891042), _891044), _891048)))], (1182 ^ _782476) ^ [_800451, _800453] : [-(class_Rings_Olinordered__semiring__1__strict(_800451)), _800453 = _800451, class_Rings_Olinordered__semiring__1__strict(_800453)], (23622 ^ _782476) ^ [_1226273] : [23624 ^ _782476 : [(23627 ^ _782476) ^ [] : [hBOOL(hAPP(_1226273, hAPP(c_Int_Onat, 23623 ^ [_1226273])))], (23625 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23623 ^ [_1226273])))]], 23628 ^ _782476 : [(23629 ^ _782476) ^ [_1226406] : [-(hBOOL(hAPP(_1226273, _1226406)))]]], (31882 ^ _782476) ^ [_1386190, _1386192, _1386194, _1386196] : [class_Divides_Osemiring__div(_1386190), -(c_Divides_Odiv__class_Omod(_1386190, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386190), _1386192), _1386194), _1386196) = c_Divides_Odiv__class_Omod(_1386190, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386190), c_Divides_Odiv__class_Omod(_1386190, _1386192, _1386196)), c_Divides_Odiv__class_Omod(_1386190, _1386194, _1386196)), _1386196))], (35168 ^ _782476) ^ [_1447393] : [-(c_Int_OBit0(_1447393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447393), _1447393))], (25353 ^ _782476) ^ [_1256198, _1256200] : [class_Rings_Olinordered__idom(_1256198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256198), c_Groups_Ozero__class_Ozero(_1256198)), _1256200)), -(c_Groups_Osgn__class_Osgn(_1256198, _1256200) = c_Groups_Oone__class_Oone(_1256198))], (39800 ^ _782476) ^ [_1553378, _1553380, _1553382, _1553384, _1553386] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553378, _1553380), _1553382), hAPP(hAPP(c_COMBS(_1553378, tc_fun(_1553380, tc_HOL_Obool), tc_fun(_1553380, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553380, tc_HOL_Obool), tc_fun(tc_fun(_1553380, tc_HOL_Obool), tc_fun(_1553380, tc_HOL_Obool)), _1553378), c_Groups_Ominus__class_Ominus(tc_fun(_1553380, tc_HOL_Obool))), _1553384)), _1553386)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553378, _1553380), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553378, _1553380), _1553382), _1553384)), hAPP(hAPP(c_Product__Type_OSigma(_1553378, _1553380), _1553382), _1553386)))], (29964 ^ _782476) ^ [_1351017, _1351019, _1351021] : [class_Fields_Olinordered__field(_1351017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351017), _1351019), c_Groups_Ozero__class_Ozero(_1351017))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351017), _1351021), c_Groups_Ozero__class_Ozero(_1351017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351017), c_Groups_Ozero__class_Ozero(_1351017)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351017), _1351019), _1351021))))], (16949 ^ _782476) ^ [_1103227, _1103229, _1103231, _1103233] : [class_Rings_Ocomm__semiring__1(_1103227), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103227), _1103229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103227), _1103231), _1103233)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103227), _1103231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103227), _1103229), _1103233)))], (8434 ^ _782476) ^ [_928520, _928522] : [class_Groups_Oordered__ab__group__add(_928520), -(hAPP(c_Set_Oimage(_928520, _928520, c_Groups_Ouminus__class_Ouminus(_928520)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_928520), _928522)) = hAPP(c_SetInterval_Oord__class_OlessThan(_928520), hAPP(c_Groups_Ouminus__class_Ouminus(_928520), _928522)))], (45440 ^ _782476) ^ [_1691986, _1691988, _1691990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691986), _1691988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691986), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1691988), _1691990))))], (16733 ^ _782476) ^ [_1098021, _1098023, _1098025] : [class_Groups_Ogroup__add(_1098021), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098021), _1098023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098021), hAPP(c_Groups_Ouminus__class_Ouminus(_1098021), _1098023)), _1098025)) = _1098025)], (8016 ^ _782476) ^ [_919007, _919009, _919011, _919013] : [class_Lattices_Osemilattice__sup(_919007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919007), _919009), _919011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919007), _919009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919007), _919013), _919011))))], (44056 ^ _782476) ^ [_1661263, _1661265, _1661267, _1661269] : [hBOOL(hAPP(c_List_Odistinct(_1661263), _1661265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661263)), _1661265))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661263)), _1661265))), 44067 ^ _782476 : [(44074 ^ _782476) ^ [] : [_1661267 = _1661269, -(hAPP(hAPP(c_List_Onth(_1661263), _1661265), _1661267) = hAPP(hAPP(c_List_Onth(_1661263), _1661265), _1661269))], (44068 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Onth(_1661263), _1661265), _1661267) = hAPP(hAPP(c_List_Onth(_1661263), _1661265), _1661269), -(_1661267 = _1661269)]]], (13481 ^ _782476) ^ [_1032118, _1032120] : [class_Enum_Oenum(_1032118), 13484 ^ _782476 : [(13492 ^ _782476) ^ [] : [13493 ^ _782476 : [(13494 ^ _782476) ^ [_1032298] : [hBOOL(hAPP(_1032120, _1032298))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032118), _1032120)))], (13485 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032118), _1032120)), -(hBOOL(hAPP(_1032120, 13488 ^ [_1032118, _1032120])))]]], (46942 ^ _782476) ^ [_1724817, _1724819, _1724821] : [hBOOL(hAPP(c_List_Odistinct(_1724817), _1724819)), -(c_List_Oremove1(_1724817, _1724821, c_List_Oremdups(_1724817, _1724819)) = c_List_Oremdups(_1724817, c_List_Oremove1(_1724817, _1724821, _1724819)))], (18198 ^ _782476) ^ [_1126626, _1126628] : [class_Groups_Olinordered__ab__group__add(_1126626), 18201 ^ _782476 : [(18208 ^ _782476) ^ [] : [_1126628 = c_Groups_Ozero__class_Ozero(_1126626), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126626), _1126628) = _1126628)], (18202 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126626), _1126628) = _1126628, -(_1126628 = c_Groups_Ozero__class_Ozero(_1126626))]]], (7349 ^ _782476) ^ [_905199, _905201, _905203, _905205] : [hBOOL(hAPP(hAPP(c_member(_905199), _905201), c_SetInterval_Oord_OgreaterThan(_905199, _905203, _905205))), -(hBOOL(hAPP(hAPP(_905203, _905205), _905201)))], (34280 ^ _782476) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22206 ^ _782476) ^ [_1199574, _1199576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199574), _1199576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199574)), hAPP(c_Nat_OSuc, _1199576))))], (8166 ^ _782476) ^ [_921892, _921894, _921896] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921892, tc_HOL_Obool)), _921894), _921896) = _921896, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921892, tc_HOL_Obool)), _921894), _921896)))], (2412 ^ _782476) ^ [_817832, _817834, _817836, _817838] : [-(c_Nitpick_Onat__gcd(_817838, _817834) = c_Nitpick_Onat__gcd(_817836, _817832)), _817838 = _817836, _817834 = _817832], (37657 ^ _782476) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25668 ^ _782476) ^ [_1262725, _1262727, _1262729] : [-(hAPP(hAPP(c_Set_Oinsert(_1262725), _1262727), _1262729) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262725, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262725), hAPP(hAPP(c_COMBC(_1262725, _1262725, tc_HOL_Obool), c_fequal), _1262727))), _1262729))], (45362 ^ _782476) ^ [_1690365, _1690367, _1690369] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690365)), hAPP(c_List_Orotate(_1690365, _1690367), _1690369)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690365)), _1690369))], (52553 ^ _782476) ^ [_1842286, _1842288] : [-(class_Finite__Set_Ofinite(tc_prod(_1842286, _1842288))), class_Finite__Set_Ofinite(_1842286), class_Finite__Set_Ofinite(_1842288)], (9991 ^ _782476) ^ [_962662, _962664, _962666, _962668] : [class_Orderings_Oorder(_962662), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962662, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962662, _962664), _962666)), c_SetInterval_Oord__class_OatLeastAtMost(_962662, _962666, _962668)) = c_Orderings_Obot__class_Obot(tc_fun(_962662, tc_HOL_Obool)))], (48206 ^ _782476) ^ [_1752073, _1752075, _1752077] : [-(hAPP(c_List_Orev(_1752073), hAPP(hAPP(c_List_Otake(_1752073), _1752075), _1752077)) = hAPP(hAPP(c_List_Odrop(_1752073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752073)), _1752077)), _1752075)), hAPP(c_List_Orev(_1752073), _1752077)))], (9909 ^ _782476) ^ [_961012, _961014, _961016, _961018, _961020] : [-(_961012 = c_Orderings_Obot__class_Obot(tc_fun(_961014, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961014, tc_fun(_961016, tc_HOL_Obool)), _961012), hAPP(hAPP(c_COMBC(_961014, tc_fun(_961016, tc_HOL_Obool), tc_fun(_961016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_961016, tc_HOL_Obool), tc_fun(tc_fun(_961016, tc_HOL_Obool), tc_fun(_961016, tc_HOL_Obool)), _961014), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961016, tc_HOL_Obool))), _961018)), _961020)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961016, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961014, tc_fun(_961016, tc_HOL_Obool)), _961012), _961018)), _961020))], (26520 ^ _782476) ^ [_1283455, _1283457, _1283459, _1283461] : [class_Orderings_Olinorder(_1283455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283455), _1283457), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283455), _1283459), _1283461))), 26527 ^ _782476 : [(26530 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283455), _1283457), _1283461)))], (26528 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283455), _1283457), _1283459)))]]], (38531 ^ _782476) ^ [_1519883, _1519885, _1519887, _1519889, _1519891, _1519893, _1519895] : [hBOOL(hAPP(_1519883, _1519885)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519887, _1519887)), hAPP(hAPP(c_Product__Type_OPair(_1519887, _1519887), _1519889), _1519891)), hAPP(_1519893, _1519885))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1519895, _1519887), tc_prod(_1519895, _1519887))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1519895, _1519887), tc_prod(_1519895, _1519887)), hAPP(hAPP(c_Product__Type_OPair(_1519895, _1519887), _1519885), _1519889)), hAPP(hAPP(c_Product__Type_OPair(_1519895, _1519887), _1519885), _1519891))), c_Recdef_Osame__fst(_1519895, _1519887, _1519883, _1519893))))], (48719 ^ _782476) ^ [_1762768, _1762770, _1762772] : [-(hAPP(c_List_Oset(_1762768), c_List_Oinsert(_1762768, _1762770, _1762772)) = hAPP(hAPP(c_Set_Oinsert(_1762768), _1762770), hAPP(c_List_Oset(_1762768), _1762772)))], (36615 ^ _782476) ^ [_1478988, _1478990, _1478992] : [class_Rings_Osemiring__1(_1478988), hBOOL(hAPP(hAPP(c_member(_1478988), _1478990), c_Nat_Osemiring__1__class_ONats(_1478988))), hBOOL(hAPP(hAPP(c_member(_1478988), _1478992), c_Nat_Osemiring__1__class_ONats(_1478988))), -(hBOOL(hAPP(hAPP(c_member(_1478988), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478988), _1478990), _1478992)), c_Nat_Osemiring__1__class_ONats(_1478988))))], (924 ^ _782476) ^ [_796556, _796558, _796560, _796562] : [-(c_Relation_Otrans(_796560, _796556)), c_Relation_Otrans(_796562, _796558), _796562 = _796560, _796558 = _796556], (35436 ^ _782476) ^ [_1452029, _1452031, _1452033] : [class_Int_Onumber__ring(_1452029), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1452029), _1452031), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452033))) = hAPP(hAPP(c_HOL_OLet(_1452029, _1452029), hAPP(hAPP(c_Power_Opower__class_Opower(_1452029), _1452031), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452033))), hAPP(hAPP(c_COMBS(_1452029, _1452029, _1452029), c_Groups_Otimes__class_Otimes(_1452029)), c_COMBI(_1452029))))], (42313 ^ _782476) ^ [_1616003, _1616005, _1616007] : [class_Groups_Oab__semigroup__mult(_1616003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616003), _1616005)), -(hBOOL(hAPP(hAPP(c_member(_1616003), _1616007), _1616005))), -(hAPP(c_Finite__Set_Ofold1(_1616003, c_Groups_Otimes__class_Otimes(_1616003)), hAPP(hAPP(c_Set_Oinsert(_1616003), _1616007), _1616005)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616003, _1616003, c_Groups_Otimes__class_Otimes(_1616003)), _1616007), _1616005))], (49134 ^ _782476) ^ [_1772876, _1772878, _1772880] : [-(hBOOL(hAPP(hAPP(c_member(_1772876), _1772878), hAPP(c_List_Oset(_1772876), _1772880)))), 49135 ^ _782476 : [(49136 ^ _782476) ^ [_1772965] : [49137 ^ _782476 : [(49138 ^ _782476) ^ [_1773038] : [_1772880 = hAPP(hAPP(c_List_Oappend(_1772876), _1772965), hAPP(hAPP(c_List_Olist_OCons(_1772876), _1772878), _1773038))]], -(hBOOL(hAPP(hAPP(c_member(_1772876), _1772878), hAPP(c_List_Oset(_1772876), _1772965))))]]], (46532 ^ _782476) ^ [_1715382, _1715384, _1715386, _1715388] : [-(hBOOL(hAPP(c_List_Olistsp(_1715382, hAPP(hAPP(c_COMBS(_1715382, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715382), c_fconj), _1715384)), _1715386)), _1715388))), hBOOL(hAPP(c_List_Olistsp(_1715382, _1715384), _1715388)), hBOOL(hAPP(c_List_Olistsp(_1715382, _1715386), _1715388))], (43807 ^ _782476) ^ [_1655687, _1655689, _1655691] : [hBOOL(hAPP(hAPP(c_member(_1655687), _1655689), hAPP(c_List_Oset(_1655687), c_List_Obutlast(_1655687, _1655691)))), -(hBOOL(hAPP(hAPP(c_member(_1655687), _1655689), hAPP(c_List_Oset(_1655687), _1655691))))], (25297 ^ _782476) ^ [_1255316] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255316), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255316) = _1255316)], (10940 ^ _782476) ^ [_984128, _984130, _984132] : [class_Orderings_Olinorder(_984128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984128), _984130), _984132)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984128, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984128, _984130, _984132)), hAPP(hAPP(c_Set_Oinsert(_984128), _984132), c_Orderings_Obot__class_Obot(tc_fun(_984128, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_984128, _984130, _984132))], (17091 ^ _782476) ^ [_1106607, _1106609, _1106611, _1106613, _1106615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106607), _1106609)), 17094 ^ _782476 : [(17101 ^ _782476) ^ [] : [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), _1106609), _1106607)), _1106611)), _1106613)), _1106615)), -(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), _1106609), _1106611)), _1106613)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106607), _1106611)), _1106615))))], (17095 ^ _782476) ^ [] : [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), _1106609), _1106611)), _1106613)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106607), _1106611)), _1106615))), -(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), _1106609), _1106607)), _1106611)), _1106613)), _1106615)))]]], (43073 ^ _782476) ^ [_1634888, _1634890, _1634892, _1634894, _1634896, _1634898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634888), tc_List_Olist(_1634888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634888), tc_List_Olist(_1634888)), hAPP(hAPP(c_List_Olist_OCons(_1634888), _1634890), _1634892)), hAPP(hAPP(c_List_Olist_OCons(_1634888), _1634894), _1634896))), c_List_Olistrel1(_1634888, _1634898))), 43078 ^ _782476 : [(43081 ^ _782476) ^ [] : [-(_1634892 = _1634896)], (43079 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634888, _1634888)), hAPP(hAPP(c_Product__Type_OPair(_1634888, _1634888), _1634890), _1634894)), _1634898)))]], 43082 ^ _782476 : [(43085 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634888), tc_List_Olist(_1634888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634888), tc_List_Olist(_1634888)), _1634892), _1634896)), c_List_Olistrel1(_1634888, _1634898))))], (43083 ^ _782476) ^ [] : [-(_1634890 = _1634894)]]], (46052 ^ _782476) ^ [_1704609, _1704611] : [-(hAPP(hAPP(c_List_Ozip(_1704609, _1704609), _1704611), _1704611) = hAPP(hAPP(c_List_Omap(_1704609, tc_prod(_1704609, _1704609)), hAPP(hAPP(c_COMBS(_1704609, _1704609, tc_prod(_1704609, _1704609)), c_Product__Type_OPair(_1704609, _1704609)), c_COMBI(_1704609))), _1704611))], (52133 ^ _782476) ^ [_1837943, _1837945] : [class_Lattices_Olattice(_1837943), -(class_Lattices_Osemilattice__inf(tc_fun(_1837945, _1837943)))], (14435 ^ _782476) ^ [_1051465, _1051467, _1051469] : [class_Rings_Olinordered__idom(_1051465), -(_1051467 = _1051469), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051465), _1051467), _1051469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051465), _1051469), _1051467)))], (43890 ^ _782476) ^ [_1657689, _1657691, _1657693, _1657695] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657689, tc_HOL_Obool)), hAPP(c_List_Oset(_1657689), hAPP(hAPP(c_List_Olist__update(_1657689, _1657691), _1657693), _1657695))), hAPP(hAPP(c_Set_Oinsert(_1657689), _1657695), hAPP(c_List_Oset(_1657689), _1657691)))))], (1146 ^ _782476) ^ [_799881, _799883, _799885, _799887, _799889, _799891, _799893, _799895, _799897, _799899] : [-(c_Finite__Set_Ofolding__image(_799897, _799893, _799889, _799885, _799881)), c_Finite__Set_Ofolding__image(_799899, _799895, _799891, _799887, _799883), _799899 = _799897, _799895 = _799893, _799891 = _799889, _799887 = _799885, _799883 = _799881], (7185 ^ _782476) ^ [_901979, _901981, _901983] : [class_Complete__Lattice_Ocomplete__lattice(_901979), 7188 ^ _782476 : [(7189 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901979), c_Complete__Lattice_OSup__class_OSup(_901979, _901981)), _901983)), 7192 ^ _782476 : [(7193 ^ _782476) ^ [_902137] : [hBOOL(hAPP(hAPP(c_member(_901979), _902137), _901981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901979), _902137), _901983)))]]], (7199 ^ _782476) ^ [] : [7201 ^ _782476 : [(7204 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901979), 7200 ^ [_901979, _901981, _901983]), _901983))], (7202 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901979), 7200 ^ [_901979, _901981, _901983]), _901981)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901979), c_Complete__Lattice_OSup__class_OSup(_901979, _901981)), _901983)))]]], (39184 ^ _782476) ^ [_1537632, _1537634] : [-(c_Wellfounded_Owf(_1537632, hAPP(c_Wellfounded_Omeasure(_1537632), _1537634)))], (30200 ^ _782476) ^ [_1354978, _1354980, _1354982] : [class_Fields_Olinordered__field(_1354978), -(_1354980 = c_Groups_Ozero__class_Ozero(_1354978)), -(hAPP(c_Groups_Oabs__class_Oabs(_1354978), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354978), _1354982), _1354980)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354978), hAPP(c_Groups_Oabs__class_Oabs(_1354978), _1354982)), hAPP(c_Groups_Oabs__class_Oabs(_1354978), _1354980)))], (41158 ^ _782476) ^ [_1588503, _1588505] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588503, _1588503), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588503, _1588505)), c_Relation_OId(_1588503)) = c_Transitive__Closure_Ortrancl(_1588503, _1588505))], (31085 ^ _782476) ^ [_1370952, _1370954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370952)), 31088 ^ _782476 : [(31097 ^ _782476) ^ [] : [-(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), _1370952), _1370954)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370954), _1370952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370954))], (31089 ^ _782476) ^ [] : [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), _1370952), _1370954))), 31092 ^ _782476 : [(31095 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370954)))], (31093 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370954), _1370952)))]]]]], (34376 ^ _782476) ^ [_1433337, _1433339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433337), _1433339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433337)), _1433339)))], (44134 ^ _782476) ^ [_1663073, _1663075, _1663077] : [hBOOL(hAPP(c_List_Odistinct(_1663073), _1663075)), -(hAPP(c_List_Oset(_1663073), c_List_Oremove1(_1663073, _1663077, _1663075)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1663073, tc_HOL_Obool)), hAPP(c_List_Oset(_1663073), _1663075)), hAPP(hAPP(c_Set_Oinsert(_1663073), _1663077), c_Orderings_Obot__class_Obot(tc_fun(_1663073, tc_HOL_Obool)))))], (726 ^ _782476) ^ [_793541, _793543, _793545, _793547, _793549, _793551, _793553, _793555] : [-(c_Nat__Transfer_Otransfer__morphism(_793553, _793549, _793545, _793541)), c_Nat__Transfer_Otransfer__morphism(_793555, _793551, _793547, _793543), _793555 = _793553, _793551 = _793549, _793547 = _793545, _793543 = _793541], (40794 ^ _782476) ^ [_1579646, _1579648, _1579650, _1579652] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579646, _1579648, _1579650, tc_prod(_1579648, _1579650)), _1579652), c_Product__Type_OPair(_1579648, _1579650)) = _1579652)], (842 ^ _782476) ^ [_795355, _795357, _795359, _795361] : [-(c_Predicate_Oreflp(_795359, _795355)), c_Predicate_Oreflp(_795361, _795357), _795361 = _795359, _795357 = _795355], (13790 ^ _782476) ^ [_1038260, _1038262, _1038264, _1038266, _1038268] : [hAPP(c_Set_Oimage(_1038260, _1038262, _1038264), c_Orderings_Otop__class_Otop(tc_fun(_1038260, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038262, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038262, _1038266, _1038268), c_Orderings_Otop__class_Otop(tc_fun(_1038262, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038266, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1038260, _1038266, hAPP(c_Fun_Ocomp(_1038262, _1038266, _1038260, _1038268), _1038264)), c_Orderings_Otop__class_Otop(tc_fun(_1038260, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038266, tc_HOL_Obool)))], (31211 ^ _782476) ^ [_1373034, _1373036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1373036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373034), _1373036)), _1373034)))], (24402 ^ _782476) ^ [_1238956, _1238958] : [c_Nat__Transfer_Onat__set(_1238956), c_Nat__Transfer_Onat__set(_1238958), 24409 ^ _782476 : [(24416 ^ _782476) ^ [] : [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), _1238956)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1238956), _1238958)))], (24410 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1238956), _1238958)), -(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), _1238956)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238958))))]]], (20523 ^ _782476) ^ [_1168576, _1168578] : [class_Rings_Osemiring__1(_1168576), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168576), _1168578) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1168576, hAPP(hAPP(c_COMBC(_1168576, _1168576, _1168576), c_Groups_Oplus__class_Oplus(_1168576)), c_Groups_Oone__class_Oone(_1168576)), _1168578, c_Groups_Ozero__class_Ozero(_1168576)))], (52245 ^ _782476) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (9169 ^ _782476) ^ [_945099, _945101, _945103] : [class_Lattices_Oboolean__algebra(_945099), -(hAPP(c_Groups_Ouminus__class_Ouminus(_945099), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945099), _945101), _945103)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_945099), hAPP(c_Groups_Ouminus__class_Ouminus(_945099), _945101)), hAPP(c_Groups_Ouminus__class_Ouminus(_945099), _945103)))], (38726 ^ _782476) ^ [] : [-(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)))))], (23813 ^ _782476) ^ [_1229379, _1229381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229379)), 23816 ^ _782476 : [(23823 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229379), _1229381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229379)), hAPP(c_Int_Onat, _1229381))))], (23817 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229379)), hAPP(c_Int_Onat, _1229381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229379), _1229381)))]]], (1752 ^ _782476) ^ [_807576, _807578] : [-(class_Rings_Ono__zero__divisors(_807576)), _807578 = _807576, class_Rings_Ono__zero__divisors(_807578)], (34842 ^ _782476) ^ [_1440827, _1440829] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440827))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440829)) = 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)))), _1440827), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440829)))], (20784 ^ _782476) ^ [_1173188, _1173190] : [20792 ^ _782476 : [(20795 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1173190, 20791 ^ [_1173188, _1173190])))], (20793 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20791 ^ [_1173188, _1173190]), _1173188)))]], 20785 ^ _782476 : [(20786 ^ _782476) ^ [_1173256] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173256), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173188))), hBOOL(hAPP(_1173190, _1173256))]]], (17323 ^ _782476) ^ [_1111263, _1111265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111263), _1111265)), _1111265 = _1111263], (40264 ^ _782476) ^ [_1566726, _1566728, _1566730] : [c_Wellfounded_OwfP(_1566726, _1566728), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566726, _1566728), _1566730)))], (39669 ^ _782476) ^ [_1549167, _1549169, _1549171, _1549173] : [hBOOL(hAPP(hAPP(c_member(_1549167), _1549173), hAPP(c_Relation_ODomain(_1549167, _1549169), _1549171))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549167, _1549169, hAPP(hAPP(c_COMBC(_1549167, tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_fun(_1549169, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549169, tc_fun(tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_fun(_1549169, tc_HOL_Obool)), _1549167), c_COMBC(_1549169, tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549169, tc_prod(_1549167, _1549169)), tc_fun(_1549169, tc_fun(tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_HOL_Obool)), _1549167), hAPP(c_COMBB(tc_prod(_1549167, _1549169), tc_fun(tc_fun(tc_prod(_1549167, _1549169), tc_HOL_Obool), tc_HOL_Obool), _1549169), c_member(tc_prod(_1549167, _1549169)))), c_Product__Type_OPair(_1549167, _1549169)))), _1549171)), _1549173)))], (44841 ^ _782476) ^ [_1678030, _1678032, _1678034] : [-(hAPP(hAPP(c_List_Oappend(_1678030), _1678032), _1678034) = c_List_Olist_ONil(_1678030)), _1678032 = c_List_Olist_ONil(_1678030), _1678034 = c_List_Olist_ONil(_1678030)], (39564 ^ _782476) ^ [_1546471, _1546473, _1546475, _1546477] : [hBOOL(hAPP(c_Predicate_ORangeP(_1546471, _1546473, _1546475), _1546477)), -(hBOOL(hAPP(hAPP(_1546475, 39567 ^ [_1546471, _1546473, _1546475, _1546477]), _1546477)))], (34790 ^ _782476) ^ [_1439906, _1439908] : [class_Int_Onumber__ring(_1439906), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439906), c_Groups_Oone__class_Oone(_1439906)), hAPP(c_Int_Onumber__class_Onumber__of(_1439906), _1439908)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439906), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439908)))], (46166 ^ _782476) ^ [_1707766, _1707768, _1707770, _1707772, _1707774] : [class_Groups_Ocomm__monoid__add(_1707766), hBOOL(hAPP(hAPP(c_member(_1707768), _1707770), hAPP(c_List_Oset(_1707768), _1707772))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707766), hAPP(hAPP(c_List_Omap(_1707768, _1707766), _1707774), _1707772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1707766), hAPP(_1707774, _1707770)), hAPP(c_List_Omonoid__add__class_Olistsum(_1707766), hAPP(hAPP(c_List_Omap(_1707768, _1707766), _1707774), c_List_Oremove1(_1707768, _1707770, _1707772)))))], (20719 ^ _782476) ^ [_1171950, _1171952] : [20727 ^ _782476 : [(20730 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1171952, 20726 ^ [_1171950, _1171952])))], (20728 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20726 ^ [_1171950, _1171952]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171950))))]], 20720 ^ _782476 : [(20721 ^ _782476) ^ [_1172019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172019), _1171950)), hBOOL(hAPP(_1171952, _1172019))]]], (7756 ^ _782476) ^ [_913644, _913646, _913648, _913650] : [class_Lattices_Olattice(_913644), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913644), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913644), _913646), _913648)), _913650) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913644), _913646), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913644), _913648), _913650)))], (43239 ^ _782476) ^ [_1640068, _1640070, _1640072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640068, tc_HOL_Obool)), _1640070), _1640072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1640068), tc_HOL_Obool)), c_List_Olists(_1640068, _1640070)), c_List_Olists(_1640068, _1640072))))], (18780 ^ _782476) ^ [_1136232, _1136234, _1136236] : [class_Rings_Oordered__ring(_1136232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136232), _1136234), c_Groups_Ozero__class_Ozero(_1136232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136232), _1136236), c_Groups_Ozero__class_Ozero(_1136232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136232), c_Groups_Ozero__class_Ozero(_1136232)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136232), _1136234), _1136236))))], (29330 ^ _782476) ^ [_1339037, _1339039, _1339041, _1339043] : [class_Rings_Olinordered__semidom(_1339037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339037), c_Groups_Oone__class_Oone(_1339037)), _1339039)), 29337 ^ _782476 : [(29344 ^ _782476) ^ [] : [_1339041 = _1339043, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339037), _1339039), _1339041) = hAPP(hAPP(c_Power_Opower__class_Opower(_1339037), _1339039), _1339043))], (29338 ^ _782476) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1339037), _1339039), _1339041) = hAPP(hAPP(c_Power_Opower__class_Opower(_1339037), _1339039), _1339043), -(_1339041 = _1339043)]]], (39249 ^ _782476) ^ [_1538817, _1538819, _1538821] : [c_Wellfounded_Owf(_1538817, _1538819), -(c_Wellfounded_Owf(_1538817, c_Wellfounded_Omlex__prod(_1538817, _1538821, _1538819)))], (20697 ^ _782476) ^ [_1171560, _1171562, _1171564] : [class_Rings_Olinordered__ring__strict(_1171560), 20700 ^ _782476 : [(20709 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171560), _1171562), _1171562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171560), _1171564), _1171564)) = c_Groups_Ozero__class_Ozero(_1171560)), _1171562 = c_Groups_Ozero__class_Ozero(_1171560), _1171564 = c_Groups_Ozero__class_Ozero(_1171560)], (20701 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171560), _1171562), _1171562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171560), _1171564), _1171564)) = c_Groups_Ozero__class_Ozero(_1171560), 20704 ^ _782476 : [(20707 ^ _782476) ^ [] : [-(_1171564 = c_Groups_Ozero__class_Ozero(_1171560))], (20705 ^ _782476) ^ [] : [-(_1171562 = c_Groups_Ozero__class_Ozero(_1171560))]]]]], (10249 ^ _782476) ^ [_968111, _968113, _968115, _968117] : [hBOOL(hAPP(hAPP(c_member(_968111), _968113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968111, tc_HOL_Obool)), _968115), _968117))), hBOOL(hAPP(hAPP(c_member(_968111), _968113), _968117))], (31661 ^ _782476) ^ [_1381521, _1381523, _1381525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1381521)), 31664 ^ _782476 : [(31665 ^ _782476) ^ [] : [-(_1381523 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381525), _1381521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381521), _1381523)), _1381525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381521), hAPP(c_Nat_OSuc, _1381523))))], (31675 ^ _782476) ^ [] : [_1381523 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381525), _1381521), 31678 ^ _782476 : [(31681 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381521), hAPP(c_Nat_OSuc, _1381523)))))], (31679 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381521), _1381523)), _1381525)))]]]]], (38891 ^ _782476) ^ [_1528802, _1528804, _1528806, _1528808] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528802, _1528804, _1528806, c_Code__Numeral_OSuc__code__numeral(_1528808)) = hAPP(_1528806, _1528808))], (19510 ^ _782476) ^ [_1149299, _1149301, _1149303] : [class_Groups_Ogroup__add(_1149299), 19513 ^ _782476 : [(19520 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149299), _1149301), _1149303) = c_Groups_Ozero__class_Ozero(_1149299), -(_1149301 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149299), _1149303))], (19514 ^ _782476) ^ [] : [_1149301 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149299), _1149303), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149299), _1149301), _1149303) = c_Groups_Ozero__class_Ozero(_1149299))]]], (35006 ^ _782476) ^ [_1444510] : [class_Rings_Osemiring__1(_1444510), -(c_Int_Oiszero(_1444510, c_Groups_Ozero__class_Ozero(_1444510)))], (23009 ^ _782476) ^ [_1214096, _1214098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214096), _1214098))), 23012 ^ _782476 : [(23015 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1214096), _1214098)))], (23013 ^ _782476) ^ [] : [_1214098 = c_Orderings_Obot__class_Obot(tc_fun(_1214096, tc_HOL_Obool))]]], (23640 ^ _782476) ^ [_1226594] : [-(hBOOL(hAPP(_1226594, 23647 ^ [_1226594]))), 23641 ^ _782476 : [(23642 ^ _782476) ^ [_1226646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226646)), hBOOL(hAPP(_1226594, hAPP(c_Int_Onat, _1226646)))]]], (5496 ^ _782476) ^ [_866566, _866568] : [_866568 = _866566, -(c_Divides_Odiv__class_Odiv(_866568) = c_Divides_Odiv__class_Odiv(_866566))], (43984 ^ _782476) ^ [_1659876, _1659878, _1659880] : [hBOOL(hAPP(c_List_Odistinct(_1659876), _1659878)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1659876)), c_Enum_On__lists(_1659876, _1659880, _1659878))))], (25127 ^ _782476) ^ [_1252161, _1252163, _1252165] : [class_Groups_Oordered__ab__group__add__abs(_1252161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252161), _1252163), _1252165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252161), hAPP(c_Groups_Ouminus__class_Ouminus(_1252161), _1252163)), _1252165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252161), hAPP(c_Groups_Oabs__class_Oabs(_1252161), _1252163)), _1252165)))], (22642 ^ _782476) ^ [_1207149] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207149)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207149))], (37589 ^ _782476) ^ [_1497878, _1497880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497880)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497878, _1497880) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1497878, _1497880)))], (52465 ^ _782476) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (16127 ^ _782476) ^ [_1085208, _1085210, _1085212, _1085214] : [hBOOL(hAPP(hAPP(c_member(_1085208), _1085210), _1085212)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085208, tc_Nat_Onat), _1085214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085208, tc_HOL_Obool)), _1085212), hAPP(hAPP(c_Set_Oinsert(_1085208), _1085210), c_Orderings_Obot__class_Obot(tc_fun(_1085208, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085208, tc_Nat_Onat), _1085214), _1085212)), hAPP(_1085214, _1085210)))], (12664 ^ _782476) ^ [_1014661, _1014663] : [-(c_Fun_Oinj__on(_1014661, _1014661, c_COMBI(_1014661), _1014663))], (14391 ^ _782476) ^ [_1050537, _1050539, _1050541, _1050543] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050537), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050537, tc_HOL_Obool)), _1050539), hAPP(hAPP(c_Set_Oinsert(_1050537), _1050541), _1050543)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050537), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050537, tc_HOL_Obool)), _1050539), _1050543))))], (1192 ^ _782476) ^ [_800576, _800578] : [-(class_Groups_Oordered__ab__group__add__abs(_800576)), _800578 = _800576, class_Groups_Oordered__ab__group__add__abs(_800578)], (6696 ^ _782476) ^ [_890648, _890650, _890652, _890654] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_890648, tc_HOL_Obool)), _890650), _890652)), hBOOL(hAPP(hAPP(c_member(_890648), _890654), _890650)), -(hBOOL(hAPP(hAPP(c_member(_890648), _890654), c_Complete__Lattice_OSup__class_OSup(tc_fun(_890648, tc_HOL_Obool), _890652))))], (52699 ^ _782476) ^ [_1843912] : [hBOOL(hAPP(c_fNot, _1843912)), hBOOL(_1843912)], (45452 ^ _782476) ^ [_1692252, _1692254, _1692256] : [class_Groups_Omonoid__add(_1692252), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692252), _1692254), hAPP(c_List_Ofoldl(_1692252, _1692252, c_Groups_Oplus__class_Oplus(_1692252), c_Groups_Ozero__class_Ozero(_1692252)), _1692256)) = hAPP(c_List_Ofoldl(_1692252, _1692252, c_Groups_Oplus__class_Oplus(_1692252), _1692254), _1692256))], (49364 ^ _782476) ^ [_1777581, _1777583, _1777585] : [c_FunDef_Ois__measure(_1777581, _1777583), -(c_FunDef_Ois__measure(tc_prod(_1777581, _1777585), hAPP(hAPP(c_COMBB(_1777581, tc_Nat_Onat, tc_prod(_1777581, _1777585)), _1777583), c_Product__Type_Ofst(_1777581, _1777585))))], (24799 ^ _782476) ^ [_1246141, _1246143] : [class_Groups_Osgn__if(_1246141), 24802 ^ _782476 : [(24809 ^ _782476) ^ [] : [-(_1246143 = c_Groups_Ozero__class_Ozero(_1246141)), 24812 ^ _782476 : [(24819 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246141), c_Groups_Ozero__class_Ozero(_1246141)), _1246143))), -(c_Groups_Osgn__class_Osgn(_1246141, _1246143) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246141), c_Groups_Oone__class_Oone(_1246141)))], (24813 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246141), c_Groups_Ozero__class_Ozero(_1246141)), _1246143)), -(c_Groups_Osgn__class_Osgn(_1246141, _1246143) = c_Groups_Oone__class_Oone(_1246141))]]], (24803 ^ _782476) ^ [] : [_1246143 = c_Groups_Ozero__class_Ozero(_1246141), -(c_Groups_Osgn__class_Osgn(_1246141, _1246143) = c_Groups_Ozero__class_Ozero(_1246141))]]], (19012 ^ _782476) ^ [_1140394, _1140396, _1140398, _1140400] : [class_Rings_Olinordered__ring__strict(_1140394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140394), _1140396), _1140398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140394), _1140400), c_Groups_Ozero__class_Ozero(_1140394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140394), _1140398), _1140400)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140394), _1140396), _1140400))))], (19040 ^ _782476) ^ [_1140932, _1140934, _1140936, _1140938] : [class_Rings_Olinordered__semiring__strict(_1140932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140932), _1140934), _1140936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140932), c_Groups_Ozero__class_Ozero(_1140932)), _1140938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140932), _1140938), _1140934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140932), _1140938), _1140936))))], (20918 ^ _782476) ^ [_1175751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175751)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9522 ^ _782476) ^ [_953187] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953187, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953187, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_953187, tc_HOL_Obool)))], (10485 ^ _782476) ^ [_973507, _973509, _973511, _973513, _973515] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973507, tc_fun(_973509, tc_HOL_Obool)), _973511), hAPP(hAPP(c_COMBC(_973507, tc_fun(_973509, tc_HOL_Obool), tc_fun(_973509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973509, tc_HOL_Obool), tc_fun(tc_fun(_973509, tc_HOL_Obool), tc_fun(_973509, tc_HOL_Obool)), _973507), c_Groups_Ominus__class_Ominus(tc_fun(_973509, tc_HOL_Obool))), _973513)), _973515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973509, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973507, tc_fun(_973509, tc_HOL_Obool)), _973511), _973513)), _973515))], (52421 ^ _782476) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (22166 ^ _782476) ^ [_1198929, _1198931] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198929), hAPP(c_Nat_OSuc, _1198931)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198929), _1198931)))], (23227 ^ _782476) ^ [_1218488, _1218490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218488), _1218490)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218488), hAPP(c_Nat_OSuc, _1218490)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1218490), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218488), _1218490)))], (16991 ^ _782476) ^ [_1104330, _1104332, _1104334, _1104336, _1104338] : [class_Groups_Ocomm__monoid__add(_1104330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104332), _1104334)), -(hBOOL(hAPP(hAPP(c_member(_1104332), _1104336), _1104334))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104332, _1104330), _1104338), hAPP(hAPP(c_Set_Oinsert(_1104332), _1104336), _1104334)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104330), hAPP(_1104338, _1104336)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104332, _1104330), _1104338), _1104334)))], (39659 ^ _782476) ^ [_1548664, _1548666, _1548668] : [-(hAPP(c_Relation_ODomain(_1548664, _1548666), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1548664, _1548666), tc_HOL_Obool), _1548668)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1548664, _1548666), tc_HOL_Obool), tc_fun(_1548664, tc_HOL_Obool)), _1548668), c_Relation_ODomain(_1548664, _1548666)))], (25736 ^ _782476) ^ [_1265321, _1265323] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265321), _1265323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265321)), _1265323)))], (13204 ^ _782476) ^ [_1025658, _1025660, _1025662, _1025664, _1025666] : [hBOOL(hAPP(hAPP(c_member(_1025658), hAPP(_1025660, _1025662)), _1025664)), -(hBOOL(hAPP(hAPP(c_member(_1025666), _1025662), hAPP(c_Set_Ovimage(_1025666, _1025658, _1025660), _1025664))))], (50532 ^ _782476) ^ [_1804366, _1804368] : [50533 ^ _782476 : [(50534 ^ _782476) ^ [_1804432] : [hBOOL(hAPP(_1804368, _1804432))]], 50536 ^ _782476 : [(50539 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1804368, 50535 ^ [_1804366, _1804368])))], (50537 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804366), 50535 ^ [_1804366, _1804368]), c_Orderings_Otop__class_Otop(tc_fun(_1804366, tc_HOL_Obool)))))]]], (47339 ^ _782476) ^ [_1735453, _1735455] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735453), _1735455) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735453, _1735455)))], (22512 ^ _782476) ^ [_1204697, _1204699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204697), _1204699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204697)), _1204699)))], (35028 ^ _782476) ^ [_1444834, _1444836] : [c_Int_Oiszero(_1444834, hAPP(c_Int_Onumber__class_Onumber__of(_1444834), c_Int_OBit1(_1444836))), class_Int_Onumber__ring(_1444834), class_Int_Oring__char__0(_1444834)], (7295 ^ _782476) ^ [_904112, _904114, _904116, _904118, _904120, _904122] : [hBOOL(hAPP(hAPP(c_member(_904112), _904114), c_SetInterval_Oord_OatLeastLessThan(_904112, _904116, _904118, _904120, _904122))), 7298 ^ _782476 : [(7301 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904118, _904114), _904122)))], (7299 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904116, _904120), _904114)))]]], (8006 ^ _782476) ^ [_918846, _918848, _918850] : [class_Lattices_Osemilattice__sup(_918846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918846), _918848), _918850)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918846), _918848), _918850) = _918850)], (49824 ^ _782476) ^ [_1788451, _1788453, _1788455, _1788457] : [-(c_Predicate_Oconversep(_1788451, _1788453, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788451, tc_fun(_1788453, tc_HOL_Obool))), _1788455), _1788457)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788453, tc_fun(_1788451, tc_HOL_Obool))), c_Predicate_Oconversep(_1788451, _1788453, _1788455)), c_Predicate_Oconversep(_1788451, _1788453, _1788457)))], (49707 ^ _782476) ^ [_1785709, _1785711, _1785713] : [c_Fun_Oinj__on(_1785709, _1785711, _1785713, c_Orderings_Otop__class_Otop(tc_fun(_1785709, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785711, _1785709, _1785709, c_Hilbert__Choice_Oinv__into(_1785709, _1785711, c_Orderings_Otop__class_Otop(tc_fun(_1785709, tc_HOL_Obool)), _1785713)), _1785713) = c_Fun_Oid(_1785709))], (52359 ^ _782476) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (28518 ^ _782476) ^ [_1323423, _1323425, _1323427] : [class_Orderings_Olinorder(_1323423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323423), _1323425)), hBOOL(hAPP(hAPP(c_member(_1323423), _1323427), _1323425)), 28529 ^ _782476 : [(28536 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323423, tc_HOL_Obool)), _1323425), hAPP(hAPP(c_Set_Oinsert(_1323423), _1323427), c_Orderings_Obot__class_Obot(tc_fun(_1323423, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323423, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1323423, c_Orderings_Oord__class_Omax(_1323423), _1323425) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323423), _1323427), c_Big__Operators_Olattice_OSup__fin(_1323423, c_Orderings_Oord__class_Omax(_1323423), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323423, tc_HOL_Obool)), _1323425), hAPP(hAPP(c_Set_Oinsert(_1323423), _1323427), c_Orderings_Obot__class_Obot(tc_fun(_1323423, tc_HOL_Obool)))))))], (28530 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323423, tc_HOL_Obool)), _1323425), hAPP(hAPP(c_Set_Oinsert(_1323423), _1323427), c_Orderings_Obot__class_Obot(tc_fun(_1323423, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323423, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1323423, c_Orderings_Oord__class_Omax(_1323423), _1323425) = _1323427)]]], (36130 ^ _782476) ^ [_1464823] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1464823), c_Int_OMin) = c_Int_Opred(_1464823))], (23269 ^ _782476) ^ [_1219285, _1219287, _1219289, _1219291, _1219293] : [c_Fun_Oinj__on(_1219285, _1219287, _1219289, _1219291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219287, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219285, _1219287, _1219289), _1219291)), _1219293)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219287), _1219293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219285), _1219291)), hAPP(c_Finite__Set_Ocard(_1219287), _1219293))))], (15669 ^ _782476) ^ [_1075603, _1075605, _1075607, _1075609, _1075611, _1075613, _1075615] : [class_Groups_Oab__semigroup__mult(_1075603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075605), _1075607)), c_Fun_Oinj__on(_1075605, _1075609, _1075611, _1075607), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075603, _1075609, c_Groups_Otimes__class_Otimes(_1075603)), _1075613), _1075615), hAPP(c_Set_Oimage(_1075605, _1075609, _1075611), _1075607)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075603, _1075605, c_Groups_Otimes__class_Otimes(_1075603)), hAPP(c_Fun_Ocomp(_1075609, _1075603, _1075605, _1075613), _1075611)), _1075615), _1075607))], (48158 ^ _782476) ^ [_1751082, _1751084, _1751086, _1751088, _1751090] : [c_List_Olist__all2(_1751082, _1751084, _1751086, hAPP(c_List_Orev(_1751082), _1751088), hAPP(c_List_Orev(_1751084), _1751090)), -(c_List_Olist__all2(_1751082, _1751084, _1751086, _1751088, _1751090))], (43574 ^ _782476) ^ [_1648666, _1648668, _1648670] : [hBOOL(hAPP(hAPP(c_member(_1648666), _1648668), hAPP(c_List_Oset(_1648666), _1648670))), -(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(_1648666)), _1648670))))], (46918 ^ _782476) ^ [_1724403, _1724405] : [-(hAPP(c_List_Oset(_1724403), c_List_Oremdups(_1724403, _1724405)) = hAPP(c_List_Oset(_1724403), _1724405))], (2510 ^ _782476) ^ [_819349, _819351] : [_819351 = _819349, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819351) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819349))], (44306 ^ _782476) ^ [_1666233, _1666235] : [_1666233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1666235, _1666233, c_List_Olist_ONil(_1666235)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666235)), c_List_Olist_ONil(_1666235)), c_List_Olist_ONil(tc_List_Olist(_1666235))))], (7103 ^ _782476) ^ [_900005, _900007, _900009] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_900005, tc_HOL_Obool)), _900009), hAPP(c_Set_OPow(_900005), _900007))), -(hBOOL(hAPP(c_Predicate_OPowp(_900005, hAPP(hAPP(c_COMBC(_900005, tc_fun(_900005, tc_HOL_Obool), tc_HOL_Obool), c_member(_900005)), _900007)), _900009)))], (19863 ^ _782476) ^ [_1155307, _1155309, _1155311, _1155313] : [class_Rings_Olinordered__ring__strict(_1155307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155307), c_Groups_Ozero__class_Ozero(_1155307)), _1155309)), 19870 ^ _782476 : [(19877 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155307), _1155311), _1155313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155307), _1155309), _1155311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155307), _1155309), _1155313))))], (19871 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155307), _1155309), _1155311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155307), _1155309), _1155313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155307), _1155311), _1155313)))]]], (16385 ^ _782476) ^ [_1091012, _1091014, _1091016, _1091018, _1091020] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1091012), 16388 ^ _782476 : [(16389 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091014), _1091018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091016), _1091020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091014), _1091020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091016), _1091018)), -(_1091014 = _1091016), -(_1091018 = _1091020)], (16399 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091014), _1091018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091016), _1091020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091014), _1091020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091012), _1091016), _1091018))), 16402 ^ _782476 : [(16405 ^ _782476) ^ [] : [_1091018 = _1091020], (16403 ^ _782476) ^ [] : [_1091014 = _1091016]]]]], (45887 ^ _782476) ^ [_1700614, _1700616, _1700618] : [c_Fun_Oinj__on(_1700614, _1700616, _1700618, c_Orderings_Otop__class_Otop(tc_fun(_1700614, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1700614), tc_List_Olist(_1700616), hAPP(c_List_Omap(_1700614, _1700616), _1700618), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1700614), tc_HOL_Obool))))], (3742 ^ _782476) ^ [_838557, _838559, _838561, _838563] : [-(c_List_OremoveAll(_838563, _838559) = c_List_OremoveAll(_838561, _838557)), _838563 = _838561, _838559 = _838557], (50258 ^ _782476) ^ [_1797558, _1797560, _1797562, _1797564, _1797566, _1797568] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1797558, _1797560, _1797562, _1797564, c_Nitpick_Opair__box_OPairBox(_1797558, _1797560, _1797566, _1797568)) = hAPP(hAPP(_1797564, _1797566), _1797568))], (9039 ^ _782476) ^ [_941024, _941026, _941028, _941030] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941024, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941024, tc_HOL_Obool)), _941026), _941028)), _941030) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941024, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941024, tc_HOL_Obool)), _941026), _941030)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941024, tc_HOL_Obool)), _941028), _941030)))], (52221 ^ _782476) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (15683 ^ _782476) ^ [_1075914, _1075916, _1075918, _1075920] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075914), _1075916)), 15689 ^ _782476 : [(15692 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075918), hAPP(_1075920, 15688 ^ [_1075914, _1075916, _1075918, _1075920])))], (15690 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1075914), 15688 ^ [_1075914, _1075916, _1075918, _1075920]), _1075916)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075918), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1075914, tc_fun(_1075918, tc_HOL_Obool)), _1075916), _1075920))))], (236 ^ _782476) ^ [_786310, _786312] : [-(class_Fields_Ofield(_786310)), _786312 = _786310, class_Fields_Ofield(_786312)], (43459 ^ _782476) ^ [_1645931, _1645933, _1645935] : [-(hAPP(c_List_Oset(_1645931), c_List_Osublist(_1645931, _1645933, _1645935)) = hAPP(c_Set_OCollect(_1645931), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1645931), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1645931, 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)), _1645931), 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)), _1645931), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1645931, tc_fun(tc_Nat_Onat, _1645931), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645931, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1645931), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1645931), c_COMBB(_1645931, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1645931), _1645933))))), 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(_1645931)), _1645933)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1645935))))))], (28808 ^ _782476) ^ [_1329820, _1329822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329820)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329820), _1329822)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329820)), _1329822))], (48500 ^ _782476) ^ [_1758253, _1758255, _1758257, _1758259, _1758261] : [-(c_List_OdropWhile(_1758253, _1758255, hAPP(hAPP(c_List_Omap(_1758257, _1758253), _1758259), _1758261)) = hAPP(hAPP(c_List_Omap(_1758257, _1758253), _1758259), c_List_OdropWhile(_1758257, hAPP(c_Fun_Ocomp(_1758253, tc_HOL_Obool, _1758257, _1758255), _1758259), _1758261)))], (37824 ^ _782476) ^ [_1502680, _1502682, _1502684] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1502680, _1502682), _1502684)), 37827 ^ _782476 : [(37836 ^ _782476) ^ [] : [-(_1502682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37839 ^ _782476 : [(37848 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502682))), 37851 ^ _782476 : [(37854 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502684)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37852 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1502682), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502684))))]]], (37840 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502682)), 37843 ^ _782476 : [(37846 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502684)), _1502682)))], (37844 ^ _782476) ^ [] : [-(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), _1502684))))]]]]], (37830 ^ _782476) ^ [] : [_1502682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1502684) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37828 ^ _782476) ^ [] : [-(_1502680 = 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), _1502684)), _1502682)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502684)))]]], (17033 ^ _782476) ^ [_1105191, _1105193, _1105195, _1105197, _1105199] : [class_Groups_Ocomm__monoid__add(_1105191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105193), _1105195)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105193, _1105191), _1105197), hAPP(hAPP(c_Set_Oinsert(_1105193), _1105199), _1105195)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105191), hAPP(_1105197, _1105199)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105193, _1105191), _1105197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1105193, tc_HOL_Obool)), _1105195), hAPP(hAPP(c_Set_Oinsert(_1105193), _1105199), c_Orderings_Obot__class_Obot(tc_fun(_1105193, tc_HOL_Obool)))))))], (38698 ^ _782476) ^ [_1523517, _1523519, _1523521, _1523523] : [-(hAPP(c_Relation_OField(_1523517), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1523517, _1523517)), hAPP(hAPP(c_Product__Type_OPair(_1523517, _1523517), _1523519), _1523521)), _1523523)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523517, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1523517), _1523519), hAPP(hAPP(c_Set_Oinsert(_1523517), _1523521), c_Orderings_Obot__class_Obot(tc_fun(_1523517, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1523517), _1523523)))], (8503 ^ _782476) ^ [_929919, _929921, _929923, _929925] : [hBOOL(hAPP(hAPP(c_member(_929919), _929921), _929923)), hBOOL(hAPP(hAPP(c_member(_929919), _929921), _929925)), -(hBOOL(hAPP(hAPP(c_member(_929919), _929921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929919, tc_HOL_Obool)), _929923), _929925))))], (11544 ^ _782476) ^ [_993349, _993351, _993353] : [class_Orderings_Olinorder(_993349), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993349), _993351), _993353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993349), _993353), _993351)))], (21397 ^ _782476) ^ [_1184209, _1184211] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184209), _1184211)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184209)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184211))))], (8615 ^ _782476) ^ [_932213, _932215, _932217] : [class_Lattices_Osemilattice__inf(_932213), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932213), _932215), _932217) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932213), _932217), _932215))], (7834 ^ _782476) ^ [_915289, _915291] : [class_Lattices_Osemilattice__sup(_915289), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915289), _915291), _915291) = _915291)], (43358 ^ _782476) ^ [_1643094, _1643096, _1643098, _1643100] : [-(_1643094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643096), hAPP(hAPP(c_List_Olist_OCons(_1643096), _1643098), _1643100)), _1643094) = hAPP(hAPP(c_List_Onth(_1643096), _1643100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643094), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42602 ^ _782476) ^ [_1621511, _1621513, _1621515, _1621517] : [class_Lattices_Osemilattice__sup(_1621511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621511), _1621513)), 42612 ^ _782476 : [(42615 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621511), 42611 ^ [_1621511, _1621513, _1621515, _1621517]), _1621515))], (42613 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621511), 42611 ^ [_1621511, _1621513, _1621515, _1621517]), _1621513)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621511), hAPP(hAPP(c_Finite__Set_Ofold(_1621511, _1621511, c_Lattices_Osemilattice__sup__class_Osup(_1621511)), _1621517), _1621513)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1621511), _1621515), _1621517))))], (45781 ^ _782476) ^ [_1698821, _1698823, _1698825] : [_1698821 = c_List_Olist_ONil(_1698823), -(c_List_Olast(_1698823, hAPP(hAPP(c_List_Olist_OCons(_1698823), _1698825), _1698821)) = _1698825)], (52419 ^ _782476) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (41224 ^ _782476) ^ [_1590115, _1590117, _1590119, _1590121, _1590123] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590115, _1590115)), hAPP(hAPP(c_Product__Type_OPair(_1590115, _1590115), _1590117), _1590119)), c_Transitive__Closure_Otrancl(_1590115, _1590121))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590115, _1590115)), hAPP(hAPP(c_Product__Type_OPair(_1590115, _1590115), _1590119), _1590123)), c_Transitive__Closure_Ortrancl(_1590115, _1590121))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590115, _1590115)), hAPP(hAPP(c_Product__Type_OPair(_1590115, _1590115), _1590117), _1590123)), c_Transitive__Closure_Otrancl(_1590115, _1590121))))], (17287 ^ _782476) ^ [] : [-(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)))], (14821 ^ _782476) ^ [_1059423, _1059425, _1059427] : [class_Lattices_Olattice(_1059423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059423), _1059425)), hBOOL(hAPP(hAPP(c_member(_1059423), _1059427), _1059425)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059423), _1059427), c_Big__Operators_Olattice__class_OInf__fin(_1059423, _1059425)) = _1059427)], (8026 ^ _782476) ^ [_919186, _919188, _919190, _919192] : [class_Lattices_Osemilattice__sup(_919186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919186), _919188), _919190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919186), _919188), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919186), _919190), _919192))))], (52173 ^ _782476) ^ [_1838467, _1838469] : [class_Orderings_Oorder(_1838467), -(class_Orderings_Oorder(tc_fun(_1838469, _1838467)))], (28358 ^ _782476) ^ [_1320502, _1320504] : [class_Orderings_Olinorder(_1320502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320502), _1320504)), -(c_Big__Operators_Olattice_OSup__fin(_1320502, c_Orderings_Oord__class_Omax(_1320502), _1320504) = hAPP(c_Finite__Set_Ofold1(_1320502, c_Orderings_Oord__class_Omax(_1320502)), _1320504))], (41938 ^ _782476) ^ [_1608021, _1608023, _1608025, _1608027, _1608029] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608021, _1608021)), hAPP(hAPP(c_Product__Type_OPair(_1608021, _1608021), _1608023), _1608025)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608021, _1608021), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608027)), _1608029))), 41942 ^ _782476 : [(41945 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608021, _1608021)), hAPP(hAPP(c_Product__Type_OPair(_1608021, _1608021), 41941 ^ [_1608021, _1608023, _1608025, _1608027, _1608029]), _1608025)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608021, _1608021), tc_HOL_Obool), _1608027), _1608029))))], (41943 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608021, _1608021)), hAPP(hAPP(c_Product__Type_OPair(_1608021, _1608021), _1608023), 41941 ^ [_1608021, _1608023, _1608025, _1608027, _1608029])), _1608029)))]]], (10695 ^ _782476) ^ [_978234, _978236] : [class_Orderings_Oorder(_978234), -(c_SetInterval_Oord__class_OatLeastAtMost(_978234, _978236, _978236) = hAPP(hAPP(c_Set_Oinsert(_978234), _978236), c_Orderings_Obot__class_Obot(tc_fun(_978234, tc_HOL_Obool))))], (19286 ^ _782476) ^ [_1145474, _1145476, _1145478] : [class_Groups_Oordered__ab__group__add(_1145474), 19289 ^ _782476 : [(19296 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145474), _1145476), _1145478)), c_Groups_Ozero__class_Ozero(_1145474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145474), _1145476), _1145478)))], (19290 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145474), _1145476), _1145478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145474), _1145476), _1145478)), c_Groups_Ozero__class_Ozero(_1145474))))]]], (39776 ^ _782476) ^ [_1552665, _1552667, _1552669, _1552671] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552665), _1552667)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552669), _1552671)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552665, _1552669)), hAPP(hAPP(c_Product__Type_OSigma(_1552665, _1552669), _1552667), hAPP(c_COMBK(tc_fun(_1552669, tc_HOL_Obool), _1552665), _1552671)))))], (20675 ^ _782476) ^ [_1171148, _1171150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1171148), _1171150)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171150)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171148)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171150), _1171148)))], (52353 ^ _782476) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (27531 ^ _782476) ^ [_1303331, _1303333, _1303335] : [class_Orderings_Olinorder(_1303331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303331), _1303333)), hBOOL(hAPP(hAPP(c_member(_1303331), _1303335), _1303333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303331), hAPP(c_Finite__Set_Ofold1(_1303331, c_Orderings_Oord__class_Omin(_1303331)), _1303333)), _1303335)))], (50335 ^ _782476) ^ [_1799473, _1799475, _1799477] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799473) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1799473, _1799475, _1799477)], (21963 ^ _782476) ^ [_1195623, _1195625, _1195627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1195623), _1195625)), hBOOL(hAPP(hAPP(c_member(_1195623), _1195627), _1195625)), -(hAPP(c_Finite__Set_Ocard(_1195623), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195623, tc_HOL_Obool)), _1195625), hAPP(hAPP(c_Set_Oinsert(_1195623), _1195627), c_Orderings_Obot__class_Obot(tc_fun(_1195623, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1195623), _1195625)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (36040 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (52777 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G)))], (18584 ^ _782476) ^ [_1132528, _1132530, _1132532, _1132534] : [class_Groups_Oordered__comm__monoid__add(_1132528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132528), c_Groups_Ozero__class_Ozero(_1132528)), _1132530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132528), _1132532), _1132534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132528), _1132532), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132528), _1132530), _1132534))))], (698 ^ _782476) ^ [_793155, _793157, _793159, _793161] : [-(c_List_Olinorder__class_Osorted(_793159, _793155)), c_List_Olinorder__class_Osorted(_793161, _793157), _793161 = _793159, _793157 = _793155], (40810 ^ _782476) ^ [_1580117, _1580119, _1580121, _1580123, _1580125] : [-(_1580117 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1580119, _1580121, _1580117, _1580123), _1580125) = hAPP(hAPP(c_Product__Type_Oscomp(_1580121, _1580119, _1580121, tc_prod(_1580119, _1580121)), hAPP(_1580123, _1580125)), c_Random_Oiterate(_1580119, _1580121, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1580117), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1580123)))], (1762 ^ _782476) ^ [_807701, _807703] : [-(class_Groups_Ocomm__monoid__add(_807701)), _807703 = _807701, class_Groups_Ocomm__monoid__add(_807703)], (13410 ^ _782476) ^ [_1030699, _1030701, _1030703, _1030705, _1030707, _1030709] : [-(_1030699 = c_Orderings_Obot__class_Obot(tc_fun(_1030701, tc_HOL_Obool))), 13416 ^ _782476 : [(13419 ^ _782476) ^ [] : [c_Fun_Oinj__on(_1030703, _1030705, _1030707, hAPP(_1030709, 13415 ^ [_1030699, _1030701, _1030703, _1030705, _1030707, _1030709]))], (13417 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030701), 13415 ^ [_1030699, _1030701, _1030703, _1030705, _1030707, _1030709]), _1030699)))]], -(c_Fun_Oinj__on(_1030703, _1030705, _1030707, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030701, tc_fun(_1030703, tc_HOL_Obool)), _1030699), _1030709)))], (1812 ^ _782476) ^ [_808326, _808328] : [-(class_Nat_Osemiring__char__0(_808326)), _808328 = _808326, class_Nat_Osemiring__char__0(_808328)], (12812 ^ _782476) ^ [_1017173, _1017175, _1017177] : [class_Complete__Lattice_Ocomplete__lattice(_1017173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017173), hAPP(_1017175, _1017177)), _1017177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017173), c_Inductive_Ocomplete__lattice__class_Olfp(_1017173, _1017175)), _1017177)))], (45098 ^ _782476) ^ [_1684501, _1684503, _1684505] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684501)), hAPP(hAPP(c_List_Odrop(_1684501), _1684503), _1684505)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684501)), _1684505)), _1684503))], (37523 ^ _782476) ^ [_1496578, _1496580, _1496582, _1496584, _1496586, _1496588] : [hAPP(_1496584, hAPP(c_Product__Type_Osnd(_1496582, _1496578), _1496586)) = hAPP(_1496588, hAPP(c_Product__Type_Osnd(_1496582, _1496578), _1496586)), -(hAPP(c_Product__Type_Oapsnd(_1496578, _1496580, _1496582, _1496584), _1496586) = hAPP(c_Product__Type_Oapsnd(_1496578, _1496580, _1496582, _1496588), _1496586))], (46766 ^ _782476) ^ [_1721129, _1721131, _1721133, _1721135] : [_1721135 = c_List_Olist_ONil(_1721131), -(c_List_Olist__all2(_1721129, _1721131, _1721133, c_List_Olist_ONil(_1721129), _1721135))], (32309 ^ _782476) ^ [_1394412, _1394414, _1394416] : [-(hBOOL(hAPP(_1394412, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1394414, _1394416)))), 32312 ^ _782476 : [(32315 ^ _782476) ^ [] : [hBOOL(hAPP(_1394412, _1394414))], (32313 ^ _782476) ^ [] : [-(_1394416 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 32318 ^ _782476 : [(32319 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394416)))], (32325 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32321 ^ [_1394412, _1394414, _1394416]), _1394416)))], (32329 ^ _782476) ^ [] : [hBOOL(hAPP(_1394412, 32321 ^ [_1394412, _1394414, _1394416]))], (32327 ^ _782476) ^ [] : [-(_1394414 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394416), 32320 ^ [_1394412, _1394414, _1394416])), 32321 ^ [_1394412, _1394414, _1394416]))], (32323 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32321 ^ [_1394412, _1394414, _1394416])))]], 32330 ^ _782476 : [(32331 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394416), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32337 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 32333 ^ [_1394412, _1394414, _1394416]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32341 ^ _782476) ^ [] : [hBOOL(hAPP(_1394412, 32333 ^ [_1394412, _1394414, _1394416]))], (32339 ^ _782476) ^ [] : [-(_1394414 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394416), 32332 ^ [_1394412, _1394414, _1394416])), 32333 ^ [_1394412, _1394414, _1394416]))], (32335 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394416), 32333 ^ [_1394412, _1394414, _1394416])))]]], (27399 ^ _782476) ^ [_1300677, _1300679, _1300681, _1300683] : [class_Orderings_Olinorder(_1300677), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300677, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300677), _1300679)), c_SetInterval_Oord__class_OatLeastAtMost(_1300677, _1300681, _1300683)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300677, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300677), _1300679), _1300681), _1300683))], (39542 ^ _782476) ^ [_1545551] : [-(c_Nitpick_Oone__frac(_1545551) = c_Nitpick_OAbs__Frac(_1545551, 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))))], (14529 ^ _782476) ^ [_1053088, _1053090, _1053092, _1053094, _1053096] : [c_Finite__Set_Ofolding__one(_1053088, _1053090, _1053092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053088), _1053094)), -(hBOOL(hAPP(hAPP(c_member(_1053088), _1053096), _1053094))), -(_1053094 = c_Orderings_Obot__class_Obot(tc_fun(_1053088, tc_HOL_Obool))), -(hAPP(_1053092, hAPP(hAPP(c_Set_Oinsert(_1053088), _1053096), _1053094)) = hAPP(hAPP(_1053090, _1053096), hAPP(_1053092, _1053094)))], (52629 ^ _782476) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52305 ^ _782476) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (36825 ^ _782476) ^ [_1483387, _1483389, _1483391, _1483393, _1483395, _1483397, _1483399] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483387, _1483389, tc_fun(_1483391, tc_HOL_Obool)), _1483393), hAPP(hAPP(c_Product__Type_OPair(_1483387, _1483389), _1483395), _1483397)), _1483399)), -(hBOOL(hAPP(hAPP(hAPP(_1483393, _1483395), _1483397), _1483399)))], (21169 ^ _782476) ^ [_1180085, _1180087] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180085), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1180087) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1180085, _1180087))], (32139 ^ _782476) ^ [_1391159, _1391161, _1391163] : [class_Divides_Osemiring__div(_1391159), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391159), c_Divides_Odiv__class_Omod(_1391159, _1391161, _1391163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391159), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391159), _1391161), _1391163)), _1391163)) = _1391161)], (1652 ^ _782476) ^ [_806326, _806328] : [-(class_Groups_Ocancel__ab__semigroup__add(_806326)), _806328 = _806326, class_Groups_Ocancel__ab__semigroup__add(_806328)], (48202 ^ _782476) ^ [_1751952, _1751954] : [-(hAPP(c_List_Orev(_1751952), _1751954) = hAPP(c_List_Ofoldl(tc_List_Olist(_1751952), _1751952, hAPP(c_COMBC(_1751952, tc_List_Olist(_1751952), tc_List_Olist(_1751952)), c_List_Olist_OCons(_1751952)), c_List_Olist_ONil(_1751952)), _1751954))], (28760 ^ _782476) ^ [_1328750, _1328752, _1328754, _1328756] : [class_Rings_Odivision__ring(_1328750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328750), _1328752), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328750), _1328754), _1328756)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328750), _1328752), _1328754)), _1328756))], (49031 ^ _782476) ^ [_1770880, _1770882, _1770884] : [-(c_List_Olist__ex(_1770880, _1770882, _1770884)), 49032 ^ _782476 : [(49033 ^ _782476) ^ [_1770945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770880)), _1770884))), hBOOL(hAPP(_1770882, hAPP(hAPP(c_List_Onth(_1770880), _1770884), _1770945)))]]], (41547 ^ _782476) ^ [_1598045, _1598047, _1598049, _1598051, _1598053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598047, tc_HOL_Obool)), _1598051), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598047, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598045, _1598047, hAPP(c_Relation_Oconverse(_1598047, _1598045), _1598049)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598045, tc_HOL_Obool)), _1598053))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598045, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598047, _1598045, _1598049), _1598051)), _1598053)))], (29434 ^ _782476) ^ [_1341047, _1341049, _1341051, _1341053] : [class_Rings_Olinordered__semidom(_1341047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341047), hAPP(hAPP(c_Power_Opower__class_Opower(_1341047), _1341049), hAPP(c_Nat_OSuc, _1341051))), hAPP(hAPP(c_Power_Opower__class_Opower(_1341047), _1341053), hAPP(c_Nat_OSuc, _1341051)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341047), c_Groups_Ozero__class_Ozero(_1341047)), _1341053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341047), _1341049), _1341053)))], (39622 ^ _782476) ^ [_1547656, _1547658, _1547660, _1547662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547656, _1547658), tc_HOL_Obool)), _1547660), _1547662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547656, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547656, _1547658), _1547660)), hAPP(c_Relation_ODomain(_1547656, _1547658), _1547662))))], (9432 ^ _782476) ^ [_951401, _951403, _951405, _951407] : [c_Orderings_Obot__class_Obot(tc_fun(_951401, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951403, _951401, _951405), _951407), -(_951407 = c_Orderings_Obot__class_Obot(tc_fun(_951403, tc_HOL_Obool)))], (32203 ^ _782476) ^ [_1392454, _1392456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392454)), 32206 ^ _782476 : [(32209 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392456, _1392454)), _1392454)))], (32207 ^ _782476) ^ [] : [-(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, _1392456, _1392454))))]]], (28888 ^ _782476) ^ [_1331236, _1331238] : [class_Rings_Odivision__ring__inverse__zero(_1331236), 28891 ^ _782476 : [(28898 ^ _782476) ^ [] : [-(_1331238 = c_Groups_Ozero__class_Ozero(_1331236)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331236), _1331238), _1331238) = c_Groups_Oone__class_Oone(_1331236))], (28892 ^ _782476) ^ [] : [_1331238 = c_Groups_Ozero__class_Ozero(_1331236), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331236), _1331238), _1331238) = c_Groups_Ozero__class_Ozero(_1331236))]]], (3334 ^ _782476) ^ [_832231, _832233, _832235, _832237] : [-(c_Enum_Osublists(_832237, _832233) = c_Enum_Osublists(_832235, _832231)), _832237 = _832235, _832233 = _832231], (35284 ^ _782476) ^ [_1449279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449279)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449279), c_Int_OPls)))], (20019 ^ _782476) ^ [_1158299, _1158301, _1158303, _1158305] : [class_Rings_Olinordered__semiring(_1158299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158299), _1158301), _1158303)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158299), _1158301), _1158305))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158299), c_Groups_Ozero__class_Ozero(_1158299)), _1158301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158299), _1158303), _1158305)))], (20111 ^ _782476) ^ [_1160021] : [class_Rings_Olinordered__semidom(_1160021), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160021), c_Groups_Ozero__class_Ozero(_1160021)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160021), c_Groups_Oone__class_Oone(_1160021)), c_Groups_Oone__class_Oone(_1160021)))))], (42939 ^ _782476) ^ [_1630424, _1630426, _1630428, _1630430, _1630432] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630424), _1630426), _1630428) = hAPP(hAPP(c_List_Olist_OCons(_1630424), _1630430), _1630432)), _1630426 = _1630430, _1630428 = _1630432], (11146 ^ _782476) ^ [_987258, _987260, _987262] : [class_Orderings_Oorder(_987258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987258), _987260), _987262)), _987262 = _987260], (39374 ^ _782476) ^ [_1541366] : [class_Orderings_Owellorder(_1541366), -(c_Wellfounded_Owf(_1541366, hAPP(c_Set_OCollect(tc_prod(_1541366, _1541366)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541366, _1541366, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1541366)))))], (32774 ^ _782476) ^ [_1403524, _1403526, _1403528] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403524), hAPP(hAPP(c_Set_Oinsert(_1403524), _1403526), c_Orderings_Obot__class_Obot(tc_fun(_1403524, tc_HOL_Obool)))), _1403528) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1403524, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403524, _1403524, _1403528), hAPP(hAPP(c_Set_Oinsert(_1403524), _1403526), c_Orderings_Obot__class_Obot(tc_fun(_1403524, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403524, tc_HOL_Obool), tc_HOL_Obool))))], (47319 ^ _782476) ^ [_1734765, _1734767, _1734769, _1734771, _1734773, _1734775, _1734777] : [-(c_List_Ofoldr(_1734765, _1734767, _1734769, hAPP(hAPP(c_List_Omap(_1734771, _1734765), _1734773), _1734775), _1734777) = c_List_Ofoldr(_1734771, _1734767, hAPP(c_Fun_Ocomp(_1734765, tc_fun(_1734767, _1734767), _1734771, _1734769), _1734773), _1734775, _1734777))], (39786 ^ _782476) ^ [_1552868, _1552870, _1552872] : [c_Equiv__Relations_Oequiv(_1552868, _1552870, _1552872), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552868, _1552868), tc_HOL_Obool)), _1552872), hAPP(hAPP(c_Product__Type_OSigma(_1552868, _1552868), _1552870), hAPP(c_COMBK(tc_fun(_1552868, tc_HOL_Obool), _1552868), _1552870)))))], (22200 ^ _782476) ^ [_1199469, _1199471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199469)), hAPP(c_Nat_OSuc, _1199471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199469), _1199471)))], (26604 ^ _782476) ^ [_1284948, _1284950, _1284952, _1284954] : [class_Orderings_Olinorder(_1284948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284948), _1284950), _1284952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284948), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284948), _1284950), _1284954)), _1284952)))], (48932 ^ _782476) ^ [_1768496, _1768498, _1768500, _1768502, _1768504] : [-(hAPP(hAPP(c_List_Olist_OCons(_1768496), _1768498), _1768500) = hAPP(c_List_Ofilter(_1768496, _1768502), _1768504)), 48933 ^ _782476 : [(48934 ^ _782476) ^ [_1768624, _1768626] : [_1768504 = hAPP(hAPP(c_List_Oappend(_1768496), _1768626), hAPP(hAPP(c_List_Olist_OCons(_1768496), _1768498), _1768624)), 48940 ^ _782476 : [(48943 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1768502, 48939 ^ [_1768496, _1768498, _1768500, _1768502, _1768504, _1768624, _1768626])))], (48941 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768496), 48939 ^ [_1768496, _1768498, _1768500, _1768502, _1768504, _1768624, _1768626]), hAPP(c_List_Oset(_1768496), _1768626))))]], hBOOL(hAPP(_1768502, _1768498)), _1768500 = hAPP(c_List_Ofilter(_1768496, _1768502), _1768624)]]], (45679 ^ _782476) ^ [_1697150, _1697152, _1697154, _1697156, _1697158] : [class_Orderings_Olinorder(_1697150), -(hBOOL(hAPP(hAPP(c_member(_1697150), hAPP(_1697152, _1697154)), hAPP(c_Set_Oimage(_1697156, _1697150, _1697152), hAPP(c_List_Oset(_1697156), _1697158))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697156, _1697150, _1697152, _1697154, _1697158) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697156, _1697150, _1697152), _1697154), _1697158))], (32672 ^ _782476) ^ [_1401110, _1401112, _1401114] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401112), _1401114)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401112), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401110), _1401112), _1401114))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401110, _1401112)))], (9728 ^ _782476) ^ [_956853, _956855, _956857] : [class_Orderings_Oorder(_956853), 9731 ^ _782476 : [(9738 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956853), _956855), _956857))), -(c_SetInterval_Oord__class_OatLeastAtMost(_956853, _956855, _956857) = c_Orderings_Obot__class_Obot(tc_fun(_956853, tc_HOL_Obool)))], (9732 ^ _782476) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_956853, _956855, _956857) = c_Orderings_Obot__class_Obot(tc_fun(_956853, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956853), _956855), _956857))]]], (12908 ^ _782476) ^ [_1018895, _1018897, _1018899, _1018901, _1018903] : [c_Fun_Oinj__on(_1018895, _1018897, _1018899, c_Orderings_Otop__class_Otop(tc_fun(_1018895, tc_HOL_Obool))), 12911 ^ _782476 : [(12918 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018895), _1018901), _1018903)), -(hBOOL(hAPP(hAPP(c_member(_1018897), hAPP(_1018899, _1018901)), hAPP(c_Set_Oimage(_1018895, _1018897, _1018899), _1018903))))], (12912 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018897), hAPP(_1018899, _1018901)), hAPP(c_Set_Oimage(_1018895, _1018897, _1018899), _1018903))), -(hBOOL(hAPP(hAPP(c_member(_1018895), _1018901), _1018903)))]]], (50452 ^ _782476) ^ [_1802238, _1802240, _1802242, _1802244, _1802246] : [c_Relation_Otrans(_1802238, _1802240), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802238, _1802238)), hAPP(hAPP(c_Product__Type_OPair(_1802238, _1802238), _1802242), _1802244)), _1802240)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802238, _1802238)), hAPP(hAPP(c_Product__Type_OPair(_1802238, _1802238), _1802244), _1802246)), _1802240)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802238, _1802238)), hAPP(hAPP(c_Product__Type_OPair(_1802238, _1802238), _1802242), _1802246)), _1802240)))], (4382 ^ _782476) ^ [_849021, _849023, _849025, _849027] : [-(c_Lazy__Sequence_Osmall__lazy_H(_849027, _849023) = c_Lazy__Sequence_Osmall__lazy_H(_849025, _849021)), _849027 = _849025, _849023 = _849021], (2852 ^ _782476) ^ [_824688, _824690, _824692, _824694] : [-(c_Relation_ODomain(_824694, _824690) = c_Relation_ODomain(_824692, _824688)), _824694 = _824692, _824690 = _824688], (22638 ^ _782476) ^ [_1207066, _1207068] : [-(hAPP(c_Finite__Set_Ocard(_1207066), _1207068) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1207066, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1207066), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1207068))], (1582 ^ _782476) ^ [_805451, _805453] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_805451)), _805453 = _805451, class_Groups_Oordered__cancel__ab__semigroup__add(_805453)], (44020 ^ _782476) ^ [_1660535, _1660537, _1660539] : [hBOOL(hAPP(c_List_Odistinct(_1660535), _1660537)), -(hBOOL(hAPP(c_List_Odistinct(_1660535), hAPP(hAPP(c_List_Otake(_1660535), _1660539), _1660537))))], (37187 ^ _782476) ^ [_1490249, _1490251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1490249), _1490251)), -(c_Divides_Odivmod__nat(_1490251, _1490249) = 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), _1490251), _1490249)), _1490249))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1490251), _1490249), _1490249)))], (49738 ^ _782476) ^ [_1786454, _1786456] : [class_Lazy__Sequence_Osmall__lazy(_1786454), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786454), _1786456) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1786454), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1786454)), c_List_Olist_ONil(_1786454)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786454))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1786456)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1786454, tc_List_Olist(_1786454)), tc_List_Olist(_1786454), c_Lazy__Sequence_Oproduct(_1786454, tc_List_Olist(_1786454), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786454, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786456), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786454), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786456), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1786454, tc_List_Olist(_1786454), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786454))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1786454), tc_List_Olist(_1786454)), tc_fun(tc_List_Olist(_1786454), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786454))), _1786454), hAPP(c_COMBB(tc_List_Olist(_1786454), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786454)), tc_List_Olist(_1786454)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1786454)))), c_List_Olist_OCons(_1786454))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1786454)))))], (17471 ^ _782476) ^ [_1113852, _1113854, _1113856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113852), _1113854)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113852), _1113856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113854), _1113856)))], (9520 ^ _782476) ^ [_953145] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953145, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_953145, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_953145, tc_HOL_Obool)))], (2354 ^ _782476) ^ [_816981, _816983] : [_816983 = _816981, -(c_Nat_Osemiring__1__class_ONats(_816983) = c_Nat_Osemiring__1__class_ONats(_816981))], (1872 ^ _782476) ^ [_809076, _809078] : [-(class_Rings_Osemiring__1(_809076)), _809078 = _809076, class_Rings_Osemiring__1(_809078)], (20189 ^ _782476) ^ [_1161525, _1161527, _1161529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161525)), 20192 ^ _782476 : [(20199 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161527), _1161529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161525), _1161527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161525), _1161529))))], (20193 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161525), _1161527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161525), _1161529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161527), _1161529)))]]], (2582 ^ _782476) ^ [_820507, _820509, _820511, _820513] : [-(c_Wellfounded_Omin__ext(_820513, _820509) = c_Wellfounded_Omin__ext(_820511, _820507)), _820513 = _820511, _820509 = _820507], (40569 ^ _782476) ^ [_1573483, _1573485, _1573487, _1573489] : [40571 ^ _782476 : [(40574 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573483, _1573483, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573483, tc_fun(_1573483, _1573485), tc_fun(_1573483, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573485, tc_HOL_Obool), tc_fun(tc_fun(_1573483, _1573485), tc_fun(_1573483, tc_HOL_Obool)), _1573483), c_COMBB(_1573485, tc_HOL_Obool, _1573483)), hAPP(hAPP(c_COMBB(_1573485, tc_fun(_1573485, tc_HOL_Obool), _1573483), c_fequal), _1573489))), _1573489)), 40570 ^ [_1573483, _1573485, _1573487, _1573489]))], (40572 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573483, _1573483)), 40570 ^ [_1573483, _1573485, _1573487, _1573489]), _1573487)))]], -(c_Equiv__Relations_Ocongruent(_1573483, _1573485, _1573487, _1573489))], (9961 ^ _782476) ^ [_962065, _962067] : [class_Lattices_Oboolean__algebra(_962065), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_962065), hAPP(c_Groups_Ouminus__class_Ouminus(_962065), _962067)), _962067) = c_Orderings_Obot__class_Obot(_962065))], (36346 ^ _782476) ^ [_1468284, _1468286] : [-(c_Divides_Odivmod__int__rel(_1468284, _1468286) = 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, _1468284))), 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), _1468286)))))), 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)), _1468286))), 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)), _1468286))))), 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)), _1468286)))), 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), _1468286))), 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))))))))], (36398 ^ _782476) ^ [_1469833, _1469835, _1469837, _1469839] : [_1469837 = _1469839, -(hAPP(hAPP(c_COMBC(_1469833, tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_fun(_1469835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469835, tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_fun(_1469835, tc_HOL_Obool)), _1469833), c_COMBC(_1469835, tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469835, tc_prod(_1469833, _1469835)), tc_fun(_1469835, tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), _1469833), hAPP(c_COMBB(tc_prod(_1469833, _1469835), tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool), _1469835), c_member(tc_prod(_1469833, _1469835)))), c_Product__Type_OPair(_1469833, _1469835)))), _1469837) = hAPP(hAPP(c_COMBC(_1469833, tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_fun(_1469835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469835, tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_fun(_1469835, tc_HOL_Obool)), _1469833), c_COMBC(_1469835, tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469835, tc_prod(_1469833, _1469835)), tc_fun(_1469835, tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool)), _1469833), hAPP(c_COMBB(tc_prod(_1469833, _1469835), tc_fun(tc_fun(tc_prod(_1469833, _1469835), tc_HOL_Obool), tc_HOL_Obool), _1469835), c_member(tc_prod(_1469833, _1469835)))), c_Product__Type_OPair(_1469833, _1469835)))), _1469839))], (24516 ^ _782476) ^ [_1241072] : [class_Rings_Oring__1(_1241072), -(hAPP(c_Int_Oring__1__class_Oof__int(_1241072), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1241072))], (23691 ^ _782476) ^ [_1227433, _1227435] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227433)), hAPP(c_Int_Onat, _1227435)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227433), _1227435))], (41591 ^ _782476) ^ [_1599135, _1599137, _1599139] : [c_Relation_Ototal__on(_1599135, _1599137, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599135, _1599135), tc_HOL_Obool)), _1599139), c_Relation_OId(_1599135))), -(c_Relation_Ototal__on(_1599135, _1599137, _1599139))], (980 ^ _782476) ^ [_797328, _797330, _797332, _797334] : [-(c_Equiv__Relations_Opart__equivp(_797332, _797328)), c_Equiv__Relations_Opart__equivp(_797334, _797330), _797334 = _797332, _797330 = _797328], (38547 ^ _782476) ^ [_1520406, _1520408, _1520410, _1520412, _1520414] : [-(hAPP(c_Product__Type_Ofst(_1520406, _1520408), hAPP(c_Product__Type_Oapfst(_1520410, _1520406, _1520408, _1520412), _1520414)) = hAPP(_1520412, hAPP(c_Product__Type_Ofst(_1520410, _1520408), _1520414)))], (39907 ^ _782476) ^ [_1556248, _1556250, _1556252, _1556254] : [_1556248 = c_Orderings_Obot__class_Obot(tc_fun(_1556250, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556252, _1556250), _1556252, c_Product__Type_Ofst(_1556252, _1556250)), hAPP(hAPP(c_Product__Type_OSigma(_1556252, _1556250), _1556254), hAPP(c_COMBK(tc_fun(_1556250, tc_HOL_Obool), _1556252), _1556248))) = c_Orderings_Obot__class_Obot(tc_fun(_1556252, tc_HOL_Obool)))], (45358 ^ _782476) ^ [_1690269, _1690271, _1690273, _1690275] : [-(hAPP(c_List_Orotate(_1690269, _1690271), hAPP(c_List_Orotate(_1690269, _1690273), _1690275)) = hAPP(c_List_Orotate(_1690269, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690271), _1690273)), _1690275))], (46412 ^ _782476) ^ [_1712866, _1712868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712866), _1712868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712866)), hAPP(c_Code__Numeral_Onat__of, _1712868))))], (11952 ^ _782476) ^ [_1000032, _1000034, _1000036, _1000038, _1000040] : [class_Orderings_Olinorder(_1000032), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000032, _1000034), _1000036) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000032, _1000038), _1000040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000032), _1000034), _1000036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000032), _1000038), _1000040)), -(_1000034 = _1000038)], (4430 ^ _782476) ^ [_849723, _849725] : [_849725 = _849723, -(c_List_Ohd(_849725) = c_List_Ohd(_849723))], (46374 ^ _782476) ^ [_1712239, _1712241] : [_1712239 = _1712241, -(hAPP(c_Code__Numeral_Onat__of, _1712239) = hAPP(c_Code__Numeral_Onat__of, _1712241))], (17656 ^ _782476) ^ [_1117244, _1117246, _1117248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117244), _1117246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117248), _1117246)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117248), _1117244))))], (23849 ^ _782476) ^ [_1229968, _1229970] : [_1229968 = hAPP(c_Int_Onat, _1229970), 23852 ^ _782476 : [(23859 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229970))), -(_1229968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23853 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229970)), -(_1229970 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229968))]]], (33126 ^ _782476) ^ [_1410455, _1410457, _1410459] : [class_Int_Onumber(_1410455), class_Orderings_Oord(_1410455), 33133 ^ _782476 : [(33140 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410455), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410457)), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410459)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410455), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410457)), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410459)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410459))], (33134 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410455), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410457)), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410459))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410455), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410457)), hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410459)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410455), _1410457))]]], (39702 ^ _782476) ^ [_1550275, _1550277, _1550279, _1550281, _1550283, _1550285] : [hBOOL(hAPP(hAPP(c_member(_1550275), _1550277), _1550279)), 39705 ^ _782476 : [(39712 ^ _782476) ^ [] : [_1550283 = _1550285, -(hAPP(hAPP(c_Product__Type_OSigma(_1550281, _1550275), _1550283), hAPP(c_COMBK(tc_fun(_1550275, tc_HOL_Obool), _1550281), _1550279)) = hAPP(hAPP(c_Product__Type_OSigma(_1550281, _1550275), _1550285), hAPP(c_COMBK(tc_fun(_1550275, tc_HOL_Obool), _1550281), _1550279)))], (39706 ^ _782476) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1550281, _1550275), _1550283), hAPP(c_COMBK(tc_fun(_1550275, tc_HOL_Obool), _1550281), _1550279)) = hAPP(hAPP(c_Product__Type_OSigma(_1550281, _1550275), _1550285), hAPP(c_COMBK(tc_fun(_1550275, tc_HOL_Obool), _1550281), _1550279)), -(_1550283 = _1550285)]]], (27002 ^ _782476) ^ [_1292772, _1292774, _1292776] : [class_Groups_Olinordered__ab__group__add(_1292772), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292772), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292772), _1292774), _1292776)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292772), hAPP(c_Groups_Ouminus__class_Ouminus(_1292772), _1292774)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292772), _1292776)))], (52225 ^ _782476) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (31157 ^ _782476) ^ [_1372095, _1372097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372095), 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)), _1372097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372095), _1372097)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9786 ^ _782476) ^ [_957894] : [class_Complete__Lattice_Ocomplete__lattice(_957894), -(c_Complete__Lattice_OInf__class_OInf(_957894, c_Orderings_Obot__class_Obot(tc_fun(_957894, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_957894))], (39636 ^ _782476) ^ [_1547992, _1547994, _1547996] : [-(hAPP(c_Set_Oimage(tc_prod(_1547992, _1547994), _1547992, c_Product__Type_Ofst(_1547992, _1547994)), _1547996) = hAPP(c_Relation_ODomain(_1547992, _1547994), _1547996))], (49647 ^ _782476) ^ [_1784149, _1784151, _1784153, _1784155] : [c_Fun_Oinj__on(_1784149, _1784151, _1784153, c_Orderings_Otop__class_Otop(tc_fun(_1784149, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1784151, _1784149, c_Hilbert__Choice_Oinv__into(_1784149, _1784151, c_Orderings_Otop__class_Otop(tc_fun(_1784149, tc_HOL_Obool)), _1784153)), hAPP(c_Set_Oimage(_1784149, _1784151, _1784153), _1784155)) = _1784155)], (12552 ^ _782476) ^ [_1012218, _1012220, _1012222, _1012224] : [class_Complete__Lattice_Ocomplete__lattice(_1012218), _1012220 = c_Inductive_Ocomplete__lattice__class_Olfp(_1012218, _1012222), c_Orderings_Oorder__class_Omono(_1012218, _1012218, _1012222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012218), hAPP(_1012222, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012218), _1012220), _1012224))), _1012224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012218), _1012220), _1012224)))], (9462 ^ _782476) ^ [_952022, _952024, _952026] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952022, tc_HOL_Obool)), _952024), _952026) = c_Orderings_Obot__class_Obot(tc_fun(_952022, tc_HOL_Obool)), 9465 ^ _782476 : [(9468 ^ _782476) ^ [] : [-(_952026 = c_Orderings_Obot__class_Obot(tc_fun(_952022, tc_HOL_Obool)))], (9466 ^ _782476) ^ [] : [-(_952024 = c_Orderings_Obot__class_Obot(tc_fun(_952022, tc_HOL_Obool)))]]], (45819 ^ _782476) ^ [_1699367, _1699369] : [-(_1699367 = c_List_Olist_ONil(_1699369)), -(hAPP(hAPP(c_List_Oappend(_1699369), c_List_Obutlast(_1699369, _1699367)), hAPP(hAPP(c_List_Olist_OCons(_1699369), c_List_Olast(_1699369, _1699367)), c_List_Olist_ONil(_1699369))) = _1699367)], (50396 ^ _782476) ^ [_1800573, _1800575, _1800577, _1800579] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800573), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1800575, _1800577, _1800573, _1800579) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1800575, 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(_1800575)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1800577, _1800579)), 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(_1800575)))), 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(_1800575)))), 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(_1800575)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1800575, 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(_1800575)))), 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(_1800575)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1800575, _1800577, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1800573), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1800579))), 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(_1800575)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575)))), 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(_1800575)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1800575, 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(_1800575)))), 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(_1800575)))), 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(_1800575))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575)))), 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(_1800575)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575))))), tc_prod(_1800575, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1800575)), hAPP(hAPP(c_COMBB(_1800575, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800575)))), tc_prod(_1800575, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1800575)), c_Product__Type_Ofst(_1800575, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (43167 ^ _782476) ^ [_1637671, _1637673, _1637675, _1637677] : [c_List_Olistrelp(_1637671, hAPP(hAPP(c_COMBC(_1637671, tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_fun(_1637671, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637671, tc_fun(tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_fun(_1637671, tc_HOL_Obool)), _1637671), c_COMBC(_1637671, tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637671, tc_prod(_1637671, _1637671)), tc_fun(_1637671, tc_fun(tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_HOL_Obool)), _1637671), hAPP(c_COMBB(tc_prod(_1637671, _1637671), tc_fun(tc_fun(tc_prod(_1637671, _1637671), tc_HOL_Obool), tc_HOL_Obool), _1637671), c_member(tc_prod(_1637671, _1637671)))), c_Product__Type_OPair(_1637671, _1637671)))), _1637673), _1637675, _1637677), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637671), tc_List_Olist(_1637671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637671), tc_List_Olist(_1637671)), _1637675), _1637677)), c_List_Olistrel(_1637671, _1637673))))], (18554 ^ _782476) ^ [_1132057, _1132059, _1132061] : [class_Groups_Oordered__comm__monoid__add(_1132057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132057), c_Groups_Ozero__class_Ozero(_1132057)), _1132059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132057), c_Groups_Ozero__class_Ozero(_1132057)), _1132061)), 18565 ^ _782476 : [(18574 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132057), _1132059), _1132061) = c_Groups_Ozero__class_Ozero(_1132057)), _1132059 = c_Groups_Ozero__class_Ozero(_1132057), _1132061 = c_Groups_Ozero__class_Ozero(_1132057)], (18566 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132057), _1132059), _1132061) = c_Groups_Ozero__class_Ozero(_1132057), 18569 ^ _782476 : [(18572 ^ _782476) ^ [] : [-(_1132061 = c_Groups_Ozero__class_Ozero(_1132057))], (18570 ^ _782476) ^ [] : [-(_1132059 = c_Groups_Ozero__class_Ozero(_1132057))]]]]], (10583 ^ _782476) ^ [_975791, _975793, _975795, _975797] : [hBOOL(hAPP(hAPP(c_member(_975791), _975793), _975795)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975791, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975791), _975793), _975797)), _975795) = hAPP(hAPP(c_Set_Oinsert(_975791), _975793), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975791, tc_HOL_Obool)), _975797), _975795)))], (1772 ^ _782476) ^ [_807826, _807828] : [-(class_Rings_Ocomm__semiring__1(_807826)), _807828 = _807826, class_Rings_Ocomm__semiring__1(_807828)], (49780 ^ _782476) ^ [_1787589, _1787591, _1787593, _1787595, _1787597] : [hBOOL(hAPP(hAPP(_1787593, _1787597), _1787595)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787589, _1787591, _1787593), _1787595), _1787597)))], (32650 ^ _782476) ^ [_1400741, _1400743, _1400745] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1400741), _1400743)), _1400745) = 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), _1400741), _1400745)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1400743), _1400745))), 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, _1400741, _1400745)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400743, _1400745))), _1400745)))], (46972 ^ _782476) ^ [_1725397, _1725399] : [-(c_List_Oconcat(_1725397, _1725399) = hAPP(c_List_Ofoldl(tc_List_Olist(_1725397), tc_List_Olist(_1725397), c_List_Oappend(_1725397), c_List_Olist_ONil(_1725397)), _1725399))], (49328 ^ _782476) ^ [_1776946, _1776948, _1776950, _1776952] : [-(c_List_Olist__ex1(_1776946, _1776948, hAPP(hAPP(c_List_Olist_OCons(_1776946), _1776950), _1776952))), 49331 ^ _782476 : [(49334 ^ _782476) ^ [] : [c_List_Olist__all(_1776946, hAPP(hAPP(c_COMBS(_1776946, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776946), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776946), c_fNot), _1776948))), hAPP(c_fequal, _1776950)), _1776952)], (49332 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1776948, _1776950)))]], 49335 ^ _782476 : [(49338 ^ _782476) ^ [] : [c_List_Olist__ex1(_1776946, _1776948, _1776952)], (49336 ^ _782476) ^ [] : [hBOOL(hAPP(_1776948, _1776950))]]], (280 ^ _782476) ^ [_786878, _786880] : [-(class_Fields_Ofield__inverse__zero(_786878)), _786880 = _786878, class_Fields_Ofield__inverse__zero(_786880)], (52471 ^ _782476) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (39949 ^ _782476) ^ [_1557307, _1557309, _1557311, _1557313, _1557315, _1557317, _1557319, _1557321] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1557307, _1557309), tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1557307, _1557309), _1557315), hAPP(c_COMBK(tc_fun(_1557309, tc_HOL_Obool), _1557307), _1557317))), hAPP(c_Product__Type_Oprod_Oprod__case(_1557307, _1557309, tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1557307, tc_fun(_1557309, tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool))), tc_fun(_1557309, tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool)), tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool)), tc_fun(tc_fun(_1557309, tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool))), tc_fun(_1557309, tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool))), _1557307), c_COMBB(tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool)), tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool), _1557309)), hAPP(hAPP(c_COMBB(tc_fun(_1557311, tc_HOL_Obool), tc_fun(tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool)), tc_fun(tc_prod(_1557311, _1557313), tc_HOL_Obool)), _1557307), c_Product__Type_OSigma(_1557311, _1557313)), _1557319))), hAPP(hAPP(c_COMBB(tc_fun(_1557313, tc_HOL_Obool), tc_fun(_1557311, tc_fun(_1557313, tc_HOL_Obool)), _1557309), c_COMBK(tc_fun(_1557313, tc_HOL_Obool), _1557311)), _1557321)))) = hAPP(hAPP(c_Product__Type_OSigma(_1557311, _1557313), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557307, tc_fun(_1557311, tc_HOL_Obool)), _1557315), _1557319)), hAPP(c_COMBK(tc_fun(_1557313, tc_HOL_Obool), _1557311), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557309, tc_fun(_1557313, tc_HOL_Obool)), _1557317), _1557321))))], (17558 ^ _782476) ^ [_1115284, _1115286] : [17559 ^ _782476 : [(17560 ^ _782476) ^ [_1115334] : [_1115286 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115284), _1115334)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115284), _1115286)))], (12398 ^ _782476) ^ [_1007693, _1007695, _1007697] : [class_Complete__Lattice_Ocomplete__lattice(_1007693), c_Orderings_Oorder__class_Omono(_1007693, _1007693, _1007695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007693), _1007697), hAPP(_1007695, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007693), _1007697), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007693, _1007695))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007693), _1007697), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007693, _1007695))))], (44422 ^ _782476) ^ [_1668366, _1668368, _1668370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668366), tc_List_Olist(_1668366))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668366), tc_List_Olist(_1668366)), c_List_Olist_ONil(_1668366)), _1668368)), c_List_Olex(_1668366, _1668370)))], (31894 ^ _782476) ^ [_1386468, _1386470, _1386472, _1386474] : [class_Divides_Osemiring__div(_1386468), -(c_Divides_Odiv__class_Omod(_1386468, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386468), _1386470), _1386472), _1386474) = c_Divides_Odiv__class_Omod(_1386468, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386468), _1386470), c_Divides_Odiv__class_Omod(_1386468, _1386472, _1386474)), _1386474))], (28874 ^ _782476) ^ [_1331006, _1331008, _1331010, _1331012] : [class_Rings_Odivision__ring(_1331006), -(_1331008 = c_Groups_Ozero__class_Ozero(_1331006)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331006), _1331010), _1331008) = _1331012, -(_1331010 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331006), _1331012), _1331008))], (5508 ^ _782476) ^ [_866736, _866738, _866740, _866742, _866744, _866746, _866748, _866750] : [-(c_SetInterval_Oord_OatLeastAtMost(_866750, _866746, _866742, _866738) = c_SetInterval_Oord_OatLeastAtMost(_866748, _866744, _866740, _866736)), _866750 = _866748, _866746 = _866744, _866742 = _866740, _866738 = _866736], (9754 ^ _782476) ^ [_957239, _957241, _957243, _957245] : [class_Orderings_Oorder(_957239), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957239, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957239, _957241), _957243)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957239, _957243), _957245)) = c_Orderings_Obot__class_Obot(tc_fun(_957239, tc_HOL_Obool)))], (14811 ^ _782476) ^ [_1059210, _1059212, _1059214, _1059216, _1059218, _1059220] : [c_Finite__Set_Ofolding(_1059210, _1059212, _1059214, _1059216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059210), _1059218)), -(hAPP(c_Fun_Ocomp(_1059212, _1059212, _1059212, hAPP(_1059214, _1059220)), hAPP(_1059216, _1059218)) = hAPP(c_Fun_Ocomp(_1059212, _1059212, _1059212, hAPP(_1059216, _1059218)), hAPP(_1059214, _1059220)))], (50094 ^ _782476) ^ [_1793884, _1793886] : [-(c_Predicate_Opred__comp(_1793884, _1793884, _1793884, c_fequal, c_Predicate_Opred__comp(_1793884, _1793884, _1793884, _1793886, c_fequal)) = _1793886)], (2768 ^ _782476) ^ [_823400, _823402] : [_823402 = _823400, -(c_HOL_OAll(_823402) = c_HOL_OAll(_823400))], (52239 ^ _782476) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51239 ^ _782476) ^ [_1818815, _1818817] : [c_Equiv__Relations_Opart__equivp(_1818815, _1818817), 51243 ^ _782476 : [(51248 ^ _782476) ^ [] : [-(c_Predicate_Otransp(_1818815, _1818817))], (51246 ^ _782476) ^ [] : [-(c_Predicate_Osymp(_1818815, _1818817))], (51244 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1818817, 51242 ^ [_1818815, _1818817]), 51242 ^ [_1818815, _1818817])))]]], (38166 ^ _782476) ^ [_1510683, _1510685, _1510687, _1510689, _1510691, _1510693] : [c_Equiv__Relations_Oequiv(_1510683, _1510685, _1510687), c_Equiv__Relations_Ocongruent(_1510683, tc_fun(_1510689, tc_HOL_Obool), _1510687, _1510691), hBOOL(hAPP(hAPP(c_member(_1510683), _1510693), _1510685)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510683, tc_fun(_1510689, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510683, _1510683, _1510687), hAPP(hAPP(c_Set_Oinsert(_1510683), _1510693), c_Orderings_Obot__class_Obot(tc_fun(_1510683, tc_HOL_Obool))))), _1510691) = hAPP(_1510691, _1510693))], (48072 ^ _782476) ^ [_1749276, _1749278, _1749280] : [hAPP(c_List_Orev(_1749276), _1749278) = hAPP(hAPP(c_List_Olist_OCons(_1749276), _1749280), c_List_Olist_ONil(_1749276)), -(_1749278 = hAPP(hAPP(c_List_Olist_OCons(_1749276), _1749280), c_List_Olist_ONil(_1749276)))], (6831 ^ _782476) ^ [_893880, _893882, _893884, _893886, _893888, _893890] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893880, tc_fun(_893882, tc_HOL_Obool)), _893884), hAPP(hAPP(c_COMBC(_893880, tc_fun(_893886, tc_fun(_893882, tc_HOL_Obool)), tc_fun(_893882, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_893886, tc_HOL_Obool), tc_fun(tc_fun(_893886, tc_fun(_893882, tc_HOL_Obool)), tc_fun(_893882, tc_HOL_Obool)), _893880), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893886, tc_fun(_893882, tc_HOL_Obool))), _893888)), _893890)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893886, tc_fun(_893882, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893880, tc_fun(_893886, tc_HOL_Obool)), _893884), _893888)), _893890))], (13266 ^ _782476) ^ [_1027369, _1027371, _1027373, _1027375] : [-(hAPP(c_Set_Oimage(_1027369, _1027371, _1027373), hAPP(c_Set_Ovimage(_1027369, _1027371, _1027373), _1027375)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027371, tc_HOL_Obool)), _1027375), hAPP(c_Set_Oimage(_1027369, _1027371, _1027373), c_Orderings_Otop__class_Otop(tc_fun(_1027369, tc_HOL_Obool)))))], (8428 ^ _782476) ^ [_928397, _928399] : [class_Groups_Oordered__ab__group__add(_928397), -(hAPP(c_Set_Oimage(_928397, _928397, c_Groups_Ouminus__class_Ouminus(_928397)), hAPP(c_SetInterval_Oord__class_OatMost(_928397), _928399)) = hAPP(c_SetInterval_Oord__class_OatLeast(_928397), hAPP(c_Groups_Ouminus__class_Ouminus(_928397), _928399)))], (4916 ^ _782476) ^ [_857520, _857522, _857524, _857526] : [-(c_Product__Type_Osnd(_857526, _857522) = c_Product__Type_Osnd(_857524, _857520)), _857526 = _857524, _857522 = _857520], (44018 ^ _782476) ^ [_1660505, _1660507] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1660505, _1660507))))], (9589 ^ _782476) ^ [_954491, _954493, _954495, _954497] : [_954491 = c_Orderings_Obot__class_Obot(tc_fun(_954493, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954493, tc_fun(_954495, tc_HOL_Obool)), _954491), hAPP(c_COMBK(tc_fun(_954495, tc_HOL_Obool), _954493), _954497)) = c_Orderings_Obot__class_Obot(tc_fun(_954495, tc_HOL_Obool)))], (38658 ^ _782476) ^ [_1522773] : [-(_1522773 = 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)), _1522773), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (10633 ^ _782476) ^ [_976921, _976923, _976925, _976927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976921, tc_HOL_Obool)), _976923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976921, tc_HOL_Obool)), _976925), _976927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976921, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976921, tc_HOL_Obool)), _976923), _976925)), _976927)))], (38913 ^ _782476) ^ [_1530076, _1530078, _1530080, _1530082, _1530084, _1530086, _1530088, _1530090] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530076, _1530078)), hAPP(hAPP(c_Product__Type_OPair(_1530076, _1530078), _1530080), _1530082)), _1530084)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530078, _1530086)), hAPP(hAPP(c_Product__Type_OPair(_1530078, _1530086), _1530082), _1530088)), _1530090)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530076, _1530086)), hAPP(hAPP(c_Product__Type_OPair(_1530076, _1530086), _1530080), _1530088)), hAPP(hAPP(c_Relation_Orel__comp(_1530076, _1530078, _1530086), _1530084), _1530090))))], (39630 ^ _782476) ^ [_1547879, _1547881, _1547883] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1547879, _1547881)), _1547883)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547879), hAPP(c_Relation_ODomain(_1547879, _1547881), _1547883))))], (44380 ^ _782476) ^ [_1667441, _1667443, _1667445] : [-(hAPP(hAPP(c_List_Olist__update(_1667441, c_List_Olist_ONil(_1667441)), _1667443), _1667445) = c_List_Olist_ONil(_1667441))], (29834 ^ _782476) ^ [_1348622, _1348624, _1348626] : [class_Fields_Olinordered__field__inverse__zero(_1348622), -(hAPP(c_Groups_Oabs__class_Oabs(_1348622), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348622), _1348624), _1348626)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348622), hAPP(c_Groups_Oabs__class_Oabs(_1348622), _1348624)), hAPP(c_Groups_Oabs__class_Oabs(_1348622), _1348626)))], (5892 ^ _782476) ^ [_875860, _875862, _875864] : [class_Orderings_Olinorder(_875860), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875860), _875862), _875864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875860), _875864), _875862)))], (32263 ^ _782476) ^ [_1393535, _1393537, _1393539] : [hBOOL(hAPP(_1393535, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393537, _1393539))), 32266 ^ _782476 : [(32291 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393539), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32294 ^ _782476 : [(32295 ^ _782476) ^ [_1394157, _1394159] : [-(hBOOL(hAPP(_1393535, _1394157))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393539), _1394157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1394157), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1393537 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393539), _1394159)), _1394157)]]], (32273 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393539)), 32276 ^ _782476 : [(32277 ^ _782476) ^ [_1393865, _1393867] : [-(hBOOL(hAPP(_1393535, _1393865))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393865), _1393539)), _1393537 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393539), _1393867)), _1393865)]]], (32267 ^ _782476) ^ [] : [_1393539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1393535, _1393537)))]]], (25483 ^ _782476) ^ [_1258660, _1258662] : [25485 ^ _782476 : [(25488 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1258662), 25484 ^ [_1258660, _1258662]))], (25486 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25484 ^ [_1258660, _1258662]), _1258660)))]], -(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)), _1258662), _1258660))], (52455 ^ _782476) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (43819 ^ _782476) ^ [_1655961, _1655963] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655961)), c_List_Obutlast(_1655961, _1655963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655961)), _1655963)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (35484 ^ _782476) ^ [_1453079] : [class_Rings_Osemiring__1(_1453079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453079), c_Groups_Ozero__class_Ozero(_1453079)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453079))], (28722 ^ _782476) ^ [_1328041, _1328043] : [c_Nat__Transfer_Ois__nat(_1328041), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328041), _1328043)))], (18338 ^ _782476) ^ [_1128565] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128565) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46970 ^ _782476) ^ [_1725365] : [-(c_List_Oconcat(_1725365, c_List_Olist_ONil(tc_List_Olist(_1725365))) = c_List_Olist_ONil(_1725365))], (38905 ^ _782476) ^ [_1529281, _1529283, _1529285] : [hBOOL(hAPP(hAPP(c_member(_1529281), _1529285), c_Wellfounded_Oacc(_1529281, _1529283))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1529281, hAPP(hAPP(c_COMBC(_1529281, tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_fun(_1529281, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529281, tc_fun(tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_fun(_1529281, tc_HOL_Obool)), _1529281), c_COMBC(_1529281, tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529281, tc_prod(_1529281, _1529281)), tc_fun(_1529281, tc_fun(tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_HOL_Obool)), _1529281), hAPP(c_COMBB(tc_prod(_1529281, _1529281), tc_fun(tc_fun(tc_prod(_1529281, _1529281), tc_HOL_Obool), tc_HOL_Obool), _1529281), c_member(tc_prod(_1529281, _1529281)))), c_Product__Type_OPair(_1529281, _1529281)))), _1529283)), _1529285)))], (47740 ^ _782476) ^ [_1742524, _1742526, _1742528, _1742530, _1742532] : [class_Orderings_Olinorder(_1742524), c_List_Olinorder__class_Osorted(_1742524, hAPP(hAPP(c_List_Omap(_1742526, _1742524), _1742528), _1742530)), -(c_List_Olinorder__class_Osorted(_1742524, hAPP(hAPP(c_List_Omap(_1742526, _1742524), _1742528), c_List_Oremove1(_1742526, _1742532, _1742530))))], (39156 ^ _782476) ^ [_1537154, _1537156, _1537158, _1537160, _1537162, _1537164, _1537166, _1537168] : [hBOOL(hAPP(hAPP(_1537154, _1537156), _1537158)), hBOOL(hAPP(hAPP(_1537160, _1537158), _1537162)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1537164, _1537166, _1537168, _1537154, _1537160), _1537156), _1537162)))], (49430 ^ _782476) ^ [_1779005, _1779007, _1779009, _1779011, _1779013, _1779015, _1779017] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1779005, _1779007, _1779009, _1779011), _1779013), _1779015), _1779017) = c_New__DSequence_Oneg__bind(_1779005, _1779007, hAPP(hAPP(hAPP(_1779009, _1779013), _1779015), _1779017), hAPP(hAPP(c_COMBC(_1779005, 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(_1779007)))), hAPP(hAPP(c_COMBC(_1779005, 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(_1779007))))), hAPP(hAPP(c_COMBC(_1779005, 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(_1779007)))))), _1779011), _1779013)), _1779015)), _1779017)))], (48066 ^ _782476) ^ [_1749127, _1749129, _1749131] : [_1749131 = hAPP(hAPP(c_List_Olist_OCons(_1749127), _1749129), c_List_Olist_ONil(_1749127)), -(hAPP(hAPP(c_List_Olist_OCons(_1749127), _1749129), c_List_Olist_ONil(_1749127)) = hAPP(c_List_Orev(_1749127), _1749131))], (45959 ^ _782476) ^ [_1702147, _1702149, _1702151, _1702153, _1702155] : [class_Groups_Ocomm__monoid__add(_1702147), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702147), hAPP(hAPP(c_List_Omap(_1702149, _1702147), hAPP(hAPP(c_COMBS(_1702149, _1702147, _1702147), hAPP(hAPP(c_COMBB(_1702147, tc_fun(_1702147, _1702147), _1702149), c_Groups_Oplus__class_Oplus(_1702147)), _1702151)), _1702153)), _1702155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1702147), hAPP(c_List_Omonoid__add__class_Olistsum(_1702147), hAPP(hAPP(c_List_Omap(_1702149, _1702147), _1702151), _1702155))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702147), hAPP(hAPP(c_List_Omap(_1702149, _1702147), _1702153), _1702155))))], (51611 ^ _782476) ^ [_1828455, _1828457, _1828459] : [c_List_Oall__interval__nat(_1828455, _1828457, _1828459), -(c_List_Olist__all(tc_Nat_Onat, _1828455, c_List_Oupt(_1828457, _1828459)))], (14413 ^ _782476) ^ [_1051020, _1051022] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051020), _1051022)), 14416 ^ _782476 : [(14423 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051020), c_Orderings_Otop__class_Otop(tc_fun(_1051020, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051020), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1051020, tc_HOL_Obool)), _1051022))))], (14417 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051020), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1051020, tc_HOL_Obool)), _1051022))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051020), c_Orderings_Otop__class_Otop(tc_fun(_1051020, tc_HOL_Obool)))))]]], (43996 ^ _782476) ^ [_1660104, _1660106, _1660108, _1660110] : [hBOOL(hAPP(c_List_Odistinct(_1660104), _1660106)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660108, _1660104)), hAPP(hAPP(c_List_Ozip(_1660108, _1660104), _1660110), _1660106))))], (26014 ^ _782476) ^ [_1274825, _1274827] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274825)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274827)), hAPP(c_Int_Onat, _1274825)) = hAPP(c_Int_Onat, _1274827))], (39835 ^ _782476) ^ [_1554367, _1554369, _1554371, _1554373, _1554375, _1554377] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554367, _1554369)), hAPP(hAPP(c_Product__Type_OPair(_1554367, _1554369), _1554371), _1554373)), hAPP(hAPP(c_Product__Type_OSigma(_1554367, _1554369), _1554375), _1554377))), -(hBOOL(hAPP(hAPP(c_member(_1554367), _1554371), _1554375)))], (18284 ^ _782476) ^ [_1127827, _1127829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127827), _1127829)), _1127829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29350 ^ _782476) ^ [_1339376, _1339378, _1339380] : [class_Power_Opower(_1339376), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339376), _1339378), hAPP(c_Nat_OSuc, _1339380)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339376), _1339378), hAPP(hAPP(c_Power_Opower__class_Opower(_1339376), _1339378), _1339380)))], (41290 ^ _782476) ^ [_1591729] : [-(hAPP(c_Relation_ODomain(_1591729, _1591729), c_Relation_OId(_1591729)) = c_Orderings_Otop__class_Otop(tc_fun(_1591729, tc_HOL_Obool)))], (22945 ^ _782476) ^ [_1212752, _1212754, _1212756] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1212752), _1212754)), 22948 ^ _782476 : [(22968 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212752, tc_Nat_Onat), _1212756), _1212754) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22969 ^ _782476 : [(22970 ^ _782476) ^ [_1213233] : [hBOOL(hAPP(hAPP(c_member(_1212752), _1213233), _1212754)), hAPP(_1212756, _1213233) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22978 ^ _782476 : [(22983 ^ _782476) ^ [] : [hAPP(_1212756, 22977 ^ [_1212752, _1212754, _1212756, _1213233]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22981 ^ _782476) ^ [] : [_1213233 = 22977 ^ [_1212752, _1212754, _1212756, _1213233]], (22979 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212752), 22977 ^ [_1212752, _1212754, _1212756, _1213233]), _1212754)))]]]]], (22949 ^ _782476) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212752, tc_Nat_Onat), _1212756), _1212754) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22953 ^ _782476 : [(22958 ^ _782476) ^ [_1213072] : [hBOOL(hAPP(hAPP(c_member(_1212752), _1213072), _1212754)), -(22952 ^ [_1212752, _1212754, _1212756] = _1213072), -(hAPP(_1212756, _1213072) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22956 ^ _782476) ^ [] : [-(hAPP(_1212756, 22952 ^ [_1212752, _1212754, _1212756]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22954 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212752), 22952 ^ [_1212752, _1212754, _1212756]), _1212754)))]]]]], (18408 ^ _782476) ^ [_1129636, _1129638] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129636), _1129638) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1129636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1129638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21355 ^ _782476) ^ [_1183430, _1183432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183430), _1183432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183430)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183432))))], (34814 ^ _782476) ^ [_1440368, _1440370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440368), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440368)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440370)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43813 ^ _782476) ^ [_1655820, _1655822, _1655824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655820), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655822)), _1655824))), -(hAPP(hAPP(c_List_Otake(_1655822), _1655820), c_List_Obutlast(_1655822, _1655824)) = hAPP(hAPP(c_List_Otake(_1655822), _1655820), _1655824))], (12864 ^ _782476) ^ [_1018065, _1018067, _1018069] : [class_Complete__Lattice_Ocomplete__lattice(_1018065), _1018067 = c_Inductive_Ocomplete__lattice__class_Olfp(_1018065, _1018069), c_Orderings_Oorder__class_Omono(_1018065, _1018065, _1018069), -(_1018067 = hAPP(_1018069, _1018067))], (29088 ^ _782476) ^ [_1334764, _1334766, _1334768, _1334770] : [class_Fields_Ofield(_1334764), -(_1334766 = c_Groups_Ozero__class_Ozero(_1334764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1334768), _1334770)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1334764), _1334766), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1334770), _1334768)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334764), hAPP(hAPP(c_Power_Opower__class_Opower(_1334764), _1334766), _1334770)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334764), _1334766), _1334768)))], (52145 ^ _782476) ^ [_1838101, _1838103] : [class_Lattices_Oboolean__algebra(_1838101), -(class_Lattices_Oboolean__algebra(tc_fun(_1838103, _1838101)))], (2576 ^ _782476) ^ [_820422, _820424] : [_820424 = _820422, -(c_Wellfounded_Omeasure(_820424) = c_Wellfounded_Omeasure(_820422))], (5787 ^ _782476) ^ [_873961, _873963] : [class_Orderings_Opreorder(_873961), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873961), _873963), _873963)))], (49085 ^ _782476) ^ [_1771937, _1771939, _1771941] : [c_List_Olist__ex(_1771937, _1771939, _1771941), 49089 ^ _782476 : [(49092 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1771939, 49088 ^ [_1771937, _1771939, _1771941])))], (49090 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771937), 49088 ^ [_1771937, _1771939, _1771941]), hAPP(c_List_Oset(_1771937), _1771941))))]]], (47369 ^ _782476) ^ [_1736010, _1736012, _1736014] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1736010), c_List_Oupt(_1736012, _1736014)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736012), _1736010), _1736014))], (9831 ^ _782476) ^ [_959084, _959086, _959088, _959090, _959092] : [_959084 = c_Orderings_Obot__class_Obot(tc_fun(_959086, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959086, tc_fun(_959088, tc_HOL_Obool)), _959084), hAPP(hAPP(c_COMBB(tc_fun(_959088, tc_HOL_Obool), tc_fun(_959088, tc_HOL_Obool), _959086), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959088, tc_HOL_Obool)), _959090)), _959092)) = c_Orderings_Obot__class_Obot(tc_fun(_959088, tc_HOL_Obool)))], (12480 ^ _782476) ^ [_1009419, _1009421, _1009423, _1009425] : [c_Orderings_Oorder__class_Omono(tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool), _1009421), hBOOL(hAPP(hAPP(c_member(_1009419), _1009423), _1009425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009419, tc_HOL_Obool)), _1009425), hAPP(_1009421, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1009419, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009419, tc_HOL_Obool), tc_fun(tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool)), tc_fun(_1009419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009419, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009419, tc_HOL_Obool), tc_fun(tc_fun(_1009419, tc_HOL_Obool), tc_fun(_1009419, tc_HOL_Obool)), tc_fun(_1009419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009419, tc_HOL_Obool))), _1009421)), _1009425))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009419, tc_HOL_Obool), _1009421)))))), -(hBOOL(hAPP(hAPP(c_member(_1009419), _1009423), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009419, tc_HOL_Obool), _1009421))))], (14026 ^ _782476) ^ [_1043164, _1043166, _1043168] : [class_Rings_Oring(_1043164), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1043164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043164), _1043166), _1043168)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043164), hAPP(c_Groups_Ouminus__class_Ouminus(_1043164), _1043166)), _1043168))], (10201 ^ _782476) ^ [_967136, _967138, _967140, _967142] : [-(hAPP(hAPP(c_Set_Oinsert(_967136), _967138), hAPP(hAPP(c_Set_Oinsert(_967136), _967140), _967142)) = hAPP(hAPP(c_Set_Oinsert(_967136), _967140), hAPP(hAPP(c_Set_Oinsert(_967136), _967138), _967142)))], (15716 ^ _782476) ^ [_1076612, _1076614, _1076616, _1076618, _1076620, _1076622, _1076624] : [c_Finite__Set_Ofolding__image(_1076612, _1076614, _1076616, _1076618, _1076620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076614), _1076622)), -(hAPP(hAPP(_1076620, _1076624), _1076622) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076612, _1076614, _1076616), _1076624), _1076618), _1076622))], (8092 ^ _782476) ^ [_920322, _920324, _920326] : [class_Lattices_Olattice(_920322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920322), _920324), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920322), _920324), _920326))))], (50731 ^ _782476) ^ [_1809698, _1809700] : [c_Equiv__Relations_Oequivp(_1809698, _1809700), 50734 ^ _782476 : [(50739 ^ _782476) ^ [] : [-(c_Predicate_Otransp(_1809698, _1809700))], (50737 ^ _782476) ^ [] : [-(c_Predicate_Osymp(_1809698, _1809700))], (50735 ^ _782476) ^ [] : [-(c_Predicate_Oreflp(_1809698, _1809700))]]], (48164 ^ _782476) ^ [_1751193, _1751195, _1751197, _1751199, _1751201] : [c_List_Olist__all2(_1751193, _1751195, _1751197, _1751199, _1751201), -(c_List_Olist__all2(_1751193, _1751195, _1751197, hAPP(c_List_Orev(_1751193), _1751199), hAPP(c_List_Orev(_1751195), _1751201)))], (50923 ^ _782476) ^ [_1813178, _1813180] : [c_Wellfounded_Oacyclic(_1813178, _1813180), -(c_Relation_Oantisym(_1813178, c_Transitive__Closure_Ortrancl(_1813178, _1813180)))], (21501 ^ _782476) ^ [_1185926, _1185928, _1185930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185926)), 21504 ^ _782476 : [(21505 ^ _782476) ^ [_1186060] : [21507 ^ _782476 : [(21513 ^ _782476) ^ [] : [-(_1186060 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21509 ^ [_1185926, _1185928, _1185930, _1186060]), 21506 ^ [_1185926, _1185928, _1185930, _1186060]))], (21511 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21509 ^ [_1185926, _1185928, _1185930, _1186060]), _1185928)))], (21508 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21506 ^ [_1185926, _1185928, _1185930, _1186060]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1185926))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185930), _1186060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185930), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186060), _1185926))))]]], (35380 ^ _782476) ^ [_1450997, _1450999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1450997)), c_Int_OBit1(_1450999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450997), _1450999)))], (16519 ^ _782476) ^ [_1093666, _1093668, _1093670, _1093672, _1093674] : [class_Rings_Ocomm__semiring__1(_1093666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), _1093668), _1093670)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), _1093672), _1093674)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), _1093668), _1093672)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093666), _1093670), _1093674)))], (43364 ^ _782476) ^ [_1643181, _1643183, _1643185, _1643187] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1643183), hAPP(hAPP(c_List_Olist_OCons(_1643183), _1643185), _1643187)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643181)) = _1643185)], (43555 ^ _782476) ^ [_1648219, _1648221, _1648223] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648219)), _1648221), c_List_Olists(_1648219, _1648223))), 43558 ^ _782476 : [(43559 ^ _782476) ^ [_1648327] : [hBOOL(hAPP(hAPP(c_member(_1648219), _1648327), hAPP(c_List_Oset(_1648219), _1648221))), -(hBOOL(hAPP(hAPP(c_member(_1648219), _1648327), _1648223)))]]], (16901 ^ _782476) ^ [_1101947, _1101949, _1101951, _1101953, _1101955, _1101957] : [class_Rings_Oordered__ring(_1101947), 16904 ^ _782476 : [(16911 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101947), _1101953), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101947), _1101955), _1101949)), _1101951)), _1101957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), _1101949), _1101951)), _1101953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), _1101955), _1101951)), _1101957))))], (16905 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), _1101949), _1101951)), _1101953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), _1101955), _1101951)), _1101957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101947), _1101953), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101947), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101947), _1101955), _1101949)), _1101951)), _1101957))))]]], (40454 ^ _782476) ^ [_1570464, _1570466] : [-(c_Nitpick_Owf_H(_1570464, _1570466)), c_Wellfounded_Oacyclic(_1570464, _1570466), 40459 ^ _782476 : [(40462 ^ _782476) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (40460 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570464, _1570464)), _1570466))]]], (29064 ^ _782476) ^ [_1334308, _1334310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334308), _1334310)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1334308, tc_HOL_Obool)), hAPP(c_Set_OPow(_1334308), _1334310)) = 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(_1334308), _1334310)))], (46232 ^ _782476) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (20866 ^ _782476) ^ [_1174973, _1174975] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174973) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174975), -(_1174973 = _1174975)], (18130 ^ _782476) ^ [_1125592, _1125594] : [class_Rings_Ocomm__semiring__1(_1125592), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125592), c_Groups_Ozero__class_Ozero(_1125592)), _1125594) = c_Groups_Ozero__class_Ozero(_1125592))], (45881 ^ _782476) ^ [_1700552, _1700554] : [-(_1700552 = c_List_Olist_ONil(_1700554)), -(c_Random_Oselect__weight(_1700554, hAPP(hAPP(c_List_Omap(_1700554, tc_prod(tc_Code__Numeral_Ocode__numeral, _1700554)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1700554), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1700552)) = c_Random_Oselect(_1700554, _1700552))], (9041 ^ _782476) ^ [_941108, _941110, _941112, _941114] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941108, tc_HOL_Obool)), _941110), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941108, tc_HOL_Obool)), _941112), _941114)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941108, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941108, tc_HOL_Obool)), _941110), _941112)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941108, tc_HOL_Obool)), _941110), _941114)))], (26292 ^ _782476) ^ [_1279476, _1279478, _1279480, _1279482, _1279484] : [class_Orderings_Olinorder(_1279476), class_Orderings_Olinorder(_1279478), c_Orderings_Oorder__class_Omono(_1279478, _1279476, _1279480), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279476), hAPP(_1279480, _1279482)), hAPP(_1279480, _1279484)) = hAPP(_1279480, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279478), _1279482), _1279484)))], (52495 ^ _782476) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (42796 ^ _782476) ^ [_1626165, _1626167, _1626169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626165), c_Nitpick_Oplus__frac(_1626165, _1626167, c_Nitpick_Ouminus__frac(_1626165, _1626169)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1626165, _1626167, _1626169))], (6762 ^ _782476) ^ [_891999, _892001, _892003, _892005, _892007, _892009] : [hBOOL(hAPP(hAPP(c_member(_891999), _892001), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892003, tc_fun(_891999, tc_HOL_Obool)), _892005), _892007))), -(hBOOL(hAPP(hAPP(c_member(_891999), _892001), hAPP(_892007, _892009)))), hBOOL(hAPP(hAPP(c_member(_892003), _892009), _892005))], (49472 ^ _782476) ^ [_1780138, _1780140] : [-(c_List_Osplice(_1780138, _1780140, c_List_Olist_ONil(_1780138)) = _1780140)], (39269 ^ _782476) ^ [_1539129, _1539131, _1539133, _1539135] : [c_Wellfounded_Owf(_1539129, _1539131), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539129, _1539129)), hAPP(hAPP(c_Product__Type_OPair(_1539129, _1539129), _1539133), _1539135)), _1539131)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539129, _1539129)), hAPP(hAPP(c_Product__Type_OPair(_1539129, _1539129), _1539135), _1539133)), _1539131))], (9025 ^ _782476) ^ [_940584, _940586, _940588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940584, tc_HOL_Obool)), _940586), _940588)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940584, tc_HOL_Obool)), _940586), _940588) = _940586)], (36954 ^ _782476) ^ [_1486388, _1486390] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1486388, _1486390) = 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), _1486388), _1486390)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1486388, _1486390)))], (12632 ^ _782476) ^ [_1013884, _1013886, _1013888, _1013890] : [c_Fun_Oinj__on(_1013884, _1013886, _1013888, _1013890), 12635 ^ _782476 : [(12636 ^ _782476) ^ [_1013992] : [hBOOL(hAPP(hAPP(c_member(_1013884), _1013992), _1013890)), 12639 ^ _782476 : [(12640 ^ _782476) ^ [_1014094] : [hBOOL(hAPP(hAPP(c_member(_1013884), _1014094), _1013890)), hAPP(_1013888, _1013992) = hAPP(_1013888, _1014094), -(_1013992 = _1014094)]]]]], (42869 ^ _782476) ^ [_1627789, _1627791, _1627793] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627789)), _1627791) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627789)), _1627793)), _1627791 = _1627793], (31798 ^ _782476) ^ [_1384493, _1384495, _1384497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384493), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31801 ^ _782476 : [(31802 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1384495, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384497), _1384493)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384497, _1384493))), 31805 ^ _782476 : [(31806 ^ _782476) ^ [_1384703, _1384705] : [-(hBOOL(hAPP(hAPP(_1384495, _1384705), _1384703))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384493), _1384703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1384703), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1384497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384493), _1384705)), _1384703)]]], (31820 ^ _782476) ^ [] : [31823 ^ _782476 : [(31826 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31822 ^ [_1384493, _1384495, _1384497]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31828 ^ _782476) ^ [] : [-(_1384497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384493), 31821 ^ [_1384493, _1384495, _1384497])), 31822 ^ [_1384493, _1384495, _1384497]))], (31830 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1384495, 31821 ^ [_1384493, _1384495, _1384497]), 31822 ^ [_1384493, _1384495, _1384497]))], (31824 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384493), 31822 ^ [_1384493, _1384495, _1384497])))]], -(hBOOL(hAPP(hAPP(_1384495, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384497), _1384493)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384497, _1384493))))]]], (5698 ^ _782476) ^ [_869749, _869751, _869753, _869755, _869757, _869759] : [-(c_COMBS(_869759, _869755, _869751) = c_COMBS(_869757, _869753, _869749)), _869759 = _869757, _869755 = _869753, _869751 = _869749], (45050 ^ _782476) ^ [_1683399, _1683401, _1683403] : [-(hAPP(hAPP(c_List_Odrop(_1683399), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1683399), _1683401), _1683403)) = _1683403)], (6143 ^ _782476) ^ [_879961, _879963, _879965, _879967, _879969] : [class_Orderings_Oorder(_879961), class_Orderings_Olinorder(_879963), c_Orderings_Oorder__class_Ostrict__mono(_879963, _879961, _879965), 6154 ^ _782476 : [(6161 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879963), _879967), _879969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879961), hAPP(_879965, _879967)), hAPP(_879965, _879969))))], (6155 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879961), hAPP(_879965, _879967)), hAPP(_879965, _879969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879963), _879967), _879969)))]]], (42243 ^ _782476) ^ [_1614517, _1614519, _1614521] : [class_Orderings_Olinorder(_1614517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614517), _1614519)), -(c_Big__Operators_Olinorder__class_OMax(_1614517, hAPP(hAPP(c_Set_Oinsert(_1614517), _1614521), _1614519)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614517, _1614517, c_Orderings_Oord__class_Omax(_1614517)), _1614521), _1614519))], (49114 ^ _782476) ^ [_1772420, _1772422, _1772424, _1772426] : [49115 ^ _782476 : [(49118 ^ _782476) ^ [] : [c_List_Olist__ex(_1772420, _1772422, _1772426)], (49116 ^ _782476) ^ [] : [c_List_Olist__ex(_1772420, _1772422, _1772424)]], -(c_List_Olist__ex(_1772420, _1772422, hAPP(hAPP(c_List_Oappend(_1772420), _1772424), _1772426)))], (39794 ^ _782476) ^ [_1553094, _1553096, _1553098, _1553100, _1553102] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553094, _1553096), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553094, tc_HOL_Obool)), _1553098), _1553100)), hAPP(c_COMBK(tc_fun(_1553096, tc_HOL_Obool), _1553094), _1553102)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553094, _1553096), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553094, _1553096), _1553098), hAPP(c_COMBK(tc_fun(_1553096, tc_HOL_Obool), _1553094), _1553102))), hAPP(hAPP(c_Product__Type_OSigma(_1553094, _1553096), _1553100), hAPP(c_COMBK(tc_fun(_1553096, tc_HOL_Obool), _1553094), _1553102))))], (30644 ^ _782476) ^ [_1363248, _1363250, _1363252, _1363254] : [class_Fields_Ofield(_1363248), -(_1363250 = c_Groups_Ozero__class_Ozero(_1363248)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363248), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363248), _1363252), _1363250)), _1363254) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363248), _1363252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363248), _1363250), _1363254))), _1363250))], (21672 ^ _782476) ^ [_1189340, _1189342, _1189344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189340)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189342), _1189344)), 21679 ^ _782476 : [(21680 ^ _782476) ^ [_1189530] : [21682 ^ _782476 : [(21688 ^ _782476) ^ [] : [-(_1189530 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21684 ^ [_1189340, _1189342, _1189344, _1189530]), 21681 ^ [_1189340, _1189342, _1189344, _1189530]))], (21686 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21684 ^ [_1189340, _1189342, _1189344, _1189530]), _1189344)))], (21683 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21681 ^ [_1189340, _1189342, _1189344, _1189530]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189340))))]], -(_1189530 = _1189342), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189530), _1189340) = _1189342]]], (47140 ^ _782476) ^ [_1729868, _1729870] : [-(hAPP(c_List_Ofilter(_1729868, _1729870), c_List_Olist_ONil(_1729868)) = c_List_Olist_ONil(_1729868))], (43829 ^ _782476) ^ [_1656219, _1656221, _1656223, _1656225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656219), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656221)), _1656223))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656219), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656221)), _1656225))), 43839 ^ _782476 : [(43842 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Onth(_1656221), _1656223), 43838 ^ [_1656219, _1656221, _1656223, _1656225]) = hAPP(hAPP(c_List_Onth(_1656221), _1656225), 43838 ^ [_1656219, _1656221, _1656223, _1656225])], (43840 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43838 ^ [_1656219, _1656221, _1656223, _1656225]), _1656219)))]], -(hAPP(hAPP(c_List_Otake(_1656221), _1656219), _1656223) = hAPP(hAPP(c_List_Otake(_1656221), _1656219), _1656225))], (8681 ^ _782476) ^ [_933507, _933509] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933507, tc_HOL_Obool)), _933509), c_Orderings_Otop__class_Otop(tc_fun(_933507, tc_HOL_Obool))) = _933509)], (42117 ^ _782476) ^ [_1612168, _1612170, _1612172, _1612174, _1612176] : [c_Finite__Set_Ofolding__one__idem(_1612168, _1612170, _1612172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612168), _1612174)), -(hAPP(_1612172, hAPP(hAPP(c_Set_Oinsert(_1612168), _1612176), _1612174)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612168, _1612168, _1612170), _1612176), _1612174))], (40169 ^ _782476) ^ [_1564221, _1564223, _1564225, _1564227, _1564229, _1564231, _1564233, _1564235, _1564237, _1564239] : [-(c_Product__Type_Omap__pair(_1564221, _1564223, _1564225, _1564227, hAPP(c_Fun_Ocomp(_1564229, _1564223, _1564221, _1564231), _1564233), hAPP(c_Fun_Ocomp(_1564235, _1564227, _1564225, _1564237), _1564239)) = hAPP(c_Fun_Ocomp(tc_prod(_1564229, _1564235), tc_prod(_1564223, _1564227), tc_prod(_1564221, _1564225), c_Product__Type_Omap__pair(_1564229, _1564223, _1564235, _1564227, _1564231, _1564237)), c_Product__Type_Omap__pair(_1564221, _1564229, _1564225, _1564235, _1564233, _1564239)))], (45404 ^ _782476) ^ [_1691215, _1691217, _1691219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691215)), _1691217)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1691215, _1691219), _1691217) = _1691217)], (1792 ^ _782476) ^ [_808076, _808078] : [-(class_Divides_Osemiring__div(_808076)), _808078 = _808076, class_Divides_Osemiring__div(_808078)], (20955 ^ _782476) ^ [_1176435] : [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)), _1176435)), _1176435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (45102 ^ _782476) ^ [_1684600, _1684602, _1684604] : [-(c_List_Obutlast(_1684600, hAPP(hAPP(c_List_Odrop(_1684600), _1684602), _1684604)) = hAPP(hAPP(c_List_Odrop(_1684600), _1684602), c_List_Obutlast(_1684600, _1684604)))], (52739 ^ _782476) ^ [_1844423, _1844425] : [hBOOL(_1844423), -(hBOOL(hAPP(hAPP(c_fdisj, _1844425), _1844423)))], (36008 ^ _782476) ^ [] : [-(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))], (38634 ^ _782476) ^ [_1522386, _1522388, _1522390, _1522392] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522386), _1522388)), 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)), _1522390), _1522386)), 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)), _1522392), _1522388)), 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)), _1522390), _1522392)), _1522388)), c_FunDef_Omax__strict)))], (52589 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (44044 ^ _782476) ^ [_1661025, _1661027] : [hAPP(c_Finite__Set_Ocard(_1661025), hAPP(c_List_Oset(_1661025), _1661027)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661025)), _1661027), -(hBOOL(hAPP(c_List_Odistinct(_1661025), _1661027)))], (41342 ^ _782476) ^ [_1592803, _1592805, _1592807, _1592809] : [-(c_Wellfounded_Owf(_1592803, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592803, _1592803)), hAPP(hAPP(c_Product__Type_OPair(_1592803, _1592803), _1592805), _1592807)), _1592809))), c_Wellfounded_Owf(_1592803, _1592809), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592803, _1592803)), hAPP(hAPP(c_Product__Type_OPair(_1592803, _1592803), _1592807), _1592805)), c_Transitive__Closure_Ortrancl(_1592803, _1592809))))], (22666 ^ _782476) ^ [_1207637, _1207639] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207637, _1207639)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207637), hAPP(c_Nat_OSuc, _1207639)))], (42489 ^ _782476) ^ [_1619205, _1619207, _1619209, _1619211, _1619213, _1619215] : [c_Finite__Set_Ofun__left__comm(_1619205, _1619207, _1619209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619205), _1619211)), -(hBOOL(hAPP(hAPP(c_member(_1619205), _1619213), _1619211))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619205, _1619207, _1619209), _1619215), hAPP(hAPP(c_Set_Oinsert(_1619205), _1619213), _1619211)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619205, _1619207, _1619209), hAPP(hAPP(_1619209, _1619213), _1619215)), _1619211))], (18502 ^ _782476) ^ [_1131101, _1131103, _1131105] : [class_Rings_Osemiring__1(_1131101), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1131103), _1131105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131101), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131101), _1131103)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131101), _1131105)))], (10077 ^ _782476) ^ [_964675, _964677, _964679, _964681, _964683] : [-(_964675 = c_Orderings_Obot__class_Obot(tc_fun(_964677, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964677, tc_fun(_964679, tc_HOL_Obool)), _964675), hAPP(hAPP(c_COMBB(tc_fun(_964679, tc_HOL_Obool), tc_fun(_964679, tc_HOL_Obool), _964677), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964679, tc_HOL_Obool)), _964681)), _964683)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964679, tc_HOL_Obool)), _964681), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_964677, tc_fun(_964679, tc_HOL_Obool)), _964675), _964683)))], (12328 ^ _782476) ^ [_1006330, _1006332, _1006334, _1006336] : [c_Orderings_Oorder__class_Omono(tc_fun(_1006330, tc_HOL_Obool), tc_fun(_1006330, tc_HOL_Obool), _1006332), hBOOL(hAPP(hAPP(c_member(_1006330), _1006334), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006330, tc_HOL_Obool), _1006332))), -(hBOOL(hAPP(hAPP(c_member(_1006330), _1006334), hAPP(_1006332, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006330, tc_HOL_Obool)), _1006336), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006330, tc_HOL_Obool), _1006332))))))], (34952 ^ _782476) ^ [_1443380, _1443382, _1443384, _1443386, _1443388] : [-(c_Nat_Onat_Onat__case(_1443380, _1443382, _1443384, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443386)), _1443388)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443380), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443386))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443380, _1443380), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443380, tc_fun(_1443380, _1443380)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443380, tc_fun(_1443380, _1443380)), tc_Int_Oint), c_If(_1443380)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1443380, _1443382, _1443384, _1443388))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443380, tc_Int_Oint), _1443384), 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)), _1443388)))))], (9201 ^ _782476) ^ [_946010, _946012, _946014, _946016] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946010, tc_fun(_946012, tc_HOL_Obool)), _946014), _946016) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_946012, tc_HOL_Obool), hAPP(c_Set_Oimage(_946010, tc_fun(_946012, tc_HOL_Obool), _946016), _946014)))], (5872 ^ _782476) ^ [_875498, _875500, _875502, _875504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875498, tc_HOL_Obool)), _875500), _875502)), hBOOL(hAPP(_875500, _875504)), -(hBOOL(hAPP(_875502, _875504)))], (31107 ^ _782476) ^ [_1371280, _1371282, _1371284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371282), _1371284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371280), _1371284)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371280), _1371282))))], (34332 ^ _782476) ^ [_1432668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432668)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432668), c_Int_OPls)))], (46656 ^ _782476) ^ [_1718723, _1718725, _1718727, _1718729, _1718731, _1718733, _1718735] : [c_List_Olist__all2(_1718723, _1718725, _1718727, hAPP(hAPP(c_List_Omap(_1718729, _1718723), _1718731), _1718733), _1718735), -(c_List_Olist__all2(_1718729, _1718725, hAPP(hAPP(c_COMBB(_1718723, tc_fun(_1718725, tc_HOL_Obool), _1718729), _1718727), _1718731), _1718733, _1718735))], (16545 ^ _782476) ^ [_1094233, _1094235, _1094237, _1094239, _1094241] : [class_Groups_Oordered__ab__semigroup__add(_1094233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094233), _1094235), _1094237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094233), _1094239), _1094241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094233), _1094235), _1094239)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094233), _1094237), _1094241))))], (22608 ^ _782476) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10647 ^ _782476) ^ [_977290, _977292, _977294] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977290, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977290, tc_HOL_Obool)), _977292), _977294)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977290, tc_HOL_Obool)), _977292), _977294)) = _977292)], (48831 ^ _782476) ^ [_1765811, _1765813, _1765815, _1765817, _1765819] : [48832 ^ _782476 : [(48835 ^ _782476) ^ [] : [hBOOL(hAPP(_1765819, hAPP(hAPP(c_List_Ozip(_1765811, _1765815), hAPP(hAPP(c_List_Otake(_1765811), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765811)), _1765813)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765815)), _1765817))), _1765813)), hAPP(hAPP(c_List_Otake(_1765815), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765811)), _1765813)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765815)), _1765817))), _1765817))))], (48833 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765811)), hAPP(hAPP(c_List_Otake(_1765811), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765811)), _1765813)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765815)), _1765817))), _1765813)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765815)), hAPP(hAPP(c_List_Otake(_1765815), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765811)), _1765813)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765815)), _1765817))), _1765817)))]], -(hBOOL(hAPP(_1765819, hAPP(hAPP(c_List_Ozip(_1765811, _1765815), _1765813), _1765817))))], (38973 ^ _782476) ^ [_1531916, _1531918, _1531920, _1531922] : [hBOOL(hAPP(hAPP(c_member(_1531916), _1531918), c_Wellfounded_Oacc(_1531916, _1531920))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531916, _1531916)), hAPP(hAPP(c_Product__Type_OPair(_1531916, _1531916), _1531922), _1531918)), _1531920)), -(hBOOL(hAPP(hAPP(c_member(_1531916), _1531922), c_Wellfounded_Oacc(_1531916, _1531920))))], (32601 ^ _782476) ^ [_1399958, _1399960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1399958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399960, _1399958)), _1399958)))], (52397 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (23631 ^ _782476) ^ [_1226451] : [23632 ^ _782476 : [(23633 ^ _782476) ^ [_1226508] : [hBOOL(hAPP(_1226451, _1226508))]], 23635 ^ _782476 : [(23638 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1226451, hAPP(c_Int_Onat, 23634 ^ [_1226451]))))], (23636 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23634 ^ [_1226451])))]]], (17576 ^ _782476) ^ [_1115660, _1115662, _1115664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115660), _1115662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115662), _1115664))))], (52603 ^ _782476) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (39472 ^ _782476) ^ [_1543860, _1543862] : [-(hAPP(c_List_Olexn(_1543860, _1543862), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1543860), tc_List_Olist(_1543860)), tc_HOL_Obool)))], (47128 ^ _782476) ^ [_1729648, _1729650, _1729652, _1729654, _1729656] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729648)), hAPP(c_List_Ofilter(_1729648, _1729650), hAPP(hAPP(c_List_Omap(_1729652, _1729648), _1729654), _1729656))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729652)), hAPP(c_List_Ofilter(_1729652, hAPP(c_Fun_Ocomp(_1729648, tc_HOL_Obool, _1729652, _1729650), _1729654)), _1729656)))], (22738 ^ _782476) ^ [_1209031] : [class_Rings_Oring__1(_1209031), -(hBOOL(hAPP(hAPP(c_member(_1209031), c_Groups_Ozero__class_Ozero(_1209031)), c_Int_Oring__1__class_OInts(_1209031))))], (34054 ^ _782476) ^ [_1428018, _1428020, _1428022] : [class_Int_Onumber__ring(_1428018), 34057 ^ _782476 : [(34064 ^ _782476) ^ [] : [-(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), _1428020)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428018), _1428022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428020))) = c_Groups_Oone__class_Oone(_1428018))], (34058 ^ _782476) ^ [] : [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), _1428020))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428018), _1428022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428020))) = hAPP(hAPP(c_HOL_OLet(_1428018, _1428018), hAPP(hAPP(c_Power_Opower__class_Opower(_1428018), _1428022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428020))), hAPP(hAPP(c_COMBS(_1428018, _1428018, _1428018), hAPP(hAPP(c_COMBB(_1428018, tc_fun(_1428018, _1428018), _1428018), c_Groups_Otimes__class_Otimes(_1428018)), hAPP(c_Groups_Otimes__class_Otimes(_1428018), _1428022))), c_COMBI(_1428018))))]]], (37752 ^ _782476) ^ [_1501171, _1501173, _1501175, _1501177, _1501179, _1501181, _1501183] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501171, _1501173, _1501175), hAPP(c_Fun_Ocomp(_1501177, tc_fun(_1501173, _1501175), _1501171, _1501179), _1501181)), _1501183) = hAPP(hAPP(_1501179, hAPP(_1501181, hAPP(c_Product__Type_Ofst(_1501171, _1501173), _1501183))), hAPP(c_Product__Type_Osnd(_1501171, _1501173), _1501183)))], (38897 ^ _782476) ^ [] : [-(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))], (3120 ^ _782476) ^ [_828850, _828852, _828854, _828856, _828858, _828860] : [-(c_List_Oset__Cons(_828860, _828856, _828852) = c_List_Oset__Cons(_828858, _828854, _828850)), _828860 = _828858, _828856 = _828854, _828852 = _828850], (45460 ^ _782476) ^ [_1692452, _1692454, _1692456, _1692458, _1692460, _1692462] : [-(hAPP(c_List_Ofoldl(_1692452, _1692454, _1692456, _1692458), hAPP(hAPP(c_List_Oappend(_1692454), _1692460), _1692462)) = hAPP(c_List_Ofoldl(_1692452, _1692454, _1692456, hAPP(c_List_Ofoldl(_1692452, _1692454, _1692456, _1692458), _1692460)), _1692462))], (32736 ^ _782476) ^ [_1402714, _1402716, _1402718, _1402720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1402714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402716), _1402718)), -(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), _1402718), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402720, _1402714))), _1402716)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402718), _1402714))))], (43948 ^ _782476) ^ [_1658877, _1658879, _1658881, _1658883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658877), tc_List_Olist(_1658877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658877), tc_List_Olist(_1658877)), _1658879), _1658881)), c_List_Olistrel1(_1658877, _1658883))), 43953 ^ _782476 : [(43958 ^ _782476) ^ [] : [-(_1658881 = hAPP(hAPP(c_List_Olist__update(_1658877, _1658879), 43952 ^ [_1658877, _1658879, _1658881, _1658883]), 43951 ^ [_1658877, _1658879, _1658881, _1658883]))], (43956 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43952 ^ [_1658877, _1658879, _1658881, _1658883]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658877)), _1658879))))], (43954 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658877, _1658877)), hAPP(hAPP(c_Product__Type_OPair(_1658877, _1658877), hAPP(hAPP(c_List_Onth(_1658877), _1658879), 43952 ^ [_1658877, _1658879, _1658881, _1658883])), 43951 ^ [_1658877, _1658879, _1658881, _1658883])), _1658883)))]]], (7934 ^ _782476) ^ [_917478, _917480, _917482] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917478, tc_HOL_Obool)), _917480), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917478, tc_HOL_Obool)), _917480), _917482)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917478, tc_HOL_Obool)), _917480), _917482))], (40958 ^ _782476) ^ [_1582800, _1582802] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582800, _1582800), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1582800, _1582802)), hAPP(hAPP(c_Product__Type_OSigma(_1582800, _1582800), hAPP(c_Relation_OField(_1582800), _1582802)), hAPP(c_COMBK(tc_fun(_1582800, tc_HOL_Obool), _1582800), hAPP(c_Relation_OField(_1582800), _1582802))))))], (9510 ^ _782476) ^ [_952947] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952947, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952947, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_952947, tc_HOL_Obool)))], (24012 ^ _782476) ^ [_1232689, _1232691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232691)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232689)), hAPP(c_Int_Onat, _1232691)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1232689, _1232691)))], (1722 ^ _782476) ^ [_807201, _807203] : [-(class_Groups_Ocomm__monoid__mult(_807201)), _807203 = _807201, class_Groups_Ocomm__monoid__mult(_807203)], (38467 ^ _782476) ^ [_1518743] : [-(c_Equiv__Relations_Oequivp(_1518743, c_fequal))], (35932 ^ _782476) ^ [_1461266, _1461268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461266)), -(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)))), _1461268))), 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)))), _1461266)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1461268), _1461266))], (8196 ^ _782476) ^ [_922916, _922918, _922920, _922922, _922924] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922916, tc_fun(_922918, tc_HOL_Obool)), _922920), hAPP(hAPP(c_COMBC(_922916, tc_fun(_922918, tc_HOL_Obool), tc_fun(_922918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922918, tc_HOL_Obool), tc_fun(tc_fun(_922918, tc_HOL_Obool), tc_fun(_922918, tc_HOL_Obool)), _922916), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922918, tc_HOL_Obool))), _922922)), _922924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922918, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922916, tc_fun(_922918, tc_HOL_Obool)), _922920), _922922)), _922924))], (24825 ^ _782476) ^ [_1246538, _1246540] : [class_Rings_Olinordered__idom(_1246538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246538), _1246540), c_Groups_Ozero__class_Ozero(_1246538))), -(c_Groups_Osgn__class_Osgn(_1246538, _1246540) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246538), c_Groups_Oone__class_Oone(_1246538)))], (6044 ^ _782476) ^ [_878193, _878195, _878197] : [class_Orderings_Oorder(_878193), 6047 ^ _782476 : [(6056 ^ _782476) ^ [] : [-(_878195 = _878197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878193), _878195), _878197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878193), _878197), _878195))], (6048 ^ _782476) ^ [] : [_878195 = _878197, 6051 ^ _782476 : [(6054 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878193), _878197), _878195)))], (6052 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878193), _878195), _878197)))]]]]], (8906 ^ _782476) ^ [_937794, _937796, _937798, _937800, _937802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937794, tc_HOL_Obool)), _937796), _937798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937800, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937794, _937800, _937802), _937796)), hAPP(c_Set_Oimage(_937794, _937800, _937802), _937798))))], (16049 ^ _782476) ^ [_1083500, _1083502, _1083504, _1083506, _1083508] : [class_Groups_Oab__group__add(_1083500), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083502, _1083500), hAPP(hAPP(c_COMBS(_1083502, _1083500, _1083500), hAPP(hAPP(c_COMBB(_1083500, tc_fun(_1083500, _1083500), _1083502), c_Groups_Ominus__class_Ominus(_1083500)), _1083504)), _1083506)), _1083508) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083500), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083502, _1083500), _1083504), _1083508)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083502, _1083500), _1083506), _1083508)))], (22586 ^ _782476) ^ [_1205986, _1205988] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205986)), _1205988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1205988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205986), _1205988)))], (8921 ^ _782476) ^ [_938173, _938175, _938177, _938179, _938181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938173, tc_HOL_Obool)), _938175), hAPP(c_Set_Oimage(_938177, _938173, _938179), _938181)))), 8922 ^ _782476 : [(8923 ^ _782476) ^ [_938253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938177, tc_HOL_Obool)), _938253), _938181)), _938175 = hAPP(c_Set_Oimage(_938177, _938173, _938179), _938253)]]], (50390 ^ _782476) ^ [_1800442, _1800444, _1800446, _1800448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800442), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1800444, _1800446, _1800442, _1800448) = 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(_1800444)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800444)))], (15853 ^ _782476) ^ [_1079074, _1079076, _1079078, _1079080] : [c_Big__Operators_Osemilattice__big(_1079074, _1079076, _1079078), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079074), _1079080)), -(hAPP(_1079078, _1079080) = hAPP(c_Finite__Set_Ofold1(_1079074, _1079076), _1079080))], (45084 ^ _782476) ^ [_1684127, _1684129, _1684131, _1684133] : [-(hAPP(hAPP(c_List_Odrop(_1684127), _1684129), hAPP(hAPP(c_List_Otake(_1684127), _1684131), _1684133)) = hAPP(hAPP(c_List_Otake(_1684127), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1684131), _1684129)), hAPP(hAPP(c_List_Odrop(_1684127), _1684129), _1684133)))], (45164 ^ _782476) ^ [_1685983, _1685985, _1685987, _1685989] : [-(hAPP(hAPP(c_List_Odrop(_1685983), _1685985), hAPP(hAPP(c_List_Olist_OCons(_1685983), _1685987), _1685989)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1685983), hAPP(hAPP(c_List_Olist_OCons(_1685983), _1685987), _1685989), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1685983), tc_List_Olist(_1685983)), c_List_Odrop(_1685983)), _1685989), _1685985))], (43465 ^ _782476) ^ [_1646164, _1646166, _1646168, _1646170] : [hBOOL(hAPP(hAPP(c_member(_1646164), _1646166), hAPP(c_List_Oset(_1646164), hAPP(hAPP(c_List_Otake(_1646164), _1646168), _1646170)))), -(hBOOL(hAPP(hAPP(c_member(_1646164), _1646166), hAPP(c_List_Oset(_1646164), _1646170))))], (11352 ^ _782476) ^ [_990481, _990483, _990485, _990487, _990489, _990491] : [-(_990481 = _990483), -(hAPP(c_Fun_Ofun__upd(_990485, _990487, _990489, _990483, _990491), _990481) = hAPP(_990489, _990481))], (33086 ^ _782476) ^ [_1409793, _1409795, _1409797] : [class_Int_Onumber__ring(_1409793), class_Rings_Olinordered__idom(_1409793), 33093 ^ _782476 : [(33100 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409795), _1409797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409793), hAPP(c_Int_Onumber__class_Onumber__of(_1409793), _1409795)), hAPP(c_Int_Onumber__class_Onumber__of(_1409793), _1409797))))], (33094 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409793), hAPP(c_Int_Onumber__class_Onumber__of(_1409793), _1409795)), hAPP(c_Int_Onumber__class_Onumber__of(_1409793), _1409797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409795), _1409797)))]]], (43201 ^ _782476) ^ [_1639042, _1639044, _1639046, _1639048, _1639050, _1639052] : [c_List_Olistrelp(_1639042, _1639044, hAPP(hAPP(c_List_Olist_OCons(_1639042), _1639046), _1639048), hAPP(hAPP(c_List_Olist_OCons(_1639042), _1639050), _1639052)), 43204 ^ _782476 : [(43207 ^ _782476) ^ [] : [-(c_List_Olistrelp(_1639042, _1639044, _1639048, _1639052))], (43205 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1639044, _1639046), _1639050)))]]], (27226 ^ _782476) ^ [_1296986, _1296988, _1296990, _1296992, _1296994] : [class_Groups_Ocomm__monoid__mult(_1296986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296988), _1296990)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296988, _1296986), hAPP(hAPP(c_COMBS(_1296988, _1296986, _1296986), hAPP(hAPP(c_COMBB(_1296986, tc_fun(_1296986, _1296986), _1296988), c_Groups_Otimes__class_Otimes(_1296986)), _1296992)), _1296994)), _1296990) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296986), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296988, _1296986), _1296992), _1296990)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296988, _1296986), _1296994), _1296990)))], (40688 ^ _782476) ^ [_1576912, _1576914, _1576916] : [40689 ^ _782476 : [(40690 ^ _782476) ^ [_1576966] : [hBOOL(hAPP(_1576912, _1576966))]], _1576914 = c_Hilbert__Choice_OEps(_1576916, _1576912), -(hBOOL(hAPP(_1576912, _1576914)))], (27805 ^ _782476) ^ [_1308230, _1308232, _1308234, _1308236, _1308238] : [class_Groups_Ocomm__monoid__mult(_1308230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308232), _1308234)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308232), _1308236)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308232, tc_HOL_Obool)), _1308234), _1308236) = c_Orderings_Obot__class_Obot(tc_fun(_1308232, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308232, _1308230), _1308238), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308232, tc_HOL_Obool)), _1308234), _1308236)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308230), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308232, _1308230), _1308238), _1308234)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308232, _1308230), _1308238), _1308236)))], (9548 ^ _782476) ^ [_953652, _953654] : [hBOOL(hAPP(hAPP(c_member(_953652), _953654), c_Orderings_Obot__class_Obot(tc_fun(_953652, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953652, tc_HOL_Obool)), _953654)))], (24570 ^ _782476) ^ [_1241888, _1241890, _1241892] : [class_Rings_Olinordered__idom(_1241888), 24573 ^ _782476 : [(24580 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241890), _1241892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241888), hAPP(c_Int_Oring__1__class_Oof__int(_1241888), _1241890)), hAPP(c_Int_Oring__1__class_Oof__int(_1241888), _1241892))))], (24574 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241888), hAPP(c_Int_Oring__1__class_Oof__int(_1241888), _1241890)), hAPP(c_Int_Oring__1__class_Oof__int(_1241888), _1241892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241890), _1241892)))]]], (10003 ^ _782476) ^ [_962920, _962922, _962924] : [class_Orderings_Oorder(_962920), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962920, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962920), _962922)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962920, _962922), _962924)) = c_Orderings_Obot__class_Obot(tc_fun(_962920, tc_HOL_Obool)))], (9195 ^ _782476) ^ [_945839, _945841, _945843] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945839, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945839, tc_HOL_Obool)), _945841), _945843)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945839, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945839, tc_HOL_Obool)), _945841)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945839, tc_HOL_Obool)), _945843)))], (24184 ^ _782476) ^ [_1235646] : [c_Nat__Transfer_Ois__nat(_1235646), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235646)))], (49725 ^ _782476) ^ [_1786128, _1786130, _1786132, _1786134, _1786136] : [c_Fun_Oinj__on(_1786128, _1786130, _1786132, c_Orderings_Otop__class_Otop(tc_fun(_1786128, tc_HOL_Obool))), 49731 ^ _782476 : [(49734 ^ _782476) ^ [] : [hBOOL(hAPP(_1786134, hAPP(c_Hilbert__Choice_Oinv__into(_1786128, _1786130, c_Orderings_Otop__class_Otop(tc_fun(_1786128, tc_HOL_Obool)), _1786132), 49730 ^ [_1786128, _1786130, _1786132, _1786134, _1786136])))], (49732 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786130), 49730 ^ [_1786128, _1786130, _1786132, _1786134, _1786136]), hAPP(c_Set_Oimage(_1786128, _1786130, _1786132), c_Orderings_Otop__class_Otop(tc_fun(_1786128, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1786134, _1786136)))], (7426 ^ _782476) ^ [_906764, _906766, _906768, _906770, _906772, _906774, _906776] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906764, tc_fun(_906766, tc_fun(_906768, tc_HOL_Obool))), _906770), _906772), _906774), _906776))), 7427 ^ _782476 : [(7428 ^ _782476) ^ [_906849] : [hBOOL(hAPP(hAPP(c_member(_906764), _906849), _906770)), hBOOL(hAPP(hAPP(hAPP(_906772, _906849), _906774), _906776))]]], (48790 ^ _782476) ^ [_1764548, _1764550] : [-(c_List_Omeasures(_1764548, _1764550) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1764548), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1764548, tc_List_Olist(tc_fun(_1764548, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764548, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1764548, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1764548), c_List_Omap(tc_fun(_1764548, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1764548, tc_Nat_Onat), _1764548, tc_Nat_Onat), c_COMBI(tc_fun(_1764548, tc_Nat_Onat))))), _1764550)))], (46356 ^ _782476) ^ [_1711872, _1711874] : [-(c_Random_Oselect(_1711872, _1711874) = 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(_1711872, 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(_1711872)), _1711874)))), hAPP(hAPP(c_COMBB(_1711872, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711872, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711872, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1711872, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1711872), _1711874)), c_Code__Numeral_Onat__of))))], (44410 ^ _782476) ^ [_1667943, _1667945, _1667947] : [-(hAPP(hAPP(c_List_Otake(_1667943), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1667943), _1667945), _1667947)) = hAPP(hAPP(c_List_Olist_OCons(_1667943), _1667945), c_List_Olist_ONil(_1667943)))], (35458 ^ _782476) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (39877 ^ _782476) ^ [_1555478, _1555480, _1555482, _1555484, _1555486, _1555488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555478, _1555480), tc_HOL_Obool)), _1555482), hAPP(hAPP(c_Product__Type_OSigma(_1555478, _1555480), _1555484), hAPP(c_COMBK(tc_fun(_1555480, tc_HOL_Obool), _1555478), _1555486)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555480, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1555478, _1555480, _1555482), _1555488)), _1555486)))], (25041 ^ _782476) ^ [_1250472, _1250474] : [class_Groups_Oordered__ab__group__add__abs(_1250472), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250472), c_Groups_Ozero__class_Ozero(_1250472)), hAPP(c_Groups_Oabs__class_Oabs(_1250472), _1250474))))], (16467 ^ _782476) ^ [_1092577, _1092579, _1092581, _1092583] : [class_Groups_Ocancel__semigroup__add(_1092577), 16470 ^ _782476 : [(16477 ^ _782476) ^ [] : [_1092581 = _1092583, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092577), _1092579), _1092581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092577), _1092579), _1092583))], (16471 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092577), _1092579), _1092581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092577), _1092579), _1092583), -(_1092581 = _1092583)]]], (8591 ^ _782476) ^ [_931745, _931747, _931749] : [class_Lattices_Olattice(_931745), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931745), _931747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931745), _931747), _931749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931745), _931747), _931749))], (41172 ^ _782476) ^ [_1588857, _1588859, _1588861, _1588863, _1588865] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588857, _1588857)), hAPP(hAPP(c_Product__Type_OPair(_1588857, _1588857), _1588859), _1588861)), c_Transitive__Closure_Ortrancl(_1588857, _1588863))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588857, _1588857)), hAPP(hAPP(c_Product__Type_OPair(_1588857, _1588857), _1588861), _1588865)), _1588863)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588857, _1588857)), hAPP(hAPP(c_Product__Type_OPair(_1588857, _1588857), _1588859), _1588865)), c_Transitive__Closure_Ortrancl(_1588857, _1588863))))], (36196 ^ _782476) ^ [_1465862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465862), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465862)), c_Int_OMin)))], (10517 ^ _782476) ^ [_974406, _974408, _974410, _974412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974406, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974406), _974408), _974410)), _974412)), 10520 ^ _782476 : [(10523 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974406, tc_HOL_Obool)), _974410), _974412)))], (10521 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_974406), _974408), _974412)))]]], (6624 ^ _782476) ^ [_889211, _889213] : [class_Orderings_Olinorder(_889211), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889211, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_889211), _889213)) = hAPP(c_SetInterval_Oord__class_OlessThan(_889211), _889213))], (41465 ^ _782476) ^ [_1595977, _1595979, _1595981] : [-(hAPP(c_Relation_Oconverse(_1595977, _1595979), hAPP(c_Relation_Oconverse(_1595979, _1595977), _1595981)) = _1595981)], (23611 ^ _782476) ^ [_1226088] : [hBOOL(hAPP(_1226088, 23612 ^ [_1226088])), 23615 ^ _782476 : [(23616 ^ _782476) ^ [_1226182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226182)), -(hBOOL(hAPP(_1226088, hAPP(c_Int_Onat, _1226182))))]]], (35044 ^ _782476) ^ [_1445058, _1445060, _1445062] : [class_Int_Onumber__ring(_1445058), 35047 ^ _782476 : [(35054 ^ _782476) ^ [] : [c_Int_Oiszero(_1445058, hAPP(c_Int_Onumber__class_Onumber__of(_1445058), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445060), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445062)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445058), _1445060) = hAPP(c_Int_Onumber__class_Onumber__of(_1445058), _1445062))], (35048 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445058), _1445060) = hAPP(c_Int_Onumber__class_Onumber__of(_1445058), _1445062), -(c_Int_Oiszero(_1445058, hAPP(c_Int_Onumber__class_Onumber__of(_1445058), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445060), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445062)))))]]], (38746 ^ _782476) ^ [_1524685, _1524687, _1524689, _1524691] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524685, _1524685)), hAPP(hAPP(c_Product__Type_OPair(_1524685, _1524685), _1524687), _1524689)), c_Relation_OId__on(_1524685, _1524691)))), _1524687 = _1524689, hBOOL(hAPP(hAPP(c_member(_1524685), _1524687), _1524691))], (43209 ^ _782476) ^ [_1639199, _1639201, _1639203, _1639205, _1639207, _1639209] : [-(c_List_Olistrelp(_1639199, _1639201, hAPP(hAPP(c_List_Olist_OCons(_1639199), _1639203), _1639205), hAPP(hAPP(c_List_Olist_OCons(_1639199), _1639207), _1639209))), hBOOL(hAPP(hAPP(_1639201, _1639203), _1639207)), c_List_Olistrelp(_1639199, _1639201, _1639205, _1639209)], (14585 ^ _782476) ^ [_1054171, _1054173, _1054175, _1054177, _1054179] : [c_Finite__Set_Ofolding__one(_1054171, _1054173, _1054175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054171), _1054177)), -(_1054177 = c_Orderings_Obot__class_Obot(tc_fun(_1054171, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054171), _1054179)), -(_1054179 = c_Orderings_Obot__class_Obot(tc_fun(_1054171, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054171, tc_HOL_Obool)), _1054177), _1054179) = c_Orderings_Obot__class_Obot(tc_fun(_1054171, tc_HOL_Obool)), -(hAPP(_1054175, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054171, tc_HOL_Obool)), _1054177), _1054179)) = hAPP(hAPP(_1054173, hAPP(_1054175, _1054177)), hAPP(_1054175, _1054179)))], (40023 ^ _782476) ^ [_1560521, _1560523, _1560525] : [-(hAPP(c_Fun_Ocomp(_1560521, _1560521, _1560523, c_Fun_Oid(_1560521)), _1560525) = _1560525)], (45617 ^ _782476) ^ [_1695914, _1695916, _1695918, _1695920] : [class_Orderings_Olinorder(_1695914), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695914, _1695914, c_COMBI(_1695914)), _1695916), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695914, _1695914, c_COMBI(_1695914)), _1695918), _1695920)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695914, _1695914, c_COMBI(_1695914)), _1695918), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695914, _1695914, c_COMBI(_1695914)), _1695916), _1695920)))], (45072 ^ _782476) ^ [_1683854, _1683856] : [hBOOL(hAPP(c_List_Odistinct(_1683854), _1683856)), -(hBOOL(hAPP(c_List_Odistinct(_1683854), hAPP(c_List_Orotate1(_1683854), _1683856))))], (49701 ^ _782476) ^ [_1785558, _1785560, _1785562] : [c_Fun_Oinj__on(_1785558, _1785560, _1785562, c_Orderings_Otop__class_Otop(tc_fun(_1785558, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785560, _1785558, _1785558, c_Hilbert__Choice_Oinv__into(_1785558, _1785560, c_Orderings_Otop__class_Otop(tc_fun(_1785558, tc_HOL_Obool)), _1785562)), _1785562) = c_Fun_Oid(_1785558))], (11490 ^ _782476) ^ [_992574, _992576, _992578] : [class_Orderings_Opreorder(_992574), 11493 ^ _782476 : [(11502 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992574), _992576), _992578))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992574), _992576), _992578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992574), _992578), _992576)))], (11494 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992574), _992576), _992578)), 11497 ^ _782476 : [(11500 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992574), _992578), _992576))], (11498 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992574), _992576), _992578)))]]]]], (24008 ^ _782476) ^ [_1232606, _1232608] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1232606, _1232608)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232608), _1232606)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10873 ^ _782476) ^ [_982659, _982661, _982663] : [-(hAPP(c_Set_OPow(_982659), hAPP(hAPP(c_Set_Oinsert(_982659), _982661), _982663)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_982659, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_982659), _982663)), hAPP(c_Set_Oimage(tc_fun(_982659, tc_HOL_Obool), tc_fun(_982659, tc_HOL_Obool), hAPP(c_Set_Oinsert(_982659), _982661)), hAPP(c_Set_OPow(_982659), _982663))))], (36849 ^ _782476) ^ [_1483937, _1483939, _1483941, _1483943, _1483945, _1483947] : [hBOOL(hAPP(hAPP(_1483937, _1483939), _1483941)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483943, tc_fun(_1483945, tc_HOL_Obool))), _1483947), _1483937), _1483939), _1483941)))], (31383 ^ _782476) ^ [_1376277, _1376279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376277)), -(c_SMT_Oz3div(_1376279, _1376277) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376279), _1376277))], (21061 ^ _782476) ^ [_1178270, _1178272, _1178274] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178272), _1178274)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178270), _1178272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178270), _1178274)))], (22754 ^ _782476) ^ [_1209309, _1209311, _1209313, _1209315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209309), _1209311)), 22757 ^ _782476 : [(22764 ^ _782476) ^ [] : [hAPP(c_Finite__Set_Ocard(_1209313), hAPP(c_Set_Oimage(_1209309, _1209313, _1209315), _1209311)) = hAPP(c_Finite__Set_Ocard(_1209309), _1209311), -(c_Fun_Oinj__on(_1209309, _1209313, _1209315, _1209311))], (22758 ^ _782476) ^ [] : [c_Fun_Oinj__on(_1209309, _1209313, _1209315, _1209311), -(hAPP(c_Finite__Set_Ocard(_1209313), hAPP(c_Set_Oimage(_1209309, _1209313, _1209315), _1209311)) = hAPP(c_Finite__Set_Ocard(_1209309), _1209311))]]], (44370 ^ _782476) ^ [_1667288] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667288)), c_List_Olist_ONil(_1667288)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36499 ^ _782476) ^ [_1475695, _1475697, _1475699, _1475701, _1475703, _1475705] : [hBOOL(hAPP(hAPP(c_member(_1475695), _1475697), _1475699)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475695, _1475701)), hAPP(hAPP(c_Product__Type_OPair(_1475695, _1475701), _1475697), _1475703)), _1475705)), -(hBOOL(hAPP(hAPP(c_member(_1475701), _1475703), hAPP(c_Relation_OImage(_1475695, _1475701, _1475705), _1475699))))], (3700 ^ _782476) ^ [_837932, _837934] : [_837934 = _837932, -(c_List_Oreturn__list(_837934) = c_List_Oreturn__list(_837932))], (31980 ^ _782476) ^ [_1388351, _1388353, _1388355, _1388357, _1388359, _1388361] : [class_Divides_Oring__div(_1388351), c_Divides_Odiv__class_Omod(_1388351, _1388353, _1388355) = c_Divides_Odiv__class_Omod(_1388351, _1388357, _1388355), c_Divides_Odiv__class_Omod(_1388351, _1388359, _1388355) = c_Divides_Odiv__class_Omod(_1388351, _1388361, _1388355), -(c_Divides_Odiv__class_Omod(_1388351, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388351), _1388353), _1388359), _1388355) = c_Divides_Odiv__class_Omod(_1388351, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388351), _1388357), _1388361), _1388355))], (44688 ^ _782476) ^ [_1674820, _1674822, _1674824, _1674826, _1674828, _1674830] : [hAPP(hAPP(c_List_Oappend(_1674820), _1674822), _1674824) = _1674826, _1674828 = hAPP(hAPP(c_List_Oappend(_1674820), _1674824), _1674830), -(hAPP(hAPP(c_List_Oappend(_1674820), _1674822), _1674828) = hAPP(hAPP(c_List_Oappend(_1674820), _1674826), _1674830))], (18192 ^ _782476) ^ [_1126544] : [class_Rings_Ozero__neq__one(_1126544), c_Groups_Ozero__class_Ozero(_1126544) = c_Groups_Oone__class_Oone(_1126544)], (23374 ^ _782476) ^ [_1221337, _1221339, _1221341, _1221343] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221337), _1221339)), hBOOL(hAPP(hAPP(c_member(_1221337), _1221341), _1221339)), hBOOL(hAPP(hAPP(c_member(_1221337), _1221343), _1221339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221337, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221337, tc_HOL_Obool)), _1221339), hAPP(hAPP(c_Set_Oinsert(_1221337), _1221341), c_Orderings_Obot__class_Obot(tc_fun(_1221337, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1221337), _1221343), c_Orderings_Obot__class_Obot(tc_fun(_1221337, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221337), _1221339))))], (42877 ^ _782476) ^ [_1628437, _1628439] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1628437))), c_Enum_Osublists(_1628437, _1628439)) = 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(_1628437)), _1628439)))], (10321 ^ _782476) ^ [_969509, _969511, _969513, _969515] : [10322 ^ _782476 : [(10325 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969509), _969511), _969515))], (10323 ^ _782476) ^ [] : [_969511 = _969513]], -(hBOOL(hAPP(hAPP(c_member(_969509), _969511), hAPP(hAPP(c_Set_Oinsert(_969509), _969513), _969515))))], (51631 ^ _782476) ^ [_1828747, _1828749, _1828751, _1828753, _1828755, _1828757, _1828759, _1828761] : [c_Finite__Set_Ofolding__image(_1828747, _1828749, _1828751, _1828753, _1828755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1828749), _1828757)), 51641 ^ _782476 : [(51644 ^ _782476) ^ [] : [hAPP(_1828759, 51640 ^ [_1828747, _1828749, _1828751, _1828753, _1828755, _1828757, _1828759, _1828761]) = hAPP(_1828761, 51640 ^ [_1828747, _1828749, _1828751, _1828753, _1828755, _1828757, _1828759, _1828761])], (51642 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1828749), 51640 ^ [_1828747, _1828749, _1828751, _1828753, _1828755, _1828757, _1828759, _1828761]), _1828757)))]], -(hAPP(hAPP(_1828755, _1828759), _1828757) = hAPP(hAPP(_1828755, _1828761), _1828757))], (17547 ^ _782476) ^ [_1115090, _1115092] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115092), _1115090))))], (12974 ^ _782476) ^ [_1020400, _1020402, _1020404, _1020406, _1020408] : [c_Fun_Oinj__on(_1020400, _1020402, _1020404, c_Orderings_Otop__class_Otop(tc_fun(_1020400, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1020400, _1020402, _1020404), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020400, tc_HOL_Obool)), _1020406), _1020408)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020402, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020400, _1020402, _1020404), _1020406)), hAPP(c_Set_Oimage(_1020400, _1020402, _1020404), _1020408)))], (48210 ^ _782476) ^ [_1752212, _1752214, _1752216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752212), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752214)), _1752216))), -(hAPP(hAPP(c_List_Onth(_1752214), hAPP(c_List_Orev(_1752214), _1752216)), _1752212) = hAPP(hAPP(c_List_Onth(_1752214), _1752216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752214)), _1752216)), hAPP(c_Nat_OSuc, _1752212))))], (8206 ^ _782476) ^ [_923517, _923519, _923521, _923523] : [class_Orderings_Olinorder(_923517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923517), _923519), _923521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923517), _923521), _923523)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923517, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923517, _923519), _923521)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923517, _923521), _923523)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923517, _923519), _923523))], (52327 ^ _782476) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (43067 ^ _782476) ^ [_1634648, _1634650, _1634652, _1634654, _1634656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634648, _1634648)), hAPP(hAPP(c_Product__Type_OPair(_1634648, _1634648), _1634650), _1634652)), _1634654)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634648), tc_List_Olist(_1634648))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634648), tc_List_Olist(_1634648)), hAPP(hAPP(c_List_Olist_OCons(_1634648), _1634650), _1634656)), hAPP(hAPP(c_List_Olist_OCons(_1634648), _1634652), _1634656))), c_List_Olistrel1(_1634648, _1634654))))], (50133 ^ _782476) ^ [_1794659, _1794661] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794659)), _1794661) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794659, tc_Lazy__Sequence_Olazy__sequence(_1794659)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794659, tc_Lazy__Sequence_Olazy__sequence(_1794659), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794659), tc_Nat_Onat), _1794659), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794659), 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(_1794659)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794659)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1794659), _1794661)))], (42835 ^ _782476) ^ [_1626987, _1626989, _1626991, _1626993] : [class_Rings_Olinordered__semidom(_1626987), 42841 ^ _782476 : [(42844 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626987), c_Groups_Ozero__class_Ozero(_1626987)), hAPP(_1626993, 42840 ^ [_1626987, _1626989, _1626991, _1626993])))], (42842 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626989), 42840 ^ [_1626987, _1626989, _1626991, _1626993]), _1626991)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626987), c_Groups_Ozero__class_Ozero(_1626987)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626989, _1626987), _1626993), _1626991))))], (21361 ^ _782476) ^ [_1183556, _1183558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183556), _1183558)), -(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)), _1183556)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183558))))], (8260 ^ _782476) ^ [_924634, _924636, _924638] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924634, tc_HOL_Obool)), _924636), c_Complete__Lattice_OInf__class_OInf(tc_fun(_924634, tc_HOL_Obool), _924638)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_924634, tc_HOL_Obool), tc_fun(_924634, tc_HOL_Obool)), _924638), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924634, tc_HOL_Obool)), _924636)))], (37363 ^ _782476) ^ [_1493436, _1493438, _1493440, _1493442] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493436, _1493438), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493440), _1493442))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493436, _1493438) = _1493442)], (37375 ^ _782476) ^ [_1493662, _1493664] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493662, _1493664), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493662), _1493664)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493662, _1493664)))))], (30304 ^ _782476) ^ [_1356915, _1356917, _1356919] : [class_Fields_Olinordered__field(_1356915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356915), _1356917), c_Groups_Ozero__class_Ozero(_1356915))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356915), c_Groups_Ozero__class_Ozero(_1356915)), _1356919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356915), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356915), _1356917), _1356919)), c_Groups_Ozero__class_Ozero(_1356915))))], (22036 ^ _782476) ^ [_1196910] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1196910)], (13242 ^ _782476) ^ [_1026758, _1026760, _1026762, _1026764, _1026766] : [hBOOL(hAPP(hAPP(c_member(_1026758), _1026760), hAPP(c_Set_Ovimage(_1026758, _1026762, _1026764), hAPP(hAPP(c_Set_Oinsert(_1026762), _1026766), c_Orderings_Obot__class_Obot(tc_fun(_1026762, tc_HOL_Obool)))))), -(hAPP(_1026764, _1026760) = _1026766)], (51484 ^ _782476) ^ [_1824046, _1824048, _1824050, _1824052, _1824054] : [hBOOL(hAPP(hAPP(c_member(_1824046), _1824048), _1824050)), -(hAPP(c_Quotient_OBabs(_1824046, _1824052, _1824050, _1824054), _1824048) = hAPP(_1824054, _1824048))], (31932 ^ _782476) ^ [_1387239, _1387241, _1387243, _1387245] : [class_Divides_Osemiring__div(_1387239), -(c_Divides_Odiv__class_Omod(_1387239, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387239), _1387241), _1387243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387239), _1387245), _1387243)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387239), c_Divides_Odiv__class_Omod(_1387239, _1387241, _1387245)), _1387243))], (36144 ^ _782476) ^ [_1465002] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1465002), c_Int_OMin) = c_Int_Osucc(_1465002))], (4758 ^ _782476) ^ [_854999, _855001, _855003, _855005] : [-(c_List_Oupto(_855005, _855001) = c_List_Oupto(_855003, _854999)), _855005 = _855003, _855001 = _854999], (8951 ^ _782476) ^ [_938969, _938971, _938973, _938975] : [class_Lattices_Odistrib__lattice(_938969), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938969), _938971), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938969), _938973), _938975)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938969), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938969), _938971), _938973)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938969), _938971), _938975)))], (37057 ^ _782476) ^ [_1488251] : [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), _1488251))), 37060 ^ _782476 : [(37067 ^ _782476) ^ [] : [-(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), _1488251)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488251)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488251)), 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), _1488251)))))], (37061 ^ _782476) ^ [] : [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), _1488251))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488251)) = 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)))]]], (16351 ^ _782476) ^ [_1090282, _1090284, _1090286, _1090288, _1090290] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1090282), 16354 ^ _782476 : [(16355 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090284), _1090286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090288), _1090290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090284), _1090290)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090288), _1090286)), -(_1090284 = _1090288), -(_1090286 = _1090290)], (16365 ^ _782476) ^ [] : [16366 ^ _782476 : [(16369 ^ _782476) ^ [] : [_1090286 = _1090290], (16367 ^ _782476) ^ [] : [_1090284 = _1090288]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090284), _1090286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090288), _1090290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090284), _1090290)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090282), _1090288), _1090286)))]]], (44252 ^ _782476) ^ [_1665294, _1665296, _1665298] : [-(hAPP(hAPP(c_List_Ozip(_1665294, _1665296), c_List_Olist_ONil(_1665294)), _1665298) = c_List_Olist_ONil(tc_prod(_1665294, _1665296)))], (45366 ^ _782476) ^ [_1690462, _1690464, _1690466] : [hAPP(c_List_Orotate(_1690462, _1690464), _1690466) = c_List_Olist_ONil(_1690462), -(_1690466 = c_List_Olist_ONil(_1690462))], (52167 ^ _782476) ^ [_1838388, _1838390] : [class_Lattices_Olattice(_1838388), -(class_Lattices_Olattice(tc_fun(_1838390, _1838388)))], (6726 ^ _782476) ^ [_891239, _891241, _891243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891239, tc_HOL_Obool)), _891241), _891243)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_891239, tc_HOL_Obool)), _891241), hAPP(c_Set_OPow(_891239), _891243))))], (34260 ^ _782476) ^ [_1431597, _1431599] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431597)), hAPP(c_Nat_OSuc, _1431599)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431597))), 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)), _1431599)))))], (42833 ^ _782476) ^ [_1626929, _1626931, _1626933, _1626935, _1626937, _1626939] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1626929, _1626931, _1626933), _1626935), hAPP(hAPP(c_Product__Type_OPair(_1626929, _1626931), _1626937), _1626939)) = hAPP(hAPP(_1626935, _1626937), _1626939))], (10505 ^ _782476) ^ [_974149, _974151, _974153] : [hBOOL(hAPP(hAPP(c_member(_974149), _974151), hAPP(hAPP(c_Set_Oinsert(_974149), _974153), c_Orderings_Obot__class_Obot(tc_fun(_974149, tc_HOL_Obool))))), -(_974151 = _974153)], (39684 ^ _782476) ^ [_1549886, _1549888, _1549890, _1549892, _1549894] : [hBOOL(hAPP(hAPP(_1549886, _1549888), _1549890)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549892, _1549894, _1549886), _1549888)))], (51440 ^ _782476) ^ [_1823252, _1823254, _1823256] : [hBOOL(hAPP(hAPP(_1823256, _1823254), _1823254)), -(hBOOL(hAPP(hAPP(c_member(_1823252), _1823254), c_Quotient_ORespects(_1823252, _1823256))))], (46878 ^ _782476) ^ [_1723689, _1723691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723689)), c_List_Oremdups(_1723689, _1723691))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723689)), _1723691))))], (49450 ^ _782476) ^ [_1779502, _1779504, _1779506, _1779508, _1779510] : [-(hAPP(c_New__DSequence_Opos__bind(_1779502, _1779504, _1779506, _1779508), _1779510) = hAPP(c_Lazy__Sequence_Obind(_1779502, _1779504, hAPP(_1779506, _1779510)), hAPP(hAPP(c_COMBC(_1779502, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779504)), _1779508), _1779510)))], (40897 ^ _782476) ^ [_1581582, _1581584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581582), _1581584)), -(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), _1581582), _1581584)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (16019 ^ _782476) ^ [_1082625, _1082627] : [class_Groups_Omonoid__mult(_1082625), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082625), _1082627), c_Groups_Oone__class_Oone(_1082625)) = _1082627)], (49653 ^ _782476) ^ [_1784292, _1784294, _1784296] : [hAPP(c_Set_Oimage(_1784292, _1784294, _1784296), c_Orderings_Otop__class_Otop(tc_fun(_1784292, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784294, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1784294, _1784292, c_Hilbert__Choice_Oinv__into(_1784292, _1784294, c_Orderings_Otop__class_Otop(tc_fun(_1784292, tc_HOL_Obool)), _1784296), c_Orderings_Otop__class_Otop(tc_fun(_1784294, tc_HOL_Obool))))], (2668 ^ _782476) ^ [_821816, _821818] : [_821818 = _821816, -(c_Equiv__Relations_Oquotient(_821818) = c_Equiv__Relations_Oquotient(_821816))], (17616 ^ _782476) ^ [_1116418, _1116420, _1116422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116418), _1116420)), _1116422)), 17619 ^ _782476 : [(17622 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116420), _1116422)))], (17620 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116418), _1116422)))]]], (42993 ^ _782476) ^ [_1632328, _1632330, _1632332, _1632334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632328), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632330), _1632332)))), -(hAPP(c_Random_Opick(_1632330, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632330)), _1632332), _1632334)), _1632328) = hAPP(c_Random_Opick(_1632330, _1632334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1632328), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632330), _1632332))))], (40551 ^ _782476) ^ [_1572845, _1572847, _1572849] : [hBOOL(hAPP(hAPP(c_member(_1572847), _1572845), c_Orderings_Obot__class_Obot(tc_fun(_1572847, tc_HOL_Obool)))), -(hBOOL(hAPP(_1572849, _1572845)))], (4146 ^ _782476) ^ [_845273, _845275, _845277, _845279, _845281, _845283, _845285, _845287] : [-(c_New__Random__Sequence_Opos__bind(_845287, _845283, _845279, _845275) = c_New__Random__Sequence_Opos__bind(_845285, _845281, _845277, _845273)), _845287 = _845285, _845283 = _845281, _845279 = _845277, _845275 = _845273], (43605 ^ _782476) ^ [_1649372, _1649374] : [-(c_List_Olists(_1649372, _1649374) = hAPP(c_Set_OCollect(tc_List_Olist(_1649372)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649372), tc_fun(_1649372, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649372, tc_HOL_Obool), tc_fun(tc_fun(_1649372, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649372)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649372, tc_HOL_Obool))), c_List_Oset(_1649372))), _1649374)))], (4258 ^ _782476) ^ [_847003, _847005, _847007, _847009, _847011, _847013, _847015, _847017] : [-(c_Hilbert__Choice_Oinv__into(_847017, _847013, _847009, _847005) = c_Hilbert__Choice_Oinv__into(_847015, _847011, _847007, _847003)), _847017 = _847015, _847013 = _847011, _847009 = _847007, _847005 = _847003], (11166 ^ _782476) ^ [_987564, _987566, _987568] : [class_Orderings_Oorder(_987564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987564), _987566), _987568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987564), _987568), _987566))], (7471 ^ _782476) ^ [_907795, _907797, _907799] : [class_Groups_Ogroup__add(_907795), 7474 ^ _782476 : [(7481 ^ _782476) ^ [] : [_907797 = _907799, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907795), _907797) = hAPP(c_Groups_Ouminus__class_Ouminus(_907795), _907799))], (7475 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907795), _907797) = hAPP(c_Groups_Ouminus__class_Ouminus(_907795), _907799), -(_907797 = _907799)]]], (44670 ^ _782476) ^ [_1674402, _1674404, _1674406, _1674408] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674402)), hAPP(hAPP(c_List_Oappend(_1674402), _1674404), _1674406)), c_List_Olists(_1674402, _1674408))), 44673 ^ _782476 : [(44676 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674402)), _1674406), c_List_Olists(_1674402, _1674408))))], (44674 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674402)), _1674404), c_List_Olists(_1674402, _1674408))))]]], (32530 ^ _782476) ^ [_1398456, _1398458, _1398460] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398456), _1398458)), c_Fun_Oinj__on(_1398456, tc_fun(tc_fun(_1398456, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1398456, tc_fun(tc_prod(_1398456, _1398456), tc_HOL_Obool), tc_fun(tc_fun(_1398456, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398456, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1398456, _1398456), tc_HOL_Obool), tc_fun(tc_fun(_1398456, tc_HOL_Obool), tc_HOL_Obool)), _1398456), c_Equiv__Relations_Oquotient(_1398456)), hAPP(hAPP(c_COMBC(_1398456, tc_fun(_1398456, tc_HOL_Obool), tc_fun(_1398456, tc_HOL_Obool)), c_Set_Oinsert(_1398456)), c_Orderings_Obot__class_Obot(tc_fun(_1398456, tc_HOL_Obool))))), _1398460), _1398458), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1398456, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398456), _1398458), _1398460)) = hAPP(c_Finite__Set_Ocard(_1398456), _1398458))], (3846 ^ _782476) ^ [_840213, _840215, _840217, _840219, _840221, _840223] : [-(c_List_OdropWhile(_840223, _840219, _840215) = c_List_OdropWhile(_840221, _840217, _840213)), _840223 = _840221, _840219 = _840217, _840215 = _840213], (20659 ^ _782476) ^ [_1170907, _1170909] : [class_Groups_Olinordered__ab__group__add(_1170907), 20662 ^ _782476 : [(20669 ^ _782476) ^ [] : [_1170909 = c_Groups_Ozero__class_Ozero(_1170907), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170907), _1170909), _1170909) = c_Groups_Ozero__class_Ozero(_1170907))], (20663 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170907), _1170909), _1170909) = c_Groups_Ozero__class_Ozero(_1170907), -(_1170909 = c_Groups_Ozero__class_Ozero(_1170907))]]], (48841 ^ _782476) ^ [_1766268, _1766270, _1766272, _1766274] : [48843 ^ _782476 : [(48846 ^ _782476) ^ [] : [hBOOL(hAPP(_1766272, 48842 ^ [_1766268, _1766270, _1766272, _1766274]))], (48844 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766268), 48842 ^ [_1766268, _1766270, _1766272, _1766274]), hAPP(c_List_Oset(_1766268), _1766270))))]], -(c_List_OdropWhile(_1766268, _1766272, hAPP(hAPP(c_List_Oappend(_1766268), _1766270), _1766274)) = c_List_OdropWhile(_1766268, _1766272, _1766274))], (45394 ^ _782476) ^ [_1690969, _1690971, _1690973] : [-(hAPP(c_List_Orotate(_1690969, hAPP(c_Nat_OSuc, _1690971)), _1690973) = hAPP(c_List_Orotate1(_1690969), hAPP(c_List_Orotate(_1690969, _1690971), _1690973)))], (44710 ^ _782476) ^ [_1675295, _1675297, _1675299, _1675301] : [hAPP(hAPP(c_List_Oappend(_1675295), _1675297), _1675299) = hAPP(hAPP(c_List_Oappend(_1675295), _1675297), _1675301), -(_1675299 = _1675301)], (12960 ^ _782476) ^ [_1020065, _1020067, _1020069, _1020071, _1020073, _1020075] : [c_Fun_Oinj__on(_1020065, _1020067, _1020069, _1020071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020065, tc_HOL_Obool)), _1020073), _1020071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020065, tc_HOL_Obool)), _1020075), _1020071)), -(hAPP(c_Set_Oimage(_1020065, _1020067, _1020069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020065, tc_HOL_Obool)), _1020073), _1020075)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020067, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020065, _1020067, _1020069), _1020073)), hAPP(c_Set_Oimage(_1020065, _1020067, _1020069), _1020075)))], (52733 ^ _782476) ^ [_1844336, _1844338] : [hBOOL(_1844336), -(hBOOL(hAPP(hAPP(c_fdisj, _1844336), _1844338)))], (18984 ^ _782476) ^ [_1139870, _1139872, _1139874] : [class_Groups_Oordered__comm__monoid__add(_1139870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139870), _1139872), c_Groups_Ozero__class_Ozero(_1139870))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139870), _1139874), c_Groups_Ozero__class_Ozero(_1139870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139870), _1139872), _1139874)), c_Groups_Ozero__class_Ozero(_1139870))))], (7804 ^ _782476) ^ [_914734, _914736, _914738] : [class_Lattices_Osemilattice__sup(_914734), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914734), _914736), _914738) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914734), _914738), _914736))], (46843 ^ _782476) ^ [_1722868, _1722870, _1722872, _1722874, _1722876, _1722878, _1722880, _1722882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722868), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722870)), _1722872))), c_List_Olist__all2(_1722870, _1722874, _1722876, _1722872, _1722878), hBOOL(hAPP(hAPP(_1722876, _1722880), _1722882)), -(c_List_Olist__all2(_1722870, _1722874, _1722876, hAPP(hAPP(c_List_Olist__update(_1722870, _1722872), _1722868), _1722880), hAPP(hAPP(c_List_Olist__update(_1722874, _1722878), _1722868), _1722882)))], (39166 ^ _782476) ^ [_1537349] : [-(c_Wellfounded_Owf(_1537349, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537349, _1537349), tc_HOL_Obool))))], (41425 ^ _782476) ^ [_1594848, _1594850] : [c_Wellfounded_Oacyclic(_1594848, _1594850), -(c_Wellfounded_Oacyclic(_1594848, hAPP(c_Relation_Oconverse(_1594848, _1594848), _1594850)))], (23085 ^ _782476) ^ [_1215684, _1215686, _1215688] : [class_Groups_Ocomm__monoid__add(_1215684), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215684), _1215686), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1215688))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215684), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215684), _1215686), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1215688))), hAPP(_1215686, hAPP(c_Nat_OSuc, _1215688))))], (42233 ^ _782476) ^ [_1614332, _1614334, _1614336] : [class_Orderings_Olinorder(_1614332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614332), _1614334)), -(c_Big__Operators_Olinorder__class_OMin(_1614332, hAPP(hAPP(c_Set_Oinsert(_1614332), _1614336), _1614334)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614332, _1614332, c_Orderings_Oord__class_Omin(_1614332)), _1614336), _1614334))], (10713 ^ _782476) ^ [_978571, _978573] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978571, tc_HOL_Obool)), _978573) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978571, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_978571, tc_HOL_Obool))), _978573))], (43135 ^ _782476) ^ [_1636680, _1636682, _1636684, _1636686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636680), tc_List_Olist(_1636680))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636680), tc_List_Olist(_1636680)), _1636682), _1636684)), c_List_Olistrel1(_1636680, _1636686))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636680), tc_List_Olist(_1636680))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636680), tc_List_Olist(_1636680)), _1636682), _1636684)), c_List_Olistrel(_1636680, c_Transitive__Closure_Ortrancl(_1636680, _1636686)))))], (45657 ^ _782476) ^ [_1696748, _1696750, _1696752, _1696754, _1696756] : [class_Orderings_Olinorder(_1696748), 45660 ^ _782476 : [(45669 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696750), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696750, _1696748, _1696752), _1696754), _1696756)))), -(hBOOL(hAPP(hAPP(c_member(_1696750), _1696754), hAPP(c_List_Oset(_1696750), _1696756)))), hBOOL(hAPP(c_List_Odistinct(_1696750), _1696756))], (45661 ^ _782476) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1696750), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696750, _1696748, _1696752), _1696754), _1696756))), 45664 ^ _782476 : [(45667 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696750), _1696756)))], (45665 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1696750), _1696754), hAPP(c_List_Oset(_1696750), _1696756)))]]]]], (290 ^ _782476) ^ [_787003, _787005, _787007, _787009] : [-(c_Nitpick_Orefl_H(_787007, _787003)), c_Nitpick_Orefl_H(_787009, _787005), _787009 = _787007, _787005 = _787003], (41140 ^ _782476) ^ [_1588012, _1588014] : [-(c_Transitive__Closure_Ortrancl(_1588012, _1588014) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588012, _1588012), tc_HOL_Obool)), c_Relation_OId(_1588012)), hAPP(hAPP(c_Relation_Orel__comp(_1588012, _1588012, _1588012), c_Transitive__Closure_Ortrancl(_1588012, _1588014)), _1588014)))], (13650 ^ _782476) ^ [_1035424, _1035426] : [class_Lattices_Oab__semigroup__idem__mult(_1035424), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035424), _1035426), _1035426) = _1035426)], (5767 ^ _782476) ^ [_873645, _873647, _873649, _873651] : [c_Hoare__Mirabelle_Ohoare__derivs(_873645, _873647, _873649), c_Hoare__Mirabelle_Ohoare__derivs(_873645, _873651, _873647), -(c_Hoare__Mirabelle_Ohoare__derivs(_873645, _873651, _873649))], (41812 ^ _782476) ^ [_1604354, _1604356, _1604358, _1604360, _1604362, _1604364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604354, _1604354)), hAPP(hAPP(c_Product__Type_OPair(_1604354, _1604354), _1604356), _1604358)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604354, _1604354), tc_HOL_Obool), _1604360), _1604362))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604354, _1604354)), hAPP(hAPP(c_Product__Type_OPair(_1604354, _1604354), _1604358), _1604364)), _1604362)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604354, _1604354)), hAPP(hAPP(c_Product__Type_OPair(_1604354, _1604354), _1604356), _1604364)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604354, _1604354), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604360)), _1604362))))], (37343 ^ _782476) ^ [_1493117, _1493119, _1493121, _1493123] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493117, _1493119), _1493121)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493117, _1493119), _1493123)), -(_1493121 = _1493123)], (29402 ^ _782476) ^ [_1340451, _1340453, _1340455, _1340457] : [class_Rings_Olinordered__semidom(_1340451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340451), hAPP(hAPP(c_Power_Opower__class_Opower(_1340451), _1340453), _1340455)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340451), _1340457), _1340455))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340451), c_Groups_Ozero__class_Ozero(_1340451)), _1340457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340451), _1340453), _1340457)))], (36122 ^ _782476) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50897 ^ _782476) ^ [_1812678, _1812680, _1812682, _1812684] : [c_Relation_Oantisym(_1812678, _1812680), hBOOL(hAPP(hAPP(c_member(tc_prod(_1812678, _1812678)), hAPP(hAPP(c_Product__Type_OPair(_1812678, _1812678), _1812682), _1812684)), _1812680)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1812678, _1812678)), hAPP(hAPP(c_Product__Type_OPair(_1812678, _1812678), _1812684), _1812682)), _1812680)), -(_1812682 = _1812684)], (28972 ^ _782476) ^ [_1332563, _1332565] : [class_Rings_Ocomm__semiring__1(_1332563), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332563), _1332565), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1332563))], (17399 ^ _782476) ^ [_1112525, _1112527, _1112529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112525), _1112527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112527), _1112529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112525), _1112529)))], (19472 ^ _782476) ^ [_1148660, _1148662] : [class_Rings_Olinordered__idom(_1148660), 19475 ^ _782476 : [(19482 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148660), _1148662), c_Groups_Ozero__class_Ozero(_1148660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148660), _1148662), hAPP(c_Groups_Ouminus__class_Ouminus(_1148660), _1148662))))], (19476 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148660), _1148662), hAPP(c_Groups_Ouminus__class_Ouminus(_1148660), _1148662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148660), _1148662), c_Groups_Ozero__class_Ozero(_1148660))))]]], (2618 ^ _782476) ^ [_821047, _821049, _821051, _821053, _821055, _821057, _821059, _821061] : [-(c_Recdef_Osame__fst(_821061, _821057, _821053, _821049) = c_Recdef_Osame__fst(_821059, _821055, _821051, _821047)), _821061 = _821059, _821057 = _821055, _821053 = _821051, _821049 = _821047], (15919 ^ _782476) ^ [_1080384, _1080386, _1080388, _1080390, _1080392] : [class_Groups_Ocomm__monoid__mult(_1080384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080386), _1080388)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080386), _1080390)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1080386, tc_HOL_Obool)), _1080388), _1080390) = c_Orderings_Obot__class_Obot(tc_fun(_1080386, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080384, _1080386, c_Groups_Otimes__class_Otimes(_1080384)), _1080392), c_Groups_Oone__class_Oone(_1080384)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080386, tc_HOL_Obool)), _1080388), _1080390)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080384), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080384, _1080386, c_Groups_Otimes__class_Otimes(_1080384)), _1080392), c_Groups_Oone__class_Oone(_1080384)), _1080388)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080384, _1080386, c_Groups_Otimes__class_Otimes(_1080384)), _1080392), c_Groups_Oone__class_Oone(_1080384)), _1080390)))], (41738 ^ _782476) ^ [_1602513, _1602515, _1602517, _1602519, _1602521] : [c_Relation_Osingle__valued(_1602513, _1602515, hAPP(c_Relation_Oconverse(_1602515, _1602513), _1602517)), -(hAPP(c_Relation_OImage(_1602515, _1602513, _1602517), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602515, tc_HOL_Obool)), _1602519), _1602521)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602513, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1602515, _1602513, _1602517), _1602519)), hAPP(c_Relation_OImage(_1602515, _1602513, _1602517), _1602521)))], (12172 ^ _782476) ^ [_1003826, _1003828] : [class_Complete__Lattice_Ocomplete__lattice(_1003826), c_Orderings_Oorder__class_Omono(_1003826, _1003826, _1003828), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1003826, _1003828) = hAPP(_1003828, c_Inductive_Ocomplete__lattice__class_Ogfp(_1003826, _1003828)))], (22993 ^ _782476) ^ [_1213731] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213731)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1213731))], (8621 ^ _782476) ^ [_932322, _932324, _932326, _932328, _932330] : [class_Lattices_Olattice(_932322), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932324, _932322)), _932326), _932328), _932330) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932322), hAPP(_932326, _932330)), hAPP(_932328, _932330)))], (44933 ^ _782476) ^ [_1680143, _1680145, _1680147, _1680149, _1680151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680143), tc_List_Olist(_1680143))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680143), tc_List_Olist(_1680143)), _1680145), _1680147)), c_List_Olexord(_1680143, _1680149))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680143), tc_List_Olist(_1680143))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680143), tc_List_Olist(_1680143)), hAPP(hAPP(c_List_Oappend(_1680143), _1680151), _1680145)), hAPP(hAPP(c_List_Oappend(_1680143), _1680151), _1680147))), c_List_Olexord(_1680143, _1680149))))], (34242 ^ _782476) ^ [_1431338, _1431340] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431338)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431338)), _1431340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1431338))), _1431340))], (33202 ^ _782476) ^ [_1412117, _1412119, _1412121] : [class_Int_Onumber__ring(_1412117), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412117), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1412119), _1412121)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1412117), hAPP(c_Int_Onumber__class_Onumber__of(_1412117), _1412119)), hAPP(c_Int_Onumber__class_Onumber__of(_1412117), _1412121)))], (38545 ^ _782476) ^ [_1520344, _1520346, _1520348, _1520350, _1520352, _1520354] : [-(hAPP(c_Product__Type_Oapfst(_1520344, _1520346, _1520348, _1520350), hAPP(hAPP(c_Product__Type_OPair(_1520344, _1520348), _1520352), _1520354)) = hAPP(hAPP(c_Product__Type_OPair(_1520346, _1520348), hAPP(_1520350, _1520352)), _1520354))], (44464 ^ _782476) ^ [_1669146, _1669148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669146)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669148))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669146), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669148)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669146)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669146)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669148))))], (39571 ^ _782476) ^ [_1546586, _1546588, _1546590, _1546592] : [39572 ^ _782476 : [(39573 ^ _782476) ^ [_1546640] : [hBOOL(hAPP(hAPP(_1546590, _1546640), _1546592))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1546586, _1546588, _1546590), _1546592)))], (39324 ^ _782476) ^ [_1540205, _1540207, _1540209] : [c_Wellfounded_Owf(_1540205, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540205, _1540205), tc_HOL_Obool)), _1540207), _1540209)), -(c_Wellfounded_Owf(_1540205, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540205, _1540205), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540205, _1540205), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540205, _1540205, _1540205), _1540207), _1540207)), hAPP(hAPP(c_Relation_Orel__comp(_1540205, _1540205, _1540205), _1540209), _1540207))), _1540209)))], (10627 ^ _782476) ^ [_976760, _976762, _976764, _976766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976760, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976760, tc_HOL_Obool)), _976762), _976764)), _976766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976760, tc_HOL_Obool)), _976762), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976760, tc_HOL_Obool)), _976764), _976766))))], (28784 ^ _782476) ^ [_1329306, _1329308, _1329310] : [class_Rings_Odivision__ring(_1329306), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1329306), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329306), _1329308), _1329310)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329306), hAPP(c_Groups_Ouminus__class_Ouminus(_1329306), _1329308)), _1329310))], (46962 ^ _782476) ^ [_1725188, _1725190] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725188)), c_List_Oremdups(_1725188, c_List_Oconcat(_1725188, _1725190))) = hAPP(c_Finite__Set_Ocard(_1725188), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1725188), tc_fun(_1725188, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1725188)), _1725190)), c_List_Oset(_1725188))))], (36006 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (13572 ^ _782476) ^ [_1033688, _1033690, _1033692, _1033694, _1033696] : [c_Fun_Obij__betw(_1033688, _1033690, _1033692, c_Orderings_Otop__class_Otop(tc_fun(_1033688, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1033690, tc_HOL_Obool))), 13575 ^ _782476 : [(13582 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033690, tc_HOL_Obool)), _1033694), hAPP(c_Set_Oimage(_1033688, _1033690, _1033692), _1033696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033688, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033688, _1033690, _1033692), _1033694)), _1033696)))], (13576 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033688, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033688, _1033690, _1033692), _1033694)), _1033696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033690, tc_HOL_Obool)), _1033694), hAPP(c_Set_Oimage(_1033688, _1033690, _1033692), _1033696))))]]], (9855 ^ _782476) ^ [_959731, _959733, _959735, _959737, _959739] : [_959731 = c_Orderings_Obot__class_Obot(tc_fun(_959733, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959735, tc_HOL_Obool)), _959737), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959733, tc_fun(_959735, tc_HOL_Obool)), _959731), _959739)) = _959737)], (10793 ^ _782476) ^ [_980589, _980591, _980593, _980595, _980597] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980589, tc_fun(_980591, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980589), _980593), _980595)), _980597) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980591, tc_HOL_Obool)), hAPP(_980597, _980593)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980589, tc_fun(_980591, tc_HOL_Obool)), _980595), _980597)))], (19692 ^ _782476) ^ [_1152308, _1152310, _1152312] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152308), _1152310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152312), _1152310)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152308), _1152312))], (36613 ^ _782476) ^ [_1478944, _1478946] : [-(c_Divides_Odivmod__int(_1478944, _1478946) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478944), _1478946)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478944, _1478946)))], (18016 ^ _782476) ^ [_1123893, _1123895] : [class_Rings_Ocomm__semiring__1(_1123893), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123893), _1123895), c_Groups_Ozero__class_Ozero(_1123893)) = _1123895)], (29046 ^ _782476) ^ [_1334023, _1334025] : [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), _1334023)), _1334025))), _1334023 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1334025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1822 ^ _782476) ^ [_808451, _808453] : [-(class_Rings_Ozero__neq__one(_808451)), _808453 = _808451, class_Rings_Ozero__neq__one(_808453)], (40528 ^ _782476) ^ [_1572401] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40524 ^ [_1572401]), c_Int_OInteg)))], (4806 ^ _782476) ^ [_855755, _855757, _855759, _855761, _855763, _855765, _855767, _855769] : [-(c_Random__Sequence_ORandom(_855769, _855765, _855761, _855757) = c_Random__Sequence_ORandom(_855767, _855763, _855759, _855755)), _855769 = _855767, _855765 = _855763, _855761 = _855759, _855757 = _855755], (17289 ^ _782476) ^ [] : [-(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)))], (43868 ^ _782476) ^ [_1657137, _1657139, _1657141, _1657143, _1657145] : [-(hAPP(hAPP(c_List_Olist__update(_1657137, hAPP(hAPP(c_List_Olist__update(_1657137, _1657139), _1657141), _1657143)), _1657141), _1657145) = hAPP(hAPP(c_List_Olist__update(_1657137, _1657139), _1657141), _1657145))], (25387 ^ _782476) ^ [_1256673, _1256675, _1256677, _1256679, _1256681] : [class_Groups_Ocomm__monoid__add(_1256673), class_Groups_Ocomm__monoid__mult(_1256673), _1256675 = _1256677, c_Nat__Transfer_Onat__set(_1256677), 25405 ^ _782476 : [(25408 ^ _782476) ^ [] : [hAPP(_1256679, 25404 ^ [_1256673, _1256675, _1256677, _1256679, _1256681]) = hAPP(_1256681, 25404 ^ [_1256673, _1256675, _1256677, _1256679, _1256681])], (25406 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25404 ^ [_1256673, _1256675, _1256677, _1256679, _1256681])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256673), _1256679), _1256675) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256673), _1256681), _1256677))], (10089 ^ _782476) ^ [_964926, _964928, _964930, _964932] : [10090 ^ _782476 : [(10093 ^ _782476) ^ [] : [_964928 = _964932], (10091 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_964926), _964928), _964930))]], -(hBOOL(hAPP(hAPP(c_member(_964926), _964928), hAPP(hAPP(c_Set_Oinsert(_964926), _964932), _964930))))], (23763 ^ _782476) ^ [_1228566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228566)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228566)) = _1228566)], (44963 ^ _782476) ^ [_1680909, _1680911, _1680913, _1680915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680909), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680911)), _1680913))), -(hAPP(hAPP(c_List_Onth(_1680911), hAPP(hAPP(c_List_Oappend(_1680911), _1680913), _1680915)), _1680909) = hAPP(hAPP(c_List_Onth(_1680911), _1680913), _1680909))], (43265 ^ _782476) ^ [_1640603, _1640605, _1640607, _1640609] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640603)), hAPP(hAPP(c_List_Olist_OCons(_1640603), _1640605), _1640607)), c_List_Olists(_1640603, _1640609)))), hBOOL(hAPP(hAPP(c_member(_1640603), _1640605), _1640609)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640603)), _1640607), c_List_Olists(_1640603, _1640609)))], (24034 ^ _782476) ^ [_1233088, _1233090, _1233092, _1233094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1233088), _1233090)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1233092), _1233094)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1233088, _1233092)), c_Sum__Type_OPlus(_1233088, _1233092, _1233090, _1233094))))], (41214 ^ _782476) ^ [_1589842, _1589844, _1589846, _1589848, _1589850] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589842, _1589842)), hAPP(hAPP(c_Product__Type_OPair(_1589842, _1589842), _1589844), _1589846)), c_Transitive__Closure_Ortrancl(_1589842, _1589848))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589842, _1589842)), hAPP(hAPP(c_Product__Type_OPair(_1589842, _1589842), _1589846), _1589850)), c_Transitive__Closure_Otrancl(_1589842, _1589848))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589842, _1589842)), hAPP(hAPP(c_Product__Type_OPair(_1589842, _1589842), _1589844), _1589850)), c_Transitive__Closure_Otrancl(_1589842, _1589848))))], (48701 ^ _782476) ^ [_1762494, _1762496, _1762498] : [-(hBOOL(hAPP(hAPP(c_member(_1762494), _1762496), hAPP(c_List_Oset(_1762494), _1762498)))), -(hAPP(c_List_OremoveAll(_1762494, _1762496), _1762498) = _1762498)], (36509 ^ _782476) ^ [_1475920, _1475922, _1475924, _1475926, _1475928, _1475930] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475920, _1475922), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475924), _1475926))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475920, _1475922), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475928), _1475930))), -(_1475922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1475926 = _1475930)], (25914 ^ _782476) ^ [_1271323, _1271325, _1271327] : [class_Lattices_Odistrib__lattice(_1271323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271323), _1271325)), -(_1271325 = c_Orderings_Obot__class_Obot(tc_fun(_1271323, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271323), _1271327), c_Big__Operators_Olattice__class_OInf__fin(_1271323, _1271325)) = c_Big__Operators_Olattice__class_OInf__fin(_1271323, hAPP(c_Set_OCollect(_1271323), hAPP(hAPP(c_COMBB(tc_fun(_1271323, tc_HOL_Obool), tc_HOL_Obool, _1271323), c_HOL_OEx(_1271323)), hAPP(hAPP(c_COMBC(_1271323, tc_fun(_1271323, tc_HOL_Obool), tc_fun(_1271323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271323, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271323, tc_HOL_Obool), tc_fun(_1271323, tc_HOL_Obool)), _1271323), c_COMBS(_1271323, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271323, tc_HOL_Obool), tc_fun(_1271323, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271323), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271323), c_fconj)), hAPP(hAPP(c_COMBC(_1271323, tc_fun(_1271323, _1271323), tc_fun(_1271323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271323, tc_HOL_Obool), tc_fun(tc_fun(_1271323, _1271323), tc_fun(_1271323, tc_HOL_Obool)), _1271323), c_COMBB(_1271323, tc_HOL_Obool, _1271323)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271323), _1271327))))), hAPP(hAPP(c_COMBC(_1271323, tc_fun(_1271323, tc_HOL_Obool), tc_HOL_Obool), c_member(_1271323)), _1271325))))))], (23049 ^ _782476) ^ [_1214930, _1214932, _1214934] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214930), _1214932)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214930), _1214934)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214930), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214930, tc_HOL_Obool)), _1214932), _1214934))), hAPP(c_Finite__Set_Ocard(_1214930), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214930, tc_HOL_Obool)), _1214932), _1214934))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214930), _1214932)), hAPP(c_Finite__Set_Ocard(_1214930), _1214934)))], (4968 ^ _782476) ^ [_858340, _858342] : [_858342 = _858340, -(c_Set_OBex(_858342) = c_Set_OBex(_858340))], (27961 ^ _782476) ^ [_1311190, _1311192, _1311194] : [class_Orderings_Olinorder(_1311190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311190), _1311192)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311190), _1311194)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311190, tc_HOL_Obool)), _1311192), _1311194) = c_Orderings_Obot__class_Obot(tc_fun(_1311190, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311190), c_Big__Operators_Olinorder__class_OMin(_1311190, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311190, tc_HOL_Obool)), _1311192), _1311194))), c_Big__Operators_Olinorder__class_OMin(_1311190, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311190, tc_HOL_Obool)), _1311192), _1311194))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311190), c_Big__Operators_Olinorder__class_OMin(_1311190, _1311192)), c_Big__Operators_Olinorder__class_OMin(_1311190, _1311194)))], (40631 ^ _782476) ^ [_1575734, _1575736] : [40633 ^ _782476 : [(40636 ^ _782476) ^ [] : [40632 ^ [_1575734, _1575736] = c_Orderings_Obot__class_Obot(tc_fun(_1575734, tc_HOL_Obool))], (40634 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575734, tc_HOL_Obool)), 40632 ^ [_1575734, _1575736]), hAPP(c_Relation_OImage(_1575734, _1575734, _1575736), 40632 ^ [_1575734, _1575736]))))]], -(c_Wellfounded_Owf(_1575734, _1575736))], (41615 ^ _782476) ^ [_1599556, _1599558, _1599560, _1599562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1599556, _1599558), tc_HOL_Obool)), _1599560), _1599562)), c_Relation_Osingle__valued(_1599556, _1599558, _1599562), -(c_Relation_Osingle__valued(_1599556, _1599558, _1599560))], (37810 ^ _782476) ^ [_1502378, _1502380, _1502382, _1502384, _1502386, _1502388] : [hBOOL(hAPP(_1502378, _1502380)), hBOOL(hAPP(_1502382, _1502384)), 37817 ^ _782476 : [(37820 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1502382, hAPP(c_Product__Type_Osnd(_1502386, _1502388), hAPP(hAPP(c_Product__Type_OPair(_1502386, _1502388), _1502380), _1502384)))))], (37818 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1502378, hAPP(c_Product__Type_Ofst(_1502386, _1502388), hAPP(hAPP(c_Product__Type_OPair(_1502386, _1502388), _1502380), _1502384)))))]]], (9484 ^ _782476) ^ [_952472, _952474, _952476] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952472, tc_HOL_Obool)), _952474), _952476) = c_Orderings_Obot__class_Obot(tc_fun(_952472, tc_HOL_Obool)), 9487 ^ _782476 : [(9488 ^ _782476) ^ [_952596] : [hBOOL(hAPP(hAPP(c_member(_952472), _952596), _952474)), 9491 ^ _782476 : [(9492 ^ _782476) ^ [_952686] : [hBOOL(hAPP(hAPP(c_member(_952472), _952686), _952476)), _952596 = _952686]]]]], (9061 ^ _782476) ^ [_941852, _941854, _941856, _941858, _941860, _941862] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941852, tc_fun(_941854, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941856, _941852, _941858), _941860)), _941862) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941856, tc_fun(_941854, tc_HOL_Obool)), _941860), hAPP(hAPP(c_COMBB(_941852, tc_fun(_941854, tc_HOL_Obool), _941856), _941862), _941858)))], (27501 ^ _782476) ^ [_1302774, _1302776, _1302778, _1302780] : [class_Groups_Ocomm__monoid__mult(_1302774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302776), _1302778)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302776, _1302774), _1302780), _1302778) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302774, _1302776, c_Groups_Otimes__class_Otimes(_1302774)), _1302780), c_Groups_Oone__class_Oone(_1302774)), _1302778))], (406 ^ _782476) ^ [_788631, _788633, _788635, _788637, _788639, _788641] : [-(c_Relation_Osingle__valued(_788639, _788635, _788631)), c_Relation_Osingle__valued(_788641, _788637, _788633), _788641 = _788639, _788637 = _788635, _788633 = _788631], (35628 ^ _782476) ^ [_1455518, _1455520, _1455522] : [class_Rings_Olinordered__semidom(_1455518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455518), hAPP(hAPP(c_Power_Opower__class_Opower(_1455518), _1455520), 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(_1455518), _1455522), 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(_1455518), c_Groups_Ozero__class_Ozero(_1455518)), _1455522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455518), _1455520), _1455522)))], (49880 ^ _782476) ^ [_1789977, _1789979, _1789981] : [c_List_Olist_ONil(_1789977) = c_List_Oreplicate(_1789977, _1789979, _1789981), -(_1789979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37802 ^ _782476) ^ [_1502148, _1502150, _1502152, _1502154, _1502156] : [-(c_Product__Type_Oprod_Oprod__size(_1502148, _1502150, _1502152, _1502154, _1502156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1502152, hAPP(c_Product__Type_Ofst(_1502148, _1502150), _1502156))), hAPP(_1502154, hAPP(c_Product__Type_Osnd(_1502148, _1502150), _1502156)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52587 ^ _782476) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (41433 ^ _782476) ^ [_1595031, _1595033, _1595035, _1595037, _1595039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595031, _1595033)), hAPP(hAPP(c_Product__Type_OPair(_1595031, _1595033), _1595035), _1595037)), hAPP(c_Relation_Oconverse(_1595033, _1595031), _1595039))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595033, _1595031)), hAPP(hAPP(c_Product__Type_OPair(_1595033, _1595031), _1595037), _1595035)), _1595039)))], (7503 ^ _782476) ^ [_908277, _908279, _908281] : [class_Groups_Ogroup__add(_908277), 7506 ^ _782476 : [(7513 ^ _782476) ^ [] : [_908281 = hAPP(c_Groups_Ouminus__class_Ouminus(_908277), _908279), -(_908279 = hAPP(c_Groups_Ouminus__class_Ouminus(_908277), _908281))], (7507 ^ _782476) ^ [] : [_908279 = hAPP(c_Groups_Ouminus__class_Ouminus(_908277), _908281), -(_908281 = hAPP(c_Groups_Ouminus__class_Ouminus(_908277), _908279))]]], (52243 ^ _782476) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (30590 ^ _782476) ^ [_1362289, _1362291, _1362293, _1362295] : [class_Fields_Ofield(_1362289), -(_1362291 = c_Groups_Ozero__class_Ozero(_1362289)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362289), _1362293), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362289), _1362295), _1362291)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362289), _1362291), _1362293)), _1362295)), _1362291))], (3912 ^ _782476) ^ [_841216, _841218, _841220, _841222, _841224, _841226, _841228, _841230, _841232, _841234, _841236, _841238, _841240, _841242] : [-(c_New__Random__Sequence_Oneg__decr__bind(_841242, _841238, _841234, _841230, _841226, _841222, _841218) = c_New__Random__Sequence_Oneg__decr__bind(_841240, _841236, _841232, _841228, _841224, _841220, _841216)), _841242 = _841240, _841238 = _841236, _841234 = _841232, _841230 = _841228, _841226 = _841224, _841222 = _841220, _841218 = _841216], (39893 ^ _782476) ^ [_1555823, _1555825, _1555827, _1555829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555823, _1555825)), hAPP(hAPP(c_Product__Type_OSigma(_1555823, _1555825), _1555827), hAPP(c_COMBK(tc_fun(_1555825, tc_HOL_Obool), _1555823), _1555829)))), -(_1555829 = c_Orderings_Obot__class_Obot(tc_fun(_1555825, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555823), _1555827)))], (41084 ^ _782476) ^ [_1586708, _1586710] : [-(c_Transitive__Closure_Ortrancl(_1586708, c_Transitive__Closure_Otrancl(_1586708, _1586710)) = c_Transitive__Closure_Ortrancl(_1586708, _1586710))], (30580 ^ _782476) ^ [_1362111, _1362113, _1362115, _1362117] : [class_Fields_Ofield__inverse__zero(_1362111), -(_1362113 = c_Groups_Ozero__class_Ozero(_1362111)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362111), _1362115), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362111), _1362117), _1362113)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362111), _1362117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362111), _1362115), _1362113))), _1362113))], (34838 ^ _782476) ^ [_1440737, _1440739] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440737, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440739)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440737, 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)))), _1440739)))], (36410 ^ _782476) ^ [_1471072, _1471074, _1471076, _1471078, _1471080, _1471082] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471072, _1471074)), hAPP(hAPP(c_Product__Type_OPair(_1471072, _1471074), _1471080), _1471082)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool)), _1471076), _1471078))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471072, tc_fun(_1471074, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471072, tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_fun(_1471074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471074, tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_fun(_1471074, tc_HOL_Obool)), _1471072), c_COMBC(_1471074, tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471074, tc_prod(_1471072, _1471074)), tc_fun(_1471074, tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), _1471072), hAPP(c_COMBB(tc_prod(_1471072, _1471074), tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool), _1471074), c_member(tc_prod(_1471072, _1471074)))), c_Product__Type_OPair(_1471072, _1471074)))), _1471076)), hAPP(hAPP(c_COMBC(_1471072, tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_fun(_1471074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471074, tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_fun(_1471074, tc_HOL_Obool)), _1471072), c_COMBC(_1471074, tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471074, tc_prod(_1471072, _1471074)), tc_fun(_1471074, tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool)), _1471072), hAPP(c_COMBB(tc_prod(_1471072, _1471074), tc_fun(tc_fun(tc_prod(_1471072, _1471074), tc_HOL_Obool), tc_HOL_Obool), _1471074), c_member(tc_prod(_1471072, _1471074)))), c_Product__Type_OPair(_1471072, _1471074)))), _1471078)), _1471080), _1471082)))], (45575 ^ _782476) ^ [_1694933, _1694935, _1694937] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694933), tc_List_Olist(_1694933))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694933), tc_List_Olist(_1694933)), c_List_Olist_ONil(_1694933)), _1694935)), c_List_Olexord(_1694933, _1694937))), -(_1694935 = hAPP(hAPP(c_List_Olist_OCons(_1694933), 45578 ^ [_1694933, _1694935, _1694937]), 45579 ^ [_1694933, _1694935, _1694937]))], (12992 ^ _782476) ^ [_1020787, _1020789] : [class_Complete__Lattice_Ocomplete__lattice(_1020787), c_Orderings_Oorder__class_Omono(_1020787, _1020787, _1020789), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020787), c_Inductive_Ocomplete__lattice__class_Olfp(_1020787, _1020789)), hAPP(_1020789, c_Inductive_Ocomplete__lattice__class_Olfp(_1020787, _1020789)))))], (32066 ^ _782476) ^ [_1389928, _1389930] : [class_Divides_Osemiring__div(_1389928), -(c_Divides_Odiv__class_Omod(_1389928, _1389930, c_Groups_Oone__class_Oone(_1389928)) = c_Groups_Ozero__class_Ozero(_1389928))], (47210 ^ _782476) ^ [_1731252, _1731254, _1731256, _1731258] : [-(hAPP(c_List_Ofilter(_1731252, _1731254), hAPP(hAPP(c_List_Oappend(_1731252), _1731256), _1731258)) = hAPP(hAPP(c_List_Oappend(_1731252), hAPP(c_List_Ofilter(_1731252, _1731254), _1731256)), hAPP(c_List_Ofilter(_1731252, _1731254), _1731258)))], (33378 ^ _782476) ^ [_1414987, _1414989, _1414991, _1414993] : [class_Int_Onumber__ring(_1414987), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414987), hAPP(c_Int_Onumber__class_Onumber__of(_1414987), _1414989)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414987), hAPP(c_Int_Onumber__class_Onumber__of(_1414987), _1414991)), _1414993)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414987), hAPP(c_Int_Onumber__class_Onumber__of(_1414987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414989), _1414991))), _1414993))], (22590 ^ _782476) ^ [_1206078, _1206080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206078), _1206080)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206080)), _1206078) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206080), _1206078)))], (22467 ^ _782476) ^ [_1203858, _1203860] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203858), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203860), _1203858)))))], (39343 ^ _782476) ^ [_1540827, _1540829] : [39345 ^ _782476 : [(39346 ^ _782476) ^ [_1540852] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540827, _1540827)), hAPP(hAPP(c_Product__Type_OPair(_1540827, _1540827), hAPP(39344 ^ [_1540827, _1540829], hAPP(c_Nat_OSuc, _1540852))), hAPP(39344 ^ [_1540827, _1540829], _1540852))), _1540829)))]], -(c_Wellfounded_Owf(_1540827, _1540829))], (17233 ^ _782476) ^ [_1109939, _1109941, _1109943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109939), _1109941)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109943), _1109941)), _1109939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109941), _1109939)))], (13544 ^ _782476) ^ [_1033188, _1033190, _1033192, _1033194, _1033196] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033188, _1033188, _1033190, _1033192, _1033194), _1033196)), -(hBOOL(hAPP(hAPP(c_member(_1033188), _1033192), _1033194))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1033188, _1033190, hAPP(hAPP(c_Set_Oinsert(_1033188), _1033192), _1033194)), _1033196)))], (38604 ^ _782476) ^ [_1521765, _1521767, _1521769, _1521771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521765), _1521767)), -(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), _1521765), _1521769)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521767), _1521771))), c_FunDef_Opair__less)))], (14234 ^ _782476) ^ [_1047623] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047623)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047623), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047623), c_Orderings_Otop__class_Otop(tc_fun(_1047623, tc_HOL_Obool)))))], (9213 ^ _782476) ^ [_946354, _946356, _946358, _946360] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_946354, tc_HOL_Obool), hAPP(c_Set_Oimage(_946356, tc_fun(_946354, tc_HOL_Obool), _946358), _946360)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946356, tc_fun(_946354, tc_HOL_Obool)), _946360), _946358))], (19648 ^ _782476) ^ [_1151513, _1151515] : [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), _1151513), _1151515))), 19651 ^ _782476 : [(19654 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151515)))], (19652 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151513)))]]], (19777 ^ _782476) ^ [_1153751] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1153751) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1153751))], (8475 ^ _782476) ^ [_929380, _929382, _929384, _929386] : [hBOOL(hAPP(_929380, _929382)), hBOOL(hAPP(_929384, _929382)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929386, tc_HOL_Obool)), _929380), _929384), _929382)))], (25934 ^ _782476) ^ [_1272170, _1272172, _1272174, _1272176] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272170), hAPP(c_Set_OCollect(_1272170), _1272172))), 25937 ^ _782476 : [(25938 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272174), hAPP(c_Set_OCollect(_1272174), hAPP(hAPP(c_COMBB(tc_fun(_1272170, tc_HOL_Obool), tc_HOL_Obool, _1272174), c_HOL_OEx(_1272170)), hAPP(hAPP(c_COMBB(tc_fun(_1272170, tc_HOL_Obool), tc_fun(_1272170, tc_HOL_Obool), _1272174), hAPP(c_COMBS(_1272170, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272170), c_fconj), _1272172))), _1272176))))), 25941 ^ _782476 : [(25942 ^ _782476) ^ [_1272453] : [hBOOL(hAPP(_1272172, _1272453)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272174), hAPP(c_Set_OCollect(_1272174), hAPP(hAPP(c_COMBC(_1272174, _1272170, tc_HOL_Obool), _1272176), _1272453)))))]]], (25948 ^ _782476) ^ [] : [25950 ^ _782476 : [(25953 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272174), hAPP(c_Set_OCollect(_1272174), hAPP(hAPP(c_COMBC(_1272174, _1272170, tc_HOL_Obool), _1272176), 25949 ^ [_1272170, _1272172, _1272174, _1272176]))))], (25951 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1272172, 25949 ^ [_1272170, _1272172, _1272174, _1272176])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272174), hAPP(c_Set_OCollect(_1272174), hAPP(hAPP(c_COMBB(tc_fun(_1272170, tc_HOL_Obool), tc_HOL_Obool, _1272174), c_HOL_OEx(_1272170)), hAPP(hAPP(c_COMBB(tc_fun(_1272170, tc_HOL_Obool), tc_fun(_1272170, tc_HOL_Obool), _1272174), hAPP(c_COMBS(_1272170, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272170), c_fconj), _1272172))), _1272176))))))]]], (10149 ^ _782476) ^ [_966209, _966211, _966213, _966215, _966217] : [class_Groups_Oab__group__add(_966209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966209), _966211), _966213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966209), _966215), _966217), 10156 ^ _782476 : [(10163 ^ _782476) ^ [] : [_966215 = _966217, -(_966211 = _966213)], (10157 ^ _782476) ^ [] : [_966211 = _966213, -(_966215 = _966217)]]], (45813 ^ _782476) ^ [_1699240, _1699242, _1699244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699240), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699242)), _1699244))), -(c_List_Olast(_1699242, hAPP(hAPP(c_List_Odrop(_1699242), _1699240), _1699244)) = c_List_Olast(_1699242, _1699244))], (23739 ^ _782476) ^ [_1228192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228192)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228192)) = _1228192)], (14863 ^ _782476) ^ [_1060059, _1060061, _1060063] : [class_Lattices_Olattice(_1060059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060059), _1060061)), -(_1060061 = c_Orderings_Obot__class_Obot(tc_fun(_1060059, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060059, hAPP(hAPP(c_Set_Oinsert(_1060059), _1060063), _1060061)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060059), _1060063), c_Big__Operators_Olattice__class_OInf__fin(_1060059, _1060061)))], (35104 ^ _782476) ^ [_1446166, _1446168] : [-(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), _1446166)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1446168)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1446166))) = 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), _1446168)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1446166)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37103 ^ _782476) ^ [_1488909, _1488911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488911)), -(c_Divides_OposDivAlg(_1488909, _1488911) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488909), _1488911)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1488909, _1488911)))], (36264 ^ _782476) ^ [_1466818] : [class_Int_Onumber__ring(_1466818), -(hAPP(c_Int_Oring__1__class_Oof__int(_1466818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1466818), c_Int_OMin))], (7056 ^ _782476) ^ [_899004, _899006, _899008, _899010, _899012] : [hBOOL(hAPP(hAPP(c_member(_899004), _899006), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_899008, tc_fun(_899004, tc_HOL_Obool)), _899010), _899012))), 7060 ^ _782476 : [(7063 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899004), _899006), hAPP(_899012, 7059 ^ [_899004, _899006, _899008, _899010, _899012]))))], (7061 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899008), 7059 ^ [_899004, _899006, _899008, _899010, _899012]), _899010)))]]], (38142 ^ _782476) ^ [_1510129, _1510131, _1510133, _1510135, _1510137] : [c_Equiv__Relations_Oequiv(_1510129, _1510131, _1510133), hBOOL(hAPP(hAPP(c_member(_1510129), _1510135), _1510131)), hBOOL(hAPP(hAPP(c_member(_1510129), _1510137), _1510131)), 38153 ^ _782476 : [(38160 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510129, _1510129)), hAPP(hAPP(c_Product__Type_OPair(_1510129, _1510129), _1510135), _1510137)), _1510133)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510129), hAPP(hAPP(c_Set_Oinsert(_1510129), _1510135), c_Orderings_Obot__class_Obot(tc_fun(_1510129, tc_HOL_Obool)))), _1510133) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510129), hAPP(hAPP(c_Set_Oinsert(_1510129), _1510137), c_Orderings_Obot__class_Obot(tc_fun(_1510129, tc_HOL_Obool)))), _1510133))], (38154 ^ _782476) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510129), hAPP(hAPP(c_Set_Oinsert(_1510129), _1510135), c_Orderings_Obot__class_Obot(tc_fun(_1510129, tc_HOL_Obool)))), _1510133) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510129), hAPP(hAPP(c_Set_Oinsert(_1510129), _1510137), c_Orderings_Obot__class_Obot(tc_fun(_1510129, tc_HOL_Obool)))), _1510133), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510129, _1510129)), hAPP(hAPP(c_Product__Type_OPair(_1510129, _1510129), _1510135), _1510137)), _1510133)))]]], (3628 ^ _782476) ^ [_836790, _836792, _836794, _836796, _836798, _836800] : [-(c_Divides_Odiv__class_Omod(_836800, _836796, _836792) = c_Divides_Odiv__class_Omod(_836798, _836794, _836790)), _836800 = _836798, _836796 = _836794, _836792 = _836790], (48194 ^ _782476) ^ [_1751855, _1751857] : [-(_1751855 = c_List_Olist_ONil(_1751857)), -(hAPP(c_List_Ohd(_1751857), hAPP(c_List_Orev(_1751857), _1751855)) = c_List_Olast(_1751857, _1751855))], (7641 ^ _782476) ^ [_910927, _910929, _910931] : [class_Orderings_Olinorder(_910927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910927), _910929), _910931)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910927, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910927), _910929)), c_SetInterval_Oord__class_OatLeastAtMost(_910927, _910929, _910931)) = hAPP(c_SetInterval_Oord__class_OatMost(_910927), _910931))], (49906 ^ _782476) ^ [_1790408, _1790410, _1790412, _1790414] : [hBOOL(hAPP(_1790408, _1790410)), -(hAPP(c_List_Ofilter(_1790412, _1790408), c_List_Oreplicate(_1790412, _1790414, _1790410)) = c_List_Oreplicate(_1790412, _1790414, _1790410))], (52391 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (32026 ^ _782476) ^ [_1389170, _1389172] : [class_Divides_Osemiring__div(_1389170), -(c_Divides_Odiv__class_Omod(_1389170, c_Groups_Ozero__class_Ozero(_1389170), _1389172) = c_Groups_Ozero__class_Ozero(_1389170))], (16853 ^ _782476) ^ [_1100683, _1100685, _1100687] : [class_Groups_Ogroup__add(_1100683), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100683), _1100685), hAPP(c_Groups_Ouminus__class_Ouminus(_1100683), _1100687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100683), _1100685), _1100687))], (13228 ^ _782476) ^ [_1026309, _1026311, _1026313, _1026315, _1026317, _1026319] : [-(hAPP(c_Set_Ovimage(_1026309, _1026311, _1026313), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026315, tc_fun(_1026311, tc_HOL_Obool)), _1026317), _1026319)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026315, tc_fun(_1026309, tc_HOL_Obool)), _1026317), hAPP(hAPP(c_COMBB(tc_fun(_1026311, tc_HOL_Obool), tc_fun(_1026309, tc_HOL_Obool), _1026315), c_Set_Ovimage(_1026309, _1026311, _1026313)), _1026319)))], (23534 ^ _782476) ^ [_1224840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224840)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224840) = 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, _1224840))))], (46018 ^ _782476) ^ [_1703901, _1703903, _1703905, _1703907, _1703909] : [-(hAPP(hAPP(c_List_Otake(_1703901), _1703903), hAPP(hAPP(c_List_Omap(_1703905, _1703901), _1703907), _1703909)) = hAPP(hAPP(c_List_Omap(_1703905, _1703901), _1703907), hAPP(hAPP(c_List_Otake(_1703905), _1703903), _1703909)))], (22580 ^ _782476) ^ [_1205849, _1205851, _1205853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205851), _1205853)), -(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, _1205849)), _1205851)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205849)), _1205853))))], (19594 ^ _782476) ^ [_1150584, _1150586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150586), _1150584)), _1150586)))], (25766 ^ _782476) ^ [_1266239, _1266241, _1266243, _1266245] : [hBOOL(hAPP(hAPP(c_member(_1266239), _1266241), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266239, tc_HOL_Obool), _1266243))), c_Orderings_Oorder__class_Omono(tc_fun(_1266239, tc_HOL_Obool), tc_fun(_1266239, tc_HOL_Obool), _1266243), 25776 ^ _782476 : [(25779 ^ _782476) ^ [] : [hBOOL(hAPP(_1266245, 25775 ^ [_1266239, _1266241, _1266243, _1266245]))], (25777 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266239), 25775 ^ [_1266239, _1266241, _1266243, _1266245]), hAPP(_1266243, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266239, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266239, tc_HOL_Obool), _1266243)), hAPP(c_Set_OCollect(_1266239), _1266245))))))]], -(hBOOL(hAPP(_1266245, _1266241)))], (32962 ^ _782476) ^ [_1407522, _1407524] : [class_Int_Onumber__ring(_1407522), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407522), _1407524) = hAPP(c_Int_Oring__1__class_Oof__int(_1407522), _1407524))], (18000 ^ _782476) ^ [_1123652, _1123654, _1123656] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1123652), 18003 ^ _782476 : [(18010 ^ _782476) ^ [] : [_1123656 = c_Groups_Ozero__class_Ozero(_1123652), -(_1123654 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123652), _1123654), _1123656))], (18004 ^ _782476) ^ [] : [_1123654 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123652), _1123654), _1123656), -(_1123656 = c_Groups_Ozero__class_Ozero(_1123652))]]], (45348 ^ _782476) ^ [_1690074, _1690076, _1690078] : [hBOOL(hAPP(c_List_Odistinct(_1690074), _1690078)), -(hBOOL(hAPP(c_List_Odistinct(_1690074), hAPP(c_List_Orotate(_1690074, _1690076), _1690078))))], (23701 ^ _782476) ^ [_1227600, _1227602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227600)), 23704 ^ _782476 : [(23711 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227602), _1227600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227602)), hAPP(c_Int_Onat, _1227600))))], (23705 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227602)), hAPP(c_Int_Onat, _1227600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227602), _1227600)))]]], (22040 ^ _782476) ^ [_1196980] : [hAPP(c_Nat_OSuc, _1196980) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16985 ^ _782476) ^ [_1104153, _1104155, _1104157, _1104159, _1104161] : [class_Rings_Ocomm__semiring__1(_1104153), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), _1104155), _1104157)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), _1104159), _1104161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), _1104155), _1104159)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104153), _1104157), _1104161)))], (47632 ^ _782476) ^ [_1740781, _1740783, _1740785, _1740787] : [class_Orderings_Olinorder(_1740781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740781), _1740783), _1740785)), c_List_Olinorder__class_Osorted(_1740781, hAPP(hAPP(c_List_Olist_OCons(_1740781), _1740785), _1740787)), -(c_List_Olinorder__class_Osorted(_1740781, hAPP(hAPP(c_List_Olist_OCons(_1740781), _1740783), hAPP(hAPP(c_List_Olist_OCons(_1740781), _1740785), _1740787))))], (32040 ^ _782476) ^ [_1389413, _1389415, _1389417] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389413), _1389415), _1389417) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389413), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389415, _1389417)), _1389417))], (5250 ^ _782476) ^ [_862731, _862733, _862735, _862737] : [-(c_Quotient_ORespects(_862737, _862733) = c_Quotient_ORespects(_862735, _862731)), _862737 = _862735, _862733 = _862731], (20864 ^ _782476) ^ [_1174930] : [-(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), _1174930))))], (10795 ^ _782476) ^ [_980666, _980668, _980670, _980672, _980674] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980666, tc_fun(_980668, tc_HOL_Obool)), _980670), hAPP(hAPP(c_COMBB(tc_fun(_980668, tc_HOL_Obool), tc_fun(_980668, tc_HOL_Obool), _980666), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980668, tc_HOL_Obool)), _980672)), _980674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980668, tc_HOL_Obool)), _980672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980666, tc_fun(_980668, tc_HOL_Obool)), _980670), _980674)))], (50096 ^ _782476) ^ [_1793921, _1793923, _1793925] : [class_Fields_Olinordered__field(_1793921), 50102 ^ _782476 : [(50105 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793921), _1793923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1793921), _1793925), 50101 ^ [_1793921, _1793923, _1793925])))], (50103 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1793921), c_Groups_Ozero__class_Ozero(_1793921)), 50101 ^ [_1793921, _1793923, _1793925])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793921), _1793923), _1793925)))], (50551 ^ _782476) ^ [_1804678, _1804680] : [-(c_Relation_Otrans(_1804678, c_Relation_OId__on(_1804678, _1804680)))], (26770 ^ _782476) ^ [_1287771, _1287773, _1287775, _1287777] : [class_Orderings_Olinorder(_1287771), 26773 ^ _782476 : [(26782 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287771), _1287775), _1287777)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), _1287775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), _1287777))], (26774 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287771), _1287775), _1287777))), 26777 ^ _782476 : [(26780 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), _1287777)))], (26778 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287771), _1287773), _1287775)))]]]]], (36795 ^ _782476) ^ [_1482667, _1482669, _1482671, _1482673, _1482675, _1482677] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482667, tc_fun(_1482669, tc_HOL_Obool))), _1482671), _1482673), _1482675), _1482677)), 36798 ^ _782476 : [(36801 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1482673, _1482675), _1482677)))], (36799 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1482671, _1482675), _1482677)))]]], (35966 ^ _782476) ^ [_1461872, _1461874] : [class_Rings_Oring__1(_1461872), 35969 ^ _782476 : [(35976 ^ _782476) ^ [] : [-(_1461874 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35979 ^ _782476 : [(35986 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461874), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461872), _1461874) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1461872), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1461872, _1461872)), tc_fun(tc_Int_Oint, _1461872)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1461872, _1461872), _1461872), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1461872, _1461872)), tc_fun(tc_Int_Oint, _1461872)), tc_Int_Oint), c_COMBB(tc_fun(_1461872, _1461872), _1461872, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1461872, tc_fun(tc_fun(_1461872, _1461872), _1461872), tc_Int_Oint), c_HOL_OLet(_1461872, _1461872)), c_Int_Oring__1__class_Oof__int(_1461872)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461872, _1461872), tc_fun(_1461872, _1461872)), hAPP(hAPP(c_COMBB(tc_fun(_1461872, tc_fun(_1461872, _1461872)), tc_fun(tc_fun(_1461872, _1461872), tc_fun(_1461872, _1461872)), tc_Int_Oint), c_COMBS(_1461872, _1461872, _1461872)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461872, _1461872), tc_fun(_1461872, tc_fun(_1461872, _1461872))), hAPP(hAPP(c_COMBB(tc_fun(_1461872, tc_fun(_1461872, _1461872)), tc_fun(tc_fun(_1461872, _1461872), tc_fun(_1461872, tc_fun(_1461872, _1461872))), tc_Int_Oint), c_COMBB(_1461872, tc_fun(_1461872, _1461872), _1461872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1461872, tc_fun(_1461872, _1461872)), tc_Int_Oint), c_If(_1461872)), 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(_1461872, _1461872, _1461872), c_Groups_Oplus__class_Oplus(_1461872)), c_COMBI(_1461872))))), hAPP(hAPP(c_COMBC(_1461872, _1461872, _1461872), hAPP(hAPP(c_COMBB(_1461872, tc_fun(_1461872, _1461872), _1461872), c_Groups_Oplus__class_Oplus(_1461872)), hAPP(hAPP(c_COMBS(_1461872, _1461872, _1461872), c_Groups_Oplus__class_Oplus(_1461872)), c_COMBI(_1461872)))), c_Groups_Oone__class_Oone(_1461872))))), c_Divides_Odivmod__int(_1461874, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35980 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461874), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461872), _1461874) = hAPP(c_Groups_Ouminus__class_Ouminus(_1461872), hAPP(c_Int_Oring__1__class_Oof__int(_1461872), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461874))))]]], (35970 ^ _782476) ^ [] : [_1461874 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461872), _1461874) = c_Groups_Ozero__class_Ozero(_1461872))]]], (19712 ^ _782476) ^ [_1152672, _1152674, _1152676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152672), _1152674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152676), _1152672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152676), _1152674))))], (9386 ^ _782476) ^ [_950632, _950634] : [-(hBOOL(hAPP(hAPP(c_member(_950632), 9387 ^ [_950632, _950634]), _950634))), -(_950634 = c_Orderings_Obot__class_Obot(tc_fun(_950632, tc_HOL_Obool)))], (12494 ^ _782476) ^ [_1009912, _1009914, _1009916, _1009918, _1009920] : [_1009912 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009914, tc_HOL_Obool), _1009916), c_Orderings_Oorder__class_Omono(tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool), _1009916), hBOOL(hAPP(hAPP(c_member(_1009914), _1009918), _1009920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009914, tc_HOL_Obool)), _1009920), hAPP(_1009916, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1009914, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009914, tc_HOL_Obool), tc_fun(tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool)), tc_fun(_1009914, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009914, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009914, tc_HOL_Obool), tc_fun(tc_fun(_1009914, tc_HOL_Obool), tc_fun(_1009914, tc_HOL_Obool)), tc_fun(_1009914, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009914, tc_HOL_Obool))), _1009916)), _1009920))), _1009912))))), -(hBOOL(hAPP(hAPP(c_member(_1009914), _1009918), _1009912)))], (5866 ^ _782476) ^ [_875399, _875401, _875403] : [_875399 = _875401, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875403, tc_HOL_Obool)), _875401), _875399)))], (45835 ^ _782476) ^ [_1699639, _1699641, _1699643, _1699645] : [-(hAPP(hAPP(c_List_Oappend(_1699639), _1699641), hAPP(hAPP(c_List_Olist_OCons(_1699639), _1699643), c_List_Olist_ONil(_1699639))) = _1699645), -(_1699645 = c_List_Olist_ONil(_1699639)), c_List_Obutlast(_1699639, _1699645) = _1699641, c_List_Olast(_1699639, _1699645) = _1699643], (51386 ^ _782476) ^ [_1822156, _1822158, _1822160, _1822162, _1822164] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1822156, _1822158, tc_HOL_Obool, _1822160), _1822162), _1822164)), -(hBOOL(hAPP(_1822160, hAPP(hAPP(c_Product__Type_OPair(_1822156, _1822158), _1822162), _1822164))))], (43741 ^ _782476) ^ [_1654360, _1654362] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1654360, _1654362) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654360), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1654362)))], (47505 ^ _782476) ^ [_1738473, _1738475, _1738477, _1738479, _1738481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738473), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1738475), _1738477))), -(hAPP(hAPP(c_List_Onth(_1738479), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738479), _1738481), c_List_Oupt(_1738477, _1738475))), _1738473) = hAPP(_1738481, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1738477), _1738473)))], (29724 ^ _782476) ^ [_1346472, _1346474, _1346476, _1346478] : [class_Fields_Olinordered__field__inverse__zero(_1346472), 29727 ^ _782476 : [(29728 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346472), _1346474), _1346476)), _1346478)), 29731 ^ _782476 : [(29738 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346476))), 29741 ^ _782476 : [(29748 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), _1346476), c_Groups_Ozero__class_Ozero(_1346472)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346478)))], (29742 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), _1346476), c_Groups_Ozero__class_Ozero(_1346472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346472), _1346478), _1346476)), _1346474)))]]], (29732 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), _1346474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346472), _1346478), _1346476))))]]], (29754 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346472), _1346474), _1346476)), _1346478))), 29757 ^ _782476 : [(29760 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), _1346474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346472), _1346478), _1346476)))], (29758 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346476)))]], 29761 ^ _782476 : [(29764 ^ _782476) ^ [] : [29765 ^ _782476 : [(29768 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346472), _1346478), _1346476)), _1346474))], (29766 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), _1346476), c_Groups_Ozero__class_Ozero(_1346472))))]], 29769 ^ _782476 : [(29772 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346478))], (29770 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), _1346476), c_Groups_Ozero__class_Ozero(_1346472)))]]], (29762 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346472), c_Groups_Ozero__class_Ozero(_1346472)), _1346476))]]]]], (22618 ^ _782476) ^ [_1206644, _1206646] : [hAPP(_1206644, 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), _1206644), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206646)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1206644), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1206646)))], (25837 ^ _782476) ^ [_1267888] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1267888) = 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), _1267888), c_Int_Onat)))))], (44658 ^ _782476) ^ [_1674111, _1674113, _1674115, _1674117] : [-(hAPP(hAPP(c_List_Oappend(_1674111), hAPP(hAPP(c_List_Olist_OCons(_1674111), _1674113), _1674115)), _1674117) = hAPP(hAPP(c_List_Olist_OCons(_1674111), _1674113), hAPP(hAPP(c_List_Oappend(_1674111), _1674115), _1674117)))], (12192 ^ _782476) ^ [_1004136, _1004138, _1004140] : [class_Orderings_Oorder(_1004136), 12195 ^ _782476 : [(12202 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004136), _1004138), _1004140))), -(c_Orderings_Obot__class_Obot(tc_fun(_1004136, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004136, _1004138), _1004140))], (12196 ^ _782476) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004136, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004136, _1004138), _1004140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004136), _1004138), _1004140))]]], (16721 ^ _782476) ^ [_1097743, _1097745, _1097747] : [class_Groups_Oab__group__add(_1097743), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097743), _1097745), _1097747)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097743), hAPP(c_Groups_Ouminus__class_Ouminus(_1097743), _1097745)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097743), _1097747)))], (26792 ^ _782476) ^ [_1288151, _1288153, _1288155, _1288157] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288151), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288151), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288151), _1288153), _1288155)), _1288157) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288151), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288151), _1288153), _1288157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288151), _1288155), _1288157)))], (20745 ^ _782476) ^ [_1172435, _1172437] : [20747 ^ _782476 : [(20750 ^ _782476) ^ [] : [hBOOL(hAPP(_1172437, 20746 ^ [_1172435, _1172437]))], (20748 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20746 ^ [_1172435, _1172437]), _1172435)))]], 20751 ^ _782476 : [(20752 ^ _782476) ^ [_1172586] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172435))), -(hBOOL(hAPP(_1172437, _1172586)))]]], (35510 ^ _782476) ^ [_1453453, _1453455] : [class_Rings_Ocomm__semiring__1(_1453453), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453453), _1453455), _1453455) = hAPP(hAPP(c_Power_Opower__class_Opower(_1453453), _1453455), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (11300 ^ _782476) ^ [_989697, _989699, _989701, _989703, _989705, _989707] : [_989697 = _989699, -(hAPP(c_Fun_Ofun__upd(_989701, _989703, _989705, _989699, _989707), _989697) = _989707)], (6997 ^ _782476) ^ [_897357, _897359] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_897357, tc_HOL_Obool), _897359) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897357, tc_HOL_Obool), tc_fun(_897357, tc_HOL_Obool)), _897359), c_COMBI(tc_fun(_897357, tc_HOL_Obool))))], (48850 ^ _782476) ^ [_1766486, _1766488, _1766490, _1766492, _1766494] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766486)), _1766488) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766490)), _1766492), 48856 ^ _782476 : [(48859 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1766494, hAPP(hAPP(c_List_Onth(_1766486), _1766488), 48855 ^ [_1766486, _1766488, _1766490, _1766492, _1766494])), hAPP(hAPP(c_List_Onth(_1766490), _1766492), 48855 ^ [_1766486, _1766488, _1766490, _1766492, _1766494])))], (48857 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48855 ^ [_1766486, _1766488, _1766490, _1766492, _1766494]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766486)), _1766488))))]], -(c_List_Olist__all2(_1766486, _1766490, _1766494, _1766488, _1766492))], (30929 ^ _782476) ^ [_1368625, _1368627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368625)), 30932 ^ _782476 : [(30939 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368627), 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), _1368627), _1368625)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30933 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368627), _1368625)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368627), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (3482 ^ _782476) ^ [_834501, _834503, _834505, _834507] : [-(c_Random_Oselect__weight(_834507, _834503) = c_Random_Oselect__weight(_834505, _834501)), _834507 = _834505, _834503 = _834501], (51875 ^ _782476) ^ [_1833195, _1833197, _1833199] : [class_Rings_Ocomm__semiring__1(_1833195), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833195), _1833197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833195), _1833197), _1833199))))], (33900 ^ _782476) ^ [_1425303, _1425305] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425303))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425305)) = 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), _1425305)))], (3238 ^ _782476) ^ [_830649, _830651, _830653, _830655, _830657, _830659] : [-(c_Big__Operators_Olattice_OInf__fin(_830659, _830655, _830651) = c_Big__Operators_Olattice_OInf__fin(_830657, _830653, _830649)), _830659 = _830657, _830655 = _830653, _830651 = _830649], (51027 ^ _782476) ^ [_1815308, _1815310] : [c_Relation_Osym(_1815308, hAPP(c_Relation_Oconverse(_1815308, _1815308), _1815310)), -(c_Relation_Osym(_1815308, _1815310))], (39796 ^ _782476) ^ [_1553204, _1553206, _1553208, _1553210, _1553212] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553204, _1553206), _1553208), hAPP(hAPP(c_COMBS(_1553204, tc_fun(_1553206, tc_HOL_Obool), tc_fun(_1553206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553206, tc_HOL_Obool), tc_fun(tc_fun(_1553206, tc_HOL_Obool), tc_fun(_1553206, tc_HOL_Obool)), _1553204), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553206, tc_HOL_Obool))), _1553210)), _1553212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553204, _1553206), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553204, _1553206), _1553208), _1553210)), hAPP(hAPP(c_Product__Type_OSigma(_1553204, _1553206), _1553208), _1553212)))], (464 ^ _782476) ^ [_789522, _789524, _789526, _789528, _789530, _789532] : [-(c_Finite__Set_Ofolding__one(_789530, _789526, _789522)), c_Finite__Set_Ofolding__one(_789532, _789528, _789524), _789532 = _789530, _789528 = _789526, _789524 = _789522], (17752 ^ _782476) ^ [_1119046, _1119048, _1119050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119048), _1119050)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119046), _1119048)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119046), _1119050)))], (30528 ^ _782476) ^ [_1361158, _1361160, _1361162, _1361164] : [class_Fields_Olinordered__field__inverse__zero(_1361158), 30531 ^ _782476 : [(30532 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361160), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361158), _1361162), _1361164))), 30535 ^ _782476 : [(30542 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), c_Groups_Ozero__class_Ozero(_1361158)), _1361164))), 30545 ^ _782476 : [(30552 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361164), c_Groups_Ozero__class_Ozero(_1361158)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361160), c_Groups_Ozero__class_Ozero(_1361158))))], (30546 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361164), c_Groups_Ozero__class_Ozero(_1361158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361158), _1361160), _1361164))))]]], (30536 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), c_Groups_Ozero__class_Ozero(_1361158)), _1361164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361158), _1361160), _1361164)), _1361162)))]]], (30558 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361160), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361158), _1361162), _1361164)))), 30561 ^ _782476 : [(30564 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361158), _1361160), _1361164)), _1361162))], (30562 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), c_Groups_Ozero__class_Ozero(_1361158)), _1361164)))]], 30565 ^ _782476 : [(30568 ^ _782476) ^ [] : [30569 ^ _782476 : [(30572 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361158), _1361160), _1361164)))], (30570 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361164), c_Groups_Ozero__class_Ozero(_1361158))))]], 30573 ^ _782476 : [(30576 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361160), c_Groups_Ozero__class_Ozero(_1361158)))], (30574 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), _1361164), c_Groups_Ozero__class_Ozero(_1361158)))]]], (30566 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361158), c_Groups_Ozero__class_Ozero(_1361158)), _1361164))]]]]], (8609 ^ _782476) ^ [_932104, _932106, _932108] : [class_Lattices_Olattice(_932104), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932104), _932106), _932108) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932104), _932108), _932106))], (38210 ^ _782476) ^ [_1511780, _1511782, _1511784] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511780, tc_HOL_Obool), tc_fun(_1511780, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511780, tc_HOL_Obool), tc_fun(_1511780, tc_HOL_Obool)), _1511782), _1511784)), c_Wellfounded_Ofinite__psubset(_1511780)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511780, tc_HOL_Obool)), _1511782), _1511784)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511780), _1511784))], (46702 ^ _782476) ^ [_1719859, _1719861, _1719863, _1719865, _1719867, _1719869, _1719871] : [c_List_Olist__all2(_1719859, _1719861, _1719863, _1719865, _1719867), c_List_Olist__all2(_1719859, _1719861, _1719863, _1719869, _1719871), -(c_List_Olist__all2(_1719859, _1719861, _1719863, hAPP(hAPP(c_List_Oappend(_1719859), _1719865), _1719869), hAPP(hAPP(c_List_Oappend(_1719861), _1719867), _1719871)))], (34698 ^ _782476) ^ [_1438412, _1438414] : [class_Int_Onumber__ring(_1438412), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438412), c_Int_Opred(_1438414)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438412), hAPP(c_Groups_Ouminus__class_Ouminus(_1438412), c_Groups_Oone__class_Oone(_1438412))), hAPP(c_Int_Onumber__class_Onumber__of(_1438412), _1438414)))], (22500 ^ _782476) ^ [_1204478, _1204480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204478), _1204480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204478), hAPP(c_Nat_OSuc, _1204480))))], (44857 ^ _782476) ^ [_1678306, _1678308, _1678310] : [_1678310 = c_List_Olist_ONil(_1678306), -(hAPP(hAPP(c_List_Oappend(_1678306), _1678308), _1678310) = _1678308)], (11306 ^ _782476) ^ [_989794, _989796, _989798, _989800, _989802, _989804] : [-(_989794 = _989796), -(hAPP(c_Fun_Ofun__upd(_989798, _989800, _989802, _989796, _989804), _989794) = hAPP(_989802, _989794))], (40580 ^ _782476) ^ [_1574023, _1574025] : [class_Complete__Lattice_Ocomplete__lattice(_1574023), -(c_Complete__Lattice_OInf__class_OInf(_1574023, _1574025) = c_Complete__Lattice_OSup__class_OSup(_1574023, hAPP(c_Set_OCollect(_1574023), hAPP(hAPP(c_COMBB(tc_fun(_1574023, tc_HOL_Obool), tc_HOL_Obool, _1574023), c_HOL_OAll(_1574023)), hAPP(hAPP(c_COMBB(tc_fun(_1574023, tc_HOL_Obool), tc_fun(_1574023, tc_HOL_Obool), _1574023), hAPP(c_COMBS(_1574023, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574023), c_fimplies), hAPP(hAPP(c_COMBC(_1574023, tc_fun(_1574023, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574023)), _1574025)))), c_Orderings_Oord__class_Oless__eq(_1574023))))))], (48786 ^ _782476) ^ [_1764451, _1764453] : [-(c_Wellfounded_Owf(_1764451, c_List_Omeasures(_1764451, _1764453)))], (14292 ^ _782476) ^ [_1048701, _1048703, _1048705] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048701, tc_HOL_Obool)), _1048703), _1048705))), 14295 ^ _782476 : [(14298 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048701), _1048705)))], (14296 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048701), _1048703)))]]], (35566 ^ _782476) ^ [] : [-(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))))], (33390 ^ _782476) ^ [_1415301, _1415303, _1415305] : [class_Int_Onumber__ring(_1415301), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1415301), hAPP(c_Int_Onumber__class_Onumber__of(_1415301), _1415303)), hAPP(c_Int_Onumber__class_Onumber__of(_1415301), _1415305)) = hAPP(c_Int_Onumber__class_Onumber__of(_1415301), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415303), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415305))))], (21041 ^ _782476) ^ [_1177871, _1177873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177871), _1177873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177871), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177873)))], (14188 ^ _782476) ^ [_1046762, _1046764] : [class_Finite__Set_Ofinite(_1046762), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046762), _1046764)))], (49952 ^ _782476) ^ [_1791182, _1791184, _1791186, _1791188] : [49959 ^ _782476 : [(49962 ^ _782476) ^ [] : [_1791184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49960 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1791188, _1791186)))]], 49953 ^ _782476 : [(49954 ^ _782476) ^ [_1791254] : [hBOOL(hAPP(hAPP(c_member(_1791182), _1791254), hAPP(c_List_Oset(_1791182), c_List_Oreplicate(_1791182, _1791184, _1791186)))), hBOOL(hAPP(_1791188, _1791254))]]], (22868 ^ _782476) ^ [_1211377, _1211379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211379)), -(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), _1211379), _1211377))))], (47056 ^ _782476) ^ [_1727117, _1727119, _1727121, _1727123, _1727125] : [class_Orderings_Olinorder(_1727117), -(c_List_Olinorder__class_Osort__key(_1727119, _1727117, _1727121, hAPP(hAPP(c_List_Olist_OCons(_1727119), _1727123), _1727125)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727119, _1727117, _1727121), _1727123), c_List_Olinorder__class_Osort__key(_1727119, _1727117, _1727121, _1727125)))], (7075 ^ _782476) ^ [_899461, _899463, _899465] : [class_Complete__Lattice_Ocomplete__lattice(_899461), hBOOL(hAPP(hAPP(c_member(_899461), _899463), _899465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899461), _899463), c_Complete__Lattice_OSup__class_OSup(_899461, _899465))))], (47902 ^ _782476) ^ [_1745667, _1745669] : [class_Orderings_Olinorder(_1745667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745667), _1745669)), 47909 ^ _782476 : [(47914 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1745667), c_List_Olinorder__class_Osorted__list__of__set(_1745667, _1745669))))], (47912 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745667, c_List_Olinorder__class_Osorted__list__of__set(_1745667, _1745669)))], (47910 ^ _782476) ^ [] : [-(hAPP(c_List_Oset(_1745667), c_List_Olinorder__class_Osorted__list__of__set(_1745667, _1745669)) = _1745669)]]], (40305 ^ _782476) ^ [_1567433, _1567435, _1567437, _1567439, _1567441] : [c_Relation_Orefl__on(_1567433, _1567435, _1567437), c_Relation_Orefl__on(_1567433, _1567439, _1567441), -(c_Relation_Orefl__on(_1567433, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567433, tc_HOL_Obool)), _1567435), _1567439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567433, _1567433), tc_HOL_Obool)), _1567437), _1567441)))], (32799 ^ _782476) ^ [_1404123, _1404125, _1404127, _1404129] : [-(hAPP(c_Relation_OImage(_1404123, _1404125, _1404127), _1404129) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404123, tc_fun(_1404125, tc_HOL_Obool)), _1404129), hAPP(hAPP(c_COMBB(tc_fun(_1404123, tc_HOL_Obool), tc_fun(_1404125, tc_HOL_Obool), _1404123), c_Relation_OImage(_1404123, _1404125, _1404127)), hAPP(hAPP(c_COMBC(_1404123, tc_fun(_1404123, tc_HOL_Obool), tc_fun(_1404123, tc_HOL_Obool)), c_Set_Oinsert(_1404123)), c_Orderings_Obot__class_Obot(tc_fun(_1404123, tc_HOL_Obool))))))], (51552 ^ _782476) ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946] : [51555 ^ _782476 : [(51562 ^ _782476) ^ [] : [hAPP(hAPP(_1826944, 51553 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946]), 51557 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946]) = hAPP(hAPP(_1826944, 51554 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946]), 51558 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946])], (51560 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826940, _1826940)), hAPP(hAPP(c_Product__Type_OPair(_1826940, _1826940), 51557 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946]), 51558 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946])), _1826942)))], (51556 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826936, _1826936)), hAPP(hAPP(c_Product__Type_OPair(_1826936, _1826936), 51553 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946]), 51554 ^ [_1826936, _1826938, _1826940, _1826942, _1826944, _1826946])), _1826938)))]], -(c_Equiv__Relations_Ocongruent2(_1826936, _1826940, _1826946, _1826938, _1826942, _1826944))], (36928 ^ _782476) ^ [_1485646, _1485648, _1485650, _1485652, _1485654] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485646, _1485648, tc_HOL_Obool), _1485650), hAPP(hAPP(c_Product__Type_OPair(_1485646, _1485648), _1485652), _1485654))), -(hBOOL(hAPP(hAPP(_1485650, _1485652), _1485654)))], (21784 ^ _782476) ^ [_1191412, _1191414, _1191416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191412)), 21787 ^ _782476 : [(21788 ^ _782476) ^ [_1191546] : [21790 ^ _782476 : [(21796 ^ _782476) ^ [] : [-(_1191546 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21792 ^ [_1191412, _1191414, _1191416, _1191546]), 21789 ^ [_1191412, _1191414, _1191416, _1191546]))], (21794 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21792 ^ [_1191412, _1191414, _1191416, _1191546]), _1191414)))], (21791 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21789 ^ [_1191412, _1191414, _1191416, _1191546]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191412))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191416), _1191546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191546), _1191412))))]]], (44851 ^ _782476) ^ [_1678211, _1678213, _1678215] : [hAPP(hAPP(c_List_Oappend(_1678211), _1678213), _1678215) = _1678213, -(_1678215 = c_List_Olist_ONil(_1678211))], (34664 ^ _782476) ^ [_1437828] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1437828))) = 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)))), _1437828))], (12240 ^ _782476) ^ [_1004854, _1004856, _1004858] : [class_Orderings_Oorder(_1004854), 12243 ^ _782476 : [(12250 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004854), _1004856), _1004858))), -(c_Orderings_Obot__class_Obot(tc_fun(_1004854, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1004854, _1004856, _1004858))], (12244 ^ _782476) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004854, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1004854, _1004856, _1004858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004854), _1004856), _1004858))]]], (41298 ^ _782476) ^ [_1591849, _1591851, _1591853, _1591855] : [-(hBOOL(hAPP(hAPP(c_member(_1591849), _1591851), hAPP(c_Relation_ODomain(_1591849, _1591849), _1591853)))), 41301 ^ _782476 : [(41308 ^ _782476) ^ [] : [_1591851 = _1591855, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591849, _1591849)), hAPP(hAPP(c_Product__Type_OPair(_1591849, _1591849), _1591851), _1591855)), c_Transitive__Closure_Ortrancl(_1591849, _1591853))))], (41302 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591849, _1591849)), hAPP(hAPP(c_Product__Type_OPair(_1591849, _1591849), _1591851), _1591855)), c_Transitive__Closure_Ortrancl(_1591849, _1591853))), -(_1591851 = _1591855)]]], (41202 ^ _782476) ^ [_1589602, _1589604, _1589606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589602, _1589602)), hAPP(hAPP(c_Product__Type_OPair(_1589602, _1589602), _1589604), _1589606)), c_Relation_OId(_1589602))), -(_1589604 = _1589606)], (34808 ^ _782476) ^ [_1440281, _1440283, _1440285] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440281), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440283)), _1440285)) = 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), _1440281), _1440283))), _1440285))], (8192 ^ _782476) ^ [_922737, _922739, _922741, _922743, _922745] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922737, tc_fun(_922739, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922737, tc_HOL_Obool)), _922741), _922743)), _922745) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922739, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922737, tc_fun(_922739, tc_HOL_Obool)), _922741), _922745)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922737, tc_fun(_922739, tc_HOL_Obool)), _922743), _922745)))], (9081 ^ _782476) ^ [_942643, _942645, _942647, _942649, _942651] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942643, tc_HOL_Obool)), _942645), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942647, tc_fun(_942643, tc_HOL_Obool)), _942649), _942651)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942647, tc_fun(_942643, tc_HOL_Obool)), _942649), hAPP(hAPP(c_COMBB(tc_fun(_942643, tc_HOL_Obool), tc_fun(_942643, tc_HOL_Obool), _942647), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942643, tc_HOL_Obool)), _942645)), _942651)))], (16483 ^ _782476) ^ [_1092842, _1092844, _1092846, _1092848] : [class_Groups_Oab__semigroup__add(_1092842), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092842), _1092844), _1092846)), _1092848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092842), _1092844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092842), _1092846), _1092848)))], (50022 ^ _782476) ^ [_1792437, _1792439, _1792441] : [-(c_List_Oreplicate(_1792437, hAPP(c_Nat_OSuc, _1792439), _1792441) = hAPP(hAPP(c_List_Olist_OCons(_1792437), _1792441), c_List_Oreplicate(_1792437, _1792439, _1792441)))], (36102 ^ _782476) ^ [_1464431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464431), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464431)), c_Int_OMin)))], (39464 ^ _782476) ^ [_1543715, _1543717, _1543719] : [c_Wellfounded_Owf(_1543715, _1543717), -(c_Wellfounded_Owf(tc_List_Olist(_1543715), hAPP(c_List_Olexn(_1543715, _1543717), _1543719)))], (22250 ^ _782476) ^ [_1200353, _1200355, _1200357] : [_1200355 = _1200357, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200353)), _1200355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200353)), _1200357))], (32249 ^ _782476) ^ [_1393248, _1393250] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393248), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393250), _1393248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393250), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393250, _1393248)))], (48721 ^ _782476) ^ [_1762817, _1762819] : [-(c_List_Oinsert(_1762817, _1762819, c_List_Olist_ONil(_1762817)) = hAPP(hAPP(c_List_Olist_OCons(_1762817), _1762819), c_List_Olist_ONil(_1762817)))], (17764 ^ _782476) ^ [_1119255, _1119257] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119255), _1119257)), _1119255 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119257 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (50424 ^ _782476) ^ [_1801562, _1801564, _1801566, _1801568] : [-(hAPP(c_Relation_OImage(_1801562, _1801564, hAPP(c_Set_OCollect(tc_prod(_1801562, _1801564)), hAPP(c_Product__Type_Oprod_Oprod__case(_1801562, _1801564, tc_HOL_Obool), _1801566))), _1801568) = hAPP(c_Set_OCollect(_1801564), hAPP(hAPP(c_COMBB(tc_fun(_1801562, tc_HOL_Obool), tc_HOL_Obool, _1801564), c_HOL_OEx(_1801562)), hAPP(hAPP(c_COMBB(tc_fun(_1801562, tc_HOL_Obool), tc_fun(_1801562, tc_HOL_Obool), _1801564), hAPP(c_COMBS(_1801562, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801562), c_fconj), hAPP(hAPP(c_COMBC(_1801562, tc_fun(_1801562, tc_HOL_Obool), tc_HOL_Obool), c_member(_1801562)), _1801568)))), hAPP(c_COMBC(_1801562, _1801564, tc_HOL_Obool), _1801566)))))], (16013 ^ _782476) ^ [_1082530, _1082532] : [class_Groups_Ocomm__monoid__mult(_1082530), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082530), c_Groups_Oone__class_Oone(_1082530)), _1082532) = _1082532)], (13858 ^ _782476) ^ [_1039652, _1039654, _1039656, _1039658] : [c_Fun_Obij__betw(_1039652, _1039654, _1039656, _1039658, c_Orderings_Otop__class_Otop(tc_fun(_1039654, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039652, _1039654, _1039656), c_Orderings_Otop__class_Otop(tc_fun(_1039652, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039654, tc_HOL_Obool)))], (47916 ^ _782476) ^ [_1745888, _1745890, _1745892] : [class_Orderings_Olinorder(_1745888), hBOOL(hAPP(hAPP(c_member(_1745888), _1745890), hAPP(c_List_Oset(_1745888), _1745892))), c_List_Olinorder__class_Osorted(_1745888, _1745892), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1745888, _1745888, c_COMBI(_1745888)), _1745890), c_List_Oremove1(_1745888, _1745890, _1745892)) = _1745892)], (8748 ^ _782476) ^ [_934978, _934980, _934982] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934978, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934978, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_934978, tc_HOL_Obool), tc_HOL_Obool)), _934980), _934982))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934978, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934978, tc_HOL_Obool), _934980)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934978, tc_HOL_Obool), _934982)))))], (38780 ^ _782476) ^ [_1525527, _1525529, _1525531, _1525533] : [c_Wellfounded_Omax__extp(_1525527, hAPP(hAPP(c_COMBC(_1525527, tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_fun(_1525527, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525527, tc_fun(tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_fun(_1525527, tc_HOL_Obool)), _1525527), c_COMBC(_1525527, tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525527, tc_prod(_1525527, _1525527)), tc_fun(_1525527, tc_fun(tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_HOL_Obool)), _1525527), hAPP(c_COMBB(tc_prod(_1525527, _1525527), tc_fun(tc_fun(tc_prod(_1525527, _1525527), tc_HOL_Obool), tc_HOL_Obool), _1525527), c_member(tc_prod(_1525527, _1525527)))), c_Product__Type_OPair(_1525527, _1525527)))), _1525529), _1525531, _1525533), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525527, tc_HOL_Obool), tc_fun(_1525527, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525527, tc_HOL_Obool), tc_fun(_1525527, tc_HOL_Obool)), _1525531), _1525533)), c_Wellfounded_Omax__ext(_1525527, _1525529))))], (46876 ^ _782476) ^ [_1723657, _1723659] : [-(hBOOL(hAPP(c_List_Odistinct(_1723657), c_List_Oremdups(_1723657, _1723659))))], (39208 ^ _782476) ^ [_1538028, _1538030] : [c_Wellfounded_Owf(_1538028, _1538030), -(c_Wellfounded_Owf(tc_fun(_1538028, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1538028, _1538030)))], (25552 ^ _782476) ^ [_1259880, _1259882, _1259884] : [hBOOL(hAPP(hAPP(c_member(_1259880), _1259882), hAPP(c_Set_OCollect(_1259880), _1259884))), -(hBOOL(hAPP(_1259884, _1259882)))], (2754 ^ _782476) ^ [_823179, _823181, _823183, _823185, _823187, _823189] : [-(c_Predicate_ORangeP(_823189, _823185, _823181) = c_Predicate_ORangeP(_823187, _823183, _823179)), _823189 = _823187, _823185 = _823183, _823181 = _823179], (21541 ^ _782476) ^ [_1186742, _1186744, _1186746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186742)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186744), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1186746)), 21548 ^ _782476 : [(21549 ^ _782476) ^ [_1186950] : [21551 ^ _782476 : [(21557 ^ _782476) ^ [] : [-(_1186950 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21553 ^ [_1186742, _1186744, _1186746, _1186950]), 21550 ^ [_1186742, _1186744, _1186746, _1186950]))], (21555 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21553 ^ [_1186742, _1186744, _1186746, _1186950]), _1186746)))], (21552 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21550 ^ [_1186742, _1186744, _1186746, _1186950]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186742))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186950), _1186744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186950), _1186742)), _1186744)))]]], (50656 ^ _782476) ^ [_1806959, _1806961, _1806963, _1806965] : [class_Complete__Lattice_Ocomplete__lattice(_1806959), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1806961, _1806959), _1806963), _1806965) = c_Complete__Lattice_OSup__class_OSup(_1806959, hAPP(c_Set_OCollect(_1806959), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool), tc_HOL_Obool, _1806959), c_HOL_OEx(tc_fun(_1806961, _1806959))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool), tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool), _1806959), hAPP(c_COMBS(tc_fun(_1806961, _1806959), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1806961, _1806959)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1806961, _1806959), tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1806961, _1806959))), _1806963)))), hAPP(hAPP(c_COMBC(_1806959, tc_fun(tc_fun(_1806961, _1806959), _1806959), tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806959, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1806961, _1806959), _1806959), tc_fun(tc_fun(_1806961, _1806959), tc_HOL_Obool)), _1806959), c_COMBB(_1806959, tc_HOL_Obool, tc_fun(_1806961, _1806959))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1806961, _1806959), _1806961, _1806959), c_COMBI(tc_fun(_1806961, _1806959))), _1806965)))))))], (23655 ^ _782476) ^ [_1226820, _1226822] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1226820), _1226822) = 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)), _1226820)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1226822))))], (45805 ^ _782476) ^ [_1699139, _1699141] : [-(_1699139 = c_List_Olist_ONil(_1699141)), -(hBOOL(hAPP(hAPP(c_member(_1699141), c_List_Olast(_1699141, _1699139)), hAPP(c_List_Oset(_1699141), _1699139))))], (52289 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (48306 ^ _782476) ^ [_1754258, _1754260, _1754262, _1754264] : [hBOOL(hAPP(hAPP(c_member(_1754258), _1754260), hAPP(c_List_Oset(_1754258), c_List_OtakeWhile(_1754258, _1754262, _1754264)))), 48309 ^ _782476 : [(48312 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1754262, _1754260)))], (48310 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754258), _1754260), hAPP(c_List_Oset(_1754258), _1754264))))]]], (26202 ^ _782476) ^ [_1277590, _1277592, _1277594] : [class_Orderings_Olinorder(_1277590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277590), _1277592)), hBOOL(hAPP(hAPP(c_member(_1277590), _1277594), _1277592)), 26213 ^ _782476 : [(26220 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277590, tc_HOL_Obool)), _1277592), hAPP(hAPP(c_Set_Oinsert(_1277590), _1277594), c_Orderings_Obot__class_Obot(tc_fun(_1277590, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277590, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1277590, _1277592) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277590), _1277594), c_Big__Operators_Olinorder__class_OMin(_1277590, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277590, tc_HOL_Obool)), _1277592), hAPP(hAPP(c_Set_Oinsert(_1277590), _1277594), c_Orderings_Obot__class_Obot(tc_fun(_1277590, tc_HOL_Obool)))))))], (26214 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277590, tc_HOL_Obool)), _1277592), hAPP(hAPP(c_Set_Oinsert(_1277590), _1277594), c_Orderings_Obot__class_Obot(tc_fun(_1277590, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277590, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1277590, _1277592) = _1277594)]]], (10881 ^ _782476) ^ [_982868, _982870, _982872, _982874] : [class_Orderings_Oorder(_982868), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982868, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982868, _982870, _982872)), c_SetInterval_Oord__class_OatLeastAtMost(_982868, _982872, _982874)) = c_Orderings_Obot__class_Obot(tc_fun(_982868, tc_HOL_Obool)))], (8513 ^ _782476) ^ [_930120, _930122, _930124, _930126] : [-(hBOOL(hAPP(hAPP(c_member(_930120), hAPP(_930122, _930124)), hAPP(c_Set_Oimage(_930126, _930120, _930122), c_Orderings_Otop__class_Otop(tc_fun(_930126, tc_HOL_Obool))))))], (22572 ^ _782476) ^ [_1205661, _1205663] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205661), _1205663)), hAPP(c_Nat_OSuc, _1205661))))], (5108 ^ _782476) ^ [_860514, _860516, _860518, _860520] : [-(c_Relation_Oconverse(_860520, _860516) = c_Relation_Oconverse(_860518, _860514)), _860520 = _860518, _860516 = _860514], (31271 ^ _782476) ^ [_1374107, _1374109, _1374111, _1374113] : [_1374107 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374109), _1374111)), _1374113), -(_1374109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374107), _1374109) = _1374111), 31278 ^ _782476 : [(31281 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374113), _1374109))], (31279 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374109)))]], 31286 ^ _782476 : [(31289 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374109), _1374113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1374113), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (31287 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374109))]]], (41439 ^ _782476) ^ [_1595202, _1595204, _1595206, _1595208, _1595210] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595202, _1595204)), hAPP(hAPP(c_Product__Type_OPair(_1595202, _1595204), _1595206), _1595208)), _1595210)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595204, _1595202)), hAPP(hAPP(c_Product__Type_OPair(_1595204, _1595202), _1595208), _1595206)), hAPP(c_Relation_Oconverse(_1595202, _1595204), _1595210))))], (2324 ^ _782476) ^ [_816510, _816512, _816514, _816516, _816518, _816520, _816522, _816524] : [-(c_Nitpick_Oprod(_816524, _816520, _816516, _816512) = c_Nitpick_Oprod(_816522, _816518, _816514, _816510)), _816524 = _816522, _816520 = _816518, _816516 = _816514, _816512 = _816510], (22328 ^ _782476) ^ [_1201696, _1201698, _1201700, _1201702] : [c_Fun_Oinj__on(_1201696, _1201698, _1201700, _1201702), -(hAPP(c_Finite__Set_Ocard(_1201698), hAPP(c_Set_Oimage(_1201696, _1201698, _1201700), _1201702)) = hAPP(c_Finite__Set_Ocard(_1201696), _1201702))], (37736 ^ _782476) ^ [_1500709, _1500711, _1500713, _1500715, _1500717] : [-(hAPP(c_Product__Type_Ofst(_1500709, _1500711), hAPP(c_Product__Type_Oapsnd(_1500713, _1500711, _1500709, _1500715), _1500717)) = hAPP(c_Product__Type_Ofst(_1500709, _1500713), _1500717))], (52375 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (22736 ^ _782476) ^ [_1208993, _1208995] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208993)), _1208995) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1208993, _1208995))], (6670 ^ _782476) ^ [_890184, _890186, _890188, _890190, _890192, _890194, _890196, _890198] : [hBOOL(hAPP(hAPP(c_member(_890184), _890186), _890188)), hBOOL(hAPP(hAPP(hAPP(_890190, _890186), _890192), _890194)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_890184, tc_fun(_890196, tc_fun(_890198, tc_HOL_Obool))), _890188), _890190), _890192), _890194)))], (10435 ^ _782476) ^ [_972338, _972340, _972342, _972344] : [c_Hoare__Mirabelle_Ohoare__derivs(_972338, _972340, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972338)), _972342), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_972338), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_972338, _972340, _972344), -(c_Hoare__Mirabelle_Ohoare__derivs(_972338, _972340, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972338)), _972342), _972344)))], (16299 ^ _782476) ^ [_1089020, _1089022, _1089024, _1089026, _1089028] : [class_Groups_Ocomm__monoid__add(_1089020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089024), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089020), _1089026), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089022, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089024), _1089028))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089020), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089020), _1089026), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089022, _1089024))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089020), _1089026), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089024), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089024), _1089028)))))], (37641 ^ _782476) ^ [_1498738] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1498738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1498738)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21053 ^ _782476) ^ [_1178102, _1178104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178102), _1178104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178104), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (20797 ^ _782476) ^ [_1173440, _1173442] : [20799 ^ _782476 : [(20802 ^ _782476) ^ [] : [hBOOL(hAPP(_1173442, 20798 ^ [_1173440, _1173442]))], (20800 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20798 ^ [_1173440, _1173442]), _1173440)))]], 20803 ^ _782476 : [(20804 ^ _782476) ^ [_1173590] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173590), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173440))), -(hBOOL(hAPP(_1173442, _1173590)))]]], (33992 ^ _782476) ^ [_1426957, _1426959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1426957)), c_Int_OBit1(_1426959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1426957), _1426959)))], (44050 ^ _782476) ^ [_1661144, _1661146] : [hBOOL(hAPP(c_List_Odistinct(_1661144), _1661146)), -(hAPP(c_Finite__Set_Ocard(_1661144), hAPP(c_List_Oset(_1661144), _1661146)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661144)), _1661146))], (9560 ^ _782476) ^ [_953862, _953864, _953866, _953868] : [class_Complete__Lattice_Ocomplete__lattice(_953862), -(_953864 = c_Orderings_Obot__class_Obot(tc_fun(_953866, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_953866, _953862), _953864), hAPP(c_COMBK(_953862, _953866), _953868)) = _953868)], (2996 ^ _782476) ^ [_826910, _826912] : [_826912 = _826910, -(c_Nitpick_Odenom(_826912) = c_Nitpick_Odenom(_826910))], (5810 ^ _782476) ^ [_874396, _874398, _874400, _874402, _874404] : [class_Orderings_Oord(_874396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874398, _874396)), _874400), _874402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874396), hAPP(_874400, _874404)), hAPP(_874402, _874404))))], (41785 ^ _782476) ^ [_1603646, _1603648, _1603650] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603646, _1603646)), _1603648), c_Transitive__Closure_Ortrancl(_1603646, _1603650))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603646, _1603646)), _1603648), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603646, _1603646), tc_HOL_Obool), 41788 ^ [_1603646, _1603648, _1603650]), _1603650))))], (32245 ^ _782476) ^ [_1393126, _1393128, _1393130] : [-(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), _1393126), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393128), _1393126))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393128, _1393126))), _1393130) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393128), _1393130))], (20999 ^ _782476) ^ [_1177144, _1177146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177146), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177144), _1177146)))], (46074 ^ _782476) ^ [_1705613, _1705615, _1705617, _1705619, _1705621] : [-(c_List_Olist_Olist__size(_1705613, _1705615, hAPP(hAPP(c_List_Omap(_1705617, _1705613), _1705619), _1705621)) = c_List_Olist_Olist__size(_1705617, hAPP(c_Fun_Ocomp(_1705613, tc_Nat_Onat, _1705617, _1705615), _1705619), _1705621))], (14493 ^ _782476) ^ [_1052416, _1052418, _1052420, _1052422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052416), hAPP(c_Set_Ovimage(_1052416, _1052418, _1052420), _1052422))), hAPP(c_Set_Oimage(_1052416, _1052418, _1052420), c_Orderings_Otop__class_Otop(tc_fun(_1052416, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052418, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052418), _1052422)))], (37369 ^ _782476) ^ [_1493547, _1493549, _1493551, _1493553] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493547, _1493549), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493551), _1493553))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493547), _1493549) = _1493551)], (24225 ^ _782476) ^ [_1236362, _1236364, _1236366] : [class_Groups_Ocomm__monoid__add(_1236362), class_Groups_Ocomm__monoid__mult(_1236362), c_Nat__Transfer_Onat__set(_1236364), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1236362), _1236366), _1236364) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1236362), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1236362, tc_Nat_Onat), _1236366), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1236364)))], (3396 ^ _782476) ^ [_833154, _833156, _833158, _833160] : [-(c_List_Olistsp(_833160, _833156) = c_List_Olistsp(_833158, _833154)), _833160 = _833158, _833156 = _833154], (40235 ^ _782476) ^ [_1566083, _1566085, _1566087] : [-(c_Relation_Orefl__on(_1566083, _1566085, _1566087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566083, _1566083), tc_HOL_Obool)), _1566087), hAPP(hAPP(c_Product__Type_OSigma(_1566083, _1566083), _1566085), hAPP(c_COMBK(tc_fun(_1566083, tc_HOL_Obool), _1566083), _1566085)))), 40241 ^ _782476 : [(40244 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566083, _1566083)), hAPP(hAPP(c_Product__Type_OPair(_1566083, _1566083), 40240 ^ [_1566083, _1566085, _1566087]), 40240 ^ [_1566083, _1566085, _1566087])), _1566087))], (40242 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566083), 40240 ^ [_1566083, _1566085, _1566087]), _1566085)))]]], (35748 ^ _782476) ^ [_1457487, _1457489, _1457491] : [class_Rings_Olinordered__semidom(_1457487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457487), hAPP(hAPP(c_Power_Opower__class_Opower(_1457487), _1457489), 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(_1457487), _1457491), 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(_1457487), c_Groups_Ozero__class_Ozero(_1457487)), _1457491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457487), _1457489), _1457491)))], (1612 ^ _782476) ^ [_805826, _805828] : [-(class_Groups_Olinordered__ab__semigroup__add(_805826)), _805828 = _805826, class_Groups_Olinordered__ab__semigroup__add(_805828)], (10875 ^ _782476) ^ [_982741, _982743, _982745, _982747] : [class_Orderings_Oorder(_982741), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982741, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_982741, _982743, _982745)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982741, _982745, _982747)) = c_Orderings_Obot__class_Obot(tc_fun(_982741, tc_HOL_Obool)))], (8194 ^ _782476) ^ [_922826, _922828, _922830, _922832, _922834] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922826, tc_fun(_922828, tc_HOL_Obool)), _922830), hAPP(hAPP(c_COMBB(tc_fun(_922828, tc_HOL_Obool), tc_fun(_922828, tc_HOL_Obool), _922826), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922828, tc_HOL_Obool)), _922832)), _922834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922828, tc_HOL_Obool)), _922832), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922826, tc_fun(_922828, tc_HOL_Obool)), _922830), _922834)))], (14381 ^ _782476) ^ [_1050325, _1050327, _1050329, _1050331, _1050333] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050325), _1050327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1050329, tc_HOL_Obool)), _1050331), hAPP(c_Set_Oimage(_1050325, _1050329, _1050333), _1050327))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050329), _1050331)))], (47179 ^ _782476) ^ [_1730676, _1730678, _1730680] : [47181 ^ _782476 : [(47184 ^ _782476) ^ [] : [hBOOL(hAPP(_1730678, 47180 ^ [_1730676, _1730678, _1730680]))], (47182 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730676), 47180 ^ [_1730676, _1730678, _1730680]), hAPP(c_List_Oset(_1730676), _1730680))))]], -(hAPP(c_List_Ofilter(_1730676, _1730678), _1730680) = _1730680)], (38389 ^ _782476) ^ [_1516395, _1516397] : [_1516395 = _1516397, -(c_Code__Numeral_OSuc__code__numeral(_1516395) = c_Code__Numeral_OSuc__code__numeral(_1516397))], (38664 ^ _782476) ^ [_1522818, _1522820, _1522822, _1522824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1522818), _1522820)), -(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), _1522818), _1522822)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1522820), _1522824))), c_FunDef_Opair__leq)))], (49822 ^ _782476) ^ [_1788396, _1788398, _1788400, _1788402, _1788404] : [-(c_Predicate_Oconversep(_1788396, _1788398, c_Predicate_Opred__comp(_1788396, _1788400, _1788398, _1788402, _1788404)) = c_Predicate_Opred__comp(_1788398, _1788400, _1788396, c_Predicate_Oconversep(_1788400, _1788398, _1788404), c_Predicate_Oconversep(_1788396, _1788400, _1788402)))], (15258 ^ _782476) ^ [_1067548, _1067550, _1067552] : [class_Lattices_Olattice(_1067548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067548), _1067550)), -(_1067552 = c_Orderings_Obot__class_Obot(tc_fun(_1067548, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1067548, tc_HOL_Obool)), _1067552), _1067550)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067548), c_Big__Operators_Olattice__class_OSup__fin(_1067548, _1067552)), c_Big__Operators_Olattice__class_OSup__fin(_1067548, _1067550)) = c_Big__Operators_Olattice__class_OSup__fin(_1067548, _1067550))], (2950 ^ _782476) ^ [_826221, _826223] : [_826223 = _826221, -(c_Nitpick_Ofrac(_826223) = c_Nitpick_Ofrac(_826221))], (39682 ^ _782476) ^ [_1549689, _1549691, _1549693, _1549695, _1549697, _1549699] : [-(hAPP(c_Set_Oimage(_1549689, tc_prod(_1549691, _1549693), hAPP(hAPP(c_COMBS(_1549689, _1549693, tc_prod(_1549691, _1549693)), hAPP(hAPP(c_COMBB(_1549691, tc_fun(_1549693, tc_prod(_1549691, _1549693)), _1549689), c_Product__Type_OPair(_1549691, _1549693)), _1549695)), _1549697)), _1549699) = hAPP(hAPP(c_Product__Type_OSigma(_1549691, _1549693), hAPP(c_Set_Oimage(_1549689, _1549691, _1549695), _1549699)), hAPP(hAPP(c_COMBB(tc_fun(_1549689, tc_HOL_Obool), tc_fun(_1549693, tc_HOL_Obool), _1549691), c_Set_Oimage(_1549689, _1549693, _1549697)), hAPP(hAPP(c_COMBC(_1549691, tc_fun(_1549689, tc_HOL_Obool), tc_fun(_1549689, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549689, tc_HOL_Obool), tc_fun(tc_fun(_1549689, tc_HOL_Obool), tc_fun(_1549689, tc_HOL_Obool)), _1549691), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549689, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549691, tc_HOL_Obool), tc_fun(_1549689, tc_HOL_Obool), _1549691), c_Set_Ovimage(_1549689, _1549691, _1549695)), hAPP(hAPP(c_COMBC(_1549691, tc_fun(_1549691, tc_HOL_Obool), tc_fun(_1549691, tc_HOL_Obool)), c_Set_Oinsert(_1549691)), c_Orderings_Obot__class_Obot(tc_fun(_1549691, tc_HOL_Obool)))))), _1549699))))], (5958 ^ _782476) ^ [_876872, _876874, _876876, _876878] : [class_Orderings_Oorder(_876872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876872), _876874), _876876)), _876874 = _876878, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876872), _876878), _876876)))], (22834 ^ _782476) ^ [_1210756, _1210758] : [class_Rings_Oring__1(_1210756), -(hBOOL(hAPP(hAPP(c_member(_1210756), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210756), _1210758)), c_Int_Oring__1__class_OInts(_1210756))))], (8184 ^ _782476) ^ [_922411, _922413, _922415, _922417] : [hBOOL(hAPP(hAPP(c_member(_922411), _922417), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922411, tc_HOL_Obool)), _922413), _922415))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922411, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922411, tc_fun(_922411, tc_HOL_Obool), tc_HOL_Obool), c_member(_922411)), _922413)), hAPP(hAPP(c_COMBC(_922411, tc_fun(_922411, tc_HOL_Obool), tc_HOL_Obool), c_member(_922411)), _922415)), _922417)))], (42005 ^ _782476) ^ [_1609712, _1609714, _1609716, _1609718] : [-(hAPP(c_Finite__Set_Ofold__image(_1609712, _1609714, _1609716), _1609718) = c_Finite__Set_Ofold(_1609714, _1609712, hAPP(hAPP(c_COMBB(_1609712, tc_fun(_1609712, _1609712), _1609714), _1609716), _1609718)))], (37081 ^ _782476) ^ [_1488661, _1488663] : [-(c_Divides_OposDivAlg(_1488661, _1488663) = hAPP(c_Divides_Oadjust(_1488663), c_Divides_OposDivAlg(_1488661, 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)))), _1488663)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488661), _1488663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488663), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25600 ^ _782476) ^ [_1261124, _1261126, _1261128] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261124, tc_HOL_Obool)), _1261126), _1261128) = hAPP(c_Set_OCollect(_1261124), hAPP(hAPP(c_COMBS(_1261124, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261124), c_fdisj), hAPP(hAPP(c_COMBC(_1261124, tc_fun(_1261124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261124)), _1261126))), hAPP(hAPP(c_COMBC(_1261124, tc_fun(_1261124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261124)), _1261128))))], (32557 ^ _782476) ^ [_1399115, _1399117, _1399119] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399115), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399117, _1399119)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399115), _1399117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399115), _1399119)))], (32187 ^ _782476) ^ [_1392198, _1392200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392198), 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, _1392200, _1392198)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47110 ^ _782476) ^ [_1728823, _1728825, _1728827, _1728829] : [-(c_List_Oconcat(_1728823, hAPP(hAPP(c_List_Omap(_1728825, tc_List_Olist(_1728823)), hAPP(hAPP(c_COMBC(_1728825, tc_List_Olist(_1728823), tc_List_Olist(_1728823)), hAPP(hAPP(c_COMBB(_1728823, tc_fun(tc_List_Olist(_1728823), tc_List_Olist(_1728823)), _1728825), c_List_Olist_OCons(_1728823)), _1728827)), c_List_Olist_ONil(_1728823))), _1728829)) = hAPP(hAPP(c_List_Omap(_1728825, _1728823), _1728827), _1728829))], (52299 ^ _782476) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (50635 ^ _782476) ^ [_1806425, _1806427, _1806429] : [-(c_List_Olist__ex(_1806425, _1806429, _1806427)), 50636 ^ _782476 : [(50637 ^ _782476) ^ [_1806482] : [hBOOL(hAPP(hAPP(c_member(_1806425), _1806482), hAPP(c_List_Oset(_1806425), _1806427))), hBOOL(hAPP(_1806429, _1806482))]]], (47526 ^ _782476) ^ [_1739146, _1739148, _1739150, _1739152, _1739154] : [class_Orderings_Olinorder(_1739146), hBOOL(hAPP(hAPP(c_member(_1739148), _1739150), hAPP(c_List_Oset(_1739148), _1739152))), c_List_Olinorder__class_Osorted(_1739146, hAPP(hAPP(c_List_Omap(_1739148, _1739146), _1739154), _1739152)), hAPP(c_List_Ohd(_1739148), hAPP(c_List_Ofilter(_1739148, hAPP(hAPP(c_COMBB(_1739146, tc_HOL_Obool, _1739148), hAPP(c_fequal, hAPP(_1739154, _1739150))), _1739154)), _1739152)) = _1739150, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739148, _1739146, _1739154), _1739150), c_List_Oremove1(_1739148, _1739150, _1739152)) = _1739152)], (34688 ^ _782476) ^ [] : [-(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)))))], (39821 ^ _782476) ^ [_1554001, _1554003, _1554005, _1554007, _1554009, _1554011] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554001, _1554003)), hAPP(hAPP(c_Product__Type_OPair(_1554001, _1554003), _1554005), _1554007)), hAPP(hAPP(c_Product__Type_OSigma(_1554001, _1554003), _1554009), _1554011))), 39824 ^ _782476 : [(39827 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554003), _1554007), hAPP(_1554011, _1554005))))], (39825 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554001), _1554005), _1554009)))]]], (24160 ^ _782476) ^ [_1235327] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235327)))], (27060 ^ _782476) ^ [_1293976, _1293978, _1293980, _1293982, _1293984] : [class_Orderings_Olinorder(_1293976), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293976, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293976, _1293978, _1293980)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293976, _1293982, _1293984)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1293976, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293976), _1293978), _1293982), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293976), _1293980), _1293984)))], (52415 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (34844 ^ _782476) ^ [_1440878, _1440880] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440878), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440880)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440878), 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)))), _1440880)))], (51849 ^ _782476) ^ [_1832730, _1832732, _1832734, _1832736] : [class_Rings_Ocomm__semiring__1(_1832730), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832730), _1832732), _1832734)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832730), _1832732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832730), _1832736), _1832734))))], (7233 ^ _782476) ^ [_902942, _902944, _902946] : [class_Orderings_Oord(_902942), 7236 ^ _782476 : [(7243 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902942), _902944), _902946)), -(hBOOL(hAPP(hAPP(c_member(_902942), _902944), hAPP(c_SetInterval_Oord__class_OatMost(_902942), _902946))))], (7237 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902942), _902944), hAPP(c_SetInterval_Oord__class_OatMost(_902942), _902946))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902942), _902944), _902946)))]]], (40700 ^ _782476) ^ [_1577150, _1577152, _1577154, _1577156] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577150, _1577152), hAPP(c_Product__Type_Oprod_Oprod__case(_1577150, _1577152, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1577150, tc_fun(_1577152, tc_HOL_Obool), tc_fun(_1577152, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1577152, tc_HOL_Obool), tc_fun(_1577152, tc_HOL_Obool)), _1577150), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1577152)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577150), c_fconj), hAPP(c_fequal, _1577154)))), hAPP(c_fequal, _1577156)))) = hAPP(hAPP(c_Product__Type_OPair(_1577150, _1577152), _1577154), _1577156))], (46794 ^ _782476) ^ [_1721652, _1721654, _1721656, _1721658, _1721660, _1721662] : [c_List_Olist__all2(_1721652, _1721654, _1721656, _1721658, _1721660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721662), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721652)), _1721658))), -(hBOOL(hAPP(hAPP(_1721656, hAPP(hAPP(c_List_Onth(_1721652), _1721658), _1721662)), hAPP(hAPP(c_List_Onth(_1721654), _1721660), _1721662))))], (50158 ^ _782476) ^ [_1795491, _1795493, _1795495] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795491), _1795495), _1795493)), -(hBOOL(hAPP(hAPP(c_member(_1795491), _1795493), hAPP(c_List_Oset(_1795491), _1795495))))], (4458 ^ _782476) ^ [_850127, _850129] : [_850129 = _850127, -(c_List_Orev(_850129) = c_List_Orev(_850127))], (46060 ^ _782476) ^ [_1705091, _1705093, _1705095, _1705097, _1705099, _1705101, _1705103, _1705105] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1705091, _1705093), _1705095), _1705097), hAPP(hAPP(c_List_Ozip(_1705091, _1705093), _1705099), hAPP(hAPP(c_List_Omap(_1705101, _1705093), _1705103), _1705105))) = hAPP(hAPP(c_List_Omap(tc_prod(_1705091, _1705101), _1705095), hAPP(c_Product__Type_Oprod_Oprod__case(_1705091, _1705101, _1705095), hAPP(hAPP(c_COMBB(tc_fun(_1705101, tc_prod(_1705091, _1705093)), tc_fun(_1705101, _1705095), _1705091), hAPP(c_COMBB(tc_prod(_1705091, _1705093), _1705095, _1705101), _1705097)), hAPP(hAPP(c_COMBC(_1705091, tc_fun(_1705101, _1705093), tc_fun(_1705101, tc_prod(_1705091, _1705093))), hAPP(hAPP(c_COMBB(tc_fun(_1705093, tc_prod(_1705091, _1705093)), tc_fun(tc_fun(_1705101, _1705093), tc_fun(_1705101, tc_prod(_1705091, _1705093))), _1705091), c_COMBB(_1705093, tc_prod(_1705091, _1705093), _1705101)), c_Product__Type_OPair(_1705091, _1705093))), _1705103)))), hAPP(hAPP(c_List_Ozip(_1705091, _1705101), _1705099), _1705105)))], (50765 ^ _782476) ^ [_1810182, _1810184] : [c_Equiv__Relations_Oequivp(_1810182, _1810184), 50768 ^ _782476 : [(50773 ^ _782476) ^ [] : [-(c_Predicate_Otransp(_1810182, _1810184))], (50771 ^ _782476) ^ [] : [-(c_Predicate_Osymp(_1810182, _1810184))], (50769 ^ _782476) ^ [] : [-(c_Predicate_Oreflp(_1810182, _1810184))]]], (20943 ^ _782476) ^ [_1176196, _1176198] : [20944 ^ _782476 : [(20945 ^ _782476) ^ [_1176249] : [_1176198 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176196), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1176249))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176196), _1176198)))], (24598 ^ _782476) ^ [_1242435] : [class_Rings_Oring__1(_1242435), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242435), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1242435))], (3706 ^ _782476) ^ [_838017, _838019] : [_838019 = _838017, -(c_List_Oembed__list(_838019) = c_List_Oembed__list(_838017))], (44404 ^ _782476) ^ [_1667894, _1667896] : [-(_1667896 = c_List_Olist_ONil(_1667894)), -(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(_1667894)), _1667896))))], (39002 ^ _782476) ^ [_1532642, _1532644, _1532646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532642, _1532642), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532642, _1532642, _1532642), _1532644), _1532646)), _1532644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532642, _1532644)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532642, _1532646)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1532642, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1532642, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1532642, tc_HOL_Obool), tc_fun(_1532642, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1532642, _1532644))))], (45769 ^ _782476) ^ [_1698660, _1698662, _1698664] : [_1698660 = c_List_Olist_ONil(_1698662), -(c_List_Olast(_1698662, hAPP(hAPP(c_List_Oappend(_1698662), _1698664), _1698660)) = c_List_Olast(_1698662, _1698664))], (45378 ^ _782476) ^ [_1690658, _1690660] : [-(c_List_Orotate(_1690658, _1690660) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1690658), tc_List_Olist(_1690658)), _1690660), c_List_Orotate1(_1690658)))], (266 ^ _782476) ^ [_786685, _786687, _786689, _786691] : [-(c_Int_Oiszero(_786689, _786685)), c_Int_Oiszero(_786691, _786687), _786691 = _786689, _786687 = _786685], (6034 ^ _782476) ^ [_878048, _878050, _878052] : [class_Orderings_Opreorder(_878048), _878050 = _878052, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878048), _878050), _878052)))], (24354 ^ _782476) ^ [_1238257] : [c_Nat__Transfer_Onat__set(_1238257), -(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), _1238257)) = _1238257)], (9075 ^ _782476) ^ [_942354, _942356, _942358, _942360, _942362] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942354, tc_fun(_942356, tc_HOL_Obool)), _942358), hAPP(hAPP(c_COMBB(tc_fun(_942356, tc_HOL_Obool), tc_fun(_942356, tc_HOL_Obool), _942354), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942356, tc_HOL_Obool)), _942360)), _942362)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942356, tc_HOL_Obool)), _942360), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942354, tc_fun(_942356, tc_HOL_Obool)), _942358), _942362)))], (19440 ^ _782476) ^ [_1148112, _1148114] : [class_Groups_Oordered__ab__group__add(_1148112), 19443 ^ _782476 : [(19450 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148112), c_Groups_Ozero__class_Ozero(_1148112)), _1148114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148112), hAPP(c_Groups_Ouminus__class_Ouminus(_1148112), _1148114)), c_Groups_Ozero__class_Ozero(_1148112))))], (19444 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148112), hAPP(c_Groups_Ouminus__class_Ouminus(_1148112), _1148114)), c_Groups_Ozero__class_Ozero(_1148112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148112), c_Groups_Ozero__class_Ozero(_1148112)), _1148114)))]]], (16321 ^ _782476) ^ [_1089685, _1089687, _1089689, _1089691] : [class_Groups_Ocomm__monoid__add(_1089685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089687), _1089689)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089685), _1089691), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089687, _1089689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089685), hAPP(_1089691, _1089687)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089685), _1089691), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1089687, _1089689))))], (49438 ^ _782476) ^ [_1779243, _1779245, _1779247, _1779249, _1779251] : [-(_1779243 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779245, _1779247, _1779249, _1779251), _1779243) = hAPP(c_Lazy__Sequence_Obind(_1779245, _1779247, hAPP(_1779249, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1779243), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1779245, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779247)), _1779251), _1779243)))], (49458 ^ _782476) ^ [_1779793, _1779795, _1779797, _1779799] : [-(c_New__Random__Sequence_Opos__map(_1779793, _1779795, _1779797, _1779799) = c_New__Random__Sequence_Opos__bind(_1779793, _1779795, _1779799, hAPP(c_Fun_Ocomp(_1779795, 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(_1779795))))), _1779793, c_New__Random__Sequence_Opos__single(_1779795)), _1779797)))], (25456 ^ _782476) ^ [_1258113, _1258115, _1258117, _1258119] : [-(c_Nat_Onat_Onat__case(_1258113, _1258115, _1258117, hAPP(c_Nat_OSuc, _1258119)) = hAPP(_1258117, _1258119))], (39014 ^ _782476) ^ [_1533384, _1533386, _1533388, _1533390, _1533392] : [c_Typedef_Otype__definition(_1533384, _1533386, _1533388, _1533390, _1533392), -(hAPP(c_Set_Oimage(_1533386, _1533384, _1533390), _1533392) = c_Orderings_Otop__class_Otop(tc_fun(_1533384, tc_HOL_Obool)))], (44753 ^ _782476) ^ [_1676262, _1676264, _1676266, _1676268] : [-(hAPP(hAPP(c_List_Oappend(_1676262), hAPP(hAPP(c_List_Oappend(_1676262), _1676264), _1676266)), _1676268) = hAPP(hAPP(c_List_Oappend(_1676262), _1676264), hAPP(hAPP(c_List_Oappend(_1676262), _1676266), _1676268)))], (21175 ^ _782476) ^ [_1180206, _1180208, _1180210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180206)), _1180206 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180206), _1180210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180208), _1180206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180210)))], (44286 ^ _782476) ^ [_1665932, _1665934, _1665936] : [hAPP(hAPP(c_List_Otake(_1665932), _1665934), _1665936) = c_List_Olist_ONil(_1665932), -(_1665934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1665936 = c_List_Olist_ONil(_1665932))], (10399 ^ _782476) ^ [_971201, _971203, _971205, _971207] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971201, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971201, tc_HOL_Obool)), _971203), _971205)), _971207) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971201, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971201, tc_HOL_Obool)), _971203), _971207)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971201, tc_HOL_Obool)), _971205), _971207)))], (41118 ^ _782476) ^ [_1587474, _1587476, _1587478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587474, _1587474), tc_HOL_Obool)), _1587476), c_Transitive__Closure_Ortrancl(_1587474, _1587478))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587474, _1587474), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587474, _1587476)), c_Transitive__Closure_Ortrancl(_1587474, _1587478))))], (49312 ^ _782476) ^ [_1776670, _1776672, _1776674, _1776676] : [c_List_Olist__ex1(_1776670, _1776672, hAPP(hAPP(c_List_Olist_OCons(_1776670), _1776674), _1776676)), 49315 ^ _782476 : [(49322 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1776672, _1776674))), -(c_List_Olist__ex1(_1776670, _1776672, _1776676))], (49316 ^ _782476) ^ [] : [hBOOL(hAPP(_1776672, _1776674)), -(c_List_Olist__all(_1776670, hAPP(hAPP(c_COMBS(_1776670, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776670), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776670), c_fNot), _1776672))), hAPP(c_fequal, _1776674)), _1776676))]]], (51057 ^ _782476) ^ [_1815763, _1815765, _1815767] : [-(c_Equiv__Relations_Oequiv(_1815763, _1815765, _1815767)), c_Relation_Orefl__on(_1815763, _1815765, _1815767), c_Relation_Osym(_1815763, _1815767), c_Relation_Otrans(_1815763, _1815767)], (52779 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (46072 ^ _782476) ^ [_1705548, _1705550, _1705552, _1705554, _1705556] : [-(hAPP(hAPP(c_List_Odrop(_1705548), _1705550), hAPP(hAPP(c_List_Omap(_1705552, _1705548), _1705554), _1705556)) = hAPP(hAPP(c_List_Omap(_1705552, _1705548), _1705554), hAPP(hAPP(c_List_Odrop(_1705552), _1705550), _1705556)))], (25231 ^ _782476) ^ [_1254123, _1254125, _1254127, _1254129, _1254131] : [class_Groups_Oordered__ab__group__add__abs(_1254123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254123), hAPP(c_Groups_Oabs__class_Oabs(_1254123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254123), _1254125), _1254127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254123), _1254129), _1254131)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254123), hAPP(c_Groups_Oabs__class_Oabs(_1254123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254123), _1254125), _1254129))), hAPP(c_Groups_Oabs__class_Oabs(_1254123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254123), _1254127), _1254131))))))], (45380 ^ _782476) ^ [_1690701, _1690703, _1690705] : [-(hAPP(c_List_Orotate1(_1690701), hAPP(c_List_Orotate(_1690701, _1690703), _1690705)) = hAPP(c_List_Orotate(_1690701, _1690703), hAPP(c_List_Orotate1(_1690701), _1690705)))], (29242 ^ _782476) ^ [_1337572, _1337574, _1337576] : [class_Rings_Olinordered__semidom(_1337572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337572), c_Groups_Ozero__class_Ozero(_1337572)), _1337574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337572), c_Groups_Ozero__class_Ozero(_1337572)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337572), _1337574), _1337576))))], (15027 ^ _782476) ^ [_1063039, _1063041, _1063043, _1063045, _1063047, _1063049] : [c_Finite__Set_Ofolding(_1063039, _1063041, _1063043, _1063045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063039), _1063047)), -(hBOOL(hAPP(hAPP(c_member(_1063039), _1063049), _1063047))), -(hAPP(_1063045, hAPP(hAPP(c_Set_Oinsert(_1063039), _1063049), _1063047)) = hAPP(c_Fun_Ocomp(_1063041, _1063041, _1063041, hAPP(_1063045, _1063047)), hAPP(_1063043, _1063049)))], (9542 ^ _782476) ^ [_953541, _953543] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953541, tc_HOL_Obool)), _953543)), -(hBOOL(hAPP(hAPP(c_member(_953541), _953543), c_Orderings_Obot__class_Obot(tc_fun(_953541, tc_HOL_Obool)))))], (52297 ^ _782476) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (15350 ^ _782476) ^ [_1069104, _1069106, _1069108] : [class_Lattices_Olattice(_1069104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069104), _1069106)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069104), _1069108)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069104, tc_HOL_Obool)), _1069106), _1069108) = c_Orderings_Obot__class_Obot(tc_fun(_1069104, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069104), c_Big__Operators_Olattice__class_OSup__fin(_1069104, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069104, tc_HOL_Obool)), _1069106), _1069108))), c_Big__Operators_Olattice__class_OSup__fin(_1069104, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069104, tc_HOL_Obool)), _1069106), _1069108))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069104), c_Big__Operators_Olattice__class_OSup__fin(_1069104, _1069106)), c_Big__Operators_Olattice__class_OSup__fin(_1069104, _1069108)))], (24708 ^ _782476) ^ [_1244308, _1244310, _1244312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244308)), 24714 ^ _782476 : [(24717 ^ _782476) ^ [] : [hBOOL(hAPP(_1244310, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24713 ^ [_1244308, _1244310, _1244312]), _1244308)))], (24715 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1244310, 24713 ^ [_1244308, _1244310, _1244312])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244312)), 24722 ^ _782476 : [(24723 ^ _782476) ^ [_1244597] : [hBOOL(hAPP(_1244310, _1244597)), -(hBOOL(hAPP(_1244310, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244312), _1244308)))))]]], (20617 ^ _782476) ^ [_1170100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170100)), -(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), _1170100))))], (26990 ^ _782476) ^ [_1292474, _1292476, _1292478, _1292480] : [class_Orderings_Olinorder(_1292474), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292474), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292474), _1292476), _1292478)), _1292480) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292474), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292474), _1292476), _1292480)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292474), _1292478), _1292480)))], (6263 ^ _782476) ^ [_882250, _882252, _882254] : [class_Orderings_Olinorder(_882250), 6266 ^ _782476 : [(6273 ^ _782476) ^ [] : [_882252 = _882254, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_882250), _882252) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882250), _882254))], (6267 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_882250), _882252) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882250), _882254), -(_882252 = _882254)]]], (22546 ^ _782476) ^ [_1205249, _1205251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205249)), _1205251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205249), _1205251)))], (50503 ^ _782476) ^ [_1803839, _1803841] : [c_Relation_Otrans(_1803839, _1803841), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1803839, _1803839), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1803839, _1803839, _1803839), _1803841), _1803841)), _1803841)))], (49272 ^ _782476) ^ [_1775841, _1775843] : [-(c_List_Olist__all(_1775841, _1775843, c_List_Olist_ONil(_1775841)))], (1732 ^ _782476) ^ [_807326, _807328] : [-(class_Groups_Oab__semigroup__add(_807326)), _807328 = _807326, class_Groups_Oab__semigroup__add(_807328)], (18646 ^ _782476) ^ [_1133665, _1133667, _1133669] : [class_Rings_Oordered__ring(_1133665), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133665), c_Groups_Ozero__class_Ozero(_1133665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133665), _1133667), _1133669)))), 18651 ^ _782476 : [(18658 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133665), _1133667), c_Groups_Ozero__class_Ozero(_1133665))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133665), _1133669), c_Groups_Ozero__class_Ozero(_1133665)))], (18652 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133665), c_Groups_Ozero__class_Ozero(_1133665)), _1133667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133665), c_Groups_Ozero__class_Ozero(_1133665)), _1133669))]]], (42009 ^ _782476) ^ [_1609809, _1609811, _1609813, _1609815, _1609817] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609809, _1609811, _1609813), _1609815), _1609817) = c_HOL_OThe(_1609811, c_Finite__Set_Ofold__graph(_1609809, _1609811, _1609813, _1609815, _1609817)))], (45104 ^ _782476) ^ [_1684649, _1684651, _1684653] : [-(hAPP(hAPP(c_List_Odrop(_1684649), _1684651), c_List_Obutlast(_1684649, _1684653)) = c_List_Obutlast(_1684649, hAPP(hAPP(c_List_Odrop(_1684649), _1684651), _1684653)))], (42953 ^ _782476) ^ [_1630699, _1630701, _1630703] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630699)), hAPP(hAPP(c_List_Olist_OCons(_1630699), _1630701), _1630703)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630699)), _1630703)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25253 ^ _782476) ^ [_1254622, _1254624] : [class_Groups_Oordered__ab__group__add__abs(_1254622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254622), _1254624), c_Groups_Ozero__class_Ozero(_1254622))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254622), _1254624) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254622), _1254624))], (35092 ^ _782476) ^ [_1445859, _1445861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445859), 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)))), _1445861)), 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)))), _1445859)) = 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), _1445861), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1445859))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31069 ^ _782476) ^ [_1370702, _1370704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370702)), 31072 ^ _782476 : [(31079 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370702), _1370704)), -(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), _1370704), _1370702))))], (31073 ^ _782476) ^ [] : [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), _1370704), _1370702))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370702), _1370704)))]]], (37754 ^ _782476) ^ [_1501248, _1501250, _1501252] : [-(c_HOL_OThe(tc_prod(_1501248, _1501250), hAPP(c_Product__Type_Oprod_Oprod__case(_1501248, _1501250, tc_HOL_Obool), _1501252)) = c_HOL_OThe(tc_prod(_1501248, _1501250), hAPP(hAPP(c_COMBS(tc_prod(_1501248, _1501250), _1501250, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1501248, tc_fun(_1501250, tc_HOL_Obool), tc_prod(_1501248, _1501250)), _1501252), c_Product__Type_Ofst(_1501248, _1501250))), c_Product__Type_Osnd(_1501248, _1501250))))], (13900 ^ _782476) ^ [_1040466, _1040468, _1040470, _1040472] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040466, _1040468, _1040470), _1040472)), _1040470 = c_Orderings_Obot__class_Obot(tc_fun(_1040466, tc_HOL_Obool))], (40851 ^ _782476) ^ [_1580970, _1580972] : [-(c_Random_Olog(_1580970, _1580972) = 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(_1580970, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1580972), _1580970)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580970), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580972), _1580970)))], (22286 ^ _782476) ^ [_1200992, _1200994] : [hBOOL(hAPP(_1200992, _1200994)), -(hBOOL(hAPP(_1200992, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1200992) = 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), _1200992), c_Nat_OSuc))))], (40937 ^ _782476) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40931 ^ _782476) ^ [_1582319, _1582321] : [c_Wellfounded_Owf(_1582319, _1582321), -(c_Wellfounded_Owf(_1582319, c_Transitive__Closure_Otrancl(_1582319, _1582321)))], (37726 ^ _782476) ^ [_1500506, _1500508, _1500510, _1500512, _1500514] : [hAPP(c_Product__Type_Ofst(_1500506, _1500508), hAPP(hAPP(c_Product__Type_OPair(_1500506, _1500508), _1500510), _1500512)) = _1500514, -(_1500510 = _1500514)], (44318 ^ _782476) ^ [_1666396, _1666398] : [-(c_Enum_On__lists(_1666396, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1666398) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666396)), c_List_Olist_ONil(_1666396)), c_List_Olist_ONil(tc_List_Olist(_1666396))))], (43646 ^ _782476) ^ [_1651656, _1651658, _1651660, _1651662, _1651664, _1651666] : [-(hAPP(hAPP(c_List_Ozip(_1651656, _1651658), hAPP(hAPP(c_List_Olist_OCons(_1651656), _1651660), _1651662)), hAPP(hAPP(c_List_Olist_OCons(_1651658), _1651664), _1651666)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1651656, _1651658)), hAPP(hAPP(c_Product__Type_OPair(_1651656, _1651658), _1651660), _1651664)), hAPP(hAPP(c_List_Ozip(_1651656, _1651658), _1651662), _1651666)))], (51003 ^ _782476) ^ [_1814916, _1814918, _1814920] : [c_Relation_Osym(_1814916, _1814918), c_Relation_Osym(_1814916, _1814920), -(c_Relation_Osym(_1814916, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1814916, _1814916), tc_HOL_Obool)), _1814918), _1814920)))], (15196 ^ _782476) ^ [_1066583, _1066585, _1066587, _1066589, _1066591] : [c_Finite__Set_Ofolding__idem(_1066583, _1066585, _1066587, _1066589), -(hAPP(c_Fun_Ocomp(_1066585, _1066585, _1066585, hAPP(_1066587, _1066591)), hAPP(_1066587, _1066591)) = hAPP(_1066587, _1066591))], (15937 ^ _782476) ^ [_1080827, _1080829, _1080831, _1080833, _1080835] : [class_Groups_Oab__group__add(_1080827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080829), _1080831)), 15944 ^ _782476 : [(15951 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1080829), _1080833), _1080831))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080829, _1080827), _1080835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080829, tc_HOL_Obool)), _1080831), hAPP(hAPP(c_Set_Oinsert(_1080829), _1080833), c_Orderings_Obot__class_Obot(tc_fun(_1080829, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080829, _1080827), _1080835), _1080831))], (15945 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1080829), _1080833), _1080831)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080829, _1080827), _1080835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080829, tc_HOL_Obool)), _1080831), hAPP(hAPP(c_Set_Oinsert(_1080829), _1080833), c_Orderings_Obot__class_Obot(tc_fun(_1080829, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080827), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080829, _1080827), _1080835), _1080831)), hAPP(_1080835, _1080833)))]]], (4174 ^ _782476) ^ [_845723, _845725, _845727, _845729] : [-(c_Lazy__Sequence_Ohb__single(_845729, _845725) = c_Lazy__Sequence_Ohb__single(_845727, _845723)), _845729 = _845727, _845725 = _845723], (8645 ^ _782476) ^ [_932736, _932738] : [class_Lattices_Obounded__lattice__top(_932736), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932736), c_Orderings_Otop__class_Otop(_932736)), _932738) = _932738)], (9927 ^ _782476) ^ [_961434, _961436, _961438, _961440, _961442] : [class_Lattices_Osemilattice__sup(_961434), class_Lattices_Osemilattice__sup(_961436), c_Orderings_Oorder__class_Omono(_961436, _961434, _961438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961434), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961434), hAPP(_961438, _961440)), hAPP(_961438, _961442))), hAPP(_961438, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961436), _961440), _961442)))))], (46062 ^ _782476) ^ [_1705272, _1705274, _1705276, _1705278, _1705280, _1705282] : [-(hAPP(hAPP(c_List_Ozip(_1705272, _1705274), _1705276), hAPP(hAPP(c_List_Omap(_1705278, _1705274), _1705280), _1705282)) = hAPP(hAPP(c_List_Omap(tc_prod(_1705272, _1705278), tc_prod(_1705272, _1705274)), hAPP(c_Product__Type_Oprod_Oprod__case(_1705272, _1705278, tc_prod(_1705272, _1705274)), hAPP(hAPP(c_COMBC(_1705272, tc_fun(_1705278, _1705274), tc_fun(_1705278, tc_prod(_1705272, _1705274))), hAPP(hAPP(c_COMBB(tc_fun(_1705274, tc_prod(_1705272, _1705274)), tc_fun(tc_fun(_1705278, _1705274), tc_fun(_1705278, tc_prod(_1705272, _1705274))), _1705272), c_COMBB(_1705274, tc_prod(_1705272, _1705274), _1705278)), c_Product__Type_OPair(_1705272, _1705274))), _1705280))), hAPP(hAPP(c_List_Ozip(_1705272, _1705278), _1705276), _1705282)))], (12610 ^ _782476) ^ [_1013436, _1013438] : [class_Groups_Oordered__ab__group__add(_1013436), -(c_Fun_Oinj__on(_1013436, _1013436, c_Groups_Ouminus__class_Ouminus(_1013436), _1013438))], (52139 ^ _782476) ^ [_1838022, _1838024] : [class_Lattices_Odistrib__lattice(_1838022), -(class_Lattices_Odistrib__lattice(tc_fun(_1838024, _1838022)))], (4710 ^ _782476) ^ [_854227, _854229, _854231, _854233] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854233, _854229) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854231, _854227)), _854233 = _854231, _854229 = _854227], (21281 ^ _782476) ^ [_1182079, _1182081] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1182079, _1182081))))], (16979 ^ _782476) ^ [_1103976, _1103978, _1103980, _1103982, _1103984] : [class_Rings_Ocomm__semiring__1(_1103976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), _1103978), _1103980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), _1103982), _1103984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), _1103982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103976), _1103978), _1103980)), _1103984)))], (39774 ^ _782476) ^ [_1552564, _1552566, _1552568, _1552570] : [-(hAPP(c_Set_Oimage(tc_prod(_1552564, _1552566), tc_prod(_1552566, _1552564), hAPP(c_Product__Type_Oprod_Oprod__case(_1552564, _1552566, tc_prod(_1552566, _1552564)), hAPP(c_COMBC(_1552566, _1552564, tc_prod(_1552566, _1552564)), c_Product__Type_OPair(_1552566, _1552564)))), hAPP(hAPP(c_Product__Type_OSigma(_1552564, _1552566), _1552568), hAPP(c_COMBK(tc_fun(_1552566, tc_HOL_Obool), _1552564), _1552570))) = hAPP(hAPP(c_Product__Type_OSigma(_1552566, _1552564), _1552570), hAPP(c_COMBK(tc_fun(_1552564, tc_HOL_Obool), _1552566), _1552568)))], (47475 ^ _782476) ^ [_1737823, _1737825] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1737823, _1737825) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1737823, hAPP(c_Nat_OSuc, _1737825))))], (37050 ^ _782476) ^ [_1488084, _1488086] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488084, _1488084)), hAPP(hAPP(c_Product__Type_OPair(_1488084, _1488084), 37051 ^ [_1488084, _1488086]), 37051 ^ [_1488084, _1488086])), _1488086)), -(c_Nitpick_Orefl_H(_1488084, _1488086))], (37804 ^ _782476) ^ [_1502215, _1502217, _1502219, _1502221, _1502223] : [hBOOL(hAPP(hAPP(_1502215, _1502217), _1502219)), -(hBOOL(hAPP(hAPP(_1502215, hAPP(c_Product__Type_Osnd(_1502221, _1502223), hAPP(hAPP(c_Product__Type_OPair(_1502221, _1502223), _1502219), _1502217))), hAPP(c_Product__Type_Ofst(_1502221, _1502223), hAPP(hAPP(c_Product__Type_OPair(_1502221, _1502223), _1502219), _1502217)))))], (17551 ^ _782476) ^ [_1115177, _1115179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115177), _1115179)), -(_1115179 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115177), 17554 ^ [_1115177, _1115179]))], (27638 ^ _782476) ^ [_1305246, _1305248, _1305250] : [class_Orderings_Olinorder(_1305246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305246), _1305248)), -(_1305248 = c_Orderings_Obot__class_Obot(tc_fun(_1305246, tc_HOL_Obool))), 27649 ^ _782476 : [(27650 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305246), _1305250), hAPP(c_Finite__Set_Ofold1(_1305246, c_Orderings_Oord__class_Omin(_1305246)), _1305248))), 27653 ^ _782476 : [(27654 ^ _782476) ^ [_1305539] : [hBOOL(hAPP(hAPP(c_member(_1305246), _1305539), _1305248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305246), _1305250), _1305539)))]]], (27660 ^ _782476) ^ [] : [27662 ^ _782476 : [(27665 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305246), _1305250), 27661 ^ [_1305246, _1305248, _1305250]))], (27663 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305246), 27661 ^ [_1305246, _1305248, _1305250]), _1305248)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305246), _1305250), hAPP(c_Finite__Set_Ofold1(_1305246, c_Orderings_Oord__class_Omin(_1305246)), _1305248))))]]], (13446 ^ _782476) ^ [_1031574, _1031576, _1031578, _1031580] : [c_Partial__Function_Omk__less(_1031574, _1031576, _1031578, _1031580), 13449 ^ _782476 : [(13452 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1031576, _1031580), _1031578))], (13450 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1031576, _1031578), _1031580)))]]], (47351 ^ _782476) ^ [_1735709, _1735711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735709), _1735711)), -(c_List_Oupt(_1735709, hAPP(c_Nat_OSuc, _1735711)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735709, _1735711)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735711), c_List_Olist_ONil(tc_Nat_Onat))))], (13074 ^ _782476) ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557] : [c_Nitpick_Ofold__graph_H(_1022545, _1022547, _1022549, _1022551, _1022553, hAPP(hAPP(_1022549, _1022555), _1022557)), 13079 ^ _782476 : [(13082 ^ _782476) ^ [] : [-(hAPP(hAPP(_1022549, _1022555), _1022557) = _1022551)], (13080 ^ _782476) ^ [] : [-(_1022553 = c_Orderings_Obot__class_Obot(tc_fun(_1022545, tc_HOL_Obool)))]], 13085 ^ _782476 : [(13090 ^ _782476) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1022545, _1022547, _1022549, _1022551, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022545, tc_HOL_Obool)), _1022553), hAPP(hAPP(c_Set_Oinsert(_1022545), 13083 ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557]), c_Orderings_Obot__class_Obot(tc_fun(_1022545, tc_HOL_Obool)))), 13084 ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557]))], (13088 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1022545), 13083 ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557]), _1022553)))], (13086 ^ _782476) ^ [] : [-(hAPP(hAPP(_1022549, _1022555), _1022557) = hAPP(hAPP(_1022549, 13083 ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557]), 13084 ^ [_1022545, _1022547, _1022549, _1022551, _1022553, _1022555, _1022557]))]]], (4214 ^ _782476) ^ [_846327, _846329, _846331, _846333] : [-(c_Hilbert__Choice_OEps(_846333, _846329) = c_Hilbert__Choice_OEps(_846331, _846327)), _846333 = _846331, _846329 = _846327], (31518 ^ _782476) ^ [_1378876, _1378878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1378876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378878), _1378876)), _1378878)))], (42445 ^ _782476) ^ [_1618371, _1618373, _1618375, _1618377, _1618379, _1618381, _1618383] : [c_Finite__Set_Ofun__left__comm(_1618371, _1618373, _1618375), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618371, _1618373, _1618375, _1618377, _1618379), _1618381)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618371, _1618373, _1618375, _1618377, _1618379), _1618383)), -(_1618383 = _1618381)], (31624 ^ _782476) ^ [_1380819, _1380821, _1380823] : [hBOOL(hAPP(_1380819, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380821), _1380823))), 31629 ^ _782476 : [(31632 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1380819, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31630 ^ _782476) ^ [] : [-(_1380823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 31634 ^ _782476 : [(31639 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1380819, 31633 ^ [_1380819, _1380821, _1380823])))], (31637 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1380821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380823), hAPP(c_Nat_OSuc, 31633 ^ [_1380819, _1380821, _1380823])))))], (31635 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380823), 31633 ^ [_1380819, _1380821, _1380823])), _1380821)))]]], (44098 ^ _782476) ^ [_1662173, _1662175] : [44100 ^ _782476 : [(44104 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44102 ^ [_1662173, _1662175]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662173)), _1662175))))], (44106 ^ _782476) ^ [] : [44099 ^ [_1662173, _1662175] = 44102 ^ [_1662173, _1662175]], (44108 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1662173), _1662175), 44099 ^ [_1662173, _1662175]) = hAPP(hAPP(c_List_Onth(_1662173), _1662175), 44102 ^ [_1662173, _1662175]))], (44101 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44099 ^ [_1662173, _1662175]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662173)), _1662175))))]], -(hBOOL(hAPP(c_List_Odistinct(_1662173), _1662175)))], (47499 ^ _782476) ^ [_1738330, _1738332, _1738334, _1738336] : [class_Groups_Ocomm__monoid__add(_1738330), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1738330), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738330), _1738332), c_List_Oupt(_1738334, _1738336))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738330), _1738332), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738334, _1738336))))], (19318 ^ _782476) ^ [_1146040, _1146042, _1146044, _1146046, _1146048, _1146050] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1146040), -(_1146042 = c_Groups_Ozero__class_Ozero(_1146040)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146040), _1146044), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146040), _1146042), _1146048)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146040), _1146046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146040), _1146042), _1146050)), _1146044 = _1146046, -(_1146048 = _1146050)], (51677 ^ _782476) ^ [_1829592] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1829592)))], (26996 ^ _782476) ^ [_1292633, _1292635, _1292637] : [class_Groups_Olinordered__ab__group__add(_1292633), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292633), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292633), _1292635), _1292637)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292633), hAPP(c_Groups_Ouminus__class_Ouminus(_1292633), _1292635)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292633), _1292637)))], (50143 ^ _782476) ^ [_1795092, _1795094, _1795096, _1795098, _1795100] : [50145 ^ _782476 : [(50148 ^ _782476) ^ [] : [c_Relation_Orefl__on(_1795096, hAPP(_1795098, 50144 ^ [_1795092, _1795094, _1795096, _1795098, _1795100]), hAPP(_1795100, 50144 ^ [_1795092, _1795094, _1795096, _1795098, _1795100]))], (50146 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795092), 50144 ^ [_1795092, _1795094, _1795096, _1795098, _1795100]), _1795094)))]], -(c_Relation_Orefl__on(_1795096, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795092, tc_fun(_1795096, tc_HOL_Obool)), _1795094), _1795098), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795092, tc_fun(tc_prod(_1795096, _1795096), tc_HOL_Obool)), _1795094), _1795100)))], (49798 ^ _782476) ^ [_1787946, _1787948, _1787950, _1787952, _1787954] : [hBOOL(hAPP(hAPP(_1787946, _1787948), _1787950)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787952, _1787954, _1787946), _1787950), _1787948)))], (27576 ^ _782476) ^ [_1304118, _1304120, _1304122] : [class_Orderings_Olinorder(_1304118), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304118), _1304120)), -(_1304120 = c_Orderings_Obot__class_Obot(tc_fun(_1304118, tc_HOL_Obool))), 27587 ^ _782476 : [(27588 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304118), _1304122), hAPP(c_Finite__Set_Ofold1(_1304118, c_Orderings_Oord__class_Omin(_1304118)), _1304120))), 27591 ^ _782476 : [(27592 ^ _782476) ^ [_1304411] : [hBOOL(hAPP(hAPP(c_member(_1304118), _1304411), _1304120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304118), _1304122), _1304411)))]]], (27598 ^ _782476) ^ [] : [27600 ^ _782476 : [(27603 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304118), _1304122), 27599 ^ [_1304118, _1304120, _1304122]))], (27601 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304118), 27599 ^ [_1304118, _1304120, _1304122]), _1304120)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304118), _1304122), hAPP(c_Finite__Set_Ofold1(_1304118, c_Orderings_Oord__class_Omin(_1304118)), _1304120))))]]], (4536 ^ _782476) ^ [_851354, _851356, _851358, _851360, _851362, _851364, _851366, _851368, _851370, _851372] : [-(c_Option_Ooption_Ooption__case(_851372, _851368, _851364, _851360, _851356) = c_Option_Ooption_Ooption__case(_851370, _851366, _851362, _851358, _851354)), _851372 = _851370, _851368 = _851366, _851364 = _851362, _851360 = _851358, _851356 = _851354], (7109 ^ _782476) ^ [_900156, _900158, _900160, _900162] : [-(hAPP(c_Set_OPow(_900156), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900158, tc_fun(_900156, tc_HOL_Obool)), _900160), _900162)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900158, tc_fun(tc_fun(_900156, tc_HOL_Obool), tc_HOL_Obool)), _900160), hAPP(hAPP(c_COMBB(tc_fun(_900156, tc_HOL_Obool), tc_fun(tc_fun(_900156, tc_HOL_Obool), tc_HOL_Obool), _900158), c_Set_OPow(_900156)), _900162)))], (50581 ^ _782476) ^ [_1805120, _1805122, _1805124] : [hBOOL(hAPP(hAPP(c_member(_1805122), _1805120), c_Orderings_Obot__class_Obot(tc_fun(_1805122, tc_HOL_Obool)))), hBOOL(hAPP(_1805124, _1805120))], (41775 ^ _782476) ^ [_1603369, _1603371] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603369, _1603369), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1603371) = _1603371)], (23155 ^ _782476) ^ [_1217134] : [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, _1217134)))))], (16611 ^ _782476) ^ [_1095508, _1095510, _1095512, _1095514] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095508), _1095510), _1095512)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095508), _1095510), _1095514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095508), _1095512), _1095514)))], (47341 ^ _782476) ^ [_1735490, _1735492] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735490, _1735492)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735490), _1735492))], (2500 ^ _782476) ^ [_819200, _819202, _819204, _819206] : [-(c_Set_Othe__elem(_819206, _819202) = c_Set_Othe__elem(_819204, _819200)), _819206 = _819204, _819202 = _819200], (38094 ^ _782476) ^ [_1508967, _1508969, _1508971, _1508973, _1508975] : [hAPP(c_Relation_OImage(_1508967, _1508967, _1508969), hAPP(hAPP(c_Set_Oinsert(_1508967), _1508971), c_Orderings_Obot__class_Obot(tc_fun(_1508967, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508967, _1508967, _1508969), hAPP(hAPP(c_Set_Oinsert(_1508967), _1508973), c_Orderings_Obot__class_Obot(tc_fun(_1508967, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1508967, _1508975, _1508969), hBOOL(hAPP(hAPP(c_member(_1508967), _1508973), _1508975)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508967, _1508967)), hAPP(hAPP(c_Product__Type_OPair(_1508967, _1508967), _1508971), _1508973)), _1508969)))], (12106 ^ _782476) ^ [_1002773, _1002775, _1002777, _1002779, _1002781] : [class_Orderings_Oorder(_1002773), class_Orderings_Olinorder(_1002775), c_Orderings_Oorder__class_Ostrict__mono(_1002775, _1002773, _1002777), 12117 ^ _782476 : [(12124 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002775), _1002779), _1002781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002773), hAPP(_1002777, _1002779)), hAPP(_1002777, _1002781))))], (12118 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002773), hAPP(_1002777, _1002779)), hAPP(_1002777, _1002781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002775), _1002779), _1002781)))]]], (21521 ^ _782476) ^ [_1186334, _1186336, _1186338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186334)), 21524 ^ _782476 : [(21525 ^ _782476) ^ [_1186468] : [21527 ^ _782476 : [(21533 ^ _782476) ^ [] : [-(_1186468 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21529 ^ [_1186334, _1186336, _1186338, _1186468]), 21526 ^ [_1186334, _1186336, _1186338, _1186468]))], (21531 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21529 ^ [_1186334, _1186336, _1186338, _1186468]), _1186336)))], (21528 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21526 ^ [_1186334, _1186336, _1186338, _1186468]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186334))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186468), _1186338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186468), _1186334)), _1186338)))]]], (12954 ^ _782476) ^ [_1019882, _1019884, _1019886, _1019888, _1019890] : [c_Fun_Oinj__on(_1019882, _1019884, _1019886, c_Orderings_Otop__class_Otop(tc_fun(_1019882, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1019882, _1019884, _1019886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019882, tc_HOL_Obool)), _1019888), _1019890)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019884, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019882, _1019884, _1019886), _1019888)), hAPP(c_Set_Oimage(_1019882, _1019884, _1019886), _1019890)))], (39008 ^ _782476) ^ [_1533013, _1533015, _1533017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533013, _1533013), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1533013, _1533013, _1533013), _1533015), _1533017)), _1533015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533013, _1533015)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533013, _1533017)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1533013, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1533013, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1533013, tc_HOL_Obool), tc_fun(_1533013, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1533013, _1533015))))], (43173 ^ _782476) ^ [_1638048, _1638050, _1638052, _1638054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638048), tc_List_Olist(_1638048))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638048), tc_List_Olist(_1638048)), _1638052), _1638054)), c_List_Olistrel(_1638048, _1638050))), -(c_List_Olistrelp(_1638048, hAPP(hAPP(c_COMBC(_1638048, tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_fun(_1638048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638048, tc_fun(tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_fun(_1638048, tc_HOL_Obool)), _1638048), c_COMBC(_1638048, tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638048, tc_prod(_1638048, _1638048)), tc_fun(_1638048, tc_fun(tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_HOL_Obool)), _1638048), hAPP(c_COMBB(tc_prod(_1638048, _1638048), tc_fun(tc_fun(tc_prod(_1638048, _1638048), tc_HOL_Obool), tc_HOL_Obool), _1638048), c_member(tc_prod(_1638048, _1638048)))), c_Product__Type_OPair(_1638048, _1638048)))), _1638050), _1638052, _1638054))], (4514 ^ _782476) ^ [_850965, _850967, _850969, _850971, _850973, _850975, _850977, _850979, _850981, _850983] : [-(c_Predicate_Opred__comp(_850983, _850979, _850975, _850971, _850967) = c_Predicate_Opred__comp(_850981, _850977, _850973, _850969, _850965)), _850983 = _850981, _850979 = _850977, _850975 = _850973, _850971 = _850969, _850967 = _850965], (3752 ^ _782476) ^ [_838706, _838708, _838710, _838712, _838714, _838716] : [-(c_List_Oinsert(_838716, _838712, _838708) = c_List_Oinsert(_838714, _838710, _838706)), _838716 = _838714, _838712 = _838710, _838708 = _838706], (6887 ^ _782476) ^ [_895303, _895305, _895307, _895309] : [_895303 = _895305, hBOOL(hAPP(hAPP(c_member(_895307), _895305), _895309)), -(hBOOL(hAPP(hAPP(c_member(_895307), _895303), _895309)))], (48538 ^ _782476) ^ [_1759148, _1759150, _1759152, _1759154, _1759156] : [class_Groups_Omonoid__add(_1759148), 48544 ^ _782476 : [(48549 ^ _782476) ^ [] : [hAPP(_1759156, 48543 ^ [_1759148, _1759150, _1759152, _1759154, _1759156]) = c_Groups_Ozero__class_Ozero(_1759148)], (48547 ^ _782476) ^ [] : [hBOOL(hAPP(_1759154, 48543 ^ [_1759148, _1759150, _1759152, _1759154, _1759156]))], (48545 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759150), 48543 ^ [_1759148, _1759150, _1759152, _1759154, _1759156]), hAPP(c_List_Oset(_1759150), _1759152))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1759148), hAPP(hAPP(c_List_Omap(_1759150, _1759148), _1759156), hAPP(c_List_Ofilter(_1759150, _1759154), _1759152))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1759148), hAPP(hAPP(c_List_Omap(_1759150, _1759148), _1759156), _1759152)))], (36340 ^ _782476) ^ [_1468231, _1468233] : [-(_1468231 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1468231, _1468233) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1468231), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1468233)))], (17005 ^ _782476) ^ [_1104580, _1104582, _1104584, _1104586, _1104588] : [class_Groups_Ocomm__monoid__add(_1104580), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104582), _1104584)), -(hBOOL(hAPP(hAPP(c_member(_1104582), _1104586), _1104584))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104582, _1104580), _1104588), hAPP(hAPP(c_Set_Oinsert(_1104582), _1104586), _1104584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104580), hAPP(_1104588, _1104586)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104582, _1104580), _1104588), _1104584)))], (35022 ^ _782476) ^ [_1444751] : [class_Int_Onumber__ring(_1444751), -(c_Int_Oiszero(_1444751, hAPP(c_Int_Onumber__class_Onumber__of(_1444751), c_Int_OPls)))], (4936 ^ _782476) ^ [_857818, _857820, _857822, _857824, _857826, _857828] : [-(c_Relation_OImage(_857828, _857824, _857820) = c_Relation_OImage(_857826, _857822, _857818)), _857828 = _857826, _857824 = _857822, _857820 = _857818], (48286 ^ _782476) ^ [_1753858, _1753860] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753858), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753858))), _1753860))), -(c_List_Otranspose(_1753858, c_List_Otranspose(_1753858, _1753860)) = c_List_OtakeWhile(tc_List_Olist(_1753858), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1753858)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753858), tc_List_Olist(_1753858), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1753858))), _1753860))], (27289 ^ _782476) ^ [_1298299, _1298301] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1298299), hAPP(c_Nat_OSuc, _1298301)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298301), 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)), _1298301)), _1298299))], (39263 ^ _782476) ^ [_1539011, _1539013, _1539015] : [c_Wellfounded_Owf(_1539011, _1539013), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539011, _1539011)), hAPP(hAPP(c_Product__Type_OPair(_1539011, _1539011), _1539015), _1539015)), _1539013))], (26942 ^ _782476) ^ [_1291282, _1291284, _1291286, _1291288] : [class_Orderings_Olinorder(_1291282), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291282), _1291284), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291282), _1291286), _1291288)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291282), _1291286), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291282), _1291284), _1291288)))], (23865 ^ _782476) ^ [_1230160, _1230162] : [-(_1230160 = hAPP(c_Int_Onat, _1230162)), 23868 ^ _782476 : [(23871 ^ _782476) ^ [] : [_1230162 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230160)], (23869 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230162)))]], 23872 ^ _782476 : [(23875 ^ _782476) ^ [] : [_1230160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23873 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230162))]]], (41036 ^ _782476) ^ [_1584689, _1584691, _1584693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584689, _1584689), tc_HOL_Obool)), _1584691), hAPP(hAPP(c_Product__Type_OSigma(_1584689, _1584689), _1584693), hAPP(c_COMBK(tc_fun(_1584689, tc_HOL_Obool), _1584689), _1584693)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584689, _1584689), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584689, _1584691)), hAPP(hAPP(c_Product__Type_OSigma(_1584689, _1584689), _1584693), hAPP(c_COMBK(tc_fun(_1584689, tc_HOL_Obool), _1584689), _1584693)))))], (49603 ^ _782476) ^ [_1783146, _1783148, _1783150, _1783152, _1783154] : [hBOOL(hAPP(hAPP(c_member(_1783146), _1783148), hAPP(c_Set_Oimage(_1783150, _1783146, _1783152), _1783154))), -(hBOOL(hAPP(hAPP(c_member(_1783150), hAPP(c_Hilbert__Choice_Oinv__into(_1783150, _1783146, _1783154, _1783152), _1783148)), _1783154)))], (11868 ^ _782476) ^ [_998555, _998557, _998559] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998555, tc_HOL_Obool)), _998557), _998559))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998555, tc_HOL_Obool)), _998557), _998559)), -(_998557 = _998559)], (35884 ^ _782476) ^ [_1460310, _1460312, _1460314] : [class_Rings_Olinordered__idom(_1460310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460310), c_Groups_Ozero__class_Ozero(_1460310)), hAPP(hAPP(c_Power_Opower__class_Opower(_1460310), _1460312), 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)))), _1460314))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460310), c_Groups_Ozero__class_Ozero(_1460310)), _1460312)))], (13198 ^ _782476) ^ [_1025527, _1025529, _1025531, _1025533, _1025535] : [hBOOL(hAPP(hAPP(c_member(_1025527), _1025529), hAPP(c_Set_Ovimage(_1025527, _1025531, _1025533), _1025535))), -(hBOOL(hAPP(hAPP(c_member(_1025531), hAPP(_1025533, _1025529)), _1025535)))], (23659 ^ _782476) ^ [_1226898, _1226900] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1226898), _1226900)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226900), _1226898)))], (44504 ^ _782476) ^ [_1669879, _1669881, _1669883, _1669885, _1669887] : [-(hAPP(hAPP(c_List_Ozip(_1669879, _1669881), _1669883), hAPP(hAPP(c_List_Olist_OCons(_1669881), _1669885), _1669887)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1669879, _1669881)), _1669879, c_List_Olist_ONil(tc_prod(_1669879, _1669881)), hAPP(hAPP(c_COMBC(_1669879, tc_fun(tc_List_Olist(_1669879), tc_List_Olist(tc_prod(_1669879, _1669881))), tc_fun(tc_List_Olist(_1669879), tc_List_Olist(tc_prod(_1669879, _1669881)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1669879, _1669881)), tc_List_Olist(tc_prod(_1669879, _1669881))), tc_fun(tc_fun(tc_List_Olist(_1669879), tc_List_Olist(tc_prod(_1669879, _1669881))), tc_fun(tc_List_Olist(_1669879), tc_List_Olist(tc_prod(_1669879, _1669881)))), _1669879), c_COMBB(tc_List_Olist(tc_prod(_1669879, _1669881)), tc_List_Olist(tc_prod(_1669879, _1669881)), tc_List_Olist(_1669879))), hAPP(hAPP(c_COMBB(tc_prod(_1669879, _1669881), tc_fun(tc_List_Olist(tc_prod(_1669879, _1669881)), tc_List_Olist(tc_prod(_1669879, _1669881))), _1669879), c_List_Olist_OCons(tc_prod(_1669879, _1669881))), hAPP(hAPP(c_COMBC(_1669879, _1669881, tc_prod(_1669879, _1669881)), c_Product__Type_OPair(_1669879, _1669881)), _1669885)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669879), tc_List_Olist(_1669881), tc_List_Olist(tc_prod(_1669879, _1669881))), c_List_Ozip(_1669879, _1669881)), _1669887))), _1669883))], (44512 ^ _782476) ^ [_1670248, _1670250, _1670252, _1670254, _1670256] : [-(hAPP(hAPP(c_List_Ozip(_1670248, _1670250), hAPP(hAPP(c_List_Olist_OCons(_1670248), _1670252), _1670254)), _1670256) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1670248, _1670250)), _1670250, c_List_Olist_ONil(tc_prod(_1670248, _1670250)), hAPP(hAPP(c_COMBC(_1670250, tc_fun(tc_List_Olist(_1670250), tc_List_Olist(tc_prod(_1670248, _1670250))), tc_fun(tc_List_Olist(_1670250), tc_List_Olist(tc_prod(_1670248, _1670250)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1670248, _1670250)), tc_List_Olist(tc_prod(_1670248, _1670250))), tc_fun(tc_fun(tc_List_Olist(_1670250), tc_List_Olist(tc_prod(_1670248, _1670250))), tc_fun(tc_List_Olist(_1670250), tc_List_Olist(tc_prod(_1670248, _1670250)))), _1670250), c_COMBB(tc_List_Olist(tc_prod(_1670248, _1670250)), tc_List_Olist(tc_prod(_1670248, _1670250)), tc_List_Olist(_1670250))), hAPP(hAPP(c_COMBB(tc_prod(_1670248, _1670250), tc_fun(tc_List_Olist(tc_prod(_1670248, _1670250)), tc_List_Olist(tc_prod(_1670248, _1670250))), _1670250), c_List_Olist_OCons(tc_prod(_1670248, _1670250))), hAPP(c_Product__Type_OPair(_1670248, _1670250), _1670252)))), hAPP(c_List_Ozip(_1670248, _1670250), _1670254))), _1670256))], (52349 ^ _782476) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (43021 ^ _782476) ^ [_1633071, _1633073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633071), tc_List_Olist(_1633071)), tc_HOL_Obool)), c_List_Olistrel1(_1633071, c_Transitive__Closure_Ortrancl(_1633071, _1633073))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633071), c_List_Olistrel1(_1633071, _1633073)))))], (13520 ^ _782476) ^ [_1032788] : [-(c_Finite__Set_Ofun__left__comm__idem(_1032788, tc_fun(_1032788, tc_HOL_Obool), c_Set_Oinsert(_1032788)))], (18752 ^ _782476) ^ [_1135694, _1135696, _1135698, _1135700] : [class_Rings_Oordered__semiring(_1135694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135694), _1135696), _1135698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135694), c_Groups_Ozero__class_Ozero(_1135694)), _1135700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135694), _1135700), _1135696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135694), _1135700), _1135698))))], (43771 ^ _782476) ^ [_1654878] : [43773 ^ _782476 : [(43776 ^ _782476) ^ [] : [43772 ^ [_1654878] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43774 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43772 ^ [_1654878]), hAPP(c_List_Oset(tc_Nat_Onat), _1654878))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654878) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12878 ^ _782476) ^ [_1018264, _1018266, _1018268, _1018270] : [c_Fun_Oinj__on(_1018264, _1018266, _1018268, c_Orderings_Otop__class_Otop(tc_fun(_1018264, tc_HOL_Obool))), 12881 ^ _782476 : [(12895 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018266), _1018270), hAPP(c_Set_Oimage(_1018264, _1018266, _1018268), c_Orderings_Otop__class_Otop(tc_fun(_1018264, tc_HOL_Obool)))))), 12896 ^ _782476 : [(12897 ^ _782476) ^ [_1018667] : [_1018270 = hAPP(_1018268, _1018667), 12901 ^ _782476 : [(12904 ^ _782476) ^ [] : [12900 ^ [_1018264, _1018266, _1018268, _1018270, _1018667] = _1018667], (12902 ^ _782476) ^ [] : [-(_1018270 = hAPP(_1018268, 12900 ^ [_1018264, _1018266, _1018268, _1018270, _1018667]))]]]]], (12882 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018266), _1018270), hAPP(c_Set_Oimage(_1018264, _1018266, _1018268), c_Orderings_Otop__class_Otop(tc_fun(_1018264, tc_HOL_Obool))))), 12886 ^ _782476 : [(12889 ^ _782476) ^ [_1018529] : [_1018270 = hAPP(_1018268, _1018529), -(_1018529 = 12885 ^ [_1018264, _1018266, _1018268, _1018270])], (12887 ^ _782476) ^ [] : [-(_1018270 = hAPP(_1018268, 12885 ^ [_1018264, _1018266, _1018268, _1018270]))]]]]], (44534 ^ _782476) ^ [_1670958, _1670960, _1670962, _1670964, _1670966] : [_1670958 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1670960, _1670962, _1670964), _1670958), _1670966) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1670962), _1670960), c_List_Olist_ONil(_1670962)), _1670966))], (10333 ^ _782476) ^ [_969757, _969759] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969757, tc_HOL_Obool)), _969759), c_Orderings_Obot__class_Obot(tc_fun(_969757, tc_HOL_Obool))) = _969759)], (18688 ^ _782476) ^ [_1134464, _1134466, _1134468, _1134470, _1134472] : [class_Rings_Oordered__semiring(_1134464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134464), _1134466), _1134468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134464), _1134470), _1134472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134464), c_Groups_Ozero__class_Ozero(_1134464)), _1134466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134464), c_Groups_Ozero__class_Ozero(_1134464)), _1134470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134464), _1134466), _1134470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134464), _1134468), _1134472))))], (52631 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (45388 ^ _782476) ^ [_1690812, _1690814, _1690816] : [-(hAPP(hAPP(c_List_Otake(_1690812), _1690814), hAPP(c_List_Otl(_1690812), _1690816)) = hAPP(c_List_Otl(_1690812), hAPP(hAPP(c_List_Otake(_1690812), hAPP(c_Nat_OSuc, _1690814)), _1690816)))], (46920 ^ _782476) ^ [_1724441, _1724443] : [-(c_List_Oremdups(_1724441, c_List_Oremdups(_1724441, _1724443)) = c_List_Oremdups(_1724441, _1724443))], (48520 ^ _782476) ^ [_1758697, _1758699, _1758701, _1758703, _1758705] : [-(c_List_OdropWhile(_1758697, _1758699, _1758701) = hAPP(hAPP(c_List_Olist_OCons(_1758697), _1758703), _1758705)), _1758701 = hAPP(hAPP(c_List_Oappend(_1758697), c_List_OtakeWhile(_1758697, _1758699, _1758701)), hAPP(hAPP(c_List_Olist_OCons(_1758697), _1758703), _1758705)), -(hBOOL(hAPP(_1758699, _1758703)))], (29040 ^ _782476) ^ [_1333946, _1333948] : [-(_1333946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333948), _1333946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1333948), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1333946), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (45042 ^ _782476) ^ [_1683155, _1683157, _1683159, _1683161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683155), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683157)), _1683159))), -(hAPP(hAPP(c_List_Olist__update(_1683157, _1683159), _1683155), _1683161) = hAPP(hAPP(c_List_Oappend(_1683157), hAPP(hAPP(c_List_Otake(_1683157), _1683155), _1683159)), hAPP(hAPP(c_List_Olist_OCons(_1683157), _1683161), hAPP(hAPP(c_List_Odrop(_1683157), hAPP(c_Nat_OSuc, _1683155)), _1683159))))], (3344 ^ _782476) ^ [_832380, _832382, _832384, _832386, _832388, _832390] : [-(c_List_Olist_Olist__size(_832390, _832386, _832382) = c_List_Olist_Olist__size(_832388, _832384, _832380)), _832390 = _832388, _832386 = _832384, _832382 = _832380], (39523 ^ _782476) ^ [_1545014, _1545016, _1545018] : [-(hAPP(c_Set_Oimage(tc_prod(_1545014, _1545016), _1545016, c_Product__Type_Osnd(_1545014, _1545016)), _1545018) = hAPP(c_Relation_ORange(_1545014, _1545016), _1545018))], (11072 ^ _782476) ^ [_986252, _986254, _986256] : [class_Orderings_Olinorder(_986252), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986252), _986254), _986256))), 11079 ^ _782476 : [(11086 ^ _782476) ^ [] : [_986256 = _986254, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986252), _986256), _986254))], (11080 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986252), _986256), _986254))), -(_986256 = _986254)]]], (22130 ^ _782476) ^ [_1198344, _1198346, _1198348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198344), _1198346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198346), _1198348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198344)), _1198348)))], (21915 ^ _782476) ^ [_1194499, _1194501, _1194503, _1194505] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194499, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21916 ^ [_1194499, _1194501, _1194503, _1194505])), _1194501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194499, 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), 21916 ^ [_1194499, _1194501, _1194503, _1194505]), _1194503))), _1194505), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194499, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194499, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194505))], (12512 ^ _782476) ^ [_1010457, _1010459, _1010461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010457, tc_HOL_Obool)), _1010459), hAPP(_1010461, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010457, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), _1010461)), _1010459))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010457, tc_HOL_Obool), _1010461)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), _1010461), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010457, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010457, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), _1010461)), _1010459))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010457, tc_HOL_Obool), _1010461)))), hAPP(_1010461, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010457, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010457, tc_HOL_Obool), tc_fun(tc_fun(_1010457, tc_HOL_Obool), tc_fun(_1010457, tc_HOL_Obool)), tc_fun(_1010457, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010457, tc_HOL_Obool))), _1010461)), _1010459))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010457, tc_HOL_Obool), _1010461)))))))], (994 ^ _782476) ^ [_797521, _797523, _797525, _797527, _797529, _797531] : [-(c_Relation_Orefl__on(_797529, _797525, _797521)), c_Relation_Orefl__on(_797531, _797527, _797523), _797531 = _797529, _797527 = _797525, _797523 = _797521], (39474 ^ _782476) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (9063 ^ _782476) ^ [_941950, _941952, _941954, _941956] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941950, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_941950, tc_fun(_941950, tc_HOL_Obool), tc_HOL_Obool), c_member(_941950)), _941952)), hAPP(hAPP(c_COMBC(_941950, tc_fun(_941950, tc_HOL_Obool), tc_HOL_Obool), c_member(_941950)), _941954)), _941956)), -(hBOOL(hAPP(hAPP(c_member(_941950), _941956), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941950, tc_HOL_Obool)), _941952), _941954))))], (7708 ^ _782476) ^ [_912734, _912736, _912738, _912740] : [7709 ^ _782476 : [(7712 ^ _782476) ^ [] : [hBOOL(hAPP(_912738, _912736))], (7710 ^ _782476) ^ [] : [hBOOL(hAPP(_912734, _912736))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912740, tc_HOL_Obool)), _912738), _912734), _912736)))], (24538 ^ _782476) ^ [_1241385, _1241387] : [class_Int_Oring__char__0(_1241385), 24541 ^ _782476 : [(24548 ^ _782476) ^ [] : [_1241387 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1241385), _1241387) = c_Groups_Ozero__class_Ozero(_1241385))], (24542 ^ _782476) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1241385), _1241387) = c_Groups_Ozero__class_Ozero(_1241385), -(_1241387 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (18372 ^ _782476) ^ [_1129093, _1129095, _1129097] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129093), _1129095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129097), _1129095), -(_1129093 = _1129097), -(_1129095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17161 ^ _782476) ^ [_1108342, _1108344, _1108346, _1108348, _1108350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108342), _1108344)), -(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), _1108342), _1108346)), _1108348)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108344), _1108346)), _1108350)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1108348), 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), _1108344), _1108342)), _1108346)), _1108350)))], (9095 ^ _782476) ^ [_943384, _943386, _943388, _943390] : [c_Orderings_Otop__class_Otop(tc_fun(_943384, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943386, tc_fun(_943384, tc_HOL_Obool)), _943388), _943390), 9098 ^ _782476 : [(9099 ^ _782476) ^ [_943500] : [hBOOL(hAPP(hAPP(c_member(_943386), _943500), _943388)), -(hAPP(_943390, _943500) = c_Orderings_Otop__class_Otop(tc_fun(_943384, tc_HOL_Obool)))]]], (6881 ^ _782476) ^ [_895179, _895181, _895183] : [hBOOL(hAPP(hAPP(c_member(_895179), _895181), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895179, tc_HOL_Obool)), _895183))), hBOOL(hAPP(hAPP(c_member(_895179), _895181), _895183))], (45114 ^ _782476) ^ [_1684841, _1684843] : [_1684843 = c_List_Olist_ONil(_1684841), -(hAPP(c_List_Orotate1(_1684841), _1684843) = c_List_Olist_ONil(_1684841))], (40057 ^ _782476) ^ [_1561175, _1561177, _1561179, _1561181] : [class_Groups_Ocomm__monoid__mult(_1561175), c_Fun_Oinj__on(_1561177, _1561175, _1561179, _1561181), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561177, _1561175), _1561179), _1561181) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561175, _1561175), c_Fun_Oid(_1561175)), hAPP(c_Set_Oimage(_1561177, _1561175, _1561179), _1561181)))], (23283 ^ _782476) ^ [_1219560, _1219562, _1219564, _1219566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219560), _1219562)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219564), _1219566)), 23290 ^ _782476 : [(23291 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219560), _1219562)), hAPP(c_Finite__Set_Ocard(_1219564), _1219566)))), 23292 ^ _782476 : [(23293 ^ _782476) ^ [_1219771] : [c_Fun_Oinj__on(_1219560, _1219564, _1219771, _1219562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219564, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219560, _1219564, _1219771), _1219562)), _1219566))]]], (23301 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219560), _1219562)), hAPP(c_Finite__Set_Ocard(_1219564), _1219566))), 23305 ^ _782476 : [(23308 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219564, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219560, _1219564, 23304 ^ [_1219560, _1219562, _1219564, _1219566]), _1219562)), _1219566)))], (23306 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1219560, _1219564, 23304 ^ [_1219560, _1219562, _1219564, _1219566], _1219562))]]]]], (39154 ^ _782476) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (13234 ^ _782476) ^ [_1026530, _1026532, _1026534, _1026536] : [hAPP(c_Set_Oimage(_1026530, _1026532, _1026534), c_Orderings_Otop__class_Otop(tc_fun(_1026530, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1026532, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1026530, _1026532, _1026534), hAPP(c_Set_Ovimage(_1026530, _1026532, _1026534), _1026536)) = _1026536)], (24863 ^ _782476) ^ [_1247259, _1247261, _1247263, _1247265] : [class_Groups_Oordered__ab__group__add__abs(_1247259), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247259), hAPP(c_Groups_Oabs__class_Oabs(_1247259), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247261, _1247259), _1247263), _1247265))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247261, _1247259), hAPP(hAPP(c_COMBB(_1247259, _1247259, _1247261), c_Groups_Oabs__class_Oabs(_1247259)), _1247263)), _1247265))))], (49213 ^ _782476) ^ [_1774779, _1774781, _1774783, _1774785] : [-(c_List_Olist__all(_1774779, _1774781, hAPP(hAPP(c_List_Olist_OCons(_1774779), _1774783), _1774785))), hBOOL(hAPP(_1774781, _1774783)), c_List_Olist__all(_1774779, _1774781, _1774785)], (35172 ^ _782476) ^ [_1447482, _1447484] : [c_Int_OBit0(_1447482) = c_Int_OBit0(_1447484), -(_1447482 = _1447484)], (45763 ^ _782476) ^ [_1698594, _1698596, _1698598] : [-(_1698594 = c_List_Olist_ONil(_1698596)), -(c_List_Olast(_1698596, hAPP(hAPP(c_List_Oappend(_1698596), _1698598), _1698594)) = c_List_Olast(_1698596, _1698594))], (50851 ^ _782476) ^ [_1811714, _1811716] : [c_Relation_Oantisym(_1811714, _1811716), -(c_Relation_Oantisym(_1811714, hAPP(c_Relation_Oconverse(_1811714, _1811714), _1811716)))], (37145 ^ _782476) ^ [_1489651, _1489653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489651)), 37148 ^ _782476 : [(37155 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489653))), 37158 ^ _782476 : [(37165 ^ _782476) ^ [] : [-(_1489651 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1489651, _1489653) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489651), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489653))))], (37159 ^ _782476) ^ [] : [_1489651 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1489651, _1489653) = 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)))]]], (37149 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489653)), -(c_Divides_Odivmod__int(_1489651, _1489653) = c_Divides_OposDivAlg(_1489651, _1489653))]]], (23259 ^ _782476) ^ [_1219127, _1219129, _1219131] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219127), _1219129)), -(hBOOL(hAPP(hAPP(c_member(_1219127), _1219131), _1219129))), -(hAPP(c_Finite__Set_Ocard(_1219127), hAPP(hAPP(c_Set_Oinsert(_1219127), _1219131), _1219129)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1219127), _1219129)))], (44358 ^ _782476) ^ [_1667100, _1667102] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667100)), _1667102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1667102 = c_List_Olist_ONil(_1667100))], (44122 ^ _782476) ^ [_1662791, _1662793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1662791), _1662793)), -(c_Nitpick_Ocard_H(_1662791, _1662793) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662791)), c_Hilbert__Choice_OEps(tc_List_Olist(_1662791), hAPP(hAPP(c_COMBS(tc_List_Olist(_1662791), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1662791)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1662791), tc_fun(_1662791, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1662791, tc_HOL_Obool), tc_fun(tc_fun(_1662791, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1662791)), c_fequal), c_List_Oset(_1662791))), _1662793))), c_List_Odistinct(_1662791)))))], (46406 ^ _782476) ^ [_1712770] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712770)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (46976 ^ _782476) ^ [_1725493, _1725495, _1725497, _1725499] : [class_Orderings_Olinorder(_1725493), 46979 ^ _782476 : [(46986 ^ _782476) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725495), _1725499)), -(hBOOL(hAPP(c_List_Odistinct(_1725495), c_List_Olinorder__class_Osort__key(_1725495, _1725493, _1725497, _1725499))))], (46980 ^ _782476) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725495), c_List_Olinorder__class_Osort__key(_1725495, _1725493, _1725497, _1725499))), -(hBOOL(hAPP(c_List_Odistinct(_1725495), _1725499)))]]], (4862 ^ _782476) ^ [_856663, _856665] : [_856665 = _856663, -(c_DSequence_Oempty(_856665) = c_DSequence_Oempty(_856663))], (18970 ^ _782476) ^ [_1139615, _1139617, _1139619] : [class_Groups_Oordered__comm__monoid__add(_1139615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139615), c_Groups_Ozero__class_Ozero(_1139615)), _1139617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139615), c_Groups_Ozero__class_Ozero(_1139615)), _1139619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139615), c_Groups_Ozero__class_Ozero(_1139615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139615), _1139617), _1139619))))], (22574 ^ _782476) ^ [_1205718, _1205720, _1205722] : [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, _1205718)), _1205720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205718)), _1205722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205720), _1205722)))], (49154 ^ _782476) ^ [_1773432, _1773434, _1773436] : [-(hBOOL(hAPP(hAPP(c_member(_1773432), _1773434), hAPP(c_List_Oset(_1773432), _1773436)))), 49155 ^ _782476 : [(49156 ^ _782476) ^ [_1773521, _1773523] : [_1773436 = hAPP(hAPP(c_List_Oappend(_1773432), _1773523), hAPP(hAPP(c_List_Olist_OCons(_1773432), _1773434), _1773521)), -(hBOOL(hAPP(hAPP(c_member(_1773432), _1773434), hAPP(c_List_Oset(_1773432), _1773521))))]]], (19947 ^ _782476) ^ [_1156915, _1156917, _1156919, _1156921, _1156923] : [class_Rings_Olinordered__semiring__strict(_1156915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156915), _1156917), _1156919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156915), _1156921), _1156923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156915), c_Groups_Ozero__class_Ozero(_1156915)), _1156917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156915), c_Groups_Ozero__class_Ozero(_1156915)), _1156921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156915), _1156917), _1156921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156915), _1156919), _1156923))))], (51361 ^ _782476) ^ [_1821543] : [-(c_Quickcheck_Obeyond(_1821543, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (8579 ^ _782476) ^ [_931477, _931479, _931481, _931483] : [class_Lattices_Osemilattice__inf(_931477), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931477), _931479), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931477), _931481), _931483)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931477), _931481), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931477), _931479), _931483)))], (662 ^ _782476) ^ [_792585, _792587] : [-(c_List_Onat__list(_792585)), _792587 = _792585, c_List_Onat__list(_792587)], (19969 ^ _782476) ^ [_1157338, _1157340, _1157342, _1157344, _1157346] : [class_Rings_Olinordered__semiring__strict(_1157338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157338), _1157340), _1157342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157338), _1157344), _1157346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157338), c_Groups_Ozero__class_Ozero(_1157338)), _1157340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157338), c_Groups_Ozero__class_Ozero(_1157338)), _1157344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157338), _1157340), _1157344)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157338), _1157342), _1157346))))], (43257 ^ _782476) ^ [_1640422, _1640424, _1640426, _1640428] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640422)), hAPP(hAPP(c_List_Olist_OCons(_1640422), _1640424), _1640426)), c_List_Olists(_1640422, _1640428))), 43260 ^ _782476 : [(43263 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640422)), _1640426), c_List_Olists(_1640422, _1640428))))], (43261 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640422), _1640424), _1640428)))]]], (39586 ^ _782476) ^ [_1546910, _1546912, _1546914] : [c_Wellfounded_Owf(_1546910, _1546912), c_Wellfounded_Owf(_1546910, _1546914), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546910, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1546910, _1546910), _1546912)), hAPP(c_Relation_ORange(_1546910, _1546910), _1546914)) = c_Orderings_Obot__class_Obot(tc_fun(_1546910, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1546910, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546910, _1546910), tc_HOL_Obool)), _1546912), _1546914)))], (29672 ^ _782476) ^ [_1345519, _1345521, _1345523, _1345525] : [class_Fields_Olinordered__field__inverse__zero(_1345519), 29675 ^ _782476 : [(29676 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345521), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345519), _1345523), _1345525))), 29679 ^ _782476 : [(29686 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), c_Groups_Ozero__class_Ozero(_1345519)), _1345525))), 29689 ^ _782476 : [(29696 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), _1345525), c_Groups_Ozero__class_Ozero(_1345519)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345521), c_Groups_Ozero__class_Ozero(_1345519))))], (29690 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), _1345525), c_Groups_Ozero__class_Ozero(_1345519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345519), _1345521), _1345525))))]]], (29680 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), c_Groups_Ozero__class_Ozero(_1345519)), _1345525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345519), _1345521), _1345525)), _1345523)))]]], (29702 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345521), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345519), _1345523), _1345525)))), 29705 ^ _782476 : [(29708 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345519), _1345521), _1345525)), _1345523))], (29706 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), c_Groups_Ozero__class_Ozero(_1345519)), _1345525)))]], 29709 ^ _782476 : [(29712 ^ _782476) ^ [] : [29713 ^ _782476 : [(29716 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345519), _1345521), _1345525)))], (29714 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), _1345525), c_Groups_Ozero__class_Ozero(_1345519))))]], 29717 ^ _782476 : [(29720 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345519), _1345521), c_Groups_Ozero__class_Ozero(_1345519)))], (29718 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345519), _1345525), c_Groups_Ozero__class_Ozero(_1345519)))]]], (29710 ^ 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[-(hAPP(c_Set_OPow(_979162), c_Orderings_Obot__class_Obot(tc_fun(_979162, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_979162, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_979162, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979162, tc_HOL_Obool), tc_HOL_Obool))))], (27697 ^ _782476) ^ [_1306240, _1306242, _1306244] : [class_Orderings_Olinorder(_1306240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306240), _1306242)), -(_1306244 = c_Orderings_Obot__class_Obot(tc_fun(_1306240, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306240, tc_HOL_Obool)), _1306244), _1306242)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306240), c_Big__Operators_Olinorder__class_OMax(_1306240, _1306244)), c_Big__Operators_Olinorder__class_OMax(_1306240, _1306242)) = c_Big__Operators_Olinorder__class_OMax(_1306240, _1306242))], (44416 ^ _782476) ^ [_1668144, _1668146] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668144), tc_List_Olist(_1668144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668144), tc_List_Olist(_1668144)), c_List_Olist_ONil(_1668144)), c_List_Olist_ONil(_1668144))), c_List_Olistrel(_1668144, _1668146))))], (3306 ^ _782476) ^ [_831781, _831783, _831785, _831787, _831789, _831791, _831793, _831795] : [-(c_Nitpick_Osetsum_H(_831795, _831791, _831787, _831783) = c_Nitpick_Osetsum_H(_831793, _831789, _831785, _831781)), _831795 = _831793, _831791 = _831789, _831787 = _831785, _831783 = _831781], (31435 ^ _782476) ^ [_1377231, _1377233, _1377235, _1377237, _1377239, _1377241, _1377243, _1377245] : [class_Groups_Ocomm__monoid__mult(_1377231), c_Fun_Oinj__on(_1377233, _1377235, _1377237, _1377239), _1377241 = hAPP(c_Set_Oimage(_1377233, _1377235, _1377237), _1377239), 31449 ^ _782476 : [(31452 ^ _782476) ^ [] : [hAPP(_1377243, 31448 ^ [_1377231, _1377233, _1377235, _1377237, _1377239, _1377241, _1377243, _1377245]) = hAPP(hAPP(c_Fun_Ocomp(_1377235, _1377231, _1377233, _1377245), _1377237), 31448 ^ [_1377231, _1377233, _1377235, _1377237, _1377239, _1377241, _1377243, _1377245])], (31450 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377233), 31448 ^ [_1377231, _1377233, _1377235, _1377237, _1377239, _1377241, _1377243, _1377245]), _1377239)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377235, _1377231), _1377245), _1377241) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377233, _1377231), _1377243), _1377239))], (8695 ^ _782476) ^ [_933834, _933836, _933838, _933840, _933842] : [hAPP(c_Set_Oimage(_933834, _933836, _933838), _933840) = _933842, -(hAPP(c_Set_Oimage(tc_fun(_933834, tc_HOL_Obool), tc_fun(_933836, tc_HOL_Obool), c_Set_Oimage(_933834, _933836, _933838)), hAPP(c_Set_OPow(_933834), _933840)) = hAPP(c_Set_OPow(_933836), _933842))], (9340 ^ _782476) ^ [_949746, _949748, _949750] : [class_Orderings_Oorder(_949746), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949746, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_949746), _949748)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949746, _949748, _949750)) = c_Orderings_Obot__class_Obot(tc_fun(_949746, tc_HOL_Obool)))], (15009 ^ _782476) ^ [_1062691, _1062693, _1062695] : [class_Lattices_Olattice(_1062691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062691), _1062693)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062691), _1062695)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062691, tc_HOL_Obool)), _1062693), _1062695) = c_Orderings_Obot__class_Obot(tc_fun(_1062691, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062691), c_Big__Operators_Olattice__class_OInf__fin(_1062691, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062691, tc_HOL_Obool)), _1062693), _1062695))), c_Big__Operators_Olattice__class_OInf__fin(_1062691, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062691, tc_HOL_Obool)), _1062693), _1062695))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062691), c_Big__Operators_Olattice__class_OInf__fin(_1062691, _1062693)), c_Big__Operators_Olattice__class_OInf__fin(_1062691, _1062695)))], (44270 ^ _782476) ^ [_1665599, _1665601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665599), _1665601)), -(c_List_Oupto(_1665601, _1665599) = c_List_Olist_ONil(tc_Int_Oint))], (49342 ^ _782476) ^ [] : [-(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))))], (8663 ^ _782476) ^ [_933033, _933035, _933037, _933039] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933033, tc_HOL_Obool)), _933035), _933037), _933039)), -(hBOOL(hAPP(_933035, _933039)))], (7173 ^ _782476) ^ [_901685, _901687, _901689, _901691, _901693] : [hBOOL(hAPP(hAPP(c_member(_901685), _901687), _901689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901691, tc_HOL_Obool)), hAPP(_901693, _901687)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_901685, tc_fun(_901691, tc_HOL_Obool)), _901689), _901693))))], (32674 ^ _782476) ^ [_1401173, _1401175, _1401177] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401173), _1401175)), _1401177) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401173), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401175), _1401177))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401173), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401175, _1401177))), _1401177)))], (16681 ^ _782476) ^ [_1096866, _1096868, _1096870, _1096872] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096866), 16684 ^ _782476 : [(16691 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096866), _1096868), _1096872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096866), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096866), _1096868), _1096870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096866), _1096872), _1096870))))], (16685 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096866), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096866), _1096868), _1096870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096866), _1096872), _1096870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096866), _1096868), _1096872)))]]], (39931 ^ _782476) ^ [_1556733, _1556735, _1556737, _1556739, _1556741, _1556743] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1556733, _1556735), hAPP(hAPP(c_Set_Oinsert(_1556733), _1556737), _1556739)), hAPP(c_COMBK(tc_fun(_1556735, tc_HOL_Obool), _1556733), hAPP(hAPP(c_Set_Oinsert(_1556735), _1556741), _1556743))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1556733, _1556735)), hAPP(hAPP(c_Product__Type_OPair(_1556733, _1556735), _1556737), _1556741)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556733, _1556735), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1556733, _1556735), _1556739), hAPP(c_COMBK(tc_fun(_1556735, tc_HOL_Obool), _1556733), hAPP(hAPP(c_Set_Oinsert(_1556735), _1556741), _1556743)))), hAPP(hAPP(c_Product__Type_OSigma(_1556733, _1556735), hAPP(hAPP(c_Set_Oinsert(_1556733), _1556737), _1556739)), hAPP(c_COMBK(tc_fun(_1556735, tc_HOL_Obool), _1556733), _1556743)))))], (23027 ^ _782476) ^ [_1214403] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214403), c_Orderings_Otop__class_Otop(tc_fun(_1214403, 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(_1214403), c_Orderings_Otop__class_Otop(tc_fun(_1214403, tc_HOL_Obool))))))], (29586 ^ _782476) ^ [_1343940, _1343942, _1343944, _1343946] : [class_Rings_Olinordered__semidom(_1343940), hAPP(hAPP(c_Power_Opower__class_Opower(_1343940), _1343942), _1343944) = hAPP(hAPP(c_Power_Opower__class_Opower(_1343940), _1343946), _1343944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343940), c_Groups_Ozero__class_Ozero(_1343940)), _1343942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343940), c_Groups_Ozero__class_Ozero(_1343940)), _1343946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1343944)), -(_1343942 = _1343946)], (51717 ^ _782476) ^ [_1830296, _1830298, _1830300, _1830302] : [class_Divides_Osemiring__div(_1830296), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830296), _1830298), _1830300)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830296), _1830302), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830296), _1830300), _1830298)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830296), _1830302), _1830300)), _1830298))], (4748 ^ _782476) ^ [_854850, _854852, _854854, _854856] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854856, _854852) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854854, _854850)), _854856 = _854854, _854852 = _854850], (48204 ^ _782476) ^ [_1752007, _1752009, _1752011] : [-(hAPP(c_List_Orev(_1752007), hAPP(hAPP(c_List_Odrop(_1752007), _1752009), _1752011)) = hAPP(hAPP(c_List_Otake(_1752007), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752007)), _1752011)), _1752009)), hAPP(c_List_Orev(_1752007), _1752011)))], (23540 ^ _782476) ^ [_1224943, _1224945, _1224947, _1224949, _1224951] : [class_Groups_Oordered__ab__group__add(_1224943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224945), _1224947)), 23550 ^ _782476 : [(23553 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224943), c_Groups_Ozero__class_Ozero(_1224943)), hAPP(_1224949, 23549 ^ [_1224943, _1224945, _1224947, _1224949, _1224951])))], (23551 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1224945), 23549 ^ [_1224943, _1224945, _1224947, _1224949, _1224951]), _1224947)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224945, _1224943), _1224949), _1224947) = c_Groups_Ozero__class_Ozero(_1224943), hBOOL(hAPP(hAPP(c_member(_1224945), _1224951), _1224947)), -(hAPP(_1224949, _1224951) = c_Groups_Ozero__class_Ozero(_1224943))], (29978 ^ _782476) ^ [_1351272, _1351274, _1351276] : [class_Fields_Olinordered__field(_1351272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351272), _1351274), c_Groups_Ozero__class_Ozero(_1351272))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351272), c_Groups_Ozero__class_Ozero(_1351272)), _1351276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351272), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351272), _1351274), _1351276)), c_Groups_Ozero__class_Ozero(_1351272))))], (31974 ^ _782476) ^ [_1388208, _1388210, _1388212, _1388214] : [class_Divides_Oring__div(_1388208), -(c_Divides_Odiv__class_Omod(_1388208, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388208), _1388210), _1388212), _1388214) = c_Divides_Odiv__class_Omod(_1388208, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388208), c_Divides_Odiv__class_Omod(_1388208, _1388210, _1388214)), c_Divides_Odiv__class_Omod(_1388208, _1388212, _1388214)), _1388214))], (16421 ^ _782476) ^ [_1091811, _1091813, _1091815, _1091817] : [class_Groups_Ocancel__semigroup__add(_1091811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091811), _1091813), _1091815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091811), _1091817), _1091815), -(_1091813 = _1091817)], (52673 ^ _782476) ^ [_1843465, _1843467] : [-(hAPP(c_COMBI(_1843465), _1843467) = _1843467)], (27022 ^ _782476) ^ [_1293229, _1293231, _1293233, _1293235, _1293237] : [class_Orderings_Olinorder(_1293229), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293229, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293229, _1293231), _1293233)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293229, _1293235), _1293237)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293229, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293229), _1293231), _1293235)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293229), _1293233), _1293237)))], (20987 ^ _782476) ^ [_1176977, _1176979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176977), _1176979)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1176979, _1176977) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (40802 ^ _782476) ^ [_1579932, _1579934, _1579936, _1579938, _1579940, _1579942, _1579944] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579932, _1579934, _1579936, _1579938), _1579940), _1579942), _1579944) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579934, _1579936, _1579938), _1579942), hAPP(_1579940, _1579944)))], (23059 ^ _782476) ^ [_1215187, _1215189, _1215191, _1215193, _1215195, _1215197] : [c_Fun_Oinj__on(_1215187, _1215189, _1215191, _1215193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215189, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215187, _1215189, _1215191), _1215193)), _1215195)), c_Fun_Oinj__on(_1215189, _1215187, _1215197, _1215195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215187, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215189, _1215187, _1215197), _1215195)), _1215193)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215187), _1215193)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215189), _1215195)), -(hAPP(c_Finite__Set_Ocard(_1215187), _1215193) = hAPP(c_Finite__Set_Ocard(_1215189), _1215195))], (2784 ^ _782476) ^ [_823634, _823636, _823638, _823640, _823642, _823644, _823646, _823648] : [-(c_Random_Oiterate(_823648, _823644, _823640, _823636) = c_Random_Oiterate(_823646, _823642, _823638, _823634)), _823648 = _823646, _823644 = _823642, _823640 = _823638, _823636 = _823634], (43219 ^ _782476) ^ [_1639396, _1639398, _1639400, _1639402, _1639404] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639396), tc_List_Olist(_1639396))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639396), tc_List_Olist(_1639396)), hAPP(hAPP(c_List_Olist_OCons(_1639396), _1639398), _1639400)), _1639402)), c_List_Olistrel(_1639396, _1639404))), 43224 ^ _782476 : [(43229 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639396), tc_List_Olist(_1639396))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639396), tc_List_Olist(_1639396)), _1639400), 43223 ^ [_1639396, _1639398, _1639400, _1639402, _1639404])), c_List_Olistrel(_1639396, _1639404))))], (43227 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639396, _1639396)), hAPP(hAPP(c_Product__Type_OPair(_1639396, _1639396), _1639398), 43222 ^ [_1639396, _1639398, _1639400, _1639402, _1639404])), _1639404)))], (43225 ^ _782476) ^ [] : [-(_1639402 = hAPP(hAPP(c_List_Olist_OCons(_1639396), 43222 ^ [_1639396, _1639398, _1639400, _1639402, _1639404]), 43223 ^ [_1639396, _1639398, _1639400, _1639402, _1639404]))]]], (7774 ^ _782476) ^ [_914073, _914075, _914077, _914079] : [class_Lattices_Olattice(_914073), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914073), _914075), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914073), _914077), _914079)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914073), _914077), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914073), _914075), _914079)))], (5156 ^ _782476) ^ [_861224, _861226, _861228, _861230, _861232, _861234, _861236, _861238, _861240, _861242] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861242, _861238, _861234, _861230, _861226) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861240, _861236, _861232, _861228, _861224)), _861242 = _861240, _861238 = _861236, _861234 = _861232, _861230 = _861228, _861226 = _861224], (15831 ^ _782476) ^ [_1078695, _1078697, _1078699] : [class_Lattices_Oab__semigroup__idem__mult(_1078695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078695), _1078697)), -(_1078697 = c_Orderings_Obot__class_Obot(tc_fun(_1078695, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078695), _1078699)), -(_1078699 = c_Orderings_Obot__class_Obot(tc_fun(_1078695, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1078695, c_Groups_Otimes__class_Otimes(_1078695)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078695, tc_HOL_Obool)), _1078697), _1078699)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078695), hAPP(c_Finite__Set_Ofold1(_1078695, c_Groups_Otimes__class_Otimes(_1078695)), _1078697)), hAPP(c_Finite__Set_Ofold1(_1078695, c_Groups_Otimes__class_Otimes(_1078695)), _1078699)))], (39100 ^ _782476) ^ [_1535981, _1535983, _1535985] : [c_Wellfounded_Owf(_1535981, _1535983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535981, _1535981), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1535981, _1535981, _1535981), _1535983), _1535985)), _1535983)), -(c_FunDef_Oreduction__pair(_1535981, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1535981, _1535981), tc_HOL_Obool), tc_fun(tc_prod(_1535981, _1535981), tc_HOL_Obool)), _1535983), _1535985)))], (4590 ^ _782476) ^ [_852219, _852221] : [_852221 = _852219, -(c_List_Olist_ONil(_852221) = c_List_Olist_ONil(_852219))], (39628 ^ _782476) ^ [_1547807, _1547809, _1547811, _1547813] : [-(hAPP(c_Relation_ODomain(_1547807, _1547809), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1547807, _1547809), tc_HOL_Obool)), _1547811), _1547813)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547807, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547807, _1547809), _1547811)), hAPP(c_Relation_ODomain(_1547807, _1547809), _1547813)))], (20205 ^ _782476) ^ [_1161826, _1161828, _1161830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161826), _1161828)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161830), _1161828))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161826), _1161830)))], (23996 ^ _782476) ^ [_1232363, _1232365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232363), _1232365)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232365), _1232363)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232365)), hAPP(c_Int_Onat, _1232363)))], (10601 ^ _782476) ^ [_976215, _976217, _976219, _976221] : [-(hBOOL(hAPP(hAPP(c_member(_976215), _976217), _976219))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976215, tc_HOL_Obool)), _976219), hAPP(hAPP(c_Set_Oinsert(_976215), _976217), _976221)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976215, tc_HOL_Obool)), _976219), _976221))], (32646 ^ _782476) ^ [_1400657, _1400659] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400657), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400659)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400657, _1400659)))], (41004 ^ _782476) ^ [_1583891, _1583893, _1583895, _1583897, _1583899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583891, _1583891)), hAPP(hAPP(c_Product__Type_OPair(_1583891, _1583891), _1583893), _1583895)), _1583897)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583891, _1583891)), hAPP(hAPP(c_Product__Type_OPair(_1583891, _1583891), _1583895), _1583899)), c_Transitive__Closure_Otrancl(_1583891, _1583897))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583891, _1583891)), hAPP(hAPP(c_Product__Type_OPair(_1583891, _1583891), _1583893), _1583899)), c_Transitive__Closure_Otrancl(_1583891, _1583897))))], (16645 ^ _782476) ^ [_1096169, _1096171, _1096173, _1096175] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096169), _1096171), _1096173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096169), _1096175), _1096171)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096169), _1096175), _1096173))))], (35254 ^ _782476) ^ [_1448753, _1448755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448753), _1448755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448753)), c_Int_OBit1(_1448755))))], (33986 ^ _782476) ^ [_1426835, _1426837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426835), _1426837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426835)), c_Int_OBit1(_1426837))))], (47112 ^ _782476) ^ [_1728910, _1728912, _1728914] : [-(c_Enum_On__lists(_1728910, hAPP(c_Nat_OSuc, _1728912), _1728914) = c_List_Oconcat(tc_List_Olist(_1728910), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728910), tc_List_Olist(tc_List_Olist(_1728910))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728910), tc_List_Olist(_1728910), tc_List_Olist(tc_List_Olist(_1728910))), hAPP(hAPP(c_COMBB(tc_fun(_1728910, tc_List_Olist(_1728910)), tc_fun(tc_List_Olist(_1728910), tc_List_Olist(tc_List_Olist(_1728910))), tc_List_Olist(_1728910)), c_List_Omap(_1728910, tc_List_Olist(_1728910))), hAPP(c_COMBC(_1728910, tc_List_Olist(_1728910), tc_List_Olist(_1728910)), c_List_Olist_OCons(_1728910)))), _1728914)), c_Enum_On__lists(_1728910, _1728912, _1728914))))], (47218 ^ _782476) ^ [_1731422, _1731424, _1731426] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1731422), tc_List_Olist(_1731422)), c_List_Opartition(_1731422, _1731424, _1731426)) = hAPP(c_List_Ofilter(_1731422, _1731424), _1731426))], (51747 ^ _782476) ^ [_1830899, _1830901, _1830903, _1830905, _1830907] : [class_Divides_Osemiring__div(_1830899), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830899), _1830901), _1830903)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830899), _1830905), _1830907)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830899), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830899), _1830903), _1830901)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830899), _1830907), _1830905)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830899), _1830903), _1830907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830899), _1830901), _1830905)))], (22987 ^ _782476) ^ [_1213586, _1213588, _1213590, _1213592] : [class_Rings_Osemiring__1(_1213586), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213588, _1213586), hAPP(c_COMBK(_1213586, _1213588), _1213590)), _1213592) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213586), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1213586), hAPP(c_Finite__Set_Ocard(_1213588), _1213592))), _1213590))], (35116 ^ _782476) ^ [_1446432, _1446434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446432)), c_Int_OBit0(_1446434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446432), _1446434)))], (14757 ^ _782476) ^ [_1057983, _1057985] : [class_Lattices_Olattice(_1057983), -(c_Big__Operators_Olattice__class_OInf__fin(_1057983, hAPP(hAPP(c_Set_Oinsert(_1057983), _1057985), c_Orderings_Obot__class_Obot(tc_fun(_1057983, tc_HOL_Obool)))) = _1057985)], (3458 ^ _782476) ^ [_834115, _834117] : [_834117 = _834115, -(c_Finite__Set_Ocard(_834117) = c_Finite__Set_Ocard(_834115))], (18808 ^ _782476) ^ [_1136742, _1136744, _1136746] : [class_Rings_Oordered__cancel__semiring(_1136742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136742), c_Groups_Ozero__class_Ozero(_1136742)), _1136744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136742), _1136746), c_Groups_Ozero__class_Ozero(_1136742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136742), _1136746), _1136744)), c_Groups_Ozero__class_Ozero(_1136742))))], (644 ^ _782476) ^ [_792316, _792318, _792320, _792322, _792324, _792326] : [-(c_Finite__Set_Ofun__left__comm(_792324, _792320, _792316)), c_Finite__Set_Ofun__left__comm(_792326, _792322, _792318), _792326 = _792324, _792322 = _792320, _792318 = _792316], (16655 ^ _782476) ^ [_1096364, _1096366, _1096368, _1096370] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096364), _1096366), _1096368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096364), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096364), _1096366), _1096370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096364), _1096368), _1096370))))], (21217 ^ _782476) ^ [_1180897, _1180899, _1180901] : [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), _1180897), _1180899)), _1180901)), 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)), _1180901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9229 ^ _782476) ^ [_946986, _946988, _946990, _946992] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946986, tc_fun(_946988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946986, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946988, tc_HOL_Obool), tc_fun(_946988, tc_HOL_Obool), _946986), hAPP(c_COMBC(_946988, tc_fun(_946988, tc_HOL_Obool), tc_HOL_Obool), c_member(_946988))), _946990)), _946992)), -(hBOOL(hAPP(hAPP(c_member(_946988), _946992), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946986, tc_fun(_946988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946986, tc_HOL_Obool))), _946990))))], (45645 ^ _782476) ^ [_1696507, _1696509, _1696511, _1696513, _1696515] : [class_Orderings_Olinorder(_1696507), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696509)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696509, _1696507, _1696511), _1696513), _1696515)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696509)), _1696515)))], (1092 ^ _782476) ^ [_799074, _799076, _799078, _799080, _799082, _799084] : [-(c_List_Olist__all(_799082, _799078, _799074)), c_List_Olist__all(_799084, _799080, _799076), _799084 = _799082, _799080 = _799078, _799076 = _799074], (52595 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (8738 ^ _782476) ^ [_934760, _934762, _934764, _934766, _934768] : [-(hBOOL(hAPP(hAPP(c_member(_934760), _934762), hAPP(c_Set_Oimage(_934764, _934760, _934766), _934768)))), 8739 ^ _782476 : [(8740 ^ _782476) ^ [_934830] : [hBOOL(hAPP(hAPP(c_member(_934764), _934830), _934768)), _934762 = hAPP(_934766, _934830)]]], (33220 ^ _782476) ^ [_1412474, _1412476] : [class_Int_Onumber__ring(_1412474), -(hBOOL(hAPP(hAPP(c_member(_1412474), hAPP(c_Int_Onumber__class_Onumber__of(_1412474), _1412476)), c_Int_Oring__1__class_OInts(_1412474))))], (10009 ^ _782476) ^ [_963051, _963053, _963055, _963057] : [class_Orderings_Oorder(_963051), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963051, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_963051, _963053, _963055)), c_SetInterval_Oord__class_OgreaterThanAtMost(_963051, _963055, _963057)) = c_Orderings_Obot__class_Obot(tc_fun(_963051, tc_HOL_Obool)))], (7007 ^ _782476) ^ [_897786, _897788, _897790] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897786, tc_HOL_Obool)), _897788), hAPP(c_Set_OPow(_897786), _897790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897786, tc_HOL_Obool)), _897788), _897790)))], (22840 ^ _782476) ^ [_1210859, _1210861, _1210863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1210859), _1210861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1210859, tc_HOL_Obool)), _1210863), _1210861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1210859), _1210863)), hAPP(c_Finite__Set_Ocard(_1210859), _1210861))))], (31231 ^ _782476) ^ [_1373423, _1373425, _1373427, _1373429] : [class_Divides_Osemiring__div(_1373423), -(_1373425 = c_Groups_Ozero__class_Ozero(_1373423)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373423), _1373427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373423), _1373429), _1373425))), _1373425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373423), _1373429), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373423), _1373427), _1373425)))], (12272 ^ _782476) ^ [_1005292, _1005294, _1005296] : [class_Orderings_Oord(_1005292), 12275 ^ _782476 : [(12282 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005292), _1005296), _1005294)), -(hBOOL(hAPP(hAPP(c_member(_1005292), _1005294), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1005292), _1005296))))], (12276 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1005292), _1005294), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1005292), _1005296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005292), _1005296), _1005294)))]]], (16037 ^ _782476) ^ [_1082978, _1082980, _1082982, _1082984, _1082986] : [class_Rings_Osemiring__0(_1082978), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082978), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082980, _1082978), _1082982), _1082984)), _1082986) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082980, _1082978), hAPP(hAPP(c_COMBC(_1082980, _1082978, _1082978), hAPP(hAPP(c_COMBB(_1082978, tc_fun(_1082978, _1082978), _1082980), c_Groups_Otimes__class_Otimes(_1082978)), _1082982)), _1082986)), _1082984))], (52393 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (3002 ^ _782476) ^ [_826995, _826997] : [_826997 = _826995, -(c_Nitpick_ORep__Frac(_826997) = c_Nitpick_ORep__Frac(_826995))], (47485 ^ _782476) ^ [_1738024, _1738026] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1738024, _1738026) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1738024), hAPP(c_Nat_OSuc, _1738026))))], (46898 ^ _782476) ^ [_1724033, _1724035] : [_1724035 = c_List_Olist_ONil(_1724033), -(c_List_Olist_ONil(_1724033) = c_List_Oremdups(_1724033, _1724035))], (8495 ^ _782476) ^ [_929744, _929746, _929748, _929750] : [hBOOL(hAPP(hAPP(c_member(_929744), _929746), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929744, tc_HOL_Obool)), _929748), _929750))), 8498 ^ _782476 : [(8501 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929744), _929746), _929750)))], (8499 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929744), _929746), _929748)))]]], (11092 ^ _782476) ^ [_986511, _986513, _986515] : [class_Orderings_Olinorder(_986511), -(_986513 = _986515), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986511), _986513), _986515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986511), _986515), _986513)))], (4788 ^ _782476) ^ [_855454, _855456, _855458, _855460, _855462, _855464, _855466, _855468] : [-(c_Product__Type_Oscomp(_855468, _855464, _855460, _855456) = c_Product__Type_Oscomp(_855466, _855462, _855458, _855454)), _855468 = _855466, _855464 = _855462, _855460 = _855458, _855456 = _855454], (16825 ^ _782476) ^ [_1100048, _1100050, _1100052, _1100054, _1100056, _1100058] : [class_Rings_Oring(_1100048), 16828 ^ _782476 : [(16835 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100048), _1100050), _1100056)), _1100052)), _1100054) = _1100058, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), _1100050), _1100052)), _1100054) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), _1100056), _1100052)), _1100058))], (16829 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), _1100050), _1100052)), _1100054) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), _1100056), _1100052)), _1100058), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100048), _1100050), _1100056)), _1100052)), _1100054) = _1100058)]]], (45929 ^ _782476) ^ [_1701512, _1701514, _1701516, _1701518] : [-(hAPP(hAPP(c_List_Omap(_1701512, _1701514), _1701516), hAPP(c_List_Otl(_1701512), _1701518)) = hAPP(c_List_Otl(_1701514), hAPP(hAPP(c_List_Omap(_1701512, _1701514), _1701516), _1701518)))], (46922 ^ _782476) ^ [_1724475, _1724477] : [hBOOL(hAPP(c_List_Odistinct(_1724475), _1724477)), -(c_List_Oremdups(_1724475, _1724477) = _1724477)], (10331 ^ _782476) ^ [_969716, _969718] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969716, tc_HOL_Obool)), _969718), _969718) = c_Orderings_Obot__class_Obot(tc_fun(_969716, tc_HOL_Obool)))], (49416 ^ _782476) ^ [_1778711, _1778713, _1778715, _1778717, _1778719] : [-(_1778711 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778713, _1778715, _1778717, _1778719), _1778711) = c_Lazy__Sequence_Ohb__bind(_1778713, _1778715, hAPP(_1778717, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1778711), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1778713, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778715))), _1778719), _1778711)))], (7141 ^ _782476) ^ [_900941, _900943, _900945, _900947] : [hBOOL(hAPP(hAPP(c_member(_900941), _900943), _900945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900941, tc_HOL_Obool)), _900945), _900947)), -(hBOOL(hAPP(hAPP(c_member(_900941), _900943), _900947)))], (32505 ^ _782476) ^ [_1398056, _1398058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398056)), -(c_SMT_Oz3mod(_1398058, _1398056) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398058, _1398056))], (9045 ^ _782476) ^ [_941276, _941278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941276, tc_HOL_Obool)), _941278), c_Orderings_Otop__class_Otop(tc_fun(_941276, tc_HOL_Obool)))))], (48443 ^ _782476) ^ [_1757223, _1757225, _1757227] : [class_Orderings_Olinorder(_1757223), c_List_Olinorder__class_Osorted(_1757223, _1757225), -(c_List_Olinorder__class_Osorted(_1757223, c_List_OdropWhile(_1757223, _1757227, _1757225)))], (38040 ^ _782476) ^ [_1507830, _1507832, _1507834, _1507836, _1507838, _1507840, _1507842] : [c_Equiv__Relations_Oequiv(_1507830, _1507832, _1507834), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507830, tc_HOL_Obool)), _1507836), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507830), _1507832), _1507834))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507830, tc_HOL_Obool)), _1507838), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507830), _1507832), _1507834))), hBOOL(hAPP(hAPP(c_member(_1507830), _1507840), _1507836)), hBOOL(hAPP(hAPP(c_member(_1507830), _1507842), _1507838)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507830, _1507830)), hAPP(hAPP(c_Product__Type_OPair(_1507830, _1507830), _1507840), _1507842)), _1507834)), -(_1507836 = _1507838)], (52637 ^ _782476) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (40640 ^ _782476) ^ [_1575931, _1575933, _1575935, _1575937, _1575939, _1575941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575931, tc_HOL_Obool)), _1575933), _1575935)), 40646 ^ _782476 : [(40649 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575937, tc_HOL_Obool)), hAPP(_1575939, 40645 ^ [_1575931, _1575933, _1575935, _1575937, _1575939, _1575941])), hAPP(_1575941, 40645 ^ [_1575931, _1575933, _1575935, _1575937, _1575939, _1575941])))], (40647 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575931), 40645 ^ [_1575931, _1575933, _1575935, _1575937, _1575939, _1575941]), _1575933)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575931, _1575937), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575931, _1575937), _1575933), _1575939)), hAPP(hAPP(c_Product__Type_OSigma(_1575931, _1575937), _1575935), _1575941))))], (32012 ^ _782476) ^ [_1388969] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1388969) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35872 ^ _782476) ^ [_1460000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1460000)), -(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), _1460000), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (27877 ^ _782476) ^ [_1309425, _1309427, _1309429] : [class_Orderings_Olinorder(_1309425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309425), _1309427)), 27884 ^ _782476 : [(27891 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309425, tc_HOL_Obool)), _1309427), hAPP(hAPP(c_Set_Oinsert(_1309425), _1309429), c_Orderings_Obot__class_Obot(tc_fun(_1309425, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309425, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1309425, hAPP(hAPP(c_Set_Oinsert(_1309425), _1309429), _1309427)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309425), _1309429), c_Big__Operators_Olinorder__class_OMax(_1309425, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309425, tc_HOL_Obool)), _1309427), hAPP(hAPP(c_Set_Oinsert(_1309425), _1309429), c_Orderings_Obot__class_Obot(tc_fun(_1309425, tc_HOL_Obool)))))))], (27885 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309425, tc_HOL_Obool)), _1309427), hAPP(hAPP(c_Set_Oinsert(_1309425), _1309429), c_Orderings_Obot__class_Obot(tc_fun(_1309425, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309425, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1309425, hAPP(hAPP(c_Set_Oinsert(_1309425), _1309429), _1309427)) = _1309429)]]], (28047 ^ _782476) ^ [_1312925, _1312927, _1312929] : [class_Orderings_Olinorder(_1312925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312925), _1312927)), hBOOL(hAPP(hAPP(c_member(_1312925), _1312929), _1312927)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312925), _1312929), c_Big__Operators_Olattice_OInf__fin(_1312925, c_Orderings_Oord__class_Omin(_1312925), _1312927)) = c_Big__Operators_Olattice_OInf__fin(_1312925, c_Orderings_Oord__class_Omin(_1312925), _1312927))], (38549 ^ _782476) ^ [_1520487, _1520489, _1520491, _1520493, _1520495, _1520497] : [hAPP(c_Product__Type_Oapfst(_1520487, _1520489, _1520491, _1520493), _1520495) = hAPP(c_Product__Type_Oapfst(_1520487, _1520489, _1520491, _1520497), _1520495), -(hAPP(_1520493, hAPP(c_Product__Type_Ofst(_1520487, _1520491), _1520495)) = hAPP(_1520497, hAPP(c_Product__Type_Ofst(_1520487, _1520491), _1520495)))], (36114 ^ _782476) ^ [_1464627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464627))))], (17123 ^ _782476) ^ [_1107389, _1107391, _1107393, _1107395, _1107397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107389), _1107391)), -(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), _1107391), _1107393)), _1107395)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107389), _1107393)), _1107397)) = 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), _1107391), _1107389)), _1107393)), _1107395)), _1107397))], (26032 ^ _782476) ^ [_1275079, _1275081] : [class_Groups_Olinordered__ab__group__add(_1275079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275079), _1275081)), -(_1275081 = c_Orderings_Obot__class_Obot(tc_fun(_1275079, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275079), c_Big__Operators_Olinorder__class_OMin(_1275079, _1275081)) = c_Big__Operators_Olinorder__class_OMax(_1275079, hAPP(c_Set_Oimage(_1275079, _1275079, c_Groups_Ouminus__class_Ouminus(_1275079)), _1275081)))], (45294 ^ _782476) ^ [_1689300, _1689302, _1689304] : [_1689300 = c_List_Olist_ONil(_1689302), -(hAPP(c_List_Ohd(_1689302), hAPP(hAPP(c_List_Oappend(_1689302), _1689300), _1689304)) = hAPP(c_List_Ohd(_1689302), _1689304))], (9873 ^ _782476) ^ [_960123, _960125, _960127, _960129, _960131] : [-(_960123 = c_Orderings_Obot__class_Obot(tc_fun(_960125, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960127, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960125, tc_fun(_960127, tc_HOL_Obool)), _960123), _960129)), _960131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960125, tc_fun(_960127, tc_HOL_Obool)), _960123), hAPP(hAPP(c_COMBC(_960125, tc_fun(_960127, tc_HOL_Obool), tc_fun(_960127, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960127, tc_HOL_Obool), tc_fun(tc_fun(_960127, tc_HOL_Obool), tc_fun(_960127, tc_HOL_Obool)), _960125), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960127, tc_HOL_Obool))), _960129)), _960131)))], (49852 ^ _782476) ^ [_1789536] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1789536) = c_Lazy__Sequence_Osmall__lazy_H(_1789536, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1789536)))], (36324 ^ _782476) ^ [] : [-(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)))))], (8420 ^ _782476) ^ [_928194, _928196, _928198] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928194, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928194, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928194, tc_HOL_Obool), _928196)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928194, tc_HOL_Obool), _928198))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928194, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_928194, tc_HOL_Obool), tc_HOL_Obool)), _928196), _928198)))))], (10926 ^ _782476) ^ [_983863, _983865, _983867, _983869] : [class_Orderings_Olinorder(_983863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983863), _983865), _983867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983863), _983867), _983869)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_983863, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983863, _983865, _983867)), c_SetInterval_Oord__class_OatLeastAtMost(_983863, _983867, _983869)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_983863, _983865, _983869))], (13439 ^ _782476) ^ [_1031408, _1031410, _1031412, _1031414] : [hBOOL(hAPP(hAPP(c_member(_1031408), _1031410), hAPP(c_Set_Oimage(_1031412, _1031408, _1031414), c_Orderings_Otop__class_Otop(tc_fun(_1031412, tc_HOL_Obool))))), -(_1031410 = hAPP(_1031414, 13442 ^ [_1031408, _1031410, _1031412, _1031414]))], (29390 ^ _782476) ^ [_1340163, _1340165, _1340167] : [class_Fields_Ofield__inverse__zero(_1340163), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340163), c_Groups_Oone__class_Oone(_1340163)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340163), _1340165), _1340167)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340163), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340163), c_Groups_Oone__class_Oone(_1340163)), _1340165)), _1340167))], (39054 ^ _782476) ^ [_1534085, _1534087, _1534089, _1534091, _1534093, _1534095, _1534097] : [c_Typedef_Otype__definition(_1534085, _1534087, _1534089, _1534091, _1534093), hBOOL(hAPP(hAPP(c_member(_1534087), _1534095), _1534093)), hBOOL(hAPP(hAPP(c_member(_1534087), _1534097), _1534093)), 39065 ^ _782476 : [(39072 ^ _782476) ^ [] : [_1534095 = _1534097, -(hAPP(_1534091, _1534095) = hAPP(_1534091, _1534097))], (39066 ^ _782476) ^ [] : [hAPP(_1534091, _1534095) = hAPP(_1534091, _1534097), -(_1534095 = _1534097)]]], (10203 ^ _782476) ^ [_967197, _967199, _967201] : [-(hAPP(hAPP(c_Set_Oinsert(_967197), _967199), hAPP(hAPP(c_Set_Oinsert(_967197), _967199), _967201)) = hAPP(hAPP(c_Set_Oinsert(_967197), _967199), _967201))], (43858 ^ _782476) ^ [_1656822, _1656824, _1656826] : [-(hAPP(hAPP(c_List_Olist__update(_1656822, _1656824), _1656826), hAPP(hAPP(c_List_Onth(_1656822), _1656824), _1656826)) = _1656824)], (12990 ^ _782476) ^ [_1020731] : [-(c_Fun_Oinj__on(_1020731, tc_fun(_1020731, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1020731, tc_fun(_1020731, tc_HOL_Obool), tc_fun(_1020731, tc_HOL_Obool)), c_Set_Oinsert(_1020731)), c_Orderings_Obot__class_Obot(tc_fun(_1020731, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1020731, tc_HOL_Obool))))], (25464 ^ _782476) ^ [_1258330, _1258332] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258330)), 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)), _1258330))), 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, _1258332))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50951 ^ _782476) ^ [_1813889, _1813891] : [c_Relation_Osym(_1813889, _1813891), 50954 ^ _782476 : [(50955 ^ _782476) ^ [_1813995, _1813997] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1813889, _1813889)), hAPP(hAPP(c_Product__Type_OPair(_1813889, _1813889), _1813997), _1813995)), _1813891)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813889, _1813889)), hAPP(hAPP(c_Product__Type_OPair(_1813889, _1813889), _1813995), _1813997)), _1813891)))]]], (37980 ^ _782476) ^ [_1506607, _1506609, _1506611, _1506613, _1506615] : [c_Equiv__Relations_Oequiv(_1506607, _1506609, _1506611), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506607, tc_HOL_Obool)), _1506613), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506607), _1506609), _1506611))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506607, tc_HOL_Obool)), _1506615), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506607), _1506609), _1506611))), -(_1506613 = _1506615), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506607, tc_HOL_Obool)), _1506613), _1506615) = c_Orderings_Obot__class_Obot(tc_fun(_1506607, tc_HOL_Obool)))], (34522 ^ _782476) ^ [_1435665, _1435667] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435665), _1435667), hAPP(c_Int_Onumber__class_Onumber__of(_1435665), c_Int_OBit1(c_Int_OPls))) = _1435667), class_Fields_Ofield(_1435665), class_Int_Onumber__ring(_1435665)], (49854 ^ _782476) ^ [_1789568, _1789570] : [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), _1789568), _1789570))), 49857 ^ _782476 : [(49864 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789568), _1789570))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789568, _1789570) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789570), c_Lazy__Sequence_Osmall__lazy_H(_1789568, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789570), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49858 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789568), _1789570)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789568, _1789570) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (13429 ^ _782476) ^ [_1031153, _1031155, _1031157, _1031159, _1031161, _1031163, _1031165] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031153, _1031155, _1031157, _1031159, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031153, tc_HOL_Obool)), _1031161), hAPP(hAPP(c_Set_Oinsert(_1031153), _1031163), c_Orderings_Obot__class_Obot(tc_fun(_1031153, tc_HOL_Obool))))), _1031165)), hBOOL(hAPP(hAPP(c_member(_1031153), _1031163), _1031161)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031153, _1031155, _1031157, _1031159, _1031161), hAPP(hAPP(_1031157, _1031163), _1031165))))], (41804 ^ _782476) ^ [_1604153, _1604155, _1604157] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604153, _1604153)), hAPP(hAPP(c_Product__Type_OPair(_1604153, _1604153), _1604155), _1604155)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604153, _1604153), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604157))))], (28414 ^ _782476) ^ [_1321452, _1321454, _1321456] : [class_Orderings_Olinorder(_1321452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321452), _1321454)), -(_1321454 = c_Orderings_Obot__class_Obot(tc_fun(_1321452, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321452), _1321456)), -(_1321456 = c_Orderings_Obot__class_Obot(tc_fun(_1321452, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321452, c_Orderings_Oord__class_Omax(_1321452), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321452, tc_HOL_Obool)), _1321454), _1321456)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321452), c_Big__Operators_Olattice_OSup__fin(_1321452, c_Orderings_Oord__class_Omax(_1321452), _1321454)), c_Big__Operators_Olattice_OSup__fin(_1321452, c_Orderings_Oord__class_Omax(_1321452), _1321456)))], (32042 ^ _782476) ^ [_1389464, _1389466, _1389468] : [class_Divides_Osemiring__div(_1389464), -(c_Divides_Odiv__class_Omod(_1389464, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389464), _1389466), _1389468), _1389466) = c_Groups_Ozero__class_Ozero(_1389464))], (33962 ^ _782476) ^ [_1426409, _1426411] : [_1426409 = _1426411, -(c_Int_OBit1(_1426409) = c_Int_OBit1(_1426411))], (52651 ^ _782476) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (51380 ^ _782476) ^ [_1822018, _1822020, _1822022, _1822024] : [-(c_Product__Type_Ocurry(_1822018, _1822020, _1822022, hAPP(c_Product__Type_Oprod_Oprod__case(_1822018, _1822020, _1822022), _1822024)) = _1822024)], (34392 ^ _782476) ^ [_1433609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433609), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433609)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42067 ^ _782476) ^ [_1611075, _1611077, _1611079] : [class_Complete__Lattice_Ocomplete__lattice(_1611075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611075), _1611077)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611075), _1611079), c_Complete__Lattice_OInf__class_OInf(_1611075, _1611077)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611075, _1611075, c_Lattices_Osemilattice__inf__class_Oinf(_1611075)), _1611079), _1611077))], (40968 ^ _782476) ^ [_1583036, _1583038] : [-(hAPP(c_Relation_ODomain(_1583036, _1583036), c_Transitive__Closure_Otrancl(_1583036, _1583038)) = hAPP(c_Relation_ODomain(_1583036, _1583036), _1583038))], (15993 ^ _782476) ^ [_1082112, _1082114, _1082116, _1082118, _1082120] : [class_Groups_Oab__group__add(_1082112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082114), _1082116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082116), _1082118)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082112), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082112), _1082120), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082114), _1082118))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082112), _1082120), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082114), _1082116))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082112), _1082120), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082116), _1082118)))], (32803 ^ _782476) ^ [_1404308, _1404310, _1404312, _1404314, _1404316] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404308, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404310, _1404308, _1404312), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404310, tc_HOL_Obool)), _1404314), _1404316))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404308, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404310, _1404308, _1404312), _1404314)), hAPP(c_Relation_OImage(_1404310, _1404308, _1404312), _1404316)))))], (34888 ^ _782476) ^ [_1441936, _1441938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441936)), hAPP(c_Nat_OSuc, _1441938))), -(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(_1441936))), 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)), _1441938)))))], (16342 ^ _782476) ^ [_1090103] : [16344 ^ _782476 : [(16347 ^ _782476) ^ [_1090213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 16343 ^ [_1090103, _1090213]), _1090213))], (16345 ^ _782476) ^ [_1090179] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 16343 ^ [_1090103, _1090179]), _1090103)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1090103)))], (39728 ^ _782476) ^ [_1551034, _1551036, _1551038] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551034, _1551036), _1551038), hAPP(c_COMBK(tc_fun(_1551036, tc_HOL_Obool), _1551034), c_Orderings_Obot__class_Obot(tc_fun(_1551036, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551034, _1551036), tc_HOL_Obool)))], (8675 ^ _782476) ^ [_933362, _933364, _933366] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933362, tc_HOL_Obool)), _933364), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933362, tc_HOL_Obool)), _933364), _933366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933362, tc_HOL_Obool)), _933364), _933366))], (21997 ^ _782476) ^ [_1196270, _1196272] : [_1196270 = _1196272, -(hAPP(c_Nat_OSuc, _1196270) = hAPP(c_Nat_OSuc, _1196272))], (39235 ^ _782476) ^ [_1538575, _1538577, _1538579] : [c_Wellfounded_Owf(_1538575, _1538577), -(c_Wellfounded_Owf(_1538575, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538575, _1538575), tc_HOL_Obool)), _1538579), _1538577)))], (27020 ^ _782476) ^ [_1293172, _1293174, _1293176] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293172), _1293174)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293176), _1293174)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1293172), _1293176)), _1293174))], (46432 ^ _782476) ^ [_1713228] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713228), 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, _1713228)) = _1713228)], (18028 ^ _782476) ^ [_1124083, _1124085] : [class_Groups_Omonoid__add(_1124083), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124083), c_Groups_Ozero__class_Ozero(_1124083)), _1124085) = _1124085)], (18850 ^ _782476) ^ [_1137507, _1137509, _1137511] : [class_Rings_Olinordered__ring__strict(_1137507), 18853 ^ _782476 : [(18868 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137507), _1137509), _1137511)), c_Groups_Ozero__class_Ozero(_1137507)))), 18869 ^ _782476 : [(18876 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), _1137509), c_Groups_Ozero__class_Ozero(_1137507))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), c_Groups_Ozero__class_Ozero(_1137507)), _1137511))], (18870 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), c_Groups_Ozero__class_Ozero(_1137507)), _1137509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), _1137511), c_Groups_Ozero__class_Ozero(_1137507)))]]], (18854 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137507), _1137509), _1137511)), c_Groups_Ozero__class_Ozero(_1137507))), 18859 ^ _782476 : [(18862 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), _1137511), c_Groups_Ozero__class_Ozero(_1137507))))], (18860 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), c_Groups_Ozero__class_Ozero(_1137507)), _1137509)))]], 18863 ^ _782476 : [(18866 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), c_Groups_Ozero__class_Ozero(_1137507)), _1137511)))], (18864 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137507), _1137509), c_Groups_Ozero__class_Ozero(_1137507))))]]]]], (24070 ^ _782476) ^ [_1233752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1233752)), -(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, _1233752))))], (48351 ^ _782476) ^ [_1755222, _1755224, _1755226, _1755228] : [hBOOL(hAPP(_1755222, _1755224)), -(c_List_OtakeWhile(_1755226, _1755222, hAPP(hAPP(c_List_Olist_OCons(_1755226), _1755224), _1755228)) = hAPP(hAPP(c_List_Olist_OCons(_1755226), _1755224), c_List_OtakeWhile(_1755226, _1755222, _1755228)))], (6578 ^ _782476) ^ [_888375, _888377] : [class_Orderings_Olinorder(_888375), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888375, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_888375), _888377)) = hAPP(c_SetInterval_Oord__class_OatMost(_888375), _888377))], (15170 ^ _782476) ^ [_1066054, _1066056, _1066058, _1066060, _1066062, _1066064] : [c_Finite__Set_Ofolding__idem(_1066054, _1066056, _1066058, _1066060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066054), _1066062)), hBOOL(hAPP(hAPP(c_member(_1066054), _1066064), _1066062)), -(hAPP(c_Fun_Ocomp(_1066056, _1066056, _1066056, hAPP(_1066060, _1066062)), hAPP(_1066058, _1066064)) = hAPP(_1066060, _1066062))], (40037 ^ _782476) ^ [_1560796] : [-(c_Fun_Obij__betw(_1560796, _1560796, c_Fun_Oid(_1560796), c_Orderings_Otop__class_Otop(tc_fun(_1560796, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1560796, tc_HOL_Obool))))], (44224 ^ _782476) ^ [_1664749, _1664751] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664749)), c_List_Olist_ONil(_1664749)), c_List_Olists(_1664749, _1664751))))], (20127 ^ _782476) ^ [_1160353, _1160355, _1160357] : [hBOOL(hAPP(_1160353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160355), _1160357))), 20130 ^ _782476 : [(20137 ^ _782476) ^ [_1160538] : [_1160355 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160357), _1160538), -(hBOOL(hAPP(_1160353, _1160538)))], (20131 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160355), _1160357)), -(hBOOL(hAPP(_1160353, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (3100 ^ _782476) ^ [_828552, _828554, _828556, _828558] : [-(c_Product__Type_OSigma(_828558, _828554) = c_Product__Type_OSigma(_828556, _828552)), _828558 = _828556, _828554 = _828552], (5850 ^ _782476) ^ [_875135, _875137, _875139, _875141] : [hBOOL(hAPP(_875135, _875137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875139, tc_HOL_Obool)), _875135), _875141)), -(hBOOL(hAPP(_875141, _875137)))], (39476 ^ _782476) ^ [_1543921, _1543923, _1543925, _1543927] : [39478 ^ _782476 : [(39481 ^ _782476) ^ [] : [c_Wellfounded_Owf(_1543923, hAPP(_1543925, 39477 ^ [_1543921, _1543923, _1543925, _1543927]))], (39479 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1543921, 39477 ^ [_1543921, _1543923, _1543925, _1543927])))]], -(c_Wellfounded_Owf(tc_prod(_1543927, _1543923), c_Recdef_Osame__fst(_1543927, _1543923, _1543921, _1543925)))], (45971 ^ _782476) ^ [_1702503, _1702505, _1702507, _1702509, _1702511] : [class_Rings_Osemiring__0(_1702503), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702503), hAPP(hAPP(c_List_Omap(_1702505, _1702503), hAPP(hAPP(c_COMBC(_1702505, _1702503, _1702503), hAPP(hAPP(c_COMBB(_1702503, tc_fun(_1702503, _1702503), _1702505), c_Groups_Otimes__class_Otimes(_1702503)), _1702507)), _1702509)), _1702511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702503), hAPP(c_List_Omonoid__add__class_Olistsum(_1702503), hAPP(hAPP(c_List_Omap(_1702505, _1702503), _1702507), _1702511))), _1702509))], (52355 ^ _782476) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (43413 ^ _782476) ^ [_1644603, _1644605, _1644607, _1644609] : [43416 ^ _782476 : [(43421 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644603, _1644603)), hAPP(hAPP(c_Product__Type_OPair(_1644603, _1644603), 43415 ^ [_1644603, _1644605, _1644607, _1644609]), 43414 ^ [_1644603, _1644605, _1644607, _1644609])), _1644605))], (43419 ^ _782476) ^ [] : [43414 ^ [_1644603, _1644605, _1644607, _1644609] = 43415 ^ [_1644603, _1644605, _1644607, _1644609]], (43417 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644603, _1644603)), hAPP(hAPP(c_Product__Type_OPair(_1644603, _1644603), 43414 ^ [_1644603, _1644605, _1644607, _1644609]), 43415 ^ [_1644603, _1644605, _1644607, _1644609])), _1644605))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644603), tc_List_Olist(_1644603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644603), tc_List_Olist(_1644603)), _1644607), _1644609)), c_List_Olexord(_1644603, _1644605)))), -(_1644607 = _1644609), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644603), tc_List_Olist(_1644603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644603), tc_List_Olist(_1644603)), _1644609), _1644607)), c_List_Olexord(_1644603, _1644605))))], (26948 ^ _782476) ^ [_1291425, _1291427, _1291429, _1291431] : [class_Orderings_Olinorder(_1291425), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291425), _1291427), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291425), _1291429), _1291431)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291425), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291425), _1291427), _1291429)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291425), _1291427), _1291431)))], (35328 ^ _782476) ^ [_1450083, _1450085] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450083)), c_Int_OBit0(_1450085)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450083), _1450085)))], (46550 ^ _782476) ^ [_1715755, _1715757, _1715759, _1715761] : [-(hBOOL(hAPP(c_List_Olistsp(_1715755, _1715757), hAPP(hAPP(c_List_Olist_OCons(_1715755), _1715759), _1715761)))), hBOOL(hAPP(_1715757, _1715759)), hBOOL(hAPP(c_List_Olistsp(_1715755, _1715757), _1715761))], (1962 ^ _782476) ^ [_810201, _810203] : [-(class_Int_Onumber(_810201)), _810203 = _810201, class_Int_Onumber(_810203)], (9193 ^ _782476) ^ [_945766, _945768, _945770] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945766, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945766, tc_HOL_Obool)), _945768), _945770)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945766, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945766, tc_HOL_Obool)), _945768)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945766, tc_HOL_Obool)), _945770)))], (19532 ^ _782476) ^ [_1149660] : [class_Rings_Osemiring__1(_1149660), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149660), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1149660))], (36982 ^ _782476) ^ [_1486881, _1486883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486881), 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)), _1486883)), -(c_Divides_OnegDivAlg(_1486881, _1486883) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1486881), _1486883)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1486881, _1486883)))], (40578 ^ _782476) ^ [_1573858, _1573860, _1573862, _1573864] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573858, tc_fun(_1573860, tc_HOL_Obool)), _1573862), _1573864) = hAPP(c_Set_OCollect(_1573860), hAPP(hAPP(c_COMBB(tc_fun(_1573858, tc_HOL_Obool), tc_HOL_Obool, _1573860), c_HOL_OAll(_1573858)), hAPP(hAPP(c_COMBB(tc_fun(_1573858, tc_HOL_Obool), tc_fun(_1573858, tc_HOL_Obool), _1573860), hAPP(c_COMBS(_1573858, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573858), c_fimplies), hAPP(hAPP(c_COMBC(_1573858, tc_fun(_1573858, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573858)), _1573862)))), hAPP(hAPP(c_COMBC(_1573860, tc_fun(_1573858, tc_fun(_1573860, tc_HOL_Obool)), tc_fun(_1573858, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573860, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573858, tc_fun(_1573860, tc_HOL_Obool)), tc_fun(_1573858, tc_HOL_Obool)), _1573860), c_COMBB(tc_fun(_1573860, tc_HOL_Obool), tc_HOL_Obool, _1573858)), c_member(_1573860))), _1573864)))))], (47327 ^ _782476) ^ [_1734951, _1734953, _1734955] : [class_Groups_Omonoid__add(_1734951), -(hAPP(c_List_Ofoldl(_1734951, _1734951, c_Groups_Oplus__class_Oplus(_1734951), _1734953), _1734955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1734951), _1734953), c_List_Ofoldr(_1734951, _1734951, c_Groups_Oplus__class_Oplus(_1734951), _1734955, c_Groups_Ozero__class_Ozero(_1734951))))], (48788 ^ _782476) ^ [_1764494, _1764496, _1764498] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764494, _1764494)), hAPP(hAPP(c_Product__Type_OPair(_1764494, _1764494), _1764496), _1764498)), c_List_Omeasures(_1764494, c_List_Olist_ONil(tc_fun(_1764494, tc_Nat_Onat)))))], (52103 ^ _782476) ^ [_1837548, _1837550] : [class_Lattices_Obounded__lattice(_1837548), -(class_Lattices_Obounded__lattice(tc_fun(_1837550, _1837548)))], (5136 ^ _782476) ^ [_860918, _860920, _860922, _860924, _860926, _860928] : [-(c_Finite__Set_Ofold__image(_860928, _860924, _860920) = c_Finite__Set_Ofold__image(_860926, _860922, _860918)), _860928 = _860926, _860924 = _860922, _860920 = _860918], (18924 ^ _782476) ^ [_1138796, _1138798, _1138800, _1138802] : [class_Rings_Olinordered__semidom(_1138796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138796), c_Groups_Ozero__class_Ozero(_1138796)), _1138798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138796), _1138800), _1138802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138796), _1138800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138796), _1138798), _1138802))))], (25878 ^ _782476) ^ [_1269738, _1269740, _1269742] : [class_Lattices_Odistrib__lattice(_1269738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269738), _1269740)), -(_1269740 = c_Orderings_Obot__class_Obot(tc_fun(_1269738, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269738), _1269742), c_Big__Operators_Olattice__class_OSup__fin(_1269738, _1269740)) = c_Big__Operators_Olattice__class_OSup__fin(_1269738, hAPP(c_Set_OCollect(_1269738), hAPP(hAPP(c_COMBB(tc_fun(_1269738, tc_HOL_Obool), tc_HOL_Obool, _1269738), c_HOL_OEx(_1269738)), hAPP(hAPP(c_COMBC(_1269738, tc_fun(_1269738, tc_HOL_Obool), tc_fun(_1269738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269738, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1269738, tc_HOL_Obool), tc_fun(_1269738, tc_HOL_Obool)), _1269738), c_COMBS(_1269738, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269738, tc_HOL_Obool), tc_fun(_1269738, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1269738), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269738), c_fconj)), hAPP(hAPP(c_COMBC(_1269738, tc_fun(_1269738, _1269738), tc_fun(_1269738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269738, tc_HOL_Obool), tc_fun(tc_fun(_1269738, _1269738), tc_fun(_1269738, tc_HOL_Obool)), _1269738), c_COMBB(_1269738, tc_HOL_Obool, _1269738)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269738), _1269742))))), hAPP(hAPP(c_COMBC(_1269738, tc_fun(_1269738, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269738)), _1269740))))))], (42790 ^ _782476) ^ [_1626054, _1626056, _1626058] : [c_Nitpick_Oless__frac(_1626054, _1626056, _1626058), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626054), c_Nitpick_Oplus__frac(_1626054, _1626056, c_Nitpick_Ouminus__frac(_1626054, _1626058)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7125 ^ _782476) ^ [_900603, _900605, _900607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900603, tc_HOL_Obool)), _900607), _900605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900603, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900603, tc_HOL_Obool)), _900605)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900603, tc_HOL_Obool)), _900607))))], (38867 ^ _782476) ^ [_1528121, _1528123, _1528125, _1528127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528121), _1528127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528125), _1528123))), -(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), _1528121), _1528123)), 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), _1528125), _1528127)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (50989 ^ _782476) ^ [_1814722, _1814724] : [c_Relation_Osym(_1814722, _1814724), -(c_Relation_Osym(_1814722, c_Transitive__Closure_Ortrancl(_1814722, _1814724)))], (12224 ^ _782476) ^ [_1004586, _1004588, _1004590] : [class_Orderings_Oord(_1004586), 12227 ^ _782476 : [(12234 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004586), _1004588), _1004590)), -(hBOOL(hAPP(hAPP(c_member(_1004586), _1004588), hAPP(c_SetInterval_Oord__class_OlessThan(_1004586), _1004590))))], (12228 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1004586), _1004588), hAPP(c_SetInterval_Oord__class_OlessThan(_1004586), _1004590))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004586), _1004588), _1004590)))]]], (40181 ^ _782476) ^ [_1564573, _1564575, _1564577, _1564579, _1564581, _1564583] : [-(c_Product__Type_Omap__pair(_1564573, _1564575, _1564577, _1564579, _1564581, _1564583) = hAPP(c_Product__Type_Oprod_Oprod__case(_1564573, _1564577, tc_prod(_1564575, _1564579)), hAPP(hAPP(c_COMBC(_1564573, tc_fun(_1564577, _1564579), tc_fun(_1564577, tc_prod(_1564575, _1564579))), hAPP(hAPP(c_COMBB(tc_fun(_1564579, tc_prod(_1564575, _1564579)), tc_fun(tc_fun(_1564577, _1564579), tc_fun(_1564577, tc_prod(_1564575, _1564579))), _1564573), c_COMBB(_1564579, tc_prod(_1564575, _1564579), _1564577)), hAPP(hAPP(c_COMBB(_1564575, tc_fun(_1564579, tc_prod(_1564575, _1564579)), _1564573), c_Product__Type_OPair(_1564575, _1564579)), _1564581))), _1564583)))], (52219 ^ _782476) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (28954 ^ _782476) ^ [_1332170, _1332172, _1332174] : [class_Rings_Ocomm__semiring__1(_1332170), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332170), hAPP(hAPP(c_Power_Opower__class_Opower(_1332170), _1332172), _1332174)), _1332172) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332170), _1332172), hAPP(c_Nat_OSuc, _1332174)))], (8148 ^ _782476) ^ [_921515, _921517, _921519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921515, tc_HOL_Obool)), _921517), _921519)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921515, tc_HOL_Obool)), _921519), _921517) = _921519)], (50861 ^ _782476) ^ [_1811858, _1811860, _1811862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1811858, _1811858), tc_HOL_Obool)), _1811860), _1811862)), c_Relation_Oantisym(_1811858, _1811862), -(c_Relation_Oantisym(_1811858, _1811860))], (20906 ^ _782476) ^ [_1175510, _1175512, _1175514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175510), _1175512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175514), _1175510)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175514), _1175512))))], (25025 ^ _782476) ^ [_1250219, _1250221] : [class_Groups_Oordered__ab__group__add__abs(_1250219), 25028 ^ _782476 : [(25035 ^ _782476) ^ [] : [_1250221 = c_Groups_Ozero__class_Ozero(_1250219), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250219), hAPP(c_Groups_Oabs__class_Oabs(_1250219), _1250221)), c_Groups_Ozero__class_Ozero(_1250219))))], (25029 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250219), hAPP(c_Groups_Oabs__class_Oabs(_1250219), _1250221)), c_Groups_Ozero__class_Ozero(_1250219))), -(_1250221 = c_Groups_Ozero__class_Ozero(_1250219))]]], (50717 ^ _782476) ^ [_1809469, _1809471, _1809473, _1809475, _1809477] : [c_Predicate_Otransp(_1809469, _1809471), hBOOL(hAPP(hAPP(_1809471, _1809473), _1809475)), hBOOL(hAPP(hAPP(_1809471, _1809475), _1809477)), -(hBOOL(hAPP(hAPP(_1809471, _1809473), _1809477)))], (43023 ^ _782476) ^ [_1633127, _1633129] : [-(c_List_Olistrel1(_1633127, hAPP(c_Relation_Oconverse(_1633127, _1633127), _1633129)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1633127), tc_List_Olist(_1633127)), c_List_Olistrel1(_1633127, _1633129)))], (7119 ^ _782476) ^ [_900456, _900458, _900460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900456, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900456, tc_HOL_Obool)), _900458)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900456, tc_HOL_Obool)), _900460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900456, tc_HOL_Obool)), _900460), _900458)))], (48578 ^ _782476) ^ [_1760031, _1760033, _1760035, _1760037] : [48580 ^ _782476 : [(48585 ^ _782476) ^ [] : [hBOOL(hAPP(_1760037, hAPP(hAPP(c_List_Onth(_1760033), _1760035), 48579 ^ [_1760031, _1760033, _1760035, _1760037])))], (48583 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1760031, _1760033, _1760035, _1760037]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760033)), _1760035))))], (48581 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1760031, _1760033, _1760035, _1760037]), _1760031)))]], 48588 ^ _782476 : [(48591 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1760037, hAPP(hAPP(c_List_Onth(_1760033), _1760035), _1760031))))], (48589 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1760031), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760033)), _1760035))))]], -(c_List_OtakeWhile(_1760033, _1760037, _1760035) = hAPP(hAPP(c_List_Otake(_1760033), _1760031), _1760035))], (18022 ^ _782476) ^ [_1123988, _1123990] : [class_Rings_Ocomm__semiring__1(_1123988), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123988), c_Groups_Ozero__class_Ozero(_1123988)), _1123990) = _1123990)], (40183 ^ _782476) ^ [_1564696, _1564698, _1564700, _1564702, _1564704, _1564706, _1564708, _1564710, _1564712, _1564714] : [hAPP(c_Set_Oimage(_1564696, _1564698, _1564700), _1564702) = _1564704, hAPP(c_Set_Oimage(_1564706, _1564708, _1564710), _1564712) = _1564714, -(hAPP(c_Set_Oimage(tc_prod(_1564696, _1564706), tc_prod(_1564698, _1564708), c_Product__Type_Omap__pair(_1564696, _1564698, _1564706, _1564708, _1564700, _1564710)), hAPP(hAPP(c_Product__Type_OSigma(_1564696, _1564706), _1564702), hAPP(c_COMBK(tc_fun(_1564706, tc_HOL_Obool), _1564696), _1564712))) = hAPP(hAPP(c_Product__Type_OSigma(_1564698, _1564708), _1564704), hAPP(c_COMBK(tc_fun(_1564708, tc_HOL_Obool), _1564698), _1564714)))], (30802 ^ _782476) ^ [_1366322, _1366324, _1366326, _1366328, _1366330] : [class_Fields_Ofield(_1366322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366324), _1366326)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366324), _1366328)), 30816 ^ _782476 : [(30819 ^ _782476) ^ [] : [-(hAPP(_1366330, 30815 ^ [_1366322, _1366324, _1366326, _1366328, _1366330]) = c_Groups_Ozero__class_Ozero(_1366322))], (30817 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366324), 30815 ^ [_1366322, _1366324, _1366326, _1366328, _1366330]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366324, tc_HOL_Obool)), _1366326), _1366328))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366324, _1366322), _1366330), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366324, tc_HOL_Obool)), _1366326), _1366328)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366322), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366324, _1366322), _1366330), _1366326)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366324, _1366322), _1366330), _1366328))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366324, _1366322), _1366330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366324, tc_HOL_Obool)), _1366326), _1366328))))], (10413 ^ _782476) ^ [_971730, _971732, _971734, _971736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971730, tc_HOL_Obool)), _971732), _971734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971730, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_971730), _971736), _971732)), hAPP(hAPP(c_Set_Oinsert(_971730), _971736), _971734))))], (35944 ^ _782476) ^ [_1461536] : [_1461536 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1461536) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52601 ^ _782476) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (8515 ^ _782476) ^ [_930171, _930173, _930175, _930177, _930179] : [_930171 = hAPP(_930173, _930175), -(hBOOL(hAPP(hAPP(c_member(_930177), _930171), hAPP(c_Set_Oimage(_930179, _930177, _930173), c_Orderings_Otop__class_Otop(tc_fun(_930179, tc_HOL_Obool))))))], (33758 ^ _782476) ^ [_1422518, _1422520, _1422522, _1422524] : [class_Fields_Olinordered__field__inverse__zero(_1422518), class_Int_Onumber(_1422518), 33765 ^ _782476 : [(33766 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422518), _1422522), _1422524))), 33769 ^ _782476 : [(33776 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), c_Groups_Ozero__class_Ozero(_1422518)), _1422524))), 33779 ^ _782476 : [(33786 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), _1422524), c_Groups_Ozero__class_Ozero(_1422518)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), c_Groups_Ozero__class_Ozero(_1422518))))], (33780 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), _1422524), c_Groups_Ozero__class_Ozero(_1422518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), _1422522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), _1422524))))]]], (33770 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), c_Groups_Ozero__class_Ozero(_1422518)), _1422524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), _1422524)), _1422522)))]]], (33792 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422518), _1422522), _1422524)))), 33795 ^ _782476 : [(33798 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), _1422524)), _1422522))], (33796 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), c_Groups_Ozero__class_Ozero(_1422518)), _1422524)))]], 33799 ^ _782476 : [(33802 ^ _782476) ^ [] : [33803 ^ _782476 : [(33806 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), _1422522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), _1422524)))], (33804 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), _1422524), c_Groups_Ozero__class_Ozero(_1422518))))]], 33807 ^ _782476 : [(33810 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422518), hAPP(c_Int_Onumber__class_Onumber__of(_1422518), _1422520)), c_Groups_Ozero__class_Ozero(_1422518)))], (33808 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), _1422524), c_Groups_Ozero__class_Ozero(_1422518)))]]], (33800 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422518), c_Groups_Ozero__class_Ozero(_1422518)), _1422524))]]]]], (20623 ^ _782476) ^ [_1170191, _1170193, _1170195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170191), _1170193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170195)), -(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), _1170195)), _1170191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170195)), _1170193))))], (44640 ^ _782476) ^ [_1673719, _1673721, _1673723, _1673725, _1673727] : [hAPP(hAPP(c_List_Oappend(_1673719), _1673721), hAPP(hAPP(c_List_Olist_OCons(_1673719), _1673723), c_List_Olist_ONil(_1673719))) = hAPP(hAPP(c_List_Oappend(_1673719), _1673725), hAPP(hAPP(c_List_Olist_OCons(_1673719), _1673727), c_List_Olist_ONil(_1673719))), 44643 ^ _782476 : [(44646 ^ _782476) ^ [] : [-(_1673723 = _1673727)], (44644 ^ _782476) ^ [] : [-(_1673721 = _1673725)]]], (21171 ^ _782476) ^ [_1180126, _1180128] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180126), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180128) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1180126, _1180128))], (27084 ^ _782476) ^ [_1294600] : [class_Orderings_Olinorder(_1294600), -(c_Finite__Set_Ofun__left__comm__idem(_1294600, _1294600, c_Orderings_Oord__class_Omax(_1294600)))], (29498 ^ _782476) ^ [_1342201, _1342203, _1342205, _1342207] : [class_Rings_Olinordered__semidom(_1342201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342201), c_Groups_Oone__class_Oone(_1342201)), _1342203)), 29505 ^ _782476 : [(29512 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342205), _1342207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342201), hAPP(hAPP(c_Power_Opower__class_Opower(_1342201), _1342203), _1342205)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342201), _1342203), _1342207))))], (29506 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342201), hAPP(hAPP(c_Power_Opower__class_Opower(_1342201), _1342203), _1342205)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342201), _1342203), _1342207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342205), _1342207)))]]], (38802 ^ _782476) ^ [_1526453, _1526455] : [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)), _1526453), 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)), _1526455), 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)), _1526453), _1526455)), c_Int_Ointrel)))], (38923 ^ _782476) ^ [_1530363, _1530365, _1530367, _1530369, _1530371, _1530373, _1530375] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530363, _1530365, _1530367), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530369, tc_fun(tc_prod(_1530363, _1530365), tc_HOL_Obool)), _1530371), _1530373)), _1530375) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530369, tc_fun(tc_prod(_1530363, _1530367), tc_HOL_Obool)), _1530371), hAPP(hAPP(c_COMBC(_1530369, tc_fun(tc_prod(_1530365, _1530367), tc_HOL_Obool), tc_fun(tc_prod(_1530363, _1530367), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530363, _1530365), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1530365, _1530367), tc_HOL_Obool), tc_fun(tc_prod(_1530363, _1530367), tc_HOL_Obool)), _1530369), c_Relation_Orel__comp(_1530363, _1530365, _1530367)), _1530373)), _1530375)))], (39192 ^ _782476) ^ [_1537770, _1537772] : [c_Wellfounded_Owf(_1537770, hAPP(hAPP(c_Relation_Orel__comp(_1537770, _1537770, _1537770), _1537772), _1537772)), -(c_Wellfounded_Owf(_1537770, _1537772))], (23428 ^ _782476) ^ [_1222564, _1222566, _1222568] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222564), _1222566)), 23431 ^ _782476 : [(23438 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222564), _1222568), _1222566))), -(hAPP(c_Finite__Set_Ocard(_1222564), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222564, tc_HOL_Obool)), _1222566), hAPP(hAPP(c_Set_Oinsert(_1222564), _1222568), c_Orderings_Obot__class_Obot(tc_fun(_1222564, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1222564), _1222566))], (23432 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1222564), _1222568), _1222566)), -(hAPP(c_Finite__Set_Ocard(_1222564), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222564, tc_HOL_Obool)), _1222566), hAPP(hAPP(c_Set_Oinsert(_1222564), _1222568), c_Orderings_Obot__class_Obot(tc_fun(_1222564, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222564), _1222566)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (7113 ^ _782476) ^ [_900287, _900289, _900291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900287, tc_HOL_Obool)), _900289), _900291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900287, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900287, tc_HOL_Obool)), _900291)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900287, tc_HOL_Obool)), _900289))))], (49846 ^ _782476) ^ [_1789474, _1789476] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789474), _1789476))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789474, _1789476) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789476), c_Lazy__Sequence_Osmall__lazy_H(_1789474, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789476), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (11684 ^ _782476) ^ [_995299, _995301, _995303, _995305] : [class_Orderings_Opreorder(_995299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995299), _995301), _995303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995299), _995303), _995305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995299), _995301), _995305)))], (43335 ^ _782476) ^ [_1642557, _1642559, _1642561] : [-(_1642557 = _1642559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642561)), _1642557) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642561)), _1642559), 43341 ^ _782476 : [(43344 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Onth(_1642561), _1642557), 43340 ^ [_1642557, _1642559, _1642561]) = hAPP(hAPP(c_List_Onth(_1642561), _1642559), 43340 ^ [_1642557, _1642559, _1642561])], (43342 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43340 ^ [_1642557, _1642559, _1642561]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642561)), _1642557))))]]], (51047 ^ _782476) ^ [_1815634, _1815636, _1815638] : [c_Equiv__Relations_Oequiv(_1815634, _1815636, _1815638), 51050 ^ _782476 : [(51055 ^ _782476) ^ [] : [-(c_Relation_Otrans(_1815634, _1815638))], (51053 ^ _782476) ^ [] : [-(c_Relation_Osym(_1815634, _1815638))], (51051 ^ _782476) ^ [] : [-(c_Relation_Orefl__on(_1815634, _1815636, _1815638))]]], (31706 ^ _782476) ^ [_1382399, _1382401, _1382403, _1382405, _1382407] : [class_Groups_Ocomm__monoid__mult(_1382399), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382401), _1382403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382401, tc_HOL_Obool)), _1382405), _1382403)), 31720 ^ _782476 : [(31723 ^ _782476) ^ [] : [hAPP(_1382407, 31719 ^ [_1382399, _1382401, _1382403, _1382405, _1382407]) = c_Groups_Oone__class_Oone(_1382399)], (31721 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382401), 31719 ^ [_1382399, _1382401, _1382403, _1382405, _1382407]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1382401, tc_HOL_Obool)), _1382403), _1382405))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382401, _1382399), _1382407), _1382403) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382401, _1382399), _1382407), _1382405))], (25592 ^ _782476) ^ [_1260845, _1260847] : [-(hAPP(c_Set_OCollect(_1260845), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260845), c_fNot), _1260847)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1260845, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260845), _1260847)))], (142 ^ _782476) ^ [_784801, _784803, _784805, _784807, _784809, _784811, _784813, _784815, _784817, _784819, _784821, _784823] : [-(c_Finite__Set_Ofolding__image__simple(_784821, _784817, _784813, _784809, _784805, _784801)), c_Finite__Set_Ofolding__image__simple(_784823, _784819, _784815, _784811, _784807, _784803), _784823 = _784821, _784819 = _784817, _784815 = _784813, _784811 = _784809, _784807 = _784805, _784803 = _784801], (38443 ^ _782476) ^ [_1517705, _1517707, _1517709, _1517711, _1517713, _1517715, _1517717, _1517719] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517705, _1517707), tc_prod(_1517705, _1517707))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517705, _1517707), tc_prod(_1517705, _1517707)), hAPP(hAPP(c_Product__Type_OPair(_1517705, _1517707), _1517709), _1517711)), hAPP(hAPP(c_Product__Type_OPair(_1517705, _1517707), _1517713), _1517715))), c_Wellfounded_Olex__prod(_1517705, _1517707, _1517717, _1517719)))), 38444 ^ _782476 : [(38447 ^ _782476) ^ [] : [_1517709 = _1517713, hBOOL(hAPP(hAPP(c_member(tc_prod(_1517707, _1517707)), hAPP(hAPP(c_Product__Type_OPair(_1517707, _1517707), _1517711), _1517715)), _1517719))], (38445 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517705, _1517705)), hAPP(hAPP(c_Product__Type_OPair(_1517705, _1517705), _1517709), _1517713)), _1517717))]]], (25644 ^ _782476) ^ [_1262231, _1262233, _1262235] : [-(hBOOL(hAPP(_1262231, _1262233))), -(hAPP(c_Set_OCollect(_1262235), hAPP(hAPP(c_COMBS(_1262235, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262235), c_fconj), hAPP(hAPP(c_COMBC(_1262235, _1262235, tc_HOL_Obool), c_fequal), _1262233))), _1262231)) = c_Orderings_Obot__class_Obot(tc_fun(_1262235, tc_HOL_Obool)))], (49756 ^ _782476) ^ [_1787039, _1787041] : [c_Wellfounded_Oacyclic(_1787039, hAPP(c_Set_OCollect(tc_prod(_1787039, _1787039)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787039, _1787039, tc_HOL_Obool), c_Predicate_Oconversep(_1787039, _1787039, _1787041)))), -(c_Wellfounded_Oacyclic(_1787039, hAPP(c_Set_OCollect(tc_prod(_1787039, _1787039)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787039, _1787039, tc_HOL_Obool), _1787041))))], (38592 ^ _782476) ^ [_1521549, _1521551] : [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), _1521549), _1521551)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521549), _1521551)))], (25730 ^ _782476) ^ [_1265218, _1265220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265218)), _1265220)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265218), _1265220)))], (20981 ^ _782476) ^ [_1176853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176853), 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)), _1176853)), _1176853)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37649 ^ _782476) ^ [_1498942, _1498944, _1498946, _1498948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498948, _1498944)), hAPP(_1498948, _1498946))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498942, _1498942)), hAPP(hAPP(c_Product__Type_OPair(_1498942, _1498942), _1498944), _1498946)), hAPP(c_Wellfounded_Omeasure(_1498942), _1498948))))], (3880 ^ _782476) ^ [_840740, _840742, _840744, _840746, _840748, _840750] : [-(c_List_Olinorder__class_Oinsort__key(_840750, _840746, _840742) = c_List_Olinorder__class_Oinsort__key(_840748, _840744, _840740)), _840750 = _840748, _840746 = _840744, _840742 = _840740], (35860 ^ _782476) ^ [_1459812] : [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, _1459812, 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, _1459812, 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))], (22032 ^ _782476) ^ [] : [-(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))], (31912 ^ _782476) ^ [_1386821, _1386823, _1386825, _1386827, _1386829, _1386831] : [class_Divides_Osemiring__div(_1386821), c_Divides_Odiv__class_Omod(_1386821, _1386823, _1386825) = c_Divides_Odiv__class_Omod(_1386821, _1386827, _1386825), c_Divides_Odiv__class_Omod(_1386821, _1386829, _1386825) = c_Divides_Odiv__class_Omod(_1386821, _1386831, _1386825), -(c_Divides_Odiv__class_Omod(_1386821, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386821), _1386823), _1386829), _1386825) = c_Divides_Odiv__class_Omod(_1386821, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386821), _1386827), _1386831), _1386825))], (47427 ^ _782476) ^ [_1736954] : [-(c_List_Oupt(_1736954, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (47580 ^ _782476) ^ [_1740061, _1740063] : [class_Orderings_Olinorder(_1740061), c_List_Olinorder__class_Osorted(_1740061, _1740063), -(c_List_Olinorder__class_Osorted(_1740061, hAPP(c_List_Otl(_1740061), _1740063)))], (2980 ^ _782476) ^ [_826676, _826678, _826680, _826682] : [-(c_Nitpick_Ouminus__frac(_826682, _826678) = c_Nitpick_Ouminus__frac(_826680, _826676)), _826682 = _826680, _826678 = _826676], (9055 ^ _782476) ^ [_941614, _941616, _941618, _941620, _941622, _941624] : [-(hAPP(c_Set_Oimage(_941614, _941616, _941618), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941620, tc_fun(_941614, tc_HOL_Obool)), _941622), _941624)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941620, tc_fun(_941616, tc_HOL_Obool)), _941622), hAPP(hAPP(c_COMBB(tc_fun(_941614, tc_HOL_Obool), tc_fun(_941616, tc_HOL_Obool), _941620), c_Set_Oimage(_941614, _941616, _941618)), _941624)))], (34936 ^ _782476) ^ [_1443099] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443099))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443099)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34930 ^ _782476) ^ [_1442960, _1442962] : [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(_1442960))), 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)), _1442962)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442960)), hAPP(c_Nat_OSuc, _1442962))))], (10387 ^ _782476) ^ [_970908, _970910, _970912, _970914, _970916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970908, tc_HOL_Obool)), _970910), _970912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970908, tc_HOL_Obool)), _970914), _970916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970908, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970908, tc_HOL_Obool)), _970910), _970916)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970908, tc_HOL_Obool)), _970912), _970914))))], (8957 ^ _782476) ^ [_939128, _939130, _939132] : [class_Lattices_Olattice(_939128), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939128), _939130), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939128), _939130), _939132)) = _939130)], (46680 ^ _782476) ^ [_1719437, _1719439, _1719441, _1719443, _1719445, _1719447, _1719449] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719437)), _1719439) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719441)), _1719443), 46683 ^ _782476 : [(46692 ^ _782476) ^ [] : [-(c_List_Olist__all2(_1719437, _1719441, _1719445, hAPP(hAPP(c_List_Oappend(_1719437), _1719439), _1719447), hAPP(hAPP(c_List_Oappend(_1719441), _1719443), _1719449))), c_List_Olist__all2(_1719437, _1719441, _1719445, _1719439, _1719443), c_List_Olist__all2(_1719437, _1719441, _1719445, _1719447, _1719449)], (46684 ^ _782476) ^ [] : [c_List_Olist__all2(_1719437, _1719441, _1719445, hAPP(hAPP(c_List_Oappend(_1719437), _1719439), _1719447), hAPP(hAPP(c_List_Oappend(_1719441), _1719443), _1719449)), 46687 ^ _782476 : [(46690 ^ _782476) ^ [] : [-(c_List_Olist__all2(_1719437, _1719441, _1719445, _1719447, _1719449))], (46688 ^ _782476) ^ [] : [-(c_List_Olist__all2(_1719437, _1719441, _1719445, _1719439, _1719443))]]]]], (27445 ^ _782476) ^ [_1301527, _1301529, _1301531, _1301533, _1301535] : [class_Groups_Ocomm__monoid__mult(_1301527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301529), _1301531)), -(hBOOL(hAPP(hAPP(c_member(_1301529), _1301533), _1301531))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301529, _1301527), _1301535), hAPP(hAPP(c_Set_Oinsert(_1301529), _1301533), _1301531)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301527), hAPP(_1301535, _1301533)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301529, _1301527), _1301535), _1301531)))], (38702 ^ _782476) ^ [_1523671] : [-(hAPP(c_Relation_OField(_1523671), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523671, _1523671), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1523671, tc_HOL_Obool)))], (21403 ^ _782476) ^ [_1184314, _1184316] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184314)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184316))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184314), _1184316)))], (5944 ^ _782476) ^ [_876659, _876661, _876663] : [class_Orderings_Oorder(_876659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876659), _876661), _876663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876659), _876663), _876661)), -(_876661 = _876663)], (29148 ^ _782476) ^ [_1335864, _1335866] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335864), _1335866) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335864 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41388 ^ _782476) ^ [_1593919, _1593921, _1593923, _1593925, _1593927] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593919, _1593919)), hAPP(hAPP(c_Product__Type_OPair(_1593919, _1593919), _1593921), _1593923)), c_Transitive__Closure_Ortrancl(_1593919, _1593925))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1593919, _1593919), tc_HOL_Obool)), _1593925), hAPP(hAPP(c_Product__Type_OSigma(_1593919, _1593919), _1593927), hAPP(c_COMBK(tc_fun(_1593919, tc_HOL_Obool), _1593919), _1593927)))), -(_1593921 = _1593923), -(hBOOL(hAPP(hAPP(c_member(_1593919), _1593921), _1593927)))], (13324 ^ _782476) ^ [_1028532, _1028534, _1028536, _1028538] : [c_Fun_Oinj__on(_1028532, _1028534, _1028536, _1028538), -(c_Fun_Oinj__on(_1028534, _1028532, c_Fun_Othe__inv__into(_1028532, _1028534, _1028538, _1028536), hAPP(c_Set_Oimage(_1028532, _1028534, _1028536), _1028538)))], (52259 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (20635 ^ _782476) ^ [_1170430, _1170432, _1170434] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170430)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170432)), _1170434)) = 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), _1170430), _1170432))), _1170434))], (21035 ^ _782476) ^ [_1177766, _1177768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177766), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177766), _1177768)))], (49124 ^ _782476) ^ [_1772621, _1772623, _1772625] : [hBOOL(hAPP(hAPP(c_member(_1772621), _1772623), hAPP(c_List_Oset(_1772621), _1772625))), 49129 ^ _782476 : [(49132 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1772621), _1772623), hAPP(c_List_Oset(_1772621), 49127 ^ [_1772621, _1772623, _1772625])))], (49130 ^ _782476) ^ [] : [-(_1772625 = hAPP(hAPP(c_List_Oappend(_1772621), 49127 ^ [_1772621, _1772623, _1772625]), hAPP(hAPP(c_List_Olist_OCons(_1772621), _1772623), 49128 ^ [_1772621, _1772623, _1772625])))]]], (37511 ^ _782476) ^ [_1496250, _1496252, _1496254, _1496256] : [-(hAPP(c_Product__Type_Osnd(_1496250, _1496252), hAPP(hAPP(c_Product__Type_OPair(_1496250, _1496252), _1496254), _1496256)) = _1496256)], (52301 ^ _782476) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (48174 ^ _782476) ^ [_1751424, _1751426, _1751428] : [-(hAPP(c_List_Orev(_1751424), hAPP(hAPP(c_List_Olist_OCons(_1751424), _1751426), _1751428)) = hAPP(hAPP(c_List_Oappend(_1751424), hAPP(c_List_Orev(_1751424), _1751428)), hAPP(hAPP(c_List_Olist_OCons(_1751424), _1751426), c_List_Olist_ONil(_1751424))))], (22156 ^ _782476) ^ [_1198734, _1198736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198734)), hAPP(c_Nat_OSuc, _1198736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198734), _1198736)))], (38411 ^ _782476) ^ [] : [-(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))], (31241 ^ _782476) ^ [_1373601, _1373603, _1373605, _1373607] : [class_Divides_Osemiring__div(_1373601), -(_1373603 = c_Groups_Ozero__class_Ozero(_1373601)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373601), _1373605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373601), _1373603), _1373607))), _1373603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373601), _1373607), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373601), _1373605), _1373603)))], (49476 ^ _782476) ^ [_1780218, _1780220, _1780222, _1780224] : [-(c_Lazy__Sequence_Oproduct(_1780218, _1780220, _1780222, _1780224) = hAPP(c_Lazy__Sequence_Obind(_1780218, tc_prod(_1780218, _1780220), _1780222), hAPP(hAPP(c_COMBB(tc_fun(_1780220, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780218, _1780220))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780218, _1780220)), _1780218), c_Lazy__Sequence_Obind(_1780220, tc_prod(_1780218, _1780220), _1780224)), hAPP(hAPP(c_COMBB(tc_fun(_1780220, tc_prod(_1780218, _1780220)), tc_fun(_1780220, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780218, _1780220))), _1780218), hAPP(c_COMBB(tc_prod(_1780218, _1780220), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780218, _1780220)), _1780220), c_Lazy__Sequence_Osingle(tc_prod(_1780218, _1780220)))), c_Product__Type_OPair(_1780218, _1780220)))))], (37920 ^ _782476) ^ [_1504626, _1504628] : [_1504626 = _1504628, -(hAPP(c_Int_ORep__Integ, _1504626) = hAPP(c_Int_ORep__Integ, _1504628))], (24987 ^ _782476) ^ [_1249624, _1249626] : [class_Rings_Olinordered__idom(_1249624), 24990 ^ _782476 : [(24997 ^ _782476) ^ [] : [_1249626 = c_Groups_Ozero__class_Ozero(_1249624), -(c_Groups_Osgn__class_Osgn(_1249624, _1249626) = c_Groups_Ozero__class_Ozero(_1249624))], (24991 ^ _782476) ^ [] : [c_Groups_Osgn__class_Osgn(_1249624, _1249626) = c_Groups_Ozero__class_Ozero(_1249624), -(_1249626 = c_Groups_Ozero__class_Ozero(_1249624))]]], (12594 ^ _782476) ^ [_1013063, _1013065, _1013067, _1013069, _1013071] : [-(c_Fun_Oinj__on(_1013063, _1013065, _1013067, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013063, tc_HOL_Obool)), _1013069), _1013071))), c_Fun_Oinj__on(_1013063, _1013065, _1013067, _1013069), c_Fun_Oinj__on(_1013063, _1013065, _1013067, _1013071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013065, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1013063, _1013065, _1013067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013063, tc_HOL_Obool)), _1013069), _1013071))), hAPP(c_Set_Oimage(_1013063, _1013065, _1013067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013063, tc_HOL_Obool)), _1013071), _1013069))) = c_Orderings_Obot__class_Obot(tc_fun(_1013065, tc_HOL_Obool))], (22368 ^ _782476) ^ [_1202364, _1202366] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202364), hAPP(c_Nat_OSuc, _1202366)))), 22369 ^ _782476 : [(22372 ^ _782476) ^ [_1202452] : [_1202364 = hAPP(c_Nat_OSuc, _1202452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202452), _1202366))], (22370 ^ _782476) ^ [] : [_1202364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29640 ^ _782476) ^ [_1344915, _1344917, _1344919, _1344921] : [class_Rings_Olinordered__semidom(_1344915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1344917), _1344919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344915), c_Groups_Ozero__class_Ozero(_1344915)), _1344921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344915), _1344921), c_Groups_Oone__class_Oone(_1344915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344915), hAPP(hAPP(c_Power_Opower__class_Opower(_1344915), _1344921), _1344919)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344915), _1344921), _1344917))))], (26652 ^ _782476) ^ [_1285763, _1285765, _1285767] : [class_Orderings_Olinorder(_1285763), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285763), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285763), _1285765), _1285767)), _1285767)))], (18320 ^ _782476) ^ [_1128305] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128305), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128305)], (9217 ^ _782476) ^ [_946521, _946523, _946525, _946527] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946521, tc_fun(_946523, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946521, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946523, tc_HOL_Obool), tc_fun(_946523, tc_HOL_Obool), _946521), hAPP(c_COMBC(_946523, tc_fun(_946523, tc_HOL_Obool), tc_HOL_Obool), c_member(_946523))), _946525)), _946527)), -(hBOOL(hAPP(hAPP(c_member(_946523), _946527), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946521, tc_fun(_946523, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946521, tc_HOL_Obool))), _946525))))], (18080 ^ _782476) ^ [_1124902, _1124904, _1124906] : [class_Rings_Oring__no__zero__divisors(_1124902), 18083 ^ _782476 : [(18084 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124902), _1124904), _1124906) = c_Groups_Ozero__class_Ozero(_1124902), -(_1124904 = c_Groups_Ozero__class_Ozero(_1124902)), -(_1124906 = c_Groups_Ozero__class_Ozero(_1124902))], (18094 ^ _782476) ^ [] : [18095 ^ _782476 : [(18098 ^ _782476) ^ [] : [_1124906 = c_Groups_Ozero__class_Ozero(_1124902)], (18096 ^ _782476) ^ [] : [_1124904 = c_Groups_Ozero__class_Ozero(_1124902)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124902), _1124904), _1124906) = c_Groups_Ozero__class_Ozero(_1124902))]]], (13256 ^ _782476) ^ [_1027126, _1027128, _1027130, _1027132, _1027134] : [hAPP(c_Set_Oimage(_1027126, _1027128, _1027130), c_Orderings_Otop__class_Otop(tc_fun(_1027126, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1027128, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027126, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027126, _1027128, _1027130), _1027132)), _1027134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027128, tc_HOL_Obool)), _1027132), hAPP(c_Set_Oimage(_1027126, _1027128, _1027130), _1027134))))], (43105 ^ _782476) ^ [_1635746, _1635748, _1635750, _1635752] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1635746), tc_List_Olist(_1635746), c_List_Olistrel(_1635746, _1635748)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635746)), hAPP(hAPP(c_List_Olist_OCons(_1635746), _1635750), _1635752)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635746), tc_HOL_Obool)))) = c_List_Oset__Cons(_1635746, hAPP(c_Relation_OImage(_1635746, _1635746, _1635748), hAPP(hAPP(c_Set_Oinsert(_1635746), _1635750), c_Orderings_Obot__class_Obot(tc_fun(_1635746, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1635746), tc_List_Olist(_1635746), c_List_Olistrel(_1635746, _1635748)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635746)), _1635752), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635746), tc_HOL_Obool))))))], (36180 ^ _782476) ^ [_1465594, _1465596] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1465594), _1465596), hAPP(c_Int_Onumber__class_Onumber__of(_1465594), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465594), _1465596)), class_Fields_Ofield__inverse__zero(_1465594), class_Int_Onumber__ring(_1465594)], (35992 ^ _782476) ^ [_1462785, _1462787] : [class_Int_Onumber__ring(_1462785), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1462785), hAPP(c_Int_Onumber__class_Onumber__of(_1462785), 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)))), _1462787))) = hAPP(c_Int_Onumber__class_Onumber__of(_1462785), c_Int_OMin))], (14182 ^ _782476) ^ [_1046651, _1046653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046651), _1046653)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046651, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046651), _1046653))))], (38738 ^ _782476) ^ [_1524524, _1524526, _1524528, _1524530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524524, _1524524)), hAPP(hAPP(c_Product__Type_OPair(_1524524, _1524524), _1524526), _1524528)), c_Relation_OId__on(_1524524, _1524530))), 38741 ^ _782476 : [(38744 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524524), _1524526), _1524530)))], (38742 ^ _782476) ^ [] : [-(_1524526 = _1524528)]]], (41806 ^ _782476) ^ [_1604211, _1604213, _1604215, _1604217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604211, _1604211)), hAPP(hAPP(c_Product__Type_OPair(_1604211, _1604211), _1604213), _1604215)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604211, _1604211), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604217))), -(_1604213 = _1604215)], (48152 ^ _782476) ^ [_1750941, _1750943, _1750945, _1750947, _1750949] : [c_List_Olist__all2(_1750941, _1750943, _1750945, _1750947, hAPP(c_List_Orev(_1750943), _1750949)), -(c_List_Olist__all2(_1750941, _1750943, _1750945, hAPP(c_List_Orev(_1750941), _1750947), _1750949))], (51566 ^ _782476) ^ [_1827500, _1827502, _1827504, _1827506] : [51569 ^ _782476 : [(51572 ^ _782476) ^ [] : [hAPP(_1827504, 51567 ^ [_1827500, _1827502, _1827504, _1827506]) = hAPP(_1827504, 51568 ^ [_1827500, _1827502, _1827504, _1827506])], (51570 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827500, _1827500)), hAPP(hAPP(c_Product__Type_OPair(_1827500, _1827500), 51567 ^ [_1827500, _1827502, _1827504, _1827506]), 51568 ^ [_1827500, _1827502, _1827504, _1827506])), _1827502)))]], -(c_Equiv__Relations_Ocongruent(_1827500, _1827506, _1827502, _1827504))], (33396 ^ _782476) ^ [_1415442, _1415444, _1415446, _1415448] : [class_Fields_Olinordered__field__inverse__zero(_1415442), class_Int_Onumber(_1415442), 33403 ^ _782476 : [(33404 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415442), _1415444), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))), _1415448)), 33407 ^ _782476 : [(33414 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)))), 33417 ^ _782476 : [(33424 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)), c_Groups_Ozero__class_Ozero(_1415442)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), _1415448)))], (33418 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)), c_Groups_Ozero__class_Ozero(_1415442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415442), _1415448), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))), _1415444)))]]], (33408 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), _1415444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415442), _1415448), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)))))]]], (33430 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415442), _1415444), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))), _1415448))), 33433 ^ _782476 : [(33436 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), _1415444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415442), _1415448), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))))], (33434 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))))]], 33437 ^ _782476 : [(33440 ^ _782476) ^ [] : [33441 ^ _782476 : [(33444 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415442), _1415448), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446))), _1415444))], (33442 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)), c_Groups_Ozero__class_Ozero(_1415442))))]], 33445 ^ _782476 : [(33448 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), _1415448))], (33446 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)), c_Groups_Ozero__class_Ozero(_1415442)))]]], (33438 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415442), c_Groups_Ozero__class_Ozero(_1415442)), hAPP(c_Int_Onumber__class_Onumber__of(_1415442), _1415446)))]]]]], (31201 ^ _782476) ^ [_1372847, _1372849, _1372851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372847), _1372849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372851), 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), _1372849), _1372851)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372847), _1372851))))], (1452 ^ _782476) ^ [_803826, _803828] : [-(class_Lattices_Obounded__lattice__top(_803826)), _803828 = _803826, class_Lattices_Obounded__lattice__top(_803828)], (8713 ^ _782476) ^ [_934228, _934230, _934232, _934234, _934236, _934238] : [hBOOL(hAPP(hAPP(c_member(_934228), _934230), _934232)), _934234 = hAPP(_934236, _934230), -(hBOOL(hAPP(hAPP(c_member(_934238), _934234), hAPP(c_Set_Oimage(_934228, _934238, _934236), _934232))))], (51071 ^ _782476) ^ [_1815956, _1815958, _1815960] : [c_Relation_Orefl__on(_1815956, _1815958, _1815960), c_Relation_Osym(_1815956, _1815960), c_Relation_Otrans(_1815956, _1815960), -(c_Equiv__Relations_Oequiv(_1815956, _1815958, _1815960))], (43453 ^ _782476) ^ [_1645628, _1645630, _1645632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1645628), _1645630)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1645628)), hAPP(c_Set_OCollect(tc_List_Olist(_1645628)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1645628), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1645628)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645628), tc_fun(_1645628, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1645628, tc_HOL_Obool), tc_fun(tc_fun(_1645628, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1645628)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1645628, tc_HOL_Obool))), c_List_Oset(_1645628))), _1645630))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645628), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1645628)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1645628)))), _1645632))))))], (2480 ^ _782476) ^ [_818902, _818904, _818906, _818908] : [-(c_Divides_Odivmod__nat(_818908, _818904) = c_Divides_Odivmod__nat(_818906, _818902)), _818908 = _818906, _818904 = _818902], (22150 ^ _782476) ^ [_1198631, _1198633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198631)), _1198633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198631), _1198633)))], (4244 ^ _782476) ^ [_846782, _846784, _846786, _846788, _846790, _846792] : [-(c_Set_Oimage(_846792, _846788, _846784) = c_Set_Oimage(_846790, _846786, _846782)), _846792 = _846790, _846788 = _846786, _846784 = _846782], (35128 ^ _782476) ^ [_1446655, _1446657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446655)), c_Int_OBit0(_1446657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446655), _1446657)))], (44797 ^ _782476) ^ [_1677257, _1677259, _1677261] : [-(c_List_Olist_ONil(_1677257) = hAPP(hAPP(c_List_Oappend(_1677257), _1677259), _1677261)), _1677259 = c_List_Olist_ONil(_1677257), _1677261 = c_List_Olist_ONil(_1677257)], (8295 ^ _782476) ^ [_925387, _925389, _925391, _925393] : [class_Orderings_Olinorder(_925387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925387), _925389), _925391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925387), _925391), _925393)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_925387, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_925387, _925389, _925391)), c_SetInterval_Oord__class_OgreaterThanAtMost(_925387, _925391, _925393)) = c_SetInterval_Oord__class_OatLeastAtMost(_925387, _925389, _925393))], (22692 ^ _782476) ^ [_1208156, _1208158] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208156), _1208158) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1208156, _1208158))], (26259 ^ _782476) ^ [_1278784, _1278786, _1278788, _1278790, _1278792, _1278794] : [c_Fun_Oinj__on(_1278784, _1278786, _1278788, _1278790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278786, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278784, _1278786, _1278788), _1278790)), _1278792)), c_Fun_Oinj__on(_1278786, _1278784, _1278794, _1278792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278784, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278786, _1278784, _1278794), _1278792)), _1278790)), -(c_Fun_Obij__betw(_1278784, _1278786, 26274 ^ [_1278784, _1278786, _1278788, _1278790, _1278792, _1278794], _1278790, _1278792))], (34512 ^ _782476) ^ [_1435514, _1435516] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435514), _1435516), hAPP(c_Int_Onumber__class_Onumber__of(_1435514), c_Int_OBit1(c_Int_OPls))) = _1435516), class_Fields_Ofield(_1435514), class_Int_Onumber__ring(_1435514)], (34482 ^ _782476) ^ [_1434985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434985), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434985)), c_Int_OPls)))], (9414 ^ _782476) ^ [_951029, _951031, _951033] : [_951029 = c_Orderings_Obot__class_Obot(tc_fun(_951031, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_951031), _951033), _951029))], (44907 ^ _782476) ^ [_1679422, _1679424, _1679426, _1679428] : [44908 ^ _782476 : [(44911 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679422), _1679424), hAPP(c_List_Oset(_1679422), c_List_Obutlast(_1679422, _1679428))))], (44909 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679422), _1679424), hAPP(c_List_Oset(_1679422), c_List_Obutlast(_1679422, _1679426))))]], -(hBOOL(hAPP(hAPP(c_member(_1679422), _1679424), hAPP(c_List_Oset(_1679422), c_List_Obutlast(_1679422, hAPP(hAPP(c_List_Oappend(_1679422), _1679426), _1679428))))))], (4646 ^ _782476) ^ [_853167, _853169, _853171, _853173, _853175, _853177, _853179, _853181, _853183, _853185] : [-(c_Nitpick_Opair__box_Opair__box__case(_853185, _853181, _853177, _853173, _853169) = c_Nitpick_Opair__box_Opair__box__case(_853183, _853179, _853175, _853171, _853167)), _853185 = _853183, _853181 = _853179, _853177 = _853175, _853173 = _853171, _853169 = _853167], (51170 ^ _782476) ^ [_1817489, _1817491] : [c_Equiv__Relations_Opart__equivp(_1817489, _1817491), 51174 ^ _782476 : [(51187 ^ _782476) ^ [_1817831, _1817833] : [-(hBOOL(hAPP(hAPP(_1817491, _1817833), _1817831))), hBOOL(hAPP(hAPP(_1817491, _1817833), _1817833)), hBOOL(hAPP(hAPP(_1817491, _1817831), _1817831)), hAPP(_1817491, _1817833) = hAPP(_1817491, _1817831)], (51177 ^ _782476) ^ [_1817662, _1817664] : [hBOOL(hAPP(hAPP(_1817491, _1817664), _1817662)), 51180 ^ _782476 : [(51185 ^ _782476) ^ [] : [-(hAPP(_1817491, _1817664) = hAPP(_1817491, _1817662))], (51183 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1817491, _1817662), _1817662)))], (51181 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1817491, _1817664), _1817664)))]]], (51175 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1817491, 51173 ^ [_1817489, _1817491]), 51173 ^ [_1817489, _1817491])))]]], (42881 ^ _782476) ^ [_1628550, _1628552, _1628554] : [-(hAPP(c_List_Olexn(_1628550, _1628552), hAPP(c_Nat_OSuc, _1628554)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1628550), tc_List_Olist(_1628550)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1628550, tc_List_Olist(_1628550)), tc_prod(_1628550, tc_List_Olist(_1628550))), tc_prod(tc_List_Olist(_1628550), tc_List_Olist(_1628550)), c_Product__Type_Omap__pair(tc_prod(_1628550, tc_List_Olist(_1628550)), tc_List_Olist(_1628550), tc_prod(_1628550, tc_List_Olist(_1628550)), tc_List_Olist(_1628550), hAPP(c_Product__Type_Oprod_Oprod__case(_1628550, tc_List_Olist(_1628550), tc_List_Olist(_1628550)), c_List_Olist_OCons(_1628550)), hAPP(c_Product__Type_Oprod_Oprod__case(_1628550, tc_List_Olist(_1628550), tc_List_Olist(_1628550)), c_List_Olist_OCons(_1628550)))), c_Wellfounded_Olex__prod(_1628550, tc_List_Olist(_1628550), _1628552, hAPP(c_List_Olexn(_1628550, _1628552), _1628554)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1628550), tc_List_Olist(_1628550))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1628550), tc_List_Olist(_1628550), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628550), tc_fun(tc_List_Olist(_1628550), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628550), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1628550), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628550), tc_HOL_Obool)), tc_List_Olist(_1628550)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1628550))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1628550)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628550), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628550)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628550)))), hAPP(c_Nat_OSuc, _1628554))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628550), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628550)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628550)))), hAPP(c_Nat_OSuc, _1628554)))))))], (49065 ^ _782476) ^ [_1771572, _1771574, _1771576, _1771578] : [49066 ^ _782476 : [(49069 ^ _782476) ^ [] : [c_List_Olist__ex(_1771572, _1771574, _1771578)], (49067 ^ _782476) ^ [] : [hBOOL(hAPP(_1771574, _1771576))]], -(c_List_Olist__ex(_1771572, _1771574, hAPP(hAPP(c_List_Olist_OCons(_1771572), _1771576), _1771578)))], (40939 ^ _782476) ^ [_1582435, _1582437] : [c_Wellfounded_Oacyclic(_1582435, _1582437), 40942 ^ _782476 : [(40943 ^ _782476) ^ [_1582520] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582435, _1582435)), hAPP(hAPP(c_Product__Type_OPair(_1582435, _1582435), _1582520), _1582520)), c_Transitive__Closure_Otrancl(_1582435, _1582437)))]]], (22034 ^ _782476) ^ [_1196875] : [hAPP(c_Nat_OSuc, _1196875) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44833 ^ _782476) ^ [_1677901, _1677903, _1677905] : [hAPP(hAPP(c_List_Oappend(_1677901), _1677903), _1677905) = c_List_Olist_ONil(_1677901), 44836 ^ _782476 : [(44839 ^ _782476) ^ [] : [-(_1677905 = c_List_Olist_ONil(_1677901))], (44837 ^ _782476) ^ [] : [-(_1677903 = c_List_Olist_ONil(_1677901))]]], (20393 ^ _782476) ^ [_1165980, _1165982, _1165984, _1165986, _1165988, _1165990] : [class_Rings_Olinordered__semiring__1__strict(_1165980), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165980), _1165982), _1165984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165980), _1165986), _1165984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165980), c_Groups_Ozero__class_Ozero(_1165980)), _1165988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165980), c_Groups_Ozero__class_Ozero(_1165980)), _1165990)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165980), _1165988), _1165990) = c_Groups_Oone__class_Oone(_1165980), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165980), _1165988), _1165982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165980), _1165990), _1165986))), _1165984)))], (51737 ^ _782476) ^ [_1830686, _1830688, _1830690, _1830692] : [class_Divides_Osemiring__div(_1830686), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830686), _1830688), _1830690)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830686), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830686), _1830690), _1830688)), _1830692) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830686), _1830690), _1830692)), _1830688))], (8567 ^ _782476) ^ [_931191, _931193, _931195, _931197] : [class_Lattices_Osemilattice__inf(_931191), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931191), _931193), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931191), _931195), _931197)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931191), _931195), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931191), _931193), _931197)))], (41597 ^ _782476) ^ [_1599246, _1599248, _1599250] : [c_Relation_Ototal__on(_1599246, _1599248, _1599250), -(c_Relation_Ototal__on(_1599246, _1599248, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599246, _1599246), tc_HOL_Obool)), _1599250), c_Relation_OId(_1599246))))], (45997 ^ _782476) ^ [_1703324, _1703326, _1703328, _1703330] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703324)), hAPP(hAPP(c_List_Omap(_1703326, _1703324), _1703328), _1703330)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703326)), _1703330))], (52115 ^ _782476) ^ [_1837706, _1837708] : [class_Lattices_Obounded__lattice(_1837706), -(class_Lattices_Obounded__lattice__top(tc_fun(_1837708, _1837706)))], (39198 ^ _782476) ^ [_1537869, _1537871, _1537873] : [c_Wellfounded_Owf(_1537869, _1537871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537869, _1537869), tc_HOL_Obool)), _1537873), _1537871)), -(c_Wellfounded_Owf(_1537869, _1537873))], (14320 ^ _782476) ^ [_1049208, _1049210, _1049212] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049208), _1049210)), 14323 ^ _782476 : [(14330 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049208), _1049212)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049208), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049208, tc_HOL_Obool)), _1049212), _1049210))))], (14324 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049208), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049208, tc_HOL_Obool)), _1049212), _1049210))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049208), _1049212)))]]], (25414 ^ _782476) ^ [_1257181, _1257183, _1257185] : [25416 ^ _782476 : [(25419 ^ _782476) ^ [] : [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(_1257183, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25415 ^ [_1257181, _1257183, _1257185]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257183, 25415 ^ [_1257181, _1257183, _1257185])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25417 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25415 ^ [_1257181, _1257183, _1257185]), _1257181)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257183, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257185), hAPP(_1257183, _1257181))), 25429 ^ _782476 : [(25432 ^ _782476) ^ [] : [-(hAPP(_1257183, 25428 ^ [_1257181, _1257183, _1257185]) = _1257185)], (25430 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25428 ^ [_1257181, _1257183, _1257185]), _1257181)))]]], (26846 ^ _782476) ^ [_1289426, _1289428] : [class_Orderings_Olinorder(_1289426), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289426), _1289428), _1289428) = _1289428)], (46948 ^ _782476) ^ [_1724944, _1724946, _1724948] : [hBOOL(hAPP(hAPP(c_member(_1724944), _1724946), hAPP(c_List_Oset(_1724944), _1724948))), -(c_List_Oremdups(_1724944, hAPP(hAPP(c_List_Olist_OCons(_1724944), _1724946), _1724948)) = c_List_Oremdups(_1724944, _1724948))], (45126 ^ _782476) ^ [_1685119, _1685121, _1685123] : [hAPP(hAPP(c_List_Odrop(_1685119), _1685121), _1685123) = c_List_Olist_ONil(_1685119), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685119)), _1685123)), _1685121)))], (24162 ^ _782476) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (49583 ^ _782476) ^ [_1782690, _1782692, _1782694, _1782696] : [hAPP(c_Set_Oimage(_1782690, _1782692, _1782694), c_Orderings_Otop__class_Otop(tc_fun(_1782690, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782692, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782690, _1782692, _1782694), hAPP(c_Set_Oimage(_1782692, _1782690, c_Hilbert__Choice_Oinv__into(_1782690, _1782692, c_Orderings_Otop__class_Otop(tc_fun(_1782690, tc_HOL_Obool)), _1782694)), _1782696)) = _1782696)], (43580 ^ _782476) ^ [_1648805, _1648807, _1648809] : [hBOOL(hAPP(hAPP(c_member(_1648805), _1648807), hAPP(c_List_Oset(_1648805), _1648809))), 43584 ^ _782476 : [(43587 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1648805), _1648809), 43583 ^ [_1648805, _1648807, _1648809]) = _1648807)], (43585 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43583 ^ [_1648805, _1648807, _1648809]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648805)), _1648809))))]]], (39398 ^ _782476) ^ [_1542098, _1542100, _1542102, _1542104] : [c_FunDef_Oreduction__pair(_1542098, _1542100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool)), _1542102), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool), tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool)), _1542100))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool)), _1542104), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool), tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool)), _1542100))), c_Wellfounded_Owf(_1542098, _1542104), -(c_Wellfounded_Owf(_1542098, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542098, _1542098), tc_HOL_Obool)), _1542102), _1542104)))], (38258 ^ _782476) ^ [_1512796, _1512798, _1512800, _1512802, _1512804, _1512806, _1512808, _1512810, _1512812] : [c_Equiv__Relations_Oequiv(_1512796, _1512798, _1512800), c_Equiv__Relations_Oequiv(_1512802, _1512804, _1512806), c_Equiv__Relations_Ocongruent2(_1512796, _1512802, tc_fun(_1512808, tc_HOL_Obool), _1512800, _1512806, _1512810), hBOOL(hAPP(hAPP(c_member(_1512802), _1512812), _1512804)), -(c_Equiv__Relations_Ocongruent(_1512796, tc_fun(_1512808, tc_HOL_Obool), _1512800, hAPP(hAPP(c_COMBB(tc_fun(_1512802, tc_fun(_1512808, tc_HOL_Obool)), tc_fun(_1512808, tc_HOL_Obool), _1512796), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512802, tc_fun(_1512808, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1512802, _1512802, _1512806), hAPP(hAPP(c_Set_Oinsert(_1512802), _1512812), c_Orderings_Obot__class_Obot(tc_fun(_1512802, tc_HOL_Obool)))))), _1512810)))], (17373 ^ _782476) ^ [_1112124, _1112126, _1112128] : [_1112126 = _1112128, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112124), _1112126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112124), _1112128))], (4874 ^ _782476) ^ [_856833, _856835, _856837, _856839, _856841, _856843, _856845, _856847] : [-(c_Random__Sequence_Omap(_856847, _856843, _856839, _856835) = c_Random__Sequence_Omap(_856845, _856841, _856837, _856833)), _856847 = _856845, _856843 = _856841, _856839 = _856837, _856835 = _856833], (5394 ^ _782476) ^ [_864975, _864977, _864979, _864981, _864983, _864985, _864987, _864989, _864991, _864993] : [-(c_New__DSequence_Opos__map(_864993, _864989, _864985, _864981, _864977) = c_New__DSequence_Opos__map(_864991, _864987, _864983, _864979, _864975)), _864993 = _864991, _864989 = _864987, _864985 = _864983, _864981 = _864979, _864977 = _864975], (49245 ^ _782476) ^ [_1775352, _1775354, _1775356] : [49247 ^ _782476 : [(49250 ^ _782476) ^ [] : [hBOOL(hAPP(_1775354, 49246 ^ [_1775352, _1775354, _1775356]))], (49248 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775352), 49246 ^ [_1775352, _1775354, _1775356]), hAPP(c_List_Oset(_1775352), _1775356))))]], -(c_List_Olist__all(_1775352, _1775354, _1775356))], (46142 ^ _782476) ^ [_1707199, _1707201, _1707203] : [c_Fun_Oinj__on(tc_List_Olist(_1707199), tc_List_Olist(_1707201), hAPP(c_List_Omap(_1707199, _1707201), _1707203), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707199), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1707199, _1707201, _1707203, c_Orderings_Otop__class_Otop(tc_fun(_1707199, tc_HOL_Obool))))], (49770 ^ _782476) ^ [_1787396] : [-(c_Predicate_Oconversep(_1787396, _1787396, c_fequal) = c_fequal)], (18136 ^ _782476) ^ [_1125691, _1125693] : [class_Rings_Ocomm__semiring__1(_1125691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125691), _1125693), c_Groups_Ozero__class_Ozero(_1125691)) = c_Groups_Ozero__class_Ozero(_1125691))], (35572 ^ _782476) ^ [_1454533, _1454535] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454535))) = 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), _1454533), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454535))))], (50406 ^ _782476) ^ [_1801033, _1801035, _1801037, _1801039] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1801033), _1801035), _1801037), _1801039) = 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(_1801033)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1801033), _1801035)))], (49641 ^ _782476) ^ [_1784006, _1784008, _1784010, _1784012] : [c_Fun_Oinj__on(_1784006, _1784008, _1784010, c_Orderings_Otop__class_Otop(tc_fun(_1784006, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1784008, _1784006, c_Hilbert__Choice_Oinv__into(_1784006, _1784008, c_Orderings_Otop__class_Otop(tc_fun(_1784006, tc_HOL_Obool)), _1784010)), hAPP(c_Set_Oimage(_1784006, _1784008, _1784010), _1784012)) = _1784012)], (45735 ^ _782476) ^ [_1698139, _1698141, _1698143, _1698145] : [-(_1698139 = c_List_Olist_ONil(_1698141)), 45738 ^ _782476 : [(45745 ^ _782476) ^ [] : [-(_1698143 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698141)), _1698139)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1698141, hAPP(hAPP(c_List_Olist__update(_1698141, _1698139), _1698143), _1698145)) = c_List_Olast(_1698141, _1698139))], (45739 ^ _782476) ^ [] : [_1698143 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698141)), _1698139)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1698141, hAPP(hAPP(c_List_Olist__update(_1698141, _1698139), _1698143), _1698145)) = _1698145)]]], (23165 ^ _782476) ^ [_1217347, _1217349] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217347), _1217349)), -(hAPP(c_Finite__Set_Ocard(_1217347), _1217349) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217347, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217347), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217349))], (50238 ^ _782476) ^ [_1797222, _1797224, _1797226, _1797228, _1797230, _1797232] : [c_Nitpick_Opair__box_OPairBox(_1797222, _1797224, _1797226, _1797228) = c_Nitpick_Opair__box_OPairBox(_1797222, _1797224, _1797230, _1797232), 50241 ^ _782476 : [(50244 ^ _782476) ^ [] : [-(_1797228 = _1797232)], (50242 ^ _782476) ^ [] : [-(_1797226 = _1797230)]]], (2900 ^ _782476) ^ [_825460, _825462, _825464, _825466, _825468, _825470] : [-(c_Nitpick_Otimes__frac(_825470, _825466, _825462) = c_Nitpick_Otimes__frac(_825468, _825464, _825460)), _825470 = _825468, _825466 = _825464, _825462 = _825460], (19498 ^ _782476) ^ [_1149089, _1149091] : [class_Groups_Oab__group__add(_1149089), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149089), hAPP(c_Groups_Ouminus__class_Ouminus(_1149089), _1149091)), _1149091) = c_Groups_Ozero__class_Ozero(_1149089))], (34912 ^ _782476) ^ [_1442522, _1442524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442522)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442524))), -(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(_1442524))), 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), _1442522)), c_Int_Onat))))))], (52543 ^ _782476) ^ [_1842157, _1842159] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1842157, _1842159))), class_Lazy__Sequence_Osmall__lazy(_1842157), class_Lazy__Sequence_Osmall__lazy(_1842159)], (10801 ^ _782476) ^ [_980923, _980925, _980927] : [class_Orderings_Oorder(_980923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980923), _980925), _980927)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_980923, _980927, _980925) = c_Orderings_Obot__class_Obot(tc_fun(_980923, tc_HOL_Obool)))], (42852 ^ _782476) ^ [_1627319, _1627321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 42853 ^ [_1627319, _1627321]), hAPP(_1627319, 42853 ^ [_1627319, _1627321]))), -(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)), _1627319)), _1627321)))))], (1342 ^ _782476) ^ [_802451, _802453] : [-(class_Rings_Ocomm__ring(_802451)), _802453 = _802451, class_Rings_Ocomm__ring(_802453)], (14403 ^ _782476) ^ [_1050849, _1050851, _1050853, _1050855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050849), hAPP(c_Set_Oimage(_1050851, _1050849, _1050853), _1050855))), c_Fun_Oinj__on(_1050851, _1050849, _1050853, _1050855), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050851), _1050855)))], (25512 ^ _782476) ^ [_1259260, _1259262] : [c_Orderings_Obot__class_Obot(tc_fun(_1259260, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259260), _1259262), 25515 ^ _782476 : [(25516 ^ _782476) ^ [_1259345] : [hBOOL(hAPP(_1259262, _1259345))]]], (19779 ^ _782476) ^ [_1153781, _1153783, _1153785] : [class_Groups_Oordered__comm__monoid__add(_1153781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153781), c_Groups_Ozero__class_Ozero(_1153781)), _1153783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153781), c_Groups_Ozero__class_Ozero(_1153781)), _1153785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153781), c_Groups_Ozero__class_Ozero(_1153781)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153781), _1153783), _1153785))))], (28011 ^ _782476) ^ [_1312116] : [class_Orderings_Olinorder(_1312116), -(c_Orderings_Oord_Omax(_1312116, hAPP(c_COMBC(_1312116, _1312116, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1312116))) = c_Orderings_Oord__class_Omin(_1312116))], (37740 ^ _782476) ^ [_1500808, _1500810, _1500812] : [-(_1500808 = hAPP(hAPP(c_Product__Type_OPair(_1500810, _1500812), hAPP(c_Product__Type_Ofst(_1500810, _1500812), _1500808)), hAPP(c_Product__Type_Osnd(_1500810, _1500812), _1500808)))], (13186 ^ _782476) ^ [_1025267, _1025269, _1025271, _1025273, _1025275] : [hBOOL(hAPP(hAPP(c_member(_1025267), _1025269), hAPP(c_Set_Ovimage(_1025267, _1025271, _1025273), _1025275))), -(hBOOL(hAPP(hAPP(c_member(_1025271), hAPP(_1025273, _1025269)), _1025275)))], (13180 ^ _782476) ^ [_1025130, _1025132, _1025134, _1025136, _1025138] : [hBOOL(hAPP(_1025136, hAPP(_1025134, _1025138))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1025130, _1025132, _1025134), _1025136), _1025138)))], (39661 ^ _782476) ^ [_1548727, _1548729, _1548731] : [-(hAPP(c_Relation_ODomain(_1548727, _1548729), hAPP(c_Set_OCollect(tc_prod(_1548727, _1548729)), hAPP(c_Product__Type_Oprod_Oprod__case(_1548727, _1548729, tc_HOL_Obool), _1548731))) = hAPP(c_Set_OCollect(_1548727), hAPP(hAPP(c_COMBB(tc_fun(_1548729, tc_HOL_Obool), tc_HOL_Obool, _1548727), c_HOL_OEx(_1548729)), _1548731)))], (52445 ^ _782476) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (37093 ^ _782476) ^ [_1488756, _1488758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488758)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1488756, _1488758), c_Divides_OposDivAlg(_1488756, _1488758))))], (43565 ^ _782476) ^ [_1648446, _1648448, _1648450] : [43567 ^ _782476 : [(43570 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648446), 43566 ^ [_1648446, _1648448, _1648450]), _1648450))], (43568 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648446), 43566 ^ [_1648446, _1648448, _1648450]), hAPP(c_List_Oset(_1648446), _1648448))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648446)), _1648448), c_List_Olists(_1648446, _1648450))))], (31683 ^ _782476) ^ [_1381905, _1381907] : [-(c_Nitpick_Onat__lcm(_1381905, _1381907) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381905), _1381907)), c_Nitpick_Onat__gcd(_1381905, _1381907)))], (23994 ^ _782476) ^ [_1232317, _1232319] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1232317), _1232319) = 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)), _1232317)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232319))))], (9205 ^ _782476) ^ [_946124, _946126, _946128, _946130, _946132] : [hBOOL(hAPP(hAPP(c_member(_946124), _946126), _946128)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946130, tc_HOL_Obool)), hAPP(_946132, _946126)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946124, tc_fun(_946130, tc_HOL_Obool)), _946128), _946132)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946124, tc_fun(_946130, tc_HOL_Obool)), _946128), _946132))], (7840 ^ _782476) ^ [_915380, _915382, _915384, _915386] : [hBOOL(hAPP(_915380, _915382)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915384, tc_HOL_Obool)), _915386), _915380), _915382)))], (25099 ^ _782476) ^ [_1251513, _1251515, _1251517] : [class_Groups_Oordered__ab__group__add__abs(_1251513), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251513), hAPP(c_Groups_Oabs__class_Oabs(_1251513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251513), hAPP(c_Groups_Oabs__class_Oabs(_1251513), _1251515)), hAPP(c_Groups_Oabs__class_Oabs(_1251513), _1251517)))), hAPP(c_Groups_Oabs__class_Oabs(_1251513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251513), _1251515), _1251517)))))], (47477 ^ _782476) ^ [_1737861] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1737861) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1737861)))], (6897 ^ _782476) ^ [_895468, _895470, _895472, _895474] : [_895468 = _895470, 6900 ^ _782476 : [(6907 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895472), _895470), _895474)), -(hBOOL(hAPP(hAPP(c_member(_895472), _895468), _895474)))], (6901 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895472), _895468), _895474)), -(hBOOL(hAPP(hAPP(c_member(_895472), _895470), _895474)))]]], (40295 ^ _782476) ^ [_1567236, _1567238, _1567240, _1567242, _1567244] : [c_Relation_Orefl__on(_1567236, _1567238, _1567240), c_Relation_Orefl__on(_1567236, _1567242, _1567244), -(c_Relation_Orefl__on(_1567236, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567236, tc_HOL_Obool)), _1567238), _1567242), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567236, _1567236), tc_HOL_Obool)), _1567240), _1567244)))], (20758 ^ _782476) ^ [_1172689, _1172691] : [20760 ^ _782476 : [(20763 ^ _782476) ^ [] : [hBOOL(hAPP(_1172691, 20759 ^ [_1172689, _1172691]))], (20761 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20759 ^ [_1172689, _1172691]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172689))))]], 20764 ^ _782476 : [(20765 ^ _782476) ^ [_1172844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172844), _1172689)), -(hBOOL(hAPP(_1172691, _1172844)))]]], (35272 ^ _782476) ^ [_1449095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449095)))], (39503 ^ _782476) ^ [_1544597, _1544599, _1544601] : [hAPP(c_Relation_ORange(_1544597, _1544599), _1544601) = c_Orderings_Obot__class_Obot(tc_fun(_1544599, tc_HOL_Obool)), -(_1544601 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544597, _1544599), tc_HOL_Obool)))], (26108 ^ _782476) ^ [_1276130, _1276132, _1276134] : [class_Orderings_Olinorder(_1276130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276130), _1276132)), hBOOL(hAPP(hAPP(c_member(_1276130), _1276134), _1276132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276130), _1276134), c_Big__Operators_Olinorder__class_OMax(_1276130, _1276132))))], (28794 ^ _782476) ^ [_1329521, _1329523] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329521)), _1329523) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329521), _1329523)))], (34802 ^ _782476) ^ [_1440162, _1440164, _1440166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440162), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440164)), _1440166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47511 ^ _782476) ^ [_1738636, _1738638, _1738640] : [47512 ^ _782476 : [(47515 ^ _782476) ^ [] : [_1738640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47513 ^ _782476) ^ [] : [-(_1738636 = c_List_Olist_ONil(tc_List_Olist(_1738638)))]], 47519 ^ _782476 : [(47522 ^ _782476) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738638)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1738638)), _1738636), 47518 ^ [_1738636, _1738638, _1738640])) = _1738640], (47520 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47518 ^ [_1738636, _1738638, _1738640]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738638))), _1738636))))]], -(c_List_Otranspose(_1738638, _1738636) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1738638)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738638)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1738638), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738638)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1738638)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1738638), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738638), tc_fun(tc_Nat_Onat, _1738638), tc_Nat_Onat), c_List_Onth(_1738638)), hAPP(c_List_Onth(tc_List_Olist(_1738638)), _1738636))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738638))), _1738636)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1738640)))], (40657 ^ _782476) ^ [_1576406, _1576408] : [hBOOL(hAPP(_1576406, c_Hilbert__Choice_OEps(_1576408, _1576406))), -(hBOOL(hAPP(_1576406, 40660 ^ [_1576406, _1576408])))], (3906 ^ _782476) ^ [_841131, _841133] : [_841133 = _841131, -(c_Lazy__Sequence_Ohit__bound(_841133) = c_Lazy__Sequence_Ohit__bound(_841131))], (1832 ^ _782476) ^ [_808576, _808578] : [-(class_Orderings_Opreorder(_808576)), _808578 = _808576, class_Orderings_Opreorder(_808578)], (5298 ^ _782476) ^ [_863479, _863481, _863483, _863485, _863487, _863489] : [-(c_Lazy__Sequence_Oappend(_863489, _863485, _863481) = c_Lazy__Sequence_Oappend(_863487, _863483, _863479)), _863489 = _863487, _863485 = _863483, _863481 = _863479], (48411 ^ _782476) ^ [_1756440] : [c_List_Onat__list(_1756440), -(c_List_Oembed__list(c_List_Oreturn__list(_1756440)) = _1756440)], (51392 ^ _782476) ^ [_1822281, _1822283, _1822285, _1822287, _1822289] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1822281, _1822283, tc_HOL_Obool, _1822285), _1822287), _1822289)), -(hBOOL(hAPP(_1822285, hAPP(hAPP(c_Product__Type_OPair(_1822281, _1822283), _1822287), _1822289))))], (35346 ^ _782476) ^ [_1450416] : [-(c_Int_Opred(c_Int_OBit0(_1450416)) = c_Int_OBit1(c_Int_Opred(_1450416)))], (52423 ^ _782476) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (40400 ^ _782476) ^ [_1569729, _1569731, _1569733] : [c_Wellfounded_Oacyclic(_1569729, _1569731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569729, _1569729), tc_HOL_Obool)), _1569733), _1569731)), -(c_Wellfounded_Oacyclic(_1569729, _1569733))], (27459 ^ _782476) ^ [_1301777, _1301779, _1301781, _1301783, _1301785] : [class_Groups_Ocomm__monoid__mult(_1301777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301779), _1301781)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301779), _1301783)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301777), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301779, _1301777), _1301785), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301779, tc_HOL_Obool)), _1301781), _1301783))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301779, _1301777), _1301785), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301779, tc_HOL_Obool)), _1301781), _1301783))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301777), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301779, _1301777), _1301785), _1301781)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301779, _1301777), _1301785), _1301783)))], (9825 ^ _782476) ^ [_958887, _958889, _958891, _958893, _958895] : [c_Orderings_Oorder__class_Omono(tc_fun(_958887, tc_HOL_Obool), tc_fun(_958889, tc_HOL_Obool), _958891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958889, tc_HOL_Obool)), hAPP(_958891, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958887, tc_HOL_Obool)), _958893), _958895))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958889, tc_HOL_Obool)), hAPP(_958891, _958893)), hAPP(_958891, _958895)))))], (22013 ^ _782476) ^ [_1196500, _1196502] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1196500, _1196502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196502)), _1196500))], (52585 ^ _782476) ^ [_1842661] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1842661)))], (25584 ^ _782476) ^ [_1260575, _1260577, _1260579] : [-(hAPP(hAPP(c_Set_Oinsert(_1260575), _1260577), hAPP(c_Set_OCollect(_1260575), _1260579)) = hAPP(c_Set_OCollect(_1260575), hAPP(hAPP(c_COMBS(_1260575, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260575), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260575), c_fNot), hAPP(hAPP(c_COMBC(_1260575, _1260575, tc_HOL_Obool), c_fequal), _1260577)))), _1260579)))], (22518 ^ _782476) ^ [_1204802, _1204804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204802), _1204804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204802), hAPP(c_Nat_OSuc, _1204804))))], (5434 ^ _782476) ^ [_865665, _865667] : [_865667 = _865665, -(c_member(_865667) = c_member(_865665))], (48480 ^ _782476) ^ [_1757927, _1757929, _1757931] : [hBOOL(hAPP(c_List_Odistinct(_1757927), _1757929)), -(hBOOL(hAPP(c_List_Odistinct(_1757927), c_List_OdropWhile(_1757927, _1757931, _1757929))))], (14653 ^ _782476) ^ [_1055599, _1055601, _1055603, _1055605, _1055607, _1055609] : [c_Finite__Set_Ofolding(_1055599, _1055601, _1055603, _1055605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055599), _1055607)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055599), _1055609)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055599, tc_HOL_Obool)), _1055607), _1055609) = c_Orderings_Obot__class_Obot(tc_fun(_1055599, tc_HOL_Obool)), -(hAPP(_1055605, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055599, tc_HOL_Obool)), _1055607), _1055609)) = hAPP(c_Fun_Ocomp(_1055601, _1055601, _1055601, hAPP(_1055605, _1055607)), hAPP(_1055605, _1055609)))], (52539 ^ _782476) ^ [_1842106] : [-(class_Nat_Osize(tc_Option_Ooption(_1842106)))], (34924 ^ _782476) ^ [_1442833, _1442835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442833)), hAPP(c_Nat_OSuc, _1442835))), -(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(_1442833))), 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)), _1442835)))))], (52657 ^ _782476) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52275 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (26728 ^ _782476) ^ [_1287064, _1287066, _1287068, _1287070] : [class_Orderings_Olinorder(_1287064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287064), _1287066), _1287068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287064), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287064), _1287070), _1287066)), _1287068)))], (10431 ^ _782476) ^ [_972196, _972198, _972200, _972202] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972196, tc_HOL_Obool)), _972198), hAPP(hAPP(c_Set_Oinsert(_972196), _972200), _972202)) = hAPP(hAPP(c_Set_Oinsert(_972196), _972200), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972196, tc_HOL_Obool)), _972198), _972202)))], (38507 ^ _782476) ^ [_1519497, _1519499, _1519501, _1519503] : [c_Equiv__Relations_Oequivp(_1519497, _1519499), hBOOL(hAPP(hAPP(_1519499, _1519501), _1519503)), -(hBOOL(hAPP(hAPP(_1519499, _1519503), _1519501)))], (43103 ^ _782476) ^ [_1635686, _1635688, _1635690, _1635692] : [-(c_List_Olist_Olist__size(_1635686, _1635688, hAPP(hAPP(c_List_Olist_OCons(_1635686), _1635690), _1635692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1635688, _1635690)), c_List_Olist_Olist__size(_1635686, _1635688, _1635692))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32540 ^ _782476) ^ [_1398805, _1398807] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398805), _1398807)), -(c_Fun_Obij__betw(_1398805, tc_Nat_Onat, 32543 ^ [_1398805, _1398807], _1398807, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1398805), _1398807))))], (30997 ^ _782476) ^ [_1369644, _1369646, _1369648, _1369650] : [class_Divides_Osemiring__div(_1369644), -(_1369646 = c_Groups_Ozero__class_Ozero(_1369644)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369644), _1369646), _1369648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369644), _1369646), _1369650)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369644), _1369648), _1369650))], (26918 ^ _782476) ^ [_1290728, _1290730, _1290732] : [class_Orderings_Olinorder(_1290728), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290728), _1290730), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290728), _1290730), _1290732)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290728), _1290730), _1290732))], (26560 ^ _782476) ^ [_1284198, _1284200, _1284202, _1284204] : [class_Orderings_Olinorder(_1284198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284198), _1284200), _1284202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284198), _1284200), _1284204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284198), _1284200), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284198), _1284202), _1284204))))], (45398 ^ _782476) ^ [_1691102, _1691104, _1691106] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691102, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691104)), _1691106)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1691104, _1691102), _1691106) = _1691106)], (31994 ^ _782476) ^ [_1388634, _1388636, _1388638] : [class_Divides_Oring__div(_1388634), -(c_Divides_Odiv__class_Omod(_1388634, hAPP(c_Groups_Ouminus__class_Ouminus(_1388634), _1388636), _1388638) = c_Divides_Odiv__class_Omod(_1388634, hAPP(c_Groups_Ouminus__class_Ouminus(_1388634), c_Divides_Odiv__class_Omod(_1388634, _1388636, _1388638)), _1388638))], (46748 ^ _782476) ^ [_1720771, _1720773, _1720775, _1720777, _1720779, _1720781] : [c_List_Olist__all2(_1720771, _1720773, _1720775, _1720777, _1720779), -(c_List_Olist__all2(_1720771, _1720773, _1720775, hAPP(hAPP(c_List_Otake(_1720771), _1720781), _1720777), hAPP(hAPP(c_List_Otake(_1720773), _1720781), _1720779)))], (7265 ^ _782476) ^ [_903478, _903480, _903482, _903484] : [class_Groups_Ouminus(_903478), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903480, _903478)), _903482), _903484) = hAPP(c_Groups_Ouminus__class_Ouminus(_903478), hAPP(_903482, _903484)))], (47022 ^ _782476) ^ [_1726342, _1726344] : [47024 ^ _782476 : [(47027 ^ _782476) ^ [] : [47023 ^ [_1726342, _1726344] = c_List_Olist_ONil(_1726342)], (47025 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726342)), 47023 ^ [_1726342, _1726344]), hAPP(c_List_Oset(tc_List_Olist(_1726342)), _1726344))))]], -(c_List_Oconcat(_1726342, _1726344) = c_List_Olist_ONil(_1726342))], (48369 ^ _782476) ^ [_1755518, _1755520, _1755522, _1755524, _1755526] : [hBOOL(hAPP(hAPP(c_member(_1755518), _1755520), hAPP(c_List_Oset(_1755518), _1755522))), -(hBOOL(hAPP(_1755524, _1755520))), -(c_List_OtakeWhile(_1755518, _1755524, hAPP(hAPP(c_List_Oappend(_1755518), _1755522), _1755526)) = c_List_OtakeWhile(_1755518, _1755524, _1755522))], (13621 ^ _782476) ^ [_1034756, _1034758, _1034760, _1034762, _1034764, _1034766] : [13623 ^ _782476 : [(13626 ^ _782476) ^ [] : [hAPP(_1034760, 13622 ^ [_1034756, _1034758, _1034760, _1034762, _1034764, _1034766]) = hAPP(_1034762, 13622 ^ [_1034756, _1034758, _1034760, _1034762, _1034764, _1034766])], (13624 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034756), 13622 ^ [_1034756, _1034758, _1034760, _1034762, _1034764, _1034766]), _1034758)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034756, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034756, _1034764, _1034760), _1034766)), _1034758) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034756, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034756, _1034764, _1034762), _1034766)), _1034758))], (43433 ^ _782476) ^ [_1645150, _1645152, _1645154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645150)), _1645152)), _1645154)), -(hAPP(hAPP(c_List_Otake(_1645150), _1645154), _1645152) = _1645152)], (47198 ^ _782476) ^ [_1731053, _1731055, _1731057, _1731059] : [hBOOL(hAPP(_1731053, _1731055)), -(hAPP(c_List_Ofilter(_1731057, _1731053), hAPP(hAPP(c_List_Olist_OCons(_1731057), _1731055), _1731059)) = hAPP(hAPP(c_List_Olist_OCons(_1731057), _1731055), hAPP(c_List_Ofilter(_1731057, _1731053), _1731059)))], (17774 ^ _782476) ^ [_1119398] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119398), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1119398)], (9261 ^ _782476) ^ [_947981, _947983] : [class_Lattices_Oboolean__algebra(_947981), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947981), hAPP(c_Groups_Ouminus__class_Ouminus(_947981), _947983)), _947983) = c_Orderings_Otop__class_Otop(_947981))], (11218 ^ _782476) ^ [_988381, _988383, _988385, _988387] : [class_Orderings_Oorder(_988381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988381), _988383), _988385)), _988383 = _988387, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988381), _988387), _988385)))], (50014 ^ _782476) ^ [_1792352, _1792354, _1792356] : [-(_1792352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1792354, c_List_Oreplicate(_1792354, _1792352, _1792356)) = _1792356)], (39470 ^ _782476) ^ [_1543810, _1543812] : [-(c_List_Olex(_1543810, _1543812) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1543810), tc_List_Olist(_1543810)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1543810, _1543812)))], (4686 ^ _782476) ^ [_853857, _853859, _853861, _853863] : [-(c_HOL_OThe(_853863, _853859) = c_HOL_OThe(_853861, _853857)), _853863 = _853861, _853859 = _853857], (44969 ^ _782476) ^ [_1681056, _1681058, _1681060, _1681062] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681056), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681058)), _1681060)))), -(hAPP(hAPP(c_List_Onth(_1681058), hAPP(hAPP(c_List_Oappend(_1681058), _1681060), _1681062)), _1681056) = hAPP(hAPP(c_List_Onth(_1681058), _1681062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681056), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681058)), _1681060))))], (32555 ^ _782476) ^ [_1399062, _1399064, _1399066] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399062, _1399064)), _1399066) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399062), _1399066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399064), _1399066)))], (47383 ^ _782476) ^ [_1736274, _1736276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736274), _1736276))), -(c_List_Oupt(_1736274, _1736276) = c_List_Olist_ONil(tc_Nat_Onat))], (49619 ^ _782476) ^ [_1783525, _1783527, _1783529, _1783531, _1783533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783525, tc_HOL_Obool)), _1783527), hAPP(c_Set_Oimage(_1783529, _1783525, _1783531), _1783533))), -(c_Fun_Oinj__on(_1783525, _1783529, c_Hilbert__Choice_Oinv__into(_1783529, _1783525, _1783533, _1783531), _1783527))], (600 ^ _782476) ^ [_791602, _791604, _791606, _791608, _791610, _791612] : [-(c_Finite__Set_Ofun__left__comm__idem(_791610, _791606, _791602)), c_Finite__Set_Ofun__left__comm__idem(_791612, _791608, _791604), _791612 = _791610, _791608 = _791606, _791604 = _791602], (23978 ^ _782476) ^ [_1232015, _1232017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232015)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232015), _1232017)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232015)), hAPP(c_Int_Onat, _1232017)))], (8963 ^ _782476) ^ [_939237, _939239, _939241] : [class_Lattices_Olattice(_939237), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939237), _939239), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939237), _939239), _939241)) = _939239)], (3368 ^ _782476) ^ [_832750, _832752] : [_832752 = _832750, -(c_Random_Orange(_832752) = c_Random_Orange(_832750))], (34016 ^ _782476) ^ [_1427388] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427388) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1427388))], (23418 ^ _782476) ^ [_1222335, _1222337, _1222339] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222335), _1222337)), hBOOL(hAPP(hAPP(c_member(_1222335), _1222339), _1222337)), -(hAPP(c_Finite__Set_Ocard(_1222335), _1222337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222335, tc_HOL_Obool)), _1222337), hAPP(hAPP(c_Set_Oinsert(_1222335), _1222339), c_Orderings_Obot__class_Obot(tc_fun(_1222335, tc_HOL_Obool)))))))], (2674 ^ _782476) ^ [_821901, _821903, _821905, _821907, _821909, _821911, _821913, _821915] : [-(c_Product__Type_Oapsnd(_821915, _821911, _821907, _821903) = c_Product__Type_Oapsnd(_821913, _821909, _821905, _821901)), _821915 = _821913, _821911 = _821909, _821907 = _821905, _821903 = _821901], (34856 ^ _782476) ^ [_1441158, _1441160] : [class_Int_Onumber__ring(_1441158), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1441158), hAPP(c_Int_Onumber__class_Onumber__of(_1441158), _1441160)), c_Groups_Oone__class_Oone(_1441158)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1441160), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (52351 ^ _782476) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (4720 ^ _782476) ^ [_854376, _854378] : [_854378 = _854376, -(c_Nat_Osize__class_Osize(_854378) = c_Nat_Osize__class_Osize(_854376))], (47188 ^ _782476) ^ [_1730868, _1730870, _1730872, _1730874] : [-(hAPP(c_List_Ofilter(_1730868, _1730870), hAPP(c_List_Ofilter(_1730868, _1730872), _1730874)) = hAPP(c_List_Ofilter(_1730868, hAPP(hAPP(c_COMBS(_1730868, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1730868), c_fconj), _1730872)), _1730870)), _1730874))], (23661 ^ _782476) ^ [_1226941, _1226943] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1226941, _1226943)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226943), _1226941)))], (18418 ^ _782476) ^ [_1129734, _1129736] : [18419 ^ _782476 : [(18422 ^ _782476) ^ [] : [_1129736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18420 ^ _782476) ^ [] : [_1129734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129734), _1129736) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15075 ^ _782476) ^ [_1064044, _1064046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1064044, tc_HOL_Obool)), _1064046)), 15081 ^ _782476 : [(15084 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064044), 15080 ^ [_1064044, _1064046]))], (15082 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1064044, tc_HOL_Obool)), 15080 ^ [_1064044, _1064046]), _1064046)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1064044), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1064044, tc_HOL_Obool), _1064046))))], (33508 ^ _782476) ^ [_1417625, _1417627, _1417629, _1417631] : [class_Fields_Olinordered__field__inverse__zero(_1417625), class_Int_Onumber(_1417625), 33515 ^ _782476 : [(33516 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417625), _1417629), _1417631))), 33519 ^ _782476 : [(33526 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), c_Groups_Ozero__class_Ozero(_1417625)), _1417631))), 33529 ^ _782476 : [(33536 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417631), c_Groups_Ozero__class_Ozero(_1417625)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), c_Groups_Ozero__class_Ozero(_1417625))))], (33530 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417631), c_Groups_Ozero__class_Ozero(_1417625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), _1417631))))]]], (33520 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), c_Groups_Ozero__class_Ozero(_1417625)), _1417631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), _1417631)), _1417629)))]]], (33542 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417625), _1417629), _1417631)))), 33545 ^ _782476 : [(33548 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), _1417631)), _1417629))], (33546 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), c_Groups_Ozero__class_Ozero(_1417625)), _1417631)))]], 33549 ^ _782476 : [(33552 ^ _782476) ^ [] : [33553 ^ _782476 : [(33556 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), _1417631)))], (33554 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417631), c_Groups_Ozero__class_Ozero(_1417625))))]], 33557 ^ _782476 : [(33560 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), hAPP(c_Int_Onumber__class_Onumber__of(_1417625), _1417627)), c_Groups_Ozero__class_Ozero(_1417625)))], (33558 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), _1417631), c_Groups_Ozero__class_Ozero(_1417625)))]]], (33550 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417625), c_Groups_Ozero__class_Ozero(_1417625)), _1417631))]]]]], (42411 ^ _782476) ^ [_1617632, _1617634, _1617636, _1617638, _1617640, _1617642] : [c_Finite__Set_Ofun__left__comm(_1617632, _1617634, _1617636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617632), _1617638)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617632, _1617634, _1617636), _1617640), hAPP(hAPP(c_Set_Oinsert(_1617632), _1617642), _1617638)) = hAPP(hAPP(_1617636, _1617642), hAPP(hAPP(c_Finite__Set_Ofold(_1617632, _1617634, _1617636), _1617640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617632, tc_HOL_Obool)), _1617638), hAPP(hAPP(c_Set_Oinsert(_1617632), _1617642), c_Orderings_Obot__class_Obot(tc_fun(_1617632, tc_HOL_Obool)))))))], (52473 ^ _782476) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (7321 ^ _782476) ^ [_904631, _904633, _904635, _904637, _904639] : [-(hBOOL(hAPP(hAPP(c_member(_904631), _904633), c_SetInterval_Oord_OgreaterThanLessThan(_904631, _904635, _904637, _904639)))), hBOOL(hAPP(hAPP(_904635, _904637), _904633)), hBOOL(hAPP(hAPP(_904635, _904633), _904639))], (13374 ^ _782476) ^ [_1029985, _1029987, _1029989, _1029991, _1029993] : [c_Fun_Oinj__on(_1029985, _1029987, _1029989, _1029991), hBOOL(hAPP(hAPP(c_member(_1029987), _1029993), hAPP(c_Set_Oimage(_1029985, _1029987, _1029989), _1029991))), -(hAPP(_1029989, hAPP(c_Fun_Othe__inv__into(_1029985, _1029987, _1029991, _1029989), _1029993)) = _1029993)], (49408 ^ _782476) ^ [] : [-(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)))], (15772 ^ _782476) ^ [_1077610, _1077612, _1077614] : [class_Lattices_Osemilattice__inf(_1077610), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077610), _1077612)), hBOOL(hAPP(hAPP(c_member(_1077610), _1077614), _1077612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077610), hAPP(c_Finite__Set_Ofold1(_1077610, c_Lattices_Osemilattice__inf__class_Oinf(_1077610)), _1077612)), _1077614)))], (18296 ^ _782476) ^ [_1127947, _1127949] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127947), _1127949) = _1127947, -(_1127949 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11156 ^ _782476) ^ [_987404, _987406, _987408] : [class_Orderings_Opreorder(_987404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987404), _987406), _987408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987404), _987408), _987406))], (19348 ^ _782476) ^ [_1146569] : [class_Rings_Olinordered__semidom(_1146569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146569), c_Groups_Oone__class_Oone(_1146569)), c_Groups_Ozero__class_Ozero(_1146569)))], (46364 ^ _782476) ^ [_1712064] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1712064)) = _1712064)], (10595 ^ _782476) ^ [_976050, _976052, _976054, _976056] : [hBOOL(hAPP(hAPP(c_member(_976050), _976052), _976054)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976050, tc_HOL_Obool)), _976054), hAPP(hAPP(c_Set_Oinsert(_976050), _976052), _976056)) = hAPP(hAPP(c_Set_Oinsert(_976050), _976052), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976050, tc_HOL_Obool)), _976054), _976056)))], (52641 ^ _782476) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (40357 ^ _782476) ^ [_1568620, _1568622] : [c_Wellfounded_Owf(_1568620, _1568622), -(c_Wellfounded_OwfP(_1568620, hAPP(hAPP(c_COMBC(_1568620, tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_fun(_1568620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568620, tc_fun(tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_fun(_1568620, tc_HOL_Obool)), _1568620), c_COMBC(_1568620, tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568620, tc_prod(_1568620, _1568620)), tc_fun(_1568620, tc_fun(tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_HOL_Obool)), _1568620), hAPP(c_COMBB(tc_prod(_1568620, _1568620), tc_fun(tc_fun(tc_prod(_1568620, _1568620), tc_HOL_Obool), tc_HOL_Obool), _1568620), c_member(tc_prod(_1568620, _1568620)))), c_Product__Type_OPair(_1568620, _1568620)))), _1568622)))], (39655 ^ _782476) ^ [_1548529, _1548531, _1548533, _1548535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548529, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1548529, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548529, _1548531), _1548533)), hAPP(c_Relation_ODomain(_1548529, _1548531), _1548535))), hAPP(c_Relation_ODomain(_1548529, _1548531), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1548529, _1548531), tc_HOL_Obool)), _1548533), _1548535)))))], (17944 ^ _782476) ^ [_1122797, _1122799] : [class_Rings_Olinordered__semidom(_1122797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122797), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122797), _1122799)), c_Groups_Ozero__class_Ozero(_1122797)))], (46426 ^ _782476) ^ [_1713111, _1713113] : [-(c_Code__Numeral_Onat__of__aux(_1713111, _1713113) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713111)), _1713113))], (1592 ^ _782476) ^ [_805576, _805578] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_805576)), _805578 = _805576, class_Groups_Oordered__ab__semigroup__add__imp__le(_805578)], (18116 ^ _782476) ^ [_1125420, _1125422, _1125424] : [class_Rings_Ono__zero__divisors(_1125420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125420), _1125422), _1125424) = c_Groups_Ozero__class_Ozero(_1125420), -(_1125422 = c_Groups_Ozero__class_Ozero(_1125420)), -(_1125424 = c_Groups_Ozero__class_Ozero(_1125420))], (44332 ^ _782476) ^ [_1666671, _1666673] : [c_Orderings_Obot__class_Obot(tc_fun(_1666671, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666671), _1666673), -(_1666673 = c_List_Olist_ONil(_1666671))], (51601 ^ _782476) ^ [_1828264, _1828266, _1828268, _1828270, _1828272] : [-(c_Lazy__Sequence_Omap(_1828264, _1828266, _1828268, c_Lazy__Sequence_Olazy__sequence_OInsert(_1828264, _1828270, _1828272)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1828266, hAPP(_1828268, _1828270), c_Lazy__Sequence_Omap(_1828264, _1828266, _1828268, _1828272)))], (52313 ^ _782476) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (18626 ^ _782476) ^ [_1133289, _1133291, _1133293] : [class_Rings_Oordered__cancel__semiring(_1133289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133289), _1133291), _1133293)), c_Groups_Ozero__class_Ozero(_1133289)))), 18631 ^ _782476 : [(18638 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133289), _1133291), c_Groups_Ozero__class_Ozero(_1133289))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133289), c_Groups_Ozero__class_Ozero(_1133289)), _1133293))], (18632 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133289), c_Groups_Ozero__class_Ozero(_1133289)), _1133291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133289), _1133293), c_Groups_Ozero__class_Ozero(_1133289)))]]], (21161 ^ _782476) ^ [_1180011, _1180013] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180011), _1180013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180013), _1180011)))], (24616 ^ _782476) ^ [_1242758, _1242760] : [class_Rings_Oring__1(_1242758), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1242760)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1242758), hAPP(c_Int_Oring__1__class_Oof__int(_1242758), _1242760)))], (45324 ^ _782476) ^ [_1689634, _1689636, _1689638] : [-(_1689634 = c_List_Olist_ONil(_1689636)), -(hAPP(c_List_Ohd(_1689636), hAPP(c_List_Orotate(_1689636, _1689638), _1689634)) = hAPP(hAPP(c_List_Onth(_1689636), _1689634), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1689638, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689636)), _1689634))))], (34254 ^ _782476) ^ [_1431524, _1431526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431524), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431526)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431524)) = 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), _1431526), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1431524)))), 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)))], (20957 ^ _782476) ^ [_1176479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176479)))], (2096 ^ _782476) ^ [_812938, _812940, _812942, _812944, _812946, _812948] : [-(c_Partial__Function_Oflat__lub(_812948, _812944, _812940) = c_Partial__Function_Oflat__lub(_812946, _812942, _812938)), _812948 = _812946, _812944 = _812942, _812940 = _812938], (1282 ^ _782476) ^ [_801701, _801703] : [-(class_Rings_Olinordered__idom(_801701)), _801703 = _801701, class_Rings_Olinordered__idom(_801703)], (42551 ^ _782476) ^ [_1620419, _1620421, _1620423, _1620425] : [class_Orderings_Olinorder(_1620419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620419), _1620421)), 42561 ^ _782476 : [(42564 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620419), 42560 ^ [_1620419, _1620421, _1620423, _1620425]), _1620423))], (42562 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620419), 42560 ^ [_1620419, _1620421, _1620423, _1620425]), _1620421)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620419), hAPP(hAPP(c_Finite__Set_Ofold(_1620419, _1620419, c_Orderings_Oord__class_Omax(_1620419)), _1620425), _1620421)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1620419), _1620423), _1620425))))], (37734 ^ _782476) ^ [_1500663, _1500665, _1500667] : [-(hAPP(c_Product__Type_Ofst(_1500663, _1500665), _1500667) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500663, _1500665, _1500663), c_COMBK(_1500663, _1500665)), _1500667))], (40664 ^ _782476) ^ [_1576505, _1576507] : [40665 ^ _782476 : [(40666 ^ _782476) ^ [_1576551] : [hBOOL(hAPP(_1576505, _1576551))]], -(hBOOL(hAPP(_1576505, c_Hilbert__Choice_OEps(_1576507, _1576505))))], (51146 ^ _782476) ^ [_1817088, _1817090, _1817092, _1817094, _1817096] : [c_Equiv__Relations_Opart__equivp(_1817088, _1817090), hBOOL(hAPP(hAPP(_1817090, _1817092), _1817094)), hBOOL(hAPP(hAPP(_1817090, _1817094), _1817096)), -(hBOOL(hAPP(hAPP(_1817090, _1817092), _1817096)))], (45306 ^ _782476) ^ [_1689469, _1689471] : [-(_1689469 = c_List_Olist_ONil(_1689471)), -(hBOOL(hAPP(hAPP(c_member(_1689471), hAPP(c_List_Ohd(_1689471), _1689469)), hAPP(c_List_Oset(_1689471), _1689469))))], (40159 ^ _782476) ^ [_1563864, _1563866, _1563868, _1563870, _1563872, _1563874, _1563876] : [-(hAPP(c_Product__Type_Osnd(_1563864, _1563866), hAPP(c_Product__Type_Omap__pair(_1563868, _1563864, _1563870, _1563866, _1563872, _1563874), _1563876)) = hAPP(_1563874, hAPP(c_Product__Type_Osnd(_1563868, _1563870), _1563876)))], (46479 ^ _782476) ^ [_1714192, _1714194, _1714196, _1714198] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714192)), _1714194), c_List_Olists(_1714192, _1714196))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714192)), _1714194), c_List_Olists(_1714192, _1714198))), -(hBOOL(hAPP(c_List_Olistsp(_1714192, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714192, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1714192, tc_fun(_1714192, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714192)), _1714196)), hAPP(hAPP(c_COMBC(_1714192, tc_fun(_1714192, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714192)), _1714198))), _1714194)))], (12208 ^ _782476) ^ [_1004361, _1004363, _1004365] : [class_Orderings_Oorder(_1004361), 12211 ^ _782476 : [(12218 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004361), _1004363), _1004365))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004361, _1004363), _1004365) = c_Orderings_Obot__class_Obot(tc_fun(_1004361, tc_HOL_Obool)))], (12212 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004361, _1004363), _1004365) = c_Orderings_Obot__class_Obot(tc_fun(_1004361, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004361), _1004363), _1004365))]]], (9215 ^ _782476) ^ [_946411, _946413, _946415, _946417, _946419] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946411, tc_fun(_946413, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946411, tc_HOL_Obool)), _946415), _946417)), _946419) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946413, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946411, tc_fun(_946413, tc_HOL_Obool)), _946415), _946419)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946411, tc_fun(_946413, tc_HOL_Obool)), _946417), _946419)))], (52451 ^ _782476) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (13702 ^ _782476) ^ [_1036542, _1036544, _1036546, _1036548, _1036550, _1036552, _1036554, _1036556] : [c_Fun_Obij__betw(_1036542, _1036544, _1036546, _1036548, _1036550), c_Fun_Obij__betw(_1036544, _1036552, _1036554, _1036550, _1036556), -(c_Fun_Obij__betw(_1036542, _1036552, hAPP(c_Fun_Ocomp(_1036544, _1036552, _1036542, _1036554), _1036546), _1036548, _1036556))], (52381 ^ _782476) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (20637 ^ _782476) ^ [_1170505, _1170507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170505)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170505), _1170507)))], (42341 ^ _782476) ^ [_1616441, _1616443, _1616445] : [class_Lattices_Olattice(_1616441), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616441), _1616443)), -(hBOOL(hAPP(hAPP(c_member(_1616441), _1616445), _1616443))), -(c_Big__Operators_Olattice__class_OInf__fin(_1616441, hAPP(hAPP(c_Set_Oinsert(_1616441), _1616445), _1616443)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616441, _1616441, c_Lattices_Osemilattice__inf__class_Oinf(_1616441)), _1616445), _1616443))], (512 ^ _782476) ^ [_790336, _790338] : [-(class_Rings_Oinverse(_790336)), _790338 = _790336, class_Rings_Oinverse(_790338)], (49041 ^ _782476) ^ [_1771118, _1771120, _1771122] : [hBOOL(hAPP(hAPP(c_member(_1771118), _1771120), hAPP(c_List_Oset(_1771118), _1771122))), -(_1771122 = hAPP(hAPP(c_List_Oappend(_1771118), 49044 ^ [_1771118, _1771120, _1771122]), hAPP(hAPP(c_List_Olist_OCons(_1771118), _1771120), 49045 ^ [_1771118, _1771120, _1771122])))], (48608 ^ _782476) ^ [_1760743, _1760745] : [class_Orderings_Olinorder(_1760743), 48611 ^ _782476 : [(48632 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760743, _1760745)), 48633 ^ _782476 : [(48636 ^ _782476) ^ [_1761303, _1761305] : [_1760745 = hAPP(hAPP(c_List_Olist_OCons(_1760743), _1761303), _1761305), 48642 ^ _782476 : [(48645 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760743), _1761303), 48641 ^ [_1760743, _1760745, _1761303, _1761305]))], (48643 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760743), 48641 ^ [_1760743, _1760745, _1761303, _1761305]), hAPP(c_List_Oset(_1760743), _1761305))))]], c_List_Olinorder__class_Osorted(_1760743, _1761305)], (48634 ^ _782476) ^ [] : [_1760745 = c_List_Olist_ONil(_1760743)]]], (48612 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1760743, _1760745), -(_1760745 = c_List_Olist_ONil(_1760743)), 48621 ^ _782476 : [(48624 ^ _782476) ^ [_1761077] : [hBOOL(hAPP(hAPP(c_member(_1760743), _1761077), hAPP(c_List_Oset(_1760743), 48619 ^ [_1760743, _1760745]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760743), 48620 ^ [_1760743, _1760745]), _1761077)))], (48630 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760743, 48619 ^ [_1760743, _1760745]))], (48622 ^ _782476) ^ [] : [-(_1760745 = hAPP(hAPP(c_List_Olist_OCons(_1760743), 48620 ^ [_1760743, _1760745]), 48619 ^ [_1760743, _1760745]))]]]]], (7303 ^ _782476) ^ [_904265, _904267, _904269, _904271, _904273, _904275] : [-(hBOOL(hAPP(hAPP(c_member(_904265), _904267), c_SetInterval_Oord_OatLeastLessThan(_904265, _904269, _904271, _904273, _904275)))), hBOOL(hAPP(hAPP(_904269, _904273), _904267)), hBOOL(hAPP(hAPP(_904271, _904267), _904275))], (40592 ^ _782476) ^ [_1574491, _1574493, _1574495] : [c_Wellfounded_OwfP(_1574491, hAPP(_1574493, 40593 ^ [_1574491, _1574493, _1574495])), 40600 ^ _782476 : [(40603 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574491, tc_HOL_Obool)), c_Predicate_ODomainP(_1574491, _1574491, hAPP(_1574493, 40598 ^ [_1574491, _1574493, _1574495]))), c_Predicate_ORangeP(_1574491, _1574491, hAPP(_1574493, 40599 ^ [_1574491, _1574493, _1574495]))) = c_Orderings_Obot__class_Obot(tc_fun(_1574491, tc_HOL_Obool))], (40601 ^ _782476) ^ [] : [hAPP(_1574493, 40598 ^ [_1574491, _1574493, _1574495]) = hAPP(_1574493, 40599 ^ [_1574491, _1574493, _1574495])]], -(c_Wellfounded_OwfP(_1574491, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1574495, tc_fun(_1574491, tc_fun(_1574491, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1574495, tc_HOL_Obool))), _1574493)))], (27715 ^ _782476) ^ [_1306554, _1306556, _1306558] : [class_Orderings_Olinorder(_1306554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306554), _1306556)), -(_1306558 = c_Orderings_Obot__class_Obot(tc_fun(_1306554, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306554, tc_HOL_Obool)), _1306558), _1306556)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306554), c_Big__Operators_Olinorder__class_OMin(_1306554, _1306558)), c_Big__Operators_Olinorder__class_OMin(_1306554, _1306556)) = c_Big__Operators_Olinorder__class_OMin(_1306554, _1306556))], (30977 ^ _782476) ^ [_1369354, _1369356, _1369358] : [class_Divides_Osemiring__div(_1369354), -(_1369356 = c_Groups_Ozero__class_Ozero(_1369354)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369354), _1369356), _1369358)), _1369356) = _1369358)], (26066 ^ _782476) ^ [_1275586, _1275588] : [class_Orderings_Olinorder(_1275586), -(c_Big__Operators_Olinorder__class_OMax(_1275586, hAPP(hAPP(c_Set_Oinsert(_1275586), _1275588), c_Orderings_Obot__class_Obot(tc_fun(_1275586, tc_HOL_Obool)))) = _1275588)], (39913 ^ _782476) ^ [_1556405, _1556407, _1556409, _1556411] : [-(_1556405 = c_Orderings_Obot__class_Obot(tc_fun(_1556407, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556409, _1556407), _1556409, c_Product__Type_Ofst(_1556409, _1556407)), hAPP(hAPP(c_Product__Type_OSigma(_1556409, _1556407), _1556411), hAPP(c_COMBK(tc_fun(_1556407, tc_HOL_Obool), _1556409), _1556405))) = _1556411)], (8154 ^ _782476) ^ [_921636, _921638, _921640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921636, tc_HOL_Obool)), _921638), _921640)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921636, tc_HOL_Obool)), _921638), _921640) = _921640)], (10511 ^ _782476) ^ [_974264, _974266, _974268] : [_974266 = _974268, -(hBOOL(hAPP(hAPP(c_member(_974264), _974266), hAPP(hAPP(c_Set_Oinsert(_974264), _974268), c_Orderings_Obot__class_Obot(tc_fun(_974264, tc_HOL_Obool))))))], (13318 ^ _782476) ^ [_1028409, _1028411, _1028413, _1028415] : [c_Fun_Oinj__on(_1028409, _1028411, _1028413, _1028415), -(hAPP(c_Set_Oimage(_1028411, _1028409, c_Fun_Othe__inv__into(_1028409, _1028411, _1028415, _1028413)), hAPP(c_Set_Oimage(_1028409, _1028411, _1028413), _1028415)) = _1028415)], (29822 ^ _782476) ^ [_1348364, _1348366, _1348368] : [class_Fields_Ofield__inverse__zero(_1348364), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348364), hAPP(c_Groups_Ouminus__class_Ouminus(_1348364), _1348366)), hAPP(c_Groups_Ouminus__class_Ouminus(_1348364), _1348368)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348364), _1348366), _1348368))], (10617 ^ _782476) ^ [_976565, _976567, _976569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976565, tc_HOL_Obool)), _976567), hAPP(hAPP(c_Set_Oinsert(_976565), _976569), c_Orderings_Obot__class_Obot(tc_fun(_976565, tc_HOL_Obool))))), -(_976567 = c_Orderings_Obot__class_Obot(tc_fun(_976565, tc_HOL_Obool))), -(_976567 = hAPP(hAPP(c_Set_Oinsert(_976565), _976569), c_Orderings_Obot__class_Obot(tc_fun(_976565, tc_HOL_Obool))))], (41042 ^ _782476) ^ [_1584898, _1584900, _1584902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584898, _1584898), tc_HOL_Obool)), _1584900), _1584902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584898, _1584898), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584898, _1584898, _1584898), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1584898, _1584898), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584898, _1584900)), _1584902)), _1584900)), _1584902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584898, _1584898), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584898, _1584900)), _1584902)))], (42077 ^ _782476) ^ [_1611260, _1611262, _1611264, _1611266, _1611268, _1611270] : [c_Finite__Set_Ofun__left__comm__idem(_1611260, _1611262, _1611264), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611260), _1611266)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611260, _1611262, _1611264), _1611268), hAPP(hAPP(c_Set_Oinsert(_1611260), _1611270), _1611266)) = hAPP(hAPP(_1611264, _1611270), hAPP(hAPP(c_Finite__Set_Ofold(_1611260, _1611262, _1611264), _1611268), _1611266)))], (9245 ^ _782476) ^ [_947561, _947563, _947565] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947561, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947561, tc_HOL_Obool), _947563)), _947565) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947561, tc_HOL_Obool), tc_fun(_947561, tc_HOL_Obool)), _947563), hAPP(hAPP(c_COMBC(tc_fun(_947561, tc_HOL_Obool), tc_fun(_947561, tc_HOL_Obool), tc_fun(_947561, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947561, tc_HOL_Obool))), _947565)))], (50030 ^ _782476) ^ [_1792645, _1792647, _1792649] : [-(c_List_Oreplicate(_1792645, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792645)), hAPP(c_List_Ofilter(_1792645, hAPP(c_fequal, _1792647)), _1792649)), _1792647) = hAPP(c_List_Ofilter(_1792645, hAPP(c_fequal, _1792647)), _1792649))], (52383 ^ _782476) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (43352 ^ _782476) ^ [_1642987, _1642989, _1642991, _1642993] : [_1642987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1642989), hAPP(hAPP(c_List_Olist_OCons(_1642989), _1642991), _1642993)), _1642987) = _1642991)], (19054 ^ _782476) ^ [_1141201, _1141203, _1141205, _1141207] : [class_Rings_Olinordered__semiring__strict(_1141201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141201), _1141203), _1141205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141201), c_Groups_Ozero__class_Ozero(_1141201)), _1141207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141201), _1141203), _1141207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141201), _1141205), _1141207))))], (5076 ^ _782476) ^ [_860046, _860048, _860050, _860052] : [-(c_Relation_OId__on(_860052, _860048) = c_Relation_OId__on(_860050, _860046)), _860052 = _860050, _860048 = _860046], (42759 ^ _782476) ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625167, _1625169)), _1625171), hAPP(hAPP(c_Relation_Orel__comp(_1625167, _1625173, _1625169), _1625175), _1625177))), 42765 ^ _782476 : [(42770 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625173, _1625169)), hAPP(hAPP(c_Product__Type_OPair(_1625173, _1625169), 42763 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177]), 42764 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177])), _1625177)))], (42768 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625167, _1625173)), hAPP(hAPP(c_Product__Type_OPair(_1625167, _1625173), 42762 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177]), 42763 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177])), _1625175)))], (42766 ^ _782476) ^ [] : [-(_1625171 = hAPP(hAPP(c_Product__Type_OPair(_1625167, _1625169), 42762 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177]), 42764 ^ [_1625167, _1625169, _1625171, _1625173, _1625175, _1625177]))]]], (50322 ^ _782476) ^ [_1799186, _1799188] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1799186)), _1799188)), 50326 ^ _782476 : [(50327 ^ _782476) ^ [_1799287] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1799186)), _1799287), _1799188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799186)), _1799287)), 50325 ^ [_1799186, _1799188])))]]], (52711 ^ _782476) ^ [_1844023, _1844025] : [hBOOL(_1844023), hBOOL(_1844025), -(hBOOL(hAPP(hAPP(c_fconj, _1844023), _1844025)))], (21141 ^ _782476) ^ [_1179703, _1179705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179703), _1179705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179705), _1179703)), -(_1179703 = _1179705)], (37307 ^ _782476) ^ [_1492463, _1492465, _1492467, _1492469, _1492471] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492463, _1492465), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492467), _1492469))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492471)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492463, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492465), _1492471)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1492467), _1492471)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492465), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1492467, _1492471))), _1492469)))))], (2282 ^ _782476) ^ [_815885, _815887, _815889, _815891] : [-(c_SMT_Oz3mod(_815891, _815887) = c_SMT_Oz3mod(_815889, _815885)), _815891 = _815889, _815887 = _815885], (45088 ^ _782476) ^ [_1684261, _1684263, _1684265, _1684267] : [hBOOL(hAPP(hAPP(c_member(_1684261), _1684263), hAPP(c_List_Oset(_1684261), hAPP(hAPP(c_List_Odrop(_1684261), _1684265), _1684267)))), -(hBOOL(hAPP(hAPP(c_member(_1684261), _1684263), hAPP(c_List_Oset(_1684261), _1684267))))], (23665 ^ _782476) ^ [_1227012] : [hAPP(c_Int_Onat, _1227012) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227012), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33208 ^ _782476) ^ [_1412252, _1412254] : [class_Int_Onumber__ring(_1412252), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412252), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412254)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1412252), hAPP(c_Int_Onumber__class_Onumber__of(_1412252), _1412254)))], (46522 ^ _782476) ^ [_1715128, _1715130, _1715132] : [-(c_List_Olistsp(_1715128, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715128, tc_HOL_Obool)), _1715130), _1715132)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1715128), tc_HOL_Obool)), c_List_Olistsp(_1715128, _1715130)), c_List_Olistsp(_1715128, _1715132)))], (28820 ^ _782476) ^ [_1330120, _1330122, _1330124, _1330126] : [class_Rings_Odivision__ring(_1330120), -(_1330122 = c_Groups_Ozero__class_Ozero(_1330120)), 28827 ^ _782476 : [(28834 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330120), _1330124), _1330122) = _1330126, -(_1330124 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330120), _1330126), _1330122))], (28828 ^ _782476) ^ [] : [_1330124 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330120), _1330126), _1330122), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330120), _1330124), _1330122) = _1330126)]]], (52583 ^ _782476) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (34476 ^ _782476) ^ [_1434890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434890)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434890), c_Int_OPls)))], (46742 ^ _782476) ^ [_1720684, _1720686, _1720688] : [c_List_Olist__all2(_1720688, _1720688, c_fequal, _1720684, _1720686), -(_1720684 = _1720686)], (41074 ^ _782476) ^ [_1586459, _1586461] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586459, _1586459)), hAPP(hAPP(c_Product__Type_OPair(_1586459, _1586459), _1586461), _1586461)), c_Relation_OId(_1586459))))], (17419 ^ _782476) ^ [_1112837, _1112839, _1112841] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112837), _1112839)), _1112841) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112837), _1112841)), _1112839))], (46264 ^ _782476) ^ [_1709835, _1709837, _1709839, _1709841] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709835)), _1709837) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709839)), _1709841), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709835, _1709839), _1709839), c_Product__Type_Osnd(_1709835, _1709839)), hAPP(hAPP(c_List_Ozip(_1709835, _1709839), _1709837), _1709841)) = _1709841)], (24869 ^ _782476) ^ [_1247422, _1247424, _1247426, _1247428] : [class_Groups_Oordered__ab__group__add__abs(_1247422), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247422), c_Groups_Ozero__class_Ozero(_1247422)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247424, _1247422), hAPP(hAPP(c_COMBB(_1247422, _1247422, _1247424), c_Groups_Oabs__class_Oabs(_1247422)), _1247426)), _1247428))))], (9967 ^ _782476) ^ [_962170] : [class_Lattices_Oboolean__algebra(_962170), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962170), c_Orderings_Otop__class_Otop(_962170)) = c_Orderings_Obot__class_Obot(_962170))], (10403 ^ _782476) ^ [_971345, _971347, _971349] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971345, tc_HOL_Obool)), _971347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971345, tc_HOL_Obool)), _971349), _971347)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971345, tc_HOL_Obool)), _971347), _971349))], (45787 ^ _782476) ^ [_1698922, _1698924, _1698926] : [-(_1698922 = c_List_Olist_ONil(_1698924)), -(c_List_Olast(_1698924, hAPP(hAPP(c_List_Olist_OCons(_1698924), _1698926), _1698922)) = c_List_Olast(_1698924, _1698922))], (522 ^ _782476) ^ [_790461, _790463, _790465, _790467, _790469, _790471] : [-(c_Nitpick_Oless__frac(_790469, _790465, _790461)), c_Nitpick_Oless__frac(_790471, _790467, _790463), _790471 = _790469, _790467 = _790465, _790463 = _790461], (6847 ^ _782476) ^ [_894396, _894398, _894400, _894402, _894404] : [6849 ^ _782476 : [(6852 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_894402, 6848 ^ [_894396, _894398, _894400, _894402, _894404]), _894404))], (6850 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894396), 6848 ^ [_894396, _894398, _894400, _894402, _894404]), _894400)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894396, tc_fun(_894398, tc_HOL_Obool)), _894400), _894402), _894404)))], (24622 ^ _782476) ^ [_1242869, _1242871] : [class_Rings_Oring__1(_1242869), -(hBOOL(hAPP(hAPP(c_member(_1242869), hAPP(c_Int_Oring__1__class_Oof__int(_1242869), _1242871)), c_Int_Oring__1__class_OInts(_1242869))))], (38684 ^ _782476) ^ [_1523236, _1523238, _1523240, _1523242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523236), _1523238)), 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)), _1523236), _1523240)), 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)), _1523238), _1523242)), 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)), _1523238), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523240), _1523242))), c_FunDef_Omin__weak)))], (10901 ^ _782476) ^ [_983331, _983333, _983335, _983337, _983339, _983341] : [hBOOL(hAPP(hAPP(c_member(_983331), _983333), _983335)), -(hAPP(c_Set_Oimage(_983331, _983337, c_Fun_Ofun__upd(_983331, _983337, _983339, _983333, _983341)), _983335) = hAPP(hAPP(c_Set_Oinsert(_983337), _983341), hAPP(c_Set_Oimage(_983331, _983337, _983339), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983331, tc_HOL_Obool)), _983335), hAPP(hAPP(c_Set_Oinsert(_983331), _983333), c_Orderings_Obot__class_Obot(tc_fun(_983331, tc_HOL_Obool)))))))], (36938 ^ _782476) ^ [_1485949, _1485951, _1485953] : [-(c_HOL_OThe(tc_prod(_1485949, _1485951), _1485953) = c_HOL_OThe(tc_prod(_1485949, _1485951), hAPP(c_Product__Type_Oprod_Oprod__case(_1485949, 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_1082815, _1082819), hAPP(c_Groups_Otimes__class_Otimes(_1082815), _1082817)), _1082821)), _1082823))], (17926 ^ _782476) ^ [_1122519] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122519)))], (40001 ^ _782476) ^ [_1560167, _1560169] : [-(hAPP(c_Fun_Oid(_1560167), _1560169) = _1560169)], (51623 ^ _782476) ^ [_1828654, _1828656, _1828658] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1828654), _1828656, _1828658)), -(c_List_Olist__ex(tc_Nat_Onat, _1828654, c_List_Oupt(_1828656, _1828658)))], (50466 ^ _782476) ^ [_1802566, _1802568] : [c_Relation_Otrans(_1802566, _1802568), 50469 ^ _782476 : [(50470 ^ _782476) ^ [_1802702, _1802704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802566, _1802566)), hAPP(hAPP(c_Product__Type_OPair(_1802566, _1802566), _1802704), _1802702)), _1802568)), 50473 ^ _782476 : [(50474 ^ _782476) ^ [_1802845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802566, _1802566)), hAPP(hAPP(c_Product__Type_OPair(_1802566, _1802566), _1802702), _1802845)), _1802568)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802566, _1802566)), hAPP(hAPP(c_Product__Type_OPair(_1802566, _1802566), _1802704), _1802845)), _1802568)))]]]]], (9698 ^ _782476) ^ [_956445, _956447, _956449] : [class_Orderings_Oorder(_956445), class_Orderings_Oorder(_956447), c_Orderings_Oorder__class_Ostrict__mono(_956447, _956445, _956449), -(c_Orderings_Oorder__class_Omono(_956447, _956445, _956449))], (1622 ^ _782476) ^ [_805951, _805953] : [-(class_Rings_Olinordered__semiring__strict(_805951)), _805953 = _805951, class_Rings_Olinordered__semiring__strict(_805953)], (8262 ^ _782476) ^ [_924701, _924703, _924705] : [class_Orderings_Olinorder(_924701), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924701), _924703), _924705)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924701, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924701, _924703, _924705)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_924701), _924705)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_924701), _924703))], (40045 ^ _782476) ^ [_1560939, _1560941] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1560939, _1560941, tc_prod(_1560939, _1560941)), c_Product__Type_OPair(_1560939, _1560941)) = c_Fun_Oid(tc_prod(_1560939, _1560941)))], (49344 ^ _782476) ^ [_1777284, _1777286] : [c_List_Olist__ex1(_1777284, _1777286, c_List_Olist_ONil(_1777284))], (42879 ^ _782476) ^ [_1628484, _1628486, _1628488] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628484)), c_List_Osublist(_1628484, _1628486, _1628488)) = 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(_1628484)), _1628486)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1628488)))))], (13018 ^ _782476) ^ [_1021308, _1021310, _1021312, _1021314, _1021316] : [c_Fun_Oinj__on(_1021308, _1021310, _1021312, hAPP(hAPP(c_Set_Oinsert(_1021308), _1021314), _1021316)), 13021 ^ _782476 : [(13024 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021310), hAPP(_1021312, _1021314)), hAPP(c_Set_Oimage(_1021308, _1021310, _1021312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021308, tc_HOL_Obool)), _1021316), hAPP(hAPP(c_Set_Oinsert(_1021308), _1021314), c_Orderings_Obot__class_Obot(tc_fun(_1021308, tc_HOL_Obool)))))))], (13022 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1021308, _1021310, _1021312, _1021316))]]], (32652 ^ _782476) ^ [_1400833, _1400835] : [_1400833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1400835, _1400833) = _1400835)], (29212 ^ _782476) ^ [_1336929, _1336931, _1336933] : [class_Rings_Osemiring__1(_1336929), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336929), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336931), _1336933)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1336929), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336929), _1336931)), _1336933))], (39925 ^ _782476) ^ [_1556655, _1556657, _1556659, _1556661] : [-(_1556655 = c_Orderings_Obot__class_Obot(tc_fun(_1556657, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556657, _1556659), _1556659, c_Product__Type_Osnd(_1556657, _1556659)), hAPP(hAPP(c_Product__Type_OSigma(_1556657, _1556659), _1556655), hAPP(c_COMBK(tc_fun(_1556659, tc_HOL_Obool), _1556657), _1556661))) = _1556661)], (18612 ^ _782476) ^ [_1133034, _1133036, _1133038] : [class_Groups_Oordered__comm__monoid__add(_1133034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133034), _1133036), c_Groups_Ozero__class_Ozero(_1133034))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133034), _1133038), c_Groups_Ozero__class_Ozero(_1133034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133034), _1133036), _1133038)), c_Groups_Ozero__class_Ozero(_1133034))))], (45040 ^ _782476) ^ [_1683061, _1683063] : [-(hAPP(c_List_Orotate1(_1683061), _1683063) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1683061), _1683061, c_List_Olist_ONil(_1683061), hAPP(hAPP(c_COMBB(tc_List_Olist(_1683061), tc_fun(tc_List_Olist(_1683061), tc_List_Olist(_1683061)), _1683061), hAPP(c_COMBC(tc_List_Olist(_1683061), tc_List_Olist(_1683061), tc_List_Olist(_1683061)), c_List_Oappend(_1683061))), hAPP(hAPP(c_COMBC(_1683061, tc_List_Olist(_1683061), tc_List_Olist(_1683061)), c_List_Olist_OCons(_1683061)), c_List_Olist_ONil(_1683061)))), _1683063))], (9372 ^ _782476) ^ [_950391, _950393, _950395] : [class_Orderings_Obot(_950391), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950393, _950391)), _950395) = c_Orderings_Obot__class_Obot(_950391))], (21113 ^ _782476) ^ [_1179316, _1179318, _1179320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179316), _1179318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179316), _1179320)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179318), _1179320))))], (51434 ^ _782476) ^ [_1823147, _1823149, _1823151] : [hBOOL(hAPP(hAPP(c_member(_1823147), _1823149), c_Quotient_ORespects(_1823147, _1823151))), -(hBOOL(hAPP(hAPP(_1823151, _1823149), _1823149)))], (8790 ^ _782476) ^ [_935801, _935803, _935805, _935807] : [class_Lattices_Osemilattice__inf(_935801), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935801), _935803), _935805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935801), _935803), _935807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935801), _935803), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935801), _935805), _935807))))], (8691 ^ _782476) ^ [_933686, _933688, _933690, _933692, _933694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933686, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933688, _933686, _933690), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933688, tc_HOL_Obool)), _933692), _933694))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933686, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933688, _933686, _933690), _933692)), hAPP(c_Set_Oimage(_933688, _933686, _933690), _933694)))))], (1222 ^ _782476) ^ [_800951, _800953] : [-(class_Rings_Olinordered__ring__strict(_800951)), _800953 = _800951, class_Rings_Olinordered__ring__strict(_800953)], (43495 ^ _782476) ^ [_1646780, _1646782] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1646780), tc_fun(_1646780, tc_HOL_Obool), c_List_Oset(_1646780)), hAPP(c_List_Oset(tc_List_Olist(_1646780)), c_Enum_Osublists(_1646780, _1646782))) = hAPP(c_Set_OPow(_1646780), hAPP(c_List_Oset(_1646780), _1646782)))], (20953 ^ _782476) ^ [_1176398] : [-(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)), _1176398))))], (33938 ^ _782476) ^ [_1425978, _1425980] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425978)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425980)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1425978), _1425980)))], (37445 ^ _782476) ^ [_1494884, _1494886, _1494888] : [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), _1494884), _1494886))), -(hBOOL(hAPP(hAPP(_1494888, _1494884), _1494886))), 37452 ^ _782476 : [(37455 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1494888, 37450 ^ [_1494884, _1494886, _1494888]), 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)))), 37451 ^ [_1494884, _1494886, _1494888])))), -(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), 37450 ^ [_1494884, _1494886, _1494888]), 37451 ^ [_1494884, _1494886, _1494888])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37451 ^ [_1494884, _1494886, _1494888]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37465 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1494888, 37450 ^ [_1494884, _1494886, _1494888]), 37451 ^ [_1494884, _1494886, _1494888]))], (37453 ^ _782476) ^ [] : [-(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), 37450 ^ [_1494884, _1494886, _1494888]), 37451 ^ [_1494884, _1494886, _1494888]))))]]], (37655 ^ _782476) ^ [_1499095, _1499097] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1499095, _1499097) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1499095, _1499097)))], (38983 ^ _782476) ^ [_1532149, _1532151, _1532153] : [hBOOL(hAPP(hAPP(c_member(_1532149), _1532151), c_Wellfounded_Oacc(_1532149, _1532153))), 38986 ^ _782476 : [(38987 ^ _782476) ^ [_1532263] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532149, _1532149)), hAPP(hAPP(c_Product__Type_OPair(_1532149, _1532149), _1532263), _1532151)), _1532153)), -(hBOOL(hAPP(hAPP(c_member(_1532149), _1532263), c_Wellfounded_Oacc(_1532149, _1532153))))]]], (52403 ^ _782476) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (35114 ^ _782476) ^ [_1446388, _1446390] : [c_Int_OBit1(_1446388) = c_Int_OBit0(_1446390)], (29320 ^ _782476) ^ [_1338882, _1338884] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338882), c_Groups_Ozero__class_Ozero(_1338882)), hAPP(c_Nat_OSuc, _1338884)) = c_Groups_Ozero__class_Ozero(_1338882)), class_Power_Opower(_1338882), class_Rings_Osemiring__0(_1338882)], (6794 ^ _782476) ^ [_892737, _892739, _892741, _892743, _892745, _892747] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892737, tc_fun(_892739, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892741, tc_fun(_892737, tc_HOL_Obool)), _892743), _892745)), _892747) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892741, tc_fun(_892739, tc_HOL_Obool)), _892743), hAPP(hAPP(c_COMBC(_892741, tc_fun(_892737, tc_fun(_892739, tc_HOL_Obool)), tc_fun(_892739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892737, tc_HOL_Obool), tc_fun(tc_fun(_892737, tc_fun(_892739, tc_HOL_Obool)), tc_fun(_892739, tc_HOL_Obool)), _892741), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892737, tc_fun(_892739, tc_HOL_Obool))), _892745)), _892747)))], (23567 ^ _782476) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24463 ^ _782476) ^ [_1240041, _1240043, _1240045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1240041, 24464 ^ [_1240041, _1240043, _1240045])), hAPP(_1240043, 24464 ^ [_1240041, _1240043, _1240045]))), -(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), _1240043), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240045))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1240041), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240045))) = 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)), _1240043)), _1240041)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240045)))], (24933 ^ _782476) ^ [_1248684, _1248686] : [class_Rings_Olinordered__idom(_1248684), -(c_Groups_Osgn__class_Osgn(_1248684, c_Groups_Osgn__class_Osgn(_1248684, _1248686)) = c_Groups_Osgn__class_Osgn(_1248684, _1248686))], (26840 ^ _782476) ^ [_1289335, _1289337] : [class_Orderings_Olinorder(_1289335), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289335), _1289337), _1289337) = _1289337)], (8723 ^ _782476) ^ [_934421, _934423, _934425, _934427, _934429] : [hBOOL(hAPP(hAPP(c_member(_934421), _934423), _934425)), -(hBOOL(hAPP(hAPP(c_member(_934427), hAPP(_934429, _934423)), hAPP(c_Set_Oimage(_934421, _934427, _934429), _934425))))], (41467 ^ _782476) ^ [_1596016, _1596018, _1596020, _1596022] : [-(hAPP(c_Relation_Oconverse(_1596016, _1596018), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1596016, _1596018), tc_HOL_Obool)), _1596020), _1596022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1596018, _1596016), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1596016, _1596018), _1596020)), hAPP(c_Relation_Oconverse(_1596016, _1596018), _1596022)))], (5572 ^ _782476) ^ [_867812, _867814] : [_867814 = _867812, -(c_Orderings_Obot__class_Obot(_867814) = c_Orderings_Obot__class_Obot(_867812))], (6981 ^ _782476) ^ [_896931, _896933, _896935] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_896931, tc_HOL_Obool)), _896933), _896935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896931, tc_HOL_Obool)), _896933), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896931, tc_HOL_Obool), _896935))))], (39974 ^ _782476) ^ [_1559369, _1559371, _1559373, _1559375] : [-(c_Fun_Oinj__on(_1559369, tc_prod(_1559371, _1559369), 39972 ^ [_1559369, _1559371, _1559373, _1559375], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559371, tc_fun(_1559369, tc_HOL_Obool)), _1559373), _1559375)))], (41757 ^ _782476) ^ [_1602975, _1602977, _1602979] : [c_Relation_Osingle__valued(_1602975, _1602975, _1602977), -(c_Relation_Osingle__valued(_1602975, _1602975, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602975, _1602975), tc_HOL_Obool), _1602979), _1602977)))], (38700 ^ _782476) ^ [_1523608, _1523610] : [-(hAPP(c_Relation_OField(_1523608), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1523608, _1523608), tc_HOL_Obool), _1523610)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1523608, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1523608, _1523608), tc_HOL_Obool), tc_fun(_1523608, tc_HOL_Obool), c_Relation_OField(_1523608)), _1523610)))], (16501 ^ _782476) ^ [_1093237, _1093239, _1093241, _1093243] : [class_Rings_Ocomm__semiring__1(_1093237), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093237), _1093239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093237), _1093241), _1093243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093237), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093237), _1093239), _1093241)), _1093243))], (43043 ^ _782476) ^ [_1633815, _1633817, _1633819, _1633821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633815), tc_List_Olist(_1633815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633815), tc_List_Olist(_1633815)), _1633817), _1633819)), c_List_Olistrel1(_1633815, _1633821))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633815)), _1633817) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633815)), _1633819))], (50341 ^ _782476) ^ [_1799585, _1799587, _1799589, _1799591] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1799585, _1799587, _1799589, _1799591, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799587)) = _1799589)], (9861 ^ _782476) ^ [_959864, _959866, _959868, _959870, _959872] : [-(_959864 = c_Orderings_Obot__class_Obot(tc_fun(_959866, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959868, tc_HOL_Obool)), _959870), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959866, tc_fun(_959868, tc_HOL_Obool)), _959864), _959872)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959866, tc_fun(_959868, tc_HOL_Obool)), _959864), hAPP(hAPP(c_COMBB(tc_fun(_959868, tc_HOL_Obool), tc_fun(_959868, tc_HOL_Obool), _959866), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959868, tc_HOL_Obool)), _959870)), _959872)))], (12288 ^ _782476) ^ [_1005560, _1005562, _1005564, _1005566] : [hBOOL(hAPP(hAPP(c_member(_1005560), _1005562), _1005564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1005560, tc_HOL_Obool)), _1005564), hAPP(_1005566, _1005564))), -(hBOOL(hAPP(hAPP(c_member(_1005560), _1005562), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1005560, tc_HOL_Obool), _1005566))))], (7131 ^ _782476) ^ [_900756, _900758, _900760, _900762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900756, tc_HOL_Obool)), _900758), _900760)), hBOOL(hAPP(hAPP(c_member(_900756), _900762), _900758)), -(hBOOL(hAPP(hAPP(c_member(_900756), _900762), _900760)))], (24610 ^ _782476) ^ [_1242657, _1242659] : [class_Rings_Oring__1(_1242657), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242657), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1242659)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1242657), _1242659))], (23571 ^ _782476) ^ [_1225506, _1225508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225508)), 23578 ^ _782476 : [(23585 ^ _782476) ^ [] : [_1225506 = _1225508, -(hAPP(c_Int_Onat, _1225506) = hAPP(c_Int_Onat, _1225508))], (23579 ^ _782476) ^ [] : [hAPP(c_Int_Onat, _1225506) = hAPP(c_Int_Onat, _1225508), -(_1225506 = _1225508)]]], (52263 ^ _782476) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (28318 ^ _782476) ^ [_1319692, _1319694] : [class_Orderings_Olinorder(_1319692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319692), _1319694)), -(_1319694 = c_Orderings_Obot__class_Obot(tc_fun(_1319692, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1319692), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319692), 28331 ^ [_1319692, _1319694]), 28332 ^ [_1319692, _1319694])), hAPP(hAPP(c_Set_Oinsert(_1319692), 28331 ^ [_1319692, _1319694]), hAPP(hAPP(c_Set_Oinsert(_1319692), 28332 ^ [_1319692, _1319694]), c_Orderings_Obot__class_Obot(tc_fun(_1319692, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1319692), c_Big__Operators_Olattice_OInf__fin(_1319692, c_Orderings_Oord__class_Omin(_1319692), _1319694)), _1319694)))], (16007 ^ _782476) ^ [_1082435, _1082437] : [class_Groups_Omonoid__mult(_1082435), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082435), c_Groups_Oone__class_Oone(_1082435)), _1082437) = _1082437)], (21279 ^ _782476) ^ [_1182048, _1182050] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1182048, _1182050))))], (27777 ^ _782476) ^ [_1307566, _1307568, _1307570, _1307572, _1307574] : [class_Groups_Ocomm__monoid__mult(_1307566), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307568), _1307570)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307568, _1307566), _1307572), hAPP(hAPP(c_Set_Oinsert(_1307568), _1307574), _1307570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307566), hAPP(_1307572, _1307574)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307568, _1307566), _1307572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307568, tc_HOL_Obool)), _1307570), hAPP(hAPP(c_Set_Oinsert(_1307568), _1307574), c_Orderings_Obot__class_Obot(tc_fun(_1307568, tc_HOL_Obool)))))))], (21329 ^ _782476) ^ [] : [-(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))))], (13129 ^ _782476) ^ [_1023992, _1023994, _1023996, _1023998, _1024000, _1024002] : [c_Fun_Oinj__on(_1023992, _1023994, _1023996, _1023998), hBOOL(hAPP(hAPP(c_member(_1023994), _1024000), hAPP(c_Set_Oimage(_1023992, _1023994, _1023996), _1023998))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023992, tc_HOL_Obool)), _1023998), _1024002)), -(hBOOL(hAPP(hAPP(c_member(_1023992), hAPP(c_Fun_Othe__inv__into(_1023992, _1023994, _1023998, _1023996), _1024000)), _1024002)))], (25111 ^ _782476) ^ [_1251829, _1251831, _1251833] : [class_Groups_Oordered__ab__group__add__abs(_1251829), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251829), hAPP(c_Groups_Oabs__class_Oabs(_1251829), _1251831)), hAPP(c_Groups_Oabs__class_Oabs(_1251829), _1251833))), hAPP(c_Groups_Oabs__class_Oabs(_1251829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251829), _1251833), _1251831)))))], (8226 ^ _782476) ^ [_923967, _923969, _923971, _923973] : [class_Orderings_Olinorder(_923967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923967), _923969), _923971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923967), _923971), _923973)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923967, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923967, _923969), _923971)), c_SetInterval_Oord__class_OatLeastAtMost(_923967, _923971, _923973)) = c_SetInterval_Oord__class_OatLeastAtMost(_923967, _923969, _923973))], (40682 ^ _782476) ^ [_1576808, _1576810] : [40683 ^ _782476 : [(40684 ^ _782476) ^ [_1576854] : [hBOOL(hAPP(_1576808, _1576854))]], -(hBOOL(hAPP(_1576808, c_Hilbert__Choice_OEps(_1576810, _1576808))))], (35012 ^ _782476) ^ [_1444587] : [class_Rings_Osemiring__1(_1444587), c_Int_Oiszero(_1444587, c_Groups_Oone__class_Oone(_1444587))], (36072 ^ _782476) ^ [_1463944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1463944)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1463944), c_Int_OMin)))], (2110 ^ _782476) ^ [_813159, _813161, _813163, _813165, _813167, _813169, _813171, _813173] : [-(c_Fun_Othe__inv__into(_813173, _813169, _813165, _813161) = c_Fun_Othe__inv__into(_813171, _813167, _813163, _813159)), _813173 = _813171, _813169 = _813167, _813165 = _813163, _813161 = _813159], (4474 ^ _782476) ^ [_850361, _850363] : [_850363 = _850361, -(c_List_Oappend(_850363) = c_List_Oappend(_850361))], (51490 ^ _782476) ^ [_1824165, _1824167, _1824169, _1824171, _1824173, _1824175, _1824177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167)), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824169), _1824171)), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824173), _1824175))), c_Transitive__Closure_Ortrancl(tc_prod(_1824165, _1824167), _1824177))), -(hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824169), _1824171) = hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824173), _1824175)), 51499 ^ _782476 : [(51502 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167)), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), 51497 ^ [_1824165, _1824167, _1824169, _1824171, _1824173, _1824175, _1824177]), 51498 ^ [_1824165, _1824167, _1824169, _1824171, _1824173, _1824175, _1824177])), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824173), _1824175))), c_Transitive__Closure_Ortrancl(tc_prod(_1824165, _1824167), _1824177))))], (51500 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824165, _1824167), tc_prod(_1824165, _1824167)), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), _1824169), _1824171)), hAPP(hAPP(c_Product__Type_OPair(_1824165, _1824167), 51497 ^ [_1824165, _1824167, _1824169, _1824171, _1824173, _1824175, _1824177]), 51498 ^ [_1824165, _1824167, _1824169, _1824171, _1824173, _1824175, _1824177]))), _1824177)))]]], (51257 ^ _782476) ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346] : [class_Groups_Ocomm__monoid__mult(_1819336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1819338), _1819340)), 51267 ^ _782476 : [(51270 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1819342), hAPP(_1819344, 51266 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346])))], (51268 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819338), 51266 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346]), _1819340)))]], 51274 ^ _782476 : [(51278 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819338), 51276 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346]), _1819340)))], (51280 ^ _782476) ^ [] : [51273 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346] = 51276 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346]], (51282 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1819342, tc_HOL_Obool)), hAPP(_1819344, 51273 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346])), hAPP(_1819344, 51276 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346])) = c_Orderings_Obot__class_Obot(tc_fun(_1819342, tc_HOL_Obool))], (51275 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819338), 51273 ^ [_1819336, _1819338, _1819340, _1819342, _1819344, _1819346]), _1819340)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1819336, _1819342, c_Groups_Otimes__class_Otimes(_1819336)), _1819346), c_Groups_Oone__class_Oone(_1819336)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1819338, tc_fun(_1819342, tc_HOL_Obool)), _1819340), _1819344)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1819336, _1819338, c_Groups_Otimes__class_Otimes(_1819336)), hAPP(hAPP(c_COMBB(tc_fun(_1819342, tc_HOL_Obool), _1819336, _1819338), hAPP(hAPP(c_Finite__Set_Ofold__image(_1819336, _1819342, c_Groups_Otimes__class_Otimes(_1819336)), _1819346), c_Groups_Oone__class_Oone(_1819336))), _1819344)), c_Groups_Oone__class_Oone(_1819336)), _1819340))], (13644 ^ _782476) ^ [_1035333, _1035335] : [class_Lattices_Oab__semigroup__idem__mult(_1035333), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035333), _1035335), _1035335) = _1035335)], (30388 ^ _782476) ^ [_1358524, _1358526, _1358528, _1358530] : [class_Fields_Olinordered__field(_1358524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358524), _1358526), c_Groups_Ozero__class_Ozero(_1358524))), 30395 ^ _782476 : [(30402 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358524), _1358530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358524), _1358528), _1358526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358524), _1358528), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358524), _1358530), _1358526))))], (30396 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358524), _1358528), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358524), _1358530), _1358526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358524), _1358530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358524), _1358528), _1358526))))]]], (3866 ^ _782476) ^ [_840519, _840521, _840523, _840525, _840527, _840529] : [-(c_List_OtakeWhile(_840529, _840525, _840521) = c_List_OtakeWhile(_840527, _840523, _840519)), _840529 = _840527, _840525 = _840523, _840521 = _840519], (22560 ^ _782476) ^ [_1205478, _1205480] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205478), _1205480) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1205478 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205480 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27607 ^ _782476) ^ [_1304696, _1304698, _1304700] : [class_Orderings_Olinorder(_1304696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304696), _1304698)), -(_1304698 = c_Orderings_Obot__class_Obot(tc_fun(_1304696, tc_HOL_Obool))), 27618 ^ _782476 : [(27628 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304696), hAPP(c_Finite__Set_Ofold1(_1304696, c_Orderings_Oord__class_Omin(_1304696)), _1304698)), _1304700))), 27629 ^ _782476 : [(27630 ^ _782476) ^ [_1305085] : [hBOOL(hAPP(hAPP(c_member(_1304696), _1305085), _1304698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304696), _1305085), _1304700))]]], (27619 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304696), hAPP(c_Finite__Set_Ofold1(_1304696, c_Orderings_Oord__class_Omin(_1304696)), _1304698)), _1304700)), 27623 ^ _782476 : [(27626 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304696), 27622 ^ [_1304696, _1304698, _1304700]), _1304700)))], (27624 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304696), 27622 ^ [_1304696, _1304698, _1304700]), _1304698)))]]]]], (16769 ^ _782476) ^ [_1098799, _1098801, _1098803, _1098805, _1098807] : [class_Groups_Ocomm__monoid__add(_1098799), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098801, _1098799), hAPP(hAPP(c_COMBS(_1098801, _1098799, _1098799), hAPP(hAPP(c_COMBB(_1098799, tc_fun(_1098799, _1098799), _1098801), c_Groups_Oplus__class_Oplus(_1098799)), _1098803)), _1098805)), _1098807) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098799), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098801, _1098799), _1098803), _1098807)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098801, _1098799), _1098805), _1098807)))], (51576 ^ _782476) ^ [_1827758, _1827760, _1827762] : [-(c_Lazy__Sequence_Oflat(_1827758, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1827758), _1827760, _1827762)) = c_Lazy__Sequence_Oappend(_1827758, _1827760, c_Lazy__Sequence_Oflat(_1827758, _1827762)))], (48595 ^ _782476) ^ [_1760435, _1760437, _1760439, _1760441] : [48597 ^ _782476 : [(48600 ^ _782476) ^ [] : [hBOOL(hAPP(_1760437, hAPP(hAPP(c_List_Onth(_1760439), _1760441), 48596 ^ [_1760435, _1760437, _1760439, _1760441])))], (48598 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48596 ^ [_1760435, _1760437, _1760439, _1760441]), _1760435)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760439)), _1760441))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760439)), c_List_OtakeWhile(_1760439, _1760437, _1760441)))))], (42169 ^ _782476) ^ [_1613162, _1613164, _1613166, _1613168] : [class_Orderings_Olinorder(_1613162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613162), _1613164)), hBOOL(hAPP(hAPP(c_member(_1613162), _1613166), _1613164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613162), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1613162), _1613166), _1613168)), hAPP(hAPP(c_Finite__Set_Ofold(_1613162, _1613162, c_Orderings_Oord__class_Omax(_1613162)), _1613168), _1613164))))], (20681 ^ _782476) ^ [_1171277, _1171279] : [class_Rings_Olinordered__idom(_1171277), 20684 ^ _782476 : [(20691 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171277), _1171279), c_Groups_Ozero__class_Ozero(_1171277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171277), _1171279), _1171279)), c_Groups_Ozero__class_Ozero(_1171277))))], (20685 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171277), _1171279), _1171279)), c_Groups_Ozero__class_Ozero(_1171277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171277), _1171279), c_Groups_Ozero__class_Ozero(_1171277))))]]], (14254 ^ _782476) ^ [_1048016, _1048018, _1048020] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048016), _1048020)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048016), hAPP(hAPP(c_Set_Oinsert(_1048016), _1048018), _1048020))))], (42619 ^ _782476) ^ [_1621875, _1621877, _1621879] : [class_Divides_Osemiring__div(_1621875), -(_1621877 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1621875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1621875), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1621875), _1621877), _1621879)), _1621879)), c_Divides_Odiv__class_Omod(_1621875, _1621877, _1621879)))], (44915 ^ _782476) ^ [_1679647, _1679649, _1679651] : [-(c_List_Obutlast(_1679647, hAPP(hAPP(c_List_Oappend(_1679647), _1679649), hAPP(hAPP(c_List_Olist_OCons(_1679647), _1679651), c_List_Olist_ONil(_1679647)))) = _1679649)], (39487 ^ _782476) ^ [_1544134, _1544136, _1544138] : [-(hAPP(c_Relation_ORange(_1544134, _1544136), hAPP(c_Set_OCollect(tc_prod(_1544134, _1544136)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544134, _1544136, tc_HOL_Obool), _1544138))) = hAPP(c_Set_OCollect(_1544136), hAPP(hAPP(c_COMBB(tc_fun(_1544134, tc_HOL_Obool), tc_HOL_Obool, _1544136), c_HOL_OEx(_1544134)), hAPP(c_COMBC(_1544134, _1544136, tc_HOL_Obool), _1544138))))], (14240 ^ _782476) ^ [_1047738] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047738), c_Orderings_Otop__class_Otop(tc_fun(_1047738, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047738)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047738), tc_HOL_Obool)))))], (27259 ^ _782476) ^ [_1297689, _1297691, _1297693, _1297695, _1297697, _1297699, _1297701, _1297703] : [class_Groups_Ocomm__monoid__mult(_1297689), c_Fun_Oinj__on(_1297691, _1297693, _1297695, _1297697), _1297699 = hAPP(c_Set_Oimage(_1297691, _1297693, _1297695), _1297697), _1297701 = hAPP(c_Fun_Ocomp(_1297693, _1297689, _1297691, _1297703), _1297695), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297693, _1297689), _1297703), _1297699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297691, _1297689), _1297701), _1297697))], (38598 ^ _782476) ^ [_1521654, _1521656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521654), _1521656)), -(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), _1521654), _1521656)), c_Wellfounded_Oless__than)))], (34034 ^ _782476) ^ [_1427691] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427691) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427691)))], (13656 ^ _782476) ^ [_1035515, _1035517, _1035519] : [class_Lattices_Oab__semigroup__idem__mult(_1035515), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035515), _1035517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035515), _1035517), _1035519)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035515), _1035517), _1035519))], (45108 ^ _782476) ^ [_1684750, _1684752] : [hAPP(c_List_Orotate1(_1684750), _1684752) = c_List_Olist_ONil(_1684750), -(_1684752 = c_List_Olist_ONil(_1684750))], (13298 ^ _782476) ^ [_1028037, _1028039, _1028041, _1028043, _1028045, _1028047] : [c_Fun_Oinj__on(_1028037, _1028039, _1028041, _1028043), hAPP(_1028041, _1028045) = _1028047, hBOOL(hAPP(hAPP(c_member(_1028037), _1028045), _1028043)), -(hAPP(c_Fun_Othe__inv__into(_1028037, _1028039, _1028043, _1028041), _1028047) = _1028045)], (35442 ^ _782476) ^ [_1452200, _1452202] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452200), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452202))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452200), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452202))), 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))))], (44390 ^ _782476) ^ [_1667645, _1667647, _1667649, _1667651] : [_1667647 = c_List_Olist_ONil(_1667645), -(hAPP(hAPP(c_List_Olist__update(_1667645, _1667647), _1667649), _1667651) = c_List_Olist_ONil(_1667645))], (28352 ^ _782476) ^ [_1320389, _1320391] : [class_Orderings_Olinorder(_1320389), -(c_Big__Operators_Olattice_OSup__fin(_1320389, c_Orderings_Oord__class_Omax(_1320389), hAPP(hAPP(c_Set_Oinsert(_1320389), _1320391), c_Orderings_Obot__class_Obot(tc_fun(_1320389, tc_HOL_Obool)))) = _1320391)], (8272 ^ _782476) ^ [_924896, _924898, _924900] : [class_Orderings_Olinorder(_924896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924896), _924898), _924900)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924896, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_924896), _924898)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924896, _924898, _924900)) = hAPP(c_SetInterval_Oord__class_OatMost(_924896), _924900))], (7762 ^ _782476) ^ [_913787, _913789, _913791, _913793] : [class_Lattices_Osemilattice__sup(_913787), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913787), _913789), _913791)), _913793) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913787), _913789), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913787), _913791), _913793)))], (13060 ^ _782476) ^ [_1022236, _1022238] : [-(c_Enum_Oenum__the(_1022236, _1022238) = c_HOL_OThe(_1022236, _1022238))], (28914 ^ _782476) ^ [_1331572, _1331574, _1331576] : [class_Rings_Odivision__ring(_1331572), -(_1331574 = c_Groups_Ozero__class_Ozero(_1331572)), 28921 ^ _782476 : [(28928 ^ _782476) ^ [] : [_1331576 = _1331574, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331572), _1331576), _1331574) = c_Groups_Oone__class_Oone(_1331572))], (28922 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331572), _1331576), _1331574) = c_Groups_Oone__class_Oone(_1331572), -(_1331576 = _1331574)]]], (9622 ^ _782476) ^ [_955234, _955236, _955238, _955240] : [class_Complete__Lattice_Ocomplete__lattice(_955234), -(_955236 = c_Orderings_Obot__class_Obot(tc_fun(_955238, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955238, _955234), _955236), hAPP(c_COMBK(_955234, _955238), _955240)) = _955240)], (37541 ^ _782476) ^ [_1496953, _1496955, _1496957] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496953, _1496955), _1496957)), 37544 ^ _782476 : [(37545 ^ _782476) ^ [_1497038] : [hBOOL(hAPP(hAPP(_1496955, _1497038), _1496957)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496953, _1496955), _1497038)))]]], (38792 ^ _782476) ^ [] : [-(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)))], (8527 ^ _782476) ^ [_930435, _930437, _930439, _930441] : [class_Lattices_Osemilattice__inf(_930435), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930435), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930435), _930437), _930439)), _930441) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930435), _930437), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930435), _930439), _930441)))], (17019 ^ _782476) ^ [_1104830, _1104832, _1104834, _1104836, _1104838] : [class_Groups_Ocomm__monoid__add(_1104830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104832), _1104834)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104832), _1104836)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104830), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104832, _1104830), _1104838), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1104832, tc_HOL_Obool)), _1104834), _1104836))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104832, _1104830), _1104838), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1104832, tc_HOL_Obool)), _1104834), _1104836))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104830), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104832, _1104830), _1104838), _1104834)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104832, _1104830), _1104838), _1104836)))], (23677 ^ _782476) ^ [_1227192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227192), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227192) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17754 ^ _782476) ^ [_1119103] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119103) = _1119103)], (32772 ^ _782476) ^ [_1403368, _1403370, _1403372] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403368), _1403370), _1403372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403368, tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool)), _1403370), hAPP(hAPP(c_COMBC(_1403368, tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1403368, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool)), _1403368), c_Set_Oinsert(tc_fun(_1403368, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1403368, tc_HOL_Obool), tc_fun(_1403368, tc_HOL_Obool), _1403368), c_Relation_OImage(_1403368, _1403368, _1403372)), hAPP(hAPP(c_COMBC(_1403368, tc_fun(_1403368, tc_HOL_Obool), tc_fun(_1403368, tc_HOL_Obool)), c_Set_Oinsert(_1403368)), c_Orderings_Obot__class_Obot(tc_fun(_1403368, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403368, tc_HOL_Obool), tc_HOL_Obool)))))], (29546 ^ _782476) ^ [_1343106, _1343108, _1343110] : [class_Rings_Olinordered__idom(_1343106), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343106), c_Groups_Ozero__class_Ozero(_1343106)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343106), hAPP(c_Groups_Oabs__class_Oabs(_1343106), _1343108)), _1343110))))], (24682 ^ _782476) ^ [_1243889, _1243891] : [class_Rings_Olinordered__idom(_1243889), 24685 ^ _782476 : [(24692 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243889), hAPP(c_Int_Oring__1__class_Oof__int(_1243889), _1243891)), c_Groups_Ozero__class_Ozero(_1243889))))], (24686 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243889), hAPP(c_Int_Oring__1__class_Oof__int(_1243889), _1243891)), c_Groups_Ozero__class_Ozero(_1243889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7525 ^ _782476) ^ [_908613, _908615] : [class_Groups_Ogroup__add(_908613), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908613), hAPP(c_Groups_Ouminus__class_Ouminus(_908613), _908615)) = _908615)], (20443 ^ _782476) ^ [_1167014, _1167016] : [class_Rings_Ocomm__semiring__1(_1167014), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167014), c_Groups_Oone__class_Oone(_1167014)), c_Groups_Oone__class_Oone(_1167014))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1167014), c_Nat_Osemiring__1__class_Oof__nat(_1167014)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1167016))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167014), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1167014), _1167016)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167014), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1167014), _1167016)), c_Groups_Oone__class_Oone(_1167014))))], (26166 ^ _782476) ^ [_1276978, _1276980, _1276982] : [class_Orderings_Olinorder(_1276978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276978, tc_HOL_Obool)), _1276980), _1276982)), -(_1276980 = c_Orderings_Obot__class_Obot(tc_fun(_1276978, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276978), _1276982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276978), c_Big__Operators_Olinorder__class_OMax(_1276978, _1276980)), c_Big__Operators_Olinorder__class_OMax(_1276978, _1276982))))], (45927 ^ _782476) ^ [_1701451, _1701453, _1701455, _1701457, _1701459] : [-(hAPP(c_List_Orotate(_1701451, _1701453), hAPP(hAPP(c_List_Omap(_1701455, _1701451), _1701457), _1701459)) = hAPP(hAPP(c_List_Omap(_1701455, _1701451), _1701457), hAPP(c_List_Orotate(_1701455, _1701453), _1701459)))], (33940 ^ _782476) ^ [_1426024, _1426026] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426024)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426026)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426024), _1426026)))], (23153 ^ _782476) ^ [_1217078] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217078)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1217078)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217078)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49659 ^ _782476) ^ [_1784439, _1784441, _1784443, _1784445, _1784447] : [c_Fun_Oinj__on(_1784439, _1784441, _1784443, c_Orderings_Otop__class_Otop(tc_fun(_1784439, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784441, _1784445, _1784439, hAPP(c_Fun_Ocomp(_1784439, _1784445, _1784441, _1784447), c_Hilbert__Choice_Oinv__into(_1784439, _1784441, c_Orderings_Otop__class_Otop(tc_fun(_1784439, tc_HOL_Obool)), _1784443))), _1784443) = _1784447)], (7563 ^ _782476) ^ [_909274, _909276, _909278] : [class_Groups_Oordered__ab__group__add(_909274), 7566 ^ _782476 : [(7573 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909274), _909278), _909276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909274), hAPP(c_Groups_Ouminus__class_Ouminus(_909274), _909276)), hAPP(c_Groups_Ouminus__class_Ouminus(_909274), _909278))))], (7567 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909274), hAPP(c_Groups_Ouminus__class_Ouminus(_909274), _909276)), hAPP(c_Groups_Ouminus__class_Ouminus(_909274), _909278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909274), _909278), _909276)))]]], (47012 ^ _782476) ^ [_1726136, _1726138] : [c_List_Oconcat(_1726136, _1726138) = c_List_Olist_ONil(_1726136), 47015 ^ _782476 : [(47016 ^ _782476) ^ [_1726227] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726136)), _1726227), hAPP(c_List_Oset(tc_List_Olist(_1726136)), _1726138))), -(_1726227 = c_List_Olist_ONil(_1726136))]]], (32805 ^ _782476) ^ [_1404392, _1404394, _1404396, _1404398, _1404400, _1404402] : [-(hAPP(c_Relation_OImage(_1404392, _1404394, _1404396), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404398, tc_fun(_1404392, tc_HOL_Obool)), _1404400), _1404402)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404398, tc_fun(_1404394, tc_HOL_Obool)), _1404400), hAPP(hAPP(c_COMBB(tc_fun(_1404392, tc_HOL_Obool), tc_fun(_1404394, tc_HOL_Obool), _1404398), c_Relation_OImage(_1404392, _1404394, _1404396)), _1404402)))], (20862 ^ _782476) ^ [_1174896] : [-(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), _1174896))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6782 ^ _782476) ^ [_892421, _892423, _892425, _892427, _892429, _892431] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892421, tc_fun(_892423, tc_HOL_Obool)), _892425), _892427), _892429)), hBOOL(hAPP(hAPP(c_member(_892421), _892431), _892425)), -(hBOOL(hAPP(hAPP(_892427, _892431), _892429)))], (11442 ^ _782476) ^ [_991911, _991913, _991915] : [class_Orderings_Olinorder(_991911), 11445 ^ _782476 : [(11452 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991911), _991915), _991913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991911), _991913), _991915))], (11446 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991911), _991913), _991915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991911), _991915), _991913)))]]], (17674 ^ _782476) ^ [_1117601, _1117603, _1117605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117601), _1117603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117601), _1117605)), 17681 ^ _782476 : [(17688 ^ _782476) ^ [] : [_1117603 = _1117605, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117603), _1117601) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117605), _1117601))], (17682 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117603), _1117601) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117605), _1117601), -(_1117603 = _1117605)]]], (46086 ^ _782476) ^ [_1705982] : [-(hAPP(c_List_Omap(_1705982, _1705982), c_Fun_Oid(_1705982)) = c_Fun_Oid(tc_List_Olist(_1705982)))], (34600 ^ _782476) ^ [_1436844, _1436846] : [class_Int_Onumber__ring(_1436844), class_Rings_Olinordered__idom(_1436844), 34607 ^ _782476 : [(34614 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436844), c_Groups_Ozero__class_Ozero(_1436844)), hAPP(c_Int_Onumber__class_Onumber__of(_1436844), _1436846))))], (34608 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436844), c_Groups_Ozero__class_Ozero(_1436844)), hAPP(c_Int_Onumber__class_Onumber__of(_1436844), _1436846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436846)))]]], (31962 ^ _782476) ^ [_1387938, _1387940, _1387942, _1387944] : [class_Divides_Oring__div(_1387938), -(c_Divides_Odiv__class_Omod(_1387938, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387938), _1387940), _1387942), _1387944) = c_Divides_Odiv__class_Omod(_1387938, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387938), _1387940), c_Divides_Odiv__class_Omod(_1387938, _1387942, _1387944)), _1387944))], (49352 ^ _782476) ^ [_1777387] : [class_Nat_Osize(_1777387), -(c_FunDef_Ois__measure(_1777387, c_Nat_Osize__class_Osize(_1777387)))], (33870 ^ _782476) ^ [_1424707] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424707))), -(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), _1424707)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2862 ^ _782476) ^ [_824837, _824839] : [_824839 = _824837, -(c_Nat_Ofunpow(_824839) = c_Nat_Ofunpow(_824837))], (9366 ^ _782476) ^ [_950294, _950296, _950298] : [class_Orderings_Obot(_950294), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950296, _950294)), _950298) = c_Orderings_Obot__class_Obot(_950294))], (6618 ^ _782476) ^ [_889100, _889102] : [class_Orderings_Olinorder(_889100), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889100, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_889100), _889102)) = hAPP(c_SetInterval_Oord__class_OatLeast(_889100), _889102))], (15651 ^ _782476) ^ [_1075304, _1075306, _1075308] : [class_Groups_Oab__semigroup__mult(_1075304), -(_1075306 = c_Orderings_Obot__class_Obot(tc_fun(_1075304, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075304), _1075306)), -(hBOOL(hAPP(hAPP(c_member(_1075304), _1075308), _1075306))), -(hAPP(c_Finite__Set_Ofold1(_1075304, c_Groups_Otimes__class_Otimes(_1075304)), hAPP(hAPP(c_Set_Oinsert(_1075304), _1075308), _1075306)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075304), _1075308), hAPP(c_Finite__Set_Ofold1(_1075304, c_Groups_Otimes__class_Otimes(_1075304)), _1075306)))], (9053 ^ _782476) ^ [_941537, _941539, _941541, _941543, _941545, _941547] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941537, tc_fun(_941539, tc_HOL_Obool)), _941541), hAPP(hAPP(c_COMBB(_941543, tc_fun(_941539, tc_HOL_Obool), _941537), _941545), _941547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941543, tc_fun(_941539, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941537, _941543, _941547), _941541)), _941545))], (12338 ^ _782476) ^ [_1006561, _1006563, _1006565, _1006567] : [class_Orderings_Olinorder(_1006561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006561), _1006563), _1006565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006561), _1006565), _1006567)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006561, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1006561, _1006563, _1006565)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1006561, _1006565), _1006567)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1006561, _1006563, _1006567))], (9049 ^ _782476) ^ [_941362, _941364] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941362, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_941362, tc_HOL_Obool))), _941364) = c_Orderings_Otop__class_Otop(tc_fun(_941362, tc_HOL_Obool)))], (46471 ^ _782476) ^ [_1713985, _1713987] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1713985), _1713987) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1713985, 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)))), _1713987))))], (52669 ^ _782476) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (35854 ^ _782476) ^ [_1459723, _1459725] : [-(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), _1459723)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459725))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459723))) = 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), _1459725)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459723)))], (41461 ^ _782476) ^ [_1595881, _1595883] : [-(hAPP(c_Relation_Oconverse(_1595881, _1595881), c_Relation_OId__on(_1595881, _1595883)) = c_Relation_OId__on(_1595881, _1595883))], (44240 ^ _782476) ^ [_1665110, _1665112] : [-(_1665110 = c_List_Olist_ONil(_1665112)), hBOOL(hAPP(c_List_Odistinct(_1665112), _1665110)), -(hBOOL(hAPP(c_List_Odistinct(_1665112), c_List_Obutlast(_1665112, _1665110))))], (31261 ^ _782476) ^ [_1373943, _1373945, _1373947] : [class_Divides_Osemiring__div(_1373943), -(_1373945 = c_Groups_Ozero__class_Ozero(_1373943)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373943), _1373947), _1373945)), _1373945) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373943), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373943), _1373947), _1373945)), c_Groups_Oone__class_Oone(_1373943)))], (6478 ^ _782476) ^ [_886380, _886382, _886384, _886386, _886388] : [class_Complete__Lattice_Ocomplete__lattice(_886380), 6481 ^ _782476 : [(6482 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886382, _886380), _886384), _886386)), _886388)), 6485 ^ _782476 : [(6486 ^ _782476) ^ [_886561] : [hBOOL(hAPP(hAPP(c_member(_886382), _886561), _886384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886380), hAPP(_886386, _886561)), _886388)))]]], (6492 ^ _782476) ^ [] : [6494 ^ _782476 : [(6497 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886380), hAPP(_886386, 6493 ^ [_886380, _886382, _886384, _886386, _886388])), _886388))], (6495 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886382), 6493 ^ [_886380, _886382, _886384, _886386, _886388]), _886384)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886382, _886380), _886384), _886386)), _886388)))]]], (52331 ^ _782476) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (31756 ^ _782476) ^ [_1383632, _1383634] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1383632), _1383634) = 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), _1383632)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1383634)))))], (15526 ^ _782476) ^ [_1072734, _1072736, _1072738, _1072740, _1072742] : [c_Finite__Set_Ofolding__one__idem(_1072734, _1072736, _1072738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072734), _1072740)), -(_1072742 = c_Orderings_Obot__class_Obot(tc_fun(_1072734, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072734, tc_HOL_Obool)), _1072742), _1072740)), -(hAPP(hAPP(_1072736, hAPP(_1072738, _1072742)), hAPP(_1072738, _1072740)) = hAPP(_1072738, _1072740))], (52611 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (36883 ^ _782476) ^ [_1484630, _1484632, _1484634, _1484636, _1484638, _1484640] : [hAPP(hAPP(c_Product__Type_OPair(_1484630, _1484632), _1484634), _1484636) = hAPP(hAPP(c_Product__Type_OPair(_1484630, _1484632), _1484638), _1484640), 36886 ^ _782476 : [(36889 ^ _782476) ^ [] : [-(_1484636 = _1484640)], (36887 ^ _782476) ^ [] : [-(_1484634 = _1484638)]]], (42808 ^ _782476) ^ [_1626411, _1626413, _1626415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626411), c_Nitpick_Oplus__frac(_1626411, _1626413, c_Nitpick_Ouminus__frac(_1626411, _1626415)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1626411, _1626413, _1626415))], (34666 ^ _782476) ^ [_1437872, _1437874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437872), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437872)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437874)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437874))], (4398 ^ _782476) ^ [_849255, _849257, _849259, _849261] : [-(c_List_Oconcat(_849261, _849257) = c_List_Oconcat(_849259, _849255)), _849261 = _849259, _849257 = _849255], (40903 ^ _782476) ^ [_1581693, _1581695, _1581697, _1581699] : [40905 ^ _782476 : [(40910 ^ _782476) ^ [] : [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(_1581697, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 40904 ^ [_1581693, _1581695, _1581697, _1581699]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1581697, 40904 ^ [_1581693, _1581695, _1581697, _1581699])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40908 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40904 ^ [_1581693, _1581695, _1581697, _1581699]), _1581695)))], (40906 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581693), 40904 ^ [_1581693, _1581695, _1581697, _1581699])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581693), _1581695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1581697, _1581693)), _1581699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1581699), hAPP(_1581697, _1581695))), 40924 ^ _782476 : [(40929 ^ _782476) ^ [] : [-(hAPP(_1581697, 40923 ^ [_1581693, _1581695, _1581697, _1581699]) = _1581699)], (40927 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 40923 ^ [_1581693, _1581695, _1581697, _1581699]), _1581695)))], (40925 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581693), 40923 ^ [_1581693, _1581695, _1581697, _1581699])))]]], (38736 ^ _782476) ^ [_1524455, _1524457, _1524459] : [-(hAPP(c_Relation_OImage(_1524455, _1524455, c_Relation_OId__on(_1524455, _1524457)), _1524459) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524455, tc_HOL_Obool)), _1524457), _1524459))], (34326 ^ _782476) ^ [_1432567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432567))))], (24116 ^ _782476) ^ [_1234605, _1234607] : [-(c_Int_Onat__aux(_1234605, _1234607) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1234605)), _1234607))], (10377 ^ _782476) ^ [_970687, _970689, _970691, _970693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970687, tc_HOL_Obool)), _970689), _970691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970687, tc_HOL_Obool)), _970691), _970693)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970687, tc_HOL_Obool)), _970691), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970687, tc_HOL_Obool)), _970693), _970689)) = _970689)], (33166 ^ _782476) ^ [_1411239, _1411241, _1411243] : [class_Int_Onumber__ring(_1411239), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411241), _1411243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411239), hAPP(c_Int_Onumber__class_Onumber__of(_1411239), _1411241)), hAPP(c_Int_Onumber__class_Onumber__of(_1411239), _1411243)))], (22650 ^ _782476) ^ [_1207306, _1207308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1207306, _1207308)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1207306, _1207308), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1207308), c_Orderings_Otop__class_Otop(tc_fun(_1207308, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1207306), c_Orderings_Otop__class_Otop(tc_fun(_1207306, tc_HOL_Obool)))))], (48461 ^ _782476) ^ [_1757535, _1757537, _1757539] : [c_List_OdropWhile(_1757535, _1757537, _1757539) = c_List_Olist_ONil(_1757535), 48464 ^ _782476 : [(48465 ^ _782476) ^ [_1757626] : [hBOOL(hAPP(hAPP(c_member(_1757535), _1757626), hAPP(c_List_Oset(_1757535), _1757539))), -(hBOOL(hAPP(_1757537, _1757626)))]]], (2272 ^ _782476) ^ [_815736, _815738, _815740, _815742] : [-(c_Nitpick_Onat__lcm(_815742, _815738) = c_Nitpick_Onat__lcm(_815740, _815736)), _815742 = _815740, _815738 = _815736], (38704 ^ _782476) ^ [_1523712, _1523714, _1523716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1523712, _1523712), tc_HOL_Obool)), _1523714), _1523716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523712, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523712), _1523714)), hAPP(c_Relation_OField(_1523712), _1523716))))], (35308 ^ _782476) ^ [_1449713, _1449715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449713)), c_Int_OBit0(_1449715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449713), _1449715)))], (35866 ^ _782476) ^ [_1459903] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1459903, 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, _1459903, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23233 ^ _782476) ^ [_1218611, _1218613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218611), _1218613))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218611), hAPP(c_Nat_OSuc, _1218613)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (20882 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (21845 ^ _782476) ^ [_1192723, _1192725, _1192727, _1192729, _1192731] : [class_Groups_Ocomm__monoid__add(_1192723), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192725), _1192727)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192725), _1192729)), 21859 ^ _782476 : [(21862 ^ _782476) ^ [] : [hAPP(_1192731, 21858 ^ [_1192723, _1192725, _1192727, _1192729, _1192731]) = c_Groups_Ozero__class_Ozero(_1192723)], (21860 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192725), 21858 ^ [_1192723, _1192725, _1192727, _1192729, _1192731]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192725, tc_HOL_Obool)), _1192727), _1192729))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192725, _1192723), _1192731), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192725, tc_HOL_Obool)), _1192727), _1192729)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192723), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192725, _1192723), _1192731), _1192727)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192725, _1192723), _1192731), _1192729)))], (17239 ^ _782476) ^ [_1110076, _1110078, _1110080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110076), _1110078)), 17242 ^ _782476 : [(17249 ^ _782476) ^ [] : [_1110078 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110080), _1110076), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110078), _1110076) = _1110080)], (17243 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110078), _1110076) = _1110080, -(_1110078 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110080), _1110076))]]], (32664 ^ _782476) ^ [_1400958, _1400960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1400958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400960, _1400958)), _1400958)))], (23787 ^ _782476) ^ [_1228926] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228926))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40432 ^ _782476) ^ [_1570186, _1570188] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570186, _1570186)), _1570188)), c_Wellfounded_Oacyclic(_1570186, _1570188), -(c_Wellfounded_Owf(_1570186, _1570188))], (4104 ^ _782476) ^ [_844586, _844588, _844590, _844592, _844594, _844596, _844598, _844600] : [-(c_New__Random__Sequence_Oneg__bind(_844600, _844596, _844592, _844588) = c_New__Random__Sequence_Oneg__bind(_844598, _844594, _844590, _844586)), _844600 = _844598, _844596 = _844594, _844592 = _844590, _844588 = _844586], (45999 ^ _782476) ^ [_1703400, _1703402, _1703404, _1703406, _1703408] : [hAPP(hAPP(c_List_Omap(_1703400, _1703402), _1703404), _1703406) = hAPP(hAPP(c_List_Omap(_1703400, _1703402), _1703408), _1703406), 46002 ^ _782476 : [(46003 ^ _782476) ^ [_1703523] : [hBOOL(hAPP(hAPP(c_member(_1703400), _1703523), hAPP(c_List_Oset(_1703400), _1703406))), -(hAPP(_1703404, _1703523) = hAPP(_1703408, _1703523))]]], (42788 ^ _782476) ^ [_1625986, _1625988] : [-(c_Nitpick_Ouminus__frac(_1625986, _1625988) = c_Nitpick_OAbs__Frac(_1625986, 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(_1625986), _1625988))), hAPP(c_Nitpick_Odenom(_1625986), _1625988))))], (7780 ^ _782476) ^ [_914216, _914218, _914220, _914222] : [class_Lattices_Osemilattice__sup(_914216), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914216), _914218), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914216), _914220), _914222)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914216), _914220), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914216), _914218), _914222)))], (40351 ^ _782476) ^ [_1568311, _1568313] : [c_Wellfounded_OwfP(_1568311, hAPP(hAPP(c_COMBC(_1568311, tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_fun(_1568311, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568311, tc_fun(tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_fun(_1568311, tc_HOL_Obool)), _1568311), c_COMBC(_1568311, tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568311, tc_prod(_1568311, _1568311)), tc_fun(_1568311, tc_fun(tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_HOL_Obool)), _1568311), hAPP(c_COMBB(tc_prod(_1568311, _1568311), tc_fun(tc_fun(tc_prod(_1568311, _1568311), tc_HOL_Obool), tc_HOL_Obool), _1568311), c_member(tc_prod(_1568311, _1568311)))), c_Product__Type_OPair(_1568311, _1568311)))), _1568313)), -(c_Wellfounded_Owf(_1568311, _1568313))], (36942 ^ _782476) ^ [_1486112, _1486114, _1486116, _1486118, _1486120] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486112, _1486114, _1486116), _1486118), _1486120)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486112, _1486114)), hAPP(hAPP(c_Product__Type_OPair(_1486112, _1486114), _1486118), _1486120)), _1486116)))], (21139 ^ _782476) ^ [_1179674] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179674)) = _1179674)], (39806 ^ _782476) ^ [_1553707, _1553709, _1553711, _1553713] : [hBOOL(hAPP(c_Predicate_ODomainP(_1553707, _1553709, _1553711), _1553713)), -(hBOOL(hAPP(hAPP(_1553711, _1553713), 39809 ^ [_1553707, _1553709, _1553711, _1553713])))], (16167 ^ _782476) ^ [_1086082, _1086084, _1086086, _1086088, _1086090, _1086092, _1086094] : [c_Big__Operators_Ocomm__monoid__big(_1086082, _1086084, _1086086, _1086088, _1086090), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1086084), _1086092))), -(hAPP(hAPP(_1086090, _1086094), _1086092) = _1086088)], (9145 ^ _782476) ^ [_944515, _944517] : [class_Lattices_Obounded__lattice__top(_944515), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944515), c_Orderings_Otop__class_Otop(_944515)), _944517) = c_Orderings_Otop__class_Otop(_944515))], (25632 ^ _782476) ^ [_1261971, _1261973, _1261975] : [-(hBOOL(hAPP(_1261971, _1261973))), -(hAPP(c_Set_OCollect(_1261975), hAPP(hAPP(c_COMBS(_1261975, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261975), c_fconj), hAPP(c_fequal, _1261973))), _1261971)) = c_Orderings_Obot__class_Obot(tc_fun(_1261975, tc_HOL_Obool)))], (50654 ^ _782476) ^ [_1806775, _1806777, _1806779, _1806781] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806775, tc_fun(_1806777, tc_HOL_Obool)), _1806779), _1806781) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1806777, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1806777, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806775, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1806777, tc_HOL_Obool)), c_HOL_OEx(_1806775)), hAPP(hAPP(c_COMBB(tc_fun(_1806775, tc_HOL_Obool), tc_fun(_1806775, tc_HOL_Obool), tc_fun(_1806777, tc_HOL_Obool)), hAPP(c_COMBS(_1806775, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1806775), c_fconj), hAPP(hAPP(c_COMBC(_1806775, tc_fun(_1806775, tc_HOL_Obool), tc_HOL_Obool), c_member(_1806775)), _1806779)))), hAPP(hAPP(c_COMBC(tc_fun(_1806777, tc_HOL_Obool), tc_fun(_1806775, tc_fun(_1806777, tc_HOL_Obool)), tc_fun(_1806775, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806777, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1806775, tc_fun(_1806777, tc_HOL_Obool)), tc_fun(_1806775, tc_HOL_Obool)), tc_fun(_1806777, tc_HOL_Obool)), c_COMBB(tc_fun(_1806777, tc_HOL_Obool), tc_HOL_Obool, _1806775)), c_fequal)), _1806781))))))], (20657 ^ _782476) ^ [_1170849, _1170851, _1170853] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170849, tc_Nat_Onat), _1170851), _1170853)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170849, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1170849), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1170851)), _1170853))], (47401 ^ _782476) ^ [_1736574, _1736576] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1736574), _1736576)) = c_List_Oupt(_1736574, _1736576))], (51085 ^ _782476) ^ [_1816147, _1816149, _1816151] : [c_Equiv__Relations_Oequiv(_1816147, _1816149, _1816151), 51088 ^ _782476 : [(51093 ^ _782476) ^ [] : [-(c_Relation_Otrans(_1816147, _1816151))], (51091 ^ _782476) ^ [] : [-(c_Relation_Osym(_1816147, _1816151))], (51089 ^ _782476) ^ [] : [-(c_Relation_Orefl__on(_1816147, _1816149, _1816151))]]], (8673 ^ _782476) ^ [_933289, _933291, _933293, _933295] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933289, tc_HOL_Obool)), _933291), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933289, tc_HOL_Obool)), _933293), _933295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933289, tc_HOL_Obool)), _933293), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933289, tc_HOL_Obool)), _933291), _933295)))], (48339 ^ _782476) ^ [_1755040, _1755042, _1755044] : [hBOOL(hAPP(c_List_Odistinct(_1755040), _1755042)), -(hBOOL(hAPP(c_List_Odistinct(_1755040), c_List_OtakeWhile(_1755040, _1755044, _1755042))))], (42027 ^ _782476) ^ [_1610221, _1610223, _1610225, _1610227] : [class_Lattices_Osemilattice__inf(_1610221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610221), _1610223)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610221, _1610221, c_Lattices_Osemilattice__inf__class_Oinf(_1610221)), _1610225), hAPP(hAPP(c_Set_Oinsert(_1610221), _1610227), _1610223)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1610221), _1610227), hAPP(hAPP(c_Finite__Set_Ofold(_1610221, _1610221, c_Lattices_Osemilattice__inf__class_Oinf(_1610221)), _1610225), _1610223)))], (34880 ^ _782476) ^ [_1441690, _1441692] : [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(_1441690))), 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)), _1441692))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441690) = hAPP(c_Nat_OSuc, _1441692))], (41859 ^ _782476) ^ [_1605679] : [-(c_Nat_Ofunpow(_1605679) = c_Nat_Ocompow(_1605679, _1605679))], (42710 ^ _782476) ^ [_1624016, _1624018, _1624020, _1624022, _1624024, _1624026, _1624028, _1624030] : [c_Finite__Set_Ofolding__image__simple__idem(_1624016, _1624018, _1624020, _1624022, _1624024, _1624026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624018), _1624028)), -(hAPP(_1624026, hAPP(hAPP(c_Set_Oinsert(_1624018), _1624030), _1624028)) = hAPP(hAPP(_1624020, hAPP(_1624024, _1624030)), hAPP(_1624026, _1624028)))], (12778 ^ _782476) ^ [_1016612, _1016614, _1016616, _1016618, _1016620] : [c_Fun_Oinj__on(_1016612, _1016614, _1016616, _1016618), c_Fun_Oinj__on(_1016612, _1016614, _1016616, _1016620), -(c_Fun_Oinj__on(_1016612, _1016614, _1016616, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016612, tc_HOL_Obool)), _1016618), _1016620)))], (17654 ^ _782476) ^ [_1117208, _1117210] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117208), _1117210)), _1117208)))], (40325 ^ _782476) ^ [_1567825, _1567827, _1567829, _1567831, _1567833] : [c_Relation_Orefl__on(_1567825, _1567827, _1567829), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567825, _1567825)), hAPP(hAPP(c_Product__Type_OPair(_1567825, _1567825), _1567831), _1567833)), _1567829)), -(hBOOL(hAPP(hAPP(c_member(_1567825), _1567831), _1567827)))], (31121 ^ _782476) ^ [_1371519, _1371521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371521), 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), _1371519), _1371521)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24076 ^ _782476) ^ [_1233843, _1233845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233843)), 24079 ^ _782476 : [(24086 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233843), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233843)), _1233845)))], (24080 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233843)), _1233845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233843), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233845))))]]], (11740 ^ _782476) ^ [_996231, _996233, _996235, _996237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996231, tc_HOL_Obool)), _996233), _996235)), hBOOL(hAPP(hAPP(c_member(_996231), _996237), _996233)), -(hBOOL(hAPP(hAPP(c_member(_996231), _996237), _996235)))], (40013 ^ _782476) ^ [_1560364, _1560366, _1560368] : [_1560366 = _1560368, -(c_Fun_Obij__betw(_1560364, _1560364, c_Fun_Oid(_1560364), _1560366, _1560368))], (33384 ^ _782476) ^ [_1415156, _1415158, _1415160] : [class_Int_Onumber__ring(_1415156), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415156), hAPP(c_Groups_Ouminus__class_Ouminus(_1415156), hAPP(c_Int_Onumber__class_Onumber__of(_1415156), _1415158))), _1415160) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415156), hAPP(c_Int_Onumber__class_Onumber__of(_1415156), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415158))), _1415160))], (49422 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45318 ^ _782476) ^ [_1689567, _1689569] : [-(_1689567 = c_List_Olist_ONil(_1689569)), -(hAPP(c_List_Orotate1(_1689569), _1689567) = hAPP(hAPP(c_List_Oappend(_1689569), hAPP(c_List_Otl(_1689569), _1689567)), hAPP(hAPP(c_List_Olist_OCons(_1689569), hAPP(c_List_Ohd(_1689569), _1689567)), c_List_Olist_ONil(_1689569))))], (1932 ^ _782476) ^ [_809826, _809828] : [-(class_Groups_Ominus(_809826)), _809828 = _809826, class_Groups_Ominus(_809828)], (20884 ^ _782476) ^ [_1175209, _1175211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175209)), 20887 ^ _782476 : [(20896 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175209), _1175211) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1175209 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1175211 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (20888 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175209), _1175211) = c_Groups_Oone__class_Oone(tc_Int_Oint), 20891 ^ _782476 : [(20894 ^ _782476) ^ [] : [-(_1175211 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (20892 ^ _782476) ^ [] : [-(_1175209 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (18074 ^ _782476) ^ [_1124803, _1124805] : [class_Rings_Omult__zero(_1124803), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124803), _1124805), c_Groups_Ozero__class_Ozero(_1124803)) = c_Groups_Ozero__class_Ozero(_1124803))], (9362 ^ _782476) ^ [_950212, _950214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950212, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_950212, tc_HOL_Obool))), _950214)))], (16513 ^ _782476) ^ [_1093523, _1093525, _1093527, _1093529] : [class_Rings_Ocomm__semiring__1(_1093523), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093523), _1093525), _1093527)), _1093529) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093523), _1093525), _1093529)), _1093527))], (48953 ^ _782476) ^ [_1769046, _1769048, _1769050, _1769052, _1769054] : [hAPP(c_List_Ofilter(_1769046, _1769048), _1769050) = hAPP(hAPP(c_List_Olist_OCons(_1769046), _1769052), _1769054), 48958 ^ _782476 : [(48967 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1769048, _1769052)))], (48969 ^ _782476) ^ [] : [-(_1769054 = hAPP(c_List_Ofilter(_1769046, _1769048), 48957 ^ [_1769046, _1769048, _1769050, _1769052, _1769054]))], (48961 ^ _782476) ^ [_1769360] : [hBOOL(hAPP(hAPP(c_member(_1769046), _1769360), hAPP(c_List_Oset(_1769046), 48956 ^ [_1769046, _1769048, _1769050, _1769052, _1769054]))), hBOOL(hAPP(_1769048, _1769360))], (48959 ^ _782476) ^ [] : [-(_1769050 = hAPP(hAPP(c_List_Oappend(_1769046), 48956 ^ [_1769046, _1769048, _1769050, _1769052, _1769054]), hAPP(hAPP(c_List_Olist_OCons(_1769046), _1769052), 48957 ^ [_1769046, _1769048, _1769050, _1769052, _1769054])))]]], (25700 ^ _782476) ^ [_1264000, _1264002, _1264004, _1264006, _1264008] : [class_Groups_Ocomm__monoid__add(_1264000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264002), _1264004)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264002, _1264000), _1264006), hAPP(c_Set_OCollect(_1264002), hAPP(hAPP(c_COMBS(_1264002, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264002), c_fconj), hAPP(hAPP(c_COMBC(_1264002, tc_fun(_1264002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264002)), _1264004))), hAPP(hAPP(c_COMBC(_1264002, tc_fun(_1264002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264002)), _1264008)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264002, _1264000), hAPP(hAPP(c_COMBC(_1264002, _1264000, _1264000), hAPP(hAPP(c_COMBS(_1264002, _1264000, tc_fun(_1264000, _1264000)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1264000, tc_fun(_1264000, _1264000)), _1264002), c_If(_1264000)), hAPP(hAPP(c_COMBC(_1264002, tc_fun(_1264002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264002)), _1264008))), _1264006)), c_Groups_Ozero__class_Ozero(_1264000))), _1264004))], (15394 ^ _782476) ^ [_1069929, _1069931] : [class_Lattices_Olattice(_1069929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069929), _1069931)), -(_1069931 = c_Orderings_Obot__class_Obot(tc_fun(_1069929, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1069929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069929), 15407 ^ [_1069929, _1069931]), 15408 ^ [_1069929, _1069931])), hAPP(hAPP(c_Set_Oinsert(_1069929), 15407 ^ [_1069929, _1069931]), hAPP(hAPP(c_Set_Oinsert(_1069929), 15408 ^ [_1069929, _1069931]), c_Orderings_Obot__class_Obot(tc_fun(_1069929, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1069929), c_Big__Operators_Olattice__class_OSup__fin(_1069929, _1069931)), _1069931)))], (25434 ^ _782476) ^ [_1257631, _1257633, _1257635] : [25436 ^ _782476 : [(25439 ^ _782476) ^ [] : [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(_1257633, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25435 ^ [_1257631, _1257633, _1257635]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257633, 25435 ^ [_1257631, _1257633, _1257635])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25437 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25435 ^ [_1257631, _1257633, _1257635]), _1257631)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257633, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257635), hAPP(_1257633, _1257631))), 25449 ^ _782476 : [(25452 ^ _782476) ^ [] : [-(hAPP(_1257633, 25448 ^ [_1257631, _1257633, _1257635]) = _1257635)], (25450 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25448 ^ [_1257631, _1257633, _1257635]), _1257631)))]]], (8345 ^ _782476) ^ [_926581, _926583, _926585, _926587, _926589] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926581, tc_fun(_926583, tc_HOL_Obool)), _926585), _926587), _926589)), 8349 ^ _782476 : [(8352 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_926587, 8348 ^ [_926581, _926583, _926585, _926587, _926589]), _926589)))], (8350 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926581), 8348 ^ [_926581, _926583, _926585, _926587, _926589]), _926585)))]]], (40653 ^ _782476) ^ [_1576322, _1576324] : [-(c_Hilbert__Choice_OEps(_1576322, hAPP(c_fequal, _1576324)) = _1576324)], (42213 ^ _782476) ^ [_1613962, _1613964, _1613966] : [class_Lattices_Olattice(_1613962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613962), _1613964)), -(c_Big__Operators_Olattice__class_OSup__fin(_1613962, hAPP(hAPP(c_Set_Oinsert(_1613962), _1613966), _1613964)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613962, _1613962, c_Lattices_Osemilattice__sup__class_Osup(_1613962)), _1613966), _1613964))], (43930 ^ _782476) ^ [_1658484, _1658486, _1658488, _1658490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658484), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658486)), _1658488))), -(hBOOL(hAPP(hAPP(c_member(_1658486), _1658490), hAPP(c_List_Oset(_1658486), hAPP(hAPP(c_List_Olist__update(_1658486, _1658488), _1658484), _1658490)))))], (47142 ^ _782476) ^ [_1729903] : [-(c_List_Otranspose(_1729903, c_List_Olist_ONil(tc_List_Olist(_1729903))) = c_List_Olist_ONil(tc_List_Olist(_1729903)))], (47873 ^ _782476) ^ [_1745141, _1745143, _1745145] : [class_Orderings_Olinorder(_1745141), 47876 ^ _782476 : [(47889 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745141, hAPP(hAPP(c_List_Olist_OCons(_1745141), _1745143), _1745145))), 47893 ^ _782476 : [(47896 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745141), _1745143), 47892 ^ [_1745141, _1745143, _1745145]))], (47894 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745141), 47892 ^ [_1745141, _1745143, _1745145]), hAPP(c_List_Oset(_1745141), _1745145))))]], c_List_Olinorder__class_Osorted(_1745141, _1745145)], (47877 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1745141, hAPP(hAPP(c_List_Olist_OCons(_1745141), _1745143), _1745145)), 47880 ^ _782476 : [(47881 ^ _782476) ^ [_1745309] : [hBOOL(hAPP(hAPP(c_member(_1745141), _1745309), hAPP(c_List_Oset(_1745141), _1745145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745141), _1745143), _1745309)))], (47887 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745141, _1745145))]]]]], (44478 ^ _782476) ^ [_1669440, _1669442] : [-(c_List_Oset__Cons(_1669440, _1669442, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669440)), c_List_Olist_ONil(_1669440)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669440), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1669440, tc_List_Olist(_1669440), hAPP(hAPP(c_COMBC(_1669440, tc_List_Olist(_1669440), tc_List_Olist(_1669440)), c_List_Olist_OCons(_1669440)), c_List_Olist_ONil(_1669440))), _1669442))], (41879 ^ _782476) ^ [_1606149, _1606151, _1606153, _1606155, _1606157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606149, _1606149)), hAPP(hAPP(c_Product__Type_OPair(_1606149, _1606149), _1606151), _1606153)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606149, _1606149), tc_HOL_Obool), _1606155), _1606157))), 41884 ^ _782476 : [(41887 ^ _782476) ^ [] : [-(_1606151 = _1606153)], (41885 ^ _782476) ^ [] : [-(_1606155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41890 ^ _782476 : [(41895 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606149, _1606149)), hAPP(hAPP(c_Product__Type_OPair(_1606149, _1606149), 41888 ^ [_1606149, _1606151, _1606153, _1606155, _1606157]), _1606153)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606149, _1606149), tc_HOL_Obool), 41889 ^ [_1606149, _1606151, _1606153, _1606155, _1606157]), _1606157))))], (41893 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606149, _1606149)), hAPP(hAPP(c_Product__Type_OPair(_1606149, _1606149), _1606151), 41888 ^ [_1606149, _1606151, _1606153, _1606155, _1606157])), _1606157)))], (41891 ^ _782476) ^ [] : [-(_1606155 = hAPP(c_Nat_OSuc, 41889 ^ [_1606149, _1606151, _1606153, _1606155, _1606157]))]]], (25337 ^ _782476) ^ [_1255951, _1255953] : [class_Rings_Olinordered__idom(_1255951), 25340 ^ _782476 : [(25347 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255951), c_Groups_Ozero__class_Ozero(_1255951)), _1255953)), -(c_Groups_Osgn__class_Osgn(_1255951, _1255953) = c_Groups_Oone__class_Oone(_1255951))], (25341 ^ _782476) ^ [] : [c_Groups_Osgn__class_Osgn(_1255951, _1255953) = c_Groups_Oone__class_Oone(_1255951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255951), c_Groups_Ozero__class_Ozero(_1255951)), _1255953)))]]], (44384 ^ _782476) ^ [_1667542, _1667544, _1667546, _1667548] : [hAPP(hAPP(c_List_Olist__update(_1667542, _1667544), _1667546), _1667548) = c_List_Olist_ONil(_1667542), -(_1667544 = c_List_Olist_ONil(_1667542))], (37605 ^ _782476) ^ [_1498152, _1498154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498154), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498152, _1498154) = 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), _1498152), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498154)))))], (44146 ^ _782476) ^ [_1663354, _1663356, _1663358, _1663360] : [_1663354 = _1663356, -(c_List_Oremove1(_1663358, _1663354, hAPP(hAPP(c_List_Olist_OCons(_1663358), _1663356), _1663360)) = _1663360)], (28742 ^ _782476) ^ [_1328393, _1328395] : [class_Rings_Odivision__ring__inverse__zero(_1328393), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328393), _1328395), c_Groups_Ozero__class_Ozero(_1328393)) = c_Groups_Ozero__class_Ozero(_1328393))], (30260 ^ _782476) ^ [_1356069, _1356071, _1356073, _1356075, _1356077] : [class_Fields_Olinordered__field(_1356069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356069), c_Groups_Ozero__class_Ozero(_1356069)), _1356071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356069), _1356071), _1356073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356069), c_Groups_Ozero__class_Ozero(_1356069)), _1356075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356069), _1356075), _1356077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356069), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356069), _1356071), _1356077)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356069), _1356073), _1356075))))], (48040 ^ _782476) ^ [_1748652, _1748654] : [_1748654 = c_List_Olist_ONil(_1748652), -(hAPP(c_List_Orev(_1748652), _1748654) = c_List_Olist_ONil(_1748652))], (27124 ^ _782476) ^ [_1295279, _1295281, _1295283, _1295285] : [class_Rings_Ocomm__semiring__1(_1295279), class_Rings_Ono__zero__divisors(_1295279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295281), _1295283)), 27135 ^ _782476 : [(27145 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295281, _1295279), _1295285), _1295283) = c_Groups_Ozero__class_Ozero(_1295279)), 27146 ^ _782476 : [(27147 ^ _782476) ^ [_1295657] : [hBOOL(hAPP(hAPP(c_member(_1295281), _1295657), _1295283)), hAPP(_1295285, _1295657) = c_Groups_Ozero__class_Ozero(_1295279)]]], (27136 ^ _782476) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295281, _1295279), _1295285), _1295283) = c_Groups_Ozero__class_Ozero(_1295279), 27140 ^ _782476 : [(27143 ^ _782476) ^ [] : [-(hAPP(_1295285, 27139 ^ [_1295279, _1295281, _1295283, _1295285]) = c_Groups_Ozero__class_Ozero(_1295279))], (27141 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295281), 27139 ^ [_1295279, _1295281, _1295283, _1295285]), _1295283)))]]]]], (6953 ^ _782476) ^ [_896460, _896462, _896464] : [hBOOL(hAPP(hAPP(c_member(_896460), _896462), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896460, tc_HOL_Obool)), _896464))), hBOOL(hAPP(hAPP(c_member(_896460), _896462), _896464))], (41655 ^ _782476) ^ [_1600381, _1600383, _1600385] : [41658 ^ _782476 : [(41664 ^ _782476) ^ [] : [41657 ^ [_1600381, _1600383, _1600385] = 41660 ^ [_1600381, _1600383, _1600385]], (41662 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600381, _1600383)), hAPP(hAPP(c_Product__Type_OPair(_1600381, _1600383), 41656 ^ [_1600381, _1600383, _1600385]), 41660 ^ [_1600381, _1600383, _1600385])), _1600385)))], (41659 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600381, _1600383)), hAPP(hAPP(c_Product__Type_OPair(_1600381, _1600383), 41656 ^ [_1600381, _1600383, _1600385]), 41657 ^ [_1600381, _1600383, _1600385])), _1600385)))]], -(c_Relation_Osingle__valued(_1600381, _1600383, _1600385))], (9634 ^ _782476) ^ [_955432, _955434, _955436, _955438] : [_955432 = c_Orderings_Obot__class_Obot(tc_fun(_955434, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955434, tc_fun(_955436, tc_HOL_Obool)), _955432), hAPP(c_COMBK(tc_fun(_955436, tc_HOL_Obool), _955434), _955438)) = c_Orderings_Otop__class_Otop(tc_fun(_955436, tc_HOL_Obool)))], (44987 ^ _782476) ^ [_1681437, _1681439, _1681441, _1681443] : [-(c_List_Osublist(_1681437, hAPP(hAPP(c_List_Oappend(_1681437), _1681439), _1681441), _1681443) = hAPP(hAPP(c_List_Oappend(_1681437), c_List_Osublist(_1681437, _1681439, _1681443)), c_List_Osublist(_1681437, _1681441, 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(_1681437)), _1681439)))), _1681443)))))], (26122 ^ _782476) ^ [_1276357, _1276359, _1276361] : [class_Orderings_Olinorder(_1276357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276357), _1276359)), hBOOL(hAPP(hAPP(c_member(_1276357), _1276361), _1276359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276357), c_Big__Operators_Olinorder__class_OMin(_1276357, _1276359)), _1276361)))], (33932 ^ _782476) ^ [_1425867, _1425869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425867), _1425869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425867)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425869))))], (4910 ^ _782476) ^ [_857435, _857437] : [_857437 = _857435, -(c_Random__Sequence_Osingle(_857437) = c_Random__Sequence_Osingle(_857435))], (26028 ^ _782476) ^ [_1275027] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1275027)))], (36190 ^ _782476) ^ [_1465767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465767)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465767), c_Int_OMin)))], (20367 ^ _782476) ^ [_1165387, _1165389, _1165391, _1165393] : [class_Groups_Ocomm__monoid__add(_1165387), 20370 ^ _782476 : [(20377 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1165389), _1165391))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165389, _1165387), _1165393), _1165391) = c_Groups_Ozero__class_Ozero(_1165387))], (20371 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165389), _1165391)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165389, _1165387), _1165393), _1165391) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165387, _1165389, c_Groups_Oplus__class_Oplus(_1165387)), _1165393), c_Groups_Ozero__class_Ozero(_1165387)), _1165391))]]], (19240 ^ _782476) ^ [_1144623, _1144625, _1144627, _1144629] : [class_Rings_Olinordered__ring__strict(_1144623), 19243 ^ _782476 : [(19258 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144623), _1144625), _1144627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144623), _1144629), _1144627)))), 19259 ^ _782476 : [(19266 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144627), c_Groups_Ozero__class_Ozero(_1144623))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144629), _1144625))], (19260 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), c_Groups_Ozero__class_Ozero(_1144623)), _1144627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144625), _1144629))]]], (19244 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144623), _1144625), _1144627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144623), _1144629), _1144627))), 19249 ^ _782476 : [(19252 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144625), _1144629)))], (19250 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), c_Groups_Ozero__class_Ozero(_1144623)), _1144627)))]], 19253 ^ _782476 : [(19256 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144629), _1144625)))], (19254 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144623), _1144627), c_Groups_Ozero__class_Ozero(_1144623))))]]]]], (5208 ^ _782476) ^ [_862060, _862062, _862064, _862066, _862068, _862070] : [-(c_Product__Type_Oprod_Oprod__case(_862070, _862066, _862062) = c_Product__Type_Oprod_Oprod__case(_862068, _862064, _862060)), _862070 = _862068, _862066 = _862064, _862062 = _862060], (24981 ^ _782476) ^ [_1249451, _1249453, _1249455, _1249457] : [class_Groups_Oordered__ab__group__add__abs(_1249451), -(hAPP(c_Groups_Oabs__class_Oabs(_1249451), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249453, _1249451), hAPP(hAPP(c_COMBB(_1249451, _1249451, _1249453), c_Groups_Oabs__class_Oabs(_1249451)), _1249455)), _1249457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249453, _1249451), hAPP(hAPP(c_COMBB(_1249451, _1249451, _1249453), c_Groups_Oabs__class_Oabs(_1249451)), _1249455)), _1249457))], (6295 ^ _782476) ^ [_882732, _882734, _882736] : [class_Orderings_Olinorder(_882732), 6298 ^ _782476 : [(6305 ^ _782476) ^ [] : [_882734 = _882736, -(hAPP(c_SetInterval_Oord__class_OatLeast(_882732), _882734) = hAPP(c_SetInterval_Oord__class_OatLeast(_882732), _882736))], (6299 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_882732), _882734) = hAPP(c_SetInterval_Oord__class_OatLeast(_882732), _882736), -(_882734 = _882736)]]], (44949 ^ _782476) ^ [_1680613, _1680615, _1680617] : [-(hBOOL(hAPP(c_List_Odistinct(_1680613), hAPP(hAPP(c_List_Oappend(_1680613), _1680615), _1680617)))), hBOOL(hAPP(c_List_Odistinct(_1680613), _1680615)), hBOOL(hAPP(c_List_Odistinct(_1680613), _1680617)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680613, tc_HOL_Obool)), hAPP(c_List_Oset(_1680613), _1680615)), hAPP(c_List_Oset(_1680613), _1680617)) = c_Orderings_Obot__class_Obot(tc_fun(_1680613, tc_HOL_Obool))], (9420 ^ _782476) ^ [_951148, _951150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951148, tc_HOL_Obool)), _951150), c_Orderings_Obot__class_Obot(tc_fun(_951148, tc_HOL_Obool)))), -(_951150 = c_Orderings_Obot__class_Obot(tc_fun(_951148, tc_HOL_Obool)))], (22044 ^ _782476) ^ [_1197050] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1197050)], (51286 ^ _782476) ^ [_1820296] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1820296), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1820296 = hAPP(c_Code__Numeral_Onat__of, 51289 ^ [_1820296]))], (44190 ^ _782476) ^ [_1664100, _1664102, _1664104] : [hBOOL(hAPP(hAPP(c_member(_1664100), _1664102), hAPP(c_List_Oset(_1664100), _1664104))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664100)), c_List_Oremove1(_1664100, _1664102, _1664104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664100)), _1664104)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (32762 ^ _782476) ^ [_1403197, _1403199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403199)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1403197, _1403199)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1403197), hAPP(c_Int_Onat, _1403199)))], (48142 ^ _782476) ^ [_1750727, _1750729] : [-(hAPP(c_List_Orev(_1750727), hAPP(c_List_Orev(_1750727), _1750729)) = _1750729)], (34464 ^ _782476) ^ [_1434706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434706)))], (41142 ^ _782476) ^ [_1588069, _1588071, _1588073, _1588075] : [41143 ^ _782476 : [(41146 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588069, _1588069)), _1588071), c_Transitive__Closure_Ortrancl(_1588069, _1588075)))], (41144 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588069, _1588069)), _1588071), c_Transitive__Closure_Ortrancl(_1588069, _1588073)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588069, _1588069)), _1588071), c_Transitive__Closure_Ortrancl(_1588069, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588069, _1588069), tc_HOL_Obool)), _1588073), _1588075)))))], (32078 ^ _782476) ^ [_1390124, _1390126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390124, _1390126)), _1390124)))], (29950 ^ _782476) ^ [_1350748, _1350750, _1350752, _1350754] : [class_Fields_Olinordered__field(_1350748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350748), _1350750), _1350752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350748), c_Groups_Ozero__class_Ozero(_1350748)), _1350754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350748), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350748), _1350750), _1350754)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350748), _1350752), _1350754))))], (10489 ^ _782476) ^ [_973725, _973727, _973729, _973731, _973733] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973725, tc_fun(_973727, tc_HOL_Obool)), _973729), hAPP(hAPP(c_COMBB(tc_fun(_973727, tc_HOL_Obool), tc_fun(_973727, tc_HOL_Obool), _973725), hAPP(c_Set_Oinsert(_973727), _973731)), _973733)) = hAPP(hAPP(c_Set_Oinsert(_973727), _973731), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973725, tc_fun(_973727, tc_HOL_Obool)), _973729), _973733)))], (39579 ^ _782476) ^ [_1546745, _1546747, _1546749, _1546751] : [hBOOL(hAPP(hAPP(c_member(_1546745), _1546747), hAPP(c_Relation_ORange(_1546749, _1546745), _1546751))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546749, _1546745)), hAPP(hAPP(c_Product__Type_OPair(_1546749, _1546745), 39582 ^ [_1546745, _1546747, _1546749, _1546751]), _1546747)), _1546751)))], (8866 ^ _782476) ^ [_937110, _937112, _937114] : [class_Lattices_Osemilattice__inf(_937110), 8869 ^ _782476 : [(8876 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937110), _937112), _937114) = _937112, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937110), _937112), _937114)))], (8870 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937110), _937112), _937114)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937110), _937112), _937114) = _937112)]]], (27291 ^ _782476) ^ [_1298347, _1298349, _1298351, _1298353, _1298355] : [class_Groups_Ocomm__monoid__mult(_1298347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298349), _1298351)), 27298 ^ _782476 : [(27305 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298349), _1298353), _1298351))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298349, _1298347), hAPP(hAPP(c_COMBC(_1298349, _1298347, _1298347), hAPP(hAPP(c_COMBS(_1298349, _1298347, tc_fun(_1298347, _1298347)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298347, tc_fun(_1298347, _1298347)), _1298349), c_If(_1298347)), hAPP(c_fequal, _1298353))), _1298355)), c_Groups_Oone__class_Oone(_1298347))), _1298351) = c_Groups_Oone__class_Oone(_1298347))], (27299 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298349), _1298353), _1298351)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298349, _1298347), hAPP(hAPP(c_COMBC(_1298349, _1298347, _1298347), hAPP(hAPP(c_COMBS(_1298349, _1298347, tc_fun(_1298347, _1298347)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298347, tc_fun(_1298347, _1298347)), _1298349), c_If(_1298347)), hAPP(c_fequal, _1298353))), _1298355)), c_Groups_Oone__class_Oone(_1298347))), _1298351) = hAPP(_1298355, _1298353))]]], (15312 ^ _782476) ^ [_1068397, _1068399, _1068401] : [class_Lattices_Olattice(_1068397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068397), _1068399)), -(hBOOL(hAPP(hAPP(c_member(_1068397), _1068401), _1068399))), -(_1068399 = c_Orderings_Obot__class_Obot(tc_fun(_1068397, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068397, hAPP(hAPP(c_Set_Oinsert(_1068397), _1068401), _1068399)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068397), _1068401), c_Big__Operators_Olattice__class_OSup__fin(_1068397, _1068399)))], (29034 ^ _782476) ^ [_1333863, _1333865] : [_1333863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333865), _1333863) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17646 ^ _782476) ^ [_1116992, _1116994, _1116996] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116992), _1116994)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116992), _1116996)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116994), _1116996))], (38431 ^ _782476) ^ [_1517380, _1517382, _1517384, _1517386, _1517388, _1517390, _1517392, _1517394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517380, _1517382), tc_prod(_1517380, _1517382))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517380, _1517382), tc_prod(_1517380, _1517382)), hAPP(hAPP(c_Product__Type_OPair(_1517380, _1517382), _1517384), _1517386)), hAPP(hAPP(c_Product__Type_OPair(_1517380, _1517382), _1517388), _1517390))), c_Wellfounded_Olex__prod(_1517380, _1517382, _1517392, _1517394))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517380, _1517380)), hAPP(hAPP(c_Product__Type_OPair(_1517380, _1517380), _1517384), _1517388)), _1517392))), 38438 ^ _782476 : [(38441 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517382, _1517382)), hAPP(hAPP(c_Product__Type_OPair(_1517382, _1517382), _1517386), _1517390)), _1517394)))], (38439 ^ _782476) ^ [] : [-(_1517384 = _1517388)]]], (24148 ^ _782476) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25586 ^ _782476) ^ [_1260660] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1260660, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260660), hAPP(c_COMBK(tc_HOL_Obool, _1260660), c_fTrue)))], (10835 ^ _782476) ^ [_981666, _981668, _981670, _981672, _981674] : [_981666 = c_Orderings_Obot__class_Obot(tc_fun(_981668, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981668, tc_fun(_981670, tc_HOL_Obool)), _981666), hAPP(hAPP(c_COMBC(_981668, tc_fun(_981670, tc_HOL_Obool), tc_fun(_981670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981670, tc_HOL_Obool), tc_fun(tc_fun(_981670, tc_HOL_Obool), tc_fun(_981670, tc_HOL_Obool)), _981668), c_Groups_Ominus__class_Ominus(tc_fun(_981670, tc_HOL_Obool))), _981672)), _981674)) = c_Orderings_Otop__class_Otop(tc_fun(_981670, tc_HOL_Obool)))], (33702 ^ _782476) ^ [_1421449, _1421451, _1421453, _1421455] : [class_Fields_Olinordered__field__inverse__zero(_1421449), class_Int_Onumber(_1421449), 33709 ^ _782476 : [(33710 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421449), _1421451), _1421453)), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455))), 33713 ^ _782476 : [(33720 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), _1421453))), 33723 ^ _782476 : [(33730 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), _1421453), c_Groups_Ozero__class_Ozero(_1421449)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455))))], (33724 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), _1421453), c_Groups_Ozero__class_Ozero(_1421449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421449), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)), _1421453)), _1421451)))]]], (33714 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), _1421453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), _1421451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421449), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)), _1421453))))]]], (33736 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421449), _1421451), _1421453)), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)))), 33739 ^ _782476 : [(33742 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), _1421451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421449), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)), _1421453)))], (33740 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), _1421453)))]], 33743 ^ _782476 : [(33746 ^ _782476) ^ [] : [33747 ^ _782476 : [(33750 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421449), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)), _1421453)), _1421451))], (33748 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), _1421453), c_Groups_Ozero__class_Ozero(_1421449))))]], 33751 ^ _782476 : [(33754 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), hAPP(c_Int_Onumber__class_Onumber__of(_1421449), _1421455)))], (33752 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), _1421453), c_Groups_Ozero__class_Ozero(_1421449)))]]], (33744 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421449), c_Groups_Ozero__class_Ozero(_1421449)), _1421453))]]]]], (20075 ^ _782476) ^ [_1159375, _1159377, _1159379] : [class_Rings_Olinordered__idom(_1159375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159375), c_Groups_Ozero__class_Ozero(_1159375)), _1159377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159375), c_Groups_Ozero__class_Ozero(_1159375)), _1159379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159375), _1159379), c_Groups_Oone__class_Oone(_1159375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159375), _1159377), _1159379)), _1159377)))], (7313 ^ _782476) ^ [_904482, _904484, _904486, _904488, _904490] : [hBOOL(hAPP(hAPP(c_member(_904482), _904484), c_SetInterval_Oord_OgreaterThanLessThan(_904482, _904486, _904488, _904490))), 7316 ^ _782476 : [(7319 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904486, _904484), _904490)))], (7317 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904486, _904488), _904484)))]]], (18440 ^ _782476) ^ [] : [-(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)))], (34316 ^ _782476) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (43691 ^ _782476) ^ [_1652841, _1652843, _1652845, _1652847, _1652849, _1652851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652841, _1652843)), hAPP(hAPP(c_Product__Type_OPair(_1652841, _1652843), _1652845), _1652847)), hAPP(c_List_Oset(tc_prod(_1652841, _1652843)), hAPP(hAPP(c_List_Ozip(_1652841, _1652843), _1652849), _1652851)))), -(hBOOL(hAPP(hAPP(c_member(_1652841), _1652845), hAPP(c_List_Oset(_1652841), _1652849))))], (9811 ^ _782476) ^ [_958536, _958538] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958536, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_958536, tc_HOL_Obool))), hAPP(c_Set_OPow(_958536), _958538))))], (3728 ^ _782476) ^ [_838336, _838338, _838340, _838342, _838344, _838346] : [-(c_List_Oremove1(_838346, _838342, _838338) = c_List_Oremove1(_838344, _838340, _838336)), _838346 = _838344, _838342 = _838340, _838338 = _838336], (36934 ^ _782476) ^ [_1485775, _1485777, _1485779, _1485781] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1485775, _1485777, _1485779), hAPP(hAPP(c_COMBB(tc_fun(_1485777, tc_prod(_1485775, _1485777)), tc_fun(_1485777, _1485779), _1485775), hAPP(c_COMBB(tc_prod(_1485775, _1485777), _1485779, _1485777), _1485781)), c_Product__Type_OPair(_1485775, _1485777))) = _1485781)], (6993 ^ _782476) ^ [_897193, _897195, _897197, _897199] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897193, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897195, tc_fun(_897193, tc_HOL_Obool)), _897197), _897199)) = 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c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (43245 ^ _782476) ^ [_1640203, _1640205, _1640207] : [c_Equiv__Relations_Oequiv(_1640203, _1640205, _1640207), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1640203), c_List_Olists(_1640203, _1640205), c_List_Olistrel(_1640203, _1640207)))], (24927 ^ _782476) ^ [_1248585, _1248587] : [class_Groups_Oordered__ab__group__add__abs(_1248585), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248585), _1248587), hAPP(c_Groups_Oabs__class_Oabs(_1248585), _1248587))))], (47054 ^ _782476) ^ [_1727061, _1727063] : [-(hAPP(c_List_Oset(_1727061), c_List_Oconcat(_1727061, _1727063)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1727061), tc_fun(_1727061, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1727061)), _1727063)), c_List_Oset(_1727061)))], (12940 ^ _782476) ^ [_1019547, _1019549, _1019551, _1019553, _1019555, _1019557] : [c_Fun_Oinj__on(_1019547, _1019549, _1019551, _1019553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019547, tc_HOL_Obool)), _1019555), _1019553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019547, tc_HOL_Obool)), _1019557), _1019553)), -(hAPP(c_Set_Oimage(_1019547, _1019549, _1019551), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019547, tc_HOL_Obool)), _1019555), _1019557)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019549, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019547, _1019549, _1019551), _1019555)), hAPP(c_Set_Oimage(_1019547, _1019549, _1019551), _1019557)))], (13036 ^ _782476) ^ [_1021778, _1021780, _1021782, _1021784] : [-(_1021778 = c_Orderings_Obot__class_Obot(tc_fun(_1021780, tc_HOL_Obool))), 13039 ^ _782476 : [(13040 ^ _782476) ^ [] : [-(hAPP(c_Set_Oimage(_1021782, _1021780, 13047 ^ [_1021778, _1021780, _1021782, _1021784]), _1021784) = _1021778), 13041 ^ _782476 : [(13042 ^ _782476) ^ [_1021919] : [c_Fun_Oinj__on(_1021780, _1021782, _1021919, _1021778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021782, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021780, _1021782, _1021919), _1021778)), _1021784))]]], (13051 ^ _782476) ^ [] : [13052 ^ _782476 : [(13053 ^ _782476) ^ [_1022111] : [hAPP(c_Set_Oimage(_1021782, _1021780, _1022111), _1021784) = _1021778]], 13055 ^ _782476 : [(13058 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021782, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021780, _1021782, 13054 ^ [_1021778, _1021780, _1021782, _1021784]), _1021778)), _1021784)))], (13056 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1021780, _1021782, 13054 ^ [_1021778, _1021780, _1021782, _1021784], _1021778))]]]]], (52329 ^ _782476) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (12096 ^ _782476) ^ [_1002602, _1002604, _1002606] : [class_Complete__Lattice_Ocomplete__lattice(_1002602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002602), _1002604), hAPP(_1002606, _1002604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002602), _1002604), c_Inductive_Ocomplete__lattice__class_Ogfp(_1002602, _1002606))))], (42831 ^ _782476) ^ [_1626894, _1626896, _1626898] : [-(c_Product__Type_Ointernal__split(_1626894, _1626896, _1626898) = c_Product__Type_Oprod_Oprod__case(_1626894, _1626896, _1626898))], (8176 ^ _782476) ^ [_922111, _922113, _922115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_922111, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_922111, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_922111), _922113)), hAPP(c_Set_OPow(_922111), _922115))), hAPP(c_Set_OPow(_922111), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922111, tc_HOL_Obool)), _922113), _922115)))))], (10407 ^ _782476) ^ [_971489, _971491, _971493, _971495] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971489, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971489, tc_HOL_Obool)), _971491), _971493)), _971495) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971489, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971489, tc_HOL_Obool)), _971491), _971495)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971489, tc_HOL_Obool)), _971493), _971495)))], (38947 ^ _782476) ^ [_1531233, _1531235, _1531237, _1531239] : [hAPP(hAPP(c_Relation_Orel__comp(_1531233, _1531233, _1531233), _1531235), _1531237) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531233, _1531233), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531233, _1531233, _1531233), _1531235), _1531239) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531233, _1531233), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531233, _1531233, _1531233), _1531235), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531233, _1531233), tc_HOL_Obool)), _1531237), _1531239)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531233, _1531233), tc_HOL_Obool)))], (48146 ^ _782476) ^ [_1750830, _1750832, _1750834, _1750836, _1750838] : [c_List_Olist__all2(_1750830, _1750832, _1750834, hAPP(c_List_Orev(_1750830), _1750836), _1750838), -(c_List_Olist__all2(_1750830, _1750832, _1750834, _1750836, hAPP(c_List_Orev(_1750832), _1750838)))], (9658 ^ _782476) ^ [_955827, _955829, _955831] : [class_Lattices_Obounded__lattice__bot(_955827), 9661 ^ _782476 : [(9670 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955827), _955829), _955831) = c_Orderings_Obot__class_Obot(_955827)), _955829 = c_Orderings_Obot__class_Obot(_955827), _955831 = c_Orderings_Obot__class_Obot(_955827)], (9662 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955827), _955829), _955831) = c_Orderings_Obot__class_Obot(_955827), 9665 ^ _782476 : [(9668 ^ _782476) ^ [] : [-(_955831 = c_Orderings_Obot__class_Obot(_955827))], (9666 ^ _782476) ^ [] : [-(_955829 = c_Orderings_Obot__class_Obot(_955827))]]]]], (28840 ^ _782476) ^ [_1330448, _1330450, _1330452, _1330454] : [class_Rings_Odivision__ring(_1330448), -(_1330450 = c_Groups_Ozero__class_Ozero(_1330448)), 28847 ^ _782476 : [(28854 ^ _782476) ^ [] : [_1330452 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330448), _1330454), _1330450), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330448), _1330452), _1330450) = _1330454)], (28848 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330448), _1330452), _1330450) = _1330454, -(_1330452 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330448), _1330454), _1330450))]]], (44278 ^ _782476) ^ [_1665746, _1665748, _1665750] : [c_List_Olist_ONil(_1665746) = hAPP(hAPP(c_List_Olist_OCons(_1665746), _1665748), _1665750)], (51398 ^ _782476) ^ [_1822406, _1822408, _1822410] : [c_Equiv__Relations_Oequivp(_1822406, _1822408), 51401 ^ _782476 : [(51402 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1822410, 51409 ^ [_1822406, _1822408, _1822410]))), 51403 ^ _782476 : [(51404 ^ _782476) ^ [_1822528] : [hBOOL(hAPP(hAPP(c_member(_1822406), _1822528), c_Quotient_ORespects(_1822406, _1822408))), hBOOL(hAPP(_1822410, _1822528))]]], (51413 ^ _782476) ^ [] : [51414 ^ _782476 : [(51415 ^ _782476) ^ [_1822695] : [hBOOL(hAPP(_1822410, _1822695))]], 51417 ^ _782476 : [(51420 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1822410, 51416 ^ [_1822406, _1822408, _1822410])))], (51418 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822406), 51416 ^ [_1822406, _1822408, _1822410]), c_Quotient_ORespects(_1822406, _1822408))))]]]]], (14983 ^ _782476) ^ [_1062214, _1062216, _1062218] : [class_Lattices_Olattice(_1062214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062214), _1062216)), -(_1062216 = c_Orderings_Obot__class_Obot(tc_fun(_1062214, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062214), _1062218)), -(_1062218 = c_Orderings_Obot__class_Obot(tc_fun(_1062214, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062214, tc_HOL_Obool)), _1062216), _1062218) = c_Orderings_Obot__class_Obot(tc_fun(_1062214, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1062214, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062214, tc_HOL_Obool)), _1062216), _1062218)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062214), c_Big__Operators_Olattice__class_OInf__fin(_1062214, _1062216)), c_Big__Operators_Olattice__class_OInf__fin(_1062214, _1062218)))], (39305 ^ _782476) ^ [_1539842, _1539844] : [hBOOL(hAPP(hAPP(c_member(_1539842), 39306 ^ [_1539842, _1539844]), c_Wellfounded_Oacc(_1539842, _1539844))), -(c_Wellfounded_Owf(_1539842, _1539844))], (10829 ^ _782476) ^ [_981499, _981501, _981503, _981505, _981507] : [hBOOL(hAPP(hAPP(c_member(_981499), _981501), _981503)), -(hAPP(c_Set_Oimage(_981499, _981505, hAPP(c_COMBK(_981505, _981499), _981507)), _981503) = hAPP(hAPP(c_Set_Oinsert(_981505), _981507), c_Orderings_Obot__class_Obot(tc_fun(_981505, tc_HOL_Obool))))], (14849 ^ _782476) ^ [_1059887, _1059889] : [class_Complete__Lattice_Ocomplete__lattice(_1059887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059887), _1059889)), -(_1059889 = c_Orderings_Obot__class_Obot(tc_fun(_1059887, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1059887, _1059889) = c_Complete__Lattice_OInf__class_OInf(_1059887, _1059889))], (32561 ^ _782476) ^ [_1399202, _1399204] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399202), c_Orderings_Obot__class_Obot(tc_fun(_1399202, tc_HOL_Obool))), _1399204) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399202, tc_HOL_Obool), tc_HOL_Obool)))], (25674 ^ _782476) ^ [_1262921, _1262923, _1262925] : [-(hAPP(c_Set_OCollect(_1262921), hAPP(hAPP(c_COMBS(_1262921, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262921), c_fimplies), _1262923)), _1262925)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262921, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262921, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262921), _1262923))), hAPP(c_Set_OCollect(_1262921), _1262925)))], (49990 ^ _782476) ^ [_1791887, _1791889, _1791891, _1791893] : [49991 ^ _782476 : [(49994 ^ _782476) ^ [] : [_1791889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49992 ^ _782476) ^ [] : [hBOOL(hAPP(_1791893, _1791891))]], 49995 ^ _782476 : [(49996 ^ _782476) ^ [_1792012] : [hBOOL(hAPP(hAPP(c_member(_1791887), _1792012), hAPP(c_List_Oset(_1791887), c_List_Oreplicate(_1791887, _1791889, _1791891)))), -(hBOOL(hAPP(_1791893, _1792012)))]]], (32241 ^ _782476) ^ [_1393006, _1393008] : [-(_1393006 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393008), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393006), _1393008))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393006, _1393008)))], (36002 ^ _782476) ^ [] : [c_Int_OPls = c_Int_OMin], (2212 ^ _782476) ^ [_814834, _814836, _814838, _814840] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_814840, _814836) = c_Inductive_Ocomplete__lattice__class_Ogfp(_814838, _814834)), _814840 = _814838, _814836 = _814834], (52449 ^ _782476) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (34690 ^ _782476) ^ [] : [-(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)))))], (28368 ^ _782476) ^ [_1320665, _1320667, _1320669] : [class_Orderings_Olinorder(_1320665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320665), _1320667)), -(_1320667 = c_Orderings_Obot__class_Obot(tc_fun(_1320665, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1320665, c_Orderings_Oord__class_Omax(_1320665), hAPP(hAPP(c_Set_Oinsert(_1320665), _1320669), _1320667)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320665), _1320669), c_Big__Operators_Olattice_OSup__fin(_1320665, c_Orderings_Oord__class_Omax(_1320665), _1320667)))], (38734 ^ _782476) ^ [_1524416] : [-(c_Relation_OId__on(_1524416, c_Orderings_Obot__class_Obot(tc_fun(_1524416, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524416, _1524416), tc_HOL_Obool)))], (52343 ^ _782476) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (5840 ^ _782476) ^ [_874960, _874962, _874964] : [-(_874960 = _874962), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874964, tc_HOL_Obool)), _874960), _874962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874964, tc_HOL_Obool)), _874962), _874960))], (48102 ^ _782476) ^ [_1749924, _1749926, _1749928] : [-(hAPP(c_List_Orev(_1749924), hAPP(c_List_Ofilter(_1749924, _1749926), _1749928)) = hAPP(c_List_Ofilter(_1749924, _1749926), hAPP(c_List_Orev(_1749924), _1749928)))], (17107 ^ _782476) ^ [_1106998, _1107000, _1107002, _1107004, _1107006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106998), _1107000)), 17110 ^ _782476 : [(17117 ^ _782476) ^ [] : [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), _1107000), _1106998)), _1107002)), _1107004)), _1107006)), -(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), _1107000), _1107002)), _1107004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106998), _1107002)), _1107006))))], (17111 ^ _782476) ^ [] : [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), _1107000), _1107002)), _1107004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106998), _1107002)), _1107006))), -(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), _1107000), _1106998)), _1107002)), _1107004)), _1107006)))]]], (1692 ^ _782476) ^ [_806826, _806828] : [-(class_Rings_Olinordered__semiring(_806826)), _806828 = _806826, class_Rings_Olinordered__semiring(_806828)], (29310 ^ _782476) ^ [_1338699, _1338701, _1338703] : [class_Rings_Olinordered__semidom(_1338699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338699), c_Groups_Oone__class_Oone(_1338699)), _1338701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338699), c_Groups_Oone__class_Oone(_1338699)), hAPP(hAPP(c_Power_Opower__class_Opower(_1338699), _1338701), _1338703))))], (35460 ^ _782476) ^ [_1452547, _1452549, _1452551] : [class_Int_Onumber__ring(_1452547), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1452547), hAPP(c_Int_Onumber__class_Onumber__of(_1452547), _1452549)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452551))) = hAPP(hAPP(c_HOL_OLet(_1452547, _1452547), hAPP(hAPP(c_Power_Opower__class_Opower(_1452547), hAPP(c_Int_Onumber__class_Onumber__of(_1452547), _1452549)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452551))), hAPP(hAPP(c_COMBS(_1452547, _1452547, _1452547), c_Groups_Otimes__class_Otimes(_1452547)), c_COMBI(_1452547))))], (42253 ^ _782476) ^ [_1614702, _1614704, _1614706] : [class_Orderings_Olinorder(_1614702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614702), _1614704)), -(c_Big__Operators_Olattice_OInf__fin(_1614702, c_Orderings_Oord__class_Omin(_1614702), hAPP(hAPP(c_Set_Oinsert(_1614702), _1614706), _1614704)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614702, _1614702, c_Orderings_Oord__class_Omin(_1614702)), _1614706), _1614704))], (29518 ^ _782476) ^ [_1342576, _1342578, _1342580, _1342582] : [class_Rings_Olinordered__semidom(_1342576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342576), c_Groups_Oone__class_Oone(_1342576)), _1342578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342576), hAPP(hAPP(c_Power_Opower__class_Opower(_1342576), _1342578), _1342580)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342576), _1342578), _1342582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342580), _1342582)))], (17523 ^ _782476) ^ [_1114746, _1114748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114746), _1114748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114746), _1114748)))], (32632 ^ _782476) ^ [_1400440, _1400442] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400440), _1400442))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400440, _1400442) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400440), _1400442), _1400442))], (39289 ^ _782476) ^ [_1539557, _1539559, _1539561] : [c_Wellfounded_Owf(_1539557, _1539559), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539557, _1539557)), hAPP(hAPP(c_Product__Type_OPair(_1539557, _1539557), _1539561), _1539561)), _1539559))], (5288 ^ _782476) ^ [_863330, _863332, _863334, _863336] : [-(c_Product__Type_OPair(_863336, _863332) = c_Product__Type_OPair(_863334, _863330)), _863336 = _863334, _863332 = _863330], (51132 ^ _782476) ^ [_1816882, _1816884] : [-(c_Equiv__Relations_Opart__equivp(_1816882, _1816884)), 51135 ^ _782476 : [(51136 ^ _782476) ^ [_1816959] : [hBOOL(hAPP(hAPP(_1816884, _1816959), _1816959))]], c_Predicate_Osymp(_1816882, _1816884), c_Predicate_Otransp(_1816882, _1816884)], (3074 ^ _782476) ^ [_828169, _828171, _828173, _828175] : [-(c_List_Olexn(_828175, _828171) = c_List_Olexn(_828173, _828169)), _828175 = _828173, _828171 = _828169], (4596 ^ _782476) ^ [_852304, _852306] : [_852306 = _852304, -(c_List_Omember(_852306) = c_List_Omember(_852304))], (38648 ^ _782476) ^ [_1522667] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522667)), -(_1522667 = 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))), _1522667)), c_FunDef_Omax__strict)))], (41513 ^ _782476) ^ [_1596992, _1596994, _1596996] : [-(hAPP(c_Relation_ODomain(_1596992, _1596994), hAPP(c_Relation_Oconverse(_1596994, _1596992), _1596996)) = hAPP(c_Relation_ORange(_1596994, _1596992), _1596996))], (1242 ^ _782476) ^ [_801201, _801203] : [-(class_Rings_Olinordered__semiring__1(_801201)), _801203 = _801201, class_Rings_Olinordered__semiring__1(_801203)], (36553 ^ _782476) ^ [_1476506, _1476508, _1476510, _1476512, _1476514, _1476516] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476506, tc_fun(_1476508, tc_fun(_1476510, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476506, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_fun(_1476508, tc_fun(_1476510, tc_HOL_Obool)), _1476506), hAPP(c_COMBC(_1476508, tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_fun(_1476510, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476510, tc_fun(tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_fun(_1476510, tc_HOL_Obool)), _1476508), c_COMBC(_1476510, tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476510, tc_prod(_1476508, _1476510)), tc_fun(_1476510, tc_fun(tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_HOL_Obool)), _1476508), hAPP(c_COMBB(tc_prod(_1476508, _1476510), tc_fun(tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool), tc_HOL_Obool), _1476510), c_member(tc_prod(_1476508, _1476510)))), c_Product__Type_OPair(_1476508, _1476510))))), _1476512)), _1476514), _1476516)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476508, _1476510)), hAPP(hAPP(c_Product__Type_OPair(_1476508, _1476510), _1476514), _1476516)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476506, tc_fun(tc_prod(_1476508, _1476510), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476506, tc_HOL_Obool))), _1476512))))], (39616 ^ _782476) ^ [_1547537, _1547539, _1547541] : [_1547541 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547537, _1547539), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1547537, _1547539), _1547541) = c_Orderings_Obot__class_Obot(tc_fun(_1547537, tc_HOL_Obool)))], (856 ^ _782476) ^ [_795548, _795550, _795552, _795554, _795556, _795558, _795560, _795562] : [-(c_Wellfounded_Omax__extp(_795560, _795556, _795552, _795548)), c_Wellfounded_Omax__extp(_795562, _795558, _795554, _795550), _795562 = _795560, _795558 = _795556, _795554 = _795552, _795550 = _795548], (30282 ^ _782476) ^ [_1356492, _1356494, _1356496, _1356498, _1356500] : [class_Fields_Olinordered__field(_1356492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356492), c_Groups_Ozero__class_Ozero(_1356492)), _1356494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356492), _1356494), _1356496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356492), c_Groups_Ozero__class_Ozero(_1356492)), _1356498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356492), _1356498), _1356500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356492), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356492), _1356494), _1356500)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356492), _1356496), _1356498))))], (49876 ^ _782476) ^ [_1789877, _1789879, _1789881, _1789883, _1789885] : [-(hAPP(hAPP(c_List_Omap(_1789877, _1789879), _1789881), c_List_Oreplicate(_1789877, _1789883, _1789885)) = c_List_Oreplicate(_1789879, _1789883, hAPP(_1789881, _1789885)))], (22405 ^ _782476) ^ [_1202984, _1202986] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1202984), _1202986), 22410 ^ _782476 : [(22413 ^ _782476) ^ [] : [-(_1202986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22411 ^ _782476) ^ [] : [-(_1202984 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 22414 ^ _782476 : [(22417 ^ _782476) ^ [] : [-(_1202986 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22415 ^ _782476) ^ [] : [-(_1202984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25540 ^ _782476) ^ [_1259668, _1259670, _1259672] : [hBOOL(hAPP(hAPP(c_member(_1259668), _1259670), hAPP(c_Set_OCollect(_1259668), _1259672))), -(hBOOL(hAPP(_1259672, _1259670)))], (49713 ^ _782476) ^ [_1785838, _1785840, _1785842] : [hAPP(c_Fun_Ocomp(_1785840, _1785838, _1785838, c_Hilbert__Choice_Oinv__into(_1785838, _1785840, c_Orderings_Otop__class_Otop(tc_fun(_1785838, tc_HOL_Obool)), _1785842)), _1785842) = c_Fun_Oid(_1785838), -(c_Fun_Oinj__on(_1785838, _1785840, _1785842, c_Orderings_Otop__class_Otop(tc_fun(_1785838, tc_HOL_Obool))))], (13968 ^ _782476) ^ [_1041936, _1041938, _1041940, _1041942, _1041944, _1041946] : [hBOOL(hAPP(hAPP(c_member(_1041936), _1041938), _1041940)), -(hAPP(c_Fun_Ooverride__on(_1041936, _1041942, _1041944, _1041946, _1041940), _1041938) = hAPP(_1041946, _1041938))], (12608 ^ _782476) ^ [_1013402, _1013404, _1013406] : [-(c_Fun_Oinj__on(_1013402, _1013404, _1013406, c_Orderings_Obot__class_Obot(tc_fun(_1013402, tc_HOL_Obool))))], (36004 ^ _782476) ^ [] : [c_Int_OMin = c_Int_OPls], (9203 ^ _782476) ^ [_946067, _946069, _946071, _946073] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_946067, tc_HOL_Obool), hAPP(c_Set_Oimage(_946069, tc_fun(_946067, tc_HOL_Obool), _946071), _946073)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946069, tc_fun(_946067, tc_HOL_Obool)), _946073), _946071))], (34042 ^ _782476) ^ [_1427818] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427818)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427818)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427818)), 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)))))], (19354 ^ _782476) ^ [_1146665] : [class_Rings_Olinordered__semidom(_1146665), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146665), c_Groups_Ozero__class_Ozero(_1146665)), c_Groups_Oone__class_Oone(_1146665))))], (44296 ^ _782476) ^ [_1666044, _1666046, _1666048] : [44297 ^ _782476 : [(44300 ^ _782476) ^ [] : [_1666048 = c_List_Olist_ONil(_1666044)], (44298 ^ _782476) ^ [] : [_1666046 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1666044), _1666046), _1666048) = c_List_Olist_ONil(_1666044))], (10491 ^ _782476) ^ [_973809, _973811, _973813, _973815, _973817] : [-(hAPP(hAPP(c_Set_Oinsert(_973809), _973811), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973813, tc_fun(_973809, tc_HOL_Obool)), _973815), _973817)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973813, tc_fun(_973809, tc_HOL_Obool)), _973815), hAPP(hAPP(c_COMBB(tc_fun(_973809, tc_HOL_Obool), tc_fun(_973809, tc_HOL_Obool), _973813), hAPP(c_Set_Oinsert(_973809), _973811)), _973817)))], (45060 ^ _782476) ^ [_1683629, _1683631, _1683633] : [hBOOL(hAPP(c_List_Odistinct(_1683629), _1683631)), -(hBOOL(hAPP(c_List_Odistinct(_1683629), hAPP(hAPP(c_List_Odrop(_1683629), _1683633), _1683631))))], (11750 ^ _782476) ^ [_996428, _996430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996428, tc_HOL_Obool)), _996430), c_Orderings_Obot__class_Obot(tc_fun(_996428, tc_HOL_Obool))))], (2248 ^ _782476) ^ [_815366, _815368, _815370, _815372, _815374, _815376] : [-(c_Power_Opower_Opower(_815376, _815372, _815368) = c_Power_Opower_Opower(_815374, _815370, _815366)), _815376 = _815374, _815372 = _815370, _815368 = _815366], (45957 ^ _782476) ^ [_1702075, _1702077, _1702079, _1702081, _1702083, _1702085] : [-(hAPP(hAPP(c_List_Omap(_1702075, _1702077), _1702079), hAPP(hAPP(c_List_Olist__update(_1702075, _1702081), _1702083), _1702085)) = hAPP(hAPP(c_List_Olist__update(_1702077, hAPP(hAPP(c_List_Omap(_1702075, _1702077), _1702079), _1702081)), _1702083), hAPP(_1702079, _1702085)))], (39720 ^ _782476) ^ [_1550718, _1550720, _1550722, _1550724] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1550718, _1550720)), hAPP(hAPP(c_Product__Type_OSigma(_1550718, _1550720), _1550722), hAPP(c_COMBK(tc_fun(_1550720, tc_HOL_Obool), _1550718), _1550724))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1550718), _1550722)), hAPP(c_Finite__Set_Ocard(_1550720), _1550724)))], (8104 ^ _782476) ^ [_920560, _920562, _920564, _920566] : [hBOOL(hAPP(hAPP(c_member(_920560), _920562), _920564)), -(hBOOL(hAPP(hAPP(c_member(_920560), _920562), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920560, tc_HOL_Obool)), _920564), _920566))))], (40970 ^ _782476) ^ [_1583076, _1583078] : [-(hAPP(c_Relation_ORange(_1583076, _1583076), c_Transitive__Closure_Otrancl(_1583076, _1583078)) = hAPP(c_Relation_ORange(_1583076, _1583076), _1583078))], (35296 ^ _782476) ^ [_1449490, _1449492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449490)), c_Int_OBit0(_1449492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449490), _1449492)))], (20005 ^ _782476) ^ [_1158030, _1158032, _1158034, _1158036] : [class_Rings_Olinordered__semiring__strict(_1158030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158030), _1158032), _1158034)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158030), _1158036), _1158034))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158030), c_Groups_Ozero__class_Ozero(_1158030)), _1158034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158030), _1158032), _1158036)))], (2658 ^ _782476) ^ [_821667, _821669, _821671, _821673] : [-(c_Nitpick_Onorm__frac(_821673, _821669) = c_Nitpick_Onorm__frac(_821671, _821667)), _821673 = _821671, _821669 = _821667], (21373 ^ _782476) ^ [_1183787, _1183789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183787), _1183789)), -(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)), _1183787)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183789))))], (37219 ^ _782476) ^ [_1490907, _1490909, _1490911, _1490913, _1490915, _1490917, _1490919] : [-(hAPP(c_Product__Type_Oapsnd(_1490907, _1490909, _1490911, _1490913), hAPP(c_Product__Type_Oapsnd(_1490915, _1490907, _1490911, _1490917), _1490919)) = hAPP(c_Product__Type_Oapsnd(_1490915, _1490909, _1490911, hAPP(c_Fun_Ocomp(_1490907, _1490909, _1490915, _1490913), _1490917)), _1490919))], (48532 ^ _782476) ^ [_1758961, _1758963, _1758965, _1758967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758963)), c_List_OdropWhile(_1758963, _1758965, _1758967)))), -(hAPP(hAPP(c_List_Onth(_1758963), c_List_OdropWhile(_1758963, _1758965, _1758967)), _1758961) = hAPP(hAPP(c_List_Onth(_1758963), _1758967), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758963)), c_List_OtakeWhile(_1758963, _1758965, _1758967)))))], (22242 ^ _782476) ^ [_1200167, _1200169, _1200171] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200167)), _1200169)), hAPP(c_Nat_OSuc, _1200171)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200167), _1200169)), _1200171))], (41182 ^ _782476) ^ [_1589124, _1589126, _1589128, _1589130, _1589132] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589124, _1589124)), hAPP(hAPP(c_Product__Type_OPair(_1589124, _1589124), _1589126), _1589128)), _1589130)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589124, _1589124)), hAPP(hAPP(c_Product__Type_OPair(_1589124, _1589124), _1589128), _1589132)), c_Transitive__Closure_Ortrancl(_1589124, _1589130))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589124, _1589124)), hAPP(hAPP(c_Product__Type_OPair(_1589124, _1589124), _1589126), _1589132)), c_Transitive__Closure_Ortrancl(_1589124, _1589130))))], (10607 ^ _782476) ^ [_976294, _976296, _976298] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976294, tc_HOL_Obool)), _976296), _976298) = c_Orderings_Obot__class_Obot(tc_fun(_976294, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976294, tc_HOL_Obool)), _976296), _976298) = _976296)], (44418 ^ _782476) ^ [_1668218, _1668220, _1668222] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668218), tc_List_Olist(_1668218))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668218), tc_List_Olist(_1668218)), _1668220), c_List_Olist_ONil(_1668218))), c_List_Olexord(_1668218, _1668222)))], (29458 ^ _782476) ^ [_1341539, _1341541, _1341543] : [class_Rings_Olinordered__semidom(_1341539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341539), c_Groups_Oone__class_Oone(_1341539)), _1341541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341539), c_Groups_Oone__class_Oone(_1341539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341539), _1341541), hAPP(hAPP(c_Power_Opower__class_Opower(_1341539), _1341541), _1341543)))))], (14248 ^ _782476) ^ [_1047909, _1047911, _1047913] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047909), hAPP(hAPP(c_Set_Oinsert(_1047909), _1047911), _1047913))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047909), _1047913)))], (45094 ^ _782476) ^ [_1684406, _1684408] : [-(hAPP(c_List_Oset(_1684406), hAPP(c_List_Orotate1(_1684406), _1684408)) = hAPP(c_List_Oset(_1684406), _1684408))], (24338 ^ _782476) ^ [_1238029, _1238031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238029)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1238029, _1238031)))], (10773 ^ _782476) ^ [_980041, _980043] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980041, tc_fun(_980041, tc_HOL_Obool)), _980043), hAPP(hAPP(c_COMBC(_980041, tc_fun(_980041, tc_HOL_Obool), tc_fun(_980041, tc_HOL_Obool)), c_Set_Oinsert(_980041)), c_Orderings_Obot__class_Obot(tc_fun(_980041, tc_HOL_Obool)))) = _980043)], (3110 ^ _782476) ^ [_828701, _828703, _828705, _828707] : [-(c_Nitpick_Ocard_H(_828707, _828703) = c_Nitpick_Ocard_H(_828705, _828701)), _828707 = _828705, _828703 = _828701], (44821 ^ _782476) ^ [_1677687, _1677689, _1677691] : [_1677687 = hAPP(hAPP(c_List_Oappend(_1677689), _1677691), _1677687), -(_1677691 = c_List_Olist_ONil(_1677689))], (2030 ^ _782476) ^ [_811905, _811907, _811909, _811911, _811913, _811915] : [-(c_SetInterval_Oord_OgreaterThan(_811915, _811911, _811907) = c_SetInterval_Oord_OgreaterThan(_811913, _811909, _811905)), _811915 = _811913, _811911 = _811909, _811907 = _811905], (11458 ^ _782476) ^ [_992120, _992122, _992124] : [class_Orderings_Olinorder(_992120), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992120), _992122), _992124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992120), _992124), _992122)))], (18310 ^ _782476) ^ [_1128162, _1128164] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128162), _1128164) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1128164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49262 ^ _782476) ^ [_1775680, _1775682, _1775684, _1775686] : [-(c_List_Olist__all(_1775680, _1775682, hAPP(hAPP(c_List_Oappend(_1775680), _1775684), _1775686))), c_List_Olist__all(_1775680, _1775682, _1775684), c_List_Olist__all(_1775680, _1775682, _1775686)], (50121 ^ _782476) ^ [_1794440, _1794442, _1794444, _1794446, _1794448] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1794440, _1794442, _1794444) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794440, _1794446, _1794448)), _1794442 = _1794446, _1794444 = _1794448], (22602 ^ _782476) ^ [_1206350, _1206352, _1206354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206352), _1206354)), -(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, _1206350)), _1206352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206350)), _1206354))))], (28183 ^ _782476) ^ [_1315339, _1315341, _1315343] : [class_Orderings_Olinorder(_1315339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315339), _1315341)), -(_1315341 = c_Orderings_Obot__class_Obot(tc_fun(_1315339, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315339), _1315343)), -(_1315343 = c_Orderings_Obot__class_Obot(tc_fun(_1315339, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315339, tc_HOL_Obool)), _1315341), _1315343) = c_Orderings_Obot__class_Obot(tc_fun(_1315339, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1315339, c_Orderings_Oord__class_Omin(_1315339), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315339, tc_HOL_Obool)), _1315341), _1315343)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315339), c_Big__Operators_Olattice_OInf__fin(_1315339, c_Orderings_Oord__class_Omin(_1315339), _1315341)), c_Big__Operators_Olattice_OInf__fin(_1315339, c_Orderings_Oord__class_Omin(_1315339), _1315343)))], (21203 ^ _782476) ^ [_1180664, _1180666, _1180668] : [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), _1180664), _1180666)), _1180668))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180668), _1180664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180666)))], (21283 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (7111 ^ _782476) ^ [_900238, _900240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_900238, tc_HOL_Obool), tc_HOL_Obool)), _900240), hAPP(c_Set_OPow(_900238), c_Complete__Lattice_OSup__class_OSup(tc_fun(_900238, tc_HOL_Obool), _900240)))))], (29572 ^ _782476) ^ [_1343657, _1343659, _1343661] : [class_Rings_Olinordered__semidom(_1343657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343657), c_Groups_Ozero__class_Ozero(_1343657)), _1343659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343657), _1343659), c_Groups_Oone__class_Oone(_1343657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343657), _1343659), hAPP(hAPP(c_Power_Opower__class_Opower(_1343657), _1343659), _1343661))), hAPP(hAPP(c_Power_Opower__class_Opower(_1343657), _1343659), _1343661))))], (12672 ^ _782476) ^ [_1014783, _1014785, _1014787, _1014789, _1014791, _1014793] : [c_Fun_Oinj__on(_1014783, _1014785, _1014787, _1014789), -(_1014791 = _1014793), hBOOL(hAPP(hAPP(c_member(_1014783), _1014791), _1014789)), hBOOL(hAPP(hAPP(c_member(_1014783), _1014793), _1014789)), hAPP(_1014787, _1014791) = hAPP(_1014787, _1014793)], (3822 ^ _782476) ^ [_839827, _839829, _839831, _839833, _839835, _839837, _839839, _839841] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_839841, _839837, _839833, _839829) = c_New__Random__Sequence_Opos__not__random__dseq(_839839, _839835, _839831, _839827)), _839841 = _839839, _839837 = _839835, _839833 = _839831, _839829 = _839827], (7161 ^ _782476) ^ [_901329, _901331, _901333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901329, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901329, tc_fun(_901329, tc_HOL_Obool), tc_HOL_Obool), c_member(_901329)), _901331)), hAPP(hAPP(c_COMBC(_901329, tc_fun(_901329, tc_HOL_Obool), tc_HOL_Obool), c_member(_901329)), _901333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901329, tc_HOL_Obool)), _901331), _901333)))], (50511 ^ _782476) ^ [_1803990, _1803992, _1803994] : [c_Relation_Otrans(_1803990, _1803992), c_Relation_Otrans(_1803990, _1803994), -(c_Relation_Otrans(_1803990, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1803990, _1803990), tc_HOL_Obool)), _1803992), _1803994)))], (39740 ^ _782476) ^ [_1551275, _1551277, _1551279, _1551281] : [39741 ^ _782476 : [(39744 ^ _782476) ^ [] : [_1551281 = c_Orderings_Obot__class_Obot(tc_fun(_1551277, tc_HOL_Obool))], (39742 ^ _782476) ^ [] : [_1551279 = c_Orderings_Obot__class_Obot(tc_fun(_1551275, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1551275, _1551277), _1551279), hAPP(c_COMBK(tc_fun(_1551277, tc_HOL_Obool), _1551275), _1551281)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551275, _1551277), tc_HOL_Obool)))], (45775 ^ _782476) ^ [_1698765, _1698767, _1698769] : [-(_1698765 = c_List_Olist_ONil(_1698767)), -(c_List_Olast(_1698767, hAPP(hAPP(c_List_Oappend(_1698767), _1698769), _1698765)) = c_List_Olast(_1698767, _1698765))], (34542 ^ _782476) ^ [_1435961, _1435963] : [34543 ^ _782476 : [(34546 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435961), c_Int_OPls))], (34544 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435961), _1435963))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435961)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435963))))], (14945 ^ _782476) ^ [_1061507, _1061509, _1061511] : [class_Lattices_Olattice(_1061507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061507), _1061509)), -(hBOOL(hAPP(hAPP(c_member(_1061507), _1061511), _1061509))), -(_1061509 = c_Orderings_Obot__class_Obot(tc_fun(_1061507, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061507, hAPP(hAPP(c_Set_Oinsert(_1061507), _1061511), _1061509)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061507), _1061511), c_Big__Operators_Olattice__class_OInf__fin(_1061507, _1061509)))], (18450 ^ _782476) ^ [_1130197, _1130199, _1130201] : [class_Rings_Olinordered__semidom(_1130197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130197), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130197), _1130199)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130197), _1130201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130199), _1130201)))], (36158 ^ _782476) ^ [_1465255] : [class_Int_Onumber__ring(_1465255), -(hAPP(c_Int_Onumber__class_Onumber__of(_1465255), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465255), c_Groups_Oone__class_Oone(_1465255)))], (2740 ^ _782476) ^ [_822958, _822960, _822962, _822964, _822966, _822968] : [-(c_Predicate_ODomainP(_822968, _822964, _822960) = c_Predicate_ODomainP(_822966, _822962, _822958)), _822968 = _822966, _822964 = _822962, _822960 = _822958], (24973 ^ _782476) ^ [_1249328] : [class_Groups_Oordered__ab__group__add__abs(_1249328), -(hAPP(c_Groups_Oabs__class_Oabs(_1249328), c_Groups_Ozero__class_Ozero(_1249328)) = c_Groups_Ozero__class_Ozero(_1249328))], (26674 ^ _782476) ^ [_1286156, _1286158, _1286160, _1286162] : [class_Orderings_Olinorder(_1286156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286156), _1286158), _1286160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286156), _1286158), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286156), _1286160), _1286162))))], (26226 ^ _782476) ^ [_1278096, _1278098, _1278100] : [class_Orderings_Olinorder(_1278096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278096), _1278098)), hBOOL(hAPP(hAPP(c_member(_1278096), _1278100), _1278098)), 26237 ^ _782476 : [(26244 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278096, tc_HOL_Obool)), _1278098), hAPP(hAPP(c_Set_Oinsert(_1278096), _1278100), c_Orderings_Obot__class_Obot(tc_fun(_1278096, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278096, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1278096, _1278098) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278096), _1278100), c_Big__Operators_Olinorder__class_OMax(_1278096, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278096, tc_HOL_Obool)), _1278098), hAPP(hAPP(c_Set_Oinsert(_1278096), _1278100), c_Orderings_Obot__class_Obot(tc_fun(_1278096, tc_HOL_Obool)))))))], (26238 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278096, tc_HOL_Obool)), _1278098), hAPP(hAPP(c_Set_Oinsert(_1278096), _1278100), c_Orderings_Obot__class_Obot(tc_fun(_1278096, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278096, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1278096, _1278098) = _1278100)]]], (10913 ^ _782476) ^ [_983601, _983603, _983605] : [10915 ^ _782476 : [(10918 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983601, tc_HOL_Obool)), 10914 ^ [_983601, _983603, _983605]), _983605))], (10916 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_983601, tc_HOL_Obool)), 10914 ^ [_983601, _983603, _983605]), _983603)))]], -(_983603 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_983601, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983601, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_983601, tc_HOL_Obool), _983603)), _983605)))], (35098 ^ _782476) ^ [_1446019, _1446021] : [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), _1446019))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1446021)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1446019))) = 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), _1446021), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1446019)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (424 ^ _782476) ^ [_788900, _788902, _788904, _788906, _788908, _788910, _788912, _788914] : [-(c_Finite__Set_Ofolding(_788912, _788908, _788904, _788900)), c_Finite__Set_Ofolding(_788914, _788910, _788906, _788902), _788914 = _788912, _788910 = _788908, _788906 = _788904, _788902 = _788900], (18438 ^ _782476) ^ [] : [-(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)))], (36300 ^ _782476) ^ [_1467392, _1467394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1467392), _1467394)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467392), _1467394) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (14397 ^ _782476) ^ [_1050690, _1050692, _1050694, _1050696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050690), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050690, tc_HOL_Obool)), _1050692), _1050696))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050690), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050690, tc_HOL_Obool)), _1050692), hAPP(hAPP(c_Set_Oinsert(_1050690), _1050694), _1050696)))))], (47646 ^ _782476) ^ [_1741034, _1741036, _1741038, _1741040] : [class_Orderings_Olinorder(_1741034), 47649 ^ _782476 : [(47658 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1741034, hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741036), hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741038), _1741040)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1741034), _1741036), _1741038)), c_List_Olinorder__class_Osorted(_1741034, hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741038), _1741040))], (47650 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1741034, hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741036), hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741038), _1741040))), 47653 ^ _782476 : [(47656 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1741034, hAPP(hAPP(c_List_Olist_OCons(_1741034), _1741038), _1741040)))], (47654 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1741034), _1741036), _1741038)))]]]]], (34314 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42037 ^ _782476) ^ [_1610444, _1610446, _1610448, _1610450] : [class_Orderings_Olinorder(_1610444), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610444), _1610446)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610444, _1610444, c_Orderings_Oord__class_Omin(_1610444)), _1610448), hAPP(hAPP(c_Set_Oinsert(_1610444), _1610450), _1610446)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1610444), _1610450), hAPP(hAPP(c_Finite__Set_Ofold(_1610444, _1610444, c_Orderings_Oord__class_Omin(_1610444)), _1610448), _1610446)))], (14835 ^ _782476) ^ [_1059652, _1059654, _1059656] : [class_Lattices_Olattice(_1059652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059652), _1059654)), hBOOL(hAPP(hAPP(c_member(_1059652), _1059656), _1059654)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1059652), _1059656), c_Big__Operators_Olattice__class_OInf__fin(_1059652, _1059654)) = c_Big__Operators_Olattice__class_OInf__fin(_1059652, _1059654))], (16967 ^ _782476) ^ [_1103656, _1103658, _1103660, _1103662] : [class_Rings_Ocomm__semiring__1(_1103656), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103656), _1103658), _1103660)), _1103662) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103656), _1103658), _1103662)), _1103660))], (7673 ^ _782476) ^ [_911780, _911782, _911784, _911786, _911788] : [7675 ^ _782476 : [(7678 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911784, tc_HOL_Obool)), hAPP(_911786, 7674 ^ [_911780, _911782, _911784, _911786, _911788])), _911788))], (7676 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911780), 7674 ^ [_911780, _911782, _911784, _911786, _911788]), _911782)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911784, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_911780, tc_fun(_911784, tc_HOL_Obool)), _911782), _911786)), _911788)))], (33646 ^ _782476) ^ [_1420335, _1420337, _1420339, _1420341] : [class_Fields_Olinordered__field__inverse__zero(_1420335), class_Int_Onumber(_1420335), 33653 ^ _782476 : [(33654 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420335), _1420337), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))), _1420341)), 33657 ^ 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c_Groups_Ozero__class_Ozero(_1420335)), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), _1420337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420335), _1420341), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339)))))]]], (33680 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420335), _1420337), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))), _1420341))), 33683 ^ _782476 : [(33686 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), _1420337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420335), _1420341), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))))], (33684 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420335), c_Groups_Ozero__class_Ozero(_1420335)), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))))]], 33687 ^ _782476 : [(33690 ^ _782476) ^ [] : [33691 ^ _782476 : [(33694 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420335), _1420341), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339))), _1420337))], (33692 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420335), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339)), c_Groups_Ozero__class_Ozero(_1420335))))]], 33695 ^ _782476 : [(33698 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420335), c_Groups_Ozero__class_Ozero(_1420335)), _1420341))], (33696 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420335), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339)), c_Groups_Ozero__class_Ozero(_1420335)))]]], (33688 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420335), c_Groups_Ozero__class_Ozero(_1420335)), hAPP(c_Int_Onumber__class_Onumber__of(_1420335), _1420339)))]]]]], (6837 ^ _782476) ^ [_894178, _894180, _894182, _894184, _894186] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894178, tc_fun(_894180, tc_HOL_Obool)), _894182), _894184), _894186)), 6840 ^ _782476 : [(6841 ^ _782476) ^ [_894287] : [hBOOL(hAPP(hAPP(c_member(_894178), _894287), _894182)), -(hBOOL(hAPP(hAPP(_894184, _894287), _894186)))]]], (46904 ^ _782476) ^ [_1724126] : [-(c_List_Oremdups(_1724126, c_List_Olist_ONil(_1724126)) = c_List_Olist_ONil(_1724126))], (18342 ^ _782476) ^ [_1128620] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128620), _1128620) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5916 ^ _782476) ^ [_876213, _876215, _876217] : [class_Orderings_Oorder(_876213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876213), _876215), _876217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876213), _876217), _876215)), -(_876217 = _876215)], (47343 ^ _782476) ^ [_1735527, _1735529] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1735527, _1735529))))], (49538 ^ _782476) ^ [_1781656, _1781658, _1781660, _1781662, _1781664] : [c_Fun_Obij__betw(_1781656, _1781658, _1781660, _1781662, _1781664), -(c_Fun_Obij__betw(_1781658, _1781656, c_Hilbert__Choice_Oinv__into(_1781656, _1781658, _1781662, _1781660), _1781664, _1781662))], (8999 ^ _782476) ^ [_939999, _940001, _940003, _940005, _940007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939999, tc_HOL_Obool)), _940001), _940003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939999, tc_HOL_Obool)), _940005), _940007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939999, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939999, tc_HOL_Obool)), _940001), _940005)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939999, tc_HOL_Obool)), _940003), _940007))))], (50808 ^ _782476) ^ [_1810909, _1810911, _1810913, _1810915] : [-(c_Wellfounded_Omax__extp(_1810909, _1810911, _1810913, _1810915)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1810909), _1810913)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1810909), _1810915)), -(_1810915 = c_Orderings_Obot__class_Obot(tc_fun(_1810909, tc_HOL_Obool))), 50822 ^ _782476 : [(50825 ^ _782476) ^ [_1811254] : [hBOOL(hAPP(hAPP(c_member(_1810909), _1811254), _1810915)), hBOOL(hAPP(hAPP(_1810911, 50821 ^ [_1810909, _1810911, _1810913, _1810915]), _1811254))], (50823 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810909), 50821 ^ [_1810909, _1810911, _1810913, _1810915]), _1810913)))]]], (45414 ^ _782476) ^ [_1691435, _1691437, _1691439] : [-(_1691435 = c_List_Olist_ONil(_1691437)), -(hAPP(hAPP(c_List_Otake(_1691437), hAPP(c_Nat_OSuc, _1691439)), _1691435) = hAPP(hAPP(c_List_Olist_OCons(_1691437), hAPP(c_List_Ohd(_1691437), _1691435)), hAPP(hAPP(c_List_Otake(_1691437), _1691439), hAPP(c_List_Otl(_1691437), _1691435))))], (32511 ^ _782476) ^ [_1398145, _1398147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398145))), -(c_SMT_Oz3mod(_1398147, _1398145) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398147, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398145)))], (49665 ^ _782476) ^ [_1784588, _1784590, _1784592, _1784594, _1784596] : [c_Fun_Obij__betw(_1784588, _1784590, _1784592, c_Orderings_Otop__class_Otop(tc_fun(_1784588, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784590, tc_HOL_Obool))), c_Fun_Obij__betw(_1784594, _1784588, _1784596, c_Orderings_Otop__class_Otop(tc_fun(_1784594, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784588, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1784594, _1784590, c_Orderings_Otop__class_Otop(tc_fun(_1784594, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1784588, _1784590, _1784594, _1784592), _1784596)) = hAPP(c_Fun_Ocomp(_1784588, _1784594, _1784590, c_Hilbert__Choice_Oinv__into(_1784594, _1784588, c_Orderings_Otop__class_Otop(tc_fun(_1784594, tc_HOL_Obool)), _1784596)), c_Hilbert__Choice_Oinv__into(_1784588, _1784590, c_Orderings_Otop__class_Otop(tc_fun(_1784588, tc_HOL_Obool)), _1784592)))], (8933 ^ _782476) ^ [_938492, _938494, _938496, _938498] : [class_Lattices_Odistrib__lattice(_938492), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938492), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938492), _938494), _938496)), _938498) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938492), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938492), _938494), _938498)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938492), _938496), _938498)))], (39762 ^ _782476) ^ [_1552122, _1552124, _1552126, _1552128, _1552130] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552122, _1552124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552122, tc_HOL_Obool)), _1552126), _1552128)), _1552130) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552122, _1552124), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552122, _1552124), _1552126), _1552130)), hAPP(hAPP(c_Product__Type_OSigma(_1552122, _1552124), _1552128), _1552130)))], (25141 ^ _782476) ^ [_1252408, _1252410, _1252412] : [class_Groups_Oordered__ab__group__add__abs(_1252408), 25144 ^ _782476 : [(25153 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), hAPP(c_Groups_Oabs__class_Oabs(_1252408), _1252410)), _1252412))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), _1252410), _1252412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), hAPP(c_Groups_Ouminus__class_Ouminus(_1252408), _1252410)), _1252412))], (25145 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), hAPP(c_Groups_Oabs__class_Oabs(_1252408), _1252410)), _1252412)), 25148 ^ _782476 : [(25151 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), hAPP(c_Groups_Ouminus__class_Ouminus(_1252408), _1252410)), _1252412)))], (25149 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252408), _1252410), _1252412)))]]]]], (16285 ^ _782476) ^ [_1088697, _1088699, _1088701, _1088703, _1088705] : [class_Groups_Ocomm__monoid__add(_1088697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088699), _1088701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088701), _1088703)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088697), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088697), _1088705), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088699), _1088701))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088697), _1088705), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088701), _1088703))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088697), _1088705), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088699), _1088703)))], (41198 ^ _782476) ^ [_1589506, _1589508, _1589510] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589506, _1589508, _1589508), _1589510), c_Relation_OId(_1589508)) = _1589510)], (46392 ^ _782476) ^ [] : [-(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))))], (37792 ^ _782476) ^ [_1501957, _1501959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501957), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1501959), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501957), _1501959) = 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), _1501957), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501959)))))], (9438 ^ _782476) ^ [_951512, _951514, _951516, _951518] : [_951518 = c_Orderings_Obot__class_Obot(tc_fun(_951514, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_951512, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951514, _951512, _951516), _951518))], (30698 ^ _782476) ^ [_1364304, _1364306, _1364308, _1364310] : [class_Fields_Olinordered__field__inverse__zero(_1364304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364304), _1364306), _1364308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364304), _1364310), c_Groups_Ozero__class_Ozero(_1364304))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364304), c_Groups_Ozero__class_Ozero(_1364304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364304), _1364306), _1364308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364304), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364304), _1364310), _1364306)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364304), _1364310), _1364308))))], (14020 ^ _782476) ^ [_1043035, _1043037, _1043039] : [class_Rings_Oring(_1043035), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1043035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043035), _1043037), _1043039)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043035), _1043037), hAPP(c_Groups_Ouminus__class_Ouminus(_1043035), _1043039)))], (49474 ^ _782476) ^ [_1780169, _1780171, _1780173] : [-(c_List_Osplice(_1780169, hAPP(hAPP(c_List_Olist_OCons(_1780169), _1780171), _1780173), c_List_Olist_ONil(_1780169)) = hAPP(hAPP(c_List_Olist_OCons(_1780169), _1780171), _1780173))], (13274 ^ _782476) ^ [_1027573, _1027575, _1027577, _1027579] : [hBOOL(hAPP(hAPP(c_member(_1027573), _1027575), _1027577)), -(hAPP(c_Set_Ovimage(_1027579, _1027573, hAPP(c_COMBK(_1027573, _1027579), _1027575)), _1027577) = c_Orderings_Otop__class_Otop(tc_fun(_1027579, tc_HOL_Obool)))], (4314 ^ _782476) ^ [_847911, _847913, _847915, _847917, _847919, _847921, _847923, _847925, _847927, _847929, _847931, _847933] : [-(c_New__Random__Sequence_Opos__union(_847933, _847929, _847925, _847921, _847917, _847913) = c_New__Random__Sequence_Opos__union(_847931, _847927, _847923, _847919, _847915, _847911)), _847933 = _847931, _847929 = _847927, _847925 = _847923, _847921 = _847919, _847917 = _847915, _847913 = _847911], (36489 ^ _782476) ^ [_1475429, _1475431, _1475433, _1475435, _1475437] : [-(hBOOL(hAPP(hAPP(c_member(_1475429), _1475431), hAPP(c_Relation_OImage(_1475433, _1475429, _1475435), _1475437)))), 36490 ^ _782476 : [(36491 ^ _782476) ^ [_1475515] : [hBOOL(hAPP(hAPP(c_member(_1475433), _1475515), _1475437)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475433, _1475429)), hAPP(hAPP(c_Product__Type_OPair(_1475433, _1475429), _1475515), _1475431)), _1475435))]]], (47487 ^ _782476) ^ [_1738065, _1738067] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1738065, _1738067) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1738065), _1738067)))], (24376 ^ _782476) ^ [_1238562] : [c_Nat__Transfer_Onat__set(_1238562), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1238562) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238562)))], (46674 ^ _782476) ^ [_1719234, _1719236, _1719238, _1719240, _1719242, _1719244, _1719246] : [c_List_Olist__all2(_1719234, _1719242, hAPP(hAPP(c_COMBC(_1719234, tc_fun(_1719242, _1719236), tc_fun(_1719242, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719236, tc_HOL_Obool), tc_fun(tc_fun(_1719242, _1719236), tc_fun(_1719242, tc_HOL_Obool)), _1719234), c_COMBB(_1719236, tc_HOL_Obool, _1719242)), _1719238)), _1719244), _1719240, _1719246), -(c_List_Olist__all2(_1719234, _1719236, _1719238, _1719240, hAPP(hAPP(c_List_Omap(_1719242, _1719236), _1719244), _1719246)))], (38365 ^ _782476) ^ [_1515866, _1515868, _1515870, _1515872, _1515874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1515866, _1515868)), hAPP(_1515866, _1515870))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515872, _1515872)), hAPP(hAPP(c_Product__Type_OPair(_1515872, _1515872), _1515868), _1515870)), _1515874)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515872, _1515872)), hAPP(hAPP(c_Product__Type_OPair(_1515872, _1515872), _1515868), _1515870)), c_Wellfounded_Omlex__prod(_1515872, _1515866, _1515874))))], (8128 ^ _782476) ^ [_921051, _921053, _921055, _921057, _921059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921051, tc_HOL_Obool)), _921053), _921055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921051, tc_HOL_Obool)), _921057), _921059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921051, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921051, tc_HOL_Obool)), _921053), _921057)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921051, tc_HOL_Obool)), _921055), _921059))))], (41523 ^ _782476) ^ [_1597263, _1597265, _1597267, _1597269] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597263, _1597263)), hAPP(hAPP(c_Product__Type_OPair(_1597263, _1597263), _1597265), _1597267)), c_Transitive__Closure_Ortrancl(_1597263, hAPP(c_Relation_Oconverse(_1597263, _1597263), _1597269)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597263, _1597263)), hAPP(hAPP(c_Product__Type_OPair(_1597263, _1597263), _1597267), _1597265)), c_Transitive__Closure_Ortrancl(_1597263, _1597269))))], (41417 ^ _782476) ^ [_1594715] : [-(hAPP(c_Relation_Oconverse(_1594715, _1594715), c_Relation_OId(_1594715)) = c_Relation_OId(_1594715))], (18724 ^ _782476) ^ [_1135156, _1135158, _1135160, _1135162] : [class_Rings_Oordered__ring(_1135156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135156), _1135158), _1135160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135156), _1135162), c_Groups_Ozero__class_Ozero(_1135156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135156), _1135160), _1135162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135156), _1135158), _1135162))))], (39026 ^ _782476) ^ [_1533610, _1533612, _1533614, _1533616, _1533618, _1533620] : [c_Typedef_Otype__definition(_1533610, _1533612, _1533614, _1533616, _1533618), -(hBOOL(hAPP(hAPP(c_member(_1533612), hAPP(_1533614, _1533620)), _1533618)))], (49920 ^ _782476) ^ [_1790632, _1790634, _1790636, _1790638] : [-(c_List_Oreplicate(_1790632, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790634), _1790636), _1790638) = hAPP(hAPP(c_List_Oappend(_1790632), c_List_Oreplicate(_1790632, _1790634, _1790638)), c_List_Oreplicate(_1790632, _1790636, _1790638)))], (46064 ^ _782476) ^ [_1705414, _1705416, _1705418, _1705420, _1705422] : [-(hAPP(hAPP(c_List_Omap(_1705414, _1705416), _1705418), hAPP(hAPP(c_List_Oappend(_1705414), _1705420), _1705422)) = hAPP(hAPP(c_List_Oappend(_1705416), hAPP(hAPP(c_List_Omap(_1705414, _1705416), _1705418), _1705420)), hAPP(hAPP(c_List_Omap(_1705414, _1705416), _1705418), _1705422)))], (39905 ^ _782476) ^ [_1556112, _1556114, _1556116, _1556118] : [-(hAPP(c_Set_OCollect(tc_prod(_1556112, _1556114)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556112, _1556114, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556112, tc_fun(_1556114, tc_HOL_Obool), tc_fun(_1556114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556114, tc_HOL_Obool), tc_fun(_1556114, tc_HOL_Obool)), _1556112), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556114)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556112), c_fconj), _1556116))), _1556118))) = hAPP(hAPP(c_Product__Type_OSigma(_1556112, _1556114), hAPP(c_Set_OCollect(_1556112), _1556116)), hAPP(c_COMBK(tc_fun(_1556114, tc_HOL_Obool), _1556112), hAPP(c_Set_OCollect(_1556114), _1556118))))], (24835 ^ _782476) ^ [_1246703, _1246705] : [class_Rings_Olinordered__idom(_1246703), 24838 ^ _782476 : [(24845 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246703), _1246705), c_Groups_Ozero__class_Ozero(_1246703))), -(c_Groups_Osgn__class_Osgn(_1246703, _1246705) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246703), c_Groups_Oone__class_Oone(_1246703)))], (24839 ^ _782476) ^ [] : [c_Groups_Osgn__class_Osgn(_1246703, _1246705) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246703), c_Groups_Oone__class_Oone(_1246703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246703), _1246705), c_Groups_Ozero__class_Ozero(_1246703))))]]], (6311 ^ _782476) ^ [_882973, _882975, _882977] : [class_Orderings_Olinorder(_882973), 6314 ^ _782476 : [(6321 ^ _782476) ^ [] : [_882975 = _882977, -(hAPP(c_SetInterval_Oord__class_OatMost(_882973), _882975) = hAPP(c_SetInterval_Oord__class_OatMost(_882973), _882977))], (6315 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_882973), _882975) = hAPP(c_SetInterval_Oord__class_OatMost(_882973), _882977), -(_882975 = _882977)]]], (10047 ^ _782476) ^ [_963964, _963966, _963968] : [class_Orderings_Oorder(_963964), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963964, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_963964, _963966, _963968)), hAPP(c_SetInterval_Oord__class_OatLeast(_963964), _963968)) = c_Orderings_Obot__class_Obot(tc_fun(_963964, tc_HOL_Obool)))], (26278 ^ _782476) ^ [_1279151, _1279153, _1279155, _1279157, _1279159] : [class_Groups_Ocomm__monoid__mult(_1279151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279153), _1279155)), hBOOL(hAPP(hAPP(c_member(_1279153), _1279157), _1279155)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279153, _1279151), _1279159), _1279155) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279151), hAPP(_1279159, _1279157)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279153, _1279151), _1279159), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279153, tc_HOL_Obool)), _1279155), hAPP(hAPP(c_Set_Oinsert(_1279153), _1279157), c_Orderings_Obot__class_Obot(tc_fun(_1279153, tc_HOL_Obool)))))))], (10743 ^ _782476) ^ [_979354, _979356, _979358, _979360, _979362, _979364] : [hBOOL(hAPP(hAPP(c_member(_979354), _979356), _979358)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979354, tc_fun(_979360, tc_HOL_Obool)), _979358), hAPP(hAPP(c_COMBB(tc_fun(_979360, tc_HOL_Obool), tc_fun(_979360, tc_HOL_Obool), _979354), hAPP(c_Set_Oinsert(_979360), _979362)), _979364)) = hAPP(hAPP(c_Set_Oinsert(_979360), _979362), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979354, tc_fun(_979360, tc_HOL_Obool)), _979358), _979364)))], (3718 ^ _782476) ^ [_838187, _838189, _838191, _838193] : [-(c_List_Oremdups(_838193, _838189) = c_List_Oremdups(_838191, _838187)), _838193 = _838191, _838189 = _838187], (50541 ^ _782476) ^ [_1804535, _1804537] : [-(c_Relation_Otrans(_1804535, c_Transitive__Closure_Ortrancl(_1804535, _1804537)))], (11176 ^ _782476) ^ [_987724, _987726, _987728, _987730] : [class_Orderings_Oord(_987724), _987726 = _987728, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987724), _987728), _987730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987724), _987726), _987730)))], (46491 ^ _782476) ^ [_1714501, _1714503] : [-(hBOOL(hAPP(c_List_Olistsp(_1714501, _1714503), c_List_Olist_ONil(_1714501))))], (11324 ^ _782476) ^ [_989970, _989972, _989974, _989976, _989978] : [hAPP(_989970, _989972) = _989974, -(c_Fun_Ofun__upd(_989976, _989978, _989970, _989972, _989974) = _989970)], (45943 ^ _782476) ^ [_1701802, _1701804, _1701806] : [-(hAPP(hAPP(c_List_Omap(_1701802, _1701804), _1701806), c_List_Olist_ONil(_1701802)) = c_List_Olist_ONil(_1701804))], (11116 ^ _782476) ^ [_986792, _986794, _986796] : [class_Orderings_Opreorder(_986792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986792), _986794), _986796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986792), _986796), _986794))], (16097 ^ _782476) ^ [_1084412, _1084414, _1084416, _1084418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084412), _1084414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084412, tc_HOL_Obool)), _1084414), _1084416)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084412, tc_Nat_Onat), _1084418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084412, tc_HOL_Obool)), _1084416), _1084414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084412, tc_Nat_Onat), _1084418), _1084416)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084412, tc_Nat_Onat), _1084418), _1084414)))], (25804 ^ _782476) ^ [_1267063, _1267065, _1267067, _1267069, _1267071] : [_1267063 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1267065, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267065, tc_HOL_Obool), tc_fun(_1267065, tc_HOL_Obool), tc_fun(_1267065, tc_HOL_Obool)), c_Set_OCollect(_1267065)), _1267067)), c_Orderings_Oorder__class_Omono(tc_fun(_1267065, tc_HOL_Obool), tc_fun(_1267065, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267065, tc_HOL_Obool), tc_fun(_1267065, tc_HOL_Obool), tc_fun(_1267065, tc_HOL_Obool)), c_Set_OCollect(_1267065)), _1267067)), hBOOL(hAPP(hAPP(c_member(_1267065), _1267069), _1267071)), 25818 ^ _782476 : [(25821 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1267067, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267065, tc_HOL_Obool)), _1267071), _1267063)), 25817 ^ [_1267063, _1267065, _1267067, _1267069, _1267071]))], (25819 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267065), 25817 ^ [_1267063, _1267065, _1267067, _1267069, _1267071]), _1267071)))]], -(hBOOL(hAPP(hAPP(c_member(_1267065), _1267069), _1267063)))], (13248 ^ _782476) ^ [_1026897, _1026899, _1026901, _1026903, _1026905] : [hAPP(_1026903, _1026899) = _1026905, -(hBOOL(hAPP(hAPP(c_member(_1026897), _1026899), hAPP(c_Set_Ovimage(_1026897, _1026901, _1026903), hAPP(hAPP(c_Set_Oinsert(_1026901), _1026905), c_Orderings_Obot__class_Obot(tc_fun(_1026901, tc_HOL_Obool)))))))], (13772 ^ _782476) ^ [_1037959, _1037961, _1037963, _1037965] : [c_Finite__Set_Ofun__left__comm__idem(_1037959, _1037961, _1037963), -(hAPP(c_Fun_Ocomp(_1037961, _1037961, _1037961, hAPP(_1037963, _1037965)), hAPP(_1037963, _1037965)) = hAPP(_1037963, _1037965))], (15696 ^ _782476) ^ [_1076201, _1076203, _1076205, _1076207, _1076209] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076201, _1076203, _1076205), _1076207), _1076209), c_Orderings_Obot__class_Obot(tc_fun(_1076203, tc_HOL_Obool))) = _1076209)], (15879 ^ _782476) ^ [_1079507, _1079509] : [class_Groups_Oab__semigroup__mult(_1079507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079507), _1079509)), -(_1079509 = c_Orderings_Obot__class_Obot(tc_fun(_1079507, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1079507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079507), 15892 ^ [_1079507, _1079509]), 15893 ^ [_1079507, _1079509])), hAPP(hAPP(c_Set_Oinsert(_1079507), 15892 ^ [_1079507, _1079509]), hAPP(hAPP(c_Set_Oinsert(_1079507), 15893 ^ [_1079507, _1079509]), c_Orderings_Obot__class_Obot(tc_fun(_1079507, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1079507), hAPP(c_Finite__Set_Ofold1(_1079507, c_Groups_Otimes__class_Otimes(_1079507)), _1079509)), _1079509)))], (8844 ^ _782476) ^ [_936730, _936732, _936734, _936736] : [class_Lattices_Osemilattice__inf(_936730), 8847 ^ _782476 : [(8856 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936730), _936734), _936736)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), _936734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), _936736))], (8848 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936730), _936734), _936736))), 8851 ^ _782476 : [(8854 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), _936736)))], (8852 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936730), _936732), _936734)))]]]]], (45242 ^ _782476) ^ [_1687989, _1687991, _1687993, _1687995] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1687991), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687989)), hAPP(hAPP(c_List_Olist_OCons(_1687991), _1687993), _1687995)) = hAPP(hAPP(c_List_Odrop(_1687991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687989)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1687995))], (46082 ^ _782476) ^ [_1705879, _1705881, _1705883, _1705885, _1705887, _1705889] : [-(hAPP(hAPP(c_List_Omap(_1705879, _1705881), _1705883), hAPP(hAPP(c_List_Omap(_1705885, _1705879), _1705887), _1705889)) = hAPP(hAPP(c_List_Omap(_1705885, _1705881), hAPP(c_Fun_Ocomp(_1705879, _1705881, _1705885, _1705883), _1705887)), _1705889))], (35506 ^ _782476) ^ [] : [-(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))))], (37235 ^ _782476) ^ [_1491225, _1491227] : [-(c_Divides_Odivmod__nat(_1491225, _1491227) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1491225), _1491227)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1491225, _1491227)))], (15414 ^ _782476) ^ [_1070373, _1070375, _1070377] : [class_Lattices_Olattice(_1070373), hAPP(_1070375, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070373), 15419 ^ [_1070373, _1070375, _1070377]), 15420 ^ [_1070373, _1070375, _1070377])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070373), hAPP(_1070375, 15419 ^ [_1070373, _1070375, _1070377])), hAPP(_1070375, 15420 ^ [_1070373, _1070375, _1070377])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070373), _1070377)), -(_1070377 = c_Orderings_Obot__class_Obot(tc_fun(_1070373, tc_HOL_Obool))), -(hAPP(_1070375, c_Big__Operators_Olattice__class_OInf__fin(_1070373, _1070377)) = c_Big__Operators_Olattice__class_OInf__fin(_1070373, hAPP(c_Set_Oimage(_1070373, _1070373, _1070375), _1070377)))], (30224 ^ _782476) ^ [_1355391, _1355393, _1355395] : [class_Fields_Olinordered__field(_1355391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355391), c_Groups_Ozero__class_Ozero(_1355391)), _1355393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355391), _1355395), c_Groups_Ozero__class_Ozero(_1355391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355391), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355391), _1355393), _1355395)), c_Groups_Ozero__class_Ozero(_1355391))))], (30861 ^ _782476) ^ [_1367537, _1367539] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367537), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367539)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367537)), _1367539))], (29056 ^ _782476) ^ [_1334172, _1334174] : [29057 ^ _782476 : [(29060 ^ _782476) ^ [] : [_1334174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29058 ^ _782476) ^ [] : [-(_1334172 = 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), _1334172)), _1334174))))], (45446 ^ _782476) ^ [_1692101, _1692103, _1692105, _1692107] : [class_Groups_Osemigroup__add(_1692101), -(hAPP(c_List_Ofoldl(_1692101, _1692101, c_Groups_Oplus__class_Oplus(_1692101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692101), _1692103), _1692105)), _1692107) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692101), _1692103), hAPP(c_List_Ofoldl(_1692101, _1692101, c_Groups_Oplus__class_Oplus(_1692101), _1692105), _1692107)))], (4 ^ _782476) ^ [_782526, _782528] : [_782528 = _782526, -(_782526 = _782528)], (29416 ^ _782476) ^ [_1340720, _1340722, _1340724, _1340726] : [class_Rings_Olinordered__semidom(_1340720), hAPP(hAPP(c_Power_Opower__class_Opower(_1340720), _1340722), hAPP(c_Nat_OSuc, _1340724)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340720), _1340726), hAPP(c_Nat_OSuc, _1340724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340720), c_Groups_Ozero__class_Ozero(_1340720)), _1340722)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340720), c_Groups_Ozero__class_Ozero(_1340720)), _1340726)), -(_1340722 = _1340726)], (36326 ^ _782476) ^ [_1467805] : [-(c_Int_Oint__ge__less__than2(_1467805) = 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), _1467805)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (25598 ^ _782476) ^ [_1261039, _1261041, _1261043] : [-(hAPP(hAPP(c_Set_Oinsert(_1261039), _1261041), _1261043) = hAPP(c_Set_OCollect(_1261039), hAPP(hAPP(c_COMBS(_1261039, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261039), c_fdisj), hAPP(hAPP(c_COMBC(_1261039, _1261039, tc_HOL_Obool), c_fequal), _1261041))), hAPP(hAPP(c_COMBC(_1261039, tc_fun(_1261039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261039)), _1261043))))], (10409 ^ _782476) ^ [_971573, _971575, _971577, _971579] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971573, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971573, tc_HOL_Obool)), _971575), _971577)), _971579) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971573, tc_HOL_Obool)), _971575), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971573, tc_HOL_Obool)), _971577), _971579)))], (17277 ^ _782476) ^ [_1110735, _1110737, _1110739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110735), _1110737)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110737), _1110735)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110739), _1110737)), _1110735))], (45300 ^ _782476) ^ [_1689413, _1689415, _1689417] : [-(_1689413 = c_List_Olist_ONil(_1689415)), -(hAPP(c_List_Ohd(_1689415), hAPP(hAPP(c_List_Oappend(_1689415), _1689413), _1689417)) = hAPP(c_List_Ohd(_1689415), _1689413))], (35830 ^ _782476) ^ [_1459140, _1459142, _1459144] : [class_Groups_Omonoid__mult(_1459140), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459140), _1459142), 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)))), _1459144))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459140), _1459142), hAPP(hAPP(c_Power_Opower__class_Opower(_1459140), hAPP(hAPP(c_Power_Opower__class_Opower(_1459140), _1459142), _1459144)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (31641 ^ _782476) ^ [_1381123, _1381125, _1381127] : [-(hBOOL(hAPP(_1381123, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381125), _1381127)))), 31642 ^ _782476 : [(31649 ^ _782476) ^ [_1381291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381127), _1381291)), _1381125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381127), hAPP(c_Nat_OSuc, _1381291)))), hBOOL(hAPP(_1381123, _1381291))], (31643 ^ _782476) ^ [] : [_1381127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1381123, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (51039 ^ _782476) ^ [_1815484, _1815486] : [c_Relation_Osym(_1815484, _1815486), -(c_Relation_Osym(tc_List_Olist(_1815484), c_List_Olistrel(_1815484, _1815486)))], (19807 ^ _782476) ^ [_1154291, _1154293, _1154295, _1154297] : [class_Groups_Oordered__comm__monoid__add(_1154291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154291), c_Groups_Ozero__class_Ozero(_1154291)), _1154293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154291), _1154295), _1154297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154291), _1154295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154291), _1154293), _1154297))))], (11712 ^ _782476) ^ [_995765, _995767, _995769, _995771] : [class_Orderings_Opreorder(_995765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995765), _995767), _995769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995765), _995769), _995771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995765), _995767), _995771)))], (43860 ^ _782476) ^ [_1656866, _1656868, _1656870, _1656872] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656866)), hAPP(hAPP(c_List_Olist__update(_1656866, _1656868), _1656870), _1656872)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656866)), _1656868))], (27545 ^ _782476) ^ [_1303568, _1303570, _1303572] : [class_Orderings_Olinorder(_1303568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303568), _1303570)), -(_1303570 = c_Orderings_Obot__class_Obot(tc_fun(_1303568, tc_HOL_Obool))), 27556 ^ _782476 : [(27566 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303568), hAPP(c_Finite__Set_Ofold1(_1303568, c_Orderings_Oord__class_Omin(_1303568)), _1303570)), _1303572))), 27567 ^ _782476 : [(27568 ^ _782476) ^ [_1303957] : [hBOOL(hAPP(hAPP(c_member(_1303568), _1303957), _1303570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303568), _1303957), _1303572))]]], (27557 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303568), hAPP(c_Finite__Set_Ofold1(_1303568, c_Orderings_Oord__class_Omin(_1303568)), _1303570)), _1303572)), 27561 ^ _782476 : [(27564 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303568), 27560 ^ [_1303568, _1303570, _1303572]), _1303572)))], (27562 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303568), 27560 ^ [_1303568, _1303570, _1303572]), _1303570)))]]]]], (22506 ^ _782476) ^ [_1204598, _1204600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204598)), _1204600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204598), _1204600)))], (30600 ^ _782476) ^ [_1362467, _1362469, _1362471, _1362473] : [class_Fields_Ofield__inverse__zero(_1362467), -(_1362469 = c_Groups_Ozero__class_Ozero(_1362467)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362467), _1362471), _1362469)), _1362473) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362467), _1362471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362467), _1362473), _1362469))), _1362469))], (52057 ^ _782476) ^ [_1836734, _1836736] : [52058 ^ _782476 : [(52061 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836736), _1836734))], (52059 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836734), _1836736)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836734, _1836736) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24206 ^ _782476) ^ [_1235965, _1235967] : [c_Nat__Transfer_Onat__set(_1235965), c_Nat__Transfer_Onat__set(_1235967), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1235965), _1235967) = 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), _1235965)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1235967))))], (36992 ^ _782476) ^ [_1487062] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1487062) = 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), _1487062), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (46348 ^ _782476) ^ [_1711591, _1711593, _1711595] : [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, _1711591), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711591)), _1711593)))), -(hBOOL(hAPP(hAPP(c_member(_1711591), hAPP(c_Product__Type_Ofst(_1711591, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1711591, _1711593), _1711595))), hAPP(c_List_Oset(_1711591), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1711591), _1711591), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1711591)), _1711593)))))], (44989 ^ _782476) ^ [_1681516, _1681518, _1681520, _1681522, _1681524, _1681526, _1681528, _1681530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681516, _1681516)), hAPP(hAPP(c_Product__Type_OPair(_1681516, _1681516), _1681518), _1681520)), _1681522)), _1681524 = hAPP(hAPP(c_List_Oappend(_1681516), _1681526), hAPP(hAPP(c_List_Olist_OCons(_1681516), _1681518), _1681528)), _1681530 = hAPP(hAPP(c_List_Oappend(_1681516), _1681526), hAPP(hAPP(c_List_Olist_OCons(_1681516), _1681520), _1681528)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681516), tc_List_Olist(_1681516))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681516), tc_List_Olist(_1681516)), _1681524), _1681530)), c_List_Olistrel1(_1681516, _1681522))))], (51603 ^ _782476) ^ [_1828316, _1828318, _1828320] : [-(c_Lazy__Sequence_Omap(_1828316, _1828318, _1828320, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1828316)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1828318))], (46630 ^ _782476) ^ [_1718056, _1718058, _1718060, _1718062, _1718064] : [-(c_List_Olist__all2(_1718056, _1718058, _1718060, _1718062, _1718064)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718056)), _1718062) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718058)), _1718064), 46636 ^ _782476 : [(46639 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1718056, _1718058, tc_HOL_Obool), _1718060), 46635 ^ [_1718056, _1718058, _1718060, _1718062, _1718064]))], (46637 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718056, _1718058)), 46635 ^ [_1718056, _1718058, _1718060, _1718062, _1718064]), hAPP(c_List_Oset(tc_prod(_1718056, _1718058)), hAPP(hAPP(c_List_Ozip(_1718056, _1718058), _1718062), _1718064)))))]]], (24422 ^ _782476) ^ [_1239259, _1239261] : [class_Rings_Oring__1(_1239259), 24425 ^ _782476 : [(24432 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239261), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1239259), _1239261) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1239259), hAPP(c_Int_Onat, _1239261)))], (24426 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239261), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1239259), _1239261) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239259), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1239259), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239261)))))]]], (25169 ^ _782476) ^ [_1252895, _1252897, _1252899] : [class_Rings_Olinordered__idom(_1252895), 25172 ^ _782476 : [(25181 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), hAPP(c_Groups_Oabs__class_Oabs(_1252895), _1252897)), _1252899))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), _1252897), _1252899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), hAPP(c_Groups_Ouminus__class_Ouminus(_1252895), _1252897)), _1252899))], (25173 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), hAPP(c_Groups_Oabs__class_Oabs(_1252895), _1252897)), _1252899)), 25176 ^ _782476 : [(25179 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), hAPP(c_Groups_Ouminus__class_Ouminus(_1252895), _1252897)), _1252899)))], (25177 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252895), _1252897), _1252899)))]]]]], (8467 ^ _782476) ^ [_929235, _929237, _929239, _929241] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929235, tc_HOL_Obool)), _929237), _929239), _929241)), 8470 ^ _782476 : [(8473 ^ _782476) ^ [] : [-(hBOOL(hAPP(_929239, _929241)))], (8471 ^ _782476) ^ [] : [-(hBOOL(hAPP(_929237, _929241)))]]], (43898 ^ _782476) ^ [_1657894, _1657896, _1657898, _1657900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657894), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657896)), _1657898))), 43901 ^ _782476 : [(43908 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Onth(_1657896), _1657898), _1657894) = _1657900, -(hAPP(hAPP(c_List_Olist__update(_1657896, _1657898), _1657894), _1657900) = _1657898)], (43902 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1657896, _1657898), _1657894), _1657900) = _1657898, -(hAPP(hAPP(c_List_Onth(_1657896), _1657898), _1657894) = _1657900)]]], (38563 ^ _782476) ^ [_1520842, _1520844, _1520846, _1520848, _1520850, _1520852, _1520854] : [-(hAPP(c_Product__Type_Oapfst(_1520842, _1520844, _1520846, _1520848), hAPP(c_Product__Type_Oapfst(_1520850, _1520842, _1520846, _1520852), _1520854)) = hAPP(c_Product__Type_Oapfst(_1520850, _1520844, _1520846, hAPP(c_Fun_Ocomp(_1520842, _1520844, _1520850, _1520848), _1520852)), _1520854))], (1892 ^ _782476) ^ [_809326, _809328] : [-(class_Rings_Omult__zero(_809326)), _809328 = _809326, class_Rings_Omult__zero(_809328)], (35370 ^ _782476) ^ [_1450769] : [-(c_Int_Osucc(c_Int_OBit1(_1450769)) = c_Int_OBit0(c_Int_Osucc(_1450769)))], (40879 ^ _782476) ^ [_1581308, _1581310] : [-(_1581308 = _1581310), -(c_Random_Oinc__shift(_1581308, _1581310) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581310), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (30859 ^ _782476) ^ [_1367511] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367511) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16715 ^ _782476) ^ [_1097634, _1097636, _1097638] : [class_Groups_Ogroup__add(_1097634), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097634), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097634), _1097636), _1097638)), _1097638) = _1097636)], (14038 ^ _782476) ^ [_1043422, _1043424, _1043426] : [class_Rings_Oring(_1043422), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043422), hAPP(c_Groups_Ouminus__class_Ouminus(_1043422), _1043424)), hAPP(c_Groups_Ouminus__class_Ouminus(_1043422), _1043426)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043422), _1043424), _1043426))], (24592 ^ _782476) ^ [_1242300, _1242302, _1242304] : [class_Rings_Oring__1(_1242300), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242302), _1242304)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242300), hAPP(c_Int_Oring__1__class_Oof__int(_1242300), _1242302)), hAPP(c_Int_Oring__1__class_Oof__int(_1242300), _1242304)))], (43321 ^ _782476) ^ [_1642196, _1642198, _1642200, _1642202] : [-(hAPP(hAPP(c_List_Onth(_1642196), hAPP(hAPP(c_List_Olist_OCons(_1642196), _1642198), _1642200)), hAPP(c_Nat_OSuc, _1642202)) = hAPP(hAPP(c_List_Onth(_1642196), _1642200), _1642202))], (37892 ^ _782476) ^ [_1503863, _1503865, _1503867] : [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), _1503863), _1503865))), -(hBOOL(hAPP(hAPP(_1503867, _1503863), _1503865))), 37899 ^ _782476 : [(37902 ^ _782476) ^ [] : [-(37898 ^ [_1503863, _1503865, _1503867] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1503867, 37898 ^ [_1503863, _1503865, _1503867]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37897 ^ [_1503863, _1503865, _1503867], 37898 ^ [_1503863, _1503865, _1503867]))))], (37908 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1503867, 37897 ^ [_1503863, _1503865, _1503867]), 37898 ^ [_1503863, _1503865, _1503867]))], (37900 ^ _782476) ^ [] : [-(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), 37897 ^ [_1503863, _1503865, _1503867]), 37898 ^ [_1503863, _1503865, _1503867]))))]]], (21065 ^ _782476) ^ [_1178384, _1178386, _1178388] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178384), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178386), _1178388)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178384), _1178386)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178384), _1178388)))], (26738 ^ _782476) ^ [_1287243, _1287245, _1287247, _1287249] : [class_Orderings_Olinorder(_1287243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287243), _1287245), _1287247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287243), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287243), _1287245), _1287249)), _1287247)))], (46726 ^ _782476) ^ [_1720380, _1720382, _1720384, _1720386, _1720388, _1720390, _1720392] : [-(c_List_Olist__all2(_1720380, _1720382, _1720384, hAPP(hAPP(c_List_Olist_OCons(_1720380), _1720386), _1720388), hAPP(hAPP(c_List_Olist_OCons(_1720382), _1720390), _1720392))), hBOOL(hAPP(hAPP(_1720384, _1720386), _1720390)), c_List_Olist__all2(_1720380, _1720382, _1720384, _1720388, _1720392)], (33814 ^ _782476) ^ [_1423587, _1423589, _1423591, _1423593] : [class_Fields_Olinordered__field__inverse__zero(_1423587), class_Int_Onumber(_1423587), 33821 ^ _782476 : [(33822 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423587), _1423591), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)))), 33825 ^ _782476 : [(33832 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), c_Groups_Ozero__class_Ozero(_1423587)), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)))), 33835 ^ _782476 : [(33842 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)), c_Groups_Ozero__class_Ozero(_1423587)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423589), c_Groups_Ozero__class_Ozero(_1423587))))], (33836 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)), c_Groups_Ozero__class_Ozero(_1423587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423587), _1423589), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)))))]]], (33826 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), c_Groups_Ozero__class_Ozero(_1423587)), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423587), _1423589), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))), _1423591)))]]], (33848 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423587), _1423591), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))))), 33851 ^ _782476 : [(33854 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423587), _1423589), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))), _1423591))], (33852 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), c_Groups_Ozero__class_Ozero(_1423587)), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))))]], 33855 ^ _782476 : [(33858 ^ _782476) ^ [] : [33859 ^ _782476 : [(33862 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423587), _1423589), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593))))], (33860 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)), c_Groups_Ozero__class_Ozero(_1423587))))]], 33863 ^ _782476 : [(33866 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423587), _1423589), c_Groups_Ozero__class_Ozero(_1423587)))], (33864 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)), c_Groups_Ozero__class_Ozero(_1423587)))]]], (33856 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423587), c_Groups_Ozero__class_Ozero(_1423587)), hAPP(c_Int_Onumber__class_Onumber__of(_1423587), _1423593)))]]]]], (7768 ^ _782476) ^ [_913930, _913932, _913934, _913936] : [class_Lattices_Osemilattice__sup(_913930), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913930), _913932), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913930), _913934), _913936)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913930), _913934), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913930), _913932), _913936)))], (35374 ^ _782476) ^ [_1450837, _1450839] : [class_Int_Onumber__ring(_1450837), -(hAPP(c_Int_Onumber__class_Onumber__of(_1450837), c_Int_OBit0(_1450839)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450837), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450837), c_Groups_Ozero__class_Ozero(_1450837)), hAPP(c_Int_Onumber__class_Onumber__of(_1450837), _1450839))), hAPP(c_Int_Onumber__class_Onumber__of(_1450837), _1450839)))], (25191 ^ _782476) ^ [_1253273, _1253275] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1253273), _1253275)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253273) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34276 ^ _782476) ^ [_1431868] : [-(c_Int_Osucc(c_Int_Opred(_1431868)) = _1431868)], (32014 ^ _782476) ^ [_1388996, _1388998] : [class_Divides_Osemiring__div(_1388996), -(c_Divides_Odiv__class_Omod(_1388996, _1388998, _1388998) = c_Groups_Ozero__class_Ozero(_1388996))], (52083 ^ _782476) ^ [_1837221, _1837223] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1837221, _1837223), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837221), _1837223)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837223), _1837221)))], (11970 ^ _782476) ^ [_1000339, _1000341, _1000343, _1000345, _1000347] : [class_Orderings_Olinorder(_1000339), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000339, _1000341), _1000343) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000339, _1000345), _1000347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000339), _1000341), _1000343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000339), _1000345), _1000347)), -(_1000343 = _1000347)], (11318 ^ _782476) ^ [_989914, _989916, _989918, _989920, _989922, _989924] : [-(_989914 = _989916), -(hAPP(c_Fun_Ofun__upd(_989918, _989920, _989922, _989916, _989924), _989914) = hAPP(_989922, _989914))], (47596 ^ _782476) ^ [_1740275, _1740277] : [class_Orderings_Olinorder(_1740275), -(_1740277 = c_List_Olist_ONil(_1740275)), c_List_Olinorder__class_Osorted(_1740275, _1740277), -(c_List_Olinorder__class_Osorted(_1740275, c_List_Obutlast(_1740275, _1740277)))], (9891 ^ _782476) ^ [_960527, _960529, _960531, _960533, _960535] : [_960527 = c_Orderings_Obot__class_Obot(tc_fun(_960529, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960531, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960529, tc_fun(_960531, tc_HOL_Obool)), _960527), _960533)), _960535) = _960535)], (17866 ^ _782476) ^ [_1121069, _1121071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121069), _1121071)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121071), _1121069)) = _1121071)], (8198 ^ _782476) ^ [_923025, _923027, _923029, _923031, _923033] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923025, tc_HOL_Obool)), _923027), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923029, tc_fun(_923025, tc_HOL_Obool)), _923031), _923033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923029, tc_fun(_923025, tc_HOL_Obool)), _923031), hAPP(hAPP(c_COMBB(tc_fun(_923025, tc_HOL_Obool), tc_fun(_923025, tc_HOL_Obool), _923029), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923025, tc_HOL_Obool)), _923027)), _923033)))], (1862 ^ _782476) ^ [_808951, _808953] : [-(class_Groups_Omonoid__add(_808951)), _808953 = _808951, class_Groups_Omonoid__add(_808953)], (8200 ^ _782476) ^ [_923115, _923117, _923119, _923121, _923123] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923115, tc_HOL_Obool)), _923117), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923119, tc_fun(_923115, tc_HOL_Obool)), _923121), _923123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923119, tc_fun(_923115, tc_HOL_Obool)), _923121), hAPP(hAPP(c_COMBB(tc_fun(_923115, tc_HOL_Obool), tc_fun(_923115, tc_HOL_Obool), _923119), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923115, tc_HOL_Obool)), _923117)), _923123)))], (7604 ^ _782476) ^ [_910056, _910058, _910060] : [hBOOL(hAPP(hAPP(c_member(_910056), _910058), c_Complete__Lattice_OSup__class_OSup(tc_fun(_910056, tc_HOL_Obool), _910060))), 7608 ^ _782476 : [(7611 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_910056, tc_HOL_Obool)), 7607 ^ [_910056, _910058, _910060]), _910060)))], (7609 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910056), _910058), 7607 ^ [_910056, _910058, _910060])))]]], (16309 ^ _782476) ^ [_1089311, _1089313, _1089315, _1089317, _1089319] : [class_Groups_Ocomm__monoid__add(_1089311), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089311), _1089313), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089315), _1089317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089319), _1089317))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089311), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089311, tc_Nat_Onat), _1089313), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089317))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1089315), _1089319)))], (25047 ^ _782476) ^ [_1250575, _1250577] : [class_Groups_Oordered__ab__group__add__abs(_1250575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250575), c_Groups_Ozero__class_Ozero(_1250575)), _1250577)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250575), _1250577) = _1250577)], (34288 ^ _782476) ^ [_1432018] : [class_Int_Onumber__ring(_1432018), -(hAPP(c_Int_Onumber__class_Onumber__of(_1432018), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1432018))], (35736 ^ _782476) ^ [_1457209, _1457211, _1457213] : [class_Rings_Ocomm__semiring__1(_1457209), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457209), _1457211), 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)))), _1457213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1457209), hAPP(hAPP(c_Power_Opower__class_Opower(_1457209), _1457211), _1457213)), hAPP(hAPP(c_Power_Opower__class_Opower(_1457209), _1457211), _1457213)))], (45078 ^ _782476) ^ [_1683959, _1683961, _1683963, _1683965, _1683967] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1683959, _1683961)), _1683963), hAPP(hAPP(c_List_Ozip(_1683959, _1683961), _1683965), _1683967)) = hAPP(hAPP(c_List_Ozip(_1683959, _1683961), hAPP(hAPP(c_List_Odrop(_1683959), _1683963), _1683965)), hAPP(hAPP(c_List_Odrop(_1683961), _1683963), _1683967)))], (27915 ^ _782476) ^ [_1310243, _1310245, _1310247] : [class_Orderings_Olinorder(_1310243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310243), _1310245)), -(_1310245 = c_Orderings_Obot__class_Obot(tc_fun(_1310243, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310243), _1310247)), -(_1310247 = c_Orderings_Obot__class_Obot(tc_fun(_1310243, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310243, tc_HOL_Obool)), _1310245), _1310247) = c_Orderings_Obot__class_Obot(tc_fun(_1310243, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1310243, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310243, tc_HOL_Obool)), _1310245), _1310247)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310243), c_Big__Operators_Olinorder__class_OMax(_1310243, _1310245)), c_Big__Operators_Olinorder__class_OMax(_1310243, _1310247)))], (44508 ^ _782476) ^ [_1670161, _1670163, _1670165, _1670167] : [-(hAPP(c_List_Olist_Olist__case(_1670161, _1670163, _1670165, _1670167), c_List_Olist_ONil(_1670163)) = _1670165)], (13254 ^ _782476) ^ [_1027042, _1027044, _1027046, _1027048, _1027050] : [-(hAPP(c_Set_Ovimage(_1027042, _1027044, _1027046), hAPP(hAPP(c_Set_Oinsert(_1027044), _1027048), _1027050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027042, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027042, _1027044, _1027046), hAPP(hAPP(c_Set_Oinsert(_1027044), _1027048), c_Orderings_Obot__class_Obot(tc_fun(_1027044, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1027042, _1027044, _1027046), _1027050)))], (46394 ^ _782476) ^ [_1712554, _1712556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712554), _1712556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712554)), hAPP(c_Code__Numeral_Onat__of, _1712556))))], (1472 ^ _782476) ^ [_804076, _804078] : [-(class_Lattices_Osemilattice__sup(_804076)), _804078 = _804076, class_Lattices_Osemilattice__sup(_804078)], (7001 ^ _782476) ^ [_897498, _897500, _897502, _897504] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897498, tc_HOL_Obool), tc_fun(_897500, tc_HOL_Obool)), _897502), hAPP(hAPP(c_COMBC(tc_fun(_897498, tc_HOL_Obool), tc_fun(_897498, tc_fun(_897500, tc_HOL_Obool)), tc_fun(_897500, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897498, tc_fun(_897500, tc_HOL_Obool))), _897504)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897498, tc_fun(_897500, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897498, tc_HOL_Obool), _897502)), _897504))], (47190 ^ _782476) ^ [_1730931, _1730933, _1730935, _1730937] : [-(hBOOL(hAPP(_1730931, _1730933))), -(c_List_Oremove1(_1730935, _1730933, hAPP(c_List_Ofilter(_1730935, _1730931), _1730937)) = hAPP(c_List_Ofilter(_1730935, _1730931), _1730937))], (29854 ^ _782476) ^ [_1349030, _1349032, _1349034, _1349036] : [class_Fields_Olinordered__field__inverse__zero(_1349030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349030), _1349032), _1349034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349030), c_Groups_Ozero__class_Ozero(_1349030)), _1349036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349030), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349030), _1349032), _1349036)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349030), _1349034), _1349036))))], (14359 ^ _782476) ^ [_1049961, _1049963, _1049965, _1049967, _1049969] : [c_Fun_Obij__betw(_1049961, _1049963, _1049965, _1049967, _1049969), 14362 ^ _782476 : [(14369 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049963), _1049969)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049961), _1049967)))], (14363 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049961), _1049967)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049963), _1049969)))]]], (16055 ^ _782476) ^ [_1083701, _1083703, _1083705, _1083707] : [class_Groups_Oab__group__add(_1083701), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083703, _1083701), hAPP(hAPP(c_COMBB(_1083701, _1083701, _1083703), c_Groups_Ouminus__class_Ouminus(_1083701)), _1083705)), _1083707) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083701), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083703, _1083701), _1083705), _1083707)))], (42193 ^ _782476) ^ [_1613598, _1613600] : [class_Complete__Lattice_Ocomplete__lattice(_1613598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613598), _1613600)), -(c_Complete__Lattice_OInf__class_OInf(_1613598, _1613600) = hAPP(hAPP(c_Finite__Set_Ofold(_1613598, _1613598, c_Lattices_Osemilattice__inf__class_Oinf(_1613598)), c_Orderings_Otop__class_Otop(_1613598)), _1613600))], (52577 ^ _782476) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (20158 ^ _782476) ^ [_1160940, _1160942, _1160944] : [hBOOL(hAPP(_1160940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160942), _1160944))), 20161 ^ _782476 : [(20168 ^ _782476) ^ [_1161131] : [_1160942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160944), _1161131), -(hBOOL(hAPP(_1160940, _1161131)))], (20162 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160942), _1160944)), -(hBOOL(hAPP(_1160940, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (52241 ^ _782476) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (31500 ^ _782476) ^ [_1378535, _1378537, _1378539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378535)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378535), _1378537)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378535), _1378539)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378537), _1378539))], (47371 ^ _782476) ^ [_1736055, _1736057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736055), _1736057)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1736055, _1736057)) = _1736055)], (16803 ^ _782476) ^ [_1099542, _1099544] : [class_Rings_Olinordered__semidom(_1099542), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099542), _1099544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099542), _1099544), c_Groups_Oone__class_Oone(_1099542)))))], (8202 ^ _782476) ^ [_923205, _923207, _923209, _923211, _923213] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923205, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923207, tc_fun(_923205, tc_HOL_Obool)), _923209), _923211)), _923213) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923207, tc_fun(_923205, tc_HOL_Obool)), _923209), hAPP(hAPP(c_COMBC(_923207, tc_fun(_923205, tc_HOL_Obool), tc_fun(_923205, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_923205, tc_HOL_Obool), tc_fun(tc_fun(_923205, tc_HOL_Obool), tc_fun(_923205, tc_HOL_Obool)), _923207), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923205, tc_HOL_Obool))), _923211)), _923213)))], (39675 ^ _782476) ^ [_1549524, _1549526, _1549528, _1549530] : [hBOOL(hAPP(hAPP(c_member(_1549524), _1549526), hAPP(c_Relation_ODomain(_1549524, _1549528), _1549530))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549524, _1549528)), hAPP(hAPP(c_Product__Type_OPair(_1549524, _1549528), _1549526), 39678 ^ [_1549524, _1549526, _1549528, _1549530])), _1549530)))], (41499 ^ _782476) ^ [_1596727, _1596729] : [c_Wellfounded_Owf(_1596727, hAPP(c_Relation_Oconverse(_1596727, _1596727), _1596729)), -(c_Wellfounded_Owf(_1596727, hAPP(c_Relation_Oconverse(_1596727, _1596727), c_Transitive__Closure_Otrancl(_1596727, _1596729))))], (22488 ^ _782476) ^ [_1204259, _1204261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204259)), _1204261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204259), _1204261)))], (49544 ^ _782476) ^ [_1781761, _1781763, _1781765, _1781767, _1781769, _1781771] : [c_Fun_Obij__betw(_1781761, _1781763, _1781765, _1781767, _1781769), hBOOL(hAPP(hAPP(c_member(_1781761), _1781771), _1781767)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1781763, _1781761, _1781769, c_Hilbert__Choice_Oinv__into(_1781761, _1781763, _1781767, _1781765)), _1781771) = hAPP(_1781765, _1781771))], (52261 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (17383 ^ _782476) ^ [_1112331, _1112333] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112331), _1112333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112333), _1112331))], (20993 ^ _782476) ^ [_1177066, _1177068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177066), _1177068))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1177068, _1177066) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1177068), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177068), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1177066)))], (44202 ^ _782476) ^ [_1664315, _1664317, _1664319] : [class_Orderings_Olinorder(_1664315), hBOOL(hAPP(c_Finite__Set_Ofinite(_1664315), _1664317)), -(c_List_Olinorder__class_Osorted__list__of__set(_1664315, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1664315, tc_HOL_Obool)), _1664317), hAPP(hAPP(c_Set_Oinsert(_1664315), _1664319), c_Orderings_Obot__class_Obot(tc_fun(_1664315, tc_HOL_Obool))))) = c_List_Oremove1(_1664315, _1664319, c_List_Olinorder__class_Osorted__list__of__set(_1664315, _1664317)))], (36667 ^ _782476) ^ [_1480064, _1480066] : [-(_1480064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480066, _1480064), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1480066), _1480064)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1480066, _1480064)))))], (10065 ^ _782476) ^ [_964345, _964347] : [class_Orderings_Olinorder(_964345), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964345, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_964345), _964347), c_Orderings_Obot__class_Obot(tc_fun(_964345, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_964345), _964347)) = hAPP(c_SetInterval_Oord__class_OatLeast(_964345), _964347))], (41100 ^ _782476) ^ [_1587051, _1587053, _1587055] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587051, _1587051), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587051, _1587051), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587051, _1587053)), c_Transitive__Closure_Ortrancl(_1587051, _1587055))), c_Transitive__Closure_Ortrancl(_1587051, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587051, _1587051), tc_HOL_Obool)), _1587053), _1587055)))))], (14513 ^ _782476) ^ [_1052798, _1052800, _1052802, _1052804] : [c_Fun_Obij__betw(_1052798, _1052800, _1052802, c_Orderings_Otop__class_Otop(tc_fun(_1052798, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1052800, tc_HOL_Obool))), 14516 ^ _782476 : [(14523 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052800), _1052804)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052798), hAPP(c_Set_Ovimage(_1052798, _1052800, _1052802), _1052804))))], (14517 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052798), hAPP(c_Set_Ovimage(_1052798, _1052800, _1052802), _1052804))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052800), _1052804)))]]], (33106 ^ _782476) ^ [_1410124, _1410126, _1410128] : [class_Int_Onumber__ring(_1410124), class_Rings_Olinordered__idom(_1410124), 33113 ^ _782476 : [(33120 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410126), _1410128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410124), hAPP(c_Int_Onumber__class_Onumber__of(_1410124), _1410126)), hAPP(c_Int_Onumber__class_Onumber__of(_1410124), _1410128))))], (33114 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410124), hAPP(c_Int_Onumber__class_Onumber__of(_1410124), _1410126)), hAPP(c_Int_Onumber__class_Onumber__of(_1410124), _1410128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410126), _1410128)))]]], (31490 ^ _782476) ^ [_1378354, _1378356, _1378358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1378354), _1378356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378358), _1378356)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378358), _1378354))))], (17221 ^ _782476) ^ [_1109665, _1109667, _1109669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109665), _1109667)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109667), _1109669)), _1109665) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109667), _1109665)), _1109669))], (37748 ^ _782476) ^ [_1501011, _1501013, _1501015, _1501017, _1501019, _1501021] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1501011, _1501013), _1501013, _1501015), hAPP(hAPP(c_COMBB(_1501017, tc_fun(_1501013, _1501015), tc_prod(_1501011, _1501013)), _1501019), hAPP(hAPP(c_COMBB(_1501011, _1501017, tc_prod(_1501011, _1501013)), _1501021), c_Product__Type_Ofst(_1501011, _1501013)))), c_Product__Type_Osnd(_1501011, _1501013)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1501011, _1501013, _1501015), hAPP(hAPP(c_COMBB(_1501017, tc_fun(_1501013, _1501015), _1501011), _1501019), _1501021)))], (2318 ^ _782476) ^ [_816425, _816427] : [_816427 = _816425, -(c_Int_Osucc(_816427) = c_Int_Osucc(_816425))], (28728 ^ _782476) ^ [_1328126, _1328128, _1328130] : [class_Rings_Oring__1(_1328126), -(hAPP(c_Int_Oring__1__class_Oof__int(_1328126), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328128), _1328130)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1328126), hAPP(c_Int_Oring__1__class_Oof__int(_1328126), _1328128)), _1328130))], (48498 ^ _782476) ^ [_1758220, _1758222] : [-(c_List_OdropWhile(_1758220, _1758222, c_List_Olist_ONil(_1758220)) = c_List_Olist_ONil(_1758220))], (25015 ^ _782476) ^ [_1250064, _1250066] : [class_Groups_Oordered__ab__group__add__abs(_1250064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250064), c_Groups_Ozero__class_Ozero(_1250064)), _1250066)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250064), _1250066) = _1250066)], (4490 ^ _782476) ^ [_850595, _850597, _850599, _850601, _850603, _850605] : [-(c_List_Oreplicate(_850605, _850601, _850597) = c_List_Oreplicate(_850603, _850599, _850595)), _850605 = _850603, _850601 = _850599, _850597 = _850595], (36354 ^ _782476) ^ [_1468439, _1468441, _1468443, _1468445, _1468447] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468439, _1468441), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468443), _1468445))), -(_1468441 = 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)), _1468447)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468439, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468441), _1468447)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468443), _1468447)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468441), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1468443, _1468447))), _1468445)))))], (49229 ^ _782476) ^ [_1775049, _1775051, _1775053] : [c_List_Olist__all(_1775049, _1775051, _1775053), -(c_List_Olist__all(_1775049, _1775051, hAPP(c_List_Orev(_1775049), _1775053)))], (25057 ^ _782476) ^ [_1250730, _1250732] : [class_Groups_Oordered__ab__group__add__abs(_1250730), 25060 ^ _782476 : [(25067 ^ _782476) ^ [] : [-(_1250732 = c_Groups_Ozero__class_Ozero(_1250730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250730), c_Groups_Ozero__class_Ozero(_1250730)), hAPP(c_Groups_Oabs__class_Oabs(_1250730), _1250732))))], (25061 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250730), c_Groups_Ozero__class_Ozero(_1250730)), hAPP(c_Groups_Oabs__class_Oabs(_1250730), _1250732))), _1250732 = c_Groups_Ozero__class_Ozero(_1250730)]]], (1422 ^ _782476) ^ [_803451, _803453] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803451)), _803453 = _803451, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803453)], (41372 ^ _782476) ^ [_1593518] : [-(c_Relation_OId(_1593518) = hAPP(c_Set_OCollect(tc_prod(_1593518, _1593518)), hAPP(hAPP(c_COMBB(tc_fun(_1593518, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1593518, _1593518)), c_HOL_OEx(_1593518)), hAPP(hAPP(c_COMBC(tc_prod(_1593518, _1593518), tc_fun(_1593518, tc_prod(_1593518, _1593518)), tc_fun(_1593518, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593518, _1593518), tc_HOL_Obool), tc_fun(tc_fun(_1593518, tc_prod(_1593518, _1593518)), tc_fun(_1593518, tc_HOL_Obool)), tc_prod(_1593518, _1593518)), c_COMBB(tc_prod(_1593518, _1593518), tc_HOL_Obool, _1593518)), c_fequal)), hAPP(hAPP(c_COMBS(_1593518, _1593518, tc_prod(_1593518, _1593518)), c_Product__Type_OPair(_1593518, _1593518)), c_COMBI(_1593518))))))], (29992 ^ _782476) ^ [_1351527, _1351529, _1351531] : [class_Fields_Olinordered__field(_1351527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351527), c_Groups_Ozero__class_Ozero(_1351527)), _1351529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351527), _1351531), c_Groups_Ozero__class_Ozero(_1351527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351527), _1351529), _1351531)), c_Groups_Ozero__class_Ozero(_1351527))))], (9019 ^ _782476) ^ [_940463, _940465, _940467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940463, tc_HOL_Obool)), _940465), _940467)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940463, tc_HOL_Obool)), _940467), _940465) = _940465)], (2710 ^ _782476) ^ [_822503, _822505, _822507, _822509, _822511, _822513] : [-(c_FunDef_Oin__rel(_822513, _822509, _822505) = c_FunDef_Oin__rel(_822511, _822507, _822503)), _822513 = _822511, _822509 = _822507, _822505 = _822503], (11404 ^ _782476) ^ [_991310, _991312, _991314, _991316] : [class_Orderings_Oord(_991310), 11407 ^ _782476 : [(11416 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991312, _991310)), _991314), _991316))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991312, _991310)), _991314), _991316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991312, _991310)), _991316), _991314)))], (11408 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991312, _991310)), _991314), _991316)), 11411 ^ _782476 : [(11414 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991312, _991310)), _991316), _991314))], (11412 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991312, _991310)), _991314), _991316)))]]]]], (25676 ^ _782476) ^ [_1263002, _1263004] : [-(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), _1263002)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1263004))))))], (44424 ^ _782476) ^ [_1668425, _1668427, _1668429, _1668431] : [-(hAPP(hAPP(c_List_Otake(_1668425), _1668427), hAPP(hAPP(c_List_Olist_OCons(_1668425), _1668429), _1668431)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1668425), c_List_Olist_ONil(_1668425), hAPP(hAPP(c_COMBB(tc_List_Olist(_1668425), tc_List_Olist(_1668425), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1668425), _1668429)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1668425), tc_List_Olist(_1668425)), c_List_Otake(_1668425)), _1668431)), _1668427))], (40627 ^ _782476) ^ [_1575525, _1575527] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1575525, tc_HOL_Obool), _1575527) = hAPP(c_Set_OCollect(_1575525), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575525, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1575525), c_HOL_OAll(tc_fun(_1575525, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575525, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1575525, tc_HOL_Obool), tc_HOL_Obool), _1575525), hAPP(c_COMBS(tc_fun(_1575525, 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(_1575525, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1575525, tc_HOL_Obool), tc_fun(tc_fun(_1575525, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1575525, tc_HOL_Obool))), _1575527)))), c_member(_1575525)))))], (47126 ^ _782476) ^ [_1729579, _1729581, _1729583, _1729585, _1729587] : [-(hAPP(c_List_Ofilter(_1729579, _1729581), hAPP(hAPP(c_List_Omap(_1729583, _1729579), _1729585), _1729587)) = hAPP(hAPP(c_List_Omap(_1729583, _1729579), _1729585), hAPP(c_List_Ofilter(_1729583, hAPP(c_Fun_Ocomp(_1729579, tc_HOL_Obool, _1729583, _1729581), _1729585)), _1729587)))], (36316 ^ _782476) ^ [] : [-(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)))], (24957 ^ _782476) ^ [_1249096, _1249098] : [class_Groups_Oordered__ab__group__add__abs(_1249096), 24960 ^ _782476 : [(24967 ^ _782476) ^ [] : [_1249098 = c_Groups_Ozero__class_Ozero(_1249096), -(hAPP(c_Groups_Oabs__class_Oabs(_1249096), _1249098) = c_Groups_Ozero__class_Ozero(_1249096))], (24961 ^ _782476) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1249096), _1249098) = c_Groups_Ozero__class_Ozero(_1249096), -(_1249098 = c_Groups_Ozero__class_Ozero(_1249096))]]], (30166 ^ _782476) ^ [_1354367, _1354369, _1354371, _1354373] : [class_Fields_Ofield__inverse__zero(_1354367), -(_1354369 = c_Groups_Ozero__class_Ozero(_1354367)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354367), _1354369), _1354371)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354367), _1354369), _1354373)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354367), _1354371), _1354373))], (52269 ^ _782476) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (17485 ^ _782476) ^ [_1114156, _1114158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114156), _1114158)), _1114156))], (14709 ^ _782476) ^ [_1056879, _1056881, _1056883] : [class_Lattices_Olattice(_1056879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056879), _1056881)), hBOOL(hAPP(hAPP(c_member(_1056879), _1056883), _1056881)), 14720 ^ _782476 : [(14727 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056879, tc_HOL_Obool)), _1056881), hAPP(hAPP(c_Set_Oinsert(_1056879), _1056883), c_Orderings_Obot__class_Obot(tc_fun(_1056879, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056879, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1056879, _1056881) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1056879), _1056883), c_Big__Operators_Olattice__class_OInf__fin(_1056879, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056879, tc_HOL_Obool)), _1056881), hAPP(hAPP(c_Set_Oinsert(_1056879), _1056883), c_Orderings_Obot__class_Obot(tc_fun(_1056879, tc_HOL_Obool)))))))], (14721 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056879, tc_HOL_Obool)), _1056881), hAPP(hAPP(c_Set_Oinsert(_1056879), _1056883), c_Orderings_Obot__class_Obot(tc_fun(_1056879, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056879, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1056879, _1056881) = _1056883)]]], (40163 ^ _782476) ^ [_1563984, _1563986, _1563988, _1563990, _1563992, _1563994] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1563984, _1563986), _1563984, tc_prod(_1563988, _1563990), c_Product__Type_Ofst(_1563984, _1563986)), c_Product__Type_Omap__pair(_1563988, _1563984, _1563990, _1563986, _1563992, _1563994)) = hAPP(c_Fun_Ocomp(_1563988, _1563984, tc_prod(_1563988, _1563990), _1563992), c_Product__Type_Ofst(_1563988, _1563990)))], (52233 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (48335 ^ _782476) ^ [_1754901, _1754903, _1754905, _1754907, _1754909] : [-(hAPP(hAPP(c_List_Ozip(_1754901, _1754903), _1754905), c_List_OtakeWhile(_1754903, _1754907, _1754909)) = c_List_OtakeWhile(tc_prod(_1754901, _1754903), hAPP(c_Fun_Ocomp(_1754903, tc_HOL_Obool, tc_prod(_1754901, _1754903), _1754907), c_Product__Type_Osnd(_1754901, _1754903)), hAPP(hAPP(c_List_Ozip(_1754901, _1754903), _1754905), _1754909)))], (35430 ^ _782476) ^ [_1451892, _1451894] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1451892)), _1451894) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1451892), _1451894))), _1451894))], (20732 ^ _782476) ^ [_1172180, _1172182] : [20740 ^ _782476 : [(20743 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1172182, 20739 ^ [_1172180, _1172182])))], (20741 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20739 ^ [_1172180, _1172182]), _1172180)))]], 20733 ^ _782476 : [(20734 ^ _782476) ^ [_1172249] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172249), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172180))), hBOOL(hAPP(_1172182, _1172249))]]], (8685 ^ _782476) ^ [_933589, _933591, _933593] : [class_Orderings_Otop(_933589), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_933591, _933589)), _933593) = c_Orderings_Otop__class_Otop(_933589))], (52321 ^ _782476) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (6929 ^ _782476) ^ [_896008, _896010, _896012] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896008, tc_HOL_Obool)), _896010) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896008, tc_HOL_Obool)), _896012), -(_896010 = _896012)], (40629 ^ _782476) ^ [_1575653, _1575655, _1575657] : [-(c_Hilbert__Choice_OEps(tc_prod(_1575653, _1575655), hAPP(c_Product__Type_Oprod_Oprod__case(_1575653, _1575655, tc_HOL_Obool), _1575657)) = c_Hilbert__Choice_OEps(tc_prod(_1575653, _1575655), hAPP(hAPP(c_COMBS(tc_prod(_1575653, _1575655), _1575655, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1575653, tc_fun(_1575655, tc_HOL_Obool), tc_prod(_1575653, _1575655)), _1575657), c_Product__Type_Ofst(_1575653, _1575655))), c_Product__Type_Osnd(_1575653, _1575655))))], (38766 ^ _782476) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (3534 ^ _782476) ^ [_835275, _835277, _835279, _835281, _835283, _835285] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_835285, _835281, _835277) = c_SetInterval_Oord__class_OgreaterThanAtMost(_835283, _835279, _835275)), _835285 = _835283, _835281 = _835279, _835277 = _835275], (21063 ^ _782476) ^ [_1178327, _1178329, _1178331] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178327), _1178329)), _1178331) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178327), _1178331)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178329), _1178331)))], (39819 ^ _782476) ^ [_1553940, _1553942] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553940, _1553942), c_Orderings_Otop__class_Otop(tc_fun(_1553940, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1553942, tc_HOL_Obool), _1553940), c_Orderings_Otop__class_Otop(tc_fun(_1553942, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool)))], (20047 ^ _782476) ^ [_1158837, _1158839, _1158841, _1158843] : [class_Rings_Olinordered__semiring__strict(_1158837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158837), _1158839), _1158841)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158837), _1158843), _1158841))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158837), c_Groups_Ozero__class_Ozero(_1158837)), _1158841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158837), _1158839), _1158843)))], (46330 ^ _782476) ^ [_1711223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1711223)), _1711223 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41981 ^ _782476) ^ [_1609303, _1609305, _1609307] : [class_Orderings_Olinorder(_1609303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609303), _1609305)), -(hBOOL(hAPP(hAPP(c_member(_1609303), _1609307), _1609305))), -(c_Big__Operators_Olattice_OSup__fin(_1609303, c_Orderings_Oord__class_Omax(_1609303), hAPP(hAPP(c_Set_Oinsert(_1609303), _1609307), _1609305)) = hAPP(hAPP(c_Finite__Set_Ofold(_1609303, _1609303, c_Orderings_Oord__class_Omax(_1609303)), _1609307), _1609305))], (35410 ^ _782476) ^ [_1451544, _1451546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451544), _1451546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451544)), c_Int_OBit0(_1451546))))], (52345 ^ _782476) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (43627 ^ _782476) ^ [_1650629, _1650631, _1650633, _1650635] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650629), tc_List_Olist(_1650629))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650629), tc_List_Olist(_1650629)), _1650631), _1650633)), c_List_Olistrel(_1650629, _1650635)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650629)), _1650631) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650629)), _1650633), 43633 ^ _782476 : [(43636 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1650629, _1650629, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1650629, tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_fun(_1650629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650629, tc_fun(tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_fun(_1650629, tc_HOL_Obool)), _1650629), c_COMBC(_1650629, tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650629, tc_prod(_1650629, _1650629)), tc_fun(_1650629, tc_fun(tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_HOL_Obool)), _1650629), hAPP(c_COMBB(tc_prod(_1650629, _1650629), tc_fun(tc_fun(tc_prod(_1650629, _1650629), tc_HOL_Obool), tc_HOL_Obool), _1650629), c_member(tc_prod(_1650629, _1650629)))), c_Product__Type_OPair(_1650629, _1650629)))), _1650635)), 43632 ^ [_1650629, _1650631, _1650633, _1650635]))], (43634 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650629, _1650629)), 43632 ^ [_1650629, _1650631, _1650633, _1650635]), hAPP(c_List_Oset(tc_prod(_1650629, _1650629)), hAPP(hAPP(c_List_Ozip(_1650629, _1650629), _1650631), _1650633)))))]]], (38561 ^ _782476) ^ [_1520791, _1520793, _1520795, _1520797, _1520799] : [-(hAPP(c_Product__Type_Osnd(_1520791, _1520793), hAPP(c_Product__Type_Oapfst(_1520795, _1520791, _1520793, _1520797), _1520799)) = hAPP(c_Product__Type_Osnd(_1520795, _1520793), _1520799))], (25672 ^ _782476) ^ [_1262849, _1262851, _1262853, _1262855] : [-(hAPP(c_Set_Ovimage(_1262849, _1262851, _1262853), _1262855) = hAPP(c_Set_OCollect(_1262849), hAPP(hAPP(c_COMBC(_1262849, tc_fun(_1262851, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1262851, tc_fun(tc_fun(_1262851, tc_HOL_Obool), tc_HOL_Obool), _1262849), c_member(_1262851)), _1262853)), _1262855)))], (10425 ^ _782476) ^ [_972020, _972022, _972024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972020, tc_HOL_Obool)), _972022), hAPP(hAPP(c_Set_Oinsert(_972020), _972024), _972022))))], (46066 ^ _782476) ^ [_1705484, _1705486, _1705488, _1705490] : [-(_1705484 = c_List_Olist_ONil(_1705486)), -(hAPP(c_List_Ohd(_1705488), hAPP(hAPP(c_List_Omap(_1705486, _1705488), _1705490), _1705484)) = hAPP(_1705490, hAPP(c_List_Ohd(_1705486), _1705484)))], (23807 ^ _782476) ^ [_1229288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229288))))], (46473 ^ _782476) ^ [_1714023, _1714025, _1714027, _1714029, _1714031] : [c_List_Opartition(_1714023, _1714025, _1714027) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714023), tc_List_Olist(_1714023)), _1714029), _1714031), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1714023, tc_HOL_Obool)), hAPP(c_List_Oset(_1714023), _1714029)), hAPP(c_List_Oset(_1714023), _1714031)) = hAPP(c_List_Oset(_1714023), _1714027))], (52503 ^ _782476) ^ [_1841647] : [-(class_Nat_Osize(tc_List_Olist(_1841647)))], (31017 ^ _782476) ^ [_1369935, _1369937] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369935), _1369937) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1369937 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31026 ^ _782476 : [(31029 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369935), _1369937)))], (31027 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369935)))]], 31030 ^ _782476 : [(31033 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369937), _1369935)))], (31031 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1369935), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10613 ^ _782476) ^ [_976427, _976429, _976431] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976427, tc_HOL_Obool)), _976429), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976427, tc_HOL_Obool)), _976431), _976429)) = c_Orderings_Obot__class_Obot(tc_fun(_976427, tc_HOL_Obool)))], (11008 ^ _782476) ^ [_985523, _985525] : [class_Orderings_Opreorder(_985523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985523), _985525), _985525))], (5722 ^ _782476) ^ [_870119, _870121] : [_870121 = _870119, -(c_Orderings_Oord__class_Oless__eq(_870121) = c_Orderings_Oord__class_Oless__eq(_870119))], (22668 ^ _782476) ^ [_1207679, _1207681, _1207683, _1207685] : [class_Groups_Ocomm__monoid__add(_1207679), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207679), _1207681), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207683), hAPP(c_Nat_OSuc, _1207685))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207679), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207679, tc_Nat_Onat), _1207681), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207683, _1207685)))], (25506 ^ _782476) ^ [_1259153] : [-(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)), _1259153)))))], (43862 ^ _782476) ^ [_1656918, _1656920, _1656922, _1656924, _1656926] : [-(hAPP(hAPP(c_List_Olist__update(_1656918, hAPP(hAPP(c_List_Olist_OCons(_1656918), _1656920), _1656922)), _1656924), _1656926) = c_Nat_Onat_Onat__case(tc_List_Olist(_1656918), hAPP(hAPP(c_List_Olist_OCons(_1656918), _1656926), _1656922), hAPP(hAPP(c_COMBB(tc_List_Olist(_1656918), tc_List_Olist(_1656918), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1656918), _1656920)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1656918, tc_List_Olist(_1656918)), c_List_Olist__update(_1656918, _1656922)), _1656926)), _1656924))], (47467 ^ _782476) ^ [_1737672, _1737674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737672), _1737674)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1737672, _1737674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1737674), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (31347 ^ _782476) ^ [_1375554, _1375556, _1375558] : [-(hBOOL(hAPP(_1375554, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1375556), _1375558)))), 31350 ^ _782476 : [(31353 ^ _782476) ^ [] : [hBOOL(hAPP(_1375554, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (31351 ^ _782476) ^ [] : [-(_1375558 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 31356 ^ _782476 : [(31357 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375558)))], (31363 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31359 ^ [_1375554, _1375556, _1375558]), _1375558)))], (31367 ^ _782476) ^ [] : [hBOOL(hAPP(_1375554, 31358 ^ [_1375554, _1375556, _1375558]))], (31365 ^ _782476) ^ [] : [-(_1375556 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375558), 31358 ^ [_1375554, _1375556, _1375558])), 31359 ^ [_1375554, _1375556, _1375558]))], (31361 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31359 ^ [_1375554, _1375556, _1375558])))]], 31368 ^ _782476 : [(31369 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375558), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31375 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31371 ^ [_1375554, _1375556, _1375558]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31379 ^ _782476) ^ [] : [hBOOL(hAPP(_1375554, 31370 ^ [_1375554, _1375556, _1375558]))], (31377 ^ _782476) ^ [] : [-(_1375556 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375558), 31370 ^ [_1375554, _1375556, _1375558])), 31371 ^ [_1375554, _1375556, _1375558]))], (31373 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375558), 31371 ^ [_1375554, _1375556, _1375558])))]]], (51201 ^ _782476) ^ [_1818070, _1818072] : [-(c_Equiv__Relations_Opart__equivp(_1818070, _1818072)), 51204 ^ _782476 : [(51205 ^ _782476) ^ [_1818190] : [hBOOL(hAPP(hAPP(_1818072, _1818190), _1818190))]], 51222 ^ _782476 : [(51225 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1818072, 51207 ^ [_1818070, _1818072]), 51207 ^ [_1818070, _1818072])))], (51227 ^ _782476) ^ [] : [-(hAPP(_1818072, 51206 ^ [_1818070, _1818072]) = hAPP(_1818072, 51207 ^ [_1818070, _1818072]))], (51229 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1818072, 51206 ^ [_1818070, _1818072]), 51207 ^ [_1818070, _1818072]))], (51223 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1818072, 51206 ^ [_1818070, _1818072]), 51206 ^ [_1818070, _1818072])))]], 51210 ^ _782476 : [(51213 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1818072, 51206 ^ [_1818070, _1818072]), 51206 ^ [_1818070, _1818072])), hBOOL(hAPP(hAPP(_1818072, 51207 ^ [_1818070, _1818072]), 51207 ^ [_1818070, _1818072])), hAPP(_1818072, 51206 ^ [_1818070, _1818072]) = hAPP(_1818072, 51207 ^ [_1818070, _1818072])], (51211 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1818072, 51206 ^ [_1818070, _1818072]), 51207 ^ [_1818070, _1818072])))]]], (43497 ^ _782476) ^ [_1646839, _1646841, _1646843] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646839, tc_HOL_Obool)), hAPP(c_List_Oset(_1646839), _1646841)), hAPP(c_List_Oset(_1646839), hAPP(hAPP(c_List_Olist_OCons(_1646839), _1646843), _1646841)))))], (50674 ^ _782476) ^ [_1808288, _1808290, _1808292, _1808294] : [class_Complete__Lattice_Ocomplete__lattice(_1808288), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1808290, _1808288), _1808292), _1808294) = c_Complete__Lattice_OInf__class_OInf(_1808288, hAPP(c_Set_OCollect(_1808288), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool), tc_HOL_Obool, _1808288), c_HOL_OEx(tc_fun(_1808290, _1808288))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool), tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool), _1808288), hAPP(c_COMBS(tc_fun(_1808290, _1808288), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1808290, _1808288)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1808290, _1808288), tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1808290, _1808288))), _1808292)))), hAPP(hAPP(c_COMBC(_1808288, tc_fun(tc_fun(_1808290, _1808288), _1808288), tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808288, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1808290, _1808288), _1808288), tc_fun(tc_fun(_1808290, _1808288), tc_HOL_Obool)), _1808288), c_COMBB(_1808288, tc_HOL_Obool, tc_fun(_1808290, _1808288))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1808290, _1808288), _1808290, _1808288), c_COMBI(tc_fun(_1808290, _1808288))), _1808294)))))))], (37822 ^ _782476) ^ [_1502625, _1502627] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1502625), _1502627) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1502625, _1502627)))], (46130 ^ _782476) ^ [_1706939, _1706941, _1706943] : [c_Fun_Oinj__on(tc_List_Olist(_1706939), tc_List_Olist(_1706941), hAPP(c_List_Omap(_1706939, _1706941), _1706943), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1706939), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1706939, _1706941, _1706943, c_Orderings_Otop__class_Otop(tc_fun(_1706939, tc_HOL_Obool))))], (16933 ^ _782476) ^ [_1102825, _1102827, _1102829, _1102831] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102825), _1102827)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1102825), _1102829)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102825, tc_Nat_Onat), _1102831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102825, tc_HOL_Obool)), _1102827), _1102829)) = 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(_1102825, tc_Nat_Onat), _1102831), _1102827)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102825, tc_Nat_Onat), _1102831), _1102829))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102825, tc_Nat_Onat), _1102831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102825, tc_HOL_Obool)), _1102827), _1102829))))], (23328 ^ _782476) ^ [_1220382] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220382)) = 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), _1220382))))], (17487 ^ _782476) ^ [_1114207, _1114209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114207), _1114209)), 17490 ^ _782476 : [(17493 ^ _782476) ^ [] : [_1114207 = _1114209], (17491 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114207), _1114209)))]]], (2012 ^ _782476) ^ [_810822, _810824, _810826, _810828, _810830, _810832] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_810830, _810826, _810822)), c_Hoare__Mirabelle_Ohoare__derivs(_810832, _810828, _810824), _810832 = _810830, _810828 = _810826, _810824 = _810822], (41779 ^ _782476) ^ [_1603477, _1603479, _1603481, _1603483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603477, _1603477)), _1603479), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603477, _1603477), tc_HOL_Obool), _1603481), _1603483))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603477, _1603477)), _1603479), c_Transitive__Closure_Ortrancl(_1603477, _1603483))))], (52371 ^ _782476) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (8533 ^ _782476) ^ [_930578, _930580, _930582, _930584] : [class_Lattices_Olattice(_930578), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930578), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930578), _930580), _930582)), _930584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930578), _930580), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930578), _930582), _930584)))], (20535 ^ _782476) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1482 ^ _782476) ^ [_804201, _804203] : [-(class_Lattices_Osemilattice__inf(_804201)), _804203 = _804201, class_Lattices_Osemilattice__inf(_804203)], (26858 ^ _782476) ^ [_1289608, _1289610] : [class_Orderings_Olinorder(_1289608), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289608), _1289610), _1289610) = _1289610)], (22804 ^ _782476) ^ [_1210233, _1210235, _1210237] : [class_Rings_Oring__1(_1210233), hBOOL(hAPP(hAPP(c_member(_1210233), _1210235), c_Int_Oring__1__class_OInts(_1210233))), hBOOL(hAPP(hAPP(c_member(_1210233), _1210237), c_Int_Oring__1__class_OInts(_1210233))), -(hBOOL(hAPP(hAPP(c_member(_1210233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1210233), _1210235), _1210237)), c_Int_Oring__1__class_OInts(_1210233))))], (17043 ^ _782476) ^ [_1105460, _1105462, _1105464, _1105466, _1105468] : [class_Groups_Ocomm__monoid__add(_1105460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105462), _1105464)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105462), _1105466)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105462, tc_HOL_Obool)), _1105464), _1105466) = c_Orderings_Obot__class_Obot(tc_fun(_1105462, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105462, _1105460), _1105468), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1105462, tc_HOL_Obool)), _1105464), _1105466)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105460), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105462, _1105460), _1105468), _1105464)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105462, _1105460), _1105468), _1105466)))], (36607 ^ _782476) ^ [_1478849] : [class_Rings_Osemiring__1(_1478849), -(hBOOL(hAPP(hAPP(c_member(_1478849), c_Groups_Ozero__class_Ozero(_1478849)), c_Nat_Osemiring__1__class_ONats(_1478849))))], (21275 ^ _782476) ^ [_1181984, _1181986] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1181984, _1181986))))], (25385 ^ _782476) ^ [_1256627, _1256629] : [-(c_Nitpick_Oint__lcm(_1256627, _1256629) = 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), _1256627)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256629)))))], (44080 ^ _782476) ^ [_1661713, _1661715] : [hBOOL(hAPP(c_List_Odistinct(_1661713), _1661715)), 44083 ^ _782476 : [(44084 ^ _782476) ^ [_1661845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661713)), _1661715))), 44087 ^ _782476 : [(44088 ^ _782476) ^ [_1661972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661972), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661713)), _1661715))), -(_1661845 = _1661972), hAPP(hAPP(c_List_Onth(_1661713), _1661715), _1661845) = hAPP(hAPP(c_List_Onth(_1661713), _1661715), _1661972)]]]]], (22862 ^ _782476) ^ [_1211268, _1211270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211268), hAPP(c_Nat_OSuc, _1211270))), _1211268)))], (45651 ^ _782476) ^ [_1696642, _1696644, _1696646, _1696648, _1696650] : [class_Orderings_Olinorder(_1696642), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696644, _1696642, _1696646), _1696648), _1696650) = c_List_Olist_ONil(_1696644)], (48182 ^ _782476) ^ [_1751657, _1751659, _1751661, _1751663] : [_1751659 = hAPP(hAPP(c_List_Oappend(_1751657), hAPP(c_List_Orev(_1751657), _1751663)), hAPP(hAPP(c_List_Olist_OCons(_1751657), _1751661), c_List_Olist_ONil(_1751657))), -(hAPP(c_List_Orev(_1751657), _1751659) = hAPP(hAPP(c_List_Olist_OCons(_1751657), _1751661), _1751663))], (10097 ^ _782476) ^ [_965091, _965093, _965095, _965097] : [hBOOL(hAPP(hAPP(c_member(_965091), _965093), hAPP(hAPP(c_Set_Oinsert(_965091), _965095), _965097))), -(_965093 = _965095), -(hBOOL(hAPP(hAPP(c_member(_965091), _965093), _965097)))], (16727 ^ _782476) ^ [_1097882, _1097884, _1097886] : [class_Groups_Ogroup__add(_1097882), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097882), _1097884), _1097886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097882), hAPP(c_Groups_Ouminus__class_Ouminus(_1097882), _1097886)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097882), _1097884)))], (43393 ^ _782476) ^ [_1643942, _1643944, _1643946, _1643948] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643942), tc_List_Olist(_1643942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643942), tc_List_Olist(_1643942)), _1643944), _1643946)), c_List_Olexord(_1643942, _1643948)))), 43394 ^ _782476 : [(43401 ^ _782476) ^ [_1644249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644249), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643942)), _1643944)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643942)), _1643946)))), hAPP(hAPP(c_List_Otake(_1643942), _1644249), _1643944) = hAPP(hAPP(c_List_Otake(_1643942), _1644249), _1643946), hBOOL(hAPP(hAPP(c_member(tc_prod(_1643942, _1643942)), hAPP(hAPP(c_Product__Type_OPair(_1643942, _1643942), hAPP(hAPP(c_List_Onth(_1643942), _1643944), _1644249)), hAPP(hAPP(c_List_Onth(_1643942), _1643946), _1644249))), _1643948))], (43395 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643942)), _1643944)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643942)), _1643946))), hAPP(hAPP(c_List_Otake(_1643942), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643942)), _1643944)), _1643946) = _1643944]]], (51233 ^ _782476) ^ [_1818738, _1818740] : [c_Equiv__Relations_Oequivp(_1818738, _1818740), -(c_Equiv__Relations_Opart__equivp(_1818738, _1818740))], (46322 ^ _782476) ^ [_1711129, _1711131, _1711133] : [-(c_List_Olist_Olist__size(_1711129, _1711131, _1711133) = 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(_1711129, tc_Nat_Onat), _1711131), _1711133))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711129)), _1711133)))], (8138 ^ _782476) ^ [_921296, _921298, _921300, _921302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921296, tc_HOL_Obool)), _921298), _921300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921296, tc_HOL_Obool)), _921302), _921300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921296, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921296, tc_HOL_Obool)), _921298), _921302)), _921300)))], (5902 ^ _782476) ^ [_875980, _875982, _875984, _875986] : [class_Orderings_Oorder(_875980), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875980), _875982), _875984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875980), _875986), _875982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875980), _875986), _875984)))], (43451 ^ _782476) ^ [_1645564, _1645566, _1645568, _1645570] : [-(hAPP(hAPP(c_List_Otake(_1645564), hAPP(c_Nat_OSuc, _1645566)), hAPP(hAPP(c_List_Olist_OCons(_1645564), _1645568), _1645570)) = hAPP(hAPP(c_List_Olist_OCons(_1645564), _1645568), hAPP(hAPP(c_List_Otake(_1645564), _1645566), _1645570)))], (51309 ^ _782476) ^ [_1820644, _1820646] : [51311 ^ _782476 : [(51314 ^ _782476) ^ [] : [hBOOL(hAPP(_1820644, hAPP(c_Code__Numeral_Oof__nat, 51310 ^ [_1820644, _1820646])))], (51312 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51310 ^ [_1820644, _1820646]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1820644, _1820646)))], (15140 ^ _782476) ^ [_1065361, _1065363, _1065365, _1065367, _1065369, _1065371] : [c_Finite__Set_Ofolding__idem(_1065361, _1065363, _1065365, _1065367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065361), _1065369)), -(hAPP(_1065367, hAPP(hAPP(c_Set_Oinsert(_1065361), _1065371), _1065369)) = hAPP(c_Fun_Ocomp(_1065363, _1065363, _1065363, hAPP(_1065367, _1065369)), hAPP(_1065365, _1065371)))], (41088 ^ _782476) ^ [_1586789, _1586791] : [-(c_Transitive__Closure_Otrancl(_1586789, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586789, _1586789), tc_HOL_Obool)), _1586791), c_Relation_OId(_1586789))) = c_Transitive__Closure_Ortrancl(_1586789, _1586791))], (34162 ^ _782476) ^ [_1430000, _1430002, _1430004] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430000)))), 34165 ^ _782476 : [(34172 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430002)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430002)), _1430004)) = 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), _1430000), _1430002))), _1430004))], (34166 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430002))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430002)), _1430004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430000)), _1430004))]]], (34090 ^ _782476) ^ [_1428751, _1428753] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428751) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428753), 34093 ^ _782476 : [(34096 ^ _782476) ^ [] : [-(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), _1428753))))], (34094 ^ _782476) ^ [] : [-(_1428751 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428753)))]]], (50 ^ _782476) ^ [_783281, _783283, _783285, _783287, _783289, _783291] : [-(c_Orderings_Oorder__class_Ostrict__mono(_783289, _783285, _783281)), c_Orderings_Oorder__class_Ostrict__mono(_783291, _783287, _783283), _783291 = _783289, _783287 = _783285, _783283 = _783281], (34874 ^ _782476) ^ [_1441567, _1441569] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441567) = hAPP(c_Nat_OSuc, _1441569), -(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(_1441567))), 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)), _1441569))))))], (1412 ^ _782476) ^ [_803326, _803328] : [-(class_Rings_Oidom(_803326)), _803328 = _803326, class_Rings_Oidom(_803328)], (21071 ^ _782476) ^ [_1178521, _1178523] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178521), _1178523)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178521)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178523)))], (45312 ^ _782476) ^ [_1689520, _1689522] : [-(_1689520 = c_List_Olist_ONil(_1689522)), -(hAPP(c_List_Ohd(_1689522), _1689520) = hAPP(hAPP(c_List_Onth(_1689522), _1689520), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13522 ^ _782476) ^ [_1032817] : [class_Lattices_Osemilattice__sup(_1032817), -(c_Finite__Set_Ofun__left__comm__idem(_1032817, _1032817, c_Lattices_Osemilattice__sup__class_Osup(_1032817)))], (37361 ^ _782476) ^ [_1493402, _1493404] : [-(c_Divides_Odivmod__nat(_1493402, _1493404) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1493402, _1493404)))], (6835 ^ _782476) ^ [_894118, _894120] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_894118, tc_HOL_Obool), hAPP(c_Set_OPow(_894118), _894120)) = _894120)], (50645 ^ _782476) ^ [_1806615, _1806617, _1806619] : [c_List_Olist__ex(_1806615, _1806619, _1806617), 50649 ^ _782476 : [(50652 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1806619, 50648 ^ [_1806615, _1806617, _1806619])))], (50650 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806615), 50648 ^ [_1806615, _1806617, _1806619]), hAPP(c_List_Oset(_1806615), _1806617))))]]], (304 ^ _782476) ^ [_787196, _787198, _787200, _787202, _787204, _787206] : [-(c_Orderings_Oorder__class_Omono(_787204, _787200, _787196)), c_Orderings_Oorder__class_Omono(_787206, _787202, _787198), _787206 = _787204, _787202 = _787200, _787198 = _787196], (32359 ^ _782476) ^ [_1395371, _1395373, _1395375, _1395377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395373), _1395375)), -(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), _1395375), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395377, _1395371))), _1395373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395375), _1395371))))], (51095 ^ _782476) ^ [_1816299, _1816301] : [c_Predicate_Osymp(_1816299, _1816301), -(c_Relation_Osym(_1816299, hAPP(c_Set_OCollect(tc_prod(_1816299, _1816299)), hAPP(c_Product__Type_Oprod_Oprod__case(_1816299, _1816299, tc_HOL_Obool), _1816301))))], (5312 ^ _782476) ^ [_863700, _863702, _863704, _863706, _863708, _863710] : [-(c_Lazy__Sequence_Obind(_863710, _863706, _863702) = c_Lazy__Sequence_Obind(_863708, _863704, _863700)), _863710 = _863708, _863706 = _863704, _863702 = _863700], (32235 ^ _782476) ^ [_1392947, _1392949] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392947, _1392949) = 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), _1392947), _1392949) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1392949), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392947, _1392949)))], (38403 ^ _782476) ^ [_1516618] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1516618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516618)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44262 ^ _782476) ^ [_1665473, _1665475] : [-(c_List_Osublist(_1665473, c_List_Olist_ONil(_1665473), _1665475) = c_List_Olist_ONil(_1665473))], (50775 ^ _782476) ^ [_1810305, _1810307] : [-(c_Equiv__Relations_Oequivp(_1810305, _1810307)), c_Predicate_Oreflp(_1810305, _1810307), c_Predicate_Osymp(_1810305, _1810307), c_Predicate_Otransp(_1810305, _1810307)], (36901 ^ _782476) ^ [_1484974, _1484976, _1484978] : [hBOOL(hAPP(_1484974, 36902 ^ [_1484974, _1484976, _1484978])), 36905 ^ _782476 : [(36906 ^ _782476) ^ [_1485085, _1485087] : [-(hBOOL(hAPP(_1484974, hAPP(hAPP(c_Product__Type_OPair(_1484976, _1484978), _1485087), _1485085))))]]], (34306 ^ _782476) ^ [_1432293, _1432295] : [class_Int_Onumber__ring(_1432293), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432293), hAPP(c_Int_Onumber__class_Onumber__of(_1432293), c_Int_OPls)), _1432295) = _1432295)], (43607 ^ _782476) ^ [_1649450, _1649452] : [-(hAPP(c_List_Oset(_1649450), _1649452) = hAPP(c_Set_OCollect(_1649450), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1649450), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1649450, 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)), _1649450), 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)), _1649450), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1649450, tc_fun(tc_Nat_Onat, _1649450), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649450, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1649450), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1649450), c_COMBB(_1649450, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1649450), _1649452))))), 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(_1649450)), _1649452))))))], (38565 ^ _782476) ^ [_1520909, _1520911, _1520913, _1520915, _1520917, _1520919, _1520921] : [-(hAPP(c_Product__Type_Oapsnd(_1520909, _1520911, _1520913, _1520915), hAPP(c_Product__Type_Oapfst(_1520917, _1520913, _1520909, _1520919), _1520921)) = hAPP(c_Product__Type_Oapfst(_1520917, _1520913, _1520911, _1520919), hAPP(c_Product__Type_Oapsnd(_1520909, _1520911, _1520917, _1520915), _1520921)))], (29608 ^ _782476) ^ [_1344315, _1344317, _1344319] : [class_Rings_Olinordered__semidom(_1344315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344315), c_Groups_Ozero__class_Ozero(_1344315)), _1344317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344315), _1344317), c_Groups_Oone__class_Oone(_1344315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344315), hAPP(hAPP(c_Power_Opower__class_Opower(_1344315), _1344317), hAPP(c_Nat_OSuc, _1344319))), c_Groups_Oone__class_Oone(_1344315))))], (39861 ^ _782476) ^ [_1555056, _1555058, _1555060, _1555062, _1555064, _1555066] : [hBOOL(hAPP(hAPP(c_member(_1555056), _1555058), _1555060)), 39864 ^ _782476 : [(39871 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555062, tc_HOL_Obool)), _1555064), _1555066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555062, _1555056), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555062, _1555056), _1555064), hAPP(c_COMBK(tc_fun(_1555056, tc_HOL_Obool), _1555062), _1555060))), hAPP(hAPP(c_Product__Type_OSigma(_1555062, _1555056), _1555066), hAPP(c_COMBK(tc_fun(_1555056, tc_HOL_Obool), _1555062), _1555060)))))], (39865 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555062, _1555056), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555062, _1555056), _1555064), hAPP(c_COMBK(tc_fun(_1555056, tc_HOL_Obool), _1555062), _1555060))), hAPP(hAPP(c_Product__Type_OSigma(_1555062, _1555056), _1555066), hAPP(c_COMBK(tc_fun(_1555056, tc_HOL_Obool), _1555062), _1555060)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555062, tc_HOL_Obool)), _1555064), _1555066)))]]], (34560 ^ _782476) ^ [_1436225, _1436227] : [class_Int_Onumber__ring(_1436225), class_Rings_Olinordered__idom(_1436225), 34567 ^ _782476 : [(34574 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436227), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436225), hAPP(c_Int_Onumber__class_Onumber__of(_1436225), _1436227)), c_Groups_Ozero__class_Ozero(_1436225))))], (34568 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436225), hAPP(c_Int_Onumber__class_Onumber__of(_1436225), _1436227)), c_Groups_Ozero__class_Ozero(_1436225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436227), c_Int_OPls)))]]], (25003 ^ _782476) ^ [_1249850] : [class_Groups_Osgn__if(_1249850), -(c_Groups_Osgn__class_Osgn(_1249850, c_Groups_Ozero__class_Ozero(_1249850)) = c_Groups_Ozero__class_Ozero(_1249850))], (17912 ^ _782476) ^ [_1122260, _1122262, _1122264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122260), _1122262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122264), _1122262))))], (47050 ^ _782476) ^ [_1726945, _1726947, _1726949, _1726951] : [-(hAPP(hAPP(c_List_Omap(_1726945, _1726947), _1726949), c_List_Oconcat(_1726945, _1726951)) = c_List_Oconcat(_1726947, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726945), tc_List_Olist(_1726947)), hAPP(c_List_Omap(_1726945, _1726947), _1726949)), _1726951)))], (45925 ^ _782476) ^ [_1701349, _1701351, _1701353, _1701355, _1701357, _1701359, _1701361] : [-(hAPP(c_List_Ofoldl(_1701349, _1701351, _1701353, _1701355), hAPP(hAPP(c_List_Omap(_1701357, _1701351), _1701359), _1701361)) = hAPP(c_List_Ofoldl(_1701349, _1701357, hAPP(hAPP(c_COMBC(_1701349, tc_fun(_1701357, _1701351), tc_fun(_1701357, _1701349)), hAPP(hAPP(c_COMBB(tc_fun(_1701351, _1701349), tc_fun(tc_fun(_1701357, _1701351), tc_fun(_1701357, _1701349)), _1701349), c_COMBB(_1701351, _1701349, _1701357)), _1701353)), _1701359), _1701355), _1701361))], (25710 ^ _782476) ^ [_1264409, _1264411, _1264413, _1264415, _1264417, _1264419] : [class_Groups_Ocomm__monoid__add(_1264409), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264411), _1264413)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264411, _1264409), _1264415), _1264413) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264417, _1264409), hAPP(hAPP(c_COMBB(tc_fun(_1264411, tc_HOL_Obool), _1264409, _1264417), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264411, _1264409), _1264415)), hAPP(hAPP(c_COMBB(tc_fun(_1264411, tc_HOL_Obool), tc_fun(_1264411, tc_HOL_Obool), _1264417), c_Set_OCollect(_1264411)), hAPP(hAPP(c_COMBB(tc_fun(_1264411, tc_HOL_Obool), tc_fun(_1264411, tc_HOL_Obool), _1264417), hAPP(c_COMBS(_1264411, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264411), c_fconj), hAPP(hAPP(c_COMBC(_1264411, tc_fun(_1264411, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264411)), _1264413)))), hAPP(c_COMBC(_1264411, _1264417, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1264417, tc_fun(_1264417, tc_HOL_Obool), _1264411), c_fequal), _1264419)))))), hAPP(c_Set_Oimage(_1264411, _1264417, _1264419), _1264413)))], (43990 ^ _782476) ^ [_1659983, _1659985, _1659987, _1659989] : [hBOOL(hAPP(c_List_Odistinct(_1659983), _1659985)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1659983, _1659987)), hAPP(hAPP(c_List_Ozip(_1659983, _1659987), _1659985), _1659989))))], (18998 ^ _782476) ^ [_1140125, _1140127, _1140129, _1140131] : [class_Rings_Olinordered__ring__strict(_1140125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140125), _1140127), _1140129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140125), _1140131), c_Groups_Ozero__class_Ozero(_1140125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140125), _1140131), _1140129)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140125), _1140131), _1140127))))], (48052 ^ _782476) ^ [_1748855, _1748857] : [_1748857 = c_List_Olist_ONil(_1748855), -(c_List_Olist_ONil(_1748855) = hAPP(c_List_Orev(_1748855), _1748857))], (41124 ^ _782476) ^ [_1587623, _1587625, _1587627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587623, _1587623), tc_HOL_Obool)), c_Relation_OId(_1587623)), _1587625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587623, _1587623), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587623, _1587623, _1587623), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1587623, _1587623), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587623, _1587627)), _1587625)), _1587627)), _1587625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587623, _1587623), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587623, _1587627)), _1587625)))], (35038 ^ _782476) ^ [_1444974] : [class_Int_Onumber__ring(_1444974), c_Int_Oiszero(_1444974, hAPP(c_Int_Onumber__class_Onumber__of(_1444974), c_Int_OBit1(c_Int_OPls)))], (21987 ^ _782476) ^ [_1196109] : [_1196109 = hAPP(c_Nat_OSuc, _1196109)], (31458 ^ _782476) ^ [_1377790, _1377792, _1377794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1377790), _1377792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377790), _1377794)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377792), _1377794))))], (1332 ^ _782476) ^ [_802326, _802328] : [-(class_Divides_Oring__div(_802326)), _802328 = _802326, class_Divides_Oring__div(_802328)], (20247 ^ _782476) ^ [_1162685, _1162687, _1162689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1162685), _1162687)), 20250 ^ _782476 : [(20270 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162685, tc_Nat_Onat), _1162689), _1162687) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 20271 ^ _782476 : [(20272 ^ _782476) ^ [_1163166] : [hBOOL(hAPP(hAPP(c_member(_1162685), _1163166), _1162687)), hAPP(_1162689, _1163166) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20280 ^ _782476 : [(20285 ^ _782476) ^ [] : [hAPP(_1162689, 20279 ^ [_1162685, _1162687, _1162689, _1163166]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20283 ^ _782476) ^ [] : [_1163166 = 20279 ^ [_1162685, _1162687, _1162689, _1163166]], (20281 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162685), 20279 ^ [_1162685, _1162687, _1162689, _1163166]), _1162687)))]]]]], (20251 ^ _782476) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162685, tc_Nat_Onat), _1162689), _1162687) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20255 ^ _782476 : [(20260 ^ _782476) ^ [_1163005] : [hBOOL(hAPP(hAPP(c_member(_1162685), _1163005), _1162687)), -(20254 ^ [_1162685, _1162687, _1162689] = _1163005), -(hAPP(_1162689, _1163005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20258 ^ _782476) ^ [] : [-(hAPP(_1162689, 20254 ^ [_1162685, _1162687, _1162689]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20256 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162685), 20254 ^ [_1162685, _1162687, _1162689]), _1162687)))]]]]], (8693 ^ _782476) ^ [_933770, _933772, _933774, _933776, _933778, _933780] : [-(hAPP(c_Set_Oimage(_933770, _933772, _933774), hAPP(c_Set_Oimage(_933776, _933770, _933778), _933780)) = hAPP(c_Set_Oimage(_933776, _933772, hAPP(hAPP(c_COMBB(_933770, _933772, _933776), _933774), _933778)), _933780))], (41066 ^ _782476) ^ [_1586285, _1586287, _1586289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586285, _1586285)), _1586287), _1586289)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586285, _1586285)), _1586287), c_Transitive__Closure_Ortrancl(_1586285, _1586289))))], (41352 ^ _782476) ^ [_1593050, _1593052, _1593054, _1593056] : [c_Wellfounded_Oacyclic(_1593050, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593050, _1593050)), hAPP(hAPP(c_Product__Type_OPair(_1593050, _1593050), _1593052), _1593054)), _1593056)), 41355 ^ _782476 : [(41358 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593050, _1593050)), hAPP(hAPP(c_Product__Type_OPair(_1593050, _1593050), _1593054), _1593052)), c_Transitive__Closure_Ortrancl(_1593050, _1593056)))], (41356 ^ _782476) ^ [] : [-(c_Wellfounded_Oacyclic(_1593050, _1593056))]]], (34990 ^ _782476) ^ [_1444299, _1444301] : [class_Rings_Osemiring__1(_1444299), 34993 ^ _782476 : [(35000 ^ _782476) ^ [] : [_1444301 = c_Groups_Ozero__class_Ozero(_1444299), -(c_Int_Oiszero(_1444299, _1444301))], (34994 ^ _782476) ^ [] : [c_Int_Oiszero(_1444299, _1444301), -(_1444301 = c_Groups_Ozero__class_Ozero(_1444299))]]], (26798 ^ _782476) ^ [_1288310, _1288312, _1288314, _1288316] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288310), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288310), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288310), _1288312), _1288314)), _1288316) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288310), _1288312), _1288316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288310), _1288314), _1288316)))], (13162 ^ _782476) ^ [_1024772, _1024774, _1024776, _1024778, _1024780, _1024782] : [hAPP(_1024772, _1024774) = _1024776, hBOOL(hAPP(hAPP(c_member(_1024778), _1024776), _1024780)), -(hBOOL(hAPP(hAPP(c_member(_1024782), _1024774), hAPP(c_Set_Ovimage(_1024782, _1024778, _1024772), _1024780))))], (35290 ^ _782476) ^ [_1449374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449374), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449374)), c_Int_OPls)))], (18332 ^ _782476) ^ [_1128478] : [_1128478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128478), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6000 ^ _782476) ^ [_877529, _877531, _877533, _877535] : [class_Orderings_Oord(_877529), _877531 = _877533, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877529), _877533), _877535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877529), _877531), _877535)))], (35122 ^ _782476) ^ [_1446533, _1446535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446533), _1446535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446533)), c_Int_OBit0(_1446535))))], (3618 ^ _782476) ^ [_836641, _836643, _836645, _836647] : [-(c_List_Orotate(_836647, _836643) = c_List_Orotate(_836645, _836641)), _836647 = _836645, _836643 = _836641], (36328 ^ _782476) ^ [_1467851] : [-(c_Int_Oint__ge__less__than(_1467851) = 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), _1467851)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (35212 ^ _782476) ^ [_1448049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448049)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448049), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7613 ^ _782476) ^ [_910248, _910250, _910252, _910254, _910256, _910258, _910260] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_910248, tc_fun(_910250, tc_fun(_910252, tc_HOL_Obool))), _910254), _910256), _910258), _910260)), 7617 ^ _782476 : [(7620 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_910256, 7616 ^ [_910248, _910250, _910252, _910254, _910256, _910258, _910260]), _910258), _910260)))], (7618 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910248), 7616 ^ [_910248, _910250, _910252, _910254, _910256, _910258, _910260]), _910254)))]]], (45264 ^ _782476) ^ [_1688604, _1688606, _1688608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688604), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688606)), _1688608))), -(_1688608 = hAPP(hAPP(c_List_Oappend(_1688606), hAPP(hAPP(c_List_Otake(_1688606), _1688604), _1688608)), hAPP(hAPP(c_List_Olist_OCons(_1688606), hAPP(hAPP(c_List_Onth(_1688606), _1688608), _1688604)), hAPP(hAPP(c_List_Odrop(_1688606), hAPP(c_Nat_OSuc, _1688604)), _1688608))))], (13172 ^ _782476) ^ [_1024965, _1024967] : [-(hAPP(c_Set_Ovimage(_1024965, _1024965, c_COMBI(_1024965)), _1024967) = _1024967)], (38710 ^ _782476) ^ [_1523857, _1523859, _1523861] : [-(hAPP(c_Relation_OField(_1523857), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523857, _1523857), tc_HOL_Obool)), _1523859), _1523861)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523857, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523857), _1523859)), hAPP(c_Relation_OField(_1523857), _1523861)))], (10559 ^ _782476) ^ [_975288, _975290, _975292, _975294] : [hBOOL(hAPP(hAPP(c_member(_975288), _975290), _975292)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975288, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975288), _975290), _975294)), _975292) = hAPP(hAPP(c_Set_Oinsert(_975288), _975290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975288, tc_HOL_Obool)), _975294), _975292)))], (28860 ^ _782476) ^ [_1330776, _1330778, _1330780, _1330782] : [class_Rings_Odivision__ring(_1330776), -(_1330778 = c_Groups_Ozero__class_Ozero(_1330776)), _1330780 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330776), _1330782), _1330778), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330776), _1330780), _1330778) = _1330782)], (47429 ^ _782476) ^ [_1736980, _1736982] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1736980, _1736982)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1736982), _1736980))], (24887 ^ _782476) ^ [_1247847, _1247849, _1247851] : [class_Rings_Olinordered__idom(_1247847), -(hAPP(c_Groups_Oabs__class_Oabs(_1247847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247847), _1247849), _1247851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247847), hAPP(c_Groups_Oabs__class_Oabs(_1247847), _1247849)), hAPP(c_Groups_Oabs__class_Oabs(_1247847), _1247851)))], (16153 ^ _782476) ^ [_1085807, _1085809, _1085811, _1085813, _1085815] : [class_Groups_Ocomm__monoid__add(_1085807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085809), _1085811)), c_Fun_Oinj__on(_1085809, _1085809, _1085813, _1085811), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085809, _1085807), _1085815), hAPP(c_Set_Oimage(_1085809, _1085809, _1085813), _1085811)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085809, _1085807), hAPP(c_Fun_Ocomp(_1085809, _1085807, _1085809, _1085815), _1085813)), _1085811))], (10735 ^ _782476) ^ [_979088, _979090, _979092] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979088, tc_HOL_Obool)), _979090), _979092) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_979088, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979088, tc_HOL_Obool)), _979090), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979088, tc_HOL_Obool)), _979092), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979088, tc_HOL_Obool), tc_HOL_Obool))))))], (22684 ^ _782476) ^ [_1208012, _1208014] : [22685 ^ _782476 : [(22688 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208012), _1208014)))], (22686 ^ _782476) ^ [] : [_1208014 = c_Orderings_Obot__class_Obot(tc_fun(_1208012, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1208012), _1208014) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29796 ^ _782476) ^ [_1347806, _1347808, _1347810, _1347812] : [class_Fields_Olinordered__field(_1347806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347806), c_Groups_Ozero__class_Ozero(_1347806)), _1347808)), 29803 ^ _782476 : [(29810 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347806), _1347810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347806), _1347812), _1347808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347806), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347806), _1347810), _1347808)), _1347812)))], (29804 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347806), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347806), _1347810), _1347808)), _1347812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347806), _1347810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347806), _1347812), _1347808))))]]], (49283 ^ _782476) ^ [_1776063, _1776065, _1776067] : [c_List_Olist__all(_1776063, _1776067, _1776065), 49286 ^ _782476 : [(49287 ^ _782476) ^ [_1776144] : [hBOOL(hAPP(hAPP(c_member(_1776063), _1776144), hAPP(c_List_Oset(_1776063), _1776065))), -(hBOOL(hAPP(_1776067, _1776144)))]]], (30951 ^ _782476) ^ [_1368920, _1368922, _1368924, _1368926] : [class_Divides_Osemiring__div(_1368920), 30954 ^ _782476 : [(30961 ^ _782476) ^ [] : [-(_1368922 = c_Groups_Ozero__class_Ozero(_1368920)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368920), _1368922), _1368924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368920), _1368922), _1368926)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368920), _1368924), _1368926))], (30955 ^ _782476) ^ [] : [_1368922 = c_Groups_Ozero__class_Ozero(_1368920), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368920), _1368922), _1368924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368920), _1368922), _1368926)) = c_Groups_Ozero__class_Ozero(_1368920))]]], (21081 ^ _782476) ^ [_1178727, _1178729, _1178731] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178729), _1178731)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178729), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178727), _1178731)))], (50941 ^ _782476) ^ [_1813661, _1813663, _1813665, _1813667] : [c_Relation_Osym(_1813661, _1813663), hBOOL(hAPP(hAPP(c_member(tc_prod(_1813661, _1813661)), hAPP(hAPP(c_Product__Type_OPair(_1813661, _1813661), _1813665), _1813667)), _1813663)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813661, _1813661)), hAPP(hAPP(c_Product__Type_OPair(_1813661, _1813661), _1813667), _1813665)), _1813663)))], (51121 ^ _782476) ^ [_1816730, _1816732] : [c_Equiv__Relations_Opart__equivp(_1816730, _1816732), 51125 ^ _782476 : [(51130 ^ _782476) ^ [] : [-(c_Predicate_Otransp(_1816730, _1816732))], (51128 ^ _782476) ^ [] : [-(c_Predicate_Osymp(_1816730, _1816732))], (51126 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1816732, 51124 ^ [_1816730, _1816732]), 51124 ^ [_1816730, _1816732])))]]], (2890 ^ _782476) ^ [_825311, _825313, _825315, _825317] : [-(c_Nitpick_Oint__lcm(_825317, _825313) = c_Nitpick_Oint__lcm(_825315, _825311)), _825317 = _825315, _825313 = _825311], (8485 ^ _782476) ^ [_929551, _929553, _929555, _929557, _929559, _929561] : [_929551 = hAPP(_929553, _929555), hBOOL(hAPP(hAPP(c_member(_929557), _929555), _929559)), -(hBOOL(hAPP(hAPP(c_member(_929561), _929551), hAPP(c_Set_Oimage(_929557, _929561, _929553), _929559))))], (40676 ^ _782476) ^ [_1576715, _1576717, _1576719] : [hBOOL(hAPP(_1576715, _1576717)), -(hBOOL(hAPP(_1576715, c_Hilbert__Choice_OEps(_1576719, _1576715))))], (8318 ^ _782476) ^ [_925883, _925885, _925887] : [8320 ^ _782476 : [(8323 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925883, tc_HOL_Obool)), 8319 ^ [_925883, _925885, _925887]), _925887))], (8321 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925883, tc_HOL_Obool)), 8319 ^ [_925883, _925885, _925887]), _925885)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925883, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_925883, tc_HOL_Obool), _925885)), _925887)))], (39318 ^ _782476) ^ [_1540074, _1540076] : [hAPP(hAPP(c_Relation_Orel__comp(_1540074, _1540074, _1540074), _1540076), _1540076) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540074, _1540074), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1540074, _1540076))], (38849 ^ _782476) ^ [_1527590, _1527592] : [-(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), _1527590), _1527592)), 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), _1527592), _1527590)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (21696 ^ _782476) ^ [_1189790, _1189792, _1189794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189790)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189792), _1189794)), 21703 ^ _782476 : [(21704 ^ _782476) ^ [_1189986] : [21706 ^ _782476 : [(21712 ^ _782476) ^ [] : [-(_1189986 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21708 ^ [_1189790, _1189792, _1189794, _1189986]), 21705 ^ [_1189790, _1189792, _1189794, _1189986]))], (21710 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21708 ^ [_1189790, _1189792, _1189794, _1189986]), _1189794)))], (21707 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21705 ^ [_1189790, _1189792, _1189794, _1189986]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189790))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189792), _1189986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189792), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189986), _1189790))))]]], (10741 ^ _782476) ^ [_979280, _979282, _979284] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979280, tc_HOL_Obool)), _979282), _979284) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_979280, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979280, tc_HOL_Obool)), _979282), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979280, tc_HOL_Obool)), _979284), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979280, tc_HOL_Obool), tc_HOL_Obool))))))], (8446 ^ _782476) ^ [_928766, _928768, _928770, _928772, _928774, _928776] : [_928766 = _928768, 8452 ^ _782476 : [(8455 ^ _782476) ^ [] : [hAPP(_928772, 8451 ^ [_928766, _928768, _928770, _928772, _928774, _928776]) = hAPP(_928774, 8451 ^ [_928766, _928768, _928770, _928772, _928774, _928776])], (8453 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928770), 8451 ^ [_928766, _928768, _928770, _928772, _928774, _928776]), _928768)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928770, tc_fun(_928776, tc_HOL_Obool)), _928766), _928772) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928770, tc_fun(_928776, tc_HOL_Obool)), _928768), _928774))], (1362 ^ _782476) ^ [_802701, _802703] : [-(class_Int_Onumber__ring(_802701)), _802703 = _802701, class_Int_Onumber__ring(_802703)], (25305 ^ _782476) ^ [_1255415, _1255417] : [class_Rings_Olinordered__idom(_1255415), 25308 ^ _782476 : [(25315 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255415), _1255417), c_Groups_Ozero__class_Ozero(_1255415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255415), c_Groups_Osgn__class_Osgn(_1255415, _1255417)), c_Groups_Ozero__class_Ozero(_1255415))))], (25309 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255415), c_Groups_Osgn__class_Osgn(_1255415, _1255417)), c_Groups_Ozero__class_Ozero(_1255415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255415), _1255417), c_Groups_Ozero__class_Ozero(_1255415))))]]], (48743 ^ _782476) ^ [_1763269, _1763271, _1763273, _1763275] : [-(c_List_Omaps(_1763269, _1763271, _1763273, _1763275) = c_List_Oconcat(_1763271, hAPP(hAPP(c_List_Omap(_1763269, tc_List_Olist(_1763271)), _1763273), _1763275)))], (15817 ^ _782476) ^ [_1078425, _1078427, _1078429] : [class_Lattices_Oab__semigroup__idem__mult(_1078425), -(_1078427 = c_Orderings_Obot__class_Obot(tc_fun(_1078425, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078425), _1078427)), -(hAPP(c_Finite__Set_Ofold1(_1078425, c_Groups_Otimes__class_Otimes(_1078425)), hAPP(hAPP(c_Set_Oinsert(_1078425), _1078429), _1078427)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078425), _1078429), hAPP(c_Finite__Set_Ofold1(_1078425, c_Groups_Otimes__class_Otimes(_1078425)), _1078427)))], (6630 ^ _782476) ^ [_889322, _889324, _889326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889322, tc_HOL_Obool), tc_HOL_Obool)), _889324), _889326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889322, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889322, tc_HOL_Obool), _889324)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889322, tc_HOL_Obool), _889326))))], (52493 ^ _782476) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (23320 ^ _782476) ^ [_1220234, _1220236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220234), _1220236)), -(c_Nat__Transfer_Otsub(_1220236, _1220234) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220236), _1220234))], (9772 ^ _782476) ^ [_957633, _957635] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957633, tc_HOL_Obool)), _957635), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957633, tc_HOL_Obool)), _957635)) = c_Orderings_Obot__class_Obot(tc_fun(_957633, tc_HOL_Obool)))], (43445 ^ _782476) ^ [_1645408, _1645410, _1645412] : [-(c_List_Osublist(_1645408, _1645410, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1645412)) = hAPP(hAPP(c_List_Otake(_1645408), _1645412), _1645410))], (9358 ^ _782476) ^ [_950131, _950133] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_950131, tc_HOL_Obool)), _950133)))], (48569 ^ _782476) ^ [_1759910, _1759912, _1759914] : [48571 ^ _782476 : [(48574 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1759912, 48570 ^ [_1759910, _1759912, _1759914])))], (48572 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759910), 48570 ^ [_1759910, _1759912, _1759914]), hAPP(c_List_Oset(_1759910), c_List_OdropWhile(_1759910, _1759912, _1759914)))))]], -(c_List_OtakeWhile(_1759910, _1759912, _1759914) = hAPP(c_List_Ofilter(_1759910, _1759912), _1759914))], (7595 ^ _782476) ^ [_909840, _909842, _909844] : [7597 ^ _782476 : [(7600 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_909840), _909844), 7596 ^ [_909840, _909842, _909844]))], (7598 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_909840, tc_HOL_Obool)), 7596 ^ [_909840, _909842, _909844]), _909842)))]], -(hBOOL(hAPP(hAPP(c_member(_909840), _909844), c_Complete__Lattice_OInf__class_OInf(tc_fun(_909840, tc_HOL_Obool), _909842))))], (26912 ^ _782476) ^ [_1290603, _1290605, _1290607] : [class_Orderings_Olinorder(_1290603), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290603), _1290605), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290603), _1290605), _1290607)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290603), _1290605), _1290607))], (28282 ^ _782476) ^ [_1318077, _1318079, _1318081] : [class_Orderings_Olinorder(_1318077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318077), _1318079)), -(_1318079 = c_Orderings_Obot__class_Obot(tc_fun(_1318077, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318077), _1318081)), -(_1318081 = c_Orderings_Obot__class_Obot(tc_fun(_1318077, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318077), c_Big__Operators_Olattice_OSup__fin(_1318077, c_Orderings_Oord__class_Omax(_1318077), _1318079)), c_Big__Operators_Olattice_OSup__fin(_1318077, c_Orderings_Oord__class_Omax(_1318077), _1318081)) = c_Big__Operators_Olattice_OSup__fin(_1318077, c_Orderings_Oord__class_Omax(_1318077), hAPP(c_Set_OCollect(_1318077), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_HOL_Obool), tc_HOL_Obool, _1318077), c_HOL_OEx(_1318077)), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool)), tc_fun(_1318077, tc_HOL_Obool), _1318077), hAPP(c_COMBB(tc_fun(_1318077, tc_HOL_Obool), tc_HOL_Obool, _1318077), c_HOL_OEx(_1318077))), hAPP(hAPP(c_COMBC(_1318077, tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool)), tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_fun(tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool))), tc_fun(tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool)), tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool))), _1318077), c_COMBS(_1318077, tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_fun(_1318077, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1318077, tc_fun(tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool))), _1318077), hAPP(c_COMBB(tc_fun(_1318077, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool)), _1318077), c_COMBS(_1318077, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool)), tc_fun(_1318077, tc_fun(_1318077, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1318077), hAPP(c_COMBB(tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1318077), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318077), c_fconj))), hAPP(hAPP(c_COMBC(_1318077, tc_fun(_1318077, tc_fun(_1318077, _1318077)), tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1318077, _1318077), tc_fun(_1318077, tc_HOL_Obool)), tc_fun(tc_fun(_1318077, tc_fun(_1318077, _1318077)), tc_fun(_1318077, tc_fun(_1318077, tc_HOL_Obool))), _1318077), c_COMBB(tc_fun(_1318077, _1318077), tc_fun(_1318077, tc_HOL_Obool), _1318077)), hAPP(hAPP(c_COMBB(tc_fun(_1318077, tc_HOL_Obool), tc_fun(tc_fun(_1318077, _1318077), tc_fun(_1318077, tc_HOL_Obool)), _1318077), c_COMBB(_1318077, tc_HOL_Obool, _1318077)), c_fequal))), c_Orderings_Oord__class_Omin(_1318077)))))), hAPP(hAPP(c_COMBC(_1318077, tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1318077, tc_HOL_Obool), tc_fun(_1318077, tc_HOL_Obool)), _1318077), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1318077)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318077), c_fconj), hAPP(hAPP(c_COMBC(_1318077, tc_fun(_1318077, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318077)), _1318079)))), hAPP(hAPP(c_COMBC(_1318077, tc_fun(_1318077, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318077)), _1318081))))))))], (4584 ^ _782476) ^ [_852134, _852136] : [_852136 = _852134, -(c_List_Olist_OCons(_852136) = c_List_Olist_OCons(_852134))], (3960 ^ _782476) ^ [_842106, _842108, _842110, _842112, _842114, _842116, _842118, _842120] : [-(c_Lazy__Sequence_Ohb__bind(_842120, _842116, _842112, _842108) = c_Lazy__Sequence_Ohb__bind(_842118, _842114, _842110, _842106)), _842120 = _842118, _842116 = _842114, _842112 = _842110, _842108 = _842106], (27755 ^ _782476) ^ [_1307217, _1307219, _1307221] : [class_Orderings_Olinorder(_1307217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307217), _1307219)), -(_1307219 = c_Orderings_Obot__class_Obot(tc_fun(_1307217, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307217), _1307221)), -(_1307221 = c_Orderings_Obot__class_Obot(tc_fun(_1307217, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307217, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307217, tc_HOL_Obool)), _1307219), _1307221)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307217), c_Big__Operators_Olinorder__class_OMin(_1307217, _1307219)), c_Big__Operators_Olinorder__class_OMin(_1307217, _1307221)))], (952 ^ _782476) ^ [_796942, _796944, _796946, _796948] : [-(c_Predicate_Osymp(_796946, _796942)), c_Predicate_Osymp(_796948, _796944), _796948 = _796946, _796944 = _796942], (43642 ^ _782476) ^ [_1651512, _1651514, _1651516, _1651518] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1651512, _1651514))), hAPP(hAPP(c_List_Ozip(_1651512, _1651514), _1651516), _1651518)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651512)), _1651516)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651514)), _1651518)))], (36096 ^ _782476) ^ [_1464336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464336)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464336), c_Int_OMin)))], (22943 ^ _782476) ^ [_1212717] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212717)) = 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), _1212717)))], (28045 ^ _782476) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (21409 ^ _782476) ^ [_1184440, _1184442] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184440) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184442), -(_1184440 = _1184442)], (43711 ^ _782476) ^ [_1653438, _1653440, _1653442, _1653444, _1653446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653438), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653440)), _1653442))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653438), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653444)), _1653446))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1653440, _1653444)), hAPP(hAPP(c_List_Ozip(_1653440, _1653444), _1653442), _1653446)), _1653438) = hAPP(hAPP(c_Product__Type_OPair(_1653440, _1653444), hAPP(hAPP(c_List_Onth(_1653440), _1653442), _1653438)), hAPP(hAPP(c_List_Onth(_1653444), _1653446), _1653438)))], (11792 ^ _782476) ^ [_997181, _997183, _997185, _997187] : [class_Lattices_Osemilattice__inf(_997181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997181), _997183), _997185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997181), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997181), _997183), _997187)), _997185)))], (49370 ^ _782476) ^ [_1777716, _1777718, _1777720] : [c_List_Olist__ex1(_1777716, _1777718, _1777720), 49374 ^ _782476 : [(49379 ^ _782476) ^ [_1777962] : [-(_1777962 = 49373 ^ [_1777716, _1777718, _1777720]), hBOOL(hAPP(hAPP(c_member(_1777716), _1777962), hAPP(c_List_Oset(_1777716), _1777720))), hBOOL(hAPP(_1777718, _1777962))], (49377 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1777718, 49373 ^ [_1777716, _1777718, _1777720])))], (49375 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777716), 49373 ^ [_1777716, _1777718, _1777720]), hAPP(c_List_Oset(_1777716), _1777720))))]]], (36940 ^ _782476) ^ [_1486027] : [-(c_Divides_Oadjust(_1486027) = 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)), _1486027))))), 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)), _1486027))))), 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))))))))], (9346 ^ _782476) ^ [_949873, _949875, _949877] : [class_Orderings_Oorder(_949873), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949873, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949873, _949875, _949877)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949873), _949877)) = c_Orderings_Obot__class_Obot(tc_fun(_949873, tc_HOL_Obool)))], (34620 ^ _782476) ^ [_1437149, _1437151] : [class_Int_Onumber__ring(_1437149), class_Rings_Olinordered__idom(_1437149), 34627 ^ _782476 : [(34634 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437151), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437149), hAPP(c_Int_Onumber__class_Onumber__of(_1437149), _1437151)), c_Groups_Ozero__class_Ozero(_1437149))))], (34628 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437149), hAPP(c_Int_Onumber__class_Onumber__of(_1437149), _1437151)), c_Groups_Ozero__class_Ozero(_1437149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437151), c_Int_OPls)))]]], (52379 ^ _782476) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (40345 ^ _782476) ^ [_1568211, _1568213] : [c_Wellfounded_Owf(_1568211, _1568213), -(c_Wellfounded_OwfP(_1568211, c_FunDef_Oin__rel(_1568211, _1568211, _1568213)))], (46600 ^ _782476) ^ [_1716806, _1716808] : [-(c_List_Opartition(_1716806, _1716808, c_List_Olist_ONil(_1716806)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716806), tc_List_Olist(_1716806)), c_List_Olist_ONil(_1716806)), c_List_Olist_ONil(_1716806)))], (29374 ^ _782476) ^ [_1339830, _1339832, _1339834, _1339836] : [class_Groups_Omonoid__mult(_1339830), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339830), _1339832), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1339834), _1339836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339830), hAPP(hAPP(c_Power_Opower__class_Opower(_1339830), _1339832), _1339834)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339830), _1339832), _1339836)))], (6935 ^ _782476) ^ [_896115, _896117, _896119] : [_896117 = _896119, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896115, tc_HOL_Obool)), _896117) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896115, tc_HOL_Obool)), _896119))], (17167 ^ _782476) ^ [_1108543, _1108545] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1108543, _1108545))))], (33980 ^ _782476) ^ [_1426734, _1426736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426734)), c_Int_OBit1(_1426736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426734), _1426736)))], (40293 ^ _782476) ^ [_1567199] : [-(c_Relation_Orefl__on(_1567199, c_Orderings_Obot__class_Obot(tc_fun(_1567199, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567199, _1567199), tc_HOL_Obool))))], (47163 ^ _782476) ^ [_1730277, _1730279, _1730281] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730277)), hAPP(c_List_Ofilter(_1730277, _1730279), _1730281))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730277)), _1730281))))], (51363 ^ _782476) ^ [_1821569, _1821571, _1821573, _1821575, _1821577, _1821579] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1821569, _1821571, _1821573, _1821575), _1821577), _1821579) = hAPP(_1821575, hAPP(hAPP(c_Product__Type_OPair(_1821569, _1821571), _1821577), _1821579)))], (45286 ^ _782476) ^ [_1689194, _1689196, _1689198] : [-(hAPP(c_List_Ohd(_1689194), hAPP(hAPP(c_List_Olist_OCons(_1689194), _1689196), _1689198)) = _1689196)], (11888 ^ _782476) ^ [_998879, _998881, _998883] : [11889 ^ _782476 : [(11892 ^ _782476) ^ [] : [_998881 = _998883], (11890 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998879, tc_HOL_Obool)), _998881), _998883))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998879, tc_HOL_Obool)), _998881), _998883)))], (46020 ^ _782476) ^ [_1703966, _1703968, _1703970, _1703972, _1703974] : [hAPP(hAPP(c_List_Omap(_1703966, _1703968), _1703970), _1703972) = hAPP(hAPP(c_List_Omap(_1703966, _1703968), _1703970), _1703974), c_Fun_Oinj__on(_1703966, _1703968, _1703970, c_Orderings_Otop__class_Otop(tc_fun(_1703966, tc_HOL_Obool))), -(_1703972 = _1703974)], (44232 ^ _782476) ^ [_1664935, _1664937, _1664939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664935), tc_List_Olist(_1664935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664935), tc_List_Olist(_1664935)), c_List_Olist_ONil(_1664935)), _1664937)), c_List_Olistrel(_1664935, _1664939))), -(_1664937 = c_List_Olist_ONil(_1664935))], (15544 ^ _782476) ^ [_1073064, _1073066, _1073068, _1073070, _1073072] : [c_Finite__Set_Ofolding__one__idem(_1073064, _1073066, _1073068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073064), _1073070)), -(_1073070 = c_Orderings_Obot__class_Obot(tc_fun(_1073064, tc_HOL_Obool))), -(hAPP(_1073068, hAPP(hAPP(c_Set_Oinsert(_1073064), _1073072), _1073070)) = hAPP(hAPP(_1073066, _1073072), hAPP(_1073068, _1073070)))], (36926 ^ _782476) ^ [_1485588, _1485590, _1485592, _1485594, _1485596, _1485598] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485588, _1485590, _1485592), _1485594), hAPP(hAPP(c_Product__Type_OPair(_1485588, _1485590), _1485596), _1485598)) = hAPP(hAPP(_1485594, _1485596), _1485598))], (7339 ^ _782476) ^ [_904991, _904993, _904995, _904997, _904999] : [-(hBOOL(hAPP(hAPP(c_member(_904991), _904993), c_SetInterval_Oord_OatLeastAtMost(_904991, _904995, _904997, _904999)))), hBOOL(hAPP(hAPP(_904995, _904997), _904993)), hBOOL(hAPP(hAPP(_904995, _904993), _904999))], (38887 ^ _782476) ^ [_1528733] : [-(_1528733 = 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), 38884 ^ [_1528733]), 38885 ^ [_1528733])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (42850 ^ _782476) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47489 ^ _782476) ^ [_1738103] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1738103) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1738103))))], (23197 ^ _782476) ^ [_1217832, _1217834, _1217836] : [class_Groups_Ocomm__monoid__add(_1217832), hAPP(_1217834, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1217832), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217832), _1217834), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1217836)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217832), _1217834), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217836)))], (45699 ^ _782476) ^ [_1697478, _1697480, _1697482, _1697484, _1697486] : [class_Orderings_Olinorder(_1697478), hBOOL(hAPP(c_List_Odistinct(_1697480), _1697482)), -(hBOOL(hAPP(c_List_Odistinct(_1697480), c_List_Olinorder__class_Oinsort__insert__key(_1697480, _1697478, _1697484, _1697486, _1697482))))], (41798 ^ _782476) ^ [_1603969, _1603971, _1603973] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603969, _1603969), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1603971)), _1603973) = hAPP(hAPP(c_Relation_Orel__comp(_1603969, _1603969, _1603969), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603969, _1603969), tc_HOL_Obool), _1603971), _1603973)), _1603973))], (13210 ^ _782476) ^ [_1025789, _1025791, _1025793] : [-(hAPP(c_Set_Ovimage(_1025789, _1025791, _1025793), c_Orderings_Obot__class_Obot(tc_fun(_1025791, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1025789, tc_HOL_Obool)))], (9460 ^ _782476) ^ [_951963, _951965] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951963, tc_HOL_Obool)), _951965), c_Orderings_Obot__class_Obot(tc_fun(_951963, tc_HOL_Obool))) = _951965)], (8376 ^ _782476) ^ [_927249, _927251, _927253, _927255] : [class_Orderings_Olinorder(_927249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927249), _927251), _927253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927249), _927253), _927255)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927249, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927249, _927251, _927253)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927249, _927253, _927255)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_927249, _927251, _927255))], (34832 ^ _782476) ^ [_1440640] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440640) = 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(_1440640)))))], (25508 ^ _782476) ^ [_1259184] : [-(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)), _1259184)))))], (43749 ^ _782476) ^ [_1654486] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654486)), -(c_List_Onat__list(_1654486))], (31848 ^ _782476) ^ [_1385459, _1385461, _1385463] : [-(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, _1385459, _1385461)), _1385463), _1385461) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385459), _1385463), _1385461))], (10131 ^ _782476) ^ [_965818, _965820, _965822, _965824] : [hBOOL(hAPP(hAPP(c_member(_965818), _965820), _965822)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965818, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965818), _965820), _965824)), _965822) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965818, tc_HOL_Obool)), _965824), _965822))], (52369 ^ _782476) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (29468 ^ _782476) ^ [_1341738, _1341740] : [class_Power_Opower(_1341738), class_Rings_Osemiring__0(_1341738), 29475 ^ _782476 : [(29482 ^ _782476) ^ [] : [-(_1341740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341738), c_Groups_Ozero__class_Ozero(_1341738)), _1341740) = c_Groups_Ozero__class_Ozero(_1341738))], (29476 ^ _782476) ^ [] : [_1341740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341738), c_Groups_Ozero__class_Ozero(_1341738)), _1341740) = c_Groups_Oone__class_Oone(_1341738))]]], (50339 ^ _782476) ^ [_1799554, _1799556] : [-(c_Lazy__Sequence_Oappend(_1799554, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799554), _1799556) = _1799556)], (34846 ^ _782476) ^ [_1440927, _1440929] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440927)))), _1440929) = 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)))), _1440927)), _1440929))], (16507 ^ _782476) ^ [_1093380, _1093382, _1093384, _1093386] : [class_Rings_Ocomm__semiring__1(_1093380), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093380), _1093382), _1093384)), _1093386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093380), _1093382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093380), _1093384), _1093386)))], (52613 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (40739 ^ _782476) ^ [_1578247, _1578249, _1578251, _1578253] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1578247, tc_HOL_Obool), tc_fun(_1578247, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1578247, tc_HOL_Obool), tc_fun(_1578247, tc_HOL_Obool)), _1578249), _1578251)), c_Wellfounded_Omax__ext(_1578247, _1578253)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578247), _1578249)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578247), _1578251)), -(_1578251 = c_Orderings_Obot__class_Obot(tc_fun(_1578247, tc_HOL_Obool))), 40753 ^ _782476 : [(40756 ^ _782476) ^ [_1578652] : [hBOOL(hAPP(hAPP(c_member(_1578247), _1578652), _1578251)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578247, _1578247)), hAPP(hAPP(c_Product__Type_OPair(_1578247, _1578247), 40752 ^ [_1578247, _1578249, _1578251, _1578253]), _1578652)), _1578253))], (40754 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578247), 40752 ^ [_1578247, _1578249, _1578251, _1578253]), _1578249)))]]], (21891 ^ _782476) ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772] : [class_Groups_Ocomm__monoid__add(_1193762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193764), _1193766)), 21901 ^ _782476 : [(21902 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193764), 21900 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772]), _1193766)))], (21907 ^ _782476) ^ [] : [21900 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772] = 21903 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772]], (21911 ^ _782476) ^ [] : [hAPP(_1193770, hAPP(_1193768, 21900 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772])) = c_Groups_Ozero__class_Ozero(_1193762)], (21909 ^ _782476) ^ [] : [-(hAPP(_1193768, 21900 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772]) = hAPP(_1193768, 21903 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772]))], (21905 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193764), 21903 ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772]), _1193766)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193772, _1193762), _1193770), hAPP(c_Set_Oimage(_1193764, _1193772, _1193768), _1193766)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193764, _1193762), hAPP(c_Fun_Ocomp(_1193772, _1193762, _1193764, _1193770), _1193768)), _1193766))], (36128 ^ _782476) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (15112 ^ _782476) ^ [_1064809, _1064811, _1064813, _1064815, _1064817, _1064819] : [c_Finite__Set_Ofolding__idem(_1064809, _1064811, _1064813, _1064815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064809), _1064817)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064809), _1064819)), -(hAPP(_1064815, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064809, tc_HOL_Obool)), _1064817), _1064819)) = hAPP(c_Fun_Ocomp(_1064811, _1064811, _1064811, hAPP(_1064815, _1064817)), hAPP(_1064815, _1064819)))], (6947 ^ _782476) ^ [_896341, _896343, _896345] : [_896343 = _896345, -(hBOOL(hAPP(hAPP(c_member(_896341), _896343), hAPP(c_fequal, _896345))))], (7930 ^ _782476) ^ [_917332, _917334, _917336, _917338] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917332, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917332, tc_HOL_Obool)), _917334), _917336)), _917338) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917332, tc_HOL_Obool)), _917334), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917332, tc_HOL_Obool)), _917336), _917338)))], (52575 ^ _782476) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (10017 ^ _782476) ^ [_963215, _963217, _963219] : [class_Orderings_Olinorder(_963215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963215), _963217), _963219)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963215, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_963215), _963217), c_Orderings_Obot__class_Obot(tc_fun(_963215, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_963215, _963217, _963219)) = c_SetInterval_Oord__class_OatLeastAtMost(_963215, _963217, _963219))], (37275 ^ _782476) ^ [_1491804, _1491806] : [_1491804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491804, _1491806) = 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)))], (774 ^ _782476) ^ [_794339, _794341, _794343, _794345, _794347, _794349, _794351, _794353] : [-(c_Fun_Oinj__on(_794351, _794347, _794343, _794339)), c_Fun_Oinj__on(_794353, _794349, _794345, _794341), _794353 = _794351, _794349 = _794347, _794345 = _794343, _794341 = _794339], (48260 ^ _782476) ^ [_1753239, _1753241] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753239), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753239))), _1753241))), 48263 ^ _782476 : [(48270 ^ _782476) ^ [] : [-(_1753241 = c_List_Olist_ONil(tc_List_Olist(_1753239))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753239))), c_List_Otranspose(_1753239, _1753241)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753239)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753239)), _1753241), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48264 ^ _782476) ^ [] : [_1753241 = c_List_Olist_ONil(tc_List_Olist(_1753239)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753239))), c_List_Otranspose(_1753239, _1753241)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9300 ^ _782476) ^ [_948916, _948918, _948920] : [class_Lattices_Oboolean__algebra(_948916), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948916), _948918), _948920) = c_Orderings_Obot__class_Obot(_948916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_948916), _948918), _948920) = c_Orderings_Otop__class_Otop(_948916), -(hAPP(c_Groups_Ouminus__class_Ouminus(_948916), _948918) = _948920)], (8080 ^ _782476) ^ [_920108, _920110, _920112] : [class_Lattices_Olattice(_920108), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920108), _920110), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920108), _920112), _920110))))], (10027 ^ _782476) ^ [_963424, _963426, _963428] : [class_Orderings_Olinorder(_963424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963424), _963426), _963428)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963424, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963424, _963426), _963428)), hAPP(hAPP(c_Set_Oinsert(_963424), _963428), c_Orderings_Obot__class_Obot(tc_fun(_963424, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_963424, _963426, _963428))], (10615 ^ _782476) ^ [_976481, _976483, _976485, _976487, _976489] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976481, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976481, tc_HOL_Obool)), hAPP(c_Set_Oimage(_976483, _976481, _976485), _976487)), hAPP(c_Set_Oimage(_976483, _976481, _976485), _976489))), hAPP(c_Set_Oimage(_976483, _976481, _976485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976483, tc_HOL_Obool)), _976487), _976489)))))], (24022 ^ _782476) ^ [_1232862, _1232864, _1232866, _1232868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1232862, _1232864)), c_Sum__Type_OPlus(_1232862, _1232864, _1232866, _1232868))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1232864), _1232868)))], (28338 ^ _782476) ^ [_1320142, _1320144, _1320146] : [class_Orderings_Olinorder(_1320142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320142), _1320144)), hBOOL(hAPP(hAPP(c_member(_1320142), _1320146), _1320144)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320142), _1320146), c_Big__Operators_Olattice_OSup__fin(_1320142, c_Orderings_Oord__class_Omax(_1320142), _1320144)) = c_Big__Operators_Olattice_OSup__fin(_1320142, c_Orderings_Oord__class_Omax(_1320142), _1320144))], (11698 ^ _782476) ^ [_995532, _995534, _995536, _995538] : [class_Orderings_Oorder(_995532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995532), _995534), _995536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995532), _995538), _995534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995532), _995538), _995536)))], (10127 ^ _782476) ^ [_965653, _965655, _965657, _965659] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965653, tc_HOL_Obool)), _965655), hAPP(hAPP(c_Set_Oinsert(_965653), _965657), _965659)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965653, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965653, tc_HOL_Obool)), _965655), hAPP(hAPP(c_Set_Oinsert(_965653), _965657), c_Orderings_Obot__class_Obot(tc_fun(_965653, tc_HOL_Obool))))), _965659))], (36765 ^ _782476) ^ [_1482043, _1482045, _1482047] : [-(hAPP(c_Divides_Oadjust(_1482043), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1482045), _1482047)) = 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), _1482047), _1482043)), 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)))), _1482045)), 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)))), _1482045)), _1482047))))], (17529 ^ _782476) ^ [_1114843, _1114845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114843), _1114845)), -(_1114843 = _1114845), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114843), _1114845)))], (36809 ^ _782476) ^ [_1483011, _1483013, _1483015, _1483017, _1483019] : [hBOOL(hAPP(hAPP(_1483011, _1483013), _1483015)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483017, _1483019, tc_HOL_Obool), _1483011), hAPP(hAPP(c_Product__Type_OPair(_1483017, _1483019), _1483013), _1483015))))], (18326 ^ _782476) ^ [_1128397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128397), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1128397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11896 ^ _782476) ^ [_999038, _999040, _999042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999038, tc_HOL_Obool)), _999040), _999042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999038, tc_HOL_Obool)), _999040), _999042)))], (33876 ^ _782476) ^ [_1424800] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424800)))), -(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), _1424800)) = 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), _1424800))))], (23717 ^ _782476) ^ [_1227859, _1227861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227861)), 23724 ^ _782476 : [(23731 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227859), _1227861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227859)), hAPP(c_Int_Onat, _1227861))))], (23725 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227859)), hAPP(c_Int_Onat, _1227861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227859), _1227861)))]]], (50680 ^ _782476) ^ [_1808731, _1808733, _1808735, _1808737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1808731), _1808733)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1808731), _1808735)), -(_1808735 = c_Orderings_Obot__class_Obot(tc_fun(_1808731, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1808731, _1808737, _1808733, _1808735)), 50694 ^ _782476 : [(50697 ^ _782476) ^ [_1809076] : [hBOOL(hAPP(hAPP(c_member(_1808731), _1809076), _1808735)), hBOOL(hAPP(hAPP(_1808737, 50693 ^ [_1808731, _1808733, _1808735, _1808737]), _1809076))], (50695 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808731), 50693 ^ [_1808731, _1808733, _1808735, _1808737]), _1808733)))]]], (19550 ^ _782476) ^ [_1149961, _1149963, _1149965] : [class_Groups_Ocomm__monoid__add(_1149961), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149963, _1149961), _1149965), c_Orderings_Obot__class_Obot(tc_fun(_1149963, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149961))], (13425 ^ _782476) ^ [_1031084, _1031086] : [-(c_HOL_OThe(_1031084, hAPP(hAPP(c_COMBC(_1031084, _1031084, tc_HOL_Obool), c_fequal), _1031086)) = _1031086)], (46100 ^ _782476) ^ [_1706277, _1706279, _1706281, _1706283] : [hBOOL(hAPP(c_List_Odistinct(_1706277), hAPP(hAPP(c_List_Omap(_1706279, _1706277), _1706281), _1706283))), 46103 ^ _782476 : [(46106 ^ _782476) ^ [] : [-(c_Fun_Oinj__on(_1706279, _1706277, _1706281, hAPP(c_List_Oset(_1706279), _1706283)))], (46104 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706279), _1706283)))]]], (52307 ^ _782476) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (24138 ^ _782476) ^ [_1235015, _1235017] : [c_Nat__Transfer_Ois__nat(_1235015), c_Nat__Transfer_Ois__nat(_1235017), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1235015, _1235017) = 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, _1235015), hAPP(c_Int_Onat, _1235017))))], (18034 ^ _782476) ^ [_1124178, _1124180] : [class_Groups_Ocomm__monoid__add(_1124178), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124178), c_Groups_Ozero__class_Ozero(_1124178)), _1124180) = _1124180)], (48737 ^ _782476) ^ [_1763205, _1763207, _1763209] : [-(hBOOL(hAPP(hAPP(c_member(_1763205), _1763207), hAPP(c_List_Oset(_1763205), _1763209)))), -(c_List_Oinsert(_1763205, _1763207, _1763209) = hAPP(hAPP(c_List_Olist_OCons(_1763205), _1763207), _1763209))], (44426 ^ _782476) ^ [_1668523, _1668525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668523), _1668525)), -(c_List_Oupto(_1668523, _1668525) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1668523), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1668523), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1668525)))], (24905 ^ _782476) ^ [_1248206, _1248208] : [class_Groups_Oordered__ab__group__add__abs(_1248206), -(hAPP(c_Groups_Oabs__class_Oabs(_1248206), hAPP(c_Groups_Ouminus__class_Ouminus(_1248206), _1248208)) = hAPP(c_Groups_Oabs__class_Oabs(_1248206), _1248208))], (23909 ^ _782476) ^ [_1230815, _1230817] : [23910 ^ _782476 : [(23913 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230817))], (23911 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230815))]], 23914 ^ _782476 : [(23921 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230815), _1230817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230815)), hAPP(c_Int_Onat, _1230817))))], (23915 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230815)), hAPP(c_Int_Onat, _1230817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230815), _1230817)))]]], (20643 ^ _782476) ^ [_1170610, _1170612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170610), _1170612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170610)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170612))))], (46857 ^ _782476) ^ [_1723167, _1723169, _1723171, _1723173, _1723175] : [46859 ^ _782476 : [(46862 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1723167, _1723169, tc_HOL_Obool), _1723175), 46858 ^ [_1723167, _1723169, _1723171, _1723173, _1723175]))], (46860 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723167, _1723169)), 46858 ^ [_1723167, _1723169, _1723171, _1723173, _1723175]), hAPP(c_List_Oset(tc_prod(_1723167, _1723169)), hAPP(hAPP(c_List_Ozip(_1723167, _1723169), _1723171), _1723173)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723167)), _1723171) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723169)), _1723173), -(c_List_Olist__all2(_1723167, _1723169, _1723175, _1723171, _1723173))], (2548 ^ _782476) ^ [_819972, _819974, _819976, _819978] : [-(c_FunDef_Orp__inv__image(_819978, _819974) = c_FunDef_Orp__inv__image(_819976, _819972)), _819978 = _819976, _819974 = _819972], (32875 ^ _782476) ^ [_1405897, _1405899, _1405901] : [_1405897 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1405899, _1405899), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1405899, _1405899), tc_HOL_Obool)), _1405897), _1405901)))], (17361 ^ _782476) ^ [_1111902, _1111904, _1111906] : [_1111902 = _1111906, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111902), _1111904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111906), _1111904))], (39750 ^ _782476) ^ [_1551560, _1551562, _1551564] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551560, _1551562), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551560, _1551562), c_Orderings_Otop__class_Otop(tc_fun(_1551560, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551562, tc_HOL_Obool), _1551560), _1551564))) = hAPP(hAPP(c_Product__Type_OSigma(_1551560, _1551562), c_Orderings_Otop__class_Otop(tc_fun(_1551560, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551562, tc_HOL_Obool), _1551560), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551562, tc_HOL_Obool)), _1551564))))], (49804 ^ _782476) ^ [_1788057, _1788059, _1788061, _1788063, _1788065] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788057, _1788059, _1788061), _1788063), _1788065)), -(hBOOL(hAPP(hAPP(_1788061, _1788065), _1788063)))], (10427 ^ _782476) ^ [_972065, _972067, _972069, _972071, _972073] : [-(hAPP(c_Set_Oimage(_972065, _972067, _972069), hAPP(hAPP(c_Set_Oinsert(_972065), _972071), _972073)) = hAPP(hAPP(c_Set_Oinsert(_972067), hAPP(_972069, _972071)), hAPP(c_Set_Oimage(_972065, _972067, _972069), _972073)))], (4990 ^ _782476) ^ [_858659, _858661] : [_858661 = _858659, -(c_List_Oset(_858661) = c_List_Oset(_858659))], (32437 ^ _782476) ^ [_1396785, _1396787] : [-(_1396785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32440 ^ _782476 : [(32447 ^ _782476) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396787, _1396785) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396787), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396785)) = 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), _1396787), _1396785))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32441 ^ _782476) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396787, _1396785) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396787), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396785)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396787), _1396785)))]]], (17648 ^ _782476) ^ [_1117043, _1117045, _1117047] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117043), _1117045)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117047), _1117045)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117043), _1117047))], (32032 ^ _782476) ^ [_1389261, _1389263, _1389265] : [class_Divides_Osemiring__div(_1389261), -(c_Divides_Odiv__class_Omod(_1389261, c_Divides_Odiv__class_Omod(_1389261, _1389263, _1389265), _1389265) = c_Divides_Odiv__class_Omod(_1389261, _1389263, _1389265))], (44152 ^ _782476) ^ [_1663453, _1663455, _1663457, _1663459] : [-(_1663453 = _1663455), -(c_List_Oremove1(_1663457, _1663453, hAPP(hAPP(c_List_Olist_OCons(_1663457), _1663455), _1663459)) = hAPP(hAPP(c_List_Olist_OCons(_1663457), _1663455), c_List_Oremove1(_1663457, _1663453, _1663459)))], (51307 ^ _782476) ^ [_1820609] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51303 ^ [_1820609]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36956 ^ _782476) ^ [_1486432] : [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), _1486432))), 36959 ^ _782476 : [(36966 ^ _782476) ^ [] : [-(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), _1486432))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486432)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486432)), 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), _1486432)))))], (36960 ^ _782476) ^ [] : [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), _1486432)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486432)) = 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), _1486432))))]]], (12422 ^ _782476) ^ [_1008137, _1008139, _1008141] : [class_Orderings_Olinorder(_1008137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008137), _1008139), _1008141)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1008137, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1008137, _1008139, _1008141)), hAPP(c_SetInterval_Oord__class_OatLeast(_1008137), _1008141)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1008137), _1008139))], (44226 ^ _782476) ^ [_1664788, _1664790, _1664792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664788), tc_List_Olist(_1664788))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664788), tc_List_Olist(_1664788)), _1664790), c_List_Olist_ONil(_1664788))), c_List_Olistrel(_1664788, _1664792))), -(_1664790 = c_List_Olist_ONil(_1664788))], (52271 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (22888 ^ _782476) ^ [_1211689, _1211691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211691), _1211689))))], (29002 ^ _782476) ^ [_1333150, _1333152, _1333154, _1333156, _1333158] : [class_Fields_Ofield__inverse__zero(_1333150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333152), _1333154)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333152, _1333150), hAPP(hAPP(c_COMBS(_1333152, _1333150, _1333150), hAPP(hAPP(c_COMBB(_1333150, tc_fun(_1333150, _1333150), _1333152), c_Rings_Oinverse__class_Odivide(_1333150)), _1333156)), _1333158)), _1333154) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333150), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333152, _1333150), _1333156), _1333154)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333152, _1333150), _1333158), _1333154)))], (3358 ^ _782476) ^ [_832601, _832603, _832605, _832607] : [-(c_Random_Oselect(_832607, _832603) = c_Random_Oselect(_832605, _832601)), _832607 = _832605, _832603 = _832601], (29176 ^ _782476) ^ [_1336287, _1336289] : [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), _1336287), _1336289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336287))), -(_1336289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21085 ^ _782476) ^ [_1178844, _1178846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178844), _1178846)), 21088 ^ _782476 : [(21091 ^ _782476) ^ [] : [_1178844 = _1178846], (21089 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178844), _1178846)))]]], (38895 ^ _782476) ^ [_1528872, _1528874, _1528876] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528872, _1528874, _1528876, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1528874)], (17169 ^ _782476) ^ [_1108574] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108574))))], (52663 ^ _782476) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (30088 ^ _782476) ^ [_1353217, _1353219, _1353221, _1353223] : [class_Fields_Ofield__inverse__zero(_1353217), 30091 ^ _782476 : [(30092 ^ _782476) ^ [] : [_1353219 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353217), _1353221), _1353223), 30095 ^ _782476 : [(30102 ^ _782476) ^ [] : [_1353223 = c_Groups_Ozero__class_Ozero(_1353217), -(_1353219 = c_Groups_Ozero__class_Ozero(_1353217))], (30096 ^ _782476) ^ [] : [-(_1353223 = c_Groups_Ozero__class_Ozero(_1353217)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353217), _1353219), _1353223) = _1353221)]]], (30108 ^ _782476) ^ [] : [-(_1353219 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353217), _1353221), _1353223)), 30111 ^ _782476 : [(30114 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353217), _1353219), _1353223) = _1353221], (30112 ^ _782476) ^ [] : [_1353223 = c_Groups_Ozero__class_Ozero(_1353217)]], 30115 ^ _782476 : [(30118 ^ _782476) ^ [] : [_1353219 = c_Groups_Ozero__class_Ozero(_1353217)], (30116 ^ _782476) ^ [] : [-(_1353223 = c_Groups_Ozero__class_Ozero(_1353217))]]]]], (9069 ^ _782476) ^ [_942149, _942151, _942153, _942155] : [hBOOL(hAPP(hAPP(c_member(_942149), _942155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942149, tc_HOL_Obool)), _942151), _942153))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942149, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_942149, tc_fun(_942149, tc_HOL_Obool), tc_HOL_Obool), c_member(_942149)), _942151)), hAPP(hAPP(c_COMBC(_942149, tc_fun(_942149, tc_HOL_Obool), tc_HOL_Obool), c_member(_942149)), _942153)), _942155)))], (31456 ^ _782476) ^ [_1377739, _1377741, _1377743] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1377741), _1377743)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377739), _1377741)), _1377743))], (47295 ^ _782476) ^ [_1734041, _1734043] : [-(c_Random_Opick(_1734041, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1734041), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1734041, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1734041, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1734041)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1734043)) = c_Random_Opick(_1734041, _1734043))], (18710 ^ _782476) ^ [_1134887, _1134889, _1134891, _1134893] : [class_Rings_Oordered__ring(_1134887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134887), _1134889), _1134891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134887), _1134893), c_Groups_Ozero__class_Ozero(_1134887))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134887), _1134893), _1134891)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134887), _1134893), _1134889))))], (10411 ^ _782476) ^ [_971646, _971648, _971650, _971652] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971646, tc_HOL_Obool)), _971648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971646, tc_HOL_Obool)), _971650), _971652)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971646, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971646, tc_HOL_Obool)), _971648), _971650)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971646, tc_HOL_Obool)), _971648), _971652)))], (43449 ^ _782476) ^ [_1645509, _1645511, _1645513] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645509)), hAPP(hAPP(c_List_Otake(_1645509), _1645511), _1645513)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645509)), _1645513)), _1645511))], (10285 ^ _782476) ^ [_968885, _968887, _968889, _968891] : [hBOOL(hAPP(hAPP(c_member(_968885), _968887), _968889)), -(hBOOL(hAPP(hAPP(c_member(_968885), _968887), hAPP(hAPP(c_Set_Oinsert(_968885), _968891), _968889))))], (52429 ^ _782476) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (26001 ^ _782476) ^ [_1274351, _1274353, _1274355, _1274357] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274351), _1274353))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274355), hAPP(c_Set_Oimage(_1274351, _1274355, _1274357), _1274353))), 26009 ^ _782476 : [(26012 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274351), hAPP(c_Set_OCollect(_1274351), hAPP(hAPP(c_COMBS(_1274351, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1274351), c_fconj), hAPP(hAPP(c_COMBC(_1274351, tc_fun(_1274351, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274351)), _1274353))), hAPP(hAPP(c_COMBC(_1274351, _1274355, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1274355, tc_fun(_1274355, tc_HOL_Obool), _1274351), c_fequal), _1274357)), hAPP(_1274357, 26008 ^ [_1274351, _1274353, _1274355, _1274357]))))))], (26010 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274351), 26008 ^ [_1274351, _1274353, _1274355, _1274357]), _1274353)))]]], (35218 ^ _782476) ^ [_1448144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448144), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448144)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21129 ^ _782476) ^ [_1179488, _1179490] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179488)), _1179490) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179488), _1179490)))], (46108 ^ _782476) ^ [_1706428, _1706430, _1706432, _1706434] : [-(hBOOL(hAPP(c_List_Odistinct(_1706428), hAPP(hAPP(c_List_Omap(_1706430, _1706428), _1706432), _1706434)))), hBOOL(hAPP(c_List_Odistinct(_1706430), _1706434)), c_Fun_Oinj__on(_1706430, _1706428, _1706432, hAPP(c_List_Oset(_1706430), _1706434))], (36737 ^ _782476) ^ [_1481639, _1481641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481639), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1481641, _1481639) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481641), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481639)))], (35516 ^ _782476) ^ [_1453560, _1453562] : [class_Groups_Omonoid__mult(_1453560), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453560), _1453562), 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(_1453560), _1453562), _1453562))], (2400 ^ _782476) ^ [_817662, _817664] : [_817664 = _817662, -(c_Divides_Oadjust(_817664) = c_Divides_Oadjust(_817662))], (3642 ^ _782476) ^ [_837011, _837013, _837015, _837017] : [-(c_List_Olist__update(_837017, _837013) = c_List_Olist__update(_837015, _837011)), _837017 = _837015, _837013 = _837011], (20633 ^ _782476) ^ [_1170384, _1170386] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170384)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170386)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1170384), _1170386)))], (41625 ^ _782476) ^ [_1599723, _1599725] : [-(c_Relation_Osingle__valued(_1599723, _1599723, c_Relation_OId__on(_1599723, _1599725)))], (38728 ^ _782476) ^ [] : [-(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)))))], (46493 ^ _782476) ^ [_1714551, _1714553, _1714555] : [hBOOL(hAPP(c_List_Olistsp(_1714551, _1714553), _1714555)), 46496 ^ _782476 : [(46497 ^ _782476) ^ [_1714640] : [hBOOL(hAPP(hAPP(c_member(_1714551), _1714640), hAPP(c_List_Oset(_1714551), _1714555))), -(hBOOL(hAPP(_1714553, _1714640)))]]], (41134 ^ _782476) ^ [_1587898, _1587900] : [-(hAPP(c_Relation_ODomain(_1587898, _1587898), c_Transitive__Closure_Ortrancl(_1587898, _1587900)) = c_Orderings_Otop__class_Otop(tc_fun(_1587898, tc_HOL_Obool)))], (49468 ^ _782476) ^ [_1780036, _1780038, _1780040, _1780042, _1780044] : [-(c_List_Osplice(_1780036, hAPP(hAPP(c_List_Olist_OCons(_1780036), _1780038), _1780040), hAPP(hAPP(c_List_Olist_OCons(_1780036), _1780042), _1780044)) = hAPP(hAPP(c_List_Olist_OCons(_1780036), _1780038), hAPP(hAPP(c_List_Olist_OCons(_1780036), _1780042), c_List_Osplice(_1780036, _1780040, _1780044))))], (49174 ^ _782476) ^ [_1773936, _1773938, _1773940] : [49176 ^ _782476 : [(49179 ^ _782476) ^ [] : [hBOOL(hAPP(_1773938, hAPP(hAPP(c_List_Onth(_1773936), _1773940), 49175 ^ [_1773936, _1773938, _1773940])))], (49177 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49175 ^ [_1773936, _1773938, _1773940]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773936)), _1773940))))]], -(c_List_Olist__all(_1773936, _1773938, _1773940))], (5684 ^ _782476) ^ [_869528, _869530, _869532, _869534, _869536, _869538] : [-(c_COMBC(_869538, _869534, _869530) = c_COMBC(_869536, _869532, _869528)), _869538 = _869536, _869534 = _869532, _869530 = _869528], (50711 ^ _782476) ^ [_1809360, _1809362] : [c_Relation_Otrans(_1809360, hAPP(c_Set_OCollect(tc_prod(_1809360, _1809360)), hAPP(c_Product__Type_Oprod_Oprod__case(_1809360, _1809360, tc_HOL_Obool), _1809362))), -(c_Predicate_Otransp(_1809360, _1809362))], (36274 ^ _782476) ^ [_1466961, _1466963] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466961), hAPP(c_Int_Onumber__class_Onumber__of(_1466961), c_Int_OMin)), _1466963) = hAPP(c_Groups_Ouminus__class_Ouminus(_1466961), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466961), c_Groups_Oone__class_Oone(_1466961)), _1466963))), class_Fields_Ofield__inverse__zero(_1466961), class_Int_Onumber__ring(_1466961)], (5550 ^ _782476) ^ [_867423, _867425, _867427, _867429, _867431, _867433, _867435, _867437, _867439, _867441] : [-(c_SetInterval_Oord_OatLeastLessThan(_867441, _867437, _867433, _867429, _867425) = c_SetInterval_Oord_OatLeastLessThan(_867439, _867435, _867431, _867427, _867423)), _867441 = _867439, _867437 = _867435, _867433 = _867431, _867429 = _867427, _867425 = _867423], (20951 ^ _782476) ^ [_1176348, _1176350] : [-(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)), _1176348)), 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), _1176350), _1176348))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1176348), _1176350))], (24062 ^ _782476) ^ [_1233608, _1233610] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1233608, _1233610)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233608), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52035 ^ _782476) ^ [_1836362, _1836364] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836362), _1836364)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1836364, _1836362) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (48112 ^ _782476) ^ [_1750194, _1750196] : [class_Groups_Ocomm__monoid__add(_1750194), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1750194), hAPP(c_List_Orev(_1750194), _1750196)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1750194), _1750196))], (190 ^ _782476) ^ [_785615, _785617, _785619, _785621, _785623, _785625, _785627, _785629, _785631, _785633] : [-(c_Big__Operators_Ocomm__monoid__big(_785631, _785627, _785623, _785619, _785615)), c_Big__Operators_Ocomm__monoid__big(_785633, _785629, _785625, _785621, _785617), _785633 = _785631, _785629 = _785627, _785625 = _785623, _785621 = _785619, _785617 = _785615], (19674 ^ _782476) ^ [_1151958, _1151960, _1151962] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151958), _1151960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151958), _1151962)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151960), _1151962))], (49816 ^ _782476) ^ [_1788324, _1788326, _1788328] : [-(_1788326 = _1788328), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788324, _1788324, hAPP(hAPP(c_COMBB(tc_fun(_1788324, tc_HOL_Obool), tc_fun(_1788324, tc_HOL_Obool), _1788324), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788324), c_fNot)), c_fequal)), _1788326), _1788328)))], (36348 ^ _782476) ^ [_1468395, _1468397] : [-(_1468395 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468397, _1468395), c_Divides_Odivmod__int(_1468397, _1468395))))], (3288 ^ _782476) ^ [_831480, _831482, _831484, _831486, _831488, _831490, _831492, _831494] : [-(c_Enum_Oproduct(_831494, _831490, _831486, _831482) = c_Enum_Oproduct(_831492, _831488, _831484, _831480)), _831494 = _831492, _831490 = _831488, _831486 = _831484, _831482 = _831480], (25538 ^ _782476) ^ [_1259605, _1259607] : [-(hAPP(c_Set_OCollect(_1259605), hAPP(hAPP(c_COMBC(_1259605, tc_fun(_1259605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1259605)), _1259607)) = _1259607)], (32843 ^ _782476) ^ [_1405335, _1405337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1405335), _1405337)), 32849 ^ _782476 : [(32852 ^ _782476) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32850 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405335), 32848 ^ [_1405335, _1405337]), _1405337)))]], -(hAPP(c_Finite__Set_Ocard(_1405335), _1405337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20936 ^ _782476) ^ [_1176083, _1176085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176083), _1176085)), -(_1176085 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176083), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20939 ^ [_1176083, _1176085])))], (47750 ^ _782476) ^ [_1742707, _1742709, _1742711, _1742713, _1742715] : [class_Orderings_Olinorder(_1742707), 47753 ^ _782476 : [(47760 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1742707, hAPP(hAPP(c_List_Omap(_1742709, _1742707), _1742711), _1742715)), -(c_List_Olinorder__class_Osorted(_1742707, hAPP(hAPP(c_List_Omap(_1742709, _1742707), _1742711), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742709, _1742707, _1742711), _1742713), _1742715))))], (47754 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1742707, hAPP(hAPP(c_List_Omap(_1742709, _1742707), _1742711), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742709, _1742707, _1742711), _1742713), _1742715))), -(c_List_Olinorder__class_Osorted(_1742707, hAPP(hAPP(c_List_Omap(_1742709, _1742707), _1742711), _1742715)))]]], (15578 ^ _782476) ^ [_1073622, _1073624, _1073626, _1073628] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073622), _1073624)), -(hAPP(c_Set_Oimage(_1073622, _1073626, _1073628), _1073624) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1073626, tc_HOL_Obool), _1073622, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073626, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1073622, tc_fun(_1073626, tc_HOL_Obool), tc_fun(_1073626, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1073626, tc_fun(tc_fun(_1073626, tc_HOL_Obool), tc_fun(_1073626, tc_HOL_Obool)), _1073622), c_Set_Oinsert(_1073626)), _1073628)), c_Orderings_Obot__class_Obot(tc_fun(_1073626, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1073626, tc_HOL_Obool))), _1073624))], (19488 ^ _782476) ^ [_1148928, _1148930, _1148932] : [class_Groups_Ogroup__add(_1148928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148928), _1148930), _1148932) = c_Groups_Ozero__class_Ozero(_1148928), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1148928), _1148930) = _1148932)], (18340 ^ _782476) ^ [_1128591] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128591), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128591)], (42659 ^ _782476) ^ [_1623018, _1623020, _1623022, _1623024, _1623026, _1623028, _1623030, _1623032] : [c_Finite__Set_Ofolding__image__simple__idem(_1623018, _1623020, _1623022, _1623024, _1623026, _1623028), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623020), _1623030)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623020), _1623032)), -(hAPP(_1623028, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623020, tc_HOL_Obool)), _1623030), _1623032)) = hAPP(hAPP(_1623022, hAPP(_1623028, _1623030)), hAPP(_1623028, _1623032)))], (22419 ^ _782476) ^ [_1203168, _1203170] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203168), _1203170)), 22420 ^ _782476 : [(22427 ^ _782476) ^ [] : [_1203168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203170 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22421 ^ _782476) ^ [] : [_1203168 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43737 ^ _782476) ^ [_1654282, _1654284] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654282, _1654284) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654282, _1654284)))], (44767 ^ _782476) ^ [_1676693, _1676695, _1676697] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676693)), hAPP(hAPP(c_List_Oappend(_1676693), _1676695), _1676697)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676693)), _1676695)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676693)), _1676697)))], (9580 ^ _782476) ^ [_954246, _954248, _954250, _954252] : [9582 ^ _782476 : [(9585 ^ _782476) ^ [] : [hAPP(_954252, 9581 ^ [_954246, _954248, _954250, _954252]) = c_Orderings_Obot__class_Obot(tc_fun(_954248, tc_HOL_Obool))], (9583 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954246), 9581 ^ [_954246, _954248, _954250, _954252]), _954250)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954246, tc_fun(_954248, tc_HOL_Obool)), _954250), _954252) = c_Orderings_Obot__class_Obot(tc_fun(_954248, tc_HOL_Obool)))], (7019 ^ _782476) ^ [_898042, _898044, _898046] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_898042, tc_HOL_Obool)), _898044), hAPP(c_Set_OPow(_898042), _898046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898042, tc_HOL_Obool)), _898044), _898046)))], (12308 ^ _782476) ^ [_1005924, _1005926] : [class_Complete__Lattice_Ocomplete__lattice(_1005924), c_Orderings_Oorder__class_Omono(_1005924, _1005924, _1005926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005924), c_Inductive_Ocomplete__lattice__class_Ogfp(_1005924, _1005926)), hAPP(_1005926, c_Inductive_Ocomplete__lattice__class_Ogfp(_1005924, _1005926)))))], (42802 ^ _782476) ^ [_1626300, _1626302, _1626304] : [c_Nitpick_Oless__eq__frac(_1626300, _1626302, _1626304), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626300), c_Nitpick_Oplus__frac(_1626300, _1626302, c_Nitpick_Ouminus__frac(_1626300, _1626304)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45029 ^ _782476) ^ [_1682742, _1682744, _1682746, _1682748, _1682750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682742), tc_List_Olist(_1682742))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682742), tc_List_Olist(_1682742)), hAPP(hAPP(c_List_Oappend(_1682742), _1682744), _1682746)), hAPP(hAPP(c_List_Oappend(_1682742), _1682744), _1682748))), c_List_Olexord(_1682742, _1682750))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682742, _1682742)), hAPP(hAPP(c_Product__Type_OPair(_1682742, _1682742), 45034 ^ [_1682742, _1682744, _1682746, _1682748, _1682750]), 45034 ^ [_1682742, _1682744, _1682746, _1682748, _1682750])), _1682750))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682742), tc_List_Olist(_1682742))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682742), tc_List_Olist(_1682742)), _1682746), _1682748)), c_List_Olexord(_1682742, _1682750))))], (20878 ^ _782476) ^ [] : [-(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))], (4300 ^ _782476) ^ [_847690, _847692, _847694, _847696, _847698, _847700] : [-(c_Predicate_Oconversep(_847700, _847696, _847692) = c_Predicate_Oconversep(_847698, _847694, _847690)), _847700 = _847698, _847696 = _847694, _847692 = _847690], (32054 ^ _782476) ^ [_1389674, _1389676, _1389678, _1389680] : [class_Divides_Osemiring__div(_1389674), -(c_Divides_Odiv__class_Omod(_1389674, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389674), _1389676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389674), _1389678), _1389680)), _1389678) = c_Divides_Odiv__class_Omod(_1389674, _1389676, _1389678))], (41475 ^ _782476) ^ [_1596224, _1596226, _1596228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596226, _1596224)), _1596228)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596224, _1596226)), hAPP(c_Relation_Oconverse(_1596226, _1596224), _1596228))))], (16061 ^ _782476) ^ [_1083850, _1083852, _1083854] : [class_Rings_Olinordered__semidom(_1083850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083850), c_Groups_Oone__class_Oone(_1083850)), _1083852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083850), c_Groups_Oone__class_Oone(_1083850)), _1083854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083850), c_Groups_Oone__class_Oone(_1083850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083850), _1083852), _1083854))))], (24281 ^ _782476) ^ [_1237210] : [c_Nat__Transfer_Onat__set(_1237210), 24284 ^ _782476 : [(24285 ^ _782476) ^ [_1237276] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1237276), _1237210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237276)))]]], (34382 ^ _782476) ^ [_1433434, _1433436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433434)), _1433436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433434), _1433436)))], (35522 ^ _782476) ^ [] : [-(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))))))], (35194 ^ _782476) ^ [_1447788] : [c_Int_OPls = _1447788, -(c_Int_OPls = c_Int_OBit0(_1447788))], (47357 ^ _782476) ^ [_1735832, _1735834] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735832), _1735834))), -(c_List_Oupt(_1735832, hAPP(c_Nat_OSuc, _1735834)) = c_List_Olist_ONil(tc_Nat_Onat))], (29116 ^ _782476) ^ [_1335289, _1335291, _1335293, _1335295] : [class_Rings_Olinordered__semidom(_1335289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335289), c_Groups_Oone__class_Oone(_1335289)), _1335291)), 29123 ^ _782476 : [(29130 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335293), _1335295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335289), hAPP(hAPP(c_Power_Opower__class_Opower(_1335289), _1335291), _1335293)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335289), _1335291), _1335295))))], (29124 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335289), hAPP(hAPP(c_Power_Opower__class_Opower(_1335289), _1335291), _1335293)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335289), _1335291), _1335295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335293), _1335295)))]]], (52357 ^ _782476) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (33172 ^ _782476) ^ [_1411374, _1411376, _1411378] : [class_Int_Onumber__ring(_1411374), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411374), hAPP(c_Int_Onumber__class_Onumber__of(_1411374), _1411376)), hAPP(c_Int_Onumber__class_Onumber__of(_1411374), _1411378)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411376), _1411378)))], (9197 ^ _782476) ^ [_945912, _945914] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945912, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945912, tc_HOL_Obool)), _945914)), _945914) = c_Orderings_Otop__class_Otop(tc_fun(_945912, tc_HOL_Obool)))], (46324 ^ _782476) ^ [_1711191] : [-(_1711191 = 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)), _1711191)))], (38543 ^ _782476) ^ [_1520266, _1520268, _1520270, _1520272, _1520274, _1520276, _1520278] : [-(hAPP(c_Product__Type_Oapsnd(_1520266, _1520268, _1520270, _1520272), hAPP(c_Product__Type_Oapfst(_1520274, _1520270, _1520266, _1520276), _1520278)) = hAPP(hAPP(c_Product__Type_OPair(_1520270, _1520268), hAPP(_1520276, hAPP(c_Product__Type_Ofst(_1520274, _1520266), _1520278))), hAPP(_1520272, hAPP(c_Product__Type_Osnd(_1520274, _1520266), _1520278))))], (4184 ^ _782476) ^ [_845872, _845874] : [_845874 = _845872, -(c_New__Random__Sequence_Opos__single(_845874) = c_New__Random__Sequence_Opos__single(_845872))], (52591 ^ _782476) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (6856 ^ _782476) ^ [_894643, _894645, _894647, _894649, _894651] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894643, tc_fun(_894645, tc_HOL_Obool)), _894647), _894649), _894651)), 6860 ^ _782476 : [(6863 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_894649, 6859 ^ [_894643, _894645, _894647, _894649, _894651]), _894651)))], (6861 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894643), 6859 ^ [_894643, _894645, _894647, _894649, _894651]), _894647)))]]], (35162 ^ _782476) ^ [_1447286, _1447288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447286), _1447288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447286)), c_Int_OBit0(_1447288))))], (5612 ^ _782476) ^ [_868456, _868458, _868460, _868462] : [-(tc_sum(_868462, _868458) = tc_sum(_868460, _868456)), _868462 = _868460, _868458 = _868456], (13764 ^ _782476) ^ [_1037804, _1037806, _1037808, _1037810, _1037812, _1037814] : [-(hAPP(c_Set_Ovimage(_1037804, _1037806, hAPP(c_Fun_Ocomp(_1037808, _1037806, _1037804, _1037810), _1037812)), _1037814) = hAPP(c_Set_Ovimage(_1037804, _1037808, _1037812), hAPP(c_Set_Ovimage(_1037808, _1037806, _1037810), _1037814)))], (26184 ^ _782476) ^ [_1277284, _1277286, _1277288] : [class_Orderings_Olinorder(_1277284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277284, tc_HOL_Obool)), _1277286), _1277288)), -(_1277286 = c_Orderings_Obot__class_Obot(tc_fun(_1277284, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277284), _1277288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277284), c_Big__Operators_Olinorder__class_OMin(_1277284, _1277288)), c_Big__Operators_Olinorder__class_OMin(_1277284, _1277286))))], (9031 ^ _782476) ^ [_940705, _940707, _940709] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940705, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940705, tc_HOL_Obool)), _940707), _940709)), _940709)))], (49719 ^ _782476) ^ [_1785973, _1785975, _1785977, _1785979] : [c_Fun_Obij__betw(_1785973, _1785975, _1785977, c_Orderings_Otop__class_Otop(tc_fun(_1785973, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1785975, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1785973, _1785975, _1785977), _1785979) = hAPP(c_Set_Oimage(_1785975, _1785973, c_Hilbert__Choice_Oinv__into(_1785973, _1785975, c_Orderings_Otop__class_Otop(tc_fun(_1785973, tc_HOL_Obool)), _1785977)), _1785979))], (50587 ^ _782476) ^ [_1805226, _1805228, _1805230, _1805232] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805226), _1805228)), 50590 ^ _782476 : [(50591 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805230), hAPP(c_Set_OCollect(_1805230), hAPP(hAPP(c_COMBB(tc_fun(_1805226, tc_HOL_Obool), tc_HOL_Obool, _1805230), c_HOL_OEx(_1805226)), hAPP(hAPP(c_COMBB(tc_fun(_1805226, tc_HOL_Obool), tc_fun(_1805226, tc_HOL_Obool), _1805230), hAPP(c_COMBS(_1805226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805226), c_fconj), hAPP(hAPP(c_COMBC(_1805226, tc_fun(_1805226, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805226)), _1805228)))), _1805232))))), 50594 ^ _782476 : [(50595 ^ _782476) ^ [_1805534] : [hBOOL(hAPP(hAPP(c_member(_1805226), _1805534), _1805228)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805230), hAPP(c_Set_OCollect(_1805230), hAPP(hAPP(c_COMBC(_1805230, _1805226, tc_HOL_Obool), _1805232), _1805534)))))]]], (50601 ^ _782476) ^ [] : [50603 ^ _782476 : [(50606 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805230), hAPP(c_Set_OCollect(_1805230), hAPP(hAPP(c_COMBC(_1805230, _1805226, tc_HOL_Obool), _1805232), 50602 ^ [_1805226, _1805228, _1805230, _1805232]))))], (50604 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805226), 50602 ^ [_1805226, _1805228, _1805230, _1805232]), _1805228)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805230), hAPP(c_Set_OCollect(_1805230), hAPP(hAPP(c_COMBB(tc_fun(_1805226, tc_HOL_Obool), tc_HOL_Obool, _1805230), c_HOL_OEx(_1805226)), hAPP(hAPP(c_COMBB(tc_fun(_1805226, tc_HOL_Obool), tc_fun(_1805226, tc_HOL_Obool), _1805230), hAPP(c_COMBS(_1805226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805226), c_fconj), hAPP(hAPP(c_COMBC(_1805226, tc_fun(_1805226, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805226)), _1805228)))), _1805232))))))]]], (1662 ^ _782476) ^ [_806451, _806453] : [-(class_Rings_Oordered__cancel__semiring(_806451)), _806453 = _806451, class_Rings_Oordered__cancel__semiring(_806453)], (25225 ^ _782476) ^ [_1253970, _1253972, _1253974] : [class_Groups_Oordered__ab__group__add__abs(_1253970), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253970), hAPP(c_Groups_Oabs__class_Oabs(_1253970), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253970), _1253972), _1253974))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253970), hAPP(c_Groups_Oabs__class_Oabs(_1253970), _1253972)), hAPP(c_Groups_Oabs__class_Oabs(_1253970), _1253974)))))], (37551 ^ _782476) ^ [_1497139, _1497141, _1497143] : [37553 ^ _782476 : [(37556 ^ _782476) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497139, _1497141), 37552 ^ [_1497139, _1497141, _1497143]))], (37554 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1497141, 37552 ^ [_1497139, _1497141, _1497143]), _1497143)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497139, _1497141), _1497143)))], (35302 ^ _782476) ^ [_1449591, _1449593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449591), _1449593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449591)), c_Int_OBit0(_1449593))))], (31968 ^ _782476) ^ [_1388073, _1388075, _1388077, _1388079] : [class_Divides_Oring__div(_1388073), -(c_Divides_Odiv__class_Omod(_1388073, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388073), _1388075), _1388077), _1388079) = c_Divides_Odiv__class_Omod(_1388073, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388073), c_Divides_Odiv__class_Omod(_1388073, _1388075, _1388079)), _1388077), _1388079))], (4370 ^ _782476) ^ [_848851, _848853] : [_848853 = _848851, -(c_Lazy__Sequence_Oempty(_848853) = c_Lazy__Sequence_Oempty(_848851))], (37197 ^ _782476) ^ [_1490469, _1490471] : [_1490469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490469, _1490471) = 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)))], (35242 ^ _782476) ^ [_1448548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448548))))], (5648 ^ _782476) ^ [_868988, _868990] : [_868990 = _868988, -(tc_Lazy__Sequence_Olazy__sequence(_868990) = tc_Lazy__Sequence_Olazy__sequence(_868988))], (38377 ^ _782476) ^ [_1516148, _1516150, _1516152, _1516154, _1516156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1516148, _1516150)), hAPP(_1516148, _1516152))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516154, _1516154)), hAPP(hAPP(c_Product__Type_OPair(_1516154, _1516154), _1516150), _1516152)), c_Wellfounded_Omlex__prod(_1516154, _1516148, _1516156))))], (43739 ^ _782476) ^ [_1654317, _1654319] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1654317), _1654319) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654317, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654319), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8521 ^ _782476) ^ [_930298, _930300, _930302, _930304, _930306] : [class_Lattices_Olattice(_930298), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930300, _930298)), _930302), _930304), _930306) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930298), hAPP(_930302, _930306)), hAPP(_930304, _930306)))], (40157 ^ _782476) ^ [_1563823, _1563825, _1563827] : [-(hAPP(c_Product__Type_Omap__pair(_1563823, _1563823, _1563825, _1563825, c_COMBI(_1563823), c_COMBI(_1563825)), _1563827) = _1563827)], (34278 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (44716 ^ _782476) ^ [_1675404, _1675406, _1675408, _1675410] : [_1675408 = _1675410, -(hAPP(hAPP(c_List_Oappend(_1675404), _1675406), _1675408) = hAPP(hAPP(c_List_Oappend(_1675404), _1675406), _1675410))], (6999 ^ _782476) ^ [_897408, _897410, _897412, _897414] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897408, tc_HOL_Obool), tc_fun(_897410, tc_HOL_Obool)), _897412), hAPP(hAPP(c_COMBC(tc_fun(_897408, tc_HOL_Obool), tc_fun(_897408, tc_fun(_897410, tc_HOL_Obool)), tc_fun(_897410, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897408, tc_fun(_897410, tc_HOL_Obool))), _897414)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897408, tc_fun(_897410, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897408, tc_HOL_Obool), _897412)), _897414))], (39933 ^ _782476) ^ [_1556886, _1556888, _1556890, _1556892] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1556886), _1556888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556886, _1556886), tc_HOL_Obool)), _1556890), hAPP(hAPP(c_Product__Type_OSigma(_1556886, _1556886), _1556888), hAPP(c_COMBK(tc_fun(_1556886, tc_HOL_Obool), _1556886), _1556888)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1556886, tc_HOL_Obool)), _1556892), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1556886), _1556888), _1556890))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556886), _1556892)))], (34410 ^ _782476) ^ [_1433862, _1433864] : [class_Int_Onumber__ring(_1433862), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433862), _1433864), hAPP(c_Int_Onumber__class_Onumber__of(_1433862), c_Int_OBit1(c_Int_OPls))) = _1433864)], (11554 ^ _782476) ^ [_993469, _993471, _993473] : [class_Orderings_Olinorder(_993469), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993469), _993471), _993473))), 11561 ^ _782476 : [(11568 ^ _782476) ^ [] : [_993471 = _993473, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993469), _993471), _993473)))], (11562 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993469), _993471), _993473)), -(_993471 = _993473)]]], (45523 ^ _782476) ^ [_1693697, _1693699, _1693701] : [class_Orderings_Olinorder(_1693697), -(c_Big__Operators_Olinorder__class_OMin(_1693697, hAPP(c_List_Oset(_1693697), hAPP(hAPP(c_List_Olist_OCons(_1693697), _1693699), _1693701))) = hAPP(c_List_Ofoldl(_1693697, _1693697, c_Orderings_Oord__class_Omin(_1693697), _1693699), _1693701))], (37579 ^ _782476) ^ [_1497715, _1497717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1497715), 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)), _1497717)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497715, _1497717) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1497715, _1497717)))], (21935 ^ _782476) ^ [_1195113, _1195115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195113), _1195115))), -(c_Nat__Transfer_Otsub(_1195115, _1195113) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5326 ^ _782476) ^ [_863921, _863923, _863925, _863927] : [-(c_Lazy__Sequence_Oflat(_863927, _863923) = c_Lazy__Sequence_Oflat(_863925, _863921)), _863927 = _863925, _863923 = _863921], (35950 ^ _782476) ^ [_1461612] : [-(_1461612 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35953 ^ _782476 : [(35960 ^ _782476) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461612, 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, _1461612) = 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), _1461612), 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)))], (35954 ^ _782476) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461612, 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, _1461612) = 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), _1461612), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (52433 ^ _782476) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (45086 ^ _782476) ^ [_1684194, _1684196, _1684198, _1684200] : [-(hAPP(hAPP(c_List_Otake(_1684194), _1684196), hAPP(hAPP(c_List_Odrop(_1684194), _1684198), _1684200)) = hAPP(hAPP(c_List_Odrop(_1684194), _1684198), hAPP(hAPP(c_List_Otake(_1684194), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684196), _1684198)), _1684200)))], (24104 ^ _782476) ^ [_1234346, _1234348, _1234350, _1234352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1234346), _1234348)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1234350), _1234352)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1234346, _1234350)), c_Sum__Type_OPlus(_1234346, _1234350, _1234348, _1234352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1234346), _1234348)), hAPP(c_Finite__Set_Ocard(_1234350), _1234352)))], (46616 ^ _782476) ^ [_1717575, _1717577, _1717579] : [-(c_List_Olistsp(_1717575, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717575, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1717575, tc_fun(_1717575, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717575)), _1717577)), hAPP(hAPP(c_COMBC(_1717575, tc_fun(_1717575, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717575)), _1717579))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1717575), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717575), tc_fun(tc_List_Olist(_1717575), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717575))), c_List_Olists(_1717575, _1717577))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717575), tc_fun(tc_List_Olist(_1717575), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717575))), c_List_Olists(_1717575, _1717579))))], (43914 ^ _782476) ^ [_1658188, _1658190, _1658192, _1658194, _1658196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658188), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658190)), _1658192))), 43917 ^ _782476 : [(43924 ^ _782476) ^ [] : [-(_1658188 = _1658194), -(hAPP(hAPP(c_List_Onth(_1658190), hAPP(hAPP(c_List_Olist__update(_1658190, _1658192), _1658188), _1658196)), _1658194) = hAPP(hAPP(c_List_Onth(_1658190), _1658192), _1658194))], (43918 ^ _782476) ^ [] : [_1658188 = _1658194, -(hAPP(hAPP(c_List_Onth(_1658190), hAPP(hAPP(c_List_Olist__update(_1658190, _1658192), _1658188), _1658196)), _1658194) = _1658196)]]], (35330 ^ _782476) ^ [_1450126, _1450128] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450126))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450126)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450128)))], (9077 ^ _782476) ^ [_942444, _942446, _942448, _942450, _942452] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942444, tc_fun(_942446, tc_HOL_Obool)), _942448), hAPP(hAPP(c_COMBC(_942444, tc_fun(_942446, tc_HOL_Obool), tc_fun(_942446, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942446, tc_HOL_Obool), tc_fun(tc_fun(_942446, tc_HOL_Obool), tc_fun(_942446, tc_HOL_Obool)), _942444), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942446, tc_HOL_Obool))), _942450)), _942452)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942446, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942444, tc_fun(_942446, tc_HOL_Obool)), _942448), _942450)), _942452))], (23591 ^ _782476) ^ [_1225791, _1225793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225793)), 23598 ^ _782476 : [(23605 ^ _782476) ^ [] : [_1225791 = _1225793, -(hAPP(c_Int_Onat, _1225791) = hAPP(c_Int_Onat, _1225793))], (23599 ^ _782476) ^ [] : [hAPP(c_Int_Onat, _1225791) = hAPP(c_Int_Onat, _1225793), -(_1225791 = _1225793)]]], (46030 ^ _782476) ^ [_1704157, _1704159, _1704161, _1704163, _1704165] : [c_Fun_Oinj__on(_1704157, _1704159, _1704161, c_Orderings_Otop__class_Otop(tc_fun(_1704157, tc_HOL_Obool))), 46033 ^ _782476 : [(46040 ^ _782476) ^ [] : [_1704163 = _1704165, -(hAPP(hAPP(c_List_Omap(_1704157, _1704159), _1704161), _1704163) = hAPP(hAPP(c_List_Omap(_1704157, _1704159), _1704161), _1704165))], (46034 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Omap(_1704157, _1704159), _1704161), _1704163) = hAPP(hAPP(c_List_Omap(_1704157, _1704159), _1704161), _1704165), -(_1704163 = _1704165)]]], (10291 ^ _782476) ^ [_969009, _969011, _969013, _969015] : [-(hBOOL(hAPP(hAPP(c_member(_969009), _969011), _969013))), -(hBOOL(hAPP(hAPP(c_member(_969009), _969011), _969015))), 10298 ^ _782476 : [(10305 ^ _782476) ^ [] : [_969013 = _969015, -(hAPP(hAPP(c_Set_Oinsert(_969009), _969011), _969013) = hAPP(hAPP(c_Set_Oinsert(_969009), _969011), _969015))], (10299 ^ _782476) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_969009), _969011), _969013) = hAPP(hAPP(c_Set_Oinsert(_969009), _969011), _969015), -(_969013 = _969015)]]], (48144 ^ _782476) ^ [_1750762, _1750764] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750762)), hAPP(c_List_Orev(_1750762), _1750764)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750762)), _1750764))], (482 ^ _782476) ^ [_789791, _789793, _789795, _789797, _789799, _789801, _789803, _789805, _789807, _789809, _789811, _789813] : [-(c_Finite__Set_Ofolding__image__simple__idem(_789811, _789807, _789803, _789799, _789795, _789791)), c_Finite__Set_Ofolding__image__simple__idem(_789813, _789809, _789805, _789801, _789797, _789793), _789813 = _789811, _789809 = _789807, _789805 = _789803, _789801 = _789799, _789797 = _789795, _789793 = _789791], (39947 ^ _782476) ^ [_1557193, _1557195, _1557197, _1557199, _1557201, _1557203] : [-(hAPP(c_Set_Ovimage(_1557193, tc_prod(_1557195, _1557197), _1557199), hAPP(hAPP(c_Product__Type_OSigma(_1557195, _1557197), _1557201), hAPP(c_COMBK(tc_fun(_1557197, tc_HOL_Obool), _1557195), _1557203))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1557193, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1557193, _1557195, hAPP(c_Fun_Ocomp(tc_prod(_1557195, _1557197), _1557195, _1557193, c_Product__Type_Ofst(_1557195, _1557197)), _1557199)), _1557201)), hAPP(c_Set_Ovimage(_1557193, _1557197, hAPP(c_Fun_Ocomp(tc_prod(_1557195, _1557197), _1557197, _1557193, c_Product__Type_Osnd(_1557195, _1557197)), _1557199)), _1557203)))], (37998 ^ _782476) ^ [_1506925, _1506927, _1506929, _1506931, _1506933] : [c_Equiv__Relations_Oequiv(_1506925, _1506927, _1506929), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506925, _1506925)), hAPP(hAPP(c_Product__Type_OPair(_1506925, _1506925), _1506931), _1506933)), _1506929)), -(hAPP(c_Relation_OImage(_1506925, _1506925, _1506929), hAPP(hAPP(c_Set_Oinsert(_1506925), _1506931), c_Orderings_Obot__class_Obot(tc_fun(_1506925, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1506925, _1506925, _1506929), hAPP(hAPP(c_Set_Oinsert(_1506925), _1506933), c_Orderings_Obot__class_Obot(tc_fun(_1506925, tc_HOL_Obool)))))], (8573 ^ _782476) ^ [_931334, _931336, _931338, _931340] : [class_Lattices_Olattice(_931334), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931334), _931336), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931334), _931338), _931340)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931334), _931338), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931334), _931336), _931340)))], (49464 ^ _782476) ^ [_1779940, _1779942, _1779944] : [-(hAPP(c_New__DSequence_Opos__single(_1779940, _1779942), _1779944) = hAPP(c_Lazy__Sequence_Osingle(_1779940), _1779942))], (11330 ^ _782476) ^ [_990071, _990073, _990075] : [class_Orderings_Olinorder(_990071), 11333 ^ _782476 : [(11340 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990071), _990073), _990075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990071, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990071), _990073)), hAPP(c_SetInterval_Oord__class_OlessThan(_990071), _990075))))], (11334 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990071, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990071), _990073)), hAPP(c_SetInterval_Oord__class_OlessThan(_990071), _990075))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990071), _990073), _990075)))]]], (7996 ^ _782476) ^ [_918685, _918687, _918689] : [class_Lattices_Osemilattice__sup(_918685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918685), _918687), _918689)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918685), _918689), _918687) = _918689)], (10357 ^ _782476) ^ [_970261, _970263, _970265, _970267, _970269] : [-(hAPP(hAPP(c_Set_Oinsert(_970261), _970263), hAPP(hAPP(c_Set_Oinsert(_970261), _970265), c_Orderings_Obot__class_Obot(tc_fun(_970261, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_970261), _970267), hAPP(hAPP(c_Set_Oinsert(_970261), _970269), c_Orderings_Obot__class_Obot(tc_fun(_970261, tc_HOL_Obool))))), 10358 ^ _782476 : [(10365 ^ _782476) ^ [] : [_970263 = _970269, _970265 = _970267], (10359 ^ _782476) ^ [] : [_970263 = _970267, _970265 = _970269]]], (4044 ^ _782476) ^ [_843598, _843600, _843602, _843604, _843606, _843608, _843610, _843612] : [-(c_New__Random__Sequence_Opos__empty(_843612, _843608, _843604, _843600) = c_New__Random__Sequence_Opos__empty(_843610, _843606, _843602, _843598)), _843612 = _843610, _843608 = _843606, _843604 = _843602, _843600 = _843598], (8309 ^ _782476) ^ [_925652, _925654, _925656] : [8311 ^ _782476 : [(8314 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925652, tc_HOL_Obool)), _925656), 8310 ^ [_925652, _925654, _925656]))], (8312 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925652, tc_HOL_Obool)), 8310 ^ [_925652, _925654, _925656]), _925654)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925652, tc_HOL_Obool)), _925656), c_Complete__Lattice_OInf__class_OInf(tc_fun(_925652, tc_HOL_Obool), _925654))))], (49577 ^ _782476) ^ [_1782543, _1782545, _1782547, _1782549] : [hAPP(c_Set_Oimage(_1782543, _1782545, _1782547), c_Orderings_Otop__class_Otop(tc_fun(_1782543, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782545, tc_HOL_Obool)), -(hAPP(_1782547, hAPP(c_Hilbert__Choice_Oinv__into(_1782543, _1782545, c_Orderings_Otop__class_Otop(tc_fun(_1782543, tc_HOL_Obool)), _1782547), _1782549)) = _1782549)], (8639 ^ _782476) ^ [_932641, _932643] : [class_Lattices_Obounded__lattice__top(_932641), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932641), _932643), c_Orderings_Otop__class_Otop(_932641)) = _932643)], (32387 ^ _782476) ^ [_1395907, _1395909, _1395911, _1395913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395909), _1395911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395911), 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), _1395909), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395913, _1395907))), _1395911)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28576 ^ _782476) ^ [_1324595, _1324597] : [class_Orderings_Olinorder(_1324595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324595), _1324597)), -(_1324597 = c_Orderings_Obot__class_Obot(tc_fun(_1324595, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324595), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324595), 28589 ^ [_1324595, _1324597]), 28590 ^ [_1324595, _1324597])), hAPP(hAPP(c_Set_Oinsert(_1324595), 28589 ^ [_1324595, _1324597]), hAPP(hAPP(c_Set_Oinsert(_1324595), 28590 ^ [_1324595, _1324597]), c_Orderings_Obot__class_Obot(tc_fun(_1324595, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324595), c_Big__Operators_Olinorder__class_OMax(_1324595, _1324597)), _1324597)))], (35878 ^ _782476) ^ [_1460095, _1460097, _1460099] : [class_Int_Onumber__ring(_1460095), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1460095), _1460097), _1460099)), 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(_1460095), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460095), hAPP(hAPP(c_Power_Opower__class_Opower(_1460095), _1460097), 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(_1460095), _1460099), 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(_1460095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1460095), hAPP(c_Int_Onumber__class_Onumber__of(_1460095), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1460097)), _1460099)))], (29236 ^ _782476) ^ [_1337481, _1337483] : [class_Groups_Omonoid__mult(_1337481), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337481), _1337483), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1337483)], (14102 ^ _782476) ^ [_1044807, _1044809, _1044811, _1044813, _1044815] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044807, _1044809, hAPP(hAPP(c_Set_Oinsert(_1044807), _1044811), _1044813)), _1044815))), 14103 ^ _782476 : [(14104 ^ _782476) ^ [_1044911, _1044913] : [hAPP(hAPP(c_Set_Oinsert(_1044807), _1044811), _1044813) = hAPP(hAPP(c_Set_Oinsert(_1044807), _1044913), _1044911), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044807, _1044807, _1044809, _1044913, _1044911), _1044815)), -(hBOOL(hAPP(hAPP(c_member(_1044807), _1044913), _1044911)))]]], (48675 ^ _782476) ^ [_1762053, _1762055, _1762057] : [hBOOL(hAPP(c_List_Odistinct(_1762053), _1762055)), -(hBOOL(hAPP(c_List_Odistinct(_1762053), c_List_Oinsert(_1762053, _1762057, _1762055))))], (39456 ^ _782476) ^ [] : [-(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))))], (23657 ^ _782476) ^ [_1226866] : [-(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)), _1226866)) = hAPP(c_Int_Onat, _1226866))], (28556 ^ _782476) ^ [_1324145, _1324147] : [class_Orderings_Olinorder(_1324145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324145), _1324147)), -(_1324147 = c_Orderings_Obot__class_Obot(tc_fun(_1324145, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324145), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324145), 28569 ^ [_1324145, _1324147]), 28570 ^ [_1324145, _1324147])), hAPP(hAPP(c_Set_Oinsert(_1324145), 28569 ^ [_1324145, _1324147]), hAPP(hAPP(c_Set_Oinsert(_1324145), 28570 ^ [_1324145, _1324147]), c_Orderings_Obot__class_Obot(tc_fun(_1324145, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324145), c_Big__Operators_Olattice_OSup__fin(_1324145, c_Orderings_Oord__class_Omax(_1324145), _1324147)), _1324147)))], (18354 ^ _782476) ^ [_1128820, _1128822, _1128824] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128820), _1128822) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128820), _1128824), -(_1128820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1128822 = _1128824)], (4848 ^ _782476) ^ [_856442, _856444, _856446, _856448, _856450, _856452] : [-(c_Random__Sequence_Oempty(_856452, _856448, _856444) = c_Random__Sequence_Oempty(_856450, _856446, _856442)), _856452 = _856450, _856448 = _856446, _856444 = _856442], (27979 ^ _782476) ^ [_1311538, _1311540, _1311542] : [class_Orderings_Olinorder(_1311538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311538), _1311540)), -(_1311540 = c_Orderings_Obot__class_Obot(tc_fun(_1311538, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311538), _1311542)), -(_1311542 = c_Orderings_Obot__class_Obot(tc_fun(_1311538, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311538, tc_HOL_Obool)), _1311540), _1311542) = c_Orderings_Obot__class_Obot(tc_fun(_1311538, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1311538, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311538, tc_HOL_Obool)), _1311540), _1311542)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311538), c_Big__Operators_Olinorder__class_OMin(_1311538, _1311540)), c_Big__Operators_Olinorder__class_OMin(_1311538, _1311542)))], (47321 ^ _782476) ^ [_1734832, _1734834] : [class_Groups_Omonoid__add(_1734832), -(hAPP(c_List_Ofoldl(_1734832, _1734832, c_Groups_Oplus__class_Oplus(_1734832), c_Groups_Ozero__class_Ozero(_1734832)), _1734834) = c_List_Ofoldr(_1734832, _1734832, c_Groups_Oplus__class_Oplus(_1734832), _1734834, c_Groups_Ozero__class_Ozero(_1734832)))], (10475 ^ _782476) ^ [_973252, _973254, _973256, _973258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973252, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973252, tc_HOL_Obool)), _973254), hAPP(hAPP(c_Set_Oinsert(_973252), _973256), c_Orderings_Obot__class_Obot(tc_fun(_973252, tc_HOL_Obool))))), _973258)), hBOOL(hAPP(hAPP(c_member(_973252), _973256), _973254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973252, tc_HOL_Obool)), _973254), hAPP(hAPP(c_Set_Oinsert(_973252), _973256), _973258))))], (18322 ^ _782476) ^ [_1128334] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128334) = _1128334)], (14044 ^ _782476) ^ [_1043551, _1043553, _1043555] : [class_Rings_Oidom(_1043551), 14047 ^ _782476 : [(14048 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043551), _1043553), _1043553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043551), _1043555), _1043555), -(_1043553 = _1043555), -(_1043553 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043551), _1043555))], (14058 ^ _782476) ^ [] : [14059 ^ _782476 : [(14062 ^ _782476) ^ [] : [_1043553 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043551), _1043555)], (14060 ^ _782476) ^ [] : [_1043553 = _1043555]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043551), _1043553), _1043553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043551), _1043555), _1043555))]]], (42223 ^ _782476) ^ [_1614147, _1614149, _1614151] : [class_Lattices_Olattice(_1614147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614147), _1614149)), -(c_Big__Operators_Olattice__class_OInf__fin(_1614147, hAPP(hAPP(c_Set_Oinsert(_1614147), _1614151), _1614149)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614147, _1614147, c_Lattices_Osemilattice__inf__class_Oinf(_1614147)), _1614151), _1614149))], (23781 ^ _782476) ^ [_1228815, _1228817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228815)), _1228817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228815), hAPP(c_Int_Onat, _1228817))))], (45288 ^ _782476) ^ [_1689230, _1689232, _1689234] : [-(_1689230 = c_List_Olist_ONil(_1689232)), -(hAPP(c_List_Ohd(_1689232), hAPP(hAPP(c_List_Oappend(_1689232), _1689230), _1689234)) = hAPP(c_List_Ohd(_1689232), _1689230))], (11284 ^ _782476) ^ [_989385, _989387, _989389, _989391, _989393] : [c_Fun_Ofun__upd(_989385, _989387, _989389, _989391, _989393) = _989389, -(hAPP(_989389, _989391) = _989393)], (7417 ^ _782476) ^ [_906546, _906548, _906550, _906552, _906554, _906556, _906558] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906546, tc_fun(_906548, tc_fun(_906550, tc_HOL_Obool))), _906552), _906554), _906556), _906558)), 7421 ^ _782476 : [(7424 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_906554, 7420 ^ [_906546, _906548, _906550, _906552, _906554, _906556, _906558]), _906556), _906558)))], (7422 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906546), 7420 ^ [_906546, _906548, _906550, _906552, _906554, _906556, _906558]), _906552)))]]], (32010 ^ _782476) ^ [_1388942] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1388942, _1388942) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45138 ^ _782476) ^ [_1685363, _1685365, _1685367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685363)), _1685365)), _1685367)), -(hAPP(hAPP(c_List_Odrop(_1685363), _1685367), _1685365) = c_List_Olist_ONil(_1685363))], (35236 ^ _782476) ^ [_1448465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448465)))], (52431 ^ _782476) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (29194 ^ _782476) ^ [_1336530, _1336532, _1336534, _1336536] : [class_Groups_Ocomm__monoid__mult(_1336530), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336530), _1336532), _1336534)), _1336536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336530), hAPP(hAPP(c_Power_Opower__class_Opower(_1336530), _1336532), _1336536)), hAPP(hAPP(c_Power_Opower__class_Opower(_1336530), _1336534), _1336536)))], (41457 ^ _782476) ^ [_1595737, _1595739, _1595741, _1595743, _1595745] : [-(hAPP(c_Relation_Oconverse(_1595737, _1595739), hAPP(hAPP(c_Relation_Orel__comp(_1595737, _1595741, _1595739), _1595743), _1595745)) = hAPP(hAPP(c_Relation_Orel__comp(_1595739, _1595741, _1595737), hAPP(c_Relation_Oconverse(_1595741, _1595739), _1595745)), hAPP(c_Relation_Oconverse(_1595737, _1595741), _1595743)))], (49940 ^ _782476) ^ [_1790962, _1790964, _1790966, _1790968, _1790970] : [-(c_List_Oreplicate(_1790962, _1790964, _1790966) = c_List_Oreplicate(_1790962, _1790968, _1790970)), _1790964 = _1790968, 49945 ^ _782476 : [(49948 ^ _782476) ^ [] : [_1790966 = _1790970], (49946 ^ _782476) ^ [] : [_1790964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23769 ^ _782476) ^ [_1228651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228651))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228651)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43609 ^ _782476) ^ [_1649576, _1649578, _1649580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649576), _1649578)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1649576)), hAPP(c_Set_OCollect(tc_List_Olist(_1649576)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1649576), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1649576)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649576), tc_fun(_1649576, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649576, tc_HOL_Obool), tc_fun(tc_fun(_1649576, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649576)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649576, tc_HOL_Obool))), c_List_Oset(_1649576))), _1649578))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649576), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1649576)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1649576)))), _1649580))))))], (44452 ^ _782476) ^ [_1668946, _1668948, _1668950, _1668952] : [_1668946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1668948), _1668946), hAPP(hAPP(c_List_Olist_OCons(_1668948), _1668950), _1668952)) = c_List_Olist_ONil(_1668948))], (28542 ^ _782476) ^ [_1323947, _1323949] : [class_Orderings_Olinorder(_1323947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323947), _1323949)), -(_1323949 = c_Orderings_Obot__class_Obot(tc_fun(_1323947, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323947), c_Big__Operators_Olattice_OInf__fin(_1323947, c_Orderings_Oord__class_Omin(_1323947), _1323949)), c_Big__Operators_Olattice_OSup__fin(_1323947, c_Orderings_Oord__class_Omax(_1323947), _1323949))))], (2390 ^ _782476) ^ [_817513, _817515, _817517, _817519] : [-(c_Divides_Opdivmod(_817519, _817515) = c_Divides_Opdivmod(_817517, _817513)), _817519 = _817517, _817515 = _817513], (50028 ^ _782476) ^ [_1792607, _1792609, _1792611] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792607)), c_List_Oreplicate(_1792607, _1792609, _1792611)) = _1792609)], (44166 ^ _782476) ^ [_1663613, _1663615, _1663617, _1663619] : [-(hBOOL(hAPP(hAPP(c_member(_1663613), _1663615), hAPP(c_List_Oset(_1663613), _1663617)))), hBOOL(hAPP(hAPP(c_member(_1663613), _1663615), hAPP(c_List_Oset(_1663613), c_List_Oremove1(_1663613, _1663619, _1663617))))], (5606 ^ _782476) ^ [_868371, _868373] : [_868373 = _868371, -(tc_List_Olist(_868373) = tc_List_Olist(_868371))], (44893 ^ _782476) ^ [_1679103, _1679105, _1679107, _1679109, _1679111] : [-(hAPP(hAPP(c_List_Olist__update(_1679103, hAPP(hAPP(c_List_Oappend(_1679103), _1679105), hAPP(hAPP(c_List_Olist_OCons(_1679103), _1679107), _1679109))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679103)), _1679105)), _1679111) = hAPP(hAPP(c_List_Oappend(_1679103), _1679105), hAPP(hAPP(c_List_Olist_OCons(_1679103), _1679111), _1679109)))], (49977 ^ _782476) ^ [_1791680, _1791682, _1791684, _1791686] : [49979 ^ _782476 : [(49982 ^ _782476) ^ [] : [hBOOL(hAPP(_1791686, 49978 ^ [_1791680, _1791682, _1791684, _1791686]))], (49980 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791680), 49978 ^ [_1791680, _1791682, _1791684, _1791686]), hAPP(c_List_Oset(_1791680), c_List_Oreplicate(_1791680, _1791682, _1791684)))))]], -(hBOOL(hAPP(_1791686, _1791684))), -(_1791682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23496 ^ _782476) ^ [_1224098, _1224100, _1224102] : [-(hAPP(c_Finite__Set_Ocard(_1224098), _1224100) = hAPP(c_Nat_OSuc, _1224102)), 23497 ^ _782476 : [(23498 ^ _782476) ^ [_1224198, _1224200] : [_1224100 = hAPP(hAPP(c_Set_Oinsert(_1224098), _1224200), _1224198), -(hBOOL(hAPP(hAPP(c_member(_1224098), _1224200), _1224198))), hAPP(c_Finite__Set_Ocard(_1224098), _1224198) = _1224102, 23509 ^ _782476 : [(23512 ^ _782476) ^ [] : [_1224198 = c_Orderings_Obot__class_Obot(tc_fun(_1224098, tc_HOL_Obool))], (23510 ^ _782476) ^ [] : [-(_1224102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (15150 ^ _782476) ^ [_1065568, _1065570, _1065572, _1065574] : [c_Finite__Set_Ofolding__one(_1065568, _1065570, _1065572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065568), _1065574)), -(_1065574 = c_Orderings_Obot__class_Obot(tc_fun(_1065568, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1065568), hAPP(hAPP(_1065570, 15163 ^ [_1065568, _1065570, _1065572, _1065574]), 15164 ^ [_1065568, _1065570, _1065572, _1065574])), hAPP(hAPP(c_Set_Oinsert(_1065568), 15163 ^ [_1065568, _1065570, _1065572, _1065574]), hAPP(hAPP(c_Set_Oinsert(_1065568), 15164 ^ [_1065568, _1065570, _1065572, _1065574]), c_Orderings_Obot__class_Obot(tc_fun(_1065568, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1065568), hAPP(_1065572, _1065574)), _1065574)))], (30823 ^ _782476) ^ [_1366818] : [class_Power_Opower(_1366818), -(c_Power_Opower__class_Opower(_1366818) = c_Power_Opower_Opower(_1366818, c_Groups_Oone__class_Oone(_1366818), c_Groups_Otimes__class_Otimes(_1366818)))], (49235 ^ _782476) ^ [_1775162, _1775164, _1775166] : [c_List_Olist__all(_1775162, _1775164, _1775166), 49238 ^ _782476 : [(49239 ^ _782476) ^ [_1775243] : [hBOOL(hAPP(hAPP(c_member(_1775162), _1775243), hAPP(c_List_Oset(_1775162), _1775166))), -(hBOOL(hAPP(_1775164, _1775243)))]]], (26984 ^ _782476) ^ [_1292315, _1292317, _1292319, _1292321] : [class_Orderings_Olinorder(_1292315), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292315), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292315), _1292317), _1292319)), _1292321) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292315), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292315), _1292317), _1292321)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292315), _1292319), _1292321)))], (3266 ^ _782476) ^ [_831091, _831093, _831095, _831097, _831099, _831101, _831103, _831105, _831107, _831109] : [-(c_Fun_Ofun__upd(_831109, _831105, _831101, _831097, _831093) = c_Fun_Ofun__upd(_831107, _831103, _831099, _831095, _831091)), _831109 = _831107, _831105 = _831103, _831101 = _831099, _831097 = _831095, _831093 = _831091], (18436 ^ _782476) ^ [_1129999] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1129999), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (49898 ^ _782476) ^ [_1790262, _1790264, _1790266] : [_1790264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1790262, _1790264, _1790266) = c_List_Olist_ONil(_1790262))], (20810 ^ _782476) ^ [_1173691, _1173693] : [20812 ^ _782476 : [(20815 ^ _782476) ^ [] : [hBOOL(hAPP(_1173693, 20811 ^ [_1173691, _1173693]))], (20813 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20811 ^ [_1173691, _1173693]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173691))))]], 20816 ^ _782476 : [(20817 ^ _782476) ^ [_1173844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173844), _1173691)), -(hBOOL(hAPP(_1173693, _1173844)))]]], (34462 ^ _782476) ^ [] : [-(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))))], (25454 ^ _782476) ^ [_1258081, _1258083, _1258085] : [-(c_Nat_Onat_Onat__case(_1258081, _1258083, _1258085, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1258083)], (29622 ^ _782476) ^ [_1344576, _1344578, _1344580, _1344582] : [class_Rings_Olinordered__semidom(_1344576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344578), _1344580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344576), c_Groups_Ozero__class_Ozero(_1344576)), _1344582)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344576), _1344582), c_Groups_Oone__class_Oone(_1344576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344576), hAPP(hAPP(c_Power_Opower__class_Opower(_1344576), _1344582), _1344580)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344576), _1344582), _1344578))))], (6426 ^ _782476) ^ [_885220, _885222, _885224, _885226, _885228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885220, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885222, tc_fun(_885220, tc_HOL_Obool)), _885224), _885226)), _885228)), 6429 ^ _782476 : [(6430 ^ _782476) ^ [_885353] : [hBOOL(hAPP(hAPP(c_member(_885222), _885353), _885224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885220, tc_HOL_Obool)), hAPP(_885226, _885353)), _885228)))]]], (3804 ^ _782476) ^ [_839526, _839528, _839530, _839532, _839534, _839536, _839538, _839540] : [-(c_List_Ofoldl(_839540, _839536, _839532, _839528) = c_List_Ofoldl(_839538, _839534, _839530, _839526)), _839540 = _839538, _839536 = _839534, _839532 = _839530, _839528 = _839526], (40262 ^ _782476) ^ [_1566697, _1566699] : [-(c_Relation_Orefl__on(_1566697, _1566699, c_Relation_OId__on(_1566697, _1566699)))], (50379 ^ _782476) ^ [_1800204, _1800206, _1800208] : [50381 ^ _782476 : [(50384 ^ _782476) ^ [] : [hBOOL(hAPP(_1800204, 50380 ^ [_1800204, _1800206, _1800208]))], (50382 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 50380 ^ [_1800204, _1800206, _1800208]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1800206, _1800208))))]], -(c_List_Oall__interval__int(_1800204, _1800206, _1800208))], (2438 ^ _782476) ^ [_818215, _818217, _818219, _818221] : [-(c_Divides_OnegDivAlg(_818221, _818217) = c_Divides_OnegDivAlg(_818219, _818215)), _818221 = _818219, _818217 = _818215], (22392 ^ _782476) ^ [_1202778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202778)), -(_1202778 = hAPP(c_Nat_OSuc, 22395 ^ [_1202778]))], (34744 ^ _782476) ^ [_1439160, _1439162] : [class_Int_Onumber__ring(_1439160), class_Rings_Olinordered__idom(_1439160), 34751 ^ _782476 : [(34758 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439162), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439160), hAPP(c_Int_Onumber__class_Onumber__of(_1439160), _1439162)), c_Groups_Oone__class_Oone(_1439160))))], (34752 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439160), hAPP(c_Int_Onumber__class_Onumber__of(_1439160), _1439162)), c_Groups_Oone__class_Oone(_1439160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439162), c_Int_OBit1(c_Int_OPls))))]]], (4200 ^ _782476) ^ [_846106, _846108, _846110, _846112, _846114, _846116] : [-(c_List_Osplice(_846116, _846112, _846108) = c_List_Osplice(_846114, _846110, _846106)), _846116 = _846114, _846112 = _846110, _846108 = _846106], (1882 ^ _782476) ^ [_809201, _809203] : [-(class_Rings_Osemiring__0(_809201)), _809203 = _809201, class_Rings_Osemiring__0(_809203)], (49293 ^ _782476) ^ [_1776277, _1776279, _1776281] : [c_List_Olist__all(_1776277, _1776279, _1776281), 49296 ^ _782476 : [(49297 ^ _782476) ^ [_1776358] : [hBOOL(hAPP(hAPP(c_member(_1776277), _1776358), hAPP(c_List_Oset(_1776277), _1776281))), -(hBOOL(hAPP(_1776279, _1776358)))]]], (42427 ^ _782476) ^ [_1618044, _1618046, _1618048, _1618050, _1618052] : [c_Finite__Set_Ofun__left__comm(_1618044, _1618046, _1618048), -(c_Finite__Set_Ofun__left__comm(_1618050, _1618046, hAPP(hAPP(c_COMBB(_1618044, tc_fun(_1618046, _1618046), _1618050), _1618048), _1618052)))], (13948 ^ _782476) ^ [_1041520, _1041522, _1041524] : [-(c_Fun_Obij__betw(_1041520, _1041522, _1041524, c_Orderings_Otop__class_Otop(tc_fun(_1041520, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041522, tc_HOL_Obool)))), c_Fun_Oinj__on(_1041520, _1041522, _1041524, c_Orderings_Otop__class_Otop(tc_fun(_1041520, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041520, _1041522, _1041524), c_Orderings_Otop__class_Otop(tc_fun(_1041520, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041522, tc_HOL_Obool))], (45356 ^ _782476) ^ [_1690239] : [-(c_List_Orotate(_1690239, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1690239)))], (3384 ^ _782476) ^ [_832984, _832986] : [_832986 = _832984, -(c_Lazy__Sequence_Ohb__not__seq(_832986) = c_Lazy__Sequence_Ohb__not__seq(_832984))], (34426 ^ _782476) ^ [_1434118] : [class_Int_Onumber__ring(_1434118), -(hAPP(c_Int_Onumber__class_Onumber__of(_1434118), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1434118))], (16441 ^ _782476) ^ [_1092145, _1092147, _1092149, _1092151] : [class_Groups_Ocancel__semigroup__add(_1092145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092145), _1092147), _1092149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092145), _1092147), _1092151), -(_1092149 = _1092151)], (30476 ^ _782476) ^ [_1360205, _1360207, _1360209, _1360211] : [class_Fields_Olinordered__field__inverse__zero(_1360205), 30479 ^ _782476 : [(30480 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360205), _1360207), _1360209)), _1360211)), 30483 ^ _782476 : [(30490 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360209))), 30493 ^ _782476 : [(30500 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360209), c_Groups_Ozero__class_Ozero(_1360205)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360211)))], (30494 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360209), c_Groups_Ozero__class_Ozero(_1360205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360205), _1360211), _1360209)), _1360207)))]]], (30484 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360205), _1360211), _1360209))))]]], (30506 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360205), _1360207), _1360209)), _1360211))), 30509 ^ _782476 : [(30512 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360205), _1360211), _1360209)))], (30510 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360209)))]], 30513 ^ _782476 : [(30516 ^ _782476) ^ [] : [30517 ^ _782476 : [(30520 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360205), _1360211), _1360209)), _1360207))], (30518 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360209), c_Groups_Ozero__class_Ozero(_1360205))))]], 30521 ^ _782476 : [(30524 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360211))], (30522 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), _1360209), c_Groups_Ozero__class_Ozero(_1360205)))]]], (30514 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360205), c_Groups_Ozero__class_Ozero(_1360205)), _1360209))]]]]], (50616 ^ _782476) ^ [_1806057, _1806059, _1806061] : [c_List_Olist__ex(_1806057, _1806059, _1806061), 50620 ^ _782476 : [(50623 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1806059, 50619 ^ [_1806057, _1806059, _1806061])))], (50621 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806057), 50619 ^ [_1806057, _1806059, _1806061]), hAPP(c_List_Oset(_1806057), _1806061))))]]], (25009 ^ _782476) ^ [_1249937, _1249939, _1249941] : [class_Rings_Olinordered__idom(_1249937), -(c_Groups_Osgn__class_Osgn(_1249937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249937), _1249939), _1249941)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249937), c_Groups_Osgn__class_Osgn(_1249937, _1249939)), c_Groups_Osgn__class_Osgn(_1249937, _1249941)))], (2516 ^ _782476) ^ [_819434, _819436, _819438, _819440, _819442, _819444, _819446, _819448, _819450, _819452] : [-(c_Product__Type_Oprod_Oprod__rec(_819452, _819448, _819444, _819440, _819436) = c_Product__Type_Oprod_Oprod__rec(_819450, _819446, _819442, _819438, _819434)), _819452 = _819450, _819448 = _819446, _819444 = _819442, _819440 = _819438, _819436 = _819434], (1702 ^ _782476) ^ [_806951, _806953] : [-(class_Rings_Olinordered__semidom(_806951)), _806953 = _806951, class_Rings_Olinordered__semidom(_806953)], (47698 ^ _782476) ^ [_1741847, _1741849, _1741851] : [class_Orderings_Olinorder(_1741847), c_List_Olinorder__class_Osorted(_1741847, _1741849), hBOOL(hAPP(c_List_Odistinct(_1741847), _1741849)), c_List_Olinorder__class_Osorted(_1741847, _1741851), hBOOL(hAPP(c_List_Odistinct(_1741847), _1741851)), hAPP(c_List_Oset(_1741847), _1741849) = hAPP(c_List_Oset(_1741847), _1741851), -(_1741849 = _1741851)], (22162 ^ _782476) ^ [_1198843, _1198845] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198843)), _1198845) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198843), hAPP(c_Nat_OSuc, _1198845)))], (22588 ^ _782476) ^ [_1206032, _1206034] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206032), hAPP(c_Nat_OSuc, _1206034)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206032), _1206034)))], (32607 ^ _782476) ^ [_1400072, _1400074] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400072, _1400074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1400072 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400074), 32610 ^ [_1400072, _1400074]))], (7982 ^ _782476) ^ [_918436, _918438, _918440, _918442] : [class_Lattices_Osemilattice__sup(_918436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918436), _918438), _918440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918436), _918442), _918440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918436), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918436), _918438), _918442)), _918440)))], (20174 ^ _782476) ^ [_1161232, _1161234, _1161236] : [-(hBOOL(hAPP(_1161232, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1161234), _1161236)))), 20177 ^ _782476 : [(20180 ^ _782476) ^ [] : [hBOOL(hAPP(_1161232, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20178 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161234), _1161236)))]], 20182 ^ _782476 : [(20185 ^ _782476) ^ [] : [hBOOL(hAPP(_1161232, 20181 ^ [_1161232, _1161234, _1161236]))], (20183 ^ _782476) ^ [] : [-(_1161234 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161236), 20181 ^ [_1161232, _1161234, _1161236]))]]], (20441 ^ _782476) ^ [_1166942, _1166944, _1166946] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166942, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1166944)), _1166946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166942, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166942, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1166944)), _1166946)), hAPP(_1166946, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34894 ^ _782476) ^ [_1442063, _1442065] : [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(_1442063))), 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)), _1442065)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442063)), hAPP(c_Nat_OSuc, _1442065))))], (52623 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (47688 ^ _782476) ^ [_1741714, _1741716] : [class_Orderings_Olinorder(_1741714), c_List_Olinorder__class_Osorted(_1741714, _1741716), -(c_List_Olinorder__class_Osorted(_1741714, c_List_Oremdups(_1741714, _1741716)))], (16191 ^ _782476) ^ [_1086635, _1086637] : [class_Rings_Ocomm__ring__1(_1086635), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1086635), _1086637) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086635), hAPP(c_Groups_Ouminus__class_Ouminus(_1086635), c_Groups_Oone__class_Oone(_1086635))), _1086637))], (31685 ^ _782476) ^ [_1381948, _1381950, _1381952, _1381954, _1381956] : [class_Groups_Ocomm__monoid__mult(_1381948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381950), _1381952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381950, tc_HOL_Obool)), _1381954), _1381952)), 31699 ^ _782476 : [(31702 ^ _782476) ^ [] : [hAPP(_1381956, 31698 ^ [_1381948, _1381950, _1381952, _1381954, _1381956]) = c_Groups_Oone__class_Oone(_1381948)], (31700 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381950), 31698 ^ [_1381948, _1381950, _1381952, _1381954, _1381956]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381950, tc_HOL_Obool)), _1381952), _1381954))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381950, _1381948), _1381956), _1381954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381950, _1381948), _1381956), _1381952))], (38993 ^ _782476) ^ [_1532402, _1532404, _1532406] : [38995 ^ _782476 : [(38998 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1532402), 38994 ^ [_1532402, _1532404, _1532406]), c_Wellfounded_Oacc(_1532402, _1532406)))], (38996 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532402, _1532402)), hAPP(hAPP(c_Product__Type_OPair(_1532402, _1532402), 38994 ^ [_1532402, _1532404, _1532406]), _1532404)), _1532406)))]], -(hBOOL(hAPP(hAPP(c_member(_1532402), _1532404), c_Wellfounded_Oacc(_1532402, _1532406))))], (52655 ^ _782476) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (6436 ^ _782476) ^ [_885478, _885480, _885482, _885484, _885486] : [6438 ^ _782476 : [(6441 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885478, tc_HOL_Obool)), hAPP(_885484, 6437 ^ [_885478, _885480, _885482, _885484, _885486])), _885486))], (6439 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885480), 6437 ^ [_885478, _885480, _885482, _885484, _885486]), _885482)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885478, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885480, tc_fun(_885478, tc_HOL_Obool)), _885482), _885484)), _885486)))], (47010 ^ _782476) ^ [_1726070, _1726072, _1726074] : [-(c_List_Oconcat(_1726070, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1726070)), _1726072), _1726074)) = hAPP(hAPP(c_List_Oappend(_1726070), _1726072), c_List_Oconcat(_1726070, _1726074)))], (40167 ^ _782476) ^ [_1564126, _1564128, _1564130, _1564132, _1564134, _1564136, _1564138, _1564140, _1564142, _1564144] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564126, _1564128), tc_prod(_1564130, _1564132), tc_prod(_1564134, _1564136), c_Product__Type_Omap__pair(_1564126, _1564130, _1564128, _1564132, _1564138, _1564140)), c_Product__Type_Omap__pair(_1564134, _1564126, _1564136, _1564128, _1564142, _1564144)) = c_Product__Type_Omap__pair(_1564134, _1564130, _1564136, _1564132, hAPP(c_Fun_Ocomp(_1564126, _1564130, _1564134, _1564138), _1564142), hAPP(c_Fun_Ocomp(_1564128, _1564132, _1564136, _1564140), _1564144)))], (41415 ^ _782476) ^ [_1594672, _1594674] : [-(c_Transitive__Closure_Ortrancl(_1594672, hAPP(c_Relation_Oconverse(_1594672, _1594672), _1594674)) = hAPP(c_Relation_Oconverse(_1594672, _1594672), c_Transitive__Closure_Ortrancl(_1594672, _1594674)))], (6327 ^ _782476) ^ [_883214, _883216, _883218, _883220, _883222, _883224] : [class_Complete__Lattice_Ocomplete__lattice(_883214), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883216, _883214), _883218), hAPP(hAPP(c_COMBB(tc_fun(_883220, _883214), _883214, _883216), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883220, _883214), _883222)), _883224)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883220, _883214), _883222), hAPP(hAPP(c_COMBB(tc_fun(_883216, _883214), _883214, _883220), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883216, _883214), _883218)), hAPP(c_COMBC(_883216, _883220, _883214), _883224))))], (47303 ^ _782476) ^ [_1734231, _1734233] : [-(c_List_Ofoldr(tc_List_Olist(_1734231), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734231)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734231))), c_List_Otranspose(_1734231, _1734233), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734231))), hAPP(c_List_Ofilter(tc_List_Olist(_1734231), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734231)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734231), tc_List_Olist(_1734231), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734231)))), _1734233)))], (51365 ^ _782476) ^ [_1821625, _1821627, _1821629, _1821631, _1821633] : [51367 ^ _782476 : [(51370 ^ _782476) ^ [] : [c_Relation_Orefl__on(_1821629, hAPP(_1821631, 51366 ^ [_1821625, _1821627, _1821629, _1821631, _1821633]), hAPP(_1821633, 51366 ^ [_1821625, _1821627, _1821629, _1821631, _1821633]))], (51368 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1821625), 51366 ^ [_1821625, _1821627, _1821629, _1821631, _1821633]), _1821627)))]], -(c_Relation_Orefl__on(_1821629, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1821625, tc_fun(_1821629, tc_HOL_Obool)), _1821627), _1821631), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1821625, tc_fun(tc_prod(_1821629, _1821629), tc_HOL_Obool)), _1821627), _1821633)))], (36062 ^ _782476) ^ [_1463789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463789), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463789)), c_Int_OMin)))], (2934 ^ _782476) ^ [_825987, _825989] : [_825989 = _825987, -(c_Int_Oring__1__class_Oof__int(_825989) = c_Int_Oring__1__class_Oof__int(_825987))], (43231 ^ _782476) ^ [_1639785, _1639787, _1639789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1639785, _1639785), tc_HOL_Obool)), _1639787), hAPP(hAPP(c_Product__Type_OSigma(_1639785, _1639785), _1639789), hAPP(c_COMBK(tc_fun(_1639785, tc_HOL_Obool), _1639785), _1639789)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1639785), tc_List_Olist(_1639785)), tc_HOL_Obool)), c_List_Olistrel(_1639785, _1639787)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1639785), tc_List_Olist(_1639785)), c_List_Olists(_1639785, _1639789)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1639785), tc_HOL_Obool), tc_List_Olist(_1639785)), c_List_Olists(_1639785, _1639789))))))], (11106 ^ _782476) ^ [_986646, _986648, _986650] : [class_Orderings_Oorder(_986646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986646), _986648), _986650)), _986648 = _986650], (1802 ^ _782476) ^ [_808201, _808203] : [-(class_Rings_Ocomm__semiring(_808201)), _808203 = _808201, class_Rings_Ocomm__semiring(_808203)], (34552 ^ _782476) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24174 ^ _782476) ^ [_1235505, _1235507] : [c_Nat__Transfer_Ois__nat(_1235505), c_Nat__Transfer_Ois__nat(_1235507), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1235505, _1235507)))], (52151 ^ _782476) ^ [_1838180, _1838182] : [class_Orderings_Opreorder(_1838180), -(class_Orderings_Opreorder(tc_fun(_1838182, _1838180)))], (49918 ^ _782476) ^ [_1790571, _1790573, _1790575, _1790577] : [-(hAPP(hAPP(c_List_Oappend(_1790571), c_List_Oreplicate(_1790571, _1790573, _1790575)), c_List_Oreplicate(_1790571, _1790577, _1790575)) = hAPP(hAPP(c_List_Oappend(_1790571), c_List_Oreplicate(_1790571, _1790577, _1790575)), c_List_Oreplicate(_1790571, _1790573, _1790575)))], (9059 ^ _782476) ^ [_941775, _941777, _941779, _941781, _941783, _941785] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941775, tc_fun(_941777, tc_HOL_Obool)), _941779), hAPP(hAPP(c_COMBB(_941781, tc_fun(_941777, tc_HOL_Obool), _941775), _941783), _941785)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941781, tc_fun(_941777, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941775, _941781, _941785), _941779)), _941783))], (10551 ^ _782476) ^ [_975095, _975097, _975099, _975101, _975103] : [hBOOL(hAPP(hAPP(c_member(_975095), _975097), _975099)), -(hAPP(hAPP(c_Set_Oinsert(_975101), hAPP(_975103, _975097)), hAPP(c_Set_Oimage(_975095, _975101, _975103), _975099)) = hAPP(c_Set_Oimage(_975095, _975101, _975103), _975099))], (8683 ^ _782476) ^ [_933548, _933550] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933548, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_933548, tc_HOL_Obool))), _933550) = _933550)], (13615 ^ _782476) ^ [_1034691, _1034693, _1034695, _1034697, _1034699, _1034701] : [-(hBOOL(hAPP(hAPP(c_member(_1034691), _1034693), _1034695))), -(hAPP(c_Fun_Ooverride__on(_1034691, _1034697, _1034699, _1034701, _1034695), _1034693) = hAPP(_1034699, _1034693))], (3652 ^ _782476) ^ [_837160, _837162, _837164, _837166, _837168, _837170, _837172, _837174, _837176, _837178] : [-(c_List_Ofoldr(_837178, _837174, _837170, _837166, _837162) = c_List_Ofoldr(_837176, _837172, _837168, _837164, _837160)), _837178 = _837176, _837174 = _837172, _837170 = _837168, _837166 = _837164, _837162 = _837160], (13630 ^ _782476) ^ [_1035047, _1035049, _1035051, _1035053] : [c_Finite__Set_Ofolding__one(_1035047, _1035049, _1035051), -(hAPP(_1035051, hAPP(hAPP(c_Set_Oinsert(_1035047), _1035053), c_Orderings_Obot__class_Obot(tc_fun(_1035047, tc_HOL_Obool)))) = _1035053)], (44863 ^ _782476) ^ [_1678425, _1678427, _1678429] : [hAPP(hAPP(c_List_Oappend(_1678425), _1678427), _1678429) = _1678429, -(_1678427 = c_List_Olist_ONil(_1678425))], (45991 ^ _782476) ^ [_1703173, _1703175, _1703177, _1703179, _1703181, _1703183, _1703185] : [hAPP(hAPP(c_List_Omap(_1703173, _1703175), _1703177), _1703179) = hAPP(hAPP(c_List_Omap(_1703181, _1703175), _1703183), _1703185), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703173)), _1703179) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703181)), _1703185))], (23364 ^ _782476) ^ [_1221104, _1221106, _1221108] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221104), _1221106)), hBOOL(hAPP(hAPP(c_member(_1221104), _1221108), _1221106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221104, tc_HOL_Obool)), _1221106), hAPP(hAPP(c_Set_Oinsert(_1221104), _1221108), c_Orderings_Obot__class_Obot(tc_fun(_1221104, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221104), _1221106))))], (11922 ^ _782476) ^ [_999551, _999553, _999555, _999557, _999559] : [class_Orderings_Olinorder(_999551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999551), _999553), _999555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999551), _999557), _999559)), 11933 ^ _782476 : [(11942 ^ _782476) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999551, _999553), _999555) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999551, _999557), _999559)), _999553 = _999557, _999555 = _999559], (11934 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999551, _999553), _999555) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999551, _999557), _999559), 11937 ^ _782476 : [(11940 ^ _782476) ^ [] : [-(_999555 = _999559)], (11938 ^ _782476) ^ [] : [-(_999553 = _999557)]]]]], (36587 ^ _782476) ^ [_1478593, _1478595, _1478597, _1478599] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478593, _1478595), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478597), _1478599))), -(_1478595 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478593, _1478595) = _1478599)], (9275 ^ _782476) ^ [_948339, _948341, _948343, _948345] : [class_Orderings_Oorder(_948339), class_Orderings_Oorder(_948341), c_Orderings_Oorder__class_Omono(_948341, _948339, _948343), -(c_Orderings_Oord__class_OLeast(_948339, hAPP(hAPP(c_COMBC(_948339, tc_fun(_948339, tc_HOL_Obool), tc_HOL_Obool), c_member(_948339)), hAPP(c_Set_Oimage(_948341, _948339, _948343), _948345))) = hAPP(_948343, c_Orderings_Oord__class_OLeast(_948341, hAPP(hAPP(c_COMBC(_948341, tc_fun(_948341, tc_HOL_Obool), tc_HOL_Obool), c_member(_948341)), _948345)))), 9288 ^ _782476 : [(9289 ^ _782476) ^ [_948623] : [hBOOL(hAPP(hAPP(c_member(_948341), _948623), _948345)), 9293 ^ _782476 : [(9296 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948341), _948623), 9292 ^ [_948339, _948341, _948343, _948345, _948623]))], (9294 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948341), 9292 ^ [_948339, _948341, _948343, _948345, _948623]), _948345)))]]]]], (9255 ^ _782476) ^ [_947846, _947848, _947850] : [class_Groups_Oordered__ab__group__add(_947846), -(hAPP(c_Set_Oimage(_947846, _947846, c_Groups_Ouminus__class_Ouminus(_947846)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947846, _947848), _947850)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_947846, hAPP(c_Groups_Ouminus__class_Ouminus(_947846), _947850), hAPP(c_Groups_Ouminus__class_Ouminus(_947846), _947848)))], (37599 ^ _782476) ^ [_1498035] : [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), _1498035))), -(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), _1498035)) = 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), _1498035))))], (11534 ^ _782476) ^ [_993229, _993231, _993233] : [class_Orderings_Olinorder(_993229), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993229), _993231), _993233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993229), _993233), _993231)))], (33942 ^ _782476) ^ [_1426070] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426070)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426070)))], (43011 ^ _782476) ^ [_1632830, _1632832, _1632834, _1632836] : [hBOOL(hAPP(hAPP(c_member(_1632830), _1632832), c_Wellfounded_Oacc(_1632830, _1632834))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632830)), _1632836), c_Wellfounded_Oacc(tc_List_Olist(_1632830), c_List_Olistrel1(_1632830, _1632834)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632830)), hAPP(hAPP(c_List_Olist_OCons(_1632830), _1632832), _1632836)), c_Wellfounded_Oacc(tc_List_Olist(_1632830), c_List_Olistrel1(_1632830, _1632834)))))], (34030 ^ _782476) ^ [_1427625] : [-(c_Int_OBit1(_1427625) = 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)), _1427625)), _1427625))], (25574 ^ _782476) ^ [_1260346, _1260348, _1260350] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260346), hAPP(c_Set_OCollect(_1260346), hAPP(hAPP(c_COMBS(_1260346, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260346), c_fdisj), _1260348)), _1260350))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260346), hAPP(c_Set_OCollect(_1260346), _1260348))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260346), hAPP(c_Set_OCollect(_1260346), _1260350)))], (9380 ^ _782476) ^ [_950530] : [class_Complete__Lattice_Ocomplete__lattice(_950530), -(c_Complete__Lattice_OSup__class_OSup(_950530, c_Orderings_Obot__class_Obot(tc_fun(_950530, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_950530))], (26930 ^ _782476) ^ [_1290996, _1290998, _1291000, _1291002] : [class_Orderings_Olinorder(_1290996), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290996), _1290998), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290996), _1291000), _1291002)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290996), _1291000), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290996), _1290998), _1291002)))], (9405 ^ _782476) ^ [_950923, _950925] : [-(_950925 = c_Orderings_Obot__class_Obot(tc_fun(_950923, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_950923), 9408 ^ [_950923, _950925]), _950925)))], (43648 ^ _782476) ^ [_1651761, _1651763, _1651765] : [_1651761 = _1651763, 43651 ^ _782476 : [(43654 ^ _782476) ^ [_1651917] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651765, _1651765)), _1651917), hAPP(c_List_Oset(tc_prod(_1651765, _1651765)), hAPP(hAPP(c_List_Ozip(_1651765, _1651765), _1651761), _1651763)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1651765, _1651765, tc_HOL_Obool), c_fequal), _1651917)))], (43652 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651765)), _1651761) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651765)), _1651763))]]], (30678 ^ _782476) ^ [_1363888, _1363890, _1363892] : [class_Fields_Olinordered__field(_1363888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363888), _1363890), _1363892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363888), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363888), _1363890), _1363892)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363888), c_Groups_Oone__class_Oone(_1363888)), c_Groups_Oone__class_Oone(_1363888)))), _1363892)))], (52389 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (17842 ^ _782476) ^ [_1120547, _1120549, _1120551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120547), _1120549)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120551), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120549), _1120547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120551), _1120547)), _1120549))], (21069 ^ _782476) ^ [_1178481, _1178483] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178481), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178483)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178481), _1178483))], (23516 ^ _782476) ^ [_1224535, _1224537, _1224539, _1224541] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1224535, _1224539)), c_Sum__Type_OPlus(_1224535, _1224539, _1224537, _1224541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1224535), _1224537)), hAPP(c_Finite__Set_Ocard(_1224539), _1224541))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224535), _1224537)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224539), _1224541))], (21093 ^ _782476) ^ [_1178971, _1178973] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178971), _1178973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178971), _1178973)), -(_1178971 = _1178973)], (47403 ^ _782476) ^ [_1736626, _1736628] : [c_List_Oupt(_1736626, _1736628) = c_List_Olist_ONil(tc_Nat_Onat), -(_1736628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736628), _1736626)))], (7446 ^ _782476) ^ [_907294, _907296, _907298, _907300, _907302, _907304, _907306] : [7448 ^ _782476 : [(7451 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_907302, 7447 ^ [_907294, _907296, _907298, _907300, _907302, _907304, _907306]), _907304), _907306))], (7449 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907294), 7447 ^ [_907294, _907296, _907298, _907300, _907302, _907304, _907306]), _907300)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907294, tc_fun(_907296, tc_fun(_907298, tc_HOL_Obool))), _907300), _907302), _907304), _907306)))], (6257 ^ _782476) ^ [_882099, _882101, _882103, _882105, _882107, _882109] : [class_Complete__Lattice_Ocomplete__lattice(_882099), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882101, tc_fun(_882103, _882099)), _882105), _882107), _882109) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882101, _882099), _882105), hAPP(hAPP(c_COMBC(_882101, _882103, _882099), _882107), _882109)))], (10211 ^ _782476) ^ [_967401, _967403, _967405] : [-(hBOOL(hAPP(hAPP(c_member(_967401), _967403), _967405))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967401, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967401), _967403), _967405)), hAPP(hAPP(c_Set_Oinsert(_967401), _967403), c_Orderings_Obot__class_Obot(tc_fun(_967401, tc_HOL_Obool)))) = _967405)], (36972 ^ _782476) ^ [_1486722, _1486724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486722), 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)), _1486724)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1486722, _1486724), c_Divides_OnegDivAlg(_1486722, _1486724))))], (48188 ^ _782476) ^ [_1751808, _1751810] : [-(_1751808 = c_List_Olist_ONil(_1751810)), -(c_List_Olast(_1751810, hAPP(c_List_Orev(_1751810), _1751808)) = hAPP(c_List_Ohd(_1751810), _1751808))], (17984 ^ _782476) ^ [_1123435, _1123437] : [class_Groups_Ozero(_1123435), 17987 ^ _782476 : [(17994 ^ _782476) ^ [] : [_1123437 = c_Groups_Ozero__class_Ozero(_1123435), -(c_Groups_Ozero__class_Ozero(_1123435) = _1123437)], (17988 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1123435) = _1123437, -(_1123437 = c_Groups_Ozero__class_Ozero(_1123435))]]], (21059 ^ _782476) ^ [_1178213, _1178215, _1178217] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178213), _1178215)), _1178217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178213), _1178217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178215), _1178217)))], (12570 ^ _782476) ^ [_1012523, _1012525, _1012527] : [class_Complete__Lattice_Ocomplete__lattice(_1012523), c_Orderings_Oorder__class_Omono(_1012523, _1012523, _1012525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012523), hAPP(_1012525, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012523), c_Inductive_Ocomplete__lattice__class_Olfp(_1012523, _1012525)), _1012527))), _1012527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012523), c_Inductive_Ocomplete__lattice__class_Olfp(_1012523, _1012525)), _1012527)))], (44276 ^ _782476) ^ [_1665692, _1665694, _1665696] : [-(c_Enum_Oproduct(_1665692, _1665694, c_List_Olist_ONil(_1665692), _1665696) = c_List_Olist_ONil(tc_prod(_1665692, _1665694)))], (52109 ^ _782476) ^ [_1837627, _1837629] : [class_Complete__Lattice_Ocomplete__lattice(_1837627), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1837629, _1837627)))], (22380 ^ _782476) ^ [_1202598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202598), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1202598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46829 ^ _782476) ^ [_1722569, _1722571, _1722573, _1722575, _1722577, _1722579, _1722581, _1722583] : [c_List_Olist__all2(_1722569, _1722571, _1722573, _1722575, _1722577), hBOOL(hAPP(hAPP(_1722573, _1722579), _1722581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722583), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722571)), _1722577))), -(c_List_Olist__all2(_1722569, _1722571, _1722573, hAPP(hAPP(c_List_Olist__update(_1722569, _1722575), _1722583), _1722579), hAPP(hAPP(c_List_Olist__update(_1722571, _1722577), _1722583), _1722581)))], (29368 ^ _782476) ^ [_1339735, _1339737] : [class_Power_Opower(_1339735), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339735), _1339737), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1339735))], (32581 ^ _782476) ^ [_1399641, _1399643, _1399645] : [_1399643 = c_Orderings_Obot__class_Obot(tc_fun(_1399641, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399641), _1399643), _1399645) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399641, tc_HOL_Obool), tc_HOL_Obool)))], (2836 ^ _782476) ^ [_824454, _824456] : [_824456 = _824454, -(c_Relation_OField(_824456) = c_Relation_OField(_824454))], (36416 ^ _782476) ^ [_1471756, _1471758, _1471760, _1471762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471756, tc_fun(_1471758, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471756, tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_fun(_1471758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471758, tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_fun(_1471758, tc_HOL_Obool)), _1471756), c_COMBC(_1471758, tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471758, tc_prod(_1471756, _1471758)), tc_fun(_1471758, tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), _1471756), hAPP(c_COMBB(tc_prod(_1471756, _1471758), tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool), _1471758), c_member(tc_prod(_1471756, _1471758)))), c_Product__Type_OPair(_1471756, _1471758)))), _1471760)), hAPP(hAPP(c_COMBC(_1471756, tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_fun(_1471758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471758, tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_fun(_1471758, tc_HOL_Obool)), _1471756), c_COMBC(_1471758, tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471758, tc_prod(_1471756, _1471758)), tc_fun(_1471758, tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool)), _1471756), hAPP(c_COMBB(tc_prod(_1471756, _1471758), tc_fun(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool), tc_HOL_Obool), _1471758), c_member(tc_prod(_1471756, _1471758)))), c_Product__Type_OPair(_1471756, _1471758)))), _1471762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1471756, _1471758), tc_HOL_Obool)), _1471760), _1471762)))], (40223 ^ _782476) ^ [_1565766, _1565768, _1565770] : [c_Relation_Orefl__on(_1565766, _1565768, _1565770), 40226 ^ _782476 : [(40229 ^ _782476) ^ [_1565948] : [hBOOL(hAPP(hAPP(c_member(_1565766), _1565948), _1565768)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565766, _1565766)), hAPP(hAPP(c_Product__Type_OPair(_1565766, _1565766), _1565948), _1565948)), _1565770)))], (40227 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565766, _1565766), tc_HOL_Obool)), _1565770), hAPP(hAPP(c_Product__Type_OSigma(_1565766, _1565766), _1565768), hAPP(c_COMBK(tc_fun(_1565766, tc_HOL_Obool), _1565766), _1565768)))))]]], (29902 ^ _782476) ^ [_1349889, _1349891, _1349893] : [class_Fields_Olinordered__field__inverse__zero(_1349889), 29905 ^ _782476 : [(29920 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349889), _1349891), _1349893)))), 29921 ^ _782476 : [(29928 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), _1349891), c_Groups_Ozero__class_Ozero(_1349889))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), _1349893), c_Groups_Ozero__class_Ozero(_1349889)))], (29922 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), _1349891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), _1349893))]]], (29906 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349889), _1349891), _1349893))), 29911 ^ _782476 : [(29914 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), _1349893)))], (29912 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), c_Groups_Ozero__class_Ozero(_1349889)), _1349891)))]], 29915 ^ _782476 : [(29918 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), _1349893), c_Groups_Ozero__class_Ozero(_1349889))))], (29916 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349889), _1349891), c_Groups_Ozero__class_Ozero(_1349889))))]]]]], (17956 ^ _782476) ^ [_1122988, _1122990, _1122992] : [class_Nat_Osemiring__char__0(_1122988), 17959 ^ _782476 : [(17966 ^ _782476) ^ [] : [_1122990 = _1122992, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122988), _1122990) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122988), _1122992))], (17960 ^ _782476) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122988), _1122990) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122988), _1122992), -(_1122990 = _1122992)]]], (34704 ^ _782476) ^ [_1438541, _1438543] : [class_Int_Onumber__ring(_1438541), class_Rings_Olinordered__idom(_1438541), 34711 ^ _782476 : [(34718 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438543), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438541), hAPP(c_Int_Onumber__class_Onumber__of(_1438541), _1438543)), c_Groups_Oone__class_Oone(_1438541))))], (34712 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438541), hAPP(c_Int_Onumber__class_Onumber__of(_1438541), _1438543)), c_Groups_Oone__class_Oone(_1438541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438543), c_Int_OBit1(c_Int_OPls))))]]], (25594 ^ _782476) ^ [_1260898, _1260900, _1260902, _1260904] : [-(hAPP(c_Set_Ovimage(_1260898, _1260900, _1260902), hAPP(c_Set_OCollect(_1260900), _1260904)) = hAPP(c_Set_OCollect(_1260898), hAPP(hAPP(c_COMBB(_1260900, tc_HOL_Obool, _1260898), _1260904), _1260902)))], (30620 ^ _782476) ^ [_1362823, _1362825, _1362827, _1362829, _1362831] : [class_Fields_Ofield(_1362823), -(_1362825 = c_Groups_Ozero__class_Ozero(_1362823)), -(_1362827 = c_Groups_Ozero__class_Ozero(_1362823)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362823), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362823), _1362829), _1362825)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362823), _1362831), _1362827)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362823), _1362829), _1362827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362823), _1362831), _1362825))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362823), _1362825), _1362827)))], (48914 ^ _782476) ^ [_1767978, _1767980, _1767982, _1767984, _1767986] : [hAPP(hAPP(c_List_Olist_OCons(_1767978), _1767980), _1767982) = hAPP(c_List_Ofilter(_1767978, _1767984), _1767986), 48919 ^ _782476 : [(48928 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1767984, _1767980)))], (48930 ^ _782476) ^ [] : [-(_1767982 = hAPP(c_List_Ofilter(_1767978, _1767984), 48918 ^ [_1767978, _1767980, _1767982, _1767984, _1767986]))], (48922 ^ _782476) ^ [_1768292] : [hBOOL(hAPP(hAPP(c_member(_1767978), _1768292), hAPP(c_List_Oset(_1767978), 48917 ^ [_1767978, _1767980, _1767982, _1767984, _1767986]))), hBOOL(hAPP(_1767984, _1768292))], (48920 ^ _782476) ^ [] : [-(_1767986 = hAPP(hAPP(c_List_Oappend(_1767978), 48917 ^ [_1767978, _1767980, _1767982, _1767984, _1767986]), hAPP(hAPP(c_List_Olist_OCons(_1767978), _1767980), 48918 ^ [_1767978, _1767980, _1767982, _1767984, _1767986])))]]], (35338 ^ _782476) ^ [_1450286] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450286))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450286)))))], (31512 ^ _782476) ^ [_1378771, _1378773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378771)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378773), _1378771)), _1378771) = _1378773)], (37321 ^ _782476) ^ [_1492770, _1492772] : [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), _1492770), _1492772))), 37324 ^ _782476 : [(37333 ^ _782476) ^ [] : [-(c_Divides_OnegDivAlg(_1492770, _1492772) = hAPP(c_Divides_Oadjust(_1492772), c_Divides_OnegDivAlg(_1492770, 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)))), _1492772)))), -(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), _1492770), _1492772)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492772), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37325 ^ _782476) ^ [] : [37326 ^ _782476 : [(37329 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492772), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37327 ^ _782476) ^ [] : [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), _1492770), _1492772)))]], -(c_Divides_OnegDivAlg(_1492770, _1492772) = 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), _1492770), _1492772)))]]], (4086 ^ _782476) ^ [_844285, _844287, _844289, _844291, _844293, _844295, _844297, _844299] : [-(c_New__Random__Sequence_Oneg__map(_844299, _844295, _844291, _844287) = c_New__Random__Sequence_Oneg__map(_844297, _844293, _844289, _844285)), _844299 = _844297, _844295 = _844293, _844291 = _844289, _844287 = _844285], (35552 ^ _782476) ^ [] : [-(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)))))], (37970 ^ _782476) ^ [_1506400, _1506402, _1506404, _1506406] : [c_Equiv__Relations_Oequiv(_1506400, _1506402, _1506404), hBOOL(hAPP(hAPP(c_member(_1506400), _1506406), _1506402)), -(hBOOL(hAPP(hAPP(c_member(_1506400), _1506406), hAPP(c_Relation_OImage(_1506400, _1506400, _1506404), hAPP(hAPP(c_Set_Oinsert(_1506400), _1506406), c_Orderings_Obot__class_Obot(tc_fun(_1506400, tc_HOL_Obool)))))))], (44346 ^ _782476) ^ [_1666918, _1666920, _1666922] : [_1666918 = c_List_Olist_ONil(_1666920), -(c_List_Obutlast(_1666920, hAPP(hAPP(c_List_Olist_OCons(_1666920), _1666922), _1666918)) = c_List_Olist_ONil(_1666920))], (24470 ^ _782476) ^ [_1240274, _1240276, _1240278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240274)), 24476 ^ _782476 : [(24479 ^ _782476) ^ [] : [hBOOL(hAPP(_1240276, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24475 ^ [_1240274, _1240276, _1240278]), _1240274)))], (24477 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1240276, 24475 ^ [_1240274, _1240276, _1240278])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240278)), 24484 ^ _782476 : [(24485 ^ _782476) ^ [_1240563] : [hBOOL(hAPP(_1240276, _1240563)), -(hBOOL(hAPP(_1240276, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1240563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240278), _1240274)))))]]], (19158 ^ _782476) ^ [_1143126, _1143128, _1143130] : [class_Rings_Olinordered__semiring__strict(_1143126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143126), c_Groups_Ozero__class_Ozero(_1143126)), _1143128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143126), _1143130), c_Groups_Ozero__class_Ozero(_1143126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143126), _1143128), _1143130)), c_Groups_Ozero__class_Ozero(_1143126))))], (24851 ^ _782476) ^ [_1246965, _1246967, _1246969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246967), 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), _1246967), _1246969))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1246965))), _1246969)))], (43823 ^ _782476) ^ [_1656058, _1656060, _1656062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1656060))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1656060), _1656058), _1656062)) = 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), _1656060)), _1656062)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1656060), _1656058)))], (44593 ^ _782476) ^ [_1672684, _1672686, _1672688, _1672690, _1672692] : [-(hAPP(hAPP(c_List_Oappend(_1672684), _1672686), _1672688) = hAPP(hAPP(c_List_Olist_OCons(_1672684), _1672690), _1672692)), 44594 ^ _782476 : [(44601 ^ _782476) ^ [_1672867] : [_1672686 = hAPP(hAPP(c_List_Olist_OCons(_1672684), _1672690), _1672867), hAPP(hAPP(c_List_Oappend(_1672684), _1672867), _1672688) = _1672692], (44595 ^ _782476) ^ [] : [_1672686 = c_List_Olist_ONil(_1672684), _1672688 = hAPP(hAPP(c_List_Olist_OCons(_1672684), _1672690), _1672692)]]], (3032 ^ _782476) ^ [_827450, _827452] : [_827452 = _827450, -(c_HOL_Obool_Obool__size(_827452) = c_HOL_Obool_Obool__size(_827450))], (24522 ^ _782476) ^ [_1241159, _1241161] : [class_Int_Oring__char__0(_1241159), 24525 ^ _782476 : [(24532 ^ _782476) ^ [] : [_1241161 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1241159) = hAPP(c_Int_Oring__1__class_Oof__int(_1241159), _1241161))], (24526 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1241159) = hAPP(c_Int_Oring__1__class_Oof__int(_1241159), _1241161), -(_1241161 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (10107 ^ _782476) ^ [_965231, _965233, _965235, _965237] : [hBOOL(hAPP(hAPP(c_member(_965231), _965233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965231, tc_HOL_Obool)), _965235), _965237))), 10110 ^ _782476 : [(10113 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_965231), _965233), _965237))], (10111 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965231), _965233), _965235)))]]], (13762 ^ _782476) ^ [_1037738, _1037740, _1037742, _1037744, _1037746, _1037748, _1037750] : [-(hAPP(c_Fun_Ocomp(_1037738, _1037740, _1037742, _1037744), c_Fun_Ofun__upd(_1037742, _1037738, _1037746, _1037748, _1037750)) = c_Fun_Ofun__upd(_1037742, _1037740, hAPP(c_Fun_Ocomp(_1037738, _1037740, _1037742, _1037744), _1037746), _1037748, hAPP(_1037744, _1037750)))], (40945 ^ _782476) ^ [_1582563, _1582565] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582563, _1582563)), hAPP(hAPP(c_Product__Type_OPair(_1582563, _1582563), 40946 ^ [_1582563, _1582565]), 40946 ^ [_1582563, _1582565])), c_Transitive__Closure_Otrancl(_1582563, _1582565)))), -(c_Wellfounded_Oacyclic(_1582563, _1582565))], (13288 ^ _782476) ^ [_1027856, _1027858, _1027860, _1027862, _1027864] : [c_Fun_Oinj__on(_1027856, _1027858, _1027860, _1027862), hBOOL(hAPP(hAPP(c_member(_1027856), _1027864), _1027862)), -(hAPP(c_Fun_Othe__inv__into(_1027856, _1027858, _1027862, _1027860), hAPP(_1027860, _1027864)) = _1027864)], (32856 ^ _782476) ^ [_1405535, _1405537, _1405539] : [32858 ^ _782476 : [(32863 ^ _782476) ^ [] : [hBOOL(hAPP(_1405537, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 32857 ^ [_1405535, _1405537, _1405539]), _1405535)))], (32861 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1405537, 32857 ^ [_1405535, _1405537, _1405539])))], (32859 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32857 ^ [_1405535, _1405537, _1405539]), _1405535)))]], hBOOL(hAPP(_1405537, _1405539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405539), _1405535)), -(hBOOL(hAPP(_1405537, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36821 ^ _782476) ^ [_1483287, _1483289, _1483291, _1483293] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1483287, tc_fun(_1483289, tc_HOL_Obool))), _1483291), _1483293))], (3900 ^ _782476) ^ [_841046, _841048] : [_841048 = _841046, -(c_Nat_Osemiring__1__class_Oof__nat(_841048) = c_Nat_Osemiring__1__class_Oof__nat(_841046))], (2174 ^ _782476) ^ [_814235, _814237, _814239, _814241] : [-(c_Int_Onat__aux(_814241, _814237) = c_Int_Onat__aux(_814239, _814235)), _814241 = _814239, _814237 = _814235], (26026 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (50050 ^ _782476) ^ [_1793039, _1793041, _1793043] : [-(hAPP(hAPP(c_List_Oappend(_1793039), c_List_Oreplicate(_1793039, _1793041, _1793043)), hAPP(hAPP(c_List_Olist_OCons(_1793039), _1793043), c_List_Olist_ONil(_1793039))) = hAPP(hAPP(c_List_Olist_OCons(_1793039), _1793043), c_List_Oreplicate(_1793039, _1793041, _1793043)))], (40155 ^ _782476) ^ [_1563752, _1563754, _1563756, _1563758, _1563760, _1563762, _1563764, _1563766] : [-(hAPP(c_Product__Type_Omap__pair(_1563752, _1563754, _1563756, _1563758, _1563760, _1563762), hAPP(hAPP(c_Product__Type_OPair(_1563752, _1563756), _1563764), _1563766)) = hAPP(hAPP(c_Product__Type_OPair(_1563754, _1563758), hAPP(_1563760, _1563764)), hAPP(_1563762, _1563766)))], (19408 ^ _782476) ^ [_1147570, _1147572] : [class_Groups_Oordered__ab__group__add(_1147570), 19411 ^ _782476 : [(19418 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147570), _1147572), c_Groups_Ozero__class_Ozero(_1147570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147570), c_Groups_Ozero__class_Ozero(_1147570)), hAPP(c_Groups_Ouminus__class_Ouminus(_1147570), _1147572))))], (19412 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147570), c_Groups_Ozero__class_Ozero(_1147570)), hAPP(c_Groups_Ouminus__class_Ouminus(_1147570), _1147572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147570), _1147572), c_Groups_Ozero__class_Ozero(_1147570))))]]], (13744 ^ _782476) ^ [_1037415, _1037417, _1037419, _1037421, _1037423, _1037425] : [c_Fun_Oinj__on(_1037415, _1037417, hAPP(c_Fun_Ocomp(_1037419, _1037417, _1037415, _1037421), _1037423), _1037425), -(c_Fun_Oinj__on(_1037415, _1037419, _1037423, _1037425))], (32587 ^ _782476) ^ [_1399764] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399764, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20969 ^ _782476) ^ [_1176643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176643)), -(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)), _1176643))))], (39241 ^ _782476) ^ [_1538682, _1538684, _1538686] : [c_Wellfounded_Owf(_1538682, _1538684), -(c_Wellfounded_Owf(_1538682, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538682, _1538682), tc_HOL_Obool)), _1538684), _1538686)))], (17878 ^ _782476) ^ [_1121503, _1121505, _1121507, _1121509] : [class_Groups_Oab__group__add(_1121503), 17881 ^ _782476 : [(17888 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121505), _1121507))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121503), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121503, _1121503), hAPP(hAPP(c_COMBB(_1121503, tc_fun(_1121503, _1121503), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121503)), _1121509)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121503, tc_Nat_Onat), _1121509), 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, _1121505, _1121507)) = c_Groups_Ozero__class_Ozero(_1121503))], (17882 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121505), _1121507)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121503), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121503, _1121503), hAPP(hAPP(c_COMBB(_1121503, tc_fun(_1121503, _1121503), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121503)), _1121509)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121503, tc_Nat_Onat), _1121509), 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, _1121505, _1121507)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1121503), hAPP(_1121509, _1121505)), hAPP(_1121509, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121507), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (34450 ^ _782476) ^ [_1434496] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434496), c_Int_OPls)))], (52689 ^ _782476) ^ [_1843781, _1843783] : [_1843781 = _1843783, -(hBOOL(hAPP(hAPP(c_fequal, _1843781), _1843783)))], (41822 ^ _782476) ^ [_1604667, _1604669, _1604671, _1604673, _1604675, _1604677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604667, _1604667)), hAPP(hAPP(c_Product__Type_OPair(_1604667, _1604667), _1604669), _1604671)), _1604673)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604667, _1604667)), hAPP(hAPP(c_Product__Type_OPair(_1604667, _1604667), _1604671), _1604675)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604667, _1604667), tc_HOL_Obool), _1604677), _1604673))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604667, _1604667)), hAPP(hAPP(c_Product__Type_OPair(_1604667, _1604667), _1604669), _1604675)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604667, _1604667), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604677)), _1604673))))], (21922 ^ _782476) ^ [_1194779, _1194781, _1194783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194779, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194779, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21923 ^ [_1194779, _1194781, _1194783])), _1194781)), _1194783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194779, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194779, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194781)), _1194783)))], (24114 ^ _782476) ^ [_1234557, _1234559] : [-(c_Sum__Type_OPlus(_1234557, _1234559, c_Orderings_Otop__class_Otop(tc_fun(_1234557, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1234559, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1234557, _1234559), tc_HOL_Obool)))], (41076 ^ _782476) ^ [_1586505, _1586507, _1586509, _1586511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586505, _1586505)), hAPP(hAPP(c_Product__Type_OPair(_1586505, _1586505), _1586507), _1586509)), c_Transitive__Closure_Otrancl(_1586505, _1586511))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586505, _1586505)), hAPP(hAPP(c_Product__Type_OPair(_1586505, _1586505), _1586507), _1586509)), c_Transitive__Closure_Ortrancl(_1586505, _1586511))))], (37531 ^ _782476) ^ [_1496768, _1496770, _1496772, _1496774] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496768, _1496770), _1496772)), hBOOL(hAPP(hAPP(_1496770, _1496774), _1496772)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496768, _1496770), _1496774)))], (6251 ^ _782476) ^ [_881948, _881950, _881952, _881954, _881956, _881958] : [class_Complete__Lattice_Ocomplete__lattice(_881948), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881950, tc_fun(_881952, _881948)), _881954), _881956), _881958) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881950, _881948), _881954), hAPP(hAPP(c_COMBC(_881950, _881952, _881948), _881956), _881958)))], (6383 ^ _782476) ^ [_884292, _884294, _884296, _884298, _884300] : [class_Orderings_Oorder(_884292), class_Orderings_Olinorder(_884294), c_Orderings_Oorder__class_Ostrict__mono(_884294, _884292, _884296), 6394 ^ _782476 : [(6401 ^ _782476) ^ [] : [_884298 = _884300, -(hAPP(_884296, _884298) = hAPP(_884296, _884300))], (6395 ^ _782476) ^ [] : [hAPP(_884296, _884298) = hAPP(_884296, _884300), -(_884298 = _884300)]]], (23663 ^ _782476) ^ [] : [-(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))))], (7385 ^ _782476) ^ [_905934, _905936, _905938, _905940] : [hBOOL(hAPP(hAPP(c_member(_905934), _905936), c_SetInterval_Oord_OatMost(_905934, _905938, _905940))), -(hBOOL(hAPP(hAPP(_905938, _905936), _905940)))], (44885 ^ _782476) ^ [_1678846, _1678848, _1678850, _1678852] : [-(hAPP(hAPP(c_List_Otake(_1678846), _1678848), hAPP(hAPP(c_List_Oappend(_1678846), _1678850), _1678852)) = hAPP(hAPP(c_List_Oappend(_1678846), hAPP(hAPP(c_List_Otake(_1678846), _1678848), _1678850)), hAPP(hAPP(c_List_Otake(_1678846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1678848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678846)), _1678850))), _1678852)))], (22058 ^ _782476) ^ [_1197251, _1197253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197251), hAPP(c_Nat_OSuc, _1197253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197251), _1197253))), -(_1197251 = _1197253)], (8585 ^ _782476) ^ [_931620, _931622, _931624] : [class_Lattices_Osemilattice__inf(_931620), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931620), _931622), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931620), _931622), _931624)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931620), _931622), _931624))], (43852 ^ _782476) ^ [_1656755, _1656757, _1656759, _1656761, _1656763] : [-(_1656755 = _1656757), -(hAPP(hAPP(c_List_Onth(_1656759), hAPP(hAPP(c_List_Olist__update(_1656759, _1656761), _1656755), _1656763)), _1656757) = hAPP(hAPP(c_List_Onth(_1656759), _1656761), _1656757))], (11902 ^ _782476) ^ [_999157, _999159, _999161, _999163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999157, tc_HOL_Obool)), _999159), _999161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999157, tc_HOL_Obool)), _999161), _999163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999157, tc_HOL_Obool)), _999159), _999163)))], (35554 ^ _782476) ^ [_1454200, _1454202] : [class_Rings_Olinordered__idom(_1454200), -(hAPP(c_Groups_Oabs__class_Oabs(_1454200), hAPP(hAPP(c_Power_Opower__class_Opower(_1454200), _1454202), 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(_1454200), _1454202), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (10261 ^ _782476) ^ [_968395, _968397, _968399, _968401] : [hBOOL(hAPP(hAPP(c_member(_968395), _968397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968395, tc_HOL_Obool)), _968399), _968401))), 10264 ^ _782476 : [(10267 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_968395), _968397), _968401))], (10265 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968395), _968397), _968399)))]]], (17800 ^ _782476) ^ [_1119763, _1119765, _1119767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119765), _1119767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119763), _1119767)), _1119765)))], (32020 ^ _782476) ^ [_1389083, _1389085] : [class_Divides_Osemiring__div(_1389083), -(c_Divides_Odiv__class_Omod(_1389083, _1389085, c_Groups_Ozero__class_Ozero(_1389083)) = _1389085)], (11296 ^ _782476) ^ [_989585, _989587, _989589, _989591, _989593, _989595] : [-(c_Fun_Ofun__upd(_989585, _989587, c_Fun_Ofun__upd(_989585, _989587, _989589, _989591, _989593), _989591, _989595) = c_Fun_Ofun__upd(_989585, _989587, _989589, _989591, _989595))], (24778 ^ _782476) ^ [_1245690, _1245692, _1245694, _1245696, _1245698] : [class_Groups_Ocomm__monoid__add(_1245690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245692), _1245694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245692, tc_HOL_Obool)), _1245696), _1245694)), 24792 ^ _782476 : [(24795 ^ _782476) ^ [] : [hAPP(_1245698, 24791 ^ [_1245690, _1245692, _1245694, _1245696, _1245698]) = c_Groups_Ozero__class_Ozero(_1245690)], (24793 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245692), 24791 ^ [_1245690, _1245692, _1245694, _1245696, _1245698]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245692, tc_HOL_Obool)), _1245694), _1245696))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245692, _1245690), _1245698), _1245694) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245692, _1245690), _1245698), _1245696))], (37469 ^ _782476) ^ [_1495379, _1495381, _1495383] : [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), _1495379), _1495381))), -(hBOOL(hAPP(hAPP(_1495383, _1495379), _1495381))), 37476 ^ _782476 : [(37479 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1495383, 37474 ^ [_1495379, _1495381, _1495383]), 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)))), 37475 ^ [_1495379, _1495381, _1495383])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37474 ^ [_1495379, _1495381, _1495383]), 37475 ^ [_1495379, _1495381, _1495383]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37475 ^ [_1495379, _1495381, _1495383]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37489 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1495383, 37474 ^ [_1495379, _1495381, _1495383]), 37475 ^ [_1495379, _1495381, _1495383]))], (37477 ^ _782476) ^ [] : [-(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), 37474 ^ [_1495379, _1495381, _1495383]), 37475 ^ [_1495379, _1495381, _1495383]))))]]], (38845 ^ _782476) ^ [_1527436, _1527438, _1527440, _1527442] : [-(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), _1527436), _1527438)), 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), _1527440), _1527442)), 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), _1527436), _1527440)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527438), _1527442))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527436), _1527442)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527438), _1527440)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (26706 ^ _782476) ^ [_1286715, _1286717, _1286719, _1286721] : [class_Orderings_Olinorder(_1286715), 26709 ^ _782476 : [(26710 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286715), _1286719), _1286721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), _1286719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), _1286721)))], (26720 ^ _782476) ^ [] : [26721 ^ _782476 : [(26724 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), _1286721))], (26722 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), _1286719))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286715), _1286717), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286715), _1286719), _1286721))))]]], (13330 ^ _782476) ^ [_1028645, _1028647, _1028649, _1028651, _1028653] : [c_Fun_Oinj__on(_1028645, _1028647, _1028649, c_Orderings_Otop__class_Otop(tc_fun(_1028645, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028647, tc_HOL_Obool)), _1028651), hAPP(c_Set_Oimage(_1028645, _1028647, _1028649), _1028653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028645, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1028645, _1028647, _1028649), _1028651)), _1028653)))], (37281 ^ _782476) ^ [_1491882, _1491884] : [-(_1491882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37284 ^ _782476 : [(37291 ^ _782476) ^ [] : [-(_1491884 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1491882, _1491884) = 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, _1491884))), 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, _1491882)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1491884))), c_Divides_Opdivmod(_1491882, _1491884)), 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), _1491884))))), c_Divides_Opdivmod(_1491882, _1491884)))))], (37285 ^ _782476) ^ [] : [_1491884 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491882, _1491884) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1491882))]]], (43801 ^ _782476) ^ [_1655534, _1655536, _1655538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655534), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655536)), _1655538))), -(c_List_Obutlast(_1655536, hAPP(hAPP(c_List_Otake(_1655536), _1655534), _1655538)) = hAPP(hAPP(c_List_Otake(_1655536), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655534), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655538))], (52627 ^ _782476) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (29816 ^ _782476) ^ [_1348187, _1348189, _1348191, _1348193, _1348195] : [class_Fields_Ofield__inverse__zero(_1348187), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348187), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348187), _1348189), _1348191)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348187), _1348193), _1348195)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348187), _1348189), _1348193)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348187), _1348191), _1348195)))], (49205 ^ _782476) ^ [_1774652, _1774654, _1774656, _1774658] : [c_List_Olist__all(_1774652, _1774654, hAPP(hAPP(c_List_Olist_OCons(_1774652), _1774656), _1774658)), 49208 ^ _782476 : [(49211 ^ _782476) ^ [] : [-(c_List_Olist__all(_1774652, _1774654, _1774658))], (49209 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1774654, _1774656)))]]], (28492 ^ _782476) ^ [_1322928, _1322930, _1322932] : [class_Orderings_Olinorder(_1322928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322928), _1322930)), -(_1322930 = c_Orderings_Obot__class_Obot(tc_fun(_1322928, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322928), _1322932)), -(_1322932 = c_Orderings_Obot__class_Obot(tc_fun(_1322928, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322928, tc_HOL_Obool)), _1322930), _1322932) = c_Orderings_Obot__class_Obot(tc_fun(_1322928, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322928, c_Orderings_Oord__class_Omax(_1322928), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322928, tc_HOL_Obool)), _1322930), _1322932)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322928), c_Big__Operators_Olattice_OSup__fin(_1322928, c_Orderings_Oord__class_Omax(_1322928), _1322930)), c_Big__Operators_Olattice_OSup__fin(_1322928, c_Orderings_Oord__class_Omax(_1322928), _1322932)))], (9033 ^ _782476) ^ [_940753, _940755, _940757] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940753, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940753, tc_HOL_Obool)), _940755), _940757)), _940755)))], (24044 ^ _782476) ^ [_1233286, _1233288, _1233290, _1233292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1233286, _1233288)), c_Sum__Type_OPlus(_1233286, _1233288, _1233290, _1233292))), 24047 ^ _782476 : [(24050 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1233288), _1233292)))], (24048 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1233286), _1233290)))]]], (19724 ^ _782476) ^ [_1152890, _1152892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152890), _1152892)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152890), _1152892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5026 ^ _782476) ^ [_859191, _859193, _859195, _859197, _859199, _859201, _859203, _859205, _859207, _859209, _859211, _859213] : [-(c_Partial__Function_Ofun__lub(_859213, _859209, _859205, _859201, _859197, _859193) = c_Partial__Function_Ofun__lub(_859211, _859207, _859203, _859199, _859195, _859191)), _859213 = _859211, _859209 = _859207, _859205 = _859203, _859201 = _859199, _859197 = _859195, _859193 = _859191], (1442 ^ _782476) ^ [_803701, _803703] : [-(class_Complete__Lattice_Ocomplete__lattice(_803701)), _803703 = _803701, class_Complete__Lattice_Ocomplete__lattice(_803703)], (46220 ^ _782476) ^ [_1709123, _1709125] : [hAPP(c_Code__Numeral_Oof__nat, _1709123) = hAPP(c_Code__Numeral_Oof__nat, _1709125), -(_1709123 = _1709125)], (29380 ^ _782476) ^ [_1339985, _1339987, _1339989, _1339991] : [class_Fields_Ofield(_1339985), -(_1339987 = c_Groups_Ozero__class_Ozero(_1339985)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339985), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339985), _1339989), _1339987)), _1339991) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339985), hAPP(hAPP(c_Power_Opower__class_Opower(_1339985), _1339989), _1339991)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339985), _1339987), _1339991)))], (38620 ^ _782476) ^ [_1522105, _1522107, _1522109, _1522111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522105), _1522107)), 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)), _1522105), _1522109)), 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)), _1522107), _1522111)), 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)), _1522107), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522109), _1522111))), c_FunDef_Omin__strict)))], (36831 ^ _782476) ^ [_1483538, _1483540, _1483542, _1483544, _1483546, _1483548] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483538, tc_fun(_1483540, tc_HOL_Obool))), _1483542), _1483544), _1483546), _1483548)), -(hBOOL(hAPP(hAPP(_1483542, _1483546), _1483548)))], (31758 ^ _782476) ^ [_1383681, _1383683, _1383685] : [class_Fields_Olinordered__field__inverse__zero(_1383681), 31764 ^ _782476 : [(31769 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383681), 31763 ^ [_1383681, _1383683, _1383685]), _1383683)), _1383685))], (31767 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383681), 31763 ^ [_1383681, _1383683, _1383685]), c_Groups_Oone__class_Oone(_1383681))))], (31765 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383681), c_Groups_Ozero__class_Ozero(_1383681)), 31763 ^ [_1383681, _1383683, _1383685])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383681), _1383683), _1383685)))], (32431 ^ _782476) ^ [_1396631, _1396633, _1396635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396631)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396633, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396635), _1396631)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396635), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396633), _1396635), _1396631))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396633, _1396635)))], (7871 ^ _782476) ^ [_916045, _916047, _916049, _916051] : [7875 ^ _782476 : [(7878 ^ _782476) ^ [] : [hBOOL(hAPP(_916051, 7874 ^ [_916045, _916047, _916049, _916051]))], (7876 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916045), 7874 ^ [_916045, _916047, _916049, _916051]), _916047)))]], 7880 ^ _782476 : [(7883 ^ _782476) ^ [] : [hBOOL(hAPP(_916051, 7879 ^ [_916045, _916047, _916049, _916051]))], (7881 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916045), 7879 ^ [_916045, _916047, _916049, _916051]), _916049)))]], 7884 ^ _782476 : [(7885 ^ _782476) ^ [_916378] : [hBOOL(hAPP(hAPP(c_member(_916045), _916378), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916045, tc_HOL_Obool)), _916047), _916049))), -(hBOOL(hAPP(_916051, _916378)))]]], (5628 ^ _782476) ^ [_868690, _868692, _868694, _868696] : [-(tc_Nitpick_Opair__box(_868696, _868692) = tc_Nitpick_Opair__box(_868694, _868690)), _868696 = _868694, _868692 = _868690], (12318 ^ _782476) ^ [_1006085, _1006087, _1006089, _1006091, _1006093, _1006095] : [hBOOL(hAPP(hAPP(c_member(_1006085), _1006087), _1006089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006091, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1006085, _1006091, _1006093), _1006089)), hAPP(_1006095, hAPP(c_Set_Oimage(_1006085, _1006091, _1006093), _1006089)))), -(hBOOL(hAPP(hAPP(c_member(_1006091), hAPP(_1006093, _1006087)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006091, tc_HOL_Obool), _1006095))))], (11312 ^ _782476) ^ [_989848, _989850, _989852, _989854, _989856, _989858, _989860] : [-(_989848 = _989850), -(c_Fun_Ofun__upd(_989852, _989854, c_Fun_Ofun__upd(_989852, _989854, _989856, _989848, _989858), _989850, _989860) = c_Fun_Ofun__upd(_989852, _989854, c_Fun_Ofun__upd(_989852, _989854, _989856, _989850, _989860), _989848, _989858))], (21137 ^ _782476) ^ [_1179648] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1179648) = _1179648)], (46148 ^ _782476) ^ [_1707330, _1707332, _1707334, _1707336] : [class_Groups_Ocomm__monoid__add(_1707330), hBOOL(hAPP(c_List_Odistinct(_1707332), _1707334)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707330), hAPP(hAPP(c_List_Omap(_1707332, _1707330), _1707336), _1707334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1707332, _1707330), _1707336), hAPP(c_List_Oset(_1707332), _1707334)))], (4996 ^ _782476) ^ [_858744, _858746, _858748, _858750] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858750, _858746) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858748, _858744)), _858750 = _858748, _858746 = _858744], (672 ^ _782476) ^ [_792710, _792712, _792714, _792716, _792718, _792720, _792722, _792724, _792726, _792728] : [-(c_List_Olist__all2(_792726, _792722, _792718, _792714, _792710)), c_List_Olist__all2(_792728, _792724, _792720, _792716, _792712), _792728 = _792726, _792724 = _792722, _792720 = _792718, _792716 = _792714, _792712 = _792710], (9235 ^ _782476) ^ [_947205, _947207, _947209, _947211] : [hBOOL(hAPP(hAPP(c_member(_947207), _947211), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947205, tc_fun(_947207, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947205, tc_HOL_Obool))), _947209))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947205, tc_fun(_947207, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947205, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_947207, tc_HOL_Obool), tc_fun(_947207, tc_HOL_Obool), _947205), hAPP(c_COMBC(_947207, tc_fun(_947207, tc_HOL_Obool), tc_HOL_Obool), c_member(_947207))), _947209)), _947211)))], (50885 ^ _782476) ^ [_1812357, _1812359] : [50888 ^ _782476 : [(50893 ^ _782476) ^ [] : [50886 ^ [_1812357, _1812359] = 50887 ^ [_1812357, _1812359]], (50891 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812357, _1812357)), hAPP(hAPP(c_Product__Type_OPair(_1812357, _1812357), 50887 ^ [_1812357, _1812359]), 50886 ^ [_1812357, _1812359])), _1812359)))], (50889 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812357, _1812357)), hAPP(hAPP(c_Product__Type_OPair(_1812357, _1812357), 50886 ^ [_1812357, _1812359]), 50887 ^ [_1812357, _1812359])), _1812359)))]], -(c_Relation_Oantisym(_1812357, _1812359))], (21479 ^ _782476) ^ [_1185542, _1185544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185542)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185544)), -(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), _1185542), _1185544))))], (49104 ^ _782476) ^ [_1772308, _1772310, _1772312, _1772314] : [c_List_Olist__ex(_1772308, _1772310, hAPP(hAPP(c_List_Oappend(_1772308), _1772312), _1772314)), -(c_List_Olist__ex(_1772308, _1772310, _1772312)), -(c_List_Olist__ex(_1772308, _1772310, _1772314))], (46736 ^ _782476) ^ [_1720603, _1720605, _1720607] : [_1720603 = _1720605, -(c_List_Olist__all2(_1720607, _1720607, c_fequal, _1720603, _1720605))], (22640 ^ _782476) ^ [_1207111, _1207113] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1207111, _1207113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207113), _1207111))], (42814 ^ _782476) ^ [_1626528] : [-(c_Nitpick_Onum(_1626528) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626528, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626528)))], (23412 ^ _782476) ^ [_1222158, _1222160, _1222162] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222158), _1222160)), -(hAPP(c_Finite__Set_Ocard(_1222158), hAPP(hAPP(c_Set_Oinsert(_1222158), _1222162), _1222160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222158, tc_HOL_Obool)), _1222160), hAPP(hAPP(c_Set_Oinsert(_1222158), _1222162), c_Orderings_Obot__class_Obot(tc_fun(_1222158, tc_HOL_Obool)))))))], (24748 ^ _782476) ^ [_1245109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245109)), 24752 ^ _782476 : [(24755 ^ _782476) ^ [] : [-(_1245109 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24751 ^ [_1245109]))], (24753 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24751 ^ [_1245109])))]]], (45611 ^ _782476) ^ [_1695805, _1695807, _1695809] : [class_Orderings_Olinorder(_1695805), -(c_List_Oremove1(_1695805, _1695807, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695805, _1695805, c_COMBI(_1695805)), _1695807), _1695809)) = _1695809)], (43640 ^ _782476) ^ [_1651367, _1651369, _1651371] : [-(hAPP(c_List_Oset(tc_List_Olist(_1651367)), c_Enum_On__lists(_1651367, _1651369, _1651371)) = hAPP(c_Set_OCollect(tc_List_Olist(_1651367)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1651367), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1651367)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651367), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1651367)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1651367)))), _1651369))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651367), tc_fun(_1651367, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1651367, tc_HOL_Obool), tc_fun(tc_fun(_1651367, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1651367)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1651367, tc_HOL_Obool))), c_List_Oset(_1651367))), hAPP(c_List_Oset(_1651367), _1651371)))))], (48729 ^ _782476) ^ [_1763021, _1763023, _1763025] : [-(hAPP(c_List_Oset(_1763021), hAPP(c_List_OremoveAll(_1763021, _1763023), _1763025)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1763021, tc_HOL_Obool)), hAPP(c_List_Oset(_1763021), _1763025)), hAPP(hAPP(c_Set_Oinsert(_1763021), _1763023), c_Orderings_Obot__class_Obot(tc_fun(_1763021, tc_HOL_Obool)))))], (35184 ^ _782476) ^ [_1447650] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1447650)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447650)))], (18430 ^ _782476) ^ [_1129918] : [class_Nat_Osemiring__char__0(_1129918), -(c_Fun_Oinj__on(tc_Nat_Onat, _1129918, c_Nat_Osemiring__1__class_Oof__nat(_1129918), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22898 ^ _782476) ^ [_1211863, _1211865] : [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), _1211863), _1211865))), 22901 ^ _782476 : [(22904 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211865)))], (22902 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211863)))]]], (336 ^ _782476) ^ [_787658, _787660, _787662, _787664] : [-(c_Nitpick_Owf_H(_787662, _787658)), c_Nitpick_Owf_H(_787664, _787660), _787664 = _787662, _787660 = _787658], (12980 ^ _782476) ^ [_1020583, _1020585, _1020587, _1020589, _1020591, _1020593] : [c_Fun_Oinj__on(_1020583, _1020585, _1020587, _1020589), -(hBOOL(hAPP(hAPP(c_member(_1020585), _1020591), hAPP(c_Set_Oimage(_1020583, _1020585, _1020587), _1020589)))), -(c_Fun_Oinj__on(_1020583, _1020585, c_Fun_Ofun__upd(_1020583, _1020585, _1020587, _1020593, _1020591), _1020589))], (23943 ^ _782476) ^ [_1231394, _1231396] : [-(hBOOL(hAPP(_1231394, hAPP(c_Int_Onat, _1231396)))), 23947 ^ _782476 : [(23950 ^ _782476) ^ [] : [hBOOL(hAPP(_1231394, 23946 ^ [_1231394, _1231396]))], (23948 ^ _782476) ^ [] : [-(_1231396 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23946 ^ [_1231394, _1231396]))]], 23951 ^ _782476 : [(23954 ^ _782476) ^ [] : [hBOOL(hAPP(_1231394, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23952 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231396), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (47070 ^ _782476) ^ [_1727455, _1727457, _1727459] : [47072 ^ _782476 : [(47075 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1727455), tc_List_Olist(_1727455), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1727455), tc_fun(tc_List_Olist(_1727455), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727455), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1727455), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727455), tc_HOL_Obool)), tc_List_Olist(_1727455)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1727455))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1727455)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1727455))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1727455)))), 47071 ^ [_1727455, _1727457, _1727459]))], (47073 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1727455), tc_List_Olist(_1727455))), 47071 ^ [_1727455, _1727457, _1727459]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1727455), tc_List_Olist(_1727455))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1727455), tc_List_Olist(_1727455)), _1727457), _1727459)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727455))), _1727457) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727455))), _1727459), 47080 ^ _782476 : [(47087 ^ _782476) ^ [] : [_1727457 = _1727459, -(c_List_Oconcat(_1727455, _1727457) = c_List_Oconcat(_1727455, _1727459))], (47081 ^ _782476) ^ [] : [c_List_Oconcat(_1727455, _1727457) = c_List_Oconcat(_1727455, _1727459), -(_1727457 = _1727459)]]], (4026 ^ _782476) ^ [_843297, _843299, _843301, _843303, _843305, _843307, _843309, _843311] : [-(c_New__DSequence_Opos__decr__bind(_843311, _843307, _843303, _843299) = c_New__DSequence_Opos__decr__bind(_843309, _843305, _843301, _843297)), _843311 = _843309, _843307 = _843305, _843303 = _843301, _843299 = _843297], (13464 ^ _782476) ^ [_1031875, _1031877] : [class_Enum_Oenum(_1031875), 13467 ^ _782476 : [(13474 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031875), _1031877)), -(hBOOL(hAPP(_1031877, 13477 ^ [_1031875, _1031877])))], (13468 ^ _782476) ^ [] : [13469 ^ _782476 : [(13470 ^ _782476) ^ [_1031977] : [hBOOL(hAPP(_1031877, _1031977))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031875), _1031877)))]]], (13280 ^ _782476) ^ [_1027698, _1027700, _1027702, _1027704] : [-(hBOOL(hAPP(hAPP(c_member(_1027698), _1027700), _1027702))), -(hAPP(c_Set_Ovimage(_1027704, _1027698, hAPP(c_COMBK(_1027698, _1027704), _1027700)), _1027702) = c_Orderings_Obot__class_Obot(tc_fun(_1027704, tc_HOL_Obool)))], (34438 ^ _782476) ^ [_1434304] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434304), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434304), c_Int_OPls)))], (23789 ^ _782476) ^ [_1228958, _1228960] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228958, _1228960) = 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), _1228958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228960))))], (46668 ^ _782476) ^ [_1719037, _1719039, _1719041, _1719043, _1719045, _1719047, _1719049] : [c_List_Olist__all2(_1719037, _1719039, _1719041, _1719043, hAPP(hAPP(c_List_Omap(_1719045, _1719039), _1719047), _1719049)), -(c_List_Olist__all2(_1719037, _1719045, hAPP(hAPP(c_COMBC(_1719037, tc_fun(_1719045, _1719039), tc_fun(_1719045, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719039, tc_HOL_Obool), tc_fun(tc_fun(_1719045, _1719039), tc_fun(_1719045, tc_HOL_Obool)), _1719037), c_COMBB(_1719039, tc_HOL_Obool, _1719045)), _1719041)), _1719047), _1719043, _1719049))], (35544 ^ _782476) ^ [_1454033, _1454035, _1454037] : [class_Groups_Omonoid__mult(_1454033), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1454033), _1454035), 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)))), _1454037)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1454033), hAPP(hAPP(c_Power_Opower__class_Opower(_1454033), _1454035), _1454037)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44372 ^ _782476) ^ [_1667320] : [-(c_List_Obutlast(_1667320, c_List_Olist_ONil(_1667320)) = c_List_Olist_ONil(_1667320))], (16451 ^ _782476) ^ [_1092312, _1092314, _1092316, _1092318] : [class_Groups_Ocancel__semigroup__add(_1092312), 16454 ^ _782476 : [(16461 ^ _782476) ^ [] : [_1092314 = _1092318, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092312), _1092314), _1092316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092312), _1092318), _1092316))], (16455 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092312), _1092314), _1092316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092312), _1092318), _1092316), -(_1092314 = _1092318)]]], (17652 ^ _782476) ^ [_1117151, _1117153, _1117155] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117151), _1117153)), _1117155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117151), _1117155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117153), _1117155)))], (46410 ^ _782476) ^ [] : [-(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))], (1128 ^ _782476) ^ [_799612, _799614, _799616, _799618, _799620, _799622] : [-(c_List_Oall__interval__nat(_799620, _799616, _799612)), c_List_Oall__interval__nat(_799622, _799618, _799614), _799622 = _799620, _799618 = _799616, _799614 = _799612], (37515 ^ _782476) ^ [_1496348, _1496350, _1496352, _1496354, _1496356] : [-(hAPP(c_Product__Type_Osnd(_1496348, _1496350), hAPP(c_Product__Type_Oapsnd(_1496352, _1496350, _1496348, _1496354), _1496356)) = hAPP(_1496354, hAPP(c_Product__Type_Osnd(_1496348, _1496352), _1496356)))], (52453 ^ _782476) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (9692 ^ _782476) ^ [_956352] : [class_Complete__Lattice_Ocomplete__lattice(_956352), -(c_Complete__Lattice_OInf__class_OInf(_956352, c_Orderings_Otop__class_Otop(tc_fun(_956352, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_956352))], (46440 ^ _782476) ^ [_1713371, _1713373] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1713371), _1713373) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713371)), hAPP(c_Code__Numeral_Onat__of, _1713373))))], (47766 ^ _782476) ^ [_1743014, _1743016, _1743018, _1743020, _1743022] : [class_Orderings_Olinorder(_1743014), c_List_Olinorder__class_Osorted(_1743014, hAPP(hAPP(c_List_Omap(_1743016, _1743014), _1743018), _1743020)), -(c_List_Olinorder__class_Osorted(_1743014, hAPP(hAPP(c_List_Omap(_1743016, _1743014), _1743018), hAPP(c_List_Ofilter(_1743016, _1743022), _1743020))))], (14300 ^ _782476) ^ [_1048848, _1048850, _1048852] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048848, tc_HOL_Obool)), _1048850), _1048852)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048848), _1048850)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048848), _1048852))], (47144 ^ _782476) ^ [_1729955, _1729957, _1729959] : [hAPP(c_List_Ofilter(_1729955, _1729957), _1729959) = c_List_Olist_ONil(_1729955), 47147 ^ _782476 : [(47148 ^ _782476) ^ [_1730052] : [hBOOL(hAPP(hAPP(c_member(_1729955), _1730052), hAPP(c_List_Oset(_1729955), _1729959))), hBOOL(hAPP(_1729957, _1730052))]]], (26090 ^ _782476) ^ [_1275916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275916), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275916)))], (9985 ^ _782476) ^ [_962513, _962515, _962517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962513, tc_HOL_Obool)), _962515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962513, tc_HOL_Obool)), _962517))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962513, tc_HOL_Obool)), _962515), _962517) = c_Orderings_Obot__class_Obot(tc_fun(_962513, tc_HOL_Obool)))], (7798 ^ _782476) ^ [_914609, _914611, _914613] : [class_Lattices_Osemilattice__sup(_914609), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914609), _914611), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914609), _914611), _914613)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914609), _914611), _914613))], (11602 ^ _782476) ^ [_994204, _994206, _994208] : [class_Orderings_Olinorder(_994204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994204), _994206), _994208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994204), _994208), _994206))], (10861 ^ _782476) ^ [_982418, _982420, _982422, _982424, _982426] : [_982418 = c_Orderings_Obot__class_Obot(tc_fun(_982420, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982422, tc_HOL_Obool)), _982424), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982420, tc_fun(_982422, tc_HOL_Obool)), _982418), _982426)) = _982424)], (45226 ^ _782476) ^ [_1687571, _1687573, _1687575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687573)), _1687575))), -(hAPP(hAPP(c_List_Olist_OCons(_1687573), hAPP(hAPP(c_List_Onth(_1687573), _1687575), _1687571)), hAPP(hAPP(c_List_Odrop(_1687573), hAPP(c_Nat_OSuc, _1687571)), _1687575)) = hAPP(hAPP(c_List_Odrop(_1687573), _1687571), _1687575))], (36368 ^ _782476) ^ [] : [-(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))], (52533 ^ _782476) ^ [_1842031] : [class_Enum_Oenum(_1842031), -(class_Enum_Oenum(tc_Option_Ooption(_1842031)))], (37698 ^ _782476) ^ [_1499983, _1499985, _1499987, _1499989] : [_1499983 = _1499985, 37701 ^ _782476 : [(37704 ^ _782476) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1499987, _1499989), _1499983) = hAPP(c_Product__Type_Osnd(_1499987, _1499989), _1499985))], (37702 ^ _782476) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1499987, _1499989), _1499983) = hAPP(c_Product__Type_Ofst(_1499987, _1499989), _1499985))]]], (25825 ^ _782476) ^ [_1267603, _1267605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267603), _1267605)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1267603, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1267603, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267603, tc_HOL_Obool), tc_fun(_1267603, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267603, tc_HOL_Obool))), _1267605)))))], (7097 ^ _782476) ^ [_899860, _899862, _899864] : [hBOOL(hAPP(c_Predicate_OPowp(_899860, hAPP(hAPP(c_COMBC(_899860, tc_fun(_899860, tc_HOL_Obool), tc_HOL_Obool), c_member(_899860)), _899862)), _899864)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_899860, tc_HOL_Obool)), _899864), hAPP(c_Set_OPow(_899860), _899862))))], (41777 ^ _782476) ^ [_1603406, _1603408, _1603410] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1603406, _1603406, _1603406), _1603408), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603406, _1603406), tc_HOL_Obool), _1603410), _1603408)) = hAPP(hAPP(c_Relation_Orel__comp(_1603406, _1603406, _1603406), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603406, _1603406), tc_HOL_Obool), _1603410), _1603408)), _1603408))], (30006 ^ _782476) ^ [_1351782, _1351784, _1351786] : [class_Fields_Olinordered__field(_1351782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351782), c_Groups_Ozero__class_Ozero(_1351782)), _1351784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351782), c_Groups_Ozero__class_Ozero(_1351782)), _1351786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351782), c_Groups_Ozero__class_Ozero(_1351782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351782), _1351784), _1351786))))], (48104 ^ _782476) ^ [_1749973, _1749975, _1749977, _1749979] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749973)), _1749975) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749977)), _1749979), -(hAPP(hAPP(c_List_Ozip(_1749973, _1749977), hAPP(c_List_Orev(_1749973), _1749975)), hAPP(c_List_Orev(_1749977), _1749979)) = hAPP(c_List_Orev(tc_prod(_1749973, _1749977)), hAPP(hAPP(c_List_Ozip(_1749973, _1749977), _1749975), _1749979)))], (10649 ^ _782476) ^ [_977350, _977352, _977354, _977356] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977350, tc_HOL_Obool)), _977352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977350, tc_HOL_Obool)), _977354), _977356)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977350, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977350, tc_HOL_Obool)), _977352), _977354)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977350, tc_HOL_Obool)), _977352), _977356)))], (49810 ^ _782476) ^ [_1788186, _1788188, _1788190] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788186, _1788186, hAPP(hAPP(c_COMBB(tc_fun(_1788186, tc_HOL_Obool), tc_fun(_1788186, tc_HOL_Obool), _1788186), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788186), c_fNot)), c_fequal)), _1788188), _1788190)), _1788188 = _1788190], (22435 ^ _782476) ^ [_1203409, _1203411] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203409), _1203411) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22440 ^ _782476 : [(22443 ^ _782476) ^ [] : [-(_1203411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22441 ^ _782476) ^ [] : [-(_1203409 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 22444 ^ _782476 : [(22447 ^ _782476) ^ [] : [-(_1203411 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22445 ^ _782476) ^ [] : [-(_1203409 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43864 ^ _782476) ^ [_1657015, _1657017, _1657019, _1657021] : [-(hAPP(hAPP(c_List_Olist__update(_1657015, hAPP(hAPP(c_List_Olist_OCons(_1657015), _1657017), _1657019)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657021) = hAPP(hAPP(c_List_Olist_OCons(_1657015), _1657021), _1657019))], (24729 ^ _782476) ^ [_1244719, _1244721] : [-(hBOOL(hAPP(_1244719, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1244719, _1244721)), 24737 ^ _782476 : [(24740 ^ _782476) ^ [_1244957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244957), 24736 ^ [_1244719, _1244721])), hBOOL(hAPP(_1244719, _1244957))], (24746 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1244719, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24736 ^ [_1244719, _1244721]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (24738 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24736 ^ [_1244719, _1244721]), _1244721)))]]], (29252 ^ _782476) ^ [_1337755, _1337757, _1337759, _1337761] : [class_Rings_Olinordered__semidom(_1337755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337755), _1337757), _1337759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337755), c_Groups_Ozero__class_Ozero(_1337755)), _1337757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337755), hAPP(hAPP(c_Power_Opower__class_Opower(_1337755), _1337757), _1337761)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337755), _1337759), _1337761))))], (17860 ^ _782476) ^ [_1120946, _1120948, _1120950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120946), _1120948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120950), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120948), _1120950)), _1120946))))], (24491 ^ _782476) ^ [_1240686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240686), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1240686 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 24494 ^ [_1240686]))))], (13026 ^ _782476) ^ [_1021527, _1021529, _1021531, _1021533, _1021535] : [-(c_Fun_Oinj__on(_1021527, _1021529, _1021531, hAPP(hAPP(c_Set_Oinsert(_1021527), _1021533), _1021535))), c_Fun_Oinj__on(_1021527, _1021529, _1021531, _1021535), -(hBOOL(hAPP(hAPP(c_member(_1021529), hAPP(_1021531, _1021533)), hAPP(c_Set_Oimage(_1021527, _1021529, _1021531), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021527, tc_HOL_Obool)), _1021535), hAPP(hAPP(c_Set_Oinsert(_1021527), _1021533), c_Orderings_Obot__class_Obot(tc_fun(_1021527, tc_HOL_Obool))))))))], (824 ^ _782476) ^ [_795086, _795088, _795090, _795092, _795094, _795096] : [-(c_List_Oall__interval__int(_795094, _795090, _795086)), c_List_Oall__interval__int(_795096, _795092, _795088), _795096 = _795094, _795092 = _795090, _795088 = _795086], (29266 ^ _782476) ^ [_1338024, _1338026, _1338028] : [class_Rings_Olinordered__semidom(_1338024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338024), c_Groups_Ozero__class_Ozero(_1338024)), _1338026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338024), c_Groups_Ozero__class_Ozero(_1338024)), hAPP(hAPP(c_Power_Opower__class_Opower(_1338024), _1338026), _1338028))))], (25612 ^ _782476) ^ [_1261498, _1261500, _1261502, _1261504] : [-(hBOOL(hAPP(hAPP(c_member(_1261498), _1261500), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261498, tc_HOL_Obool)), _1261502), hAPP(c_Set_OCollect(_1261498), _1261504))))), hBOOL(hAPP(hAPP(c_member(_1261498), _1261500), _1261502)), hBOOL(hAPP(_1261504, _1261500))], (45276 ^ _782476) ^ [_1688995, _1688997, _1688999] : [-(_1688995 = c_List_Olist_ONil(_1688997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688999), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688997)), _1688995))), -(hAPP(c_List_Ohd(_1688997), hAPP(hAPP(c_List_Odrop(_1688997), _1688999), _1688995)) = hAPP(hAPP(c_List_Onth(_1688997), _1688995), _1688999))], (51669 ^ _782476) ^ [_1829471] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829471), _1829471)))], (45422 ^ _782476) ^ [_1691591, _1691593] : [class_Lattices_Oab__semigroup__idem__mult(_1691591), -(_1691593 = c_List_Olist_ONil(_1691591)), -(hAPP(c_Finite__Set_Ofold1(_1691591, c_Groups_Otimes__class_Otimes(_1691591)), hAPP(c_List_Oset(_1691591), _1691593)) = hAPP(c_List_Ofoldl(_1691591, _1691591, c_Groups_Otimes__class_Otimes(_1691591), hAPP(c_List_Ohd(_1691591), _1691593)), hAPP(c_List_Otl(_1691591), _1691593)))], (52467 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (47395 ^ _782476) ^ [_1736437, _1736439, _1736441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736437), _1736439)), _1736441)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1736439), c_List_Oupt(_1736437, _1736441)) = c_List_Oupt(_1736437, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736437), _1736439)))], (24857 ^ _782476) ^ [_1247112, _1247114, _1247116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247116), 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), _1247116), _1247114))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247112)))))], (47220 ^ _782476) ^ [_1731469, _1731471, _1731473] : [-(c_List_Opartition(_1731469, _1731471, _1731473) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731469), tc_List_Olist(_1731469)), hAPP(c_List_Ofilter(_1731469, _1731471), _1731473)), hAPP(c_List_Ofilter(_1731469, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731469, c_fNot), _1731471)), _1731473)))], (42848 ^ _782476) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33046 ^ _782476) ^ [_1408821, _1408823, _1408825, _1408827] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408821), _1408823), _1408825)), hAPP(c_Int_Onumber__class_Onumber__of(_1408821), _1408827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408821), _1408823), hAPP(c_Int_Onumber__class_Onumber__of(_1408821), _1408827))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408821), _1408825), hAPP(c_Int_Onumber__class_Onumber__of(_1408821), _1408827)))), class_Int_Onumber(_1408821), class_Rings_Osemiring(_1408821)], (10775 ^ _782476) ^ [_980119, _980121, _980123, _980125, _980127] : [_980119 = c_Orderings_Obot__class_Obot(tc_fun(_980121, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980121, tc_fun(_980123, tc_HOL_Obool)), _980119), hAPP(hAPP(c_COMBB(tc_fun(_980123, tc_HOL_Obool), tc_fun(_980123, tc_HOL_Obool), _980121), hAPP(c_Set_Oinsert(_980123), _980125)), _980127)) = c_Orderings_Obot__class_Obot(tc_fun(_980123, tc_HOL_Obool)))], (43703 ^ _782476) ^ [_1653203, _1653205, _1653207, _1653209, _1653211, _1653213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653203, _1653205)), hAPP(hAPP(c_Product__Type_OPair(_1653203, _1653205), _1653207), _1653209)), hAPP(c_List_Oset(tc_prod(_1653203, _1653205)), hAPP(hAPP(c_List_Ozip(_1653203, _1653205), _1653211), _1653213)))), 43706 ^ _782476 : [(43709 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653205), _1653209), hAPP(c_List_Oset(_1653205), _1653213))))], (43707 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653203), _1653207), hAPP(c_List_Oset(_1653203), _1653211))))]]], (49514 ^ _782476) ^ [_1781073, _1781075, _1781077, _1781079, _1781081] : [c_Fun_Oinj__on(_1781073, _1781075, _1781077, c_Orderings_Otop__class_Otop(tc_fun(_1781073, tc_HOL_Obool))), hAPP(_1781077, _1781079) = _1781081, -(hAPP(c_Hilbert__Choice_Oinv__into(_1781073, _1781075, c_Orderings_Otop__class_Otop(tc_fun(_1781073, tc_HOL_Obool)), _1781077), _1781081) = _1781079)], (35568 ^ _782476) ^ [_1454452] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454452)), 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, _1454452, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (30839 ^ _782476) ^ [_1367096, _1367098, _1367100] : [class_Orderings_Olinorder(_1367096), hAPP(_1367098, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367096), 30844 ^ [_1367096, _1367098, _1367100]), 30845 ^ [_1367096, _1367098, _1367100])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367096), hAPP(_1367098, 30844 ^ [_1367096, _1367098, _1367100])), hAPP(_1367098, 30845 ^ [_1367096, _1367098, _1367100])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367096), _1367100)), -(_1367100 = c_Orderings_Obot__class_Obot(tc_fun(_1367096, tc_HOL_Obool))), -(hAPP(_1367098, c_Big__Operators_Olattice_OInf__fin(_1367096, c_Orderings_Oord__class_Omin(_1367096), _1367100)) = c_Big__Operators_Olattice_OInf__fin(_1367096, c_Orderings_Oord__class_Omin(_1367096), hAPP(c_Set_Oimage(_1367096, _1367096, _1367098), _1367100)))], (30903 ^ _782476) ^ [_1368204, _1368206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368204), 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)), _1368206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368204), _1368206)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52157 ^ _782476) ^ [_1838259, _1838261] : [-(class_Finite__Set_Ofinite(tc_fun(_1838259, _1838261))), class_Finite__Set_Ofinite(_1838259), class_Finite__Set_Ofinite(_1838261)], (44514 ^ _782476) ^ [_1670449, _1670451, _1670453] : [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), _1670449), _1670451))), -(hBOOL(hAPP(hAPP(_1670453, _1670449), _1670451))), 44521 ^ _782476 : [(44524 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 44519 ^ [_1670449, _1670451, _1670453]), 44520 ^ [_1670449, _1670451, _1670453])), -(hBOOL(hAPP(hAPP(_1670453, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 44519 ^ [_1670449, _1670451, _1670453]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 44520 ^ [_1670449, _1670451, _1670453])))], (44530 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1670453, 44519 ^ [_1670449, _1670451, _1670453]), 44520 ^ [_1670449, _1670451, _1670453]))], (44522 ^ _782476) ^ [] : [-(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), 44519 ^ [_1670449, _1670451, _1670453]), 44520 ^ [_1670449, _1670451, _1670453]))))]]], (22995 ^ _782476) ^ [_1213763, _1213765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213763), hAPP(c_Nat_OSuc, _1213765))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213763, hAPP(c_Nat_OSuc, _1213765)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213765)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213763, _1213765)))], (36120 ^ _782476) ^ [] : [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)], (6798 ^ _782476) ^ [_892999, _893001, _893003, _893005, _893007] : [6800 ^ _782476 : [(6803 ^ _782476) ^ [] : [hBOOL(hAPP(_893007, 6799 ^ [_892999, _893001, _893003, _893005, _893007]))], (6801 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_892999), 6799 ^ [_892999, _893001, _893003, _893005, _893007]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893001, tc_fun(_892999, tc_HOL_Obool)), _893003), _893005))))]], 6804 ^ _782476 : [(6805 ^ _782476) ^ [_893221] : [hBOOL(hAPP(hAPP(c_member(_893001), _893221), _893003)), 6808 ^ _782476 : [(6809 ^ _782476) ^ [_893318] : [hBOOL(hAPP(hAPP(c_member(_892999), _893318), hAPP(_893005, _893221))), -(hBOOL(hAPP(_893007, _893318)))]]]]], (31876 ^ _782476) ^ [_1386055, _1386057, _1386059, _1386061] : [class_Divides_Osemiring__div(_1386055), -(c_Divides_Odiv__class_Omod(_1386055, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386055), _1386057), c_Divides_Odiv__class_Omod(_1386055, _1386059, _1386061)), _1386061) = c_Divides_Odiv__class_Omod(_1386055, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386055), _1386057), _1386059), _1386061))], (32145 ^ _782476) ^ [_1391292, _1391294, _1391296] : [class_Divides_Osemiring__div(_1391292), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391292), _1391294), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391292), _1391296), _1391294))), c_Divides_Odiv__class_Omod(_1391292, _1391296, _1391294)) = _1391296)], (7734 ^ _782476) ^ [_913204, _913206, _913208, _913210] : [hBOOL(hAPP(hAPP(c_member(_913204), _913206), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913204, tc_HOL_Obool)), _913208), _913210))), -(hBOOL(hAPP(hAPP(c_member(_913204), _913206), _913208))), -(hBOOL(hAPP(hAPP(c_member(_913204), _913206), _913210)))], (28616 ^ _782476) ^ [_1325483, _1325485, _1325487, _1325489, _1325491] : [class_Groups_Ocomm__monoid__mult(_1325483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325485), _1325487)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325485), _1325489)), 28630 ^ _782476 : [(28633 ^ _782476) ^ [] : [hAPP(_1325491, 28629 ^ [_1325483, _1325485, _1325487, _1325489, _1325491]) = c_Groups_Oone__class_Oone(_1325483)], (28631 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325485), 28629 ^ [_1325483, _1325485, _1325487, _1325489, _1325491]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325485, tc_HOL_Obool)), _1325487), _1325489))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325485, _1325483), _1325491), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325485, tc_HOL_Obool)), _1325487), _1325489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325483), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325485, _1325483), _1325491), _1325487)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325485, _1325483), _1325491), _1325489)))], (13864 ^ _782476) ^ [_1039783, _1039785, _1039787] : [c_Fun_Obij__betw(_1039783, _1039785, _1039787, c_Orderings_Otop__class_Otop(tc_fun(_1039783, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039785, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039783, _1039785, _1039787), c_Orderings_Otop__class_Otop(tc_fun(_1039783, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039785, tc_HOL_Obool)))], (35260 ^ _782476) ^ [_1448875, _1448877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448875)), c_Int_OBit1(_1448877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448875), _1448877)))], (18954 ^ _782476) ^ [_1139332, _1139334] : [class_Groups_Olinordered__ab__group__add(_1139332), 18957 ^ _782476 : [(18964 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139332), _1139334), c_Groups_Ozero__class_Ozero(_1139332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139332), _1139334), _1139334)), c_Groups_Ozero__class_Ozero(_1139332))))], (18958 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139332), _1139334), _1139334)), c_Groups_Ozero__class_Ozero(_1139332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139332), _1139334), c_Groups_Ozero__class_Ozero(_1139332))))]]], (31227 ^ _782476) ^ [_1373324, _1373326, _1373328, _1373330] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373324, _1373326, _1373328), _1373330), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1373326)], (39792 ^ _782476) ^ [_1553011, _1553013, _1553015, _1553017, _1553019] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553011, _1553013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553011, tc_HOL_Obool)), _1553015), _1553017)), _1553019) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553011, _1553013), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553011, _1553013), _1553015), _1553019)), hAPP(hAPP(c_Product__Type_OSigma(_1553011, _1553013), _1553017), _1553019)))], (21103 ^ _782476) ^ [_1179125, _1179127, _1179129, _1179131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179125), _1179127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179129), _1179131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179125), _1179129)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179127), _1179131))))], (17459 ^ _782476) ^ [_1113612, _1113614, _1113616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113612), _1113614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113616), _1113614))))], (41154 ^ _782476) ^ [_1588389, _1588391] : [-(c_Transitive__Closure_Ortrancl(_1588389, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588389, _1588389), tc_HOL_Obool)), _1588391), c_Relation_OId(_1588389))) = c_Transitive__Closure_Ortrancl(_1588389, _1588391))], (45412 ^ _782476) ^ [_1691380, _1691382, _1691384] : [-(hAPP(c_List_Otl(_1691380), hAPP(hAPP(c_List_Otake(_1691380), _1691382), _1691384)) = hAPP(hAPP(c_List_Otake(_1691380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1691382), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1691380), _1691384)))], (49675 ^ _782476) ^ [_1784873, _1784875, _1784877, _1784879, _1784881, _1784883, _1784885] : [c_Fun_Oinj__on(_1784873, _1784875, _1784877, hAPP(c_Set_Oimage(_1784879, _1784873, _1784881), _1784883)), c_Fun_Oinj__on(_1784879, _1784873, _1784881, _1784883), hBOOL(hAPP(hAPP(c_member(_1784875), _1784885), hAPP(c_Set_Oimage(_1784873, _1784875, _1784877), hAPP(c_Set_Oimage(_1784879, _1784873, _1784881), _1784883)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784879, _1784875, _1784883, hAPP(c_Fun_Ocomp(_1784873, _1784875, _1784879, _1784877), _1784881)), _1784885) = hAPP(hAPP(c_Fun_Ocomp(_1784873, _1784879, _1784875, c_Hilbert__Choice_Oinv__into(_1784879, _1784873, _1784883, _1784881)), c_Hilbert__Choice_Oinv__into(_1784873, _1784875, hAPP(c_Set_Oimage(_1784879, _1784873, _1784881), _1784883), _1784877)), _1784885))], (5670 ^ _782476) ^ [_869307, _869309, _869311, _869313, _869315, _869317] : [-(c_COMBB(_869317, _869313, _869309) = c_COMBB(_869315, _869311, _869307)), _869317 = _869315, _869313 = _869311, _869309 = _869307], (18524 ^ _782476) ^ [_1131519, _1131521] : [class_Groups_Olinordered__ab__group__add(_1131519), 18527 ^ _782476 : [(18534 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131519), _1131521), c_Groups_Ozero__class_Ozero(_1131519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131519), _1131521), _1131521)), c_Groups_Ozero__class_Ozero(_1131519))))], (18528 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131519), _1131521), _1131521)), c_Groups_Ozero__class_Ozero(_1131519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131519), _1131521), c_Groups_Ozero__class_Ozero(_1131519))))]]], (45865 ^ _782476) ^ [_1700190, _1700192, _1700194] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700190)), _1700192), c_List_Olists(_1700190, _1700194)))), 45866 ^ _782476 : [(45869 ^ _782476) ^ [_1700318, _1700320] : [_1700192 = hAPP(hAPP(c_List_Olist_OCons(_1700190), _1700320), _1700318), hBOOL(hAPP(hAPP(c_member(_1700190), _1700320), _1700194)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700190)), _1700318), c_List_Olists(_1700190, _1700194)))], (45867 ^ _782476) ^ [] : [_1700192 = c_List_Olist_ONil(_1700190)]]], (30865 ^ _782476) ^ [_1367623, _1367625] : [class_Divides_Osemiring__div(_1367623), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367623), c_Groups_Ozero__class_Ozero(_1367623)), _1367625) = c_Groups_Ozero__class_Ozero(_1367623))], (34318 ^ _782476) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (34826 ^ _782476) ^ [_1440549] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1440549)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440549) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50845 ^ _782476) ^ [_1811629, _1811631] : [c_Relation_Oantisym(_1811629, hAPP(c_Relation_Oconverse(_1811629, _1811629), _1811631)), -(c_Relation_Oantisym(_1811629, _1811631))], (25759 ^ _782476) ^ [_1266120, _1266122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266120), _1266122)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1266120, 25762 ^ [_1266120, _1266122], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1266120), _1266122)), _1266122))], (8098 ^ _782476) ^ [_920429, _920431, _920433, _920435] : [hBOOL(hAPP(hAPP(c_member(_920429), _920431), _920433)), -(hBOOL(hAPP(hAPP(c_member(_920429), _920431), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920429, tc_HOL_Obool)), _920435), _920433))))], (3528 ^ _782476) ^ [_835190, _835192] : [_835192 = _835190, -(c_SetInterval_Oord__class_OlessThan(_835192) = c_SetInterval_Oord__class_OlessThan(_835190))], (22694 ^ _782476) ^ [_1208192, _1208194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1208192), _1208194))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208192), _1208194)))], (6792 ^ _782476) ^ [_892618, _892620, _892622, _892624, _892626, _892628] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892618, tc_fun(_892620, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892622, tc_fun(_892618, tc_HOL_Obool)), _892624), _892626)), _892628) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892622, tc_fun(_892620, tc_HOL_Obool)), _892624), hAPP(hAPP(c_COMBC(_892622, tc_fun(_892618, tc_fun(_892620, tc_HOL_Obool)), tc_fun(_892620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892618, tc_HOL_Obool), tc_fun(tc_fun(_892618, tc_fun(_892620, tc_HOL_Obool)), tc_fun(_892620, tc_HOL_Obool)), _892622), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892618, tc_fun(_892620, tc_HOL_Obool))), _892626)), _892628)))], (25558 ^ _782476) ^ [_1259987, _1259989, _1259991] : [hBOOL(hAPP(hAPP(c_member(_1259987), _1259989), hAPP(c_Set_OCollect(_1259987), _1259991))), -(hBOOL(hAPP(_1259991, _1259989)))], (9181 ^ _782476) ^ [_945390, _945392, _945394, _945396] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945390, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945390, tc_HOL_Obool)), _945392), _945394)), _945396) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945390, tc_HOL_Obool)), _945392), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945390, tc_HOL_Obool)), _945394), _945396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945390, tc_HOL_Obool)), _945396), _945392)))], (23113 ^ _782476) ^ [_1216424, _1216426, _1216428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216424), _1216426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216424, tc_HOL_Obool)), _1216428), _1216426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216424), _1216428)), hAPP(c_Finite__Set_Ocard(_1216424), _1216426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1216424, tc_HOL_Obool)), _1216428), _1216426)))], (21435 ^ _782476) ^ [_1184805] : [-(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), _1184805))))], (4424 ^ _782476) ^ [_849638, _849640] : [_849640 = _849638, -(c_List_Odrop(_849640) = c_List_Odrop(_849638))], (24666 ^ _782476) ^ [_1243636, _1243638] : [class_Rings_Olinordered__idom(_1243636), 24669 ^ _782476 : [(24676 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243636), c_Groups_Ozero__class_Ozero(_1243636)), hAPP(c_Int_Oring__1__class_Oof__int(_1243636), _1243638))))], (24670 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243636), c_Groups_Ozero__class_Ozero(_1243636)), hAPP(c_Int_Oring__1__class_Oof__int(_1243636), _1243638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243638)))]]], (10115 ^ _782476) ^ [_965410, _965412, _965414, _965416] : [hBOOL(hAPP(hAPP(c_member(_965410), _965412), _965414)), -(hBOOL(hAPP(hAPP(c_member(_965410), _965412), _965416))), -(hBOOL(hAPP(hAPP(c_member(_965410), _965412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965410, tc_HOL_Obool)), _965414), _965416))))], (29070 ^ _782476) ^ [_1334435, _1334437, _1334439, _1334441] : [class_Rings_Olinordered__semidom(_1334435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334435), _1334437), _1334439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334435), c_Groups_Ozero__class_Ozero(_1334435)), _1334437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1334441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334435), hAPP(hAPP(c_Power_Opower__class_Opower(_1334435), _1334437), _1334441)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334435), _1334439), _1334441))))], (50857 ^ _782476) ^ [_1811805] : [-(c_Relation_Oantisym(_1811805, c_Relation_OId(_1811805)))], (39608 ^ _782476) ^ [_1547362, _1547364] : [-(hAPP(c_Relation_ODomain(_1547362, _1547364), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547362, _1547364), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1547362, tc_HOL_Obool)))], (28766 ^ _782476) ^ [_1328893, _1328895, _1328897, _1328899] : [class_Rings_Odivision__ring(_1328893), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328893), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328893), _1328895), _1328897)), _1328899) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328893), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328893), _1328895), _1328899)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328893), _1328897), _1328899)))], (22104 ^ _782476) ^ [_1197969, _1197971] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197969), _1197971))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197969), hAPP(c_Nat_OSuc, _1197971))), -(_1197971 = _1197969)], (21975 ^ _782476) ^ [_1195889, _1195891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195889), _1195891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195889)), hAPP(c_Nat_OSuc, _1195891))))], (10817 ^ _782476) ^ [_981217, _981219, _981221] : [class_Complete__Lattice_Ocomplete__lattice(_981217), -(c_Complete__Lattice_OSup__class_OSup(_981217, hAPP(hAPP(c_Set_Oinsert(_981217), _981219), hAPP(hAPP(c_Set_Oinsert(_981217), _981221), c_Orderings_Obot__class_Obot(tc_fun(_981217, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_981217), _981219), _981221))], (25105 ^ _782476) ^ [_1251676, _1251678, _1251680] : [class_Groups_Oordered__ab__group__add__abs(_1251676), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251676), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251676), hAPP(c_Groups_Oabs__class_Oabs(_1251676), _1251678)), hAPP(c_Groups_Oabs__class_Oabs(_1251676), _1251680))), hAPP(c_Groups_Oabs__class_Oabs(_1251676), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251676), _1251678), _1251680)))))], (40861 ^ _782476) ^ [_1581052, _1581054, _1581056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581052), _1581054)), -(c_Random_Ominus__shift(_1581056, _1581052, _1581054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581056), _1581052)), _1581054))], (27096 ^ _782476) ^ [_1294758, _1294760, _1294762] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1294758), _1294760), _1294762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1294758), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294758, tc_Int_Oint), _1294760), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1294762))), class_Groups_Ocomm__monoid__add(_1294758), class_Groups_Ocomm__monoid__mult(_1294758)], (15202 ^ _782476) ^ [_1066704, _1066706, _1066708] : [class_Lattices_Olattice(_1066704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066704), _1066706)), hBOOL(hAPP(hAPP(c_member(_1066704), _1066708), _1066706)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066704), _1066708), c_Big__Operators_Olattice__class_OSup__fin(_1066704, _1066706)) = c_Big__Operators_Olattice__class_OSup__fin(_1066704, _1066706))], (40867 ^ _782476) ^ [_1581167, _1581169, _1581171] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581167), _1581169))), -(c_Random_Ominus__shift(_1581171, _1581167, _1581169) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1581167), _1581169))], (6183 ^ _782476) ^ [_880654, _880656, _880658] : [class_Orderings_Olinorder(_880654), 6186 ^ _782476 : [(6193 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880654), _880656), _880658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880654, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880654), _880656)), hAPP(c_SetInterval_Oord__class_OlessThan(_880654), _880658))))], (6187 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880654, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880654), _880656)), hAPP(c_SetInterval_Oord__class_OlessThan(_880654), _880658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880654), _880656), _880658)))]]], (15126 ^ _782476) ^ [_1065090, _1065092, _1065094, _1065096, _1065098, _1065100] : [c_Finite__Set_Ofolding__idem(_1065090, _1065092, _1065094, _1065096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065090), _1065098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1065090, tc_HOL_Obool)), _1065100), _1065098)), -(hAPP(c_Fun_Ocomp(_1065092, _1065092, _1065092, hAPP(_1065096, _1065098)), hAPP(_1065096, _1065100)) = hAPP(_1065096, _1065098))], (41324 ^ _782476) ^ [_1592366, _1592368, _1592370, _1592372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592366, _1592366)), hAPP(hAPP(c_Product__Type_OPair(_1592366, _1592366), _1592368), _1592370)), c_Transitive__Closure_Ortrancl(_1592366, _1592372))), hBOOL(hAPP(hAPP(c_member(_1592366), _1592370), c_Wellfounded_Oacc(_1592366, _1592372))), -(hBOOL(hAPP(hAPP(c_member(_1592366), _1592368), c_Wellfounded_Oacc(_1592366, _1592372))))], (31415 ^ _782476) ^ [_1376828, _1376830, _1376832] : [class_Orderings_Olinorder(_1376828), hAPP(_1376830, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376828), 31420 ^ [_1376828, _1376830, _1376832]), 31421 ^ [_1376828, _1376830, _1376832])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376828), hAPP(_1376830, 31420 ^ [_1376828, _1376830, _1376832])), hAPP(_1376830, 31421 ^ [_1376828, _1376830, _1376832])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376828), _1376832)), -(_1376832 = c_Orderings_Obot__class_Obot(tc_fun(_1376828, tc_HOL_Obool))), -(hAPP(_1376830, c_Big__Operators_Olinorder__class_OMin(_1376828, _1376832)) = c_Big__Operators_Olinorder__class_OMin(_1376828, hAPP(c_Set_Oimage(_1376828, _1376828, _1376830), _1376832)))], (41750 ^ _782476) ^ [_1602903, _1602905] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602903, _1602903)), hAPP(hAPP(c_Product__Type_OPair(_1602903, _1602903), 41751 ^ [_1602903, _1602905]), 41751 ^ [_1602903, _1602905])), c_Transitive__Closure_Otrancl(_1602903, _1602905)))), -(c_Wellfounded_Oacyclic(_1602903, _1602905))], (16117 ^ _782476) ^ [_1084878, _1084880, _1084882, _1084884, _1084886] : [class_Groups_Ocomm__monoid__mult(_1084878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084880), _1084882)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084878, _1084880, c_Groups_Otimes__class_Otimes(_1084878)), hAPP(hAPP(c_COMBS(_1084880, _1084878, _1084878), hAPP(hAPP(c_COMBB(_1084878, tc_fun(_1084878, _1084878), _1084880), c_Groups_Otimes__class_Otimes(_1084878)), _1084884)), _1084886)), c_Groups_Oone__class_Oone(_1084878)), _1084882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084878), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084878, _1084880, c_Groups_Otimes__class_Otimes(_1084878)), _1084884), c_Groups_Oone__class_Oone(_1084878)), _1084882)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084878, _1084880, c_Groups_Otimes__class_Otimes(_1084878)), _1084886), c_Groups_Oone__class_Oone(_1084878)), _1084882)))], (46960 ^ _782476) ^ [_1725143, _1725145] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725143)), c_List_Oremdups(_1725143, _1725145)) = hAPP(c_Finite__Set_Ocard(_1725143), hAPP(c_List_Oset(_1725143), _1725145)))], (35266 ^ _782476) ^ [_1448976, _1448978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448976), _1448978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448976)), c_Int_OBit1(_1448978))))], (45204 ^ _782476) ^ [_1686983, _1686985, _1686987, _1686989, _1686991] : [-(hAPP(hAPP(c_List_Oappend(_1686983), _1686985), _1686987) = hAPP(hAPP(c_List_Oappend(_1686983), _1686989), _1686991)), 45207 ^ _782476 : [(45210 ^ _782476) ^ [] : [_1686985 = hAPP(hAPP(c_List_Otake(_1686983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686985)), _1686989), _1686987 = hAPP(hAPP(c_List_Oappend(_1686983), hAPP(hAPP(c_List_Odrop(_1686983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686985)), _1686989)), _1686991)], (45208 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686985)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686989))))]], 45215 ^ _782476 : [(45218 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Otake(_1686983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686989)), _1686985) = _1686989, hAPP(hAPP(c_List_Oappend(_1686983), hAPP(hAPP(c_List_Odrop(_1686983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686989)), _1686985)), _1686987) = _1686991], (45216 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686985)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686983)), _1686989)))]]], (47788 ^ _782476) ^ [_1743479, _1743481, _1743483] : [class_Orderings_Olinorder(_1743479), 47791 ^ _782476 : [(47804 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743479, hAPP(hAPP(c_List_Olist_OCons(_1743479), _1743481), _1743483))), c_List_Olinorder__class_Osorted(_1743479, _1743483), 47810 ^ _782476 : [(47813 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743479), _1743481), 47809 ^ [_1743479, _1743481, _1743483]))], (47811 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743479), 47809 ^ [_1743479, _1743481, _1743483]), hAPP(c_List_Oset(_1743479), _1743483))))]]], (47792 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1743479, hAPP(hAPP(c_List_Olist_OCons(_1743479), _1743481), _1743483)), 47795 ^ _782476 : [(47798 ^ _782476) ^ [_1743665] : [hBOOL(hAPP(hAPP(c_member(_1743479), _1743665), hAPP(c_List_Oset(_1743479), _1743483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743479), _1743481), _1743665)))], (47796 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743479, _1743483))]]]]], (8597 ^ _782476) ^ [_931870, _931872, _931874] : [class_Lattices_Osemilattice__inf(_931870), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931870), _931872), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931870), _931872), _931874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931870), _931872), _931874))], (9514 ^ _782476) ^ [_953029, _953031] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_953029, _953031, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_953029), tc_HOL_Obool))))], (21415 ^ _782476) ^ [_1184525, _1184527] : [_1184525 = _1184527, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184525) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184527))], (2724 ^ _782476) ^ [_822724, _822726, _822728, _822730] : [-(c_Predicate_OPowp(_822730, _822726) = c_Predicate_OPowp(_822728, _822724)), _822730 = _822728, _822726 = _822724], (22308 ^ _782476) ^ [_1201410] : [-(hAPP(c_Finite__Set_Ocard(_1201410), c_Orderings_Obot__class_Obot(tc_fun(_1201410, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36428 ^ _782476) ^ [_1472991, _1472993, _1472995, _1472997, _1472999, _1473001] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472991, tc_fun(_1472993, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472991, tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_fun(_1472993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472993, tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_fun(_1472993, tc_HOL_Obool)), _1472991), c_COMBC(_1472993, tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472993, tc_prod(_1472991, _1472993)), tc_fun(_1472993, tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), _1472991), hAPP(c_COMBB(tc_prod(_1472991, _1472993), tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool), _1472993), c_member(tc_prod(_1472991, _1472993)))), c_Product__Type_OPair(_1472991, _1472993)))), _1472995)), hAPP(hAPP(c_COMBC(_1472991, tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_fun(_1472993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472993, tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_fun(_1472993, tc_HOL_Obool)), _1472991), c_COMBC(_1472993, tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472993, tc_prod(_1472991, _1472993)), tc_fun(_1472993, tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool)), _1472991), hAPP(c_COMBB(tc_prod(_1472991, _1472993), tc_fun(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool), tc_HOL_Obool), _1472993), c_member(tc_prod(_1472991, _1472993)))), c_Product__Type_OPair(_1472991, _1472993)))), _1472997)), _1472999), _1473001)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472991, _1472993)), hAPP(hAPP(c_Product__Type_OPair(_1472991, _1472993), _1472999), _1473001)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1472991, _1472993), tc_HOL_Obool)), _1472995), _1472997))))], (9334 ^ _782476) ^ [_949619, _949621, _949623] : [class_Orderings_Oorder(_949619), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949619, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949619, _949621, _949623)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949619), _949623)) = c_Orderings_Obot__class_Obot(tc_fun(_949619, tc_HOL_Obool)))], (7852 ^ _782476) ^ [_915623, _915625, _915627, _915629] : [7854 ^ _782476 : [(7857 ^ _782476) ^ [] : [hBOOL(hAPP(_915629, 7853 ^ [_915623, _915625, _915627, _915629]))], (7855 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915623), 7853 ^ [_915623, _915625, _915627, _915629]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915623, tc_HOL_Obool)), _915625), _915627))))]], 7858 ^ _782476 : [(7865 ^ _782476) ^ [_915940] : [hBOOL(hAPP(hAPP(c_member(_915623), _915940), _915627)), -(hBOOL(hAPP(_915629, _915940)))], (7859 ^ _782476) ^ [_915843] : [hBOOL(hAPP(hAPP(c_member(_915623), _915843), _915625)), -(hBOOL(hAPP(_915629, _915843)))]]], (43866 ^ _782476) ^ [_1657069, _1657071, _1657073, _1657075, _1657077] : [-(hAPP(hAPP(c_List_Olist__update(_1657069, hAPP(hAPP(c_List_Olist_OCons(_1657069), _1657071), _1657073)), hAPP(c_Nat_OSuc, _1657075)), _1657077) = hAPP(hAPP(c_List_Olist_OCons(_1657069), _1657071), hAPP(hAPP(c_List_Olist__update(_1657069, _1657073), _1657075), _1657077)))], (43936 ^ _782476) ^ [_1658646, _1658648, _1658650, _1658652] : [_1658646 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658648)), _1658650)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1658648, hAPP(hAPP(c_List_Olist__update(_1658648, _1658650), _1658646), _1658652)) = c_List_Obutlast(_1658648, _1658650))], (50569 ^ _782476) ^ [_1804942, _1804944] : [c_Relation_Otrans(_1804942, _1804944), -(c_Relation_Otrans(_1804942, hAPP(c_Relation_Oconverse(_1804942, _1804942), _1804944)))], (17194 ^ _782476) ^ [_1109101] : [17196 ^ _782476 : [(17199 ^ _782476) ^ [_1109211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17195 ^ [_1109101, _1109211]), _1109211))], (17197 ^ _782476) ^ [_1109177] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17195 ^ [_1109101, _1109177]), _1109101)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1109101)))], (42183 ^ _782476) ^ [_1613429, _1613431] : [class_Complete__Lattice_Ocomplete__lattice(_1613429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613429), _1613431)), -(c_Complete__Lattice_OSup__class_OSup(_1613429, _1613431) = hAPP(hAPP(c_Finite__Set_Ofold(_1613429, _1613429, c_Lattices_Osemilattice__sup__class_Osup(_1613429)), c_Orderings_Obot__class_Obot(_1613429)), _1613431))], (25531 ^ _782476) ^ [_1259548, _1259550] : [-(hBOOL(hAPP(_1259550, 25532 ^ [_1259548, _1259550]))), -(hAPP(c_Set_OCollect(_1259548), _1259550) = c_Orderings_Obot__class_Obot(tc_fun(_1259548, tc_HOL_Obool)))], (45725 ^ _782476) ^ [_1697945, _1697947, _1697949, _1697951, _1697953] : [class_Orderings_Olinorder(_1697945), hBOOL(hAPP(hAPP(c_member(_1697945), hAPP(_1697947, _1697949)), hAPP(c_Set_Oimage(_1697951, _1697945, _1697947), hAPP(c_List_Oset(_1697951), _1697953)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697951, _1697945, _1697947, _1697949, _1697953) = _1697953)], (13192 ^ _782476) ^ [_1025394, _1025396, _1025398, _1025400, _1025402] : [hBOOL(hAPP(hAPP(c_member(_1025398), hAPP(_1025400, _1025396)), _1025402)), -(hBOOL(hAPP(hAPP(c_member(_1025394), _1025396), hAPP(c_Set_Ovimage(_1025394, _1025398, _1025400), _1025402))))], (36244 ^ _782476) ^ [_1466526, _1466528] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466526), _1466528) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 36245 ^ _782476 : [(36252 ^ _782476) ^ [] : [_1466526 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1466528 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (36246 ^ _782476) ^ [] : [_1466526 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1466528 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (35540 ^ _782476) ^ [_1453966] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1453966), 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), _1453966), _1453966))], (11426 ^ _782476) ^ [_991702, _991704, _991706] : [class_Orderings_Olinorder(_991702), 11429 ^ _782476 : [(11436 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991702), _991706), _991704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991702), _991704), _991706))], (11430 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991702), _991704), _991706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991702), _991706), _991704)))]]], (52505 ^ _782476) ^ [_1841671, _1841673] : [-(class_Finite__Set_Ofinite(tc_sum(_1841671, _1841673))), class_Finite__Set_Ofinite(_1841671), class_Finite__Set_Ofinite(_1841673)], (4602 ^ _782476) ^ [_852389, _852391, _852393, _852395, _852397, _852399, _852401, _852403, _852405, _852407] : [-(c_Nitpick_Opair__box_Opair__box__size(_852407, _852403, _852399, _852395, _852391) = c_Nitpick_Opair__box_Opair__box__size(_852405, _852401, _852397, _852393, _852389)), _852407 = _852405, _852403 = _852401, _852399 = _852397, _852395 = _852393, _852391 = _852389], (14116 ^ _782476) ^ [_1045168, _1045170, _1045172, _1045174, _1045176] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1045168, _1045170, hAPP(hAPP(c_Set_Oinsert(_1045168), _1045172), _1045174)), _1045176)), 14121 ^ _782476 : [(14126 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1045168), 14119 ^ [_1045168, _1045170, _1045172, _1045174, _1045176]), 14120 ^ [_1045168, _1045170, _1045172, _1045174, _1045176]))], (14124 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1045168, _1045168, _1045170, 14119 ^ [_1045168, _1045170, _1045172, _1045174, _1045176], 14120 ^ [_1045168, _1045170, _1045172, _1045174, _1045176]), _1045176)))], (14122 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1045168), _1045172), _1045174) = hAPP(hAPP(c_Set_Oinsert(_1045168), 14119 ^ [_1045168, _1045170, _1045172, _1045174, _1045176]), 14120 ^ [_1045168, _1045170, _1045172, _1045174, _1045176]))]]], (28792 ^ _782476) ^ [_1329478, _1329480] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329478)), _1329480) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329478), _1329480)))], (46992 ^ _782476) ^ [_1725749, _1725751, _1725753, _1725755] : [class_Orderings_Olinorder(_1725749), -(hAPP(c_List_Oset(_1725751), c_List_Olinorder__class_Osort__key(_1725751, _1725749, _1725753, _1725755)) = hAPP(c_List_Oset(_1725751), _1725755))], (17564 ^ _782476) ^ [_1115416, _1115418, _1115420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115416), _1115418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115416), _1115420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115418), _1115420)))], (43615 ^ _782476) ^ [_1649900, _1649902, _1649904, _1649906] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649900), tc_List_Olist(_1649900))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649900), tc_List_Olist(_1649900)), _1649902), _1649904)), c_List_Olistrel(_1649900, _1649906))), 43618 ^ _782476 : [(43621 ^ _782476) ^ [_1650236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649900, _1649900)), _1650236), hAPP(c_List_Oset(tc_prod(_1649900, _1649900)), hAPP(hAPP(c_List_Ozip(_1649900, _1649900), _1649902), _1649904)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1649900, _1649900, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1649900, tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_fun(_1649900, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649900, tc_fun(tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_fun(_1649900, tc_HOL_Obool)), _1649900), c_COMBC(_1649900, tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649900, tc_prod(_1649900, _1649900)), tc_fun(_1649900, tc_fun(tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_HOL_Obool)), _1649900), hAPP(c_COMBB(tc_prod(_1649900, _1649900), tc_fun(tc_fun(tc_prod(_1649900, _1649900), tc_HOL_Obool), tc_HOL_Obool), _1649900), c_member(tc_prod(_1649900, _1649900)))), c_Product__Type_OPair(_1649900, _1649900)))), _1649906)), _1650236)))], (43619 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649900)), _1649902) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649900)), _1649904))]]], (20143 ^ _782476) ^ [_1160637, _1160639, _1160641] : [-(hBOOL(hAPP(_1160637, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160639), _1160641)))), 20146 ^ _782476 : [(20149 ^ _782476) ^ [] : [hBOOL(hAPP(_1160637, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20147 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160639), _1160641)))]], 20151 ^ _782476 : [(20154 ^ _782476) ^ [] : [hBOOL(hAPP(_1160637, 20150 ^ [_1160637, _1160639, _1160641]))], (20152 ^ _782476) ^ [] : [-(_1160639 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160641), 20150 ^ [_1160637, _1160639, _1160641]))]]], (34370 ^ _782476) ^ [_1433270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433270), 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), _1433270)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433270)))], (24118 ^ _782476) ^ [] : [-(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))))], (13149 ^ _782476) ^ [_1024511, _1024513, _1024515, _1024517] : [-(_1024511 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1024513, tc_HOL_Obool), tc_HOL_Obool))), 13155 ^ _782476 : [(13158 ^ _782476) ^ [] : [c_Fun_Oinj__on(_1024513, _1024515, _1024517, 13154 ^ [_1024511, _1024513, _1024515, _1024517])], (13156 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1024513, tc_HOL_Obool)), 13154 ^ [_1024511, _1024513, _1024515, _1024517]), _1024511)))]], -(c_Fun_Oinj__on(_1024513, _1024515, _1024517, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1024513, tc_HOL_Obool), _1024511)))], (21764 ^ _782476) ^ [_1191073, _1191075, _1191077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191073)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191075), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1191077)), 21774 ^ _782476 : [(21780 ^ _782476) ^ [] : [-(_1191075 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21776 ^ [_1191073, _1191075, _1191077]), 21773 ^ [_1191073, _1191075, _1191077]))], (21778 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21776 ^ [_1191073, _1191075, _1191077]), _1191077)))], (21775 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21773 ^ [_1191073, _1191075, _1191077]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191073))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191075), _1191073) = _1191075)], (43055 ^ _782476) ^ [_1634184, _1634186, _1634188, _1634190] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634184), tc_List_Olist(_1634184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634184), tc_List_Olist(_1634184)), _1634186), _1634188)), c_List_Olistrel1(_1634184, hAPP(c_Relation_Oconverse(_1634184, _1634184), _1634190)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634184), tc_List_Olist(_1634184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634184), tc_List_Olist(_1634184)), _1634186), _1634188)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634184), tc_List_Olist(_1634184)), c_List_Olistrel1(_1634184, _1634190)))))], (35368 ^ _782476) ^ [_1450740] : [-(c_Int_Osucc(c_Int_OBit0(_1450740)) = c_Int_OBit1(_1450740))], (51160 ^ _782476) ^ [_1817317, _1817319, _1817321, _1817323] : [c_Equiv__Relations_Opart__equivp(_1817317, _1817319), hBOOL(hAPP(hAPP(_1817319, _1817321), _1817323)), -(hBOOL(hAPP(hAPP(_1817319, _1817323), _1817321)))], (10237 ^ _782476) ^ [_967833, _967835] : [class_Orderings_Oorder(_967833), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967833, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967833), _967835), c_Orderings_Obot__class_Obot(tc_fun(_967833, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_967833), _967835)) = hAPP(hAPP(c_Set_Oinsert(_967833), _967835), c_Orderings_Obot__class_Obot(tc_fun(_967833, tc_HOL_Obool))))], (52469 ^ _782476) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (26150 ^ _782476) ^ [_1276764, _1276766] : [class_Orderings_Olinorder(_1276764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276764), _1276766)), -(_1276766 = c_Orderings_Obot__class_Obot(tc_fun(_1276764, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276764), c_Big__Operators_Olinorder__class_OMax(_1276764, _1276766)), _1276766)))], (52659 ^ _782476) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (32832 ^ _782476) ^ [_1405138, _1405140, _1405142] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405138, _1405140) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405142, _1405140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1405142), _1405138)), -(_1405138 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1405140), 32839 ^ [_1405138, _1405140, _1405142])))], (44755 ^ _782476) ^ [_1676323, _1676325, _1676327] : [-(hAPP(c_List_Oset(_1676323), hAPP(hAPP(c_List_Oappend(_1676323), _1676325), _1676327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1676323, tc_HOL_Obool)), hAPP(c_List_Oset(_1676323), _1676325)), hAPP(c_List_Oset(_1676323), _1676327)))], (36318 ^ _782476) ^ [_1467676, _1467678] : [class_Int_Onumber__ring(_1467676), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1467676), hAPP(c_Int_Onumber__class_Onumber__of(_1467676), 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)))), _1467678)) = c_Groups_Oone__class_Oone(_1467676))], (14625 ^ _782476) ^ [_1054985, _1054987, _1054989, _1054991, _1054993, _1054995, _1054997, _1054999] : [c_Finite__Set_Ofolding__image__simple(_1054985, _1054987, _1054989, _1054991, _1054993, _1054995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054987), _1054997)), hBOOL(hAPP(hAPP(c_member(_1054987), _1054999), _1054997)), -(hAPP(_1054995, _1054997) = hAPP(hAPP(_1054989, hAPP(_1054993, _1054999)), hAPP(_1054995, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054987, tc_HOL_Obool)), _1054997), hAPP(hAPP(c_Set_Oinsert(_1054987), _1054999), c_Orderings_Obot__class_Obot(tc_fun(_1054987, tc_HOL_Obool)))))))], (32137 ^ _782476) ^ [_1391076, _1391078, _1391080] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1391076), _1391078)), _1391080) = 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), _1391076), _1391080)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391078), _1391080))), 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, _1391076, _1391080)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391078, _1391080))), _1391080)))], (27393 ^ _782476) ^ [_1300534, _1300536, _1300538, _1300540] : [class_Orderings_Olinorder(_1300534), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300534, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300534, _1300536, _1300538)), hAPP(c_SetInterval_Oord__class_OatMost(_1300534), _1300540)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300534, _1300536, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300534), _1300538), _1300540)))], (30967 ^ _782476) ^ [_1369226, _1369228, _1369230] : [class_Divides_Osemiring__div(_1369226), -(_1369228 = c_Groups_Ozero__class_Ozero(_1369226)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369226), _1369230), _1369228)), _1369228) = _1369230)], (52459 ^ _782476) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (8204 ^ _782476) ^ [_923314, _923316, _923318, _923320, _923322, _923324, _923326] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923314, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923316, tc_fun(_923314, tc_HOL_Obool)), _923318), _923320)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923322, tc_fun(_923314, tc_HOL_Obool)), _923324), _923326)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923316, tc_fun(_923314, tc_HOL_Obool)), _923318), hAPP(hAPP(c_COMBB(tc_fun(_923322, tc_fun(_923314, tc_HOL_Obool)), tc_fun(_923314, tc_HOL_Obool), _923316), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923322, tc_fun(_923314, tc_HOL_Obool)), _923324)), hAPP(hAPP(c_COMBC(_923316, tc_fun(_923322, tc_fun(_923314, tc_HOL_Obool)), tc_fun(_923322, tc_fun(_923314, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_923314, tc_HOL_Obool), tc_fun(_923314, tc_HOL_Obool)), tc_fun(tc_fun(_923322, tc_fun(_923314, tc_HOL_Obool)), tc_fun(_923322, tc_fun(_923314, tc_HOL_Obool))), _923316), c_COMBB(tc_fun(_923314, tc_HOL_Obool), tc_fun(_923314, tc_HOL_Obool), _923322)), hAPP(hAPP(c_COMBB(tc_fun(_923314, tc_HOL_Obool), tc_fun(tc_fun(_923314, tc_HOL_Obool), tc_fun(_923314, tc_HOL_Obool)), _923316), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923314, tc_HOL_Obool))), _923320))), _923326))))], (52287 ^ _782476) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (34070 ^ _782476) ^ [_1428385, _1428387] : [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), _1428385))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428387), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428385))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428387), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428385))), 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), _1428387))), c_COMBI(tc_Int_Oint))))], (3144 ^ _782476) ^ [_829220, _829222, _829224, _829226] : [-(c_List_Olistrel1(_829226, _829222) = c_List_Olistrel1(_829224, _829220)), _829226 = _829224, _829222 = _829220], (15276 ^ _782476) ^ [_1067862, _1067864, _1067866] : [class_Lattices_Olattice(_1067862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067862), _1067864)), -(_1067864 = c_Orderings_Obot__class_Obot(tc_fun(_1067862, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067862), _1067866)), -(_1067866 = c_Orderings_Obot__class_Obot(tc_fun(_1067862, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067862, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1067862, tc_HOL_Obool)), _1067864), _1067866)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067862), c_Big__Operators_Olattice__class_OSup__fin(_1067862, _1067864)), c_Big__Operators_Olattice__class_OSup__fin(_1067862, _1067866)))], (39663 ^ _782476) ^ [_1548816, _1548818, _1548820, _1548822] : [hBOOL(hAPP(c_Predicate_ODomainP(_1548816, _1548818, hAPP(hAPP(c_COMBC(_1548816, tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_fun(_1548818, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548818, tc_fun(tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_fun(_1548818, tc_HOL_Obool)), _1548816), c_COMBC(_1548818, tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548818, tc_prod(_1548816, _1548818)), tc_fun(_1548818, tc_fun(tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_HOL_Obool)), _1548816), hAPP(c_COMBB(tc_prod(_1548816, _1548818), tc_fun(tc_fun(tc_prod(_1548816, _1548818), tc_HOL_Obool), tc_HOL_Obool), _1548818), c_member(tc_prod(_1548816, _1548818)))), c_Product__Type_OPair(_1548816, _1548818)))), _1548820)), _1548822)), -(hBOOL(hAPP(hAPP(c_member(_1548816), _1548822), hAPP(c_Relation_ODomain(_1548816, _1548818), _1548820))))], (52335 ^ _782476) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (19883 ^ _782476) ^ [_1155688, _1155690, _1155692, _1155694] : [class_Rings_Olinordered__ring__strict(_1155688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155688), _1155690), c_Groups_Ozero__class_Ozero(_1155688))), 19890 ^ _782476 : [(19897 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155688), _1155694), _1155692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155688), _1155690), _1155692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155688), _1155690), _1155694))))], (19891 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155688), _1155690), _1155692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155688), _1155690), _1155694))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155688), _1155694), _1155692)))]]], (38407 ^ _782476) ^ [_1516710] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516710) = _1516710)], (3464 ^ _782476) ^ [_834200, _834202, _834204, _834206, _834208, _834210, _834212, _834214] : [-(c_List_Olist_Olist__case(_834214, _834210, _834206, _834202) = c_List_Olist_Olist__case(_834212, _834208, _834204, _834200)), _834214 = _834212, _834210 = _834208, _834206 = _834204, _834202 = _834200], (8240 ^ _782476) ^ [_924236, _924238, _924240] : [class_Orderings_Olinorder(_924236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924236), _924238), _924240)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924236, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_924236), _924238)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924236, _924238), _924240)) = hAPP(c_SetInterval_Oord__class_OlessThan(_924236), _924240))], (33968 ^ _782476) ^ [_1426511, _1426513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426511)), c_Int_OBit1(_1426513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426511), _1426513)))], (45893 ^ _782476) ^ [_1700741, _1700743, _1700745, _1700747] : [-(_1700741 = c_List_Olist_ONil(_1700743)), -(c_List_Olast(_1700745, hAPP(hAPP(c_List_Omap(_1700743, _1700745), _1700747), _1700741)) = hAPP(_1700747, c_List_Olast(_1700743, _1700741)))], (52697 ^ _782476) ^ [] : [-(hBOOL(c_fTrue))], (45096 ^ _782476) ^ [_1684446, _1684448, _1684450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684446, tc_HOL_Obool)), hAPP(c_List_Oset(_1684446), hAPP(hAPP(c_List_Odrop(_1684446), _1684448), _1684450))), hAPP(c_List_Oset(_1684446), _1684450))))], (1682 ^ _782476) ^ [_806701, _806703] : [-(class_Groups_Ocancel__semigroup__add(_806701)), _806703 = _806701, class_Groups_Ocancel__semigroup__add(_806703)], (22916 ^ _782476) ^ [_1212141, _1212143, _1212145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212141), _1212143)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212143), _1212141))), _1212145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1212143)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212141), _1212145)))], (50186 ^ _782476) ^ [_1796021, _1796023, _1796025] : [hBOOL(hAPP(hAPP(c_List_Omember(_1796021), _1796023), _1796025)), -(hBOOL(hAPP(hAPP(c_member(_1796021), _1796025), hAPP(c_List_Oset(_1796021), _1796023))))], (14963 ^ _782476) ^ [_1061744, _1061746, _1061748] : [class_Lattices_Olattice(_1061744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061744), _1061746)), 14970 ^ _782476 : [(14977 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061744, tc_HOL_Obool)), _1061746), hAPP(hAPP(c_Set_Oinsert(_1061744), _1061748), c_Orderings_Obot__class_Obot(tc_fun(_1061744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061744, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061744, hAPP(hAPP(c_Set_Oinsert(_1061744), _1061748), _1061746)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061744), _1061748), c_Big__Operators_Olattice__class_OInf__fin(_1061744, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061744, tc_HOL_Obool)), _1061746), hAPP(hAPP(c_Set_Oinsert(_1061744), _1061748), c_Orderings_Obot__class_Obot(tc_fun(_1061744, tc_HOL_Obool)))))))], (14971 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061744, tc_HOL_Obool)), _1061746), hAPP(hAPP(c_Set_Oinsert(_1061744), _1061748), c_Orderings_Obot__class_Obot(tc_fun(_1061744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061744, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1061744, hAPP(hAPP(c_Set_Oinsert(_1061744), _1061748), _1061746)) = _1061748)]]], (30788 ^ _782476) ^ [_1366053, _1366055, _1366057, _1366059] : [class_Fields_Olinordered__field(_1366053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366053), c_Groups_Ozero__class_Ozero(_1366053)), _1366055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366053), _1366057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366053), _1366059), _1366055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366053), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366053), _1366057), _1366055)), _1366059)))], (1512 ^ _782476) ^ [_804576, _804578] : [-(class_Lattices_Olattice(_804576)), _804578 = _804576, class_Lattices_Olattice(_804578)], (37529 ^ _782476) ^ [_1496733, _1496735] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1496733, _1496735) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1496733, _1496735)))], (48651 ^ _782476) ^ [_1761612, _1761614, _1761616, _1761618, _1761620] : [c_Fun_Oinj__on(_1761612, _1761614, _1761616, hAPP(hAPP(c_Set_Oinsert(_1761612), _1761618), hAPP(c_List_Oset(_1761612), _1761620))), -(hAPP(hAPP(c_List_Omap(_1761612, _1761614), _1761616), hAPP(c_List_OremoveAll(_1761612, _1761618), _1761620)) = hAPP(c_List_OremoveAll(_1761614, hAPP(_1761616, _1761618)), hAPP(hAPP(c_List_Omap(_1761612, _1761614), _1761616), _1761620)))], (13092 ^ _782476) ^ [_1022982, _1022984, _1022986, _1022988, _1022990, _1022992, _1022994] : [-(c_Nitpick_Ofold__graph_H(_1022982, _1022984, _1022986, _1022988, _1022990, hAPP(hAPP(_1022986, _1022992), _1022994))), 13093 ^ _782476 : [(13100 ^ _782476) ^ [_1023211, _1023213] : [hAPP(hAPP(_1022986, _1022992), _1022994) = hAPP(hAPP(_1022986, _1023213), _1023211), hBOOL(hAPP(hAPP(c_member(_1022982), _1023213), _1022990)), c_Nitpick_Ofold__graph_H(_1022982, _1022984, _1022986, _1022988, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022982, tc_HOL_Obool)), _1022990), hAPP(hAPP(c_Set_Oinsert(_1022982), _1023213), c_Orderings_Obot__class_Obot(tc_fun(_1022982, tc_HOL_Obool)))), _1023211)], (13094 ^ _782476) ^ [] : [_1022990 = c_Orderings_Obot__class_Obot(tc_fun(_1022982, tc_HOL_Obool)), hAPP(hAPP(_1022986, _1022992), _1022994) = _1022988]]], (46386 ^ _782476) ^ [_1712430, _1712432] : [_1712430 = _1712432, -(hAPP(c_Code__Numeral_Onat__of, _1712430) = hAPP(c_Code__Numeral_Onat__of, _1712432))], (2238 ^ _782476) ^ [_815217, _815219, _815221, _815223] : [-(c_Orderings_Oord_Omin(_815223, _815219) = c_Orderings_Oord_Omin(_815221, _815217)), _815223 = _815221, _815219 = _815217], (36126 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (49274 ^ _782476) ^ [_1775887, _1775889, _1775891] : [49276 ^ _782476 : [(49279 ^ _782476) ^ [] : [hBOOL(hAPP(_1775891, 49275 ^ [_1775887, _1775889, _1775891]))], (49277 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775887), 49275 ^ [_1775887, _1775889, _1775891]), hAPP(c_List_Oset(_1775887), _1775889))))]], -(c_List_Olist__all(_1775887, _1775891, _1775889))], (45915 ^ _782476) ^ [_1701126, _1701128, _1701130, _1701132, _1701134] : [hAPP(hAPP(c_List_Omap(_1701126, _1701128), _1701130), _1701132) = hAPP(hAPP(c_List_Omap(_1701126, _1701128), _1701130), _1701134), c_Fun_Oinj__on(_1701126, _1701128, _1701130, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701126, tc_HOL_Obool)), hAPP(c_List_Oset(_1701126), _1701132)), hAPP(c_List_Oset(_1701126), _1701134))), -(_1701132 = _1701134)], (37113 ^ _782476) ^ [_1489084, _1489086] : [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), _1489084))), 37116 ^ _782476 : [(37123 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489086)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489084)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489086), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489084)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489084)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489086), 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), _1489084)))))], (37117 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489086)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489084))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489086), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489084)) = 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), _1489086)))]]], (34018 ^ _782476) ^ [_1427429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427429)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23651 ^ _782476) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (39279 ^ _782476) ^ [_1539343, _1539345, _1539347, _1539349] : [c_Wellfounded_Owf(_1539343, _1539345), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539343, _1539343)), hAPP(hAPP(c_Product__Type_OPair(_1539343, _1539343), _1539347), _1539349)), _1539345)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539343, _1539343)), hAPP(hAPP(c_Product__Type_OPair(_1539343, _1539343), _1539349), _1539347)), _1539345))], (32113 ^ _782476) ^ [_1390696, _1390698] : [32114 ^ _782476 : [(32115 ^ _782476) ^ [_1390745] : [_1390696 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390698), _1390745)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390696, _1390698) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44172 ^ _782476) ^ [_1663736, _1663738, _1663740, _1663742] : [-(_1663736 = _1663738), 44175 ^ _782476 : [(44182 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663740), _1663736), hAPP(c_List_Oset(_1663740), _1663742))), -(hBOOL(hAPP(hAPP(c_member(_1663740), _1663736), hAPP(c_List_Oset(_1663740), c_List_Oremove1(_1663740, _1663738, _1663742)))))], (44176 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663740), _1663736), hAPP(c_List_Oset(_1663740), c_List_Oremove1(_1663740, _1663738, _1663742)))), -(hBOOL(hAPP(hAPP(c_member(_1663740), _1663736), hAPP(c_List_Oset(_1663740), _1663742))))]]], (23879 ^ _782476) ^ [_1230399, _1230401] : [hAPP(c_Int_Onat, _1230399) = _1230401, 23882 ^ _782476 : [(23889 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230399))), -(_1230401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23883 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230399)), -(_1230399 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230401))]]], (33264 ^ _782476) ^ [_1413187, _1413189, _1413191, _1413193] : [class_Fields_Ofield__inverse__zero(_1413187), class_Int_Onumber(_1413187), 33271 ^ _782476 : [(33272 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413187), _1413189), _1413191) = hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193), 33275 ^ _782476 : [(33282 ^ _782476) ^ [] : [_1413191 = c_Groups_Ozero__class_Ozero(_1413187), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193) = c_Groups_Ozero__class_Ozero(_1413187))], (33276 ^ _782476) ^ [] : [-(_1413191 = c_Groups_Ozero__class_Ozero(_1413187)), -(_1413189 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413187), hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193)), _1413191))]]], (33288 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413187), _1413189), _1413191) = hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193)), 33291 ^ _782476 : [(33294 ^ _782476) ^ [] : [_1413189 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413187), hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193)), _1413191)], (33292 ^ _782476) ^ [] : [_1413191 = c_Groups_Ozero__class_Ozero(_1413187)]], 33295 ^ _782476 : [(33298 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413187), _1413193) = c_Groups_Ozero__class_Ozero(_1413187)], (33296 ^ _782476) ^ [] : [-(_1413191 = c_Groups_Ozero__class_Ozero(_1413187))]]]]], (52203 ^ _782476) ^ [_1838862, _1838864] : [class_Groups_Ominus(_1838862), -(class_Groups_Ominus(tc_fun(_1838864, _1838862)))], (9603 ^ _782476) ^ [_954775, _954777, _954779, _954781] : [c_Orderings_Obot__class_Obot(tc_fun(_954775, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954777, tc_fun(_954775, tc_HOL_Obool)), _954779), _954781), 9606 ^ _782476 : [(9607 ^ _782476) ^ [_954891] : [hBOOL(hAPP(hAPP(c_member(_954777), _954891), _954779)), -(hAPP(_954781, _954891) = c_Orderings_Obot__class_Obot(tc_fun(_954775, tc_HOL_Obool)))]]], (27028 ^ _782476) ^ [_1293400, _1293402, _1293404, _1293406, _1293408] : [class_Orderings_Olinorder(_1293400), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293400, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1293400, _1293402, _1293404)), c_SetInterval_Oord__class_OatLeastAtMost(_1293400, _1293406, _1293408)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293400, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293400), _1293402), _1293406), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293400), _1293404), _1293408)))], (34906 ^ _782476) ^ [_1442356, _1442358] : [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(_1442358))), 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), _1442356)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442356)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442358))))], (7487 ^ _782476) ^ [_908036, _908038, _908040] : [class_Groups_Ogroup__add(_908036), 7490 ^ _782476 : [(7497 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_908036), _908040) = _908038, -(hAPP(c_Groups_Ouminus__class_Ouminus(_908036), _908038) = _908040)], (7491 ^ _782476) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_908036), _908038) = _908040, -(hAPP(c_Groups_Ouminus__class_Ouminus(_908036), _908040) = _908038)]]], (7355 ^ _782476) ^ [_905308, _905310, _905312, _905314] : [hBOOL(hAPP(hAPP(_905312, _905314), _905310)), -(hBOOL(hAPP(hAPP(c_member(_905308), _905310), c_SetInterval_Oord_OgreaterThan(_905308, _905312, _905314))))], (33196 ^ _782476) ^ [_1411948, _1411950, _1411952, _1411954] : [class_Int_Onumber__ring(_1411948), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411948), hAPP(c_Int_Onumber__class_Onumber__of(_1411948), _1411950)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411948), hAPP(c_Int_Onumber__class_Onumber__of(_1411948), _1411952)), _1411954)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411948), hAPP(c_Int_Onumber__class_Onumber__of(_1411948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411950), _1411952))), _1411954))], (9163 ^ _782476) ^ [_944960, _944962, _944964] : [class_Lattices_Oboolean__algebra(_944960), -(hAPP(c_Groups_Ouminus__class_Ouminus(_944960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944960), _944962), _944964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944960), hAPP(c_Groups_Ouminus__class_Ouminus(_944960), _944962)), hAPP(c_Groups_Ouminus__class_Ouminus(_944960), _944964)))], (26020 ^ _782476) ^ [_1274930, _1274932] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274930))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274932)), hAPP(c_Int_Onat, _1274930)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1274932), _1274930)), 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)))], (9079 ^ _782476) ^ [_942553, _942555, _942557, _942559, _942561] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942553, tc_HOL_Obool)), _942555), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942557, tc_fun(_942553, tc_HOL_Obool)), _942559), _942561)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942557, tc_fun(_942553, tc_HOL_Obool)), _942559), hAPP(hAPP(c_COMBB(tc_fun(_942553, tc_HOL_Obool), tc_fun(_942553, tc_HOL_Obool), _942557), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942553, tc_HOL_Obool)), _942555)), _942561)))], (36891 ^ _782476) ^ [_1484773, _1484775, _1484777, _1484779, _1484781, _1484783] : [-(hAPP(hAPP(c_Product__Type_OPair(_1484773, _1484775), _1484777), _1484779) = hAPP(hAPP(c_Product__Type_OPair(_1484773, _1484775), _1484781), _1484783)), _1484777 = _1484781, _1484779 = _1484783], (21047 ^ _782476) ^ [_1177997, _1177999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177997), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177999), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177997), _1177999)))], (42786 ^ _782476) ^ [_1625940, _1625942] : [-(c_Nitpick_Oinverse__frac(_1625940, _1625942) = hAPP(hAPP(c_Nitpick_Ofrac(_1625940), hAPP(c_Nitpick_Odenom(_1625940), _1625942)), hAPP(c_Nitpick_Onum(_1625940), _1625942)))], (14699 ^ _782476) ^ [_1056616, _1056618, _1056620, _1056622, _1056624, _1056626, _1056628, _1056630] : [c_Finite__Set_Ofolding__image__simple(_1056616, _1056618, _1056620, _1056622, _1056624, _1056626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056618), _1056628)), -(hAPP(_1056626, hAPP(hAPP(c_Set_Oinsert(_1056618), _1056630), _1056628)) = hAPP(hAPP(_1056620, hAPP(_1056624, _1056630)), hAPP(_1056626, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056618, tc_HOL_Obool)), _1056628), hAPP(hAPP(c_Set_Oinsert(_1056618), _1056630), c_Orderings_Obot__class_Obot(tc_fun(_1056618, tc_HOL_Obool)))))))], (44264 ^ _782476) ^ [_1665506, _1665508] : [-(c_List_Olistrelp(_1665506, _1665508, c_List_Olist_ONil(_1665506), c_List_Olist_ONil(_1665506)))], (31395 ^ _782476) ^ [_1376425, _1376427, _1376429] : [class_Orderings_Olinorder(_1376425), hAPP(_1376427, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376425), 31400 ^ [_1376425, _1376427, _1376429]), 31401 ^ [_1376425, _1376427, _1376429])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376425), hAPP(_1376427, 31400 ^ [_1376425, _1376427, _1376429])), hAPP(_1376427, 31401 ^ [_1376425, _1376427, _1376429])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376425), _1376429)), -(_1376429 = c_Orderings_Obot__class_Obot(tc_fun(_1376425, tc_HOL_Obool))), -(hAPP(_1376427, c_Big__Operators_Olinorder__class_OMax(_1376425, _1376429)) = c_Big__Operators_Olinorder__class_OMax(_1376425, hAPP(c_Set_Oimage(_1376425, _1376425, _1376427), _1376429)))], (16559 ^ _782476) ^ [_1094504, _1094506, _1094508, _1094510] : [class_Groups_Oordered__ab__semigroup__add(_1094504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094504), _1094506), _1094508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094504), _1094510), _1094506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094504), _1094510), _1094508))))], (41635 ^ _782476) ^ [_1599892, _1599894, _1599896] : [c_Relation_Ototal__on(_1599892, _1599894, _1599896), -(c_Relation_Ototal__on(_1599892, _1599894, hAPP(c_Relation_Oconverse(_1599892, _1599892), _1599896)))], (48776 ^ _782476) ^ [_1764178, _1764180, _1764182, _1764184, _1764186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1764178, _1764180)), hAPP(_1764178, _1764182))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764184, _1764184)), hAPP(hAPP(c_Product__Type_OPair(_1764184, _1764184), _1764180), _1764182)), c_List_Omeasures(_1764184, _1764186))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764184, _1764184)), hAPP(hAPP(c_Product__Type_OPair(_1764184, _1764184), _1764180), _1764182)), c_List_Omeasures(_1764184, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764184, tc_Nat_Onat)), _1764178), _1764186)))))], (6660 ^ _782476) ^ [_889961, _889963, _889965, _889967, _889969, _889971, _889973, _889975] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889961, tc_fun(_889963, tc_fun(_889965, tc_HOL_Obool))), _889967), _889969), _889971), _889973)), hBOOL(hAPP(hAPP(c_member(_889961), _889975), _889967)), -(hBOOL(hAPP(hAPP(hAPP(_889969, _889975), _889971), _889973)))], (22449 ^ _782476) ^ [_1203593, _1203595] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203593), _1203595) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22450 ^ _782476 : [(22457 ^ _782476) ^ [] : [_1203593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203595 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22451 ^ _782476) ^ [] : [_1203593 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2150 ^ _782476) ^ [_813849, _813851, _813853, _813855, _813857, _813859, _813861, _813863] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_813863, _813859, _813855, _813851) = c_Nat_Osemiring__1__class_Oof__nat__aux(_813861, _813857, _813853, _813849)), _813863 = _813861, _813859 = _813857, _813855 = _813853, _813851 = _813849], (10565 ^ _782476) ^ [_975459, _975461, _975463, _975465] : [hBOOL(hAPP(hAPP(c_member(_975459), _975461), _975463)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975459, tc_HOL_Obool)), _975463), hAPP(hAPP(c_Set_Oinsert(_975459), _975461), _975465)) = hAPP(hAPP(c_Set_Oinsert(_975459), _975461), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975459, tc_HOL_Obool)), _975463), _975465)))], (23151 ^ _782476) ^ [_1217034] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217034)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1217034)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1217034), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (52185 ^ _782476) ^ [_1838625, _1838627] : [class_Orderings_Oord(_1838625), -(class_Orderings_Oord(tc_fun(_1838627, _1838625)))], (18056 ^ _782476) ^ [_1124514, _1124516] : [class_Groups_Omonoid__add(_1124514), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124514), _1124516), c_Groups_Ozero__class_Ozero(_1124514)) = _1124516)], (22386 ^ _782476) ^ [_1202679] : [_1202679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202679), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (22716 ^ _782476) ^ [_1208615, _1208617, _1208619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208615), _1208617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208615, tc_HOL_Obool)), _1208619), _1208617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208615), _1208617)), hAPP(c_Finite__Set_Ocard(_1208615), _1208619))), -(_1208619 = _1208617)], (40394 ^ _782476) ^ [_1569640, _1569642, _1569644] : [c_Predicate_Oreflp(_1569640, _1569642), -(hBOOL(hAPP(hAPP(_1569642, _1569644), _1569644)))], (14128 ^ _782476) ^ [_1045561] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045561), c_Orderings_Obot__class_Obot(tc_fun(_1045561, tc_HOL_Obool)))))], (48687 ^ _782476) ^ [_1762278, _1762280, _1762282, _1762284] : [_1762278 = _1762280, -(hAPP(c_List_OremoveAll(_1762282, _1762278), hAPP(hAPP(c_List_Olist_OCons(_1762282), _1762280), _1762284)) = hAPP(c_List_OremoveAll(_1762282, _1762278), _1762284))], (26366 ^ _782476) ^ [_1280807, _1280809, _1280811, _1280813, _1280815] : [class_Orderings_Olinorder(_1280807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280807), _1280809), _1280811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280807), _1280813), _1280815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280807), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280807), _1280809), _1280813)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280807), _1280811), _1280815))))], (35140 ^ _782476) ^ [_1446863, _1446865] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1446863)), c_Int_OBit0(_1446865)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446863), _1446865)))], (22465 ^ _782476) ^ [_1203819, _1203821] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203819), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203819), _1203821)))))], (36030 ^ _782476) ^ [_1463339] : [c_Int_OMin = _1463339, -(c_Int_OMin = c_Int_OBit1(_1463339))], (52625 ^ _782476) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (15786 ^ _782476) ^ [_1077847, _1077849, _1077851] : [class_Lattices_Osemilattice__inf(_1077847), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077847), _1077849)), -(_1077849 = c_Orderings_Obot__class_Obot(tc_fun(_1077847, tc_HOL_Obool))), 15797 ^ _782476 : [(15798 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077847), _1077851), hAPP(c_Finite__Set_Ofold1(_1077847, c_Lattices_Osemilattice__inf__class_Oinf(_1077847)), _1077849))), 15801 ^ _782476 : [(15802 ^ _782476) ^ [_1078140] : [hBOOL(hAPP(hAPP(c_member(_1077847), _1078140), _1077849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077847), _1077851), _1078140)))]]], (15808 ^ _782476) ^ [] : [15810 ^ _782476 : [(15813 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077847), _1077851), 15809 ^ [_1077847, _1077849, _1077851]))], (15811 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1077847), 15809 ^ [_1077847, _1077849, _1077851]), _1077849)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077847), _1077851), hAPP(c_Finite__Set_Ofold1(_1077847, c_Lattices_Osemilattice__inf__class_Oinf(_1077847)), _1077849))))]]], (28796 ^ _782476) ^ [_1329564, _1329566, _1329568, _1329570] : [class_Rings_Ocomm__semiring__1(_1329564), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329564), hAPP(hAPP(c_Power_Opower__class_Opower(_1329564), _1329566), _1329568)), _1329570) = hAPP(hAPP(c_Power_Opower__class_Opower(_1329564), _1329566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1329568), _1329570)))], (47782 ^ _782476) ^ [_1743364, _1743366, _1743368] : [class_Orderings_Olinorder(_1743364), -(c_List_Olinorder__class_Osorted(_1743364, hAPP(c_List_Ofilter(_1743364, hAPP(hAPP(c_COMBC(_1743364, _1743364, tc_HOL_Obool), c_fequal), hAPP(_1743366, _1743368))), _1743368)))], (38826 ^ _782476) ^ [_1527042, _1527044, _1527046] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527042, _1527042)), _1527044), c_Relation_OId__on(_1527042, _1527046))), 38830 ^ _782476 : [(38833 ^ _782476) ^ [] : [-(_1527044 = hAPP(hAPP(c_Product__Type_OPair(_1527042, _1527042), 38829 ^ [_1527042, _1527044, _1527046]), 38829 ^ [_1527042, _1527044, _1527046]))], (38831 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527042), 38829 ^ [_1527042, _1527044, _1527046]), _1527046)))]]], (1392 ^ _782476) ^ [_803076, _803078] : [-(class_Rings_Oring__1(_803076)), _803078 = _803076, class_Rings_Oring__1(_803078)], (4230 ^ _782476) ^ [_846561, _846563, _846565, _846567, _846569, _846571] : [-(c_Set_Ovimage(_846571, _846567, _846563) = c_Set_Ovimage(_846569, _846565, _846561)), _846571 = _846569, _846567 = _846565, _846563 = _846561], (48892 ^ _782476) ^ [_1767401, _1767403, _1767405, _1767407] : [48894 ^ _782476 : [(48897 ^ _782476) ^ [] : [hBOOL(hAPP(_1767405, 48893 ^ [_1767401, _1767403, _1767405, _1767407]))], (48895 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767401), 48893 ^ [_1767401, _1767403, _1767405, _1767407]), hAPP(c_List_Oset(_1767401), _1767403))))]], -(c_List_OtakeWhile(_1767401, _1767405, hAPP(hAPP(c_List_Oappend(_1767401), _1767403), _1767407)) = hAPP(hAPP(c_List_Oappend(_1767401), _1767403), c_List_OtakeWhile(_1767401, _1767405, _1767407)))], (48657 ^ _782476) ^ [_1761787, _1761789, _1761791] : [-(hBOOL(hAPP(hAPP(c_member(_1761787), _1761789), hAPP(c_List_Oset(_1761787), _1761791)))), -(c_List_Oinsert(_1761787, _1761789, _1761791) = hAPP(hAPP(c_List_Olist_OCons(_1761787), _1761789), _1761791))], (39978 ^ _782476) ^ [_1559509, _1559511, _1559513, _1559515, _1559517, _1559519] : [class_Groups_Ocomm__monoid__mult(_1559509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559511), _1559513)), 39988 ^ _782476 : [(39991 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559515), hAPP(_1559517, 39987 ^ [_1559509, _1559511, _1559513, _1559515, _1559517, _1559519])))], (39989 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559511), 39987 ^ [_1559509, _1559511, _1559513, _1559515, _1559517, _1559519]), _1559513)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559509, _1559511, c_Groups_Otimes__class_Otimes(_1559509)), hAPP(hAPP(c_COMBS(_1559511, tc_fun(_1559515, tc_HOL_Obool), _1559509), hAPP(hAPP(c_COMBC(_1559511, _1559509, tc_fun(tc_fun(_1559515, tc_HOL_Obool), _1559509)), hAPP(hAPP(c_COMBB(tc_fun(_1559515, _1559509), tc_fun(_1559509, tc_fun(tc_fun(_1559515, tc_HOL_Obool), _1559509)), _1559511), c_Finite__Set_Ofold__image(_1559509, _1559515, c_Groups_Otimes__class_Otimes(_1559509))), _1559519)), c_Groups_Oone__class_Oone(_1559509))), _1559517)), c_Groups_Oone__class_Oone(_1559509)), _1559513) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559509, tc_prod(_1559511, _1559515), c_Groups_Otimes__class_Otimes(_1559509)), hAPP(c_Product__Type_Oprod_Oprod__case(_1559511, _1559515, _1559509), _1559519)), c_Groups_Oone__class_Oone(_1559509)), hAPP(hAPP(c_Product__Type_OSigma(_1559511, _1559515), _1559513), _1559517)))], (22015 ^ _782476) ^ [_1196541, _1196543] : [class_Orderings_Oorder(_1196541), 22018 ^ _782476 : [(22025 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196541), hAPP(_1196543, 22026 ^ [_1196541, _1196543])), hAPP(_1196543, hAPP(c_Nat_OSuc, 22026 ^ [_1196541, _1196543])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196541, _1196543))], (22019 ^ _782476) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196541, _1196543), 22022 ^ _782476 : [(22023 ^ _782476) ^ [_1196675] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196541), hAPP(_1196543, _1196675)), hAPP(_1196543, hAPP(c_Nat_OSuc, _1196675)))))]]]]], (10823 ^ _782476) ^ [_981358, _981360, _981362] : [class_Complete__Lattice_Ocomplete__lattice(_981358), -(c_Complete__Lattice_OInf__class_OInf(_981358, hAPP(hAPP(c_Set_Oinsert(_981358), _981360), hAPP(hAPP(c_Set_Oinsert(_981358), _981362), c_Orderings_Obot__class_Obot(tc_fun(_981358, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981358), _981360), _981362))], (37221 ^ _782476) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (33884 ^ _782476) ^ [_1424896, _1424898, _1424900] : [class_Int_Onumber__ring(_1424896), 33887 ^ _782476 : [(33894 ^ _782476) ^ [] : [-(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), _1424898)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424896), hAPP(c_Int_Onumber__class_Onumber__of(_1424896), _1424900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424898))) = c_Groups_Oone__class_Oone(_1424896))], (33888 ^ _782476) ^ [] : [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), _1424898))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424896), hAPP(c_Int_Onumber__class_Onumber__of(_1424896), _1424900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424898))) = hAPP(hAPP(c_HOL_OLet(_1424896, _1424896), hAPP(hAPP(c_Power_Opower__class_Opower(_1424896), hAPP(c_Int_Onumber__class_Onumber__of(_1424896), _1424900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424898))), hAPP(hAPP(c_COMBS(_1424896, _1424896, _1424896), hAPP(hAPP(c_COMBB(_1424896, tc_fun(_1424896, _1424896), _1424896), c_Groups_Otimes__class_Otimes(_1424896)), hAPP(c_Groups_Otimes__class_Otimes(_1424896), hAPP(c_Int_Onumber__class_Onumber__of(_1424896), _1424900)))), c_COMBI(_1424896))))]]], (51422 ^ _782476) ^ [_1822804, _1822806, _1822808] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1822804, _1822804)), hAPP(hAPP(c_Product__Type_OPair(_1822804, _1822804), hAPP(_1822806, hAPP(c_Nat_OSuc, 51423 ^ [_1822804, _1822806, _1822808]))), hAPP(_1822806, 51423 ^ [_1822804, _1822806, _1822808]))), c_Transitive__Closure_Ortrancl(_1822804, _1822808))), c_Wellfounded_Owf(_1822804, c_Transitive__Closure_Otrancl(_1822804, _1822808)), 51431 ^ _782476 : [(51432 ^ _782476) ^ [_1823070] : [-(hAPP(_1822806, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 51430 ^ [_1822804, _1822806, _1822808]), _1823070)) = hAPP(_1822806, 51430 ^ [_1822804, _1822806, _1822808]))]]], (36661 ^ _782476) ^ [_1479891, _1479893, _1479895, _1479897, _1479899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479895, _1479891)), hAPP(hAPP(c_Product__Type_OPair(_1479895, _1479891), _1479899), _1479893)), _1479897)), -(hBOOL(hAPP(hAPP(c_member(_1479891), _1479893), hAPP(c_Relation_OImage(_1479895, _1479891, _1479897), hAPP(hAPP(c_Set_Oinsert(_1479895), _1479899), c_Orderings_Obot__class_Obot(tc_fun(_1479895, tc_HOL_Obool)))))))], (27411 ^ _782476) ^ [_1300963, _1300965] : [class_Orderings_Olinorder(_1300963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300963), _1300965)), -(c_Big__Operators_Olinorder__class_OMax(_1300963, _1300965) = hAPP(c_Finite__Set_Ofold1(_1300963, c_Orderings_Oord__class_Omax(_1300963)), _1300965))], (45535 ^ _782476) ^ [_1693955, _1693957, _1693959] : [class_Orderings_Olinorder(_1693955), -(c_Big__Operators_Olattice_OInf__fin(_1693955, c_Orderings_Oord__class_Omin(_1693955), hAPP(c_List_Oset(_1693955), hAPP(hAPP(c_List_Olist_OCons(_1693955), _1693957), _1693959))) = hAPP(c_List_Ofoldl(_1693955, _1693955, c_Orderings_Oord__class_Omin(_1693955), _1693957), _1693959))], (31850 ^ _782476) ^ [_1385510, _1385512] : [-(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, _1385510, _1385512)), _1385512) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385510), _1385512))], (17748 ^ _782476) ^ [_1118955] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118955), _1118955))))], (39509 ^ _782476) ^ [_1544710, _1544712, _1544714] : [_1544714 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544710, _1544712), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1544710, _1544712), _1544714) = c_Orderings_Obot__class_Obot(tc_fun(_1544712, tc_HOL_Obool)))], (44546 ^ _782476) ^ [_1671375, _1671377, _1671379, _1671381] : [-(c_List_Osublist(_1671375, hAPP(hAPP(c_List_Olist_OCons(_1671375), _1671377), _1671379), _1671381) = hAPP(hAPP(c_List_Oappend(_1671375), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1671375)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1671381)), hAPP(hAPP(c_List_Olist_OCons(_1671375), _1671377), c_List_Olist_ONil(_1671375))), c_List_Olist_ONil(_1671375))), c_List_Osublist(_1671375, _1671379, 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)), _1671381)))))], (41515 ^ _782476) ^ [_1597037, _1597039, _1597041] : [-(hAPP(c_Relation_ORange(_1597037, _1597039), hAPP(c_Relation_Oconverse(_1597039, _1597037), _1597041)) = hAPP(c_Relation_ODomain(_1597039, _1597037), _1597041))], (43323 ^ _782476) ^ [_1642270, _1642272, _1642274] : [_1642270 = _1642272, 43326 ^ _782476 : [(43329 ^ _782476) ^ [_1642418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642418), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642274)), _1642270))), -(hAPP(hAPP(c_List_Onth(_1642274), _1642270), _1642418) = hAPP(hAPP(c_List_Onth(_1642274), _1642272), _1642418))], (43327 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642274)), _1642270) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642274)), _1642272))]]], (41082 ^ _782476) ^ [_1586674, _1586676] : [-(c_Transitive__Closure_Otrancl(_1586674, c_Transitive__Closure_Ortrancl(_1586674, _1586676)) = c_Transitive__Closure_Ortrancl(_1586674, _1586676))], (1742 ^ _782476) ^ [_807451, _807453] : [-(class_Rings_Oordered__semiring(_807451)), _807453 = _807451, class_Rings_Oordered__semiring(_807453)], (33066 ^ _782476) ^ [_1409307, _1409309, _1409311, _1409313] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409307), hAPP(c_Int_Onumber__class_Onumber__of(_1409307), _1409309)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409307), _1409311), _1409313)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409307), hAPP(c_Int_Onumber__class_Onumber__of(_1409307), _1409309)), _1409311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409307), hAPP(c_Int_Onumber__class_Onumber__of(_1409307), _1409309)), _1409313))), class_Int_Onumber(_1409307), class_Rings_Oring(_1409307)], (41913 ^ _782476) ^ [_1607150, _1607152, _1607154, _1607156, _1607158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607150, _1607150)), hAPP(hAPP(c_Product__Type_OPair(_1607150, _1607150), _1607152), _1607154)), c_Transitive__Closure_Ortrancl(_1607150, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607150, _1607150), tc_HOL_Obool)), _1607156), _1607158)))), 41919 ^ _782476 : [(41925 ^ _782476) ^ [] : [41918 ^ [_1607150, _1607152, _1607154, _1607156, _1607158] = 41921 ^ [_1607150, _1607152, _1607154, _1607156, _1607158]], (41923 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607150, _1607150)), hAPP(hAPP(c_Product__Type_OPair(_1607150, _1607150), 41918 ^ [_1607150, _1607152, _1607154, _1607156, _1607158]), 41921 ^ [_1607150, _1607152, _1607154, _1607156, _1607158])), _1607158)))], (41920 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607150, _1607150)), hAPP(hAPP(c_Product__Type_OPair(_1607150, _1607150), _1607152), 41918 ^ [_1607150, _1607152, _1607154, _1607156, _1607158])), c_Transitive__Closure_Ortrancl(_1607150, _1607156))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607150, _1607150)), hAPP(hAPP(c_Product__Type_OPair(_1607150, _1607150), _1607152), _1607154)), c_Transitive__Closure_Ortrancl(_1607150, _1607156))))], (20599 ^ _782476) ^ [_1169787, _1169789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169787)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169787), _1169789)))], (25694 ^ _782476) ^ [_1263885, _1263887, _1263889, _1263891] : [_1263885 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1263887, _1263889), 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)), _1263891))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263887), _1263885)))], (22244 ^ _782476) ^ [_1200242, _1200244, _1200246] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200242)), _1200244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200242)), _1200246), -(_1200244 = _1200246)], (17872 ^ _782476) ^ [_1121180, _1121182, _1121184, _1121186] : [class_Rings_Ocomm__semiring__1(_1121180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121180), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121180), c_Groups_Oone__class_Oone(_1121180)), c_Groups_Oone__class_Oone(_1121180))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121180), hAPP(hAPP(c_COMBB(_1121180, _1121180, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1121180), _1121182)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1121180, _1121180), hAPP(hAPP(c_COMBB(_1121180, tc_fun(_1121180, _1121180), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1121180)), c_Nat_Osemiring__1__class_Oof__nat(_1121180))), _1121184))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1121186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121180), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121180), _1121186)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121180), _1121182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121180), _1121182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121180), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121180), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121186), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1121184)))))], (892 ^ _782476) ^ [_796094, _796096, _796098, _796100] : [-(c_Relation_Oantisym(_796098, _796094)), c_Relation_Oantisym(_796100, _796096), _796100 = _796098, _796096 = _796094], (41857 ^ _782476) ^ [_1605608, _1605610] : [-(c_Transitive__Closure_Ortrancl(_1605608, _1605610) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1605608, _1605608), 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(_1605608, _1605608), tc_HOL_Obool), tc_fun(tc_prod(_1605608, _1605608), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1605608, _1605608), tc_HOL_Obool)), _1605610)))], (43589 ^ _782476) ^ [_1648993, _1648995, _1648997] : [-(hBOOL(hAPP(hAPP(c_member(_1648993), _1648995), hAPP(c_List_Oset(_1648993), _1648997)))), 43590 ^ _782476 : [(43591 ^ _782476) ^ [_1649067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649067), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648993)), _1648997))), hAPP(hAPP(c_List_Onth(_1648993), _1648997), _1649067) = _1648995]]], (45623 ^ _782476) ^ [_1696089, _1696091, _1696093, _1696095, _1696097, _1696099] : [class_Orderings_Olinorder(_1696089), -(hAPP(_1696091, _1696093) = hAPP(_1696091, _1696095)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696097, _1696089, _1696091), _1696095), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696097, _1696089, _1696091), _1696093), _1696099)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696097, _1696089, _1696091), _1696093), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696097, _1696089, _1696091), _1696095), _1696099)))], (46212 ^ _782476) ^ [_1708979, _1708981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708979), _1708981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708979)), hAPP(c_Code__Numeral_Oof__nat, _1708981))))], (11828 ^ _782476) ^ [_997822, _997824, _997826] : [class_Groups_Oordered__ab__group__add(_997822), 11831 ^ _782476 : [(11838 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997822), hAPP(c_Groups_Ouminus__class_Ouminus(_997822), _997826)), _997824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997822), hAPP(c_Groups_Ouminus__class_Ouminus(_997822), _997824)), _997826)))], (11832 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997822), hAPP(c_Groups_Ouminus__class_Ouminus(_997822), _997824)), _997826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997822), hAPP(c_Groups_Ouminus__class_Ouminus(_997822), _997826)), _997824)))]]], (37223 ^ _782476) ^ [_1490992, _1490994, _1490996, _1490998, _1491000, _1491002] : [-(hAPP(c_Product__Type_Oapsnd(_1490992, _1490994, _1490996, _1490998), hAPP(hAPP(c_Product__Type_OPair(_1490996, _1490992), _1491000), _1491002)) = hAPP(hAPP(c_Product__Type_OPair(_1490996, _1490994), _1491000), hAPP(_1490998, _1491002)))], (10867 ^ _782476) ^ [_982551, _982553, _982555, _982557, _982559] : [-(_982551 = c_Orderings_Obot__class_Obot(tc_fun(_982553, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982555, tc_HOL_Obool)), _982557), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982553, tc_fun(_982555, tc_HOL_Obool)), _982551), _982559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982553, tc_fun(_982555, tc_HOL_Obool)), _982551), hAPP(hAPP(c_COMBB(tc_fun(_982555, tc_HOL_Obool), tc_fun(_982555, tc_HOL_Obool), _982553), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982555, tc_HOL_Obool)), _982557)), _982559)))], (52621 ^ _782476) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (43545 ^ _782476) ^ [_1648002, _1648004, _1648006, _1648008, _1648010] : [hBOOL(hAPP(hAPP(c_member(_1648002), _1648004), hAPP(c_List_Oset(_1648002), _1648006))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648008), hAPP(_1648010, _1648004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648008), c_List_Olist_Olist__size(_1648002, _1648010, _1648006))))], (43761 ^ _782476) ^ [_1654710] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654710) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43764 ^ _782476 : [(43765 ^ _782476) ^ [_1654785] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1654785), hAPP(c_List_Oset(tc_Nat_Onat), _1654710))), -(_1654785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (35550 ^ _782476) ^ [] : [-(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)))))], (7271 ^ _782476) ^ [_903595, _903597, _903599, _903601] : [class_Groups_Ouminus(_903595), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903597, _903595)), _903599), _903601) = hAPP(c_Groups_Ouminus__class_Ouminus(_903595), hAPP(_903599, _903601)))], (38820 ^ _782476) ^ [_1526889, _1526891, _1526893, _1526895] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526889), _1526895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526893), _1526891), -(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), _1526889), _1526891)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526893), _1526895))), c_Int_Ointrel)))], (39718 ^ _782476) ^ [_1550628, _1550630, _1550632, _1550634] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550628, _1550630), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1550628, tc_HOL_Obool), _1550632)), _1550634) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1550628, tc_HOL_Obool), tc_fun(tc_prod(_1550628, _1550630), tc_HOL_Obool)), _1550632), hAPP(hAPP(c_COMBC(tc_fun(_1550628, tc_HOL_Obool), tc_fun(_1550628, tc_fun(_1550630, tc_HOL_Obool)), tc_fun(tc_prod(_1550628, _1550630), tc_HOL_Obool)), c_Product__Type_OSigma(_1550628, _1550630)), _1550634)))], (47266 ^ _782476) ^ [_1732716, _1732718] : [47268 ^ _782476 : [(47271 ^ _782476) ^ [] : [47267 ^ [_1732716, _1732718] = c_List_Olist_ONil(_1732716)], (47269 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732716)), 47267 ^ [_1732716, _1732718]), hAPP(c_List_Oset(tc_List_Olist(_1732716)), _1732718))))]], -(c_List_Otranspose(_1732716, _1732718) = c_List_Olist_ONil(tc_List_Olist(_1732716)))], (46078 ^ _782476) ^ [_1705740, _1705742, _1705744, _1705746, _1705748] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705740), tc_List_Olist(_1705742), tc_List_Olist(_1705744), hAPP(c_List_Omap(_1705740, _1705742), _1705746)), hAPP(c_List_Omap(_1705744, _1705740), _1705748)) = hAPP(c_List_Omap(_1705744, _1705742), hAPP(c_Fun_Ocomp(_1705740, _1705742, _1705744, _1705746), _1705748)))], (17750 ^ _782476) ^ [_1118989, _1118991, _1118993] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118989), _1118991)), _1118993) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118989), _1118993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118991), _1118993)))], (9613 ^ _782476) ^ [_955004, _955006, _955008, _955010] : [9615 ^ _782476 : [(9618 ^ _782476) ^ [] : [hAPP(_955010, 9614 ^ [_955004, _955006, _955008, _955010]) = c_Orderings_Obot__class_Obot(tc_fun(_955004, tc_HOL_Obool))], (9616 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_955006), 9614 ^ [_955004, _955006, _955008, _955010]), _955008)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_955004, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_955006, tc_fun(_955004, tc_HOL_Obool)), _955008), _955010))], (47154 ^ _782476) ^ [_1730160, _1730162, _1730164] : [47156 ^ _782476 : [(47159 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1730162, 47155 ^ [_1730160, _1730162, _1730164])))], (47157 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730160), 47155 ^ [_1730160, _1730162, _1730164]), hAPP(c_List_Oset(_1730160), _1730164))))]], -(hAPP(c_List_Ofilter(_1730160, _1730162), _1730164) = c_List_Olist_ONil(_1730160))], (35170 ^ _782476) ^ [_1447424, _1447426] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1447424)), c_Int_OBit0(_1447426)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447424), _1447426)))], (47313 ^ _782476) ^ [_1734652, _1734654, _1734656] : [class_Groups_Oab__semigroup__add(_1734652), -(c_List_Ofoldr(_1734652, _1734652, c_Groups_Oplus__class_Oplus(_1734652), _1734654, _1734656) = hAPP(c_List_Ofoldl(_1734652, _1734652, c_Groups_Oplus__class_Oplus(_1734652), _1734656), _1734654))], (50164 ^ _782476) ^ [_1795631, _1795633, _1795635, _1795637] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795631), hAPP(hAPP(c_List_Olist_OCons(_1795631), _1795633), _1795635)), _1795637)), -(_1795633 = _1795637), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795631), _1795635), _1795637)))], (13062 ^ _782476) ^ [_1022279, _1022281, _1022283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022279, tc_HOL_Obool)), _1022281), hAPP(hAPP(c_Set_Oinsert(_1022279), _1022283), c_Orderings_Obot__class_Obot(tc_fun(_1022279, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1022279, _1022283, _1022281) = _1022283)], (48502 ^ _782476) ^ [_1758318, _1758320, _1758322, _1758324, _1758326] : [hBOOL(hAPP(hAPP(c_member(_1758318), _1758320), hAPP(c_List_Oset(_1758318), _1758322))), -(hBOOL(hAPP(_1758324, _1758320))), -(c_List_OdropWhile(_1758318, _1758324, hAPP(hAPP(c_List_Oappend(_1758318), _1758322), _1758326)) = hAPP(hAPP(c_List_Oappend(_1758318), c_List_OdropWhile(_1758318, _1758324, _1758322)), _1758326))], (15184 ^ _782476) ^ [_1066319, _1066321] : [class_Lattices_Olattice(_1066319), -(c_Big__Operators_Olattice__class_OSup__fin(_1066319, hAPP(hAPP(c_Set_Oinsert(_1066319), _1066321), c_Orderings_Obot__class_Obot(tc_fun(_1066319, tc_HOL_Obool)))) = _1066321)], (41832 ^ _782476) ^ [_1604980, _1604982, _1604984] : [-(hAPP(hAPP(c_Nat_Ocompow(_1604980, _1604980), hAPP(c_Nat_OSuc, _1604982)), _1604984) = hAPP(c_Fun_Ocomp(_1604980, _1604980, _1604980, _1604984), hAPP(hAPP(c_Nat_Ocompow(_1604980, _1604980), _1604982), _1604984)))], (5360 ^ _782476) ^ [_864440, _864442] : [_864442 = _864440, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_864442) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_864440))], (32084 ^ _782476) ^ [_1390223, _1390225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390225)), -(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, _1390223, _1390225))))], (19026 ^ _782476) ^ [_1140663, _1140665, _1140667, _1140669] : [class_Rings_Olinordered__comm__semiring__strict(_1140663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140663), _1140665), _1140667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140663), c_Groups_Ozero__class_Ozero(_1140663)), _1140669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140663), _1140669), _1140665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140663), _1140669), _1140667))))], (46928 ^ _782476) ^ [_1724581, _1724583] : [c_List_Oremdups(_1724581, _1724583) = _1724583, -(hBOOL(hAPP(c_List_Odistinct(_1724581), _1724583)))], (48046 ^ _782476) ^ [_1748764, _1748766] : [c_List_Olist_ONil(_1748764) = hAPP(c_List_Orev(_1748764), _1748766), -(_1748766 = c_List_Olist_ONil(_1748764))], (17906 ^ _782476) ^ [_1122163, _1122165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122163), _1122165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122163), _1122165)))], (27823 ^ _782476) ^ [_1308625, _1308627, _1308629] : [class_Orderings_Olinorder(_1308625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308625), _1308627)), -(hBOOL(hAPP(hAPP(c_member(_1308625), _1308629), _1308627))), -(_1308627 = c_Orderings_Obot__class_Obot(tc_fun(_1308625, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308625, hAPP(hAPP(c_Set_Oinsert(_1308625), _1308629), _1308627)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308625), _1308629), c_Big__Operators_Olinorder__class_OMax(_1308625, _1308627)))], (17321 ^ _782476) ^ [_1111235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111235), _1111235))], (45009 ^ _782476) ^ [_1682144, _1682146, _1682148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682146)), _1682148))), -(hAPP(hAPP(c_List_Otake(_1682146), hAPP(c_Nat_OSuc, _1682144)), _1682148) = hAPP(hAPP(c_List_Oappend(_1682146), hAPP(hAPP(c_List_Otake(_1682146), _1682144), _1682148)), hAPP(hAPP(c_List_Olist_OCons(_1682146), hAPP(hAPP(c_List_Onth(_1682146), _1682148), _1682144)), c_List_Olist_ONil(_1682146))))], (44807 ^ _782476) ^ [_1677420, _1677422] : [-(hAPP(hAPP(c_List_Oappend(_1677420), _1677422), c_List_Olist_ONil(_1677420)) = _1677422)], (4578 ^ _782476) ^ [_852049, _852051] : [_852051 = _852049, -(c_Lazy__Sequence_Oyield(_852051) = c_Lazy__Sequence_Oyield(_852049))], (16431 ^ _782476) ^ [_1091978, _1091980, _1091982, _1091984] : [class_Groups_Ocancel__ab__semigroup__add(_1091978), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091978), _1091980), _1091982) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091978), _1091980), _1091984), -(_1091982 = _1091984)], (40816 ^ _782476) ^ [_1580197, _1580199, _1580201, _1580203, _1580205, _1580207, _1580209, _1580211] : [class_Groups_Ocomm__monoid__add(_1580197), class_Orderings_Oord(_1580199), _1580201 = _1580203, _1580205 = _1580207, 40834 ^ _782476 : [(40839 ^ _782476) ^ [] : [hAPP(_1580209, 40833 ^ [_1580197, _1580199, _1580201, _1580203, _1580205, _1580207, _1580209, _1580211]) = hAPP(_1580211, 40833 ^ [_1580197, _1580199, _1580201, _1580203, _1580205, _1580207, _1580209, _1580211])], (40837 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1580199), 40833 ^ [_1580197, _1580199, _1580201, _1580203, _1580205, _1580207, _1580209, _1580211]), _1580207)))], (40835 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1580199), _1580203), 40833 ^ [_1580197, _1580199, _1580201, _1580203, _1580205, _1580207, _1580209, _1580211])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580199, _1580197), _1580209), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580199, _1580201), _1580205)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580199, _1580197), _1580211), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580199, _1580203), _1580207)))], (3766 ^ _782476) ^ [_838927, _838929, _838931, _838933, _838935, _838937, _838939, _838941] : [-(c_List_Omaps(_838941, _838937, _838933, _838929) = c_List_Omaps(_838939, _838935, _838931, _838927)), _838941 = _838939, _838937 = _838935, _838933 = _838931, _838929 = _838927], (32247 ^ _782476) ^ [_1393187, _1393189, _1393191] : [-(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), _1393187), _1393189)), _1393189)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393187, _1393189))), _1393191) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393187), _1393191))], (7013 ^ _782476) ^ [_897911, _897913, _897915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897911, tc_HOL_Obool)), _897913), _897915)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_897911, tc_HOL_Obool)), _897913), hAPP(c_Set_OPow(_897911), _897915))))], (52767 ^ _782476) ^ [_1844731, _1844733] : [hBOOL(hAPP(hAPP(c_fimplies, _1844731), _1844733)), hBOOL(_1844731), -(hBOOL(_1844733))], (41094 ^ _782476) ^ [_1586918, _1586920, _1586922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1586918, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586918, _1586918, _1586920), _1586922)), _1586922)), -(hAPP(c_Relation_OImage(_1586918, _1586918, c_Transitive__Closure_Ortrancl(_1586918, _1586920)), _1586922) = _1586922)], (43735 ^ _782476) ^ [_1654247, _1654249] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654247, _1654249)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654247, _1654249))], (45080 ^ _782476) ^ [_1684035, _1684037] : [-(hAPP(hAPP(c_List_Odrop(_1684035), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1684037) = _1684037)], (12412 ^ _782476) ^ [_1007942, _1007944, _1007946] : [class_Orderings_Olinorder(_1007942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007942), _1007944), _1007946)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007942, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1007942), _1007944)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1007942, _1007944, _1007946)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1007942), _1007946))], (23217 ^ _782476) ^ [_1218254, _1218256, _1218258, _1218260] : [class_Groups_Ocomm__monoid__add(_1218254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218256), _1218258)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218254), _1218260), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1218256, _1218258)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218254), hAPP(_1218260, _1218256)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218254), _1218260), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218256), _1218258))))], (38756 ^ _782476) ^ [_1524882, _1524884, _1524886, _1524888] : [_1524882 = _1524884, hBOOL(hAPP(hAPP(c_member(_1524886), _1524882), _1524888)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524886, _1524886)), hAPP(hAPP(c_Product__Type_OPair(_1524886, _1524886), _1524882), _1524884)), c_Relation_OId__on(_1524886, _1524888))))], (21347 ^ _782476) ^ [_1183264, _1183266] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183264)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183266)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1183264), _1183266)))], (51825 ^ _782476) ^ [_1832294, _1832296, _1832298, _1832300] : [class_Rings_Odvd(_1832294), _1832296 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832294), _1832298), _1832300), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832294), _1832298), _1832296)))], (3084 ^ _782476) ^ [_828318, _828320, _828322, _828324] : [-(c_Wellfounded_Oacc(_828324, _828320) = c_Wellfounded_Oacc(_828322, _828318)), _828324 = _828322, _828320 = _828318], (6014 ^ _782476) ^ [_877748, _877750, _877752] : [class_Orderings_Oorder(_877748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877748), _877750), _877752)), 6021 ^ _782476 : [(6028 ^ _782476) ^ [] : [_877752 = _877750, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877748), _877752), _877750)))], (6022 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877748), _877752), _877750)), -(_877752 = _877750)]]], (38409 ^ _782476) ^ [] : [-(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))], (22164 ^ _782476) ^ [_1198886, _1198888] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198886)), _1198888) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198886), _1198888)))], (24945 ^ _782476) ^ [_1248882, _1248884] : [class_Rings_Olinordered__idom(_1248882), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248882), c_Groups_Osgn__class_Osgn(_1248882, _1248884)), hAPP(c_Groups_Oabs__class_Oabs(_1248882), _1248884)) = _1248884)], (52367 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (42673 ^ _782476) ^ [_1623311, _1623313] : [-(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)))), _1623311)) = 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)))), _1623313))), 42675 ^ _782476 : [(42678 ^ _782476) ^ [] : [42679 ^ _782476 : [(42682 ^ _782476) ^ [] : [hBOOL(hAPP(_1623313, 42674 ^ [_1623311, _1623313]))], (42680 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1623311, 42674 ^ [_1623311, _1623313])))]], 42683 ^ _782476 : [(42686 ^ _782476) ^ [] : [hBOOL(hAPP(_1623311, 42674 ^ [_1623311, _1623313]))], (42684 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1623313, 42674 ^ [_1623311, _1623313])))]]], (42676 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42674 ^ [_1623311, _1623313])))]]], (35590 ^ _782476) ^ [_1454861, _1454863] : [class_Fields_Olinordered__field__inverse__zero(_1454861), class_Int_Onumber__ring(_1454861), 35597 ^ _782476 : [(35604 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454861), c_Groups_Ozero__class_Ozero(_1454861)), _1454863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454861), c_Groups_Ozero__class_Ozero(_1454861)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454861), _1454863), hAPP(c_Int_Onumber__class_Onumber__of(_1454861), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35598 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454861), c_Groups_Ozero__class_Ozero(_1454861)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454861), _1454863), hAPP(c_Int_Onumber__class_Onumber__of(_1454861), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454861), c_Groups_Ozero__class_Ozero(_1454861)), _1454863)))]]], (43061 ^ _782476) ^ [_1634413, _1634415, _1634417, _1634419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634413), tc_List_Olist(_1634413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634413), tc_List_Olist(_1634413)), _1634415), _1634417)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634413), tc_List_Olist(_1634413)), c_List_Olistrel1(_1634413, _1634419)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634413), tc_List_Olist(_1634413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634413), tc_List_Olist(_1634413)), _1634415), _1634417)), c_List_Olistrel1(_1634413, hAPP(c_Relation_Oconverse(_1634413, _1634413), _1634419)))))], (6231 ^ _782476) ^ [_881530, _881532, _881534, _881536, _881538] : [class_Complete__Lattice_Ocomplete__lattice(_881530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881532, tc_HOL_Obool)), _881534), _881536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881530), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881532, _881530), _881534), _881538)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881532, _881530), _881536), _881538))))], (49358 ^ _782476) ^ [_1777464, _1777466, _1777468] : [c_FunDef_Ois__measure(_1777464, _1777466), -(c_FunDef_Ois__measure(tc_prod(_1777468, _1777464), hAPP(hAPP(c_COMBB(_1777464, tc_Nat_Onat, tc_prod(_1777468, _1777464)), _1777466), c_Product__Type_Osnd(_1777468, _1777464))))], (48401 ^ _782476) ^ [_1756193, _1756195, _1756197, _1756199, _1756201] : [class_Orderings_Olinorder(_1756193), c_List_Olinorder__class_Osorted(_1756193, hAPP(c_List_Orev(_1756193), hAPP(hAPP(c_List_Omap(_1756195, _1756193), _1756197), _1756199))), -(hAPP(c_List_Ofilter(_1756195, hAPP(hAPP(c_COMBB(_1756193, tc_HOL_Obool, _1756195), hAPP(c_Orderings_Oord__class_Oless(_1756193), _1756201)), _1756197)), _1756199) = c_List_OtakeWhile(_1756195, hAPP(hAPP(c_COMBB(_1756193, tc_HOL_Obool, _1756195), hAPP(c_Orderings_Oord__class_Oless(_1756193), _1756201)), _1756197), _1756199))], (25604 ^ _782476) ^ [_1261331, _1261333, _1261335, _1261337] : [hBOOL(hAPP(hAPP(c_member(_1261331), _1261333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261331, tc_HOL_Obool)), _1261335), hAPP(c_Set_OCollect(_1261331), _1261337)))), 25607 ^ _782476 : [(25610 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1261337, _1261333)))], (25608 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261331), _1261333), _1261335)))]]], (17477 ^ _782476) ^ [_1113971, _1113973, _1113975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113973), _1113975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113971), _1113973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113971), _1113975))))], (19456 ^ _782476) ^ [_1148386, _1148388] : [class_Groups_Oordered__ab__group__add(_1148386), 19459 ^ _782476 : [(19466 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), _1148388), c_Groups_Ozero__class_Ozero(_1148386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), c_Groups_Ozero__class_Ozero(_1148386)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148386), _1148388))))], (19460 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), c_Groups_Ozero__class_Ozero(_1148386)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148386), _1148388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), _1148388), c_Groups_Ozero__class_Ozero(_1148386))))]]], (25079 ^ _782476) ^ [_1251049, _1251051, _1251053] : [class_Groups_Oordered__ab__group__add__abs(_1251049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251049), hAPP(c_Groups_Oabs__class_Oabs(_1251049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251049), _1251051), _1251053))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251049), hAPP(c_Groups_Oabs__class_Oabs(_1251049), _1251051)), hAPP(c_Groups_Oabs__class_Oabs(_1251049), _1251053)))))], (21985 ^ _782476) ^ [_1196068] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1196068)) = hAPP(c_Nat_OSuc, _1196068))], (25285 ^ _782476) ^ [_1255126] : [_1255126 = 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), _1255126)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7277 ^ _782476) ^ [_903739, _903741, _903743, _903745, _903747, _903749] : [hBOOL(hAPP(hAPP(c_member(_903739), _903741), c_SetInterval_Oord_OgreaterThanAtMost(_903739, _903743, _903745, _903747, _903749))), 7280 ^ _782476 : [(7283 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_903743, _903741), _903749)))], (7281 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_903745, _903747), _903741)))]]], (52447 ^ _782476) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (1462 ^ _782476) ^ [_803951, _803953] : [-(class_Lattices_Obounded__lattice__bot(_803951)), _803953 = _803951, class_Lattices_Obounded__lattice__bot(_803953)], (17175 ^ _782476) ^ [_1108661, _1108663] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1108661, _1108663))))], (9680 ^ _782476) ^ [_956154, _956156] : [class_Lattices_Obounded__lattice__bot(_956154), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956154), c_Orderings_Obot__class_Obot(_956154)), _956156) = c_Orderings_Obot__class_Obot(_956154))], (40702 ^ _782476) ^ [_1577256, _1577258, _1577260] : [40704 ^ _782476 : [(40707 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577256), 40703 ^ [_1577256, _1577258, _1577260]), c_Wellfounded_Oacc(_1577256, _1577260)))], (40705 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577256, _1577256)), hAPP(hAPP(c_Product__Type_OPair(_1577256, _1577256), 40703 ^ [_1577256, _1577258, _1577260]), _1577258)), _1577260)))]], -(hBOOL(hAPP(hAPP(c_member(_1577256), _1577258), c_Wellfounded_Oacc(_1577256, _1577260))))], (40798 ^ _782476) ^ [_1579743, _1579745, _1579747, _1579749, _1579751, _1579753, _1579755, _1579757, _1579759] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579743, _1579745, _1579747, _1579749), hAPP(hAPP(c_Product__Type_Oscomp(_1579743, _1579751, _1579753, tc_prod(_1579745, _1579747)), _1579755), _1579757)), _1579759) = hAPP(hAPP(c_Product__Type_Oscomp(_1579743, _1579751, _1579753, _1579749), _1579755), hAPP(hAPP(c_COMBC(_1579751, tc_fun(_1579745, tc_fun(_1579747, _1579749)), tc_fun(_1579753, _1579749)), hAPP(hAPP(c_COMBB(tc_fun(_1579753, tc_prod(_1579745, _1579747)), tc_fun(tc_fun(_1579745, tc_fun(_1579747, _1579749)), tc_fun(_1579753, _1579749)), _1579751), c_Product__Type_Oscomp(_1579753, _1579745, _1579747, _1579749)), _1579757)), _1579759)))], (34654 ^ _782476) ^ [] : [-(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)))], (34840 ^ _782476) ^ [_1440782, _1440784] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440782))), _1440784) = 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)))), _1440782), _1440784))], (14216 ^ _782476) ^ [_1047249, _1047251] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047249, _1047251)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047249, _1047251), tc_HOL_Obool)))), 14219 ^ _782476 : [(14222 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047251), c_Orderings_Otop__class_Otop(tc_fun(_1047251, tc_HOL_Obool)))))], (14220 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047249), c_Orderings_Otop__class_Otop(tc_fun(_1047249, tc_HOL_Obool)))))]]], (50995 ^ _782476) ^ [_1814805, _1814807] : [-(c_Relation_Osym(_1814805, c_Relation_OId__on(_1814805, _1814807)))], (9273 ^ _782476) ^ [_948297, _948299, _948301] : [hAPP(c_Set_Oimage(_948299, tc_fun(_948299, tc_HOL_Obool), _948297), _948301) = hAPP(c_Set_OPow(_948299), _948301)], (40800 ^ _782476) ^ [_1579870, _1579872, _1579874, _1579876, _1579878, _1579880, _1579882] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579870, _1579872, _1579874, _1579876), _1579878), _1579880), _1579882) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579872, _1579874, _1579876), _1579880), hAPP(_1579878, _1579882)))], (46974 ^ _782476) ^ [_1725441, _1725443, _1725445] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1725441), tc_List_Olist(_1725441), c_List_Oappend(_1725441), _1725443), _1725445) = hAPP(hAPP(c_List_Oappend(_1725441), _1725443), c_List_Oconcat(_1725441, _1725445)))], (50789 ^ _782476) ^ [_1810509, _1810511, _1810513, _1810515] : [c_Wellfounded_Omax__extp(_1810509, _1810511, _1810513, _1810515), 50792 ^ _782476 : [(50795 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1810509), _1810515)))], (50797 ^ _782476) ^ [] : [_1810515 = c_Orderings_Obot__class_Obot(tc_fun(_1810509, tc_HOL_Obool))], (50799 ^ _782476) ^ [_1810725] : [hBOOL(hAPP(hAPP(c_member(_1810509), _1810725), _1810513)), 50803 ^ _782476 : [(50806 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1810511, _1810725), 50802 ^ [_1810509, _1810511, _1810513, _1810515, _1810725])))], (50804 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810509), 50802 ^ [_1810509, _1810511, _1810513, _1810515, _1810725]), _1810515)))]]], (50793 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1810509), _1810513)))]]], (13554 ^ _782476) ^ [_1033344, _1033346, _1033348, _1033350, _1033352] : [class_Groups_Oab__semigroup__mult(_1033344), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033344, _1033344, c_Groups_Otimes__class_Otimes(_1033344), _1033346, _1033348), _1033350)), hBOOL(hAPP(hAPP(c_member(_1033344), _1033352), _1033348)), -(hBOOL(hAPP(hAPP(c_member(_1033344), _1033346), _1033348))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033344, _1033344, c_Groups_Otimes__class_Otimes(_1033344), _1033352, hAPP(hAPP(c_Set_Oinsert(_1033344), _1033346), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033344, tc_HOL_Obool)), _1033348), hAPP(hAPP(c_Set_Oinsert(_1033344), _1033352), c_Orderings_Obot__class_Obot(tc_fun(_1033344, tc_HOL_Obool)))))), _1033350)))], (20823 ^ _782476) ^ [_1173963, _1173965, _1173967] : [hBOOL(hAPP(_1173963, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1173965), _1173967)))), 20826 ^ _782476 : [(20833 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173965), _1173967)), -(hBOOL(hAPP(_1173963, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20827 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173967), _1173965)), -(hBOOL(hAPP(_1173963, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173965)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173967)))))]]], (37493 ^ _782476) ^ [_1495865, _1495867, _1495869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495865, tc_fun(_1495865, tc_HOL_Obool))), _1495867), _1495869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495865, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1495865, _1495869)), c_Wellfounded_Oaccp(_1495865, _1495867))))], (48667 ^ _782476) ^ [_1761953, _1761955] : [-(c_List_OremoveAll(_1761953, _1761955) = c_List_Ofilter(_1761953, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1761953), c_fNot), hAPP(c_fequal, _1761955))))], (43350 ^ _782476) ^ [_1642917, _1642919, _1642921, _1642923] : [-(hAPP(hAPP(c_List_Onth(_1642917), hAPP(hAPP(c_List_Olist_OCons(_1642917), _1642919), _1642921)), _1642923) = c_Nat_Onat_Onat__case(_1642917, _1642919, hAPP(c_List_Onth(_1642917), _1642921), _1642923))], (1972 ^ _782476) ^ [_810326, _810328] : [-(class_Groups_Oone(_810326)), _810328 = _810326, class_Groups_Oone(_810328)], (50917 ^ _782476) ^ [_1813067, _1813069] : [c_Relation_Oantisym(_1813067, _1813069), -(c_Relation_Oantisym(_1813067, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813067, _1813067), tc_HOL_Obool)), _1813069), c_Relation_OId(_1813067))))], (47335 ^ _782476) ^ [_1735145, _1735147, _1735149] : [-(c_List_Osublist(_1735145, _1735147, _1735149) = hAPP(hAPP(c_List_Omap(tc_prod(_1735145, tc_Nat_Onat), _1735145), c_Product__Type_Ofst(_1735145, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735145, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735145, 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(_1735145, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735145, tc_Nat_Onat))), _1735149)), hAPP(hAPP(c_List_Ozip(_1735145, tc_Nat_Onat), _1735147), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735145)), _1735147))))))], (46258 ^ _782476) ^ [_1709678, _1709680, _1709682, _1709684] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709678)), _1709680) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709682)), _1709684), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709678, _1709682), _1709678), c_Product__Type_Ofst(_1709678, _1709682)), hAPP(hAPP(c_List_Ozip(_1709678, _1709682), _1709680), _1709684)) = _1709680)], (7810 ^ _782476) ^ [_914843, _914845, _914847] : [class_Lattices_Olattice(_914843), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914843), _914845), _914847) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914843), _914847), _914845))], (27683 ^ _782476) ^ [_1306032, _1306034, _1306036] : [class_Orderings_Olinorder(_1306032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306032), _1306034)), -(_1306034 = c_Orderings_Obot__class_Obot(tc_fun(_1306032, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1306032, hAPP(hAPP(c_Set_Oinsert(_1306032), _1306036), _1306034)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306032), _1306036), c_Big__Operators_Olinorder__class_OMin(_1306032, _1306034)))], (12794 ^ _782476) ^ [_1016900, _1016902, _1016904, _1016906] : [-(c_Nitpick_Ofold__graph_H(_1016900, _1016902, _1016904, _1016906, c_Orderings_Obot__class_Obot(tc_fun(_1016900, tc_HOL_Obool)), _1016906))], (52525 ^ _782476) ^ [_1841929, _1841931] : [-(class_Nat_Osize(tc_sum(_1841929, _1841931)))], (23127 ^ _782476) ^ [_1216689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216689)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216689), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1216689)], (9955 ^ _782476) ^ [_961960, _961962] : [class_Lattices_Oboolean__algebra(_961960), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961960), _961962), hAPP(c_Groups_Ouminus__class_Ouminus(_961960), _961962)) = c_Orderings_Obot__class_Obot(_961960))], (2914 ^ _782476) ^ [_825681, _825683, _825685, _825687, _825689, _825691] : [-(c_Nitpick_Oof__frac(_825691, _825687, _825683) = c_Nitpick_Oof__frac(_825689, _825685, _825681)), _825691 = _825689, _825687 = _825685, _825683 = _825681], (36815 ^ _782476) ^ [_1483140, _1483142, _1483144, _1483146, _1483148] : [hBOOL(hAPP(hAPP(_1483140, _1483142), _1483144)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483146, _1483148, tc_HOL_Obool), _1483140), hAPP(hAPP(c_Product__Type_OPair(_1483146, _1483148), _1483142), _1483144))))], (34010 ^ _782476) ^ [_1427281, _1427283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427281), _1427283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427281)), c_Int_OBit1(_1427283))))], (26594 ^ _782476) ^ [_1284769, _1284771, _1284773, _1284775] : [class_Orderings_Olinorder(_1284769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284769), _1284771), _1284773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284769), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284769), _1284775), _1284771)), _1284773)))], (40335 ^ _782476) ^ [_1568020, _1568022, _1568024, _1568026] : [c_Relation_Orefl__on(_1568020, _1568022, _1568024), hBOOL(hAPP(hAPP(c_member(_1568020), _1568026), _1568022)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568020, _1568020)), hAPP(hAPP(c_Product__Type_OPair(_1568020, _1568020), _1568026), _1568026)), _1568024)))], (49498 ^ _782476) ^ [_1780765, _1780767, _1780769, _1780771, _1780773] : [c_Fun_Oinj__on(_1780765, _1780767, _1780769, _1780771), hBOOL(hAPP(hAPP(c_member(_1780765), _1780773), _1780771)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780765, _1780767, _1780771, _1780769), hAPP(_1780769, _1780773)) = _1780773)], (52481 ^ _782476) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (44382 ^ _782476) ^ [_1667481, _1667483, _1667485] : [-(hAPP(hAPP(c_List_Olist__update(_1667481, c_List_Olist_ONil(_1667481)), _1667483), _1667485) = c_List_Olist_ONil(_1667481))], (34390 ^ _782476) ^ [_1433572] : [-(c_Int_Opred(_1433572) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1433572), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32072 ^ _782476) ^ [_1390019, _1390021, _1390023] : [class_Divides_Osemiring__div(_1390019), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1390019), c_Divides_Odiv__class_Omod(_1390019, _1390021, _1390023)), _1390023) = c_Groups_Ozero__class_Ozero(_1390019))], (44510 ^ _782476) ^ [_1670200, _1670202, _1670204] : [-(c_List_Olistset(_1670200, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1670200, tc_HOL_Obool)), _1670202), _1670204)) = c_List_Oset__Cons(_1670200, _1670202, c_List_Olistset(_1670200, _1670204)))], (12768 ^ _782476) ^ [_1016399, _1016401, _1016403, _1016405, _1016407] : [c_Fun_Oinj__on(_1016399, _1016401, _1016403, _1016405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016399, tc_HOL_Obool)), _1016407), _1016405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016401, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1016399, _1016401, _1016403), _1016407)), hAPP(c_Set_Oimage(_1016399, _1016401, _1016403), _1016405))))], (17177 ^ _782476) ^ [_1108692, _1108694, _1108696, _1108698] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108692), _1108694)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108696), _1108694)), _1108698)) = 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), _1108692), _1108696)), _1108694)), _1108698))], (39186 ^ _782476) ^ [_1537677, _1537679] : [c_Wellfounded_Owf(_1537677, _1537679), -(c_Wellfounded_Owf(_1537677, hAPP(hAPP(c_Relation_Orel__comp(_1537677, _1537677, _1537677), _1537679), _1537679)))], (49005 ^ _782476) ^ [_1770376, _1770378, _1770380] : [class_Orderings_Olinorder(_1770376), 49011 ^ _782476 : [(49014 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770376), _1770380), 49010 ^ [_1770376, _1770378, _1770380]))], (49012 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770376), 49010 ^ [_1770376, _1770378, _1770380]), hAPP(c_List_Oset(_1770376), _1770378))))]], c_List_Olinorder__class_Osorted(_1770376, _1770378), -(c_List_Olinorder__class_Osorted(_1770376, hAPP(hAPP(c_List_Olist_OCons(_1770376), _1770380), _1770378)))], (42749 ^ _782476) ^ [_1624914, _1624916, _1624918, _1624920] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624914, _1624916)), _1624918), hAPP(c_Relation_Oconverse(_1624916, _1624914), _1624920))), 42754 ^ _782476 : [(42757 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624916, _1624914)), hAPP(hAPP(c_Product__Type_OPair(_1624916, _1624914), 42752 ^ [_1624914, _1624916, _1624918, _1624920]), 42753 ^ [_1624914, _1624916, _1624918, _1624920])), _1624920)))], (42755 ^ _782476) ^ [] : [-(_1624918 = hAPP(hAPP(c_Product__Type_OPair(_1624914, _1624916), 42753 ^ [_1624914, _1624916, _1624918, _1624920]), 42752 ^ [_1624914, _1624916, _1624918, _1624920]))]]], (5490 ^ _782476) ^ [_866481, _866483] : [_866483 = _866481, -(c_Groups_Ozero__class_Ozero(_866483) = c_Groups_Ozero__class_Ozero(_866481))], (12924 ^ _782476) ^ [_1019206, _1019208, _1019210, _1019212, _1019214] : [c_Fun_Oinj__on(_1019206, _1019208, _1019210, c_Orderings_Otop__class_Otop(tc_fun(_1019206, tc_HOL_Obool))), 12927 ^ _782476 : [(12934 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019206, tc_HOL_Obool)), _1019212), _1019214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019208, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019206, _1019208, _1019210), _1019212)), hAPP(c_Set_Oimage(_1019206, _1019208, _1019210), _1019214))))], (12928 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019208, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019206, _1019208, _1019210), _1019212)), hAPP(c_Set_Oimage(_1019206, _1019208, _1019210), _1019214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019206, tc_HOL_Obool)), _1019212), _1019214)))]]], (47413 ^ _782476) ^ [_1736728, _1736730] : [47414 ^ _782476 : [(47417 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736730), _1736728))], (47415 ^ _782476) ^ [] : [_1736730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1736728, _1736730) = c_List_Olist_ONil(tc_Nat_Onat))], (41072 ^ _782476) ^ [_1586410, _1586412, _1586414] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586410, _1586410)), hAPP(hAPP(c_Product__Type_OPair(_1586410, _1586410), _1586412), _1586412)), c_Transitive__Closure_Ortrancl(_1586410, _1586414))))], (8459 ^ _782476) ^ [_929093, _929095] : [class_Lattices_Oboolean__algebra(_929093), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_929093), _929095), hAPP(c_Groups_Ouminus__class_Ouminus(_929093), _929095)) = c_Orderings_Otop__class_Otop(_929093))], (20579 ^ _782476) ^ [] : [-(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))], (22616 ^ _782476) ^ [_1206598, _1206600] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206598), hAPP(c_Nat_OSuc, _1206600)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206598), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1206600))], (41517 ^ _782476) ^ [_1597082, _1597084, _1597086, _1597088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597082, _1597082)), hAPP(hAPP(c_Product__Type_OPair(_1597082, _1597082), _1597084), _1597086)), c_Transitive__Closure_Ortrancl(_1597082, _1597088))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597082, _1597082)), hAPP(hAPP(c_Product__Type_OPair(_1597082, _1597082), _1597086), _1597084)), c_Transitive__Closure_Ortrancl(_1597082, hAPP(c_Relation_Oconverse(_1597082, _1597082), _1597088)))))], (24650 ^ _782476) ^ [_1243374, _1243376] : [class_Rings_Olinordered__idom(_1243374), 24653 ^ _782476 : [(24660 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243376), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243374), hAPP(c_Int_Oring__1__class_Oof__int(_1243374), _1243376)), c_Groups_Ozero__class_Ozero(_1243374))))], (24654 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243374), hAPP(c_Int_Oring__1__class_Oof__int(_1243374), _1243376)), c_Groups_Ozero__class_Ozero(_1243374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243376), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37756 ^ _782476) ^ [_1501329, _1501331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501329), 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)), _1501331)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501329), _1501331) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1501329, _1501331)))], (43237 ^ _782476) ^ [_1640030] : [-(c_List_Olists(_1640030, c_Orderings_Otop__class_Otop(tc_fun(_1640030, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1640030), tc_HOL_Obool)))], (45082 ^ _782476) ^ [_1684068, _1684070, _1684072, _1684074] : [-(hAPP(hAPP(c_List_Odrop(_1684068), _1684070), hAPP(hAPP(c_List_Odrop(_1684068), _1684072), _1684074)) = hAPP(hAPP(c_List_Odrop(_1684068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684070), _1684072)), _1684074))], (19576 ^ _782476) ^ [_1150333, _1150335] : [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), _1150333), _1150335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150335)))], (9973 ^ _782476) ^ [_962261] : [class_Lattices_Oboolean__algebra(_962261), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962261), c_Orderings_Obot__class_Obot(_962261)) = c_Orderings_Otop__class_Otop(_962261))], (47256 ^ _782476) ^ [_1732506, _1732508] : [c_List_Otranspose(_1732506, _1732508) = c_List_Olist_ONil(tc_List_Olist(_1732506)), 47259 ^ _782476 : [(47260 ^ _782476) ^ [_1732601] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732506)), _1732601), hAPP(c_List_Oset(tc_List_Olist(_1732506)), _1732508))), -(_1732601 = c_List_Olist_ONil(_1732506))]]], (10329 ^ _782476) ^ [_969674, _969676, _969678] : [-(hBOOL(hAPP(hAPP(c_member(_969674), _969676), hAPP(hAPP(c_Set_Oinsert(_969674), _969676), _969678))))], (37261 ^ _782476) ^ [_1491591, _1491593] : [-(c_Divides_Opdivmod(_1491591, _1491593) = 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), _1491591)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491593))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491591), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491593))))], (26664 ^ _782476) ^ [_1285977, _1285979, _1285981, _1285983] : [class_Orderings_Olinorder(_1285977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285977), _1285979), _1285981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285977), _1285979), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285977), _1285983), _1285981))))], (32253 ^ _782476) ^ [_1393342, _1393344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393342), _1393344)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393342, _1393344) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393342), _1393344))], (46218 ^ _782476) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50072 ^ _782476) ^ [_1793380, _1793382, _1793384] : [-(hAPP(c_List_Oset(_1793380), c_List_Oreplicate(_1793380, hAPP(c_Nat_OSuc, _1793382), _1793384)) = hAPP(hAPP(c_Set_Oinsert(_1793380), _1793384), c_Orderings_Obot__class_Obot(tc_fun(_1793380, tc_HOL_Obool))))], (19302 ^ _782476) ^ [_1145757, _1145759, _1145761] : [class_Groups_Oordered__ab__group__add(_1145757), 19305 ^ _782476 : [(19312 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145757), _1145759), _1145761)), c_Groups_Ozero__class_Ozero(_1145757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145757), _1145759), _1145761)))], (19306 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145757), _1145759), _1145761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145757), _1145759), _1145761)), c_Groups_Ozero__class_Ozero(_1145757))))]]], (39088 ^ _782476) ^ [_1534705, _1534707, _1534709, _1534711, _1534713, _1534715, _1534717] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534705, _1534707, _1534709, hAPP(hAPP(c_COMBC(_1534705, tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_fun(_1534707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534707, tc_fun(tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_fun(_1534707, tc_HOL_Obool)), _1534705), c_COMBC(_1534707, tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534707, tc_prod(_1534705, _1534707)), tc_fun(_1534707, tc_fun(tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_HOL_Obool)), _1534705), hAPP(c_COMBB(tc_prod(_1534705, _1534707), tc_fun(tc_fun(tc_prod(_1534705, _1534707), tc_HOL_Obool), tc_HOL_Obool), _1534707), c_member(tc_prod(_1534705, _1534707)))), c_Product__Type_OPair(_1534705, _1534707)))), _1534711), hAPP(hAPP(c_COMBC(_1534707, tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_fun(_1534709, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534709, tc_fun(tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_fun(_1534709, tc_HOL_Obool)), _1534707), c_COMBC(_1534709, tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534709, tc_prod(_1534707, _1534709)), tc_fun(_1534709, tc_fun(tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_HOL_Obool)), _1534707), hAPP(c_COMBB(tc_prod(_1534707, _1534709), tc_fun(tc_fun(tc_prod(_1534707, _1534709), tc_HOL_Obool), tc_HOL_Obool), _1534709), c_member(tc_prod(_1534707, _1534709)))), c_Product__Type_OPair(_1534707, _1534709)))), _1534713)), _1534715), _1534717)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534705, _1534709)), hAPP(hAPP(c_Product__Type_OPair(_1534705, _1534709), _1534715), _1534717)), hAPP(hAPP(c_Relation_Orel__comp(_1534705, _1534707, _1534709), _1534711), _1534713))))], (9360 ^ _782476) ^ [_950175, _950177] : [hBOOL(hAPP(hAPP(c_member(_950175), _950177), c_Orderings_Obot__class_Obot(tc_fun(_950175, tc_HOL_Obool))))], (10755 ^ _782476) ^ [_979695, _979697, _979699, _979701] : [-(_979695 = c_Orderings_Obot__class_Obot(tc_fun(_979697, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_979697, _979699, hAPP(c_COMBK(_979699, _979697), _979701)), _979695) = hAPP(hAPP(c_Set_Oinsert(_979699), _979701), c_Orderings_Obot__class_Obot(tc_fun(_979699, tc_HOL_Obool))))], (10433 ^ _782476) ^ [_972263, _972265, _972267, _972269] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972263, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972263), _972265), _972267)), hAPP(hAPP(c_Set_Oinsert(_972263), _972265), _972269)) = hAPP(hAPP(c_Set_Oinsert(_972263), _972265), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972263, tc_HOL_Obool)), _972267), _972269)))], (5260 ^ _782476) ^ [_862880, _862882, _862884, _862886, _862888, _862890, _862892, _862894] : [-(c_Quotient_OBabs(_862894, _862890, _862886, _862882) = c_Quotient_OBabs(_862892, _862888, _862884, _862880)), _862894 = _862892, _862890 = _862888, _862886 = _862884, _862882 = _862880], (12854 ^ _782476) ^ [_1017918, _1017920] : [class_Complete__Lattice_Ocomplete__lattice(_1017918), c_Orderings_Oorder__class_Omono(_1017918, _1017918, _1017920), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1017918, _1017920) = hAPP(_1017920, c_Inductive_Ocomplete__lattice__class_Olfp(_1017918, _1017920)))], (16789 ^ _782476) ^ [_1099271, _1099273, _1099275, _1099277, _1099279] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1099271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099271), _1099273), _1099275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099271), _1099277), _1099279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099271), _1099273), _1099277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099271), _1099275), _1099279))))], (29868 ^ _782476) ^ [_1349299, _1349301, _1349303] : [class_Fields_Olinordered__field__inverse__zero(_1349299), 29871 ^ _782476 : [(29886 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349299), _1349301), _1349303)), c_Groups_Ozero__class_Ozero(_1349299)))), 29887 ^ _782476 : [(29894 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), _1349301), c_Groups_Ozero__class_Ozero(_1349299))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), c_Groups_Ozero__class_Ozero(_1349299)), _1349303))], (29888 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), c_Groups_Ozero__class_Ozero(_1349299)), _1349301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), _1349303), c_Groups_Ozero__class_Ozero(_1349299)))]]], (29872 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349299), _1349301), _1349303)), c_Groups_Ozero__class_Ozero(_1349299))), 29877 ^ _782476 : [(29880 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), _1349303), c_Groups_Ozero__class_Ozero(_1349299))))], (29878 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), c_Groups_Ozero__class_Ozero(_1349299)), _1349301)))]], 29881 ^ _782476 : [(29884 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), c_Groups_Ozero__class_Ozero(_1349299)), _1349303)))], (29882 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349299), _1349301), c_Groups_Ozero__class_Ozero(_1349299))))]]]]], (19082 ^ _782476) ^ [_1141725, _1141727, _1141729] : [class_Rings_Olinordered__semiring__strict(_1141725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141725), _1141727), c_Groups_Ozero__class_Ozero(_1141725))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141725), c_Groups_Ozero__class_Ozero(_1141725)), _1141729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141725), _1141727), _1141729)), c_Groups_Ozero__class_Ozero(_1141725))))], (27841 ^ _782476) ^ [_1308862, _1308864, _1308866] : [class_Orderings_Olinorder(_1308862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308862), _1308864)), -(hBOOL(hAPP(hAPP(c_member(_1308862), _1308866), _1308864))), -(_1308864 = c_Orderings_Obot__class_Obot(tc_fun(_1308862, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1308862, hAPP(hAPP(c_Set_Oinsert(_1308862), _1308866), _1308864)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1308862), _1308866), c_Big__Operators_Olinorder__class_OMin(_1308862, _1308864)))], (52293 ^ _782476) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (31926 ^ _782476) ^ [_1387104, _1387106, _1387108, _1387110] : [class_Divides_Osemiring__div(_1387104), -(c_Divides_Odiv__class_Omod(_1387104, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387104), c_Divides_Odiv__class_Omod(_1387104, _1387106, _1387108)), _1387110), _1387108) = c_Divides_Odiv__class_Omod(_1387104, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387104), _1387106), _1387110), _1387108))], (21720 ^ _782476) ^ [_1190262, _1190264, _1190266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190262)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1190264), _1190266)), 21727 ^ _782476 : [(21728 ^ _782476) ^ [_1190458] : [21730 ^ _782476 : [(21736 ^ _782476) ^ [] : [-(_1190458 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21732 ^ [_1190262, _1190264, _1190266, _1190458]), 21729 ^ [_1190262, _1190264, _1190266, _1190458]))], (21734 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21732 ^ [_1190262, _1190264, _1190266, _1190458]), _1190266)))], (21731 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21729 ^ [_1190262, _1190264, _1190266, _1190458]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190262))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190458), _1190264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190458), _1190262)), _1190264)))]]], (35524 ^ _782476) ^ [_1453685] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1453685), 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, _1453685)))], (8036 ^ _782476) ^ [_919365, _919367, _919369, _919371] : [class_Lattices_Osemilattice__sup(_919365), 8039 ^ _782476 : [(8048 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919365), _919367), _919369)), _919371))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), _919367), _919371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), _919369), _919371))], (8040 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919365), _919367), _919369)), _919371)), 8043 ^ _782476 : [(8046 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), _919369), _919371)))], (8044 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919365), _919367), _919371)))]]]]], (31836 ^ _782476) ^ [_1385277, _1385279] : [c_Nat__Transfer_Ois__nat(_1385277), c_Nat__Transfer_Ois__nat(_1385279), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385277, _1385279)))], (31474 ^ _782476) ^ [_1378089, _1378091, _1378093] : [_1378089 = 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), _1378089), _1378091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378089), _1378093)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37706 ^ _782476) ^ [_1500134, _1500136, _1500138, _1500140] : [-(_1500134 = _1500136), hAPP(c_Product__Type_Ofst(_1500138, _1500140), _1500134) = hAPP(c_Product__Type_Ofst(_1500138, _1500140), _1500136), hAPP(c_Product__Type_Osnd(_1500138, _1500140), _1500134) = hAPP(c_Product__Type_Osnd(_1500138, _1500140), _1500136)], (1532 ^ _782476) ^ [_804826, _804828] : [-(class_Orderings_Obot(_804826)), _804828 = _804826, class_Orderings_Obot(_804828)], (26748 ^ _782476) ^ [_1287422, _1287424, _1287426, _1287428] : [class_Orderings_Olinorder(_1287422), 26751 ^ _782476 : [(26752 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287422), _1287424), _1287426)), _1287428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), _1287424), _1287428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), _1287426), _1287428)))], (26762 ^ _782476) ^ [] : [26763 ^ _782476 : [(26766 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), _1287426), _1287428))], (26764 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), _1287424), _1287428))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287422), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287422), _1287424), _1287426)), _1287428)))]]], (41897 ^ _782476) ^ [_1606591, _1606593, _1606595, _1606597, _1606599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606591, _1606591)), hAPP(hAPP(c_Product__Type_OPair(_1606591, _1606591), _1606593), _1606595)), c_Transitive__Closure_Ortrancl(_1606591, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606591, _1606591), tc_HOL_Obool)), _1606597), _1606599)))), 41903 ^ _782476 : [(41909 ^ _782476) ^ [] : [41905 ^ [_1606591, _1606593, _1606595, _1606597, _1606599] = 41902 ^ [_1606591, _1606593, _1606595, _1606597, _1606599]], (41907 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606591, _1606591)), hAPP(hAPP(c_Product__Type_OPair(_1606591, _1606591), 41905 ^ [_1606591, _1606593, _1606595, _1606597, _1606599]), 41902 ^ [_1606591, _1606593, _1606595, _1606597, _1606599])), _1606599)))], (41904 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606591, _1606591)), hAPP(hAPP(c_Product__Type_OPair(_1606591, _1606591), 41902 ^ [_1606591, _1606593, _1606595, _1606597, _1606599]), _1606595)), c_Transitive__Closure_Ortrancl(_1606591, _1606597))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606591, _1606591)), hAPP(hAPP(c_Product__Type_OPair(_1606591, _1606591), _1606593), _1606595)), c_Transitive__Closure_Ortrancl(_1606591, _1606597))))], (14773 ^ _782476) ^ [_1058351, _1058353, _1058355, _1058357, _1058359, _1058361, _1058363, _1058365] : [c_Finite__Set_Ofolding(_1058351, _1058353, _1058355, _1058357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058351), _1058359)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058351), _1058361)), -(hAPP(c_Fun_Ocomp(_1058353, _1058353, _1058363, hAPP(_1058357, _1058361)), hAPP(c_Fun_Ocomp(_1058353, _1058353, _1058363, hAPP(_1058357, _1058359)), _1058365)) = hAPP(c_Fun_Ocomp(_1058353, _1058353, _1058363, hAPP(_1058357, _1058359)), hAPP(c_Fun_Ocomp(_1058353, _1058353, _1058363, hAPP(_1058357, _1058361)), _1058365)))], (20117 ^ _782476) ^ [_1160136, _1160138, _1160140] : [class_Rings_Oring__1(_1160136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160138), _1160140)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160136), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160140), _1160138)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160136), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160136), _1160140)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160136), _1160138)))], (52727 ^ _782476) ^ [_1844249, _1844251] : [hBOOL(hAPP(hAPP(c_fconj, _1844249), _1844251)), -(hBOOL(_1844251))], (14266 ^ _782476) ^ [_1048254, _1048256, _1048258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048254, tc_HOL_Obool)), _1048256), _1048258)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048254), _1048258)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048254), _1048256)))], (26826 ^ _782476) ^ [_1288943, _1288945] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288943)), hAPP(c_Nat_OSuc, _1288945)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288943), _1288945)))], (34656 ^ _782476) ^ [_1437687, _1437689] : [class_Groups_Omonoid__mult(_1437687), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1437687), _1437689), 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(_1437687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437687), _1437689), _1437689)), _1437689))], (35156 ^ _782476) ^ [_1447185, _1447187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447185)), c_Int_OBit0(_1447187))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447185), _1447187)))], (45172 ^ _782476) ^ [_1686197, _1686199, _1686201, _1686203] : [-(_1686197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1686199), _1686197), hAPP(hAPP(c_List_Olist_OCons(_1686199), _1686201), _1686203)) = hAPP(hAPP(c_List_Odrop(_1686199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1686197), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1686203))], (10373 ^ _782476) ^ [_970592, _970594, _970596] : [hAPP(hAPP(c_Set_Oinsert(_970592), _970594), _970596) = c_Orderings_Obot__class_Obot(tc_fun(_970592, tc_HOL_Obool))], (47491 ^ _782476) ^ [_1738138, _1738140] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738138), hAPP(c_List_Onth(_1738138), _1738140)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738138)), _1738140))) = _1738140)], (43439 ^ _782476) ^ [_1645269, _1645271, _1645273, _1645275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645269), _1645271)), -(hAPP(hAPP(c_List_Onth(_1645273), hAPP(hAPP(c_List_Otake(_1645273), _1645271), _1645275)), _1645269) = hAPP(hAPP(c_List_Onth(_1645273), _1645275), _1645269))], (39216 ^ _782476) ^ [_1538165, _1538167, _1538169, _1538171, _1538173, _1538175, _1538177] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538165, _1538167, _1538169, _1538171, _1538173), _1538175), _1538177)), 39220 ^ _782476 : [(39223 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1538173, 39219 ^ [_1538165, _1538167, _1538169, _1538171, _1538173, _1538175, _1538177]), _1538177)))], (39221 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1538171, _1538175), 39219 ^ [_1538165, _1538167, _1538169, _1538171, _1538173, _1538175, _1538177])))]]], (47493 ^ _782476) ^ [_1738187, _1738189, _1738191, _1738193] : [class_Groups_Ocomm__monoid__add(_1738187), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738187), _1738189), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738191, _1738193))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1738187), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738187), _1738189), c_List_Oupt(_1738191, _1738193))))], (25510 ^ _782476) ^ [_1259215, _1259217] : [-(hAPP(c_Set_OCollect(_1259215), _1259217) = _1259217)], (41292 ^ _782476) ^ [_1591765] : [-(hAPP(c_Relation_ORange(_1591765, _1591765), c_Relation_OId(_1591765)) = c_Orderings_Otop__class_Otop(tc_fun(_1591765, tc_HOL_Obool)))], (41451 ^ _782476) ^ [_1595564, _1595566, _1595568, _1595570, _1595572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595566, _1595564)), hAPP(hAPP(c_Product__Type_OPair(_1595566, _1595564), _1595570), _1595568)), _1595572)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595564, _1595566)), hAPP(hAPP(c_Product__Type_OPair(_1595564, _1595566), _1595568), _1595570)), hAPP(c_Relation_Oconverse(_1595566, _1595564), _1595572))))], (14751 ^ _782476) ^ [_1057874, _1057876, _1057878, _1057880, _1057882, _1057884] : [c_Finite__Set_Ofolding__image__simple(_1057874, _1057876, _1057878, _1057880, _1057882, _1057884), -(hAPP(_1057884, c_Orderings_Obot__class_Obot(tc_fun(_1057876, tc_HOL_Obool))) = _1057880)], (25987 ^ _782476) ^ [_1274085, _1274087] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274085), _1274087)), -(_1274087 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274085, 25991 ^ [_1274085, _1274087]), 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)), 25990 ^ [_1274085, _1274087]))))], (36855 ^ _782476) ^ [_1484070, _1484072, _1484074, _1484076, _1484078, _1484080] : [hBOOL(hAPP(hAPP(_1484070, _1484072), _1484074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484076, tc_fun(_1484078, tc_HOL_Obool))), _1484070), _1484080)), -(hBOOL(hAPP(hAPP(_1484080, _1484072), _1484074)))], (31773 ^ _782476) ^ [_1384030, _1384032, _1384034, _1384036, _1384038] : [class_Groups_Ocomm__monoid__add(_1384030), class_Groups_Ocomm__monoid__mult(_1384030), _1384032 = _1384034, c_Nat__Transfer_Onat__set(_1384034), 31791 ^ _782476 : [(31794 ^ _782476) ^ [] : [hAPP(_1384036, 31790 ^ [_1384030, _1384032, _1384034, _1384036, _1384038]) = hAPP(_1384038, 31790 ^ [_1384030, _1384032, _1384034, _1384036, _1384038])], (31792 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31790 ^ [_1384030, _1384032, _1384034, _1384036, _1384038])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1384030), _1384036), _1384032) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1384030), _1384038), _1384034))], (50977 ^ _782476) ^ [_1814516, _1814518] : [-(c_Relation_Osym(_1814516, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1814516, _1814516), tc_HOL_Obool)), _1814518), hAPP(c_Relation_Oconverse(_1814516, _1814516), _1814518))))], (36577 ^ _782476) ^ [_1478477, _1478479, _1478481] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478477, _1478477), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478479), _1478481))), -(_1478477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1478479 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (3252 ^ _782476) ^ [_830870, _830872, _830874, _830876, _830878, _830880] : [-(c_Big__Operators_Olattice_OSup__fin(_830880, _830876, _830872) = c_Big__Operators_Olattice_OSup__fin(_830878, _830874, _830870)), _830880 = _830878, _830876 = _830874, _830872 = _830870], (52497 ^ _782476) ^ [_1841572] : [class_Lazy__Sequence_Osmall__lazy(_1841572), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1841572)))], (24554 ^ _782476) ^ [_1241611, _1241613, _1241615] : [class_Rings_Olinordered__idom(_1241611), 24557 ^ _782476 : [(24564 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241613), _1241615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241611), hAPP(c_Int_Oring__1__class_Oof__int(_1241611), _1241613)), hAPP(c_Int_Oring__1__class_Oof__int(_1241611), _1241615))))], (24558 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241611), hAPP(c_Int_Oring__1__class_Oof__int(_1241611), _1241613)), hAPP(c_Int_Oring__1__class_Oof__int(_1241611), _1241615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241613), _1241615)))]]], (4128 ^ _782476) ^ [_844972, _844974, _844976, _844978, _844980, _844982, _844984, _844986] : [-(c_New__Random__Sequence_Opos__map(_844986, _844982, _844978, _844974) = c_New__Random__Sequence_Opos__map(_844984, _844980, _844976, _844972)), _844986 = _844984, _844982 = _844980, _844978 = _844976, _844974 = _844972], (21073 ^ _782476) ^ [_1178567, _1178569, _1178571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178567), _1178569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178571), _1178567)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178571), _1178569))))], (49183 ^ _782476) ^ [_1774144, _1774146, _1774148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1774144), _1774146)), hBOOL(hAPP(_1774148, c_Orderings_Obot__class_Obot(tc_fun(_1774144, tc_HOL_Obool)))), 49194 ^ _782476 : [(49197 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1774144), 49192 ^ [_1774144, _1774146, _1774148]), 49193 ^ [_1774144, _1774146, _1774148]))], (49199 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1774148, 49193 ^ [_1774144, _1774146, _1774148])))], (49201 ^ _782476) ^ [] : [hBOOL(hAPP(_1774148, hAPP(hAPP(c_Set_Oinsert(_1774144), 49192 ^ [_1774144, _1774146, _1774148]), 49193 ^ [_1774144, _1774146, _1774148])))], (49195 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1774144), 49193 ^ [_1774144, _1774146, _1774148])))]], -(hBOOL(hAPP(_1774148, _1774146)))], (46448 ^ _782476) ^ [_1713510] : [-(_1713510 = 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, _1713510)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1713510))))], (5464 ^ _782476) ^ [_866090, _866092, _866094, _866096, _866098, _866100] : [-(c_Finite__Set_Ofold1Set(_866100, _866096, _866092) = c_Finite__Set_Ofold1Set(_866098, _866094, _866090)), _866100 = _866098, _866096 = _866094, _866092 = _866090], (44326 ^ _782476) ^ [_1666553, _1666555] : [_1666555 = c_List_Olist_ONil(_1666553), -(hAPP(c_List_Oset(_1666553), _1666555) = c_Orderings_Obot__class_Obot(tc_fun(_1666553, tc_HOL_Obool)))], (24586 ^ _782476) ^ [_1242165, _1242167, _1242169] : [class_Rings_Oring__1(_1242165), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242167), _1242169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1242165), hAPP(c_Int_Oring__1__class_Oof__int(_1242165), _1242167)), hAPP(c_Int_Oring__1__class_Oof__int(_1242165), _1242169)))], (42585 ^ _782476) ^ [_1621147, _1621149, _1621151, _1621153] : [class_Lattices_Osemilattice__inf(_1621147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621147), _1621149)), 42595 ^ _782476 : [(42598 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621147), _1621151), 42594 ^ [_1621147, _1621149, _1621151, _1621153]))], (42596 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621147), 42594 ^ [_1621147, _1621149, _1621151, _1621153]), _1621149)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621147), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621147), _1621151), _1621153)), hAPP(hAPP(c_Finite__Set_Ofold(_1621147, _1621147, c_Lattices_Osemilattice__inf__class_Oinf(_1621147)), _1621153), _1621149))))], (35206 ^ _782476) ^ [_1447956] : [_1447956 = c_Int_OPls, -(c_Int_OBit0(_1447956) = c_Int_OPls)], (45154 ^ _782476) ^ [_1685768, _1685770, _1685772, _1685774] : [-(hAPP(hAPP(c_List_Oappend(_1685768), _1685770), _1685772) = _1685774), _1685770 = hAPP(hAPP(c_List_Otake(_1685768), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685768)), _1685770)), _1685774), _1685772 = hAPP(hAPP(c_List_Odrop(_1685768), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685768)), _1685770)), _1685774)], (46614 ^ _782476) ^ [_1717156, _1717158, _1717160, _1717162] : [-(c_List_Opartition(_1717156, _1717158, hAPP(hAPP(c_List_Olist_OCons(_1717156), _1717160), _1717162)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1717156), tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717156), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717156), tc_fun(tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), tc_fun(tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), tc_List_Olist(_1717156)), c_COMBS(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_fun(tc_List_Olist(_1717156), tc_fun(tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), tc_List_Olist(_1717156)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_fun(tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_List_Olist(_1717156)), hAPP(c_If(tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), hAPP(_1717158, _1717160)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1717156), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_List_Olist(_1717156)), c_Product__Type_OPair(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), hAPP(c_List_Olist_OCons(_1717156), _1717160))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717156), tc_fun(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156))), tc_fun(tc_fun(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_fun(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), tc_List_Olist(_1717156)), c_COMBB(tc_List_Olist(_1717156), tc_prod(tc_List_Olist(_1717156), tc_List_Olist(_1717156)), tc_List_Olist(_1717156))), c_Product__Type_OPair(tc_List_Olist(_1717156), tc_List_Olist(_1717156)))), hAPP(c_List_Olist_OCons(_1717156), _1717160)))), c_List_Opartition(_1717156, _1717158, _1717162)))], (38066 ^ _782476) ^ [_1508367, _1508369, _1508371, _1508373, _1508375] : [c_Equiv__Relations_Oequiv(_1508367, _1508369, _1508371), 38069 ^ _782476 : [(38080 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508367, _1508367)), hAPP(hAPP(c_Product__Type_OPair(_1508367, _1508367), _1508373), _1508375)), _1508371))), hAPP(c_Relation_OImage(_1508367, _1508367, _1508371), hAPP(hAPP(c_Set_Oinsert(_1508367), _1508373), c_Orderings_Obot__class_Obot(tc_fun(_1508367, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508367, _1508367, _1508371), hAPP(hAPP(c_Set_Oinsert(_1508367), _1508375), c_Orderings_Obot__class_Obot(tc_fun(_1508367, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1508367), _1508373), _1508369)), hBOOL(hAPP(hAPP(c_member(_1508367), _1508375), _1508369))], (38070 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508367, _1508367)), hAPP(hAPP(c_Product__Type_OPair(_1508367, _1508367), _1508373), _1508375)), _1508371)), 38073 ^ _782476 : [(38078 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508367), _1508375), _1508369)))], (38076 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508367), _1508373), _1508369)))], (38074 ^ _782476) ^ [] : [-(hAPP(c_Relation_OImage(_1508367, _1508367, _1508371), hAPP(hAPP(c_Set_Oinsert(_1508367), _1508373), c_Orderings_Obot__class_Obot(tc_fun(_1508367, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508367, _1508367, _1508371), hAPP(hAPP(c_Set_Oinsert(_1508367), _1508375), c_Orderings_Obot__class_Obot(tc_fun(_1508367, tc_HOL_Obool)))))]]]]], (25291 ^ _782476) ^ [_1255225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255225), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255225) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255225))], (8336 ^ _782476) ^ [_926335, _926337, _926339, _926341, _926343] : [8338 ^ _782476 : [(8341 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926339), _926341), hAPP(_926343, 8337 ^ [_926335, _926337, _926339, _926341, _926343])))], (8339 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926335), 8337 ^ [_926335, _926337, _926339, _926341, _926343]), _926337)))]], -(hBOOL(hAPP(hAPP(c_member(_926339), _926341), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926335, tc_fun(_926339, tc_HOL_Obool)), _926337), _926343))))], (44140 ^ _782476) ^ [_1663236, _1663238, _1663240] : [hBOOL(hAPP(c_List_Odistinct(_1663236), _1663238)), -(hBOOL(hAPP(c_List_Odistinct(_1663236), c_List_Oremove1(_1663236, _1663240, _1663238))))], (21067 ^ _782476) ^ [_1178441, _1178443] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178441), _1178443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178441), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178443)))], (17644 ^ _782476) ^ [_1116941, _1116943, _1116945] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116941), _1116943)), _1116945) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116943), _1116945)))], (25546 ^ _782476) ^ [_1259771, _1259773, _1259775] : [hBOOL(hAPP(_1259775, _1259773)), -(hBOOL(hAPP(hAPP(c_member(_1259771), _1259773), hAPP(c_Set_OCollect(_1259771), _1259775))))], (4668 ^ _782476) ^ [_853556, _853558, _853560, _853562, _853564, _853566, _853568, _853570] : [-(c_Nitpick_Opair__box_OPairBox(_853570, _853566, _853562, _853558) = c_Nitpick_Opair__box_OPairBox(_853568, _853564, _853560, _853556)), _853570 = _853568, _853566 = _853564, _853562 = _853560, _853558 = _853556], (27177 ^ _782476) ^ [_1296154, _1296156, _1296158, _1296160] : [class_Groups_Ocomm__monoid__mult(_1296154), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296156), _1296158))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296156, _1296154), _1296160), _1296158) = c_Groups_Oone__class_Oone(_1296154))], (17203 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (37570 ^ _782476) ^ [_1497529, _1497531, _1497533] : [37572 ^ _782476 : [(37575 ^ _782476) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497529, _1497531), 37571 ^ [_1497529, _1497531, _1497533]))], (37573 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1497531, 37571 ^ [_1497529, _1497531, _1497533]), _1497533)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497529, _1497531), _1497533)))], (47948 ^ _782476) ^ [_1746456, _1746458] : [class_Orderings_Olinorder(_1746456), 47951 ^ _782476 : [(47952 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1746456, _1746458), 47955 ^ _782476 : [(47956 ^ _782476) ^ [_1746627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746627), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746456)), _1746458))), 47959 ^ _782476 : [(47960 ^ _782476) ^ [_1746744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746744), _1746627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746456), hAPP(hAPP(c_List_Onth(_1746456), _1746458), _1746744)), hAPP(hAPP(c_List_Onth(_1746456), _1746458), _1746627))))]]]]], (47966 ^ _782476) ^ [] : [47968 ^ _782476 : [(47974 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746456), hAPP(hAPP(c_List_Onth(_1746456), _1746458), 47970 ^ [_1746456, _1746458])), hAPP(hAPP(c_List_Onth(_1746456), _1746458), 47967 ^ [_1746456, _1746458])))], (47972 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47970 ^ [_1746456, _1746458]), 47967 ^ [_1746456, _1746458])))], (47969 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47967 ^ [_1746456, _1746458]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746456)), _1746458))))]], -(c_List_Olinorder__class_Osorted(_1746456, _1746458))]]], (27431 ^ _782476) ^ [_1301277, _1301279, _1301281, _1301283, _1301285] : [class_Groups_Ocomm__monoid__mult(_1301277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301279), _1301281)), -(hBOOL(hAPP(hAPP(c_member(_1301279), _1301283), _1301281))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301279, _1301277), _1301285), hAPP(hAPP(c_Set_Oinsert(_1301279), _1301283), _1301281)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301277), hAPP(_1301285, _1301283)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301279, _1301277), _1301285), _1301281)))], (26046 ^ _782476) ^ [_1275279, _1275281] : [class_Groups_Olinordered__ab__group__add(_1275279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275279), _1275281)), -(_1275281 = c_Orderings_Obot__class_Obot(tc_fun(_1275279, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275279), c_Big__Operators_Olinorder__class_OMax(_1275279, _1275281)) = c_Big__Operators_Olinorder__class_OMin(_1275279, hAPP(c_Set_Oimage(_1275279, _1275279, c_Groups_Ouminus__class_Ouminus(_1275279)), _1275281)))], (32469 ^ _782476) ^ [_1397332, _1397334, _1397336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397332)), 32472 ^ _782476 : [(32473 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1397334, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397336), _1397332)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397336, _1397332))), 32476 ^ _782476 : [(32477 ^ _782476) ^ [_1397533, _1397535] : [-(hBOOL(hAPP(hAPP(_1397334, _1397535), _1397533))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397533), _1397332)), _1397336 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397332), _1397535)), _1397533)]]], (32491 ^ _782476) ^ [] : [32494 ^ _782476 : [(32497 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32493 ^ [_1397332, _1397334, _1397336]), _1397332)))], (32499 ^ _782476) ^ [] : [-(_1397336 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397332), 32492 ^ [_1397332, _1397334, _1397336])), 32493 ^ [_1397332, _1397334, _1397336]))], (32501 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1397334, 32492 ^ [_1397332, _1397334, _1397336]), 32493 ^ [_1397332, _1397334, _1397336]))], (32495 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32493 ^ [_1397332, _1397334, _1397336])))]], -(hBOOL(hAPP(hAPP(_1397334, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397336), _1397332)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397336, _1397332))))]]], (25856 ^ _782476) ^ [_1268639, _1268641, _1268643] : [class_Lattices_Odistrib__lattice(_1268639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268639), _1268641)), -(_1268641 = c_Orderings_Obot__class_Obot(tc_fun(_1268639, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268639), _1268643)), -(_1268643 = c_Orderings_Obot__class_Obot(tc_fun(_1268639, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1268639), c_Big__Operators_Olattice__class_OSup__fin(_1268639, _1268641)), c_Big__Operators_Olattice__class_OSup__fin(_1268639, _1268643)) = c_Big__Operators_Olattice__class_OSup__fin(_1268639, hAPP(c_Set_OCollect(_1268639), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_HOL_Obool), tc_HOL_Obool, _1268639), c_HOL_OEx(_1268639)), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool)), tc_fun(_1268639, tc_HOL_Obool), _1268639), hAPP(c_COMBB(tc_fun(_1268639, tc_HOL_Obool), tc_HOL_Obool, _1268639), c_HOL_OEx(_1268639))), hAPP(hAPP(c_COMBC(_1268639, tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool)), tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_fun(tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool))), tc_fun(tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool)), tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool))), _1268639), c_COMBS(_1268639, tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_fun(_1268639, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1268639, tc_fun(tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool))), _1268639), hAPP(c_COMBB(tc_fun(_1268639, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool)), _1268639), c_COMBS(_1268639, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool)), tc_fun(_1268639, tc_fun(_1268639, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1268639), hAPP(c_COMBB(tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1268639), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268639), c_fconj))), hAPP(hAPP(c_COMBC(_1268639, tc_fun(_1268639, tc_fun(_1268639, _1268639)), tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268639, _1268639), tc_fun(_1268639, tc_HOL_Obool)), tc_fun(tc_fun(_1268639, tc_fun(_1268639, _1268639)), tc_fun(_1268639, tc_fun(_1268639, tc_HOL_Obool))), _1268639), c_COMBB(tc_fun(_1268639, _1268639), tc_fun(_1268639, tc_HOL_Obool), _1268639)), hAPP(hAPP(c_COMBB(tc_fun(_1268639, tc_HOL_Obool), tc_fun(tc_fun(_1268639, _1268639), tc_fun(_1268639, tc_HOL_Obool)), _1268639), c_COMBB(_1268639, tc_HOL_Obool, _1268639)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1268639)))))), hAPP(hAPP(c_COMBC(_1268639, tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1268639, tc_HOL_Obool), tc_fun(_1268639, tc_HOL_Obool)), _1268639), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1268639)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268639), c_fconj), hAPP(hAPP(c_COMBC(_1268639, tc_fun(_1268639, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268639)), _1268641)))), hAPP(hAPP(c_COMBC(_1268639, tc_fun(_1268639, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268639)), _1268643))))))))], (46238 ^ _782476) ^ [_1709381, _1709383] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709381), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709383), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 46245 ^ _782476 : [(46252 ^ _782476) ^ [] : [_1709381 = _1709383, -(hAPP(c_Code__Numeral_Oof__nat, _1709381) = hAPP(c_Code__Numeral_Oof__nat, _1709383))], (46246 ^ _782476) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1709381) = hAPP(c_Code__Numeral_Oof__nat, _1709383), -(_1709381 = _1709383)]]], (40526 ^ _782476) ^ [_1572373] : [-(_1572373 = hAPP(c_Int_OAbs__Integ, 40524 ^ [_1572373]))], (12256 ^ _782476) ^ [_1005073, _1005075, _1005077] : [class_Orderings_Oorder(_1005073), 12259 ^ _782476 : [(12266 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005073), _1005075), _1005077))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1005073, _1005075, _1005077) = c_Orderings_Obot__class_Obot(tc_fun(_1005073, tc_HOL_Obool)))], (12260 ^ _782476) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1005073, _1005075, _1005077) = c_Orderings_Obot__class_Obot(tc_fun(_1005073, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005073), _1005075), _1005077))]]], (10847 ^ _782476) ^ [_982018, _982020, _982022, _982024, _982026] : [_982018 = c_Orderings_Obot__class_Obot(tc_fun(_982020, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982022, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982020, tc_fun(_982022, tc_HOL_Obool)), _982018), _982024)), _982026) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982022, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_982022, tc_HOL_Obool))), _982026))], (47062 ^ _782476) ^ [_1727254, _1727256, _1727258] : [-(c_List_Oconcat(_1727254, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1727254)), _1727256), _1727258)) = hAPP(hAPP(c_List_Oappend(_1727254), c_List_Oconcat(_1727254, _1727256)), c_List_Oconcat(_1727254, _1727258)))], (2636 ^ _782476) ^ [_821348, _821350] : [_821350 = _821348, -(c_Nitpick_Ozero__frac(_821350) = c_Nitpick_Ozero__frac(_821348))], (43461 ^ _782476) ^ [_1646075, _1646077] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1646075), hAPP(c_List_Oset(_1646075), _1646077))))], (3390 ^ _782476) ^ [_833069, _833071] : [_833071 = _833069, -(c_Int_OBit1(_833071) = c_Int_OBit1(_833069))], (41102 ^ _782476) ^ [_1587128, _1587130, _1587132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587128, _1587128), tc_HOL_Obool)), _1587130), _1587132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587128, _1587128), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587128, _1587130)), c_Transitive__Closure_Ortrancl(_1587128, _1587132))))], (44312 ^ _782476) ^ [_1666348, _1666350] : [-(_1666348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1666350, _1666348, c_List_Olist_ONil(_1666350)) = c_List_Olist_ONil(tc_List_Olist(_1666350)))], (10761 ^ _782476) ^ [_979786, _979788, _979790, _979792, _979794] : [_979786 = c_Orderings_Obot__class_Obot(tc_fun(_979788, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_979790), _979792), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979788, tc_fun(_979790, tc_HOL_Obool)), _979786), _979794)) = hAPP(hAPP(c_Set_Oinsert(_979790), _979792), c_Orderings_Obot__class_Obot(tc_fun(_979790, tc_HOL_Obool))))], (5222 ^ _782476) ^ [_862281, _862283, _862285, _862287, _862289, _862291, _862293, _862295] : [-(c_Product__Type_Ocurry(_862295, _862291, _862287, _862283) = c_Product__Type_Ocurry(_862293, _862289, _862285, _862281)), _862295 = _862293, _862291 = _862289, _862287 = _862285, _862283 = _862281], (40363 ^ _782476) ^ [_1568950, _1568952] : [c_Predicate_Oreflp(_1568950, _1568952), -(c_Relation_Orefl__on(_1568950, c_Orderings_Otop__class_Otop(tc_fun(_1568950, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1568950, _1568950)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568950, _1568950, tc_HOL_Obool), _1568952))))], (34358 ^ _782476) ^ [_1433118] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433118), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433118)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433118)))], (50131 ^ _782476) ^ [_1794599, _1794601, _1794603, _1794605] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794599, _1794601), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794599, _1794603, _1794605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1794601, _1794603)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794599, _1794601), _1794605))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25835 ^ _782476) ^ [_1267847] : [-(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)))), _1267847)) = 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), _1267847), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (40175 ^ _782476) ^ [_1564446, _1564448, _1564450, _1564452] : [-(c_Product__Type_Oapsnd(_1564446, _1564448, _1564450, _1564452) = c_Product__Type_Omap__pair(_1564450, _1564450, _1564446, _1564448, c_Fun_Oid(_1564450), _1564452))], (40711 ^ _782476) ^ [_1577493, _1577495, _1577497] : [-(hBOOL(hAPP(hAPP(c_member(_1577493), _1577495), c_Wellfounded_Oacc(_1577493, _1577497)))), 40715 ^ _782476 : [(40718 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577493), 40714 ^ [_1577493, _1577495, _1577497]), c_Wellfounded_Oacc(_1577493, _1577497)))], (40716 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577493, _1577493)), hAPP(hAPP(c_Product__Type_OPair(_1577493, _1577493), 40714 ^ [_1577493, _1577495, _1577497]), _1577495)), _1577497)))]]], (3228 ^ _782476) ^ [_830500, _830502, _830504, _830506] : [-(c_Big__Operators_Olinorder__class_OMax(_830506, _830502) = c_Big__Operators_Olinorder__class_OMax(_830504, _830500)), _830506 = _830504, _830502 = _830500], (10493 ^ _782476) ^ [_973893, _973895, _973897] : [class_Lattices_Oboolean__algebra(_973893), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973893), _973895), _973897) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973893), _973895), hAPP(c_Groups_Ouminus__class_Ouminus(_973893), _973897)))], (49892 ^ _782476) ^ [_1790175, _1790177, _1790179] : [c_List_Oreplicate(_1790175, _1790177, _1790179) = c_List_Olist_ONil(_1790175), -(_1790177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9646 ^ _782476) ^ [_955637, _955639] : [class_Lattices_Obounded__lattice__bot(_955637), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955637), c_Orderings_Obot__class_Obot(_955637)), _955639) = _955639)], (47196 ^ _782476) ^ [_1730989, _1730991, _1730993, _1730995] : [-(hAPP(c_List_Ofilter(_1730989, _1730991), c_List_Oremove1(_1730989, _1730993, _1730995)) = c_List_Oremove1(_1730989, _1730993, hAPP(c_List_Ofilter(_1730989, _1730991), _1730995)))], (35576 ^ _782476) ^ [_1454620, _1454622] : [class_Fields_Olinordered__field__inverse__zero(_1454620), class_Int_Onumber__ring(_1454620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454620), c_Groups_Ozero__class_Ozero(_1454620)), _1454622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454620), c_Groups_Ozero__class_Ozero(_1454620)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454620), _1454622), hAPP(c_Int_Onumber__class_Onumber__of(_1454620), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (2648 ^ _782476) ^ [_821518, _821520, _821522, _821524] : [-(c_Nitpick_Onumber__of__frac(_821524, _821520) = c_Nitpick_Onumber__of__frac(_821522, _821518)), _821524 = _821522, _821520 = _821518], (14194 ^ _782476) ^ [_1046845, _1046847] : [class_Finite__Set_Ofinite(_1046845), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046845), _1046847)))], (6815 ^ _782476) ^ [_893435, _893437, _893439, _893441, _893443] : [6817 ^ _782476 : [(6823 ^ _782476) ^ [] : [hBOOL(hAPP(_893443, 6819 ^ [_893435, _893437, _893439, _893441, _893443]))], (6821 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893435), 6819 ^ [_893435, _893437, _893439, _893441, _893443]), hAPP(_893441, 6816 ^ [_893435, _893437, _893439, _893441, _893443]))))], (6818 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893437), 6816 ^ [_893435, _893437, _893439, _893441, _893443]), _893439)))]], 6824 ^ _782476 : [(6825 ^ _782476) ^ [_893745] : [hBOOL(hAPP(hAPP(c_member(_893435), _893745), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893437, tc_fun(_893435, tc_HOL_Obool)), _893439), _893441))), -(hBOOL(hAPP(_893443, _893745)))]]], (40843 ^ _782476) ^ [_1580835, _1580837] : [40844 ^ _782476 : [(40847 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580837), _1580835))], (40845 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580835), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1580835, _1580837) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38786 ^ _782476) ^ [_1525912, _1525914, _1525916, _1525918] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525912, tc_HOL_Obool), tc_fun(_1525912, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525912, tc_HOL_Obool), tc_fun(_1525912, tc_HOL_Obool)), _1525916), _1525918)), c_Wellfounded_Omax__ext(_1525912, _1525914))), -(c_Wellfounded_Omax__extp(_1525912, hAPP(hAPP(c_COMBC(_1525912, tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_fun(_1525912, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525912, tc_fun(tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_fun(_1525912, tc_HOL_Obool)), _1525912), c_COMBC(_1525912, tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525912, tc_prod(_1525912, _1525912)), tc_fun(_1525912, tc_fun(tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_HOL_Obool)), _1525912), hAPP(c_COMBB(tc_prod(_1525912, _1525912), tc_fun(tc_fun(tc_prod(_1525912, _1525912), tc_HOL_Obool), tc_HOL_Obool), _1525912), c_member(tc_prod(_1525912, _1525912)))), c_Product__Type_OPair(_1525912, _1525912)))), _1525914), _1525916, _1525918))], (35324 ^ _782476) ^ [_1450007] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1450007)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1450007)))], (20975 ^ _782476) ^ [_1176744] : [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)), _1176744)), _1176744)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176744), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52617 ^ _782476) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (35404 ^ _782476) ^ [_1451443, _1451445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451443)), c_Int_OBit0(_1451445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451443), _1451445)))], (27331 ^ _782476) ^ [_1299395, _1299397, _1299399] : [class_Orderings_Olinorder(_1299395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299395), _1299397)), hBOOL(hAPP(hAPP(c_member(_1299395), _1299399), _1299397)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299395), _1299399), c_Big__Operators_Olinorder__class_OMax(_1299395, _1299397)) = c_Big__Operators_Olinorder__class_OMax(_1299395, _1299397))], (27090 ^ _782476) ^ [_1294679] : [class_Orderings_Olinorder(_1294679), -(c_Finite__Set_Ofun__left__comm__idem(_1294679, _1294679, c_Orderings_Oord__class_Omin(_1294679)))], (22234 ^ _782476) ^ [_1200015, _1200017, _1200019, _1200021, _1200023] : [c_Fun_Obij__betw(_1200015, _1200017, _1200019, _1200021, _1200023), -(hAPP(c_Finite__Set_Ocard(_1200015), _1200021) = hAPP(c_Finite__Set_Ocard(_1200017), _1200023))], (13670 ^ _782476) ^ [_1035833, _1035835, _1035837, _1035839, _1035841, _1035843, _1035845] : [-(hAPP(c_Fun_Ocomp(_1035833, _1035835, _1035837, _1035839), hAPP(c_Fun_Ocomp(_1035841, _1035833, _1035837, _1035843), _1035845)) = hAPP(c_Fun_Ocomp(_1035841, _1035835, _1035837, hAPP(c_Fun_Ocomp(_1035833, _1035835, _1035841, _1035839), _1035843)), _1035845))], (26820 ^ _782476) ^ [_1288842] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288842) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18302 ^ _782476) ^ [_1128051, _1128053] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128051), _1128053) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18305 ^ _782476 : [(18308 ^ _782476) ^ [] : [-(_1128053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18306 ^ _782476) ^ [] : [-(_1128051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (52303 ^ _782476) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (35248 ^ _782476) ^ [_1448652, _1448654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448652)), c_Int_OBit1(_1448654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448652), _1448654)))], (52399 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (21477 ^ _782476) ^ [] : [-(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))))], (31191 ^ _782476) ^ [_1372666, _1372668, _1372670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372666), _1372668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372666), _1372670)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372668), _1372670))))], (42690 ^ _782476) ^ [_1623632, _1623634, _1623636, _1623638, _1623640, _1623642, _1623644] : [c_Finite__Set_Ofolding__image__simple__idem(_1623632, _1623634, _1623636, _1623638, _1623640, _1623642), -(hAPP(hAPP(_1623636, _1623644), _1623644) = _1623644)], (32589 ^ _782476) ^ [_1399800, _1399802] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399800, _1399802)) = _1399802, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399800), _1399802) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31464 ^ _782476) ^ [_1377913, _1377915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377913), _1377915)), _1377913)))], (7744 ^ _782476) ^ [_913364, _913366, _913368, _913370, _913372] : [class_Lattices_Olattice(_913364), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913366, _913364)), _913368), _913370), _913372) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913364), hAPP(_913368, _913372)), hAPP(_913370, _913372)))], (48170 ^ _782476) ^ [_1751310, _1751312, _1751314, _1751316, _1751318] : [-(hAPP(c_List_Ofoldl(_1751310, _1751312, _1751314, _1751316), _1751318) = c_List_Ofoldr(_1751312, _1751310, hAPP(c_COMBC(_1751310, _1751312, _1751310), _1751314), hAPP(c_List_Orev(_1751312), _1751318), _1751316))], (38730 ^ _782476) ^ [_1524198, _1524200] : [-(c_Relation_OId__on(_1524198, _1524200) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524198, tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool)), _1524200), hAPP(hAPP(c_COMBC(_1524198, tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool), tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1524198, _1524198), tc_fun(tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool), tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool)), _1524198), c_Set_Oinsert(tc_prod(_1524198, _1524198))), hAPP(hAPP(c_COMBS(_1524198, _1524198, tc_prod(_1524198, _1524198)), c_Product__Type_OPair(_1524198, _1524198)), c_COMBI(_1524198)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524198, _1524198), tc_HOL_Obool)))))], (49570 ^ _782476) ^ [_1782343, _1782345, _1782347] : [hAPP(_1782347, hAPP(c_Hilbert__Choice_Oinv__into(_1782343, _1782345, c_Orderings_Otop__class_Otop(tc_fun(_1782343, tc_HOL_Obool)), _1782347), 49571 ^ [_1782343, _1782345, _1782347])) = 49571 ^ [_1782343, _1782345, _1782347], -(hAPP(c_Set_Oimage(_1782343, _1782345, _1782347), c_Orderings_Otop__class_Otop(tc_fun(_1782343, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782345, tc_HOL_Obool)))], (44396 ^ _782476) ^ [_1667754, _1667756] : [-(c_List_Osublist(_1667754, _1667756, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1667754))], (14739 ^ _782476) ^ [_1057548, _1057550, _1057552, _1057554, _1057556, _1057558] : [c_Finite__Set_Ofolding(_1057548, _1057550, _1057552, _1057554), -(hAPP(c_Fun_Ocomp(_1057550, _1057550, _1057550, hAPP(_1057552, _1057556)), hAPP(_1057552, _1057558)) = hAPP(c_Fun_Ocomp(_1057550, _1057550, _1057550, hAPP(_1057552, _1057558)), hAPP(_1057552, _1057556)))], (40127 ^ _782476) ^ [_1562946, _1562948, _1562950, _1562952, _1562954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562946, _1562948)), _1562950), hAPP(hAPP(c_Product__Type_OSigma(_1562946, _1562948), _1562952), _1562954))), 40131 ^ _782476 : [(40137 ^ _782476) ^ [] : [-(_1562950 = hAPP(hAPP(c_Product__Type_OPair(_1562946, _1562948), 40130 ^ [_1562946, _1562948, _1562950, _1562952, _1562954]), 40133 ^ [_1562946, _1562948, _1562950, _1562952, _1562954]))], (40135 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562948), 40133 ^ [_1562946, _1562948, _1562950, _1562952, _1562954]), hAPP(_1562954, 40130 ^ [_1562946, _1562948, _1562950, _1562952, _1562954]))))], (40132 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562946), 40130 ^ [_1562946, _1562948, _1562950, _1562952, _1562954]), _1562952)))]]], (51617 ^ _782476) ^ [_1828564, _1828566, _1828568] : [c_List_Olist__ex(tc_Nat_Onat, _1828564, c_List_Oupt(_1828566, _1828568)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1828564), _1828566, _1828568)], (20589 ^ _782476) ^ [_1169623, _1169625] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169623)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169625)), _1169623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1169625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1232 ^ _782476) ^ [_801076, _801078] : [-(class_Rings_Oring__no__zero__divisors(_801076)), _801078 = _801076, class_Rings_Oring__no__zero__divisors(_801078)], (2734 ^ _782476) ^ [_822873, _822875] : [_822875 = _822873, -(c_Set_OBall(_822875) = c_Set_OBall(_822873))], (19068 ^ _782476) ^ [_1141470, _1141472, _1141474] : [class_Rings_Olinordered__ring__strict(_1141470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141470), _1141472), c_Groups_Ozero__class_Ozero(_1141470))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141470), _1141474), c_Groups_Ozero__class_Ozero(_1141470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141470), c_Groups_Ozero__class_Ozero(_1141470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141470), _1141472), _1141474))))], (20355 ^ _782476) ^ [_1165096, _1165098] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165096, 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(_1165096, tc_HOL_Obool)), tc_fun(_1165096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1165096, tc_HOL_Obool)), tc_fun(_1165096, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165096, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1165098)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165096, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1165098))], (34098 ^ _782476) ^ [_1428884, _1428886] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428884) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428886)), _1428884 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428886)), 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), _1428886)))], (36731 ^ _782476) ^ [_1481445, _1481447, _1481449, _1481451, _1481453, _1481455, _1481457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481445, _1481447)), hAPP(hAPP(c_Product__Type_OPair(_1481445, _1481447), _1481449), _1481451)), _1481453)), -(hBOOL(hAPP(hAPP(c_member(_1481455), hAPP(hAPP(_1481457, _1481449), _1481451)), hAPP(c_Set_Oimage(tc_prod(_1481445, _1481447), _1481455, hAPP(c_Product__Type_Oprod_Oprod__case(_1481445, _1481447, _1481455), _1481457)), _1481453))))], (18938 ^ _782476) ^ [_1139049, _1139051] : [class_Groups_Olinordered__ab__group__add(_1139049), 18941 ^ _782476 : [(18948 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139049), c_Groups_Ozero__class_Ozero(_1139049)), _1139051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139049), c_Groups_Ozero__class_Ozero(_1139049)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139049), _1139051), _1139051))))], (18942 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139049), c_Groups_Ozero__class_Ozero(_1139049)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139049), _1139051), _1139051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139049), c_Groups_Ozero__class_Ozero(_1139049)), _1139051)))]]], (23444 ^ _782476) ^ [_1222928, _1222930, _1222932] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222928), _1222930)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222928), _1222932)), 23454 ^ _782476 : [(23457 ^ _782476) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23455 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222928), 23453 ^ [_1222928, _1222930, _1222932]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222928, tc_HOL_Obool)), _1222930), _1222932))))]], -(hAPP(c_Finite__Set_Ocard(_1222928), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222928, tc_HOL_Obool)), _1222930), _1222932)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222928), _1222930)), hAPP(c_Finite__Set_Ocard(_1222928), _1222932)))], (37091 ^ _782476) ^ [_1488730] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1488730) = 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)))], (44026 ^ _782476) ^ [_1660664, _1660666, _1660668] : [hBOOL(hAPP(c_List_Odistinct(_1660664), hAPP(hAPP(c_List_Olist_OCons(_1660664), _1660666), _1660668))), 44029 ^ _782476 : [(44032 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660664), _1660668)))], (44030 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660664), _1660666), hAPP(c_List_Oset(_1660664), _1660668)))]]], (28934 ^ _782476) ^ [_1331874, _1331876, _1331878] : [class_Rings_Odivision__ring(_1331874), -(_1331876 = c_Groups_Ozero__class_Ozero(_1331874)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1331874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331874), _1331878), _1331876)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331874), _1331878), hAPP(c_Groups_Ouminus__class_Ouminus(_1331874), _1331876)))], (41682 ^ _782476) ^ [_1601052, _1601054, _1601056] : [c_Relation_Ototal__on(_1601052, _1601054, _1601056), 41685 ^ _782476 : [(41686 ^ _782476) ^ [_1601196] : [hBOOL(hAPP(hAPP(c_member(_1601052), _1601196), _1601054)), 41689 ^ _782476 : [(41690 ^ _782476) ^ [_1601336] : [hBOOL(hAPP(hAPP(c_member(_1601052), _1601336), _1601054)), -(_1601196 = _1601336), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601052, _1601052)), hAPP(hAPP(c_Product__Type_OPair(_1601052, _1601052), _1601196), _1601336)), _1601056))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601052, _1601052)), hAPP(hAPP(c_Product__Type_OPair(_1601052, _1601052), _1601336), _1601196)), _1601056)))]]]]], (11014 ^ _782476) ^ [_985613, _985615, _985617] : [class_Orderings_Olinorder(_985613), 11017 ^ _782476 : [(11018 ^ _782476) ^ [] : [-(_985615 = _985617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985613), _985615), _985617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985613), _985617), _985615)))], (11028 ^ _782476) ^ [] : [11029 ^ _782476 : [(11032 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985613), _985617), _985615))], (11030 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985613), _985615), _985617))]], _985615 = _985617]]], (5366 ^ _782476) ^ [_864525, _864527, _864529, _864531] : [-(c_List_Oupt(_864531, _864527) = c_List_Oupt(_864529, _864525)), _864531 = _864529, _864527 = _864525], (50410 ^ _782476) ^ [_1801165, _1801167, _1801169, _1801171, _1801173, _1801175, _1801177] : [hBOOL(hAPP(hAPP(_1801165, hAPP(c_Product__Type_Osnd(_1801167, _1801169), _1801171)), hAPP(c_Product__Type_Ofst(_1801167, _1801169), _1801171))), 50417 ^ _782476 : [(50420 ^ _782476) ^ [] : [hBOOL(hAPP(_1801173, hAPP(hAPP(_1801175, 50415 ^ [_1801165, _1801167, _1801169, _1801171, _1801173, _1801175, _1801177]), 50416 ^ [_1801165, _1801167, _1801169, _1801171, _1801173, _1801175, _1801177])))], (50418 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1801165, 50416 ^ [_1801165, _1801167, _1801169, _1801171, _1801173, _1801175, _1801177]), 50415 ^ [_1801165, _1801167, _1801169, _1801171, _1801173, _1801175, _1801177])))]], -(hBOOL(hAPP(_1801173, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1801167, _1801169, _1801177), _1801175), _1801171))))], (33178 ^ _782476) ^ [_1411509, _1411511, _1411513, _1411515] : [class_Int_Onumber__ring(_1411509), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411509), hAPP(c_Int_Onumber__class_Onumber__of(_1411509), _1411511)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411509), hAPP(c_Int_Onumber__class_Onumber__of(_1411509), _1411513)), _1411515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411509), hAPP(c_Int_Onumber__class_Onumber__of(_1411509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411511), _1411513))), _1411515))], (12838 ^ _782476) ^ [_1017625, _1017627, _1017629, _1017631, _1017633] : [c_Fun_Oinj__on(_1017625, _1017627, _1017629, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017625, tc_HOL_Obool)), _1017631), _1017633)), 12841 ^ _782476 : [(12848 ^ _782476) ^ [] : [_1017631 = _1017633, -(hAPP(c_Set_Oimage(_1017625, _1017627, _1017629), _1017631) = hAPP(c_Set_Oimage(_1017625, _1017627, _1017629), _1017633))], (12842 ^ _782476) ^ [] : [hAPP(c_Set_Oimage(_1017625, _1017627, _1017629), _1017631) = hAPP(c_Set_Oimage(_1017625, _1017627, _1017629), _1017633), -(_1017631 = _1017633)]]], (20419 ^ _782476) ^ [_1166521, _1166523, _1166525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166521), _1166523)), -(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)), _1166521)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166525), _1166523)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166525), _1166521)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166523), _1166521)))], (22614 ^ _782476) ^ [_1206566] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206566)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1206566)], (34820 ^ _782476) ^ [_1440473, _1440475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440473), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440473)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440475)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1440473), _1440475)))], (36785 ^ _782476) ^ [_1482464, _1482466, _1482468, _1482470, _1482472, _1482474] : [hBOOL(hAPP(hAPP(_1482464, _1482466), _1482468)), hBOOL(hAPP(hAPP(_1482470, _1482466), _1482468)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482472, tc_fun(_1482474, tc_HOL_Obool))), _1482464), _1482470), _1482466), _1482468)))], (35386 ^ _782476) ^ [_1451098, _1451100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451098), _1451100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451098)), c_Int_OBit1(_1451100))))], (28005 ^ _782476) ^ [_1312015] : [class_Orderings_Olinorder(_1312015), -(c_Orderings_Oord_Omin(_1312015, hAPP(c_COMBC(_1312015, _1312015, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1312015))) = c_Orderings_Oord__class_Omax(_1312015))], (44827 ^ _782476) ^ [_1677782, _1677784, _1677786] : [_1677786 = c_List_Olist_ONil(_1677784), -(_1677782 = hAPP(hAPP(c_List_Oappend(_1677784), _1677786), _1677782))], (7786 ^ _782476) ^ [_914359, _914361, _914363] : [class_Lattices_Osemilattice__sup(_914359), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914359), _914361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914359), _914361), _914363)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914359), _914361), _914363))], (37738 ^ _782476) ^ [_1500760, _1500762, _1500764] : [-(hAPP(hAPP(c_Product__Type_OPair(_1500760, _1500762), hAPP(c_Product__Type_Ofst(_1500760, _1500762), _1500764)), hAPP(c_Product__Type_Osnd(_1500760, _1500762), _1500764)) = _1500764)], (44875 ^ _782476) ^ [_1678621, _1678623, _1678625] : [_1678621 = _1678623, -(_1678621 = hAPP(hAPP(c_List_Oappend(_1678625), c_List_Olist_ONil(_1678625)), _1678623))], (27277 ^ _782476) ^ [_1298038, _1298040, _1298042, _1298044, _1298046, _1298048] : [class_Groups_Ocomm__monoid__mult(_1298038), c_Fun_Oinj__on(_1298040, _1298042, _1298044, _1298046), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298042, _1298038), _1298048), hAPP(c_Set_Oimage(_1298040, _1298042, _1298044), _1298046)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298040, _1298038), hAPP(c_Fun_Ocomp(_1298042, _1298038, _1298040, _1298048), _1298044)), _1298046))], (35322 ^ _782476) ^ [_1449964, _1449966] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1449964)), c_Int_OBit0(_1449966)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449964), _1449966)))], (43463 ^ _782476) ^ [_1646109, _1646111, _1646113] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646109, tc_HOL_Obool)), hAPP(c_List_Oset(_1646109), hAPP(hAPP(c_List_Otake(_1646109), _1646111), _1646113))), hAPP(c_List_Oset(_1646109), _1646113))))], (41192 ^ _782476) ^ [_1589391, _1589393] : [-(c_Transitive__Closure_Ortrancl(_1589391, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1589391, _1589391), tc_HOL_Obool)), _1589393), c_Relation_OId(_1589391))) = c_Transitive__Closure_Ortrancl(_1589391, _1589393))], (45336 ^ _782476) ^ [_1689850, _1689852] : [hBOOL(hAPP(c_List_Odistinct(_1689850), _1689852)), -(hBOOL(hAPP(c_List_Odistinct(_1689850), hAPP(c_List_Otl(_1689850), _1689852))))], (39804 ^ _782476) ^ [_1553603, _1553605, _1553607, _1553609, _1553611] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553603, _1553605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553603, tc_HOL_Obool)), _1553607), _1553609)), _1553611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553603, _1553605), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553603, _1553605), _1553607), _1553611)), hAPP(hAPP(c_Product__Type_OSigma(_1553603, _1553605), _1553609), _1553611)))], (45468 ^ _782476) ^ [_1692627, _1692629] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692627), _1692629) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45471 ^ _782476 : [(45474 ^ _782476) ^ [_1692741] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1692741), hAPP(c_List_Oset(tc_Nat_Onat), _1692629))), -(_1692741 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45472 ^ _782476) ^ [] : [-(_1692627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31528 ^ _782476) ^ [_1379035, _1379037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1379035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379037), _1379035))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379037), _1379035) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379037), _1379035)), _1379035)))], (29224 ^ _782476) ^ [_1337193, _1337195, _1337197, _1337199] : [class_Fields_Ofield__inverse__zero(_1337193), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337193), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337193), _1337195), _1337197)), _1337199) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337193), hAPP(hAPP(c_Power_Opower__class_Opower(_1337193), _1337195), _1337199)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337193), _1337197), _1337199)))], (18918 ^ _782476) ^ [_1138687, _1138689] : [class_Rings_Olinordered__ring(_1138687), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138687), c_Groups_Ozero__class_Ozero(_1138687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138687), _1138689), _1138689))))], (26888 ^ _782476) ^ [_1290135, _1290137, _1290139] : [class_Orderings_Olinorder(_1290135), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290135), _1290137), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290135), _1290137), _1290139)) = _1290137)], (22596 ^ _782476) ^ [_1206219, _1206221, _1206223] : [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, _1206219)), _1206221)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206219)), _1206223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206221), _1206223)))], (17570 ^ _782476) ^ [_1115535, _1115537, _1115539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115537), _1115539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115535), _1115537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115535), _1115539))))], (44420 ^ _782476) ^ [_1668292, _1668294, _1668296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668292), tc_List_Olist(_1668292))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668292), tc_List_Olist(_1668292)), _1668294), c_List_Olist_ONil(_1668292))), c_List_Olex(_1668292, _1668296)))], (33950 ^ _782476) ^ [_1426212] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426212))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426212)))))], (30877 ^ _782476) ^ [_1367821, _1367823] : [c_Nat__Transfer_Ois__nat(_1367821), c_Nat__Transfer_Ois__nat(_1367823), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367821), _1367823)))], (49912 ^ _782476) ^ [_1790515, _1790517, _1790519, _1790521] : [-(hBOOL(hAPP(_1790515, _1790517))), -(hAPP(c_List_Ofilter(_1790519, _1790515), c_List_Oreplicate(_1790519, _1790521, _1790517)) = c_List_Olist_ONil(_1790519))], (22318 ^ _782476) ^ [_1201509, _1201511] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201509), c_Orderings_Otop__class_Otop(tc_fun(_1201509, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1201509), _1201511) = hAPP(c_Finite__Set_Ocard(_1201509), c_Orderings_Otop__class_Otop(tc_fun(_1201509, tc_HOL_Obool))), -(_1201511 = c_Orderings_Otop__class_Otop(tc_fun(_1201509, tc_HOL_Obool)))], (36270 ^ _782476) ^ [_1466911] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1466911), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466911))], (41419 ^ _782476) ^ [_1594763, _1594765] : [c_Wellfounded_Oacyclic(_1594763, hAPP(c_Relation_Oconverse(_1594763, _1594763), _1594765)), -(c_Wellfounded_Oacyclic(_1594763, _1594765))], (39951 ^ _782476) ^ [_1557581, _1557583, _1557585, _1557587] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1557581, _1557583), _1557585), _1557587) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557581, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), _1557585), hAPP(hAPP(c_COMBS(_1557581, tc_fun(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557583, tc_HOL_Obool), tc_fun(tc_fun(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), _1557581), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), _1557587)), hAPP(hAPP(c_COMBC(_1557581, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557583, tc_fun(tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), _1557581), c_COMBC(_1557583, tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557583, tc_prod(_1557581, _1557583)), tc_fun(_1557583, tc_fun(tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))), _1557581), hAPP(c_COMBB(tc_prod(_1557581, _1557583), tc_fun(tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool), tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool)), _1557583), c_Set_Oinsert(tc_prod(_1557581, _1557583)))), c_Product__Type_OPair(_1557581, _1557583)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557581, _1557583), tc_HOL_Obool))))))], (27210 ^ _782476) ^ [_1296698, _1296700, _1296702] : [class_Groups_Ocomm__monoid__add(_1296698), class_Groups_Ocomm__monoid__mult(_1296698), c_Nat__Transfer_Onat__set(_1296700), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1296698), _1296702), _1296700) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1296698), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1296698, tc_Nat_Onat), _1296702), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1296700)))], (45583 ^ _782476) ^ [_1695116, _1695118, _1695120] : [45584 ^ _782476 : [(45585 ^ _782476) ^ [_1695205, _1695207] : [_1695118 = hAPP(hAPP(c_List_Olist_OCons(_1695116), _1695207), _1695205)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695116), tc_List_Olist(_1695116))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695116), tc_List_Olist(_1695116)), c_List_Olist_ONil(_1695116)), _1695118)), c_List_Olexord(_1695116, _1695120))))], (30368 ^ _782476) ^ [_1358143, _1358145, _1358147, _1358149] : [class_Fields_Olinordered__field(_1358143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358143), _1358145), c_Groups_Ozero__class_Ozero(_1358143))), 30375 ^ _782476 : [(30382 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358143), _1358149), _1358145)), _1358147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358143), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358143), _1358147), _1358145)), _1358149)))], (30376 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358143), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358143), _1358147), _1358145)), _1358149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358143), _1358149), _1358145)), _1358147)))]]], (23101 ^ _782476) ^ [_1216068, _1216070, _1216072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216068), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216068, tc_HOL_Obool)), _1216070), _1216072))), -(hAPP(c_Finite__Set_Ocard(_1216068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216068, tc_HOL_Obool)), _1216070), _1216072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216068), _1216070)), hAPP(c_Finite__Set_Ocard(_1216068), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216068, tc_HOL_Obool)), _1216070), _1216072))))], (23207 ^ _782476) ^ [_1218021, _1218023, _1218025, _1218027] : [class_Groups_Ocomm__monoid__add(_1218021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218023), _1218025)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218021), _1218027), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218023), _1218025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218021), hAPP(_1218027, _1218023)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218021), _1218027), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218023)), _1218025))))], (16955 ^ _782476) ^ [_1103370, _1103372, _1103374, _1103376] : [class_Rings_Ocomm__semiring__1(_1103370), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103370), _1103372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103370), _1103374), _1103376)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103370), _1103372), _1103374)), _1103376))], (39225 ^ _782476) ^ [_1538355, _1538357, _1538359, _1538361, _1538363, _1538365, _1538367] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538355, _1538357, _1538359, _1538361, _1538363), _1538365), _1538367))), 39226 ^ _782476 : [(39227 ^ _782476) ^ [_1538426] : [hBOOL(hAPP(hAPP(_1538361, _1538365), _1538426)), hBOOL(hAPP(hAPP(_1538363, _1538426), _1538367))]]], (8465 ^ _782476) ^ [_929198, _929200] : [-(hBOOL(hAPP(hAPP(c_member(_929198), _929200), c_Orderings_Otop__class_Otop(tc_fun(_929198, tc_HOL_Obool)))))], (45480 ^ _782476) ^ [_1692838, _1692840] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692838), _1692840) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1692838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45486 ^ _782476 : [(45489 ^ _782476) ^ [] : [45485 ^ [_1692838, _1692840] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45487 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45485 ^ [_1692838, _1692840]), hAPP(c_List_Oset(tc_Nat_Onat), _1692840))))]]], (44238 ^ _782476) ^ [_1665082] : [-(hBOOL(hAPP(c_List_Odistinct(_1665082), c_List_Olist_ONil(_1665082))))], (4564 ^ _782476) ^ [_851828, _851830, _851832, _851834, _851836, _851838] : [-(c_Lazy__Sequence_Oanamorph(_851838, _851834, _851830) = c_Lazy__Sequence_Oanamorph(_851836, _851832, _851828)), _851838 = _851836, _851834 = _851832, _851830 = _851828], (42861 ^ _782476) ^ [_1627587, _1627589, _1627591, _1627593, _1627595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627587), tc_List_Olist(_1627587))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627587), tc_List_Olist(_1627587)), _1627589), _1627591)), hAPP(c_List_Olexn(_1627587, _1627593), _1627595))), 42864 ^ _782476 : [(42867 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627587)), _1627591) = _1627595)], (42865 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627587)), _1627589) = _1627595)]]], (2448 ^ _782476) ^ [_818364, _818366, _818368, _818370] : [-(c_Divides_OposDivAlg(_818370, _818366) = c_Divides_OposDivAlg(_818368, _818364)), _818370 = _818368, _818366 = _818364], (35904 ^ _782476) ^ [_1460700, _1460702] : [class_Rings_Oring__1(_1460700), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460700), hAPP(c_Groups_Ouminus__class_Ouminus(_1460700), c_Groups_Oone__class_Oone(_1460700))), 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)))), _1460702))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1460700), c_Groups_Oone__class_Oone(_1460700)))], (22524 ^ _782476) ^ [_1204905, _1204907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204905), _1204907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204905)), _1204907)))], (39247 ^ _782476) ^ [_1538789] : [-(c_Wellfounded_Owf(tc_fun(_1538789, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1538789)))], (27733 ^ _782476) ^ [_1306868, _1306870, _1306872] : [class_Orderings_Olinorder(_1306868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306868), _1306870)), -(_1306870 = c_Orderings_Obot__class_Obot(tc_fun(_1306868, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306868), _1306872)), -(_1306872 = c_Orderings_Obot__class_Obot(tc_fun(_1306868, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306868, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306868, tc_HOL_Obool)), _1306870), _1306872)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306868), c_Big__Operators_Olinorder__class_OMax(_1306868, _1306870)), c_Big__Operators_Olinorder__class_OMax(_1306868, _1306872)))], (48792 ^ _782476) ^ [_1764669, _1764671, _1764673, _1764675, _1764677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764669, _1764669)), hAPP(hAPP(c_Product__Type_OPair(_1764669, _1764669), _1764671), _1764673)), c_List_Omeasures(_1764669, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764669, tc_Nat_Onat)), _1764675), _1764677)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764675, _1764671)), hAPP(_1764675, _1764673)))), 48799 ^ _782476 : [(48802 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764669, _1764669)), hAPP(hAPP(c_Product__Type_OPair(_1764669, _1764669), _1764671), _1764673)), c_List_Omeasures(_1764669, _1764677))))], (48800 ^ _782476) ^ [] : [-(hAPP(_1764675, _1764671) = hAPP(_1764675, _1764673))]]], (17335 ^ _782476) ^ [_1111439, _1111441, _1111443] : [17336 ^ _782476 : [(17339 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1111443, _1111441), _1111439))], (17337 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111439), _1111441)))]], 17342 ^ _782476 : [(17345 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1111443, _1111441), _1111439))], (17343 ^ _782476) ^ [] : [-(_1111439 = _1111441)]], 17348 ^ _782476 : [(17351 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1111443, _1111441), _1111439))], (17349 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111441), _1111439)))]], -(hBOOL(hAPP(hAPP(_1111443, _1111441), _1111439)))], (52667 ^ _782476) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (26894 ^ _782476) ^ [_1290244, _1290246, _1290248] : [class_Orderings_Olinorder(_1290244), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290244), _1290246), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290244), _1290246), _1290248)) = _1290246)], (48304 ^ _782476) ^ [_1754208, _1754210, _1754212] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754208)), c_List_OtakeWhile(_1754208, _1754210, _1754212))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754208)), _1754212))))], (48379 ^ _782476) ^ [_1755676, _1755678, _1755680, _1755682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755678)), c_List_OtakeWhile(_1755678, _1755680, _1755682)))), -(hAPP(hAPP(c_List_Onth(_1755678), c_List_OtakeWhile(_1755678, _1755680, _1755682)), _1755676) = hAPP(hAPP(c_List_Onth(_1755678), _1755682), _1755676))], (43733 ^ _782476) ^ [_1654200, _1654202] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1654200, _1654202) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654200), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654202), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (29012 ^ _782476) ^ [_1333417, _1333419, _1333421] : [class_Fields_Ofield(_1333417), -(_1333419 = c_Groups_Oone__class_Oone(_1333417)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1333417), hAPP(c_Power_Opower__class_Opower(_1333417), _1333419)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1333421)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333417), hAPP(hAPP(c_Power_Opower__class_Opower(_1333417), _1333419), _1333421)), c_Groups_Oone__class_Oone(_1333417))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333417), _1333419), c_Groups_Oone__class_Oone(_1333417))))], (14156 ^ _782476) ^ [_1046095, _1046097] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046095), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1046095, tc_HOL_Obool), _1046097)))), 14157 ^ _782476 : [(14158 ^ _782476) ^ [_1046159] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1046095, tc_HOL_Obool)), _1046159), _1046097)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046095), _1046159))]]], (2406 ^ _782476) ^ [_817747, _817749] : [_817749 = _817747, -(c_Int_OBit0(_817749) = c_Int_OBit0(_817747))], (34646 ^ _782476) ^ [_1437560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437560)), -(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), _1437560))))], (38967 ^ _782476) ^ [_1531779, _1531781, _1531783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531779, _1531779), tc_HOL_Obool)), _1531781), _1531783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531779, tc_HOL_Obool)), c_Wellfounded_Oacc(_1531779, _1531783)), c_Wellfounded_Oacc(_1531779, _1531781))))], (35762 ^ _782476) ^ [_1457750, _1457752, _1457754] : [class_Rings_Olinordered__idom(_1457750), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457750), c_Groups_Ozero__class_Ozero(_1457750)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457750), hAPP(hAPP(c_Power_Opower__class_Opower(_1457750), _1457752), 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(_1457750), _1457754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (21866 ^ _782476) ^ [_1193218, _1193220, _1193222, _1193224, _1193226] : [class_Groups_Ocomm__monoid__add(_1193218), class_Groups_Oordered__ab__semigroup__add(_1193218), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193220), _1193222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1193220, tc_HOL_Obool)), _1193224), _1193222)), 21884 ^ _782476 : [(21887 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193218), c_Groups_Ozero__class_Ozero(_1193218)), hAPP(_1193226, 21883 ^ [_1193218, _1193220, _1193222, _1193224, _1193226])))], (21885 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193220), 21883 ^ [_1193218, _1193220, _1193222, _1193224, _1193226]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1193220, tc_HOL_Obool)), _1193222), _1193224))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193218), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193220, _1193218), _1193226), _1193224)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193220, _1193218), _1193226), _1193222))))], (50408 ^ _782476) ^ [_1801094, _1801096, _1801098, _1801100] : [-(c_Random__Sequence_Omap(_1801094, _1801096, _1801098, _1801100) = c_Random__Sequence_Obind(_1801094, _1801096, _1801100, hAPP(c_Fun_Ocomp(_1801096, 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(_1801096)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1801094, c_Random__Sequence_Osingle(_1801096)), _1801098)))], (25412 ^ _782476) ^ [_1257136, _1257138] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257136), hAPP(c_Nat_OSuc, _1257138)) = 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), _1257136), _1257138)))], (17854 ^ _782476) ^ [_1120821, _1120823, _1120825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120825), _1120823))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120821), _1120823)), _1120825)))], (52609 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (41408 ^ _782476) ^ [_1594379, _1594381, _1594383, _1594385, _1594387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594379, _1594379)), hAPP(hAPP(c_Product__Type_OPair(_1594379, _1594379), hAPP(_1594381, hAPP(c_Nat_OSuc, 41409 ^ [_1594379, _1594381, _1594383, _1594385, _1594387]))), hAPP(_1594381, 41409 ^ [_1594379, _1594381, _1594383, _1594385, _1594387]))), c_Transitive__Closure_Ortrancl(_1594379, _1594383))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594379, _1594379)), hAPP(hAPP(c_Product__Type_OPair(_1594379, _1594379), hAPP(_1594381, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1594385), _1594387))), hAPP(_1594381, _1594385))), c_Transitive__Closure_Ortrancl(_1594379, _1594383))))], (31007 ^ _782476) ^ [_1369806, _1369808] : [class_Divides_Osemiring__div(_1369806), -(_1369808 = c_Groups_Ozero__class_Ozero(_1369806)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369806), _1369808), _1369808) = c_Groups_Oone__class_Oone(_1369806))], (13358 ^ _782476) ^ [_1029480, _1029482, _1029484, _1029486, _1029488, _1029490] : [-(hBOOL(hAPP(hAPP(c_member(_1029480), _1029482), _1029484))), 13361 ^ _782476 : [(13368 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1029480), _1029486), _1029484))), -(hAPP(c_Set_Ovimage(_1029488, _1029480, hAPP(hAPP(c_COMBC(_1029488, _1029480, _1029480), hAPP(hAPP(c_COMBC(_1029488, _1029480, tc_fun(_1029480, _1029480)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029480, tc_fun(_1029480, _1029480)), _1029488), c_If(_1029480)), hAPP(hAPP(c_COMBC(_1029488, tc_fun(_1029488, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029488)), _1029490))), _1029482)), _1029486)), _1029484) = c_Orderings_Obot__class_Obot(tc_fun(_1029488, tc_HOL_Obool)))], (13362 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1029480), _1029486), _1029484)), -(hAPP(c_Set_Ovimage(_1029488, _1029480, hAPP(hAPP(c_COMBC(_1029488, _1029480, _1029480), hAPP(hAPP(c_COMBC(_1029488, _1029480, tc_fun(_1029480, _1029480)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029480, tc_fun(_1029480, _1029480)), _1029488), c_If(_1029480)), hAPP(hAPP(c_COMBC(_1029488, tc_fun(_1029488, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029488)), _1029490))), _1029482)), _1029486)), _1029484) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1029488, tc_HOL_Obool)), _1029490))]]], (7391 ^ _782476) ^ [_906043, _906045, _906047, _906049] : [hBOOL(hAPP(hAPP(_906047, _906045), _906049)), -(hBOOL(hAPP(hAPP(c_member(_906043), _906045), c_SetInterval_Oord_OatMost(_906043, _906047, _906049))))], (16413 ^ _782476) ^ [_1091589, _1091591, _1091593] : [-(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)), _1091589)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091591), _1091593)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091591), _1091589)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091593), _1091589)))], (42568 ^ _782476) ^ [_1620783, _1620785, _1620787, _1620789] : [class_Orderings_Olinorder(_1620783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620783), _1620785)), 42578 ^ _782476 : [(42581 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620783), _1620787), 42577 ^ [_1620783, _1620785, _1620787, _1620789]))], (42579 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620783), 42577 ^ [_1620783, _1620785, _1620787, _1620789]), _1620785)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620783), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1620783), _1620787), _1620789)), hAPP(hAPP(c_Finite__Set_Ofold(_1620783, _1620783, c_Orderings_Oord__class_Omin(_1620783)), _1620789), _1620785))))], (25073 ^ _782476) ^ [_1250945, _1250947] : [class_Groups_Oordered__ab__group__add__abs(_1250945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250945), hAPP(c_Groups_Oabs__class_Oabs(_1250945), _1250947)), c_Groups_Ozero__class_Ozero(_1250945)))], (52427 ^ _782476) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (34134 ^ _782476) ^ [_1429449, _1429451] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429449) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429451)), 34137 ^ _782476 : [(34140 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429451)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34138 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429449))))]], 34141 ^ _782476 : [(34144 ^ _782476) ^ [] : [34145 ^ _782476 : [(34148 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429449) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34146 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429451))))]], 34149 ^ _782476 : [(34152 ^ _782476) ^ [] : [_1429449 = _1429451], (34150 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429451)))]]], (34142 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429449)))]]], (42517 ^ _782476) ^ [_1619709, _1619711, _1619713, _1619715, _1619717, _1619719, _1619721] : [c_Finite__Set_Ofun__left__comm(_1619709, _1619711, _1619713), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619709, _1619711, _1619713, _1619715, _1619717), _1619719)), hBOOL(hAPP(hAPP(c_member(_1619709), _1619721), _1619717)), 42529 ^ _782476 : [(42532 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619709, _1619711, _1619713, _1619715, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1619709, tc_HOL_Obool)), _1619717), hAPP(hAPP(c_Set_Oinsert(_1619709), _1619721), c_Orderings_Obot__class_Obot(tc_fun(_1619709, tc_HOL_Obool))))), 42528 ^ [_1619709, _1619711, _1619713, _1619715, _1619717, _1619719, _1619721])))], (42530 ^ _782476) ^ [] : [-(_1619719 = hAPP(hAPP(_1619713, _1619721), 42528 ^ [_1619709, _1619711, _1619713, _1619715, _1619717, _1619719, _1619721]))]]], (34456 ^ _782476) ^ [_1434583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434583), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434583) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52003 ^ _782476) ^ [_1835850, _1835852, _1835854] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835850, _1835852) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1835854), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 52006 ^ _782476 : [(52009 ^ _782476) ^ [] : [-(_1835852 = _1835854)], (52007 ^ _782476) ^ [] : [-(_1835850 = _1835852)]]], (32060 ^ _782476) ^ [_1389801, _1389803, _1389805, _1389807] : [class_Divides_Osemiring__div(_1389801), -(c_Divides_Odiv__class_Omod(_1389801, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389801), _1389803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389801), _1389805), _1389807)), _1389807) = c_Divides_Odiv__class_Omod(_1389801, _1389803, _1389807))], (52191 ^ _782476) ^ [_1838704, _1838706] : [class_Orderings_Obot(_1838704), -(class_Orderings_Obot(tc_fun(_1838706, _1838704)))], (6356 ^ _782476) ^ [_883885, _883887] : [class_Enum_Oenum(_883885), 6359 ^ _782476 : [(6366 ^ _782476) ^ [] : [hBOOL(hAPP(_883887, 6367 ^ [_883885, _883887])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883885), _883887)))], (6360 ^ _782476) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883885), _883887)), 6363 ^ _782476 : [(6364 ^ _782476) ^ [_884011] : [-(hBOOL(hAPP(_883887, _884011)))]]]]], (45146 ^ _782476) ^ [_1685589, _1685591, _1685593, _1685595] : [hAPP(hAPP(c_List_Oappend(_1685589), _1685591), _1685593) = _1685595, 45149 ^ _782476 : [(45152 ^ _782476) ^ [] : [-(_1685593 = hAPP(hAPP(c_List_Odrop(_1685589), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685589)), _1685591)), _1685595))], (45150 ^ _782476) ^ [] : [-(_1685591 = hAPP(hAPP(c_List_Otake(_1685589), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685589)), _1685591)), _1685595))]]], (42696 ^ _782476) ^ [_1623739, _1623741, _1623743, _1623745, _1623747, _1623749, _1623751, _1623753] : [c_Finite__Set_Ofolding__image__simple__idem(_1623739, _1623741, _1623743, _1623745, _1623747, _1623749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623741), _1623751)), hBOOL(hAPP(hAPP(c_member(_1623741), _1623753), _1623751)), -(hAPP(hAPP(_1623743, hAPP(_1623747, _1623753)), hAPP(_1623749, _1623751)) = hAPP(_1623749, _1623751))], (15244 ^ _782476) ^ [_1067340, _1067342, _1067344] : [class_Lattices_Olattice(_1067340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067340), _1067342)), -(_1067342 = c_Orderings_Obot__class_Obot(tc_fun(_1067340, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067340, hAPP(hAPP(c_Set_Oinsert(_1067340), _1067344), _1067342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067340), _1067344), c_Big__Operators_Olattice__class_OSup__fin(_1067340, _1067342)))], (8882 ^ _782476) ^ [_937366, _937368, _937370] : [class_Lattices_Osemilattice__inf(_937366), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937366), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937366), _937368), _937370)), _937370)))], (43141 ^ _782476) ^ [_1636887, _1636889, _1636891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636887, _1636887), tc_HOL_Obool)), _1636889), _1636891)), c_Relation_Orefl__on(_1636887, c_Orderings_Otop__class_Otop(tc_fun(_1636887, tc_HOL_Obool)), _1636891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636887), tc_List_Olist(_1636887)), tc_HOL_Obool)), c_List_Olistrel1(_1636887, _1636889)), c_List_Olistrel(_1636887, _1636891))))], (34652 ^ _782476) ^ [] : [-(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)))))], (9316 ^ _782476) ^ [_949185, _949187, _949189, _949191, _949193] : [hBOOL(hAPP(hAPP(c_member(_949185), _949187), hAPP(c_Set_Oimage(_949189, _949185, _949191), _949193))), 9320 ^ _782476 : [(9323 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949189), 9319 ^ [_949185, _949187, _949189, _949191, _949193]), _949193)))], (9321 ^ _782476) ^ [] : [-(_949187 = hAPP(_949191, 9319 ^ [_949185, _949187, _949189, _949191, _949193]))]]], (37659 ^ _782476) ^ [_1499163, _1499165] : [c_Relation_Oirrefl(_1499163, _1499165), 37662 ^ _782476 : [(37663 ^ _782476) ^ [_1499245] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499163, _1499163)), hAPP(hAPP(c_Product__Type_OPair(_1499163, _1499163), _1499245), _1499245)), _1499165))]]], (35712 ^ _782476) ^ [] : [-(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))))], (45517 ^ _782476) ^ [_1693568, _1693570, _1693572] : [class_Lattices_Olattice(_1693568), -(c_Big__Operators_Olattice__class_OInf__fin(_1693568, hAPP(c_List_Oset(_1693568), hAPP(hAPP(c_List_Olist_OCons(_1693568), _1693570), _1693572))) = hAPP(c_List_Ofoldl(_1693568, _1693568, c_Lattices_Osemilattice__inf__class_Oinf(_1693568), _1693570), _1693572))], (44352 ^ _782476) ^ [_1667021, _1667023, _1667025] : [-(_1667021 = c_List_Olist_ONil(_1667023)), -(c_List_Obutlast(_1667023, hAPP(hAPP(c_List_Olist_OCons(_1667023), _1667025), _1667021)) = hAPP(hAPP(c_List_Olist_OCons(_1667023), _1667025), c_List_Obutlast(_1667023, _1667021)))], (19775 ^ _782476) ^ [_1153722] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153722) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1153722))], (44470 ^ _782476) ^ [_1669305, _1669307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669305)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669307)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669305), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669307)) = c_List_Olist_ONil(tc_Int_Oint))], (30829 ^ _782476) ^ [_1366911, _1366913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366913)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366913), _1366911)), _1366913) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366911), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (5860 ^ _782476) ^ [_875300, _875302, _875304] : [_875300 = _875302, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875304, tc_HOL_Obool)), _875300), _875302)))], (9776 ^ _782476) ^ [_957731, _957733, _957735] : [class_Orderings_Oorder(_957731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957731), _957733), _957735)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_957731, _957735, _957733) = c_Orderings_Obot__class_Obot(tc_fun(_957731, tc_HOL_Obool)))], (42642 ^ _782476) ^ [_1622542, _1622544] : [-(c_Wellfounded_Owf(_1622542, _1622544)), 42645 ^ _782476 : [(42648 ^ _782476) ^ [_1622762] : [hBOOL(hAPP(hAPP(c_member(_1622542), _1622762), 42643 ^ [_1622542, _1622544])), 42652 ^ _782476 : [(42655 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622542), 42651 ^ [_1622542, _1622544, _1622762]), 42643 ^ [_1622542, _1622544])))], (42653 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622542, _1622542)), hAPP(hAPP(c_Product__Type_OPair(_1622542, _1622542), 42651 ^ [_1622542, _1622544, _1622762]), _1622762)), _1622544)))]]], (42646 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622542), 42644 ^ [_1622542, _1622544]), 42643 ^ [_1622542, _1622544])))]]], (39813 ^ _782476) ^ [_1553822, _1553824, _1553826, _1553828] : [39814 ^ _782476 : [(39815 ^ _782476) ^ [_1553876] : [hBOOL(hAPP(hAPP(_1553826, _1553828), _1553876))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1553822, _1553824, _1553826), _1553828)))], (25263 ^ _782476) ^ [_1254787, _1254789] : [class_Groups_Oabs__if(_1254787), 25266 ^ _782476 : [(25273 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254787), _1254789), c_Groups_Ozero__class_Ozero(_1254787)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254787), _1254789) = _1254789)], (25267 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254787), _1254789), c_Groups_Ozero__class_Ozero(_1254787))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254787), _1254789) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254787), _1254789))]]], (8975 ^ _782476) ^ [_939477, _939479, _939481, _939483] : [hBOOL(hAPP(hAPP(c_member(_939477), _939479), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939477, tc_HOL_Obool)), _939481), _939483))), -(hBOOL(hAPP(hAPP(c_member(_939477), _939479), _939481)))], (39094 ^ _782476) ^ [_1535340, _1535342, _1535344, _1535346, _1535348, _1535350, _1535352] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535340, _1535344)), hAPP(hAPP(c_Product__Type_OPair(_1535340, _1535344), _1535350), _1535352)), hAPP(hAPP(c_Relation_Orel__comp(_1535340, _1535342, _1535344), _1535346), _1535348))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1535340, _1535342, _1535344, hAPP(hAPP(c_COMBC(_1535340, tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_fun(_1535342, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535342, tc_fun(tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_fun(_1535342, tc_HOL_Obool)), _1535340), c_COMBC(_1535342, tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535342, tc_prod(_1535340, _1535342)), tc_fun(_1535342, tc_fun(tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_HOL_Obool)), _1535340), hAPP(c_COMBB(tc_prod(_1535340, _1535342), tc_fun(tc_fun(tc_prod(_1535340, _1535342), tc_HOL_Obool), tc_HOL_Obool), _1535342), c_member(tc_prod(_1535340, _1535342)))), c_Product__Type_OPair(_1535340, _1535342)))), _1535346), hAPP(hAPP(c_COMBC(_1535342, tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_fun(_1535344, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535344, tc_fun(tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_fun(_1535344, tc_HOL_Obool)), _1535342), c_COMBC(_1535344, tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535344, tc_prod(_1535342, _1535344)), tc_fun(_1535344, tc_fun(tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_HOL_Obool)), _1535342), hAPP(c_COMBB(tc_prod(_1535342, _1535344), tc_fun(tc_fun(tc_prod(_1535342, _1535344), tc_HOL_Obool), tc_HOL_Obool), _1535344), c_member(tc_prod(_1535342, _1535344)))), c_Product__Type_OPair(_1535342, _1535344)))), _1535348)), _1535350), _1535352)))], (46442 ^ _782476) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (1502 ^ _782476) ^ [_804451, _804453] : [-(class_Lattices_Oboolean__algebra(_804451)), _804453 = _804451, class_Lattices_Oboolean__algebra(_804453)], (46366 ^ _782476) ^ [_1712093, _1712095] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1712093), _1712095) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712093)), hAPP(c_Code__Numeral_Onat__of, _1712095))))], (23565 ^ _782476) ^ [_1225441] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225441)) = _1225441)], (45178 ^ _782476) ^ [_1686269, _1686271, _1686273, _1686275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686269), _1686271)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686273)), _1686275))), -(hAPP(hAPP(c_List_Onth(_1686273), hAPP(hAPP(c_List_Odrop(_1686273), _1686269), _1686275)), _1686271) = hAPP(hAPP(c_List_Onth(_1686273), _1686275), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686269), _1686271)))], (6552 ^ _782476) ^ [_887903, _887905, _887907, _887909, _887911] : [class_Complete__Lattice_Ocomplete__lattice(_887903), hBOOL(hAPP(hAPP(c_member(_887905), _887907), _887909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887903), hAPP(_887911, _887907)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_887905, _887903), _887909), _887911))))], (41483 ^ _782476) ^ [_1596404, _1596406, _1596408] : [c_Relation_Orefl__on(_1596404, _1596406, hAPP(c_Relation_Oconverse(_1596404, _1596404), _1596408)), -(c_Relation_Orefl__on(_1596404, _1596406, _1596408))], (36272 ^ _782476) ^ [] : [-(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))], (15454 ^ _782476) ^ [_1071179, _1071181, _1071183] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071179), _1071181)), hBOOL(hAPP(_1071183, _1071181)), 15465 ^ _782476 : [(15468 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071179), 15463 ^ [_1071179, _1071181, _1071183]), 15464 ^ [_1071179, _1071181, _1071183])))], (15470 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1071183, 15464 ^ [_1071179, _1071181, _1071183])))], (15472 ^ _782476) ^ [] : [hBOOL(hAPP(_1071183, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071179, tc_HOL_Obool)), 15464 ^ [_1071179, _1071181, _1071183]), hAPP(hAPP(c_Set_Oinsert(_1071179), 15463 ^ [_1071179, _1071181, _1071183]), c_Orderings_Obot__class_Obot(tc_fun(_1071179, tc_HOL_Obool))))))], (15466 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071179), 15464 ^ [_1071179, _1071181, _1071183])))]], -(hBOOL(hAPP(_1071183, c_Orderings_Obot__class_Obot(tc_fun(_1071179, tc_HOL_Obool)))))], (10645 ^ _782476) ^ [_977231, _977233, _977235] : [-(hAPP(hAPP(c_Set_Oinsert(_977231), _977233), _977235) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977231, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977231), _977233), c_Orderings_Obot__class_Obot(tc_fun(_977231, tc_HOL_Obool)))), _977235))], (12534 ^ _782476) ^ [_1011624, _1011626, _1011628] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011624, tc_HOL_Obool)), _1011626), _1011628))), 12540 ^ _782476 : [(12544 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011624, tc_HOL_Obool)), 12542 ^ [_1011624, _1011626, _1011628]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011624, tc_HOL_Obool)), _1011626), _1011628))))], (12546 ^ _782476) ^ [] : [12539 ^ [_1011624, _1011626, _1011628] = 12542 ^ [_1011624, _1011626, _1011628]], (12548 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011624, tc_HOL_Obool)), 12539 ^ [_1011624, _1011626, _1011628]), 12542 ^ [_1011624, _1011626, _1011628]) = c_Orderings_Obot__class_Obot(tc_fun(_1011624, tc_HOL_Obool))], (12541 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011624, tc_HOL_Obool)), 12539 ^ [_1011624, _1011626, _1011628]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011624, tc_HOL_Obool)), _1011626), _1011628))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011624, tc_HOL_Obool)), _1011626), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1011624, tc_HOL_Obool), _1011628)) = c_Orderings_Obot__class_Obot(tc_fun(_1011624, tc_HOL_Obool)))], (45719 ^ _782476) ^ [_1697816, _1697818, _1697820] : [class_Orderings_Olinorder(_1697816), -(hAPP(c_List_Oset(_1697816), c_List_Olinorder__class_Oinsort__insert__key(_1697816, _1697816, c_COMBI(_1697816), _1697818, _1697820)) = hAPP(hAPP(c_Set_Oinsert(_1697816), _1697818), hAPP(c_List_Oset(_1697816), _1697820)))], (41459 ^ _782476) ^ [_1595806, _1595808, _1595810, _1595812] : [-(hAPP(c_Relation_Oconverse(_1595806, _1595808), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595806, _1595808), tc_HOL_Obool)), _1595810), _1595812)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595808, _1595806), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595806, _1595808), _1595810)), hAPP(c_Relation_Oconverse(_1595806, _1595808), _1595812)))], (34284 ^ _782476) ^ [_1431963] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1431963) = _1431963)], (51648 ^ _782476) ^ [_1829152, _1829154, _1829156] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1829152), _1829154)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1829152), _1829156))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1829152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1829154), _1829156)))], (28382 ^ _782476) ^ [_1320885, _1320887, _1320889] : [class_Orderings_Olinorder(_1320885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320885), _1320887)), -(_1320889 = c_Orderings_Obot__class_Obot(tc_fun(_1320885, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320885, tc_HOL_Obool)), _1320889), _1320887)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320885), c_Big__Operators_Olattice_OSup__fin(_1320885, c_Orderings_Oord__class_Omax(_1320885), _1320889)), c_Big__Operators_Olattice_OSup__fin(_1320885, c_Orderings_Oord__class_Omax(_1320885), _1320887)) = c_Big__Operators_Olattice_OSup__fin(_1320885, c_Orderings_Oord__class_Omax(_1320885), _1320887))], (3218 ^ _782476) ^ [_830351, _830353, _830355, _830357] : [-(c_Big__Operators_Olinorder__class_OMin(_830357, _830353) = c_Big__Operators_Olinorder__class_OMin(_830355, _830351)), _830357 = _830355, _830353 = _830351], (22260 ^ _782476) ^ [_1200540, _1200542, _1200544] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200540), _1200542)), 22263 ^ _782476 : [(22270 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200540), _1200544), _1200542))), -(hAPP(c_Finite__Set_Ocard(_1200540), hAPP(hAPP(c_Set_Oinsert(_1200540), _1200544), _1200542)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200540), _1200542)))], (22264 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1200540), _1200544), _1200542)), -(hAPP(c_Finite__Set_Ocard(_1200540), hAPP(hAPP(c_Set_Oinsert(_1200540), _1200544), _1200542)) = hAPP(c_Finite__Set_Ocard(_1200540), _1200542))]]], (30893 ^ _782476) ^ [_1368051, _1368053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368053)), -(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), _1368051), _1368053))))], (37129 ^ _782476) ^ [_1489402, _1489404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489402)), 37132 ^ _782476 : [(37139 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489404), _1489402))), -(c_Divides_OposDivAlg(_1489404, _1489402) = hAPP(c_Divides_Oadjust(_1489402), c_Divides_OposDivAlg(_1489404, 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)))), _1489402))))], (37133 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489404), _1489402)), -(c_Divides_OposDivAlg(_1489404, _1489402) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489404))]]], (45334 ^ _782476) ^ [_1689810, _1689812, _1689814] : [-(hAPP(c_List_Otl(_1689810), hAPP(hAPP(c_List_Olist_OCons(_1689810), _1689812), _1689814)) = _1689814)], (7968 ^ _782476) ^ [_918187, _918189, _918191, _918193] : [class_Lattices_Osemilattice__sup(_918187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918187), _918189), _918191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918187), _918193), _918191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918187), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918187), _918189), _918193)), _918191)))], (44917 ^ _782476) ^ [_1679695, _1679697, _1679699, _1679701, _1679703, _1679705] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679695), tc_List_Olist(_1679695))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679695), tc_List_Olist(_1679695)), hAPP(hAPP(c_List_Oappend(_1679695), _1679697), _1679703)), hAPP(hAPP(c_List_Oappend(_1679695), _1679699), _1679705))), c_List_Olistrel1(_1679695, _1679701)))), 44918 ^ _782476 : [(44925 ^ _782476) ^ [] : [_1679697 = _1679699, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679695), tc_List_Olist(_1679695))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679695), tc_List_Olist(_1679695)), _1679703), _1679705)), c_List_Olistrel1(_1679695, _1679701)))], (44919 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679695), tc_List_Olist(_1679695))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679695), tc_List_Olist(_1679695)), _1679697), _1679699)), c_List_Olistrel1(_1679695, _1679701))), _1679703 = _1679705]]], (25303 ^ _782476) ^ [_1255360, _1255362] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255360), _1255362))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255360))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255362))))], (15298 ^ _782476) ^ [_1068211, _1068213] : [class_Lattices_Olattice(_1068211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068211), _1068213)), -(_1068213 = c_Orderings_Obot__class_Obot(tc_fun(_1068211, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068211), c_Big__Operators_Olattice__class_OInf__fin(_1068211, _1068213)), c_Big__Operators_Olattice__class_OSup__fin(_1068211, _1068213))))], (33214 ^ _782476) ^ [_1412363, _1412365] : [class_Int_Onumber__ring(_1412363), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1412363), hAPP(c_Int_Onumber__class_Onumber__of(_1412363), _1412365)) = hAPP(c_Int_Onumber__class_Onumber__of(_1412363), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412365)))], (24291 ^ _782476) ^ [_1237367] : [24293 ^ _782476 : [(24296 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24292 ^ [_1237367]))], (24294 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24292 ^ [_1237367]), _1237367)))]], -(c_Nat__Transfer_Onat__set(_1237367))], (23239 ^ _782476) ^ [_1218663, _1218665, _1218667] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218663), _1218665)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218663), _1218667)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218663, tc_HOL_Obool)), _1218665), _1218667) = c_Orderings_Obot__class_Obot(tc_fun(_1218663, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1218663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218663, tc_HOL_Obool)), _1218665), _1218667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218663), _1218665)), hAPP(c_Finite__Set_Ocard(_1218663), _1218667)))], (50559 ^ _782476) ^ [_1804789, _1804791] : [-(c_Relation_Otrans(_1804789, c_Transitive__Closure_Otrancl(_1804789, _1804791)))], (46712 ^ _782476) ^ [_1720058, _1720060, _1720062, _1720064, _1720066, _1720068] : [c_List_Olist__all2(_1720058, _1720060, _1720062, _1720064, _1720066), -(c_List_Olist__all2(_1720058, _1720060, _1720062, hAPP(hAPP(c_List_Odrop(_1720058), _1720068), _1720064), hAPP(hAPP(c_List_Odrop(_1720060), _1720068), _1720066)))], (38312 ^ _782476) ^ [_1514353, _1514355, _1514357, _1514359, _1514361, _1514363, _1514365, _1514367, _1514369, _1514371, _1514373] : [c_Equiv__Relations_Oequiv(_1514353, _1514355, _1514357), c_Equiv__Relations_Oequiv(_1514359, _1514361, _1514363), c_Equiv__Relations_Ocongruent2(_1514353, _1514359, tc_fun(_1514365, tc_HOL_Obool), _1514357, _1514363, _1514367), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514353, tc_HOL_Obool)), _1514369), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514353), _1514355), _1514357))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514359, tc_HOL_Obool)), _1514371), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514359), _1514361), _1514363))), 38334 ^ _782476 : [(38340 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1514365, tc_HOL_Obool)), hAPP(hAPP(_1514367, 38333 ^ [_1514353, _1514355, _1514357, _1514359, _1514361, _1514363, _1514365, _1514367, _1514369, _1514371, _1514373]), 38336 ^ [_1514353, _1514355, _1514357, _1514359, _1514361, _1514363, _1514365, _1514367, _1514369, _1514371, _1514373])), _1514373))], (38338 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514359), 38336 ^ [_1514353, _1514355, _1514357, _1514359, _1514361, _1514363, _1514365, _1514367, _1514369, _1514371, _1514373]), _1514361)))], (38335 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514353), 38333 ^ [_1514353, _1514355, _1514357, _1514359, _1514361, _1514363, _1514365, _1514367, _1514369, _1514371, _1514373]), _1514355)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1514365, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514353, tc_fun(_1514365, tc_HOL_Obool)), _1514369), hAPP(hAPP(c_COMBB(tc_fun(_1514359, tc_fun(_1514365, tc_HOL_Obool)), tc_fun(_1514365, tc_HOL_Obool), _1514353), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514359, tc_fun(_1514365, tc_HOL_Obool)), _1514371)), _1514367))), _1514373)))], (30122 ^ _782476) ^ [_1353711, _1353713, _1353715, _1353717] : [class_Fields_Ofield__inverse__zero(_1353711), 30125 ^ _782476 : [(30126 ^ _782476) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353711), _1353713), _1353715) = _1353717, 30129 ^ _782476 : [(30136 ^ _782476) ^ [] : [_1353715 = c_Groups_Ozero__class_Ozero(_1353711), -(_1353717 = c_Groups_Ozero__class_Ozero(_1353711))], (30130 ^ _782476) ^ [] : [-(_1353715 = c_Groups_Ozero__class_Ozero(_1353711)), -(_1353713 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353711), _1353717), _1353715))]]], (30142 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353711), _1353713), _1353715) = _1353717), 30145 ^ _782476 : [(30148 ^ _782476) ^ [] : [_1353713 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353711), _1353717), _1353715)], (30146 ^ _782476) ^ [] : [_1353715 = c_Groups_Ozero__class_Ozero(_1353711)]], 30149 ^ _782476 : [(30152 ^ _782476) ^ [] : [_1353717 = c_Groups_Ozero__class_Ozero(_1353711)], (30150 ^ _782476) ^ [] : [-(_1353715 = c_Groups_Ozero__class_Ozero(_1353711))]]]]], (13890 ^ _782476) ^ [_1040299, _1040301, _1040303, _1040305, _1040307] : [-(c_Fun_Obij__betw(_1040299, _1040301, _1040303, _1040305, _1040307)), c_Fun_Oinj__on(_1040299, _1040301, _1040303, _1040305), hAPP(c_Set_Oimage(_1040299, _1040301, _1040303), _1040305) = _1040307], (51478 ^ _782476) ^ [_1823949, _1823951, _1823953, _1823955] : [c_Equiv__Relations_Oequivp(_1823949, _1823951), -(c_Quotient_OBabs(_1823949, _1823953, c_Quotient_ORespects(_1823949, _1823951), _1823955) = _1823955)], (27167 ^ _782476) ^ [_1296030, _1296032, _1296034, _1296036] : [class_Groups_Ocomm__monoid__mult(_1296030), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296032), _1296034))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296032, _1296030), _1296036), _1296034) = c_Groups_Oone__class_Oone(_1296030))], (38927 ^ _782476) ^ [_1530599, _1530601, _1530603, _1530605] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530599, _1530601, _1530603), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530599, _1530601), tc_HOL_Obool))), _1530605) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530599, _1530603), tc_HOL_Obool)))], (21804 ^ _782476) ^ [_1191820, _1191822, _1191824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191820)), 21807 ^ _782476 : [(21808 ^ _782476) ^ [_1191954] : [21810 ^ _782476 : [(21816 ^ _782476) ^ [] : [-(_1191954 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21812 ^ [_1191820, _1191822, _1191824, _1191954]), 21809 ^ [_1191820, _1191822, _1191824, _1191954]))], (21814 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21812 ^ [_1191820, _1191822, _1191824, _1191954]), _1191822)))], (21811 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21809 ^ [_1191820, _1191822, _1191824, _1191954]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191820))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191954), _1191824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191954), _1191820)), _1191824)))]]], (17604 ^ _782476) ^ [_1116196, _1116198, _1116200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116196), _1116198)), _1116200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116198), _1116200)))], (45052 ^ _782476) ^ [_1683442, _1683444, _1683446, _1683448] : [-(hAPP(hAPP(c_List_Odrop(_1683442), hAPP(c_Nat_OSuc, _1683444)), hAPP(hAPP(c_List_Olist_OCons(_1683442), _1683446), _1683448)) = hAPP(hAPP(c_List_Odrop(_1683442), _1683444), _1683448))], (41314 ^ _782476) ^ [_1592145, _1592147, _1592149, _1592151] : [hBOOL(hAPP(hAPP(c_member(_1592145), _1592147), c_Wellfounded_Oacc(_1592145, _1592149))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592145, _1592145)), hAPP(hAPP(c_Product__Type_OPair(_1592145, _1592145), _1592151), _1592147)), c_Transitive__Closure_Ortrancl(_1592145, _1592149))), -(hBOOL(hAPP(hAPP(c_member(_1592145), _1592151), c_Wellfounded_Oacc(_1592145, _1592149))))], (34692 ^ _782476) ^ [_1438293, _1438295] : [class_Int_Onumber__ring(_1438293), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438293), c_Int_Osucc(_1438295)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438293), c_Groups_Oone__class_Oone(_1438293)), hAPP(c_Int_Onumber__class_Onumber__of(_1438293), _1438295)))], (17539 ^ _782476) ^ [_1114955, _1114957] : [17540 ^ _782476 : [(17543 ^ _782476) ^ [] : [_1114955 = _1114957], (17541 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114955), _1114957))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114955), _1114957)))], (9105 ^ _782476) ^ [_943613, _943615, _943617, _943619] : [9107 ^ _782476 : [(9110 ^ _782476) ^ [] : [hAPP(_943619, 9106 ^ [_943613, _943615, _943617, _943619]) = c_Orderings_Otop__class_Otop(tc_fun(_943613, tc_HOL_Obool))], (9108 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943615), 9106 ^ [_943613, _943615, _943617, _943619]), _943617)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_943613, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943615, tc_fun(_943613, tc_HOL_Obool)), _943617), _943619))], (45689 ^ _782476) ^ [_1697322, _1697324, _1697326] : [class_Orderings_Olinorder(_1697322), -(hBOOL(hAPP(hAPP(c_member(_1697322), _1697324), hAPP(c_List_Oset(_1697322), _1697326)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697322, _1697322, c_COMBI(_1697322), _1697324, _1697326) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697322, _1697322, c_COMBI(_1697322)), _1697324), _1697326))], (34320 ^ _782476) ^ [_1432484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432484)))], (18040 ^ _782476) ^ [_1124273, _1124275] : [class_Groups_Olinordered__ab__group__add(_1124273), 18043 ^ _782476 : [(18050 ^ _782476) ^ [] : [_1124275 = c_Groups_Ozero__class_Ozero(_1124273), -(c_Groups_Ozero__class_Ozero(_1124273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124273), _1124275), _1124275))], (18044 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1124273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124273), _1124275), _1124275), -(_1124275 = c_Groups_Ozero__class_Ozero(_1124273))]]], (20489 ^ _782476) ^ [_1167888, _1167890, _1167892] : [class_Rings_Olinordered__ring(_1167888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167888), c_Groups_Ozero__class_Ozero(_1167888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167888), _1167890), _1167890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167888), _1167892), _1167892)))))], (32000 ^ _782476) ^ [_1388755, _1388757, _1388759, _1388761] : [class_Divides_Oring__div(_1388755), c_Divides_Odiv__class_Omod(_1388755, _1388757, _1388759) = c_Divides_Odiv__class_Omod(_1388755, _1388761, _1388759), -(c_Divides_Odiv__class_Omod(_1388755, hAPP(c_Groups_Ouminus__class_Ouminus(_1388755), _1388757), _1388759) = c_Divides_Odiv__class_Omod(_1388755, hAPP(c_Groups_Ouminus__class_Ouminus(_1388755), _1388761), _1388759))], (10797 ^ _782476) ^ [_980756, _980758, _980760, _980762, _980764] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980756, tc_HOL_Obool)), _980758), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980760, tc_fun(_980756, tc_HOL_Obool)), _980762), _980764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980760, tc_fun(_980756, tc_HOL_Obool)), _980762), hAPP(hAPP(c_COMBB(tc_fun(_980756, tc_HOL_Obool), tc_fun(_980756, tc_HOL_Obool), _980760), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980756, tc_HOL_Obool)), _980758)), _980764)))], (50032 ^ _782476) ^ [_1792722, _1792724, _1792726, _1792728] : [hBOOL(hAPP(hAPP(c_member(_1792722), _1792724), hAPP(c_List_Oset(_1792722), c_List_Oreplicate(_1792722, _1792726, _1792728)))), 50035 ^ _782476 : [(50038 ^ _782476) ^ [] : [_1792726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50036 ^ _782476) ^ [] : [-(_1792724 = _1792728)]]], (43370 ^ _782476) ^ [_1643300, _1643302, _1643304, _1643306] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643300) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643302), hAPP(hAPP(c_List_Olist_OCons(_1643302), _1643304), _1643306)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643300)) = hAPP(hAPP(c_List_Onth(_1643302), _1643306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643300)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41090 ^ _782476) ^ [_1586836, _1586838] : [-(c_Transitive__Closure_Otrancl(_1586836, _1586838) = hAPP(hAPP(c_Relation_Orel__comp(_1586836, _1586836, _1586836), _1586838), c_Transitive__Closure_Ortrancl(_1586836, _1586838)))], (48681 ^ _782476) ^ [_1762156, _1762158, _1762160] : [hBOOL(hAPP(c_List_Odistinct(_1762156), _1762158)), -(hBOOL(hAPP(c_List_Odistinct(_1762156), hAPP(c_List_OremoveAll(_1762156, _1762160), _1762158))))], (48078 ^ _782476) ^ [_1749401, _1749403, _1749405] : [_1749403 = hAPP(hAPP(c_List_Olist_OCons(_1749401), _1749405), c_List_Olist_ONil(_1749401)), -(hAPP(c_List_Orev(_1749401), _1749403) = hAPP(hAPP(c_List_Olist_OCons(_1749401), _1749405), c_List_Olist_ONil(_1749401)))], (48431 ^ _782476) ^ [_1756883, _1756885, _1756887] : [hBOOL(hAPP(c_List_Odistinct(_1756883), _1756885)), hBOOL(hAPP(hAPP(c_member(_1756883), _1756887), hAPP(c_List_Oset(_1756883), _1756885))), -(c_List_OdropWhile(_1756883, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756883), c_fNot), hAPP(hAPP(c_COMBC(_1756883, _1756883, tc_HOL_Obool), c_fequal), _1756887)), hAPP(c_List_Orev(_1756883), _1756885)) = hAPP(hAPP(c_List_Olist_OCons(_1756883), _1756887), hAPP(c_List_Orev(_1756883), c_List_OtakeWhile(_1756883, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756883), c_fNot), hAPP(hAPP(c_COMBC(_1756883, _1756883, tc_HOL_Obool), c_fequal), _1756887)), _1756885))))], (47930 ^ _782476) ^ [_1746129, _1746131, _1746133, _1746135] : [class_Orderings_Olinorder(_1746129), c_List_Olinorder__class_Osorted(_1746129, _1746131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746133), _1746135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746135), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746129)), _1746131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746129), hAPP(hAPP(c_List_Onth(_1746129), _1746131), _1746133)), hAPP(hAPP(c_List_Onth(_1746129), _1746131), _1746135))))], (17255 ^ _782476) ^ [_1110335, _1110337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110335), _1110337)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110337), _1110335)), _1110335) = _1110337)], (10557 ^ _782476) ^ [_975242, _975244] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975242, tc_HOL_Obool)), _975244), c_Orderings_Otop__class_Otop(tc_fun(_975242, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_975242, tc_HOL_Obool)))], (48100 ^ _782476) ^ [_1749867, _1749869, _1749871, _1749873] : [-(hAPP(c_List_Orev(_1749867), hAPP(hAPP(c_List_Omap(_1749869, _1749867), _1749871), _1749873)) = hAPP(hAPP(c_List_Omap(_1749869, _1749867), _1749871), hAPP(c_List_Orev(_1749869), _1749873)))], (16847 ^ _782476) ^ [_1100564, _1100566, _1100568] : [class_Groups_Oab__group__add(_1100564), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100564), _1100566), _1100568) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100564), _1100566), hAPP(c_Groups_Ouminus__class_Ouminus(_1100564), _1100568)))], (37950 ^ _782476) ^ [_1505938, _1505940, _1505942, _1505944, _1505946] : [c_Equiv__Relations_Oequiv(_1505938, _1505940, _1505942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505938, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505938, _1505938, _1505942), hAPP(hAPP(c_Set_Oinsert(_1505938), _1505944), c_Orderings_Obot__class_Obot(tc_fun(_1505938, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505938, _1505938, _1505942), hAPP(hAPP(c_Set_Oinsert(_1505938), _1505946), c_Orderings_Obot__class_Obot(tc_fun(_1505938, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1505938), _1505944), _1505940)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505938, _1505938)), hAPP(hAPP(c_Product__Type_OPair(_1505938, _1505938), _1505946), _1505944)), _1505942)))], (41160 ^ _782476) ^ [_1588550, _1588552] : [-(c_Transitive__Closure_Ortrancl(_1588550, c_Transitive__Closure_Ortrancl(_1588550, _1588552)) = c_Transitive__Closure_Ortrancl(_1588550, _1588552))], (15706 ^ _782476) ^ [_1076415, _1076417, _1076419, _1076421, _1076423, _1076425, _1076427] : [c_Finite__Set_Ofolding__image__simple(_1076415, _1076417, _1076419, _1076421, _1076423, _1076425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076417), _1076427)), -(hAPP(_1076425, _1076427) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076415, _1076417, _1076419), _1076423), _1076421), _1076427))], (52461 ^ _782476) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (8058 ^ _782476) ^ [_919745, _919747, _919749] : [class_Lattices_Osemilattice__sup(_919745), 8061 ^ _782476 : [(8068 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919745), _919747), _919749) = _919749, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919745), _919747), _919749)))], (8062 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919745), _919747), _919749)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919745), _919747), _919749) = _919749)]]], (18382 ^ _782476) ^ [_1129205, _1129207, _1129209] : [18383 ^ _782476 : [(18386 ^ _782476) ^ [] : [_1129207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18384 ^ _782476) ^ [] : [_1129205 = _1129209]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129205), _1129207) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129209), _1129207))], (33924 ^ _782476) ^ [_1425721] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425721) = _1425721)], (45232 ^ _782476) ^ [_1687742, _1687744, _1687746, _1687748] : [-(hAPP(c_List_Orotate1(_1687742), c_List_Olist_ONil(_1687742)) = c_List_Olist_ONil(_1687742))], (3172 ^ _782476) ^ [_829670, _829672, _829674, _829676] : [-(c_Nat_Ocompow(_829676, _829672) = c_Nat_Ocompow(_829674, _829670)), _829676 = _829674, _829672 = _829670], (36214 ^ _782476) ^ [_1466147] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1466147, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50002 ^ _782476) ^ [_1792139, _1792141, _1792143, _1792145, _1792147, _1792149] : [-(hAPP(hAPP(c_List_Ozip(_1792139, _1792141), c_List_Oreplicate(_1792139, _1792143, _1792145)), c_List_Oreplicate(_1792141, _1792147, _1792149)) = c_List_Oreplicate(tc_prod(_1792139, _1792141), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792143), _1792147), hAPP(hAPP(c_Product__Type_OPair(_1792139, _1792141), _1792145), _1792149)))], (32151 ^ _782476) ^ [_1391425, _1391427, _1391429] : [class_Divides_Osemiring__div(_1391425), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391425), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391425), _1391427), _1391429)), _1391429)), c_Divides_Odiv__class_Omod(_1391425, _1391427, _1391429)) = _1391427)], (19392 ^ _782476) ^ [_1147302, _1147304] : [class_Groups_Olinordered__ab__group__add(_1147302), 19395 ^ _782476 : [(19402 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147302), _1147304), c_Groups_Ozero__class_Ozero(_1147302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147302), _1147304), hAPP(c_Groups_Ouminus__class_Ouminus(_1147302), _1147304))))], (19396 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147302), _1147304), hAPP(c_Groups_Ouminus__class_Ouminus(_1147302), _1147304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147302), _1147304), c_Groups_Ozero__class_Ozero(_1147302))))]]], (22610 ^ _782476) ^ [_1206505] : [-(hAPP(c_Nat_OSuc, _1206505) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206505), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16075 ^ _782476) ^ [_1084105, _1084107] : [class_Rings_Oring__1__no__zero__divisors(_1084105), 16078 ^ _782476 : [(16079 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084105), _1084107), _1084107) = c_Groups_Oone__class_Oone(_1084105), -(_1084107 = c_Groups_Oone__class_Oone(_1084105)), -(_1084107 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084105), c_Groups_Oone__class_Oone(_1084105)))], (16089 ^ _782476) ^ [] : [16090 ^ _782476 : [(16093 ^ _782476) ^ [] : [_1084107 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084105), c_Groups_Oone__class_Oone(_1084105))], (16091 ^ _782476) ^ [] : [_1084107 = c_Groups_Oone__class_Oone(_1084105)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084105), _1084107), _1084107) = c_Groups_Oone__class_Oone(_1084105))]]], (15863 ^ _782476) ^ [_1079239, _1079241, _1079243, _1079245, _1079247, _1079249, _1079251] : [c_Big__Operators_Ocomm__monoid__big(_1079239, _1079241, _1079243, _1079245, _1079247), 15866 ^ _782476 : [(15873 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1079241), _1079249))), -(hAPP(hAPP(_1079247, _1079251), _1079249) = _1079245)], (15867 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1079241), _1079249)), -(hAPP(hAPP(_1079247, _1079251), _1079249) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1079239, _1079241, _1079243), _1079251), _1079245), _1079249))]]], (24628 ^ _782476) ^ [_1242972, _1242974, _1242976, _1242978] : [class_Rings_Oring__1(_1242972), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242972), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1242974, tc_Int_Oint), _1242976), _1242978)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1242974, _1242972), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1242972, _1242974), c_Int_Oring__1__class_Oof__int(_1242972)), _1242976)), _1242978))], (5118 ^ _782476) ^ [_860663, _860665] : [_860665 = _860663, -(c_Set_OCollect(_860665) = c_Set_OCollect(_860663))], (10673 ^ _782476) ^ [_977890, _977892, _977894, _977896] : [class_Orderings_Oorder(_977890), 10676 ^ _782476 : [(10685 ^ _782476) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_977890, _977892, _977894) = hAPP(hAPP(c_Set_Oinsert(_977890), _977896), c_Orderings_Obot__class_Obot(tc_fun(_977890, tc_HOL_Obool)))), _977892 = _977894, _977894 = _977896], (10677 ^ _782476) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_977890, _977892, _977894) = hAPP(hAPP(c_Set_Oinsert(_977890), _977896), c_Orderings_Obot__class_Obot(tc_fun(_977890, tc_HOL_Obool))), 10680 ^ _782476 : [(10683 ^ _782476) ^ [] : [-(_977894 = _977896)], (10681 ^ _782476) ^ [] : [-(_977892 = _977894)]]]]], (13002 ^ _782476) ^ [_1020948, _1020950] : [class_Complete__Lattice_Ocomplete__lattice(_1020948), c_Orderings_Oorder__class_Omono(_1020948, _1020948, _1020950), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020948), hAPP(_1020950, c_Inductive_Ocomplete__lattice__class_Olfp(_1020948, _1020950))), c_Inductive_Ocomplete__lattice__class_Olfp(_1020948, _1020950))))], (43107 ^ _782476) ^ [_1635869, _1635871, _1635873] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635869), tc_List_Olist(_1635869))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635869), tc_List_Olist(_1635869)), _1635871), _1635871)), c_List_Olistrel(_1635869, c_Transitive__Closure_Ortrancl(_1635869, _1635873)))))], (50343 ^ _782476) ^ [_1799622, _1799624] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1799622, _1799624), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799622)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41974 ^ _782476) ^ [_1609161, _1609163] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609161, _1609161)), _1609163), c_Relation_OId(_1609161))), -(_1609163 = hAPP(hAPP(c_Product__Type_OPair(_1609161, _1609161), 41977 ^ [_1609161, _1609163]), 41977 ^ [_1609161, _1609163]))], (15055 ^ _782476) ^ [_1063600, _1063602] : [class_Lattices_Olattice(_1063600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063600), _1063602)), -(_1063602 = c_Orderings_Obot__class_Obot(tc_fun(_1063600, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1063600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063600), 15068 ^ [_1063600, _1063602]), 15069 ^ [_1063600, _1063602])), hAPP(hAPP(c_Set_Oinsert(_1063600), 15068 ^ [_1063600, _1063602]), hAPP(hAPP(c_Set_Oinsert(_1063600), 15069 ^ [_1063600, _1063602]), c_Orderings_Obot__class_Obot(tc_fun(_1063600, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1063600), c_Big__Operators_Olattice__class_OInf__fin(_1063600, _1063602)), _1063602)))], (16973 ^ _782476) ^ [_1103799, _1103801, _1103803, _1103805, _1103807] : [class_Rings_Ocomm__semiring__1(_1103799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), _1103801), _1103803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), _1103805), _1103807)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), _1103801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), _1103803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103799), _1103805), _1103807))))], (2002 ^ _782476) ^ [_810701, _810703] : [-(hBOOL(_810701)), _810703 = _810701, hBOOL(_810703)], (34550 ^ _782476) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (8174 ^ _782476) ^ [_922063, _922065, _922067] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922063, tc_HOL_Obool)), _922065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922063, tc_HOL_Obool)), _922065), _922067))))], (50404 ^ _782476) ^ [_1800984, _1800986, _1800988] : [-(c_Random__Sequence_Oempty(_1800984, _1800986, _1800988) = 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(_1800984)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800984)))], (40283 ^ _782476) ^ [_1567040, _1567042, _1567044] : [c_Wellfounded_OwfP(_1567040, _1567042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567040, tc_fun(_1567040, tc_HOL_Obool))), _1567044), _1567042)), -(c_Wellfounded_OwfP(_1567040, _1567044))], (4624 ^ _782476) ^ [_852778, _852780, _852782, _852784, _852786, _852788, _852790, _852792, _852794, _852796] : [-(c_Nitpick_Opair__box_Opair__box__rec(_852796, _852792, _852788, _852784, _852780) = c_Nitpick_Opair__box_Opair__box__rec(_852794, _852790, _852786, _852782, _852778)), _852796 = _852794, _852792 = _852790, _852788 = _852786, _852784 = _852782, _852780 = _852778], (2360 ^ _782476) ^ [_817066, _817068, _817070, _817072] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817072, _817068) = c_Code__Numeral_Odiv__mod__code__numeral(_817070, _817066)), _817072 = _817070, _817068 = _817066], (36908 ^ _782476) ^ [_1485121, _1485123, _1485125] : [hBOOL(hAPP(_1485121, hAPP(hAPP(c_Product__Type_OPair(_1485123, _1485125), 36909 ^ [_1485121, _1485123, _1485125]), 36910 ^ [_1485121, _1485123, _1485125]))), 36913 ^ _782476 : [(36914 ^ _782476) ^ [_1485268] : [-(hBOOL(hAPP(_1485121, _1485268)))]]], (9482 ^ _782476) ^ [_952408, _952410] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952408, tc_HOL_Obool)), _952410), c_Orderings_Obot__class_Obot(tc_fun(_952408, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952408, tc_HOL_Obool)))], (41569 ^ _782476) ^ [_1598560, _1598562] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1598560, _1598560)), _1598562)), c_Wellfounded_Oacyclic(_1598560, _1598562), -(c_Wellfounded_Owf(_1598560, hAPP(c_Relation_Oconverse(_1598560, _1598560), _1598562)))], (11988 ^ _782476) ^ [_1000646, _1000648, _1000650] : [class_Complete__Lattice_Ocomplete__lattice(_1000646), class_Orderings_Olinorder(_1000646), 11995 ^ _782476 : [(12005 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000646), _1000648), c_Complete__Lattice_OSup__class_OSup(_1000646, _1000650)))), 12006 ^ _782476 : [(12007 ^ _782476) ^ [_1000952] : [hBOOL(hAPP(hAPP(c_member(_1000646), _1000952), _1000650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000646), _1000648), _1000952))]]], (11996 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000646), _1000648), c_Complete__Lattice_OSup__class_OSup(_1000646, _1000650))), 12000 ^ _782476 : [(12003 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000646), _1000648), 11999 ^ [_1000646, _1000648, _1000650])))], (12001 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000646), 11999 ^ [_1000646, _1000648, _1000650]), _1000650)))]]]]], (4464 ^ _782476) ^ [_850212, _850214, _850216, _850218] : [-(c_List_Ofilter(_850218, _850214) = c_List_Ofilter(_850216, _850212)), _850218 = _850216, _850214 = _850212], (25839 ^ _782476) ^ [_1267929, _1267931, _1267933, _1267935, _1267937, _1267939] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267929), _1267931)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267933), _1267935)), 25849 ^ _782476 : [(25852 ^ _782476) ^ [] : [hAPP(c_Finite__Set_Ocard(_1267929), hAPP(c_Set_OCollect(_1267929), hAPP(hAPP(c_COMBS(_1267929, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267929), c_fconj), hAPP(hAPP(c_COMBC(_1267929, tc_fun(_1267929, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267929)), _1267931))), hAPP(hAPP(c_COMBC(_1267929, _1267933, tc_HOL_Obool), _1267937), 25848 ^ [_1267929, _1267931, _1267933, _1267935, _1267937, _1267939])))) = hAPP(_1267939, 25848 ^ [_1267929, _1267931, _1267933, _1267935, _1267937, _1267939])], (25850 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267933), 25848 ^ [_1267929, _1267931, _1267933, _1267935, _1267937, _1267939]), _1267935)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267929, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1267933, tc_HOL_Obool), tc_Nat_Onat, _1267929), c_Finite__Set_Ocard(_1267933)), hAPP(hAPP(c_COMBB(tc_fun(_1267933, tc_HOL_Obool), tc_fun(_1267933, tc_HOL_Obool), _1267929), c_Set_OCollect(_1267933)), hAPP(hAPP(c_COMBB(tc_fun(_1267933, tc_HOL_Obool), tc_fun(_1267933, tc_HOL_Obool), _1267929), hAPP(c_COMBS(_1267933, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267933), c_fconj), hAPP(hAPP(c_COMBC(_1267933, tc_fun(_1267933, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267933)), _1267935)))), _1267937)))), _1267931) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267933, tc_Nat_Onat), _1267939), _1267935))], (13662 ^ _782476) ^ [_1035640, _1035642, _1035644, _1035646] : [class_Groups_Oab__semigroup__mult(_1035640), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035640), _1035642), _1035644)), _1035646) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035640), _1035642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035640), _1035644), _1035646)))], (51605 ^ _782476) ^ [_1828370, _1828372, _1828374] : [c_List_Olist__all(tc_Nat_Onat, _1828370, c_List_Oupt(_1828372, _1828374)), -(c_List_Oall__interval__nat(_1828370, _1828372, _1828374))], (8776 ^ _782476) ^ [_935552, _935554, _935556, _935558] : [class_Lattices_Osemilattice__inf(_935552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935552), _935554), _935556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935552), _935554), _935558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935552), _935554), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935552), _935556), _935558))))], (36124 ^ _782476) ^ [_1464758] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1464758) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464758))], (37766 ^ _782476) ^ [_1501496, _1501498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501498)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501496), _1501498) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1501496, _1501498)))], (47165 ^ _782476) ^ [_1730329, _1730331, _1730333] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730329)), hAPP(c_List_Ofilter(_1730329, _1730331), _1730333))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730329)), hAPP(c_List_Ofilter(_1730329, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730329), c_fNot), _1730331)), _1730333))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730329)), _1730333))], (18428 ^ _782476) ^ [_1129892] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1129892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4340 ^ _782476) ^ [_848396, _848398, _848400, _848402, _848404, _848406] : [-(c_New__DSequence_Opos__union(_848406, _848402, _848398) = c_New__DSequence_Opos__union(_848404, _848400, _848396)), _848406 = _848404, _848402 = _848400, _848398 = _848396], (52647 ^ _782476) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (36948 ^ _782476) ^ [_1486247, _1486249, _1486251, _1486253, _1486255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486247, _1486249)), hAPP(hAPP(c_Product__Type_OPair(_1486247, _1486249), _1486253), _1486255)), _1486251)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486247, _1486249, _1486251), _1486253), _1486255)))], (13712 ^ _782476) ^ [_1036729, _1036731, _1036733, _1036735, _1036737] : [c_Fun_Obij__betw(_1036729, _1036731, _1036733, c_Orderings_Otop__class_Otop(tc_fun(_1036729, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036731, tc_HOL_Obool))), c_Fun_Obij__betw(_1036731, _1036735, _1036737, c_Orderings_Otop__class_Otop(tc_fun(_1036731, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036735, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1036729, _1036735, hAPP(c_Fun_Ocomp(_1036731, _1036735, _1036729, _1036737), _1036733), c_Orderings_Otop__class_Otop(tc_fun(_1036729, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036735, tc_HOL_Obool))))], (46058 ^ _782476) ^ [_1704948, _1704950, _1704952, _1704954, _1704956, _1704958, _1704960, _1704962] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1704948, _1704950), _1704952), _1704954), hAPP(hAPP(c_List_Ozip(_1704948, _1704950), hAPP(hAPP(c_List_Omap(_1704956, _1704948), _1704958), _1704960)), _1704962)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704956, _1704950), _1704952), hAPP(c_Product__Type_Oprod_Oprod__case(_1704956, _1704950, _1704952), hAPP(hAPP(c_COMBB(tc_fun(_1704950, tc_prod(_1704948, _1704950)), tc_fun(_1704950, _1704952), _1704956), hAPP(c_COMBB(tc_prod(_1704948, _1704950), _1704952, _1704950), _1704954)), hAPP(hAPP(c_COMBB(_1704948, tc_fun(_1704950, tc_prod(_1704948, _1704950)), _1704956), c_Product__Type_OPair(_1704948, _1704950)), _1704958)))), hAPP(hAPP(c_List_Ozip(_1704956, _1704950), _1704960), _1704962)))], (9570 ^ _782476) ^ [_954017, _954019, _954021, _954023] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954017, tc_fun(_954019, tc_HOL_Obool)), _954021), _954023) = c_Orderings_Obot__class_Obot(tc_fun(_954019, tc_HOL_Obool)), 9573 ^ _782476 : [(9574 ^ _782476) ^ [_954133] : [hBOOL(hAPP(hAPP(c_member(_954017), _954133), _954021)), -(hAPP(_954023, _954133) = c_Orderings_Obot__class_Obot(tc_fun(_954019, tc_HOL_Obool)))]]], (47363 ^ _782476) ^ [_1735881, _1735883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735881), _1735883)), -(c_List_Oupt(_1735881, hAPP(c_Nat_OSuc, _1735883)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735881, _1735883)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735883), c_List_Olist_ONil(tc_Nat_Onat))))], (47730 ^ _782476) ^ [_1742337, _1742339, _1742341, _1742343, _1742345] : [class_Orderings_Olinorder(_1742337), c_List_Olinorder__class_Osorted(_1742337, hAPP(hAPP(c_List_Omap(_1742339, _1742337), _1742341), _1742343)), -(c_List_Olinorder__class_Osorted(_1742337, hAPP(hAPP(c_List_Omap(_1742339, _1742337), _1742341), c_List_Olinorder__class_Oinsort__insert__key(_1742339, _1742337, _1742341, _1742345, _1742343))))], (50004 ^ _782476) ^ [_1792211, _1792213, _1792215, _1792217] : [-(hAPP(hAPP(c_List_Odrop(_1792211), _1792213), c_List_Oreplicate(_1792211, _1792215, _1792217)) = c_List_Oreplicate(_1792211, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1792215), _1792213), _1792217))], (806 ^ _782476) ^ [_794817, _794819, _794821, _794823, _794825, _794827] : [-(c_List_Olist__ex1(_794825, _794821, _794817)), c_List_Olist__ex1(_794827, _794823, _794819), _794827 = _794825, _794823 = _794821, _794819 = _794817], (38485 ^ _782476) ^ [_1519079, _1519081] : [-(c_Equiv__Relations_Oequivp(_1519079, _1519081)), 38490 ^ _782476 : [(38493 ^ _782476) ^ [] : [hAPP(_1519081, 38486 ^ [_1519079, _1519081]) = hAPP(_1519081, 38487 ^ [_1519079, _1519081])], (38491 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1519081, 38486 ^ [_1519079, _1519081]), 38487 ^ [_1519079, _1519081])))]], 38494 ^ _782476 : [(38497 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1519081, 38486 ^ [_1519079, _1519081]), 38487 ^ [_1519079, _1519081]))], (38495 ^ _782476) ^ [] : [-(hAPP(_1519081, 38486 ^ [_1519079, _1519081]) = hAPP(_1519081, 38487 ^ [_1519079, _1519081]))]]], (40477 ^ _782476) ^ [_1570823] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570823), c_Int_OInteg)), -(_1570823 = hAPP(c_Int_ORep__Integ, 40480 ^ [_1570823]))], (52435 ^ _782476) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (48222 ^ _782476) ^ [_1752588, _1752590, _1752592, _1752594] : [class_Orderings_Olinorder(_1752588), c_List_Olinorder__class_Osorted(_1752588, hAPP(c_List_Orev(_1752588), _1752590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1752592), _1752594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752594), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752588)), _1752590))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1752588), hAPP(hAPP(c_List_Onth(_1752588), _1752590), _1752594)), hAPP(hAPP(c_List_Onth(_1752588), _1752590), _1752592))))], (43729 ^ _782476) ^ [_1653905, _1653907, _1653909, _1653911] : [-(hAPP(c_List_Oset(tc_prod(_1653905, _1653907)), hAPP(hAPP(c_List_Ozip(_1653905, _1653907), _1653909), _1653911)) = hAPP(c_Set_OCollect(tc_prod(_1653905, _1653907)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1653905, _1653907)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1653905, _1653907), 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(_1653905, _1653907)), 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(_1653905, _1653907)), 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(_1653905, _1653907), tc_fun(tc_Nat_Onat, tc_prod(_1653905, _1653907)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1653905, _1653907), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1653905, _1653907)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1653905, _1653907)), c_COMBB(tc_prod(_1653905, _1653907), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1653907, tc_prod(_1653905, _1653907)), hAPP(hAPP(c_COMBB(_1653905, tc_fun(_1653907, tc_prod(_1653905, _1653907)), tc_Nat_Onat), c_Product__Type_OPair(_1653905, _1653907)), hAPP(c_List_Onth(_1653905), _1653909))), hAPP(c_List_Onth(_1653907), _1653911)))))), 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(_1653905)), _1653909)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653907)), _1653911)))))))], (5757 ^ _782476) ^ [_873480, _873482, _873484, _873486] : [c_Hoare__Mirabelle_Ohoare__derivs(_873480, _873482, _873484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873480), tc_HOL_Obool)), _873486), _873484)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873480, _873482, _873486))], (40984 ^ _782476) ^ [_1583351, _1583353, _1583355, _1583357, _1583359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), _1583353), _1583355)), c_Transitive__Closure_Otrancl(_1583351, _1583357))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), _1583355), _1583359)), c_Transitive__Closure_Otrancl(_1583351, _1583357))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), _1583353), _1583359)), c_Transitive__Closure_Otrancl(_1583351, _1583357))))], (36010 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (14801 ^ _782476) ^ [_1058957, _1058959, _1058961, _1058963, _1058965, _1058967, _1058969, _1058971] : [c_Finite__Set_Ofolding(_1058957, _1058959, _1058961, _1058963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058957), _1058965)), -(hAPP(c_Fun_Ocomp(_1058959, _1058959, _1058967, hAPP(_1058961, _1058969)), hAPP(c_Fun_Ocomp(_1058959, _1058959, _1058967, hAPP(_1058963, _1058965)), _1058971)) = hAPP(c_Fun_Ocomp(_1058959, _1058959, _1058967, hAPP(_1058963, _1058965)), hAPP(c_Fun_Ocomp(_1058959, _1058959, _1058967, hAPP(_1058961, _1058969)), _1058971)))], (24300 ^ _782476) ^ [_1237515] : [-(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)), _1237515)))], (45989 ^ _782476) ^ [_1703120, _1703122, _1703124, _1703126] : [-(hAPP(hAPP(c_List_Omap(_1703120, _1703122), _1703124), c_List_Obutlast(_1703120, _1703126)) = c_List_Obutlast(_1703122, hAPP(hAPP(c_List_Omap(_1703120, _1703122), _1703124), _1703126)))], (32100 ^ _782476) ^ [_1390471, _1390473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390471), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390471), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390473, _1390471))))], (17734 ^ _782476) ^ [_1118669, _1118671, _1118673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118669), _1118671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118673), _1118669)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118673), _1118671))))], (41376 ^ _782476) ^ [_1593703, _1593705] : [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), _1593703), _1593705)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593703), _1593705)))], (24514 ^ _782476) ^ [_1241040] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241040)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241040))], (17483 ^ _782476) ^ [_1114108, _1114110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114108), _1114110)), _1114110))], (5751 ^ _782476) ^ [_873375, _873377, _873379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873375), tc_HOL_Obool)), _873377), _873379)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873375, _873379, _873377))], (42279 ^ _782476) ^ [_1615351, _1615353, _1615355, _1615357, _1615359] : [c_Finite__Set_Ofolding__one(_1615351, _1615353, _1615355), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615351), _1615357)), -(hBOOL(hAPP(hAPP(c_member(_1615351), _1615359), _1615357))), -(hAPP(_1615355, hAPP(hAPP(c_Set_Oinsert(_1615351), _1615359), _1615357)) = hAPP(hAPP(c_Finite__Set_Ofold(_1615351, _1615351, _1615353), _1615359), _1615357))], (52515 ^ _782476) ^ [_1841800, _1841802] : [-(class_Enum_Oenum(tc_sum(_1841800, _1841802))), class_Enum_Oenum(_1841800), class_Enum_Oenum(_1841802)], (32193 ^ _782476) ^ [_1392303, _1392305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392303), _1392305)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392303, _1392305) = _1392303)], (22570 ^ _782476) ^ [_1205621, _1205623] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1205621), _1205623)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205623), _1205621))], (16218 ^ _782476) ^ [_1087293, _1087295] : [class_Rings_Ocomm__semiring__1(_1087293), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087293), c_Groups_Oone__class_Oone(_1087293)), _1087295) = _1087295)], (3416 ^ _782476) ^ [_833452, _833454, _833456, _833458, _833460, _833462] : [-(c_Finite__Set_Ofold(_833462, _833458, _833454) = c_Finite__Set_Ofold(_833460, _833456, _833452)), _833462 = _833460, _833458 = _833456, _833454 = _833452], (35702 ^ _782476) ^ [_1456786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1456786), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1456786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1456786 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41497 ^ _782476) ^ [_1596684, _1596686] : [-(c_Transitive__Closure_Otrancl(_1596684, hAPP(c_Relation_Oconverse(_1596684, _1596684), _1596686)) = hAPP(c_Relation_Oconverse(_1596684, _1596684), c_Transitive__Closure_Otrancl(_1596684, _1596686)))], (51671 ^ _782476) ^ [_1829499, _1829501] : [class_Rings_Ocomm__semiring__1(_1829499), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829499), _1829501), c_Groups_Ozero__class_Ozero(_1829499))))], (18364 ^ _782476) ^ [_1128932, _1128934, _1128936] : [18365 ^ _782476 : [(18368 ^ _782476) ^ [] : [_1128934 = _1128936], (18366 ^ _782476) ^ [] : [_1128932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128932), _1128934) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128932), _1128936))], (39859 ^ _782476) ^ [_1554983, _1554985, _1554987, _1554989] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1554983, _1554985)), hAPP(hAPP(c_Product__Type_OSigma(_1554983, _1554985), hAPP(hAPP(c_Set_Oinsert(_1554983), _1554987), c_Orderings_Obot__class_Obot(tc_fun(_1554983, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1554985, tc_HOL_Obool), _1554983), _1554989))) = hAPP(c_Finite__Set_Ocard(_1554985), _1554989))], (35768 ^ _782476) ^ [_1457893, _1457895, _1457897] : [class_Rings_Olinordered__idom(_1457893), 35771 ^ _782476 : [(35780 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457893), hAPP(hAPP(c_Power_Opower__class_Opower(_1457893), _1457895), 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(_1457893), _1457897), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457893)))), _1457895 = c_Groups_Ozero__class_Ozero(_1457893), _1457897 = c_Groups_Ozero__class_Ozero(_1457893)], (35772 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457893), hAPP(hAPP(c_Power_Opower__class_Opower(_1457893), _1457895), 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(_1457893), _1457897), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457893))), 35775 ^ _782476 : [(35778 ^ _782476) ^ [] : [-(_1457897 = c_Groups_Ozero__class_Ozero(_1457893))], (35776 ^ _782476) ^ [] : [-(_1457895 = c_Groups_Ozero__class_Ozero(_1457893))]]]]], (48110 ^ _782476) ^ [_1750154, _1750156] : [-(hAPP(c_List_Oset(_1750154), hAPP(c_List_Orev(_1750154), _1750156)) = hAPP(c_List_Oset(_1750154), _1750156))], (9941 ^ _782476) ^ [_961697, _961699, _961701, _961703, _961705] : [class_Lattices_Osemilattice__inf(_961697), class_Lattices_Osemilattice__inf(_961699), c_Orderings_Oorder__class_Omono(_961699, _961697, _961701), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961697), hAPP(_961701, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961699), _961703), _961705))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961697), hAPP(_961701, _961703)), hAPP(_961701, _961705)))))], (8701 ^ _782476) ^ [_933985, _933987, _933989] : [-(hAPP(c_Set_OPow(_933985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933985, tc_HOL_Obool)), _933987), _933989)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_933985, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_933985), _933987)), hAPP(c_Set_OPow(_933985), _933989)))], (52425 ^ _782476) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52249 ^ _782476) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (41234 ^ _782476) ^ [_1590388, _1590390, _1590392, _1590394, _1590396] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590388, _1590388)), hAPP(hAPP(c_Product__Type_OPair(_1590388, _1590388), _1590390), _1590392)), c_Transitive__Closure_Ortrancl(_1590388, _1590394))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590388, _1590388)), hAPP(hAPP(c_Product__Type_OPair(_1590388, _1590388), _1590392), _1590396)), _1590394)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590388, _1590388)), hAPP(hAPP(c_Product__Type_OPair(_1590388, _1590388), _1590390), _1590396)), c_Transitive__Closure_Otrancl(_1590388, _1590394))))], (46358 ^ _782476) ^ [_1711960, _1711962] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1711960)), hAPP(c_Code__Numeral_Oof__nat, _1711962)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1711960), _1711962)))], (14200 ^ _782476) ^ [_1046928, _1046930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046928), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1046928, tc_HOL_Obool), _1046930))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046928, tc_HOL_Obool)), _1046930)))], (10429 ^ _782476) ^ [_972129, _972131, _972133, _972135] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972129, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972129), _972131), _972133)), _972135) = hAPP(hAPP(c_Set_Oinsert(_972129), _972131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972129, tc_HOL_Obool)), _972133), _972135)))], (46446 ^ _782476) ^ [_1713472, _1713474] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1713472, _1713474) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1713472), hAPP(c_Code__Numeral_Onat__of, _1713474))))], (27859 ^ _782476) ^ [_1309099, _1309101, _1309103] : [class_Orderings_Olinorder(_1309099), -(_1309101 = c_Orderings_Obot__class_Obot(tc_fun(_1309099, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309099, tc_HOL_Obool)), _1309101), _1309103)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309099), _1309103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309099), hAPP(c_Finite__Set_Ofold1(_1309099, c_Orderings_Oord__class_Omin(_1309099)), _1309103)), hAPP(c_Finite__Set_Ofold1(_1309099, c_Orderings_Oord__class_Omin(_1309099)), _1309101))))], (46380 ^ _782476) ^ [_1712345, _1712347] : [hAPP(c_Code__Numeral_Onat__of, _1712345) = hAPP(c_Code__Numeral_Onat__of, _1712347), -(_1712345 = _1712347)], (38590 ^ _782476) ^ [_1521503] : [-(c_Wellfounded_Omeasure(_1521503) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1521503), c_Wellfounded_Oless__than))], (37513 ^ _782476) ^ [_1496294, _1496296, _1496298] : [-(hAPP(c_Product__Type_Osnd(_1496294, _1496296), _1496298) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1496294, _1496296, _1496296), hAPP(c_COMBK(tc_fun(_1496296, _1496296), _1496294), c_COMBI(_1496296))), _1496298))], (8120 ^ _782476) ^ [_920866, _920868, _920870, _920872] : [8121 ^ _782476 : [(8124 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920866), _920868), _920872))], (8122 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920866), _920868), _920870))]], -(hBOOL(hAPP(hAPP(c_member(_920866), _920868), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920866, tc_HOL_Obool)), _920870), _920872))))], (42047 ^ _782476) ^ [_1610667, _1610669, _1610671, _1610673] : [class_Orderings_Olinorder(_1610667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610667), _1610669)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610667, _1610667, c_Orderings_Oord__class_Omax(_1610667)), _1610671), hAPP(hAPP(c_Set_Oinsert(_1610667), _1610673), _1610669)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1610667), _1610673), hAPP(hAPP(c_Finite__Set_Ofold(_1610667, _1610667, c_Orderings_Oord__class_Omax(_1610667)), _1610671), _1610669)))], (16775 ^ _782476) ^ [_1099000, _1099002, _1099004, _1099006, _1099008] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1099000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099000), _1099002), _1099004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099000), _1099006), _1099008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099000), _1099002), _1099006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099000), _1099004), _1099008))))], (44981 ^ _782476) ^ [_1681334, _1681336, _1681338, _1681340, _1681342] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681334), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681336)), _1681338)))), -(hAPP(hAPP(c_List_Olist__update(_1681336, hAPP(hAPP(c_List_Oappend(_1681336), _1681338), _1681340)), _1681334), _1681342) = hAPP(hAPP(c_List_Oappend(_1681336), _1681338), hAPP(hAPP(c_List_Olist__update(_1681336, _1681340), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681334), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681336)), _1681338))), _1681342)))], (27311 ^ _782476) ^ [_1298857, _1298859, _1298861, _1298863, _1298865] : [class_Groups_Ocomm__monoid__mult(_1298857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298859), _1298861)), 27318 ^ _782476 : [(27325 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298859), _1298863), _1298861))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298859, _1298857), hAPP(hAPP(c_COMBC(_1298859, _1298857, _1298857), hAPP(hAPP(c_COMBS(_1298859, _1298857, tc_fun(_1298857, _1298857)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298857, tc_fun(_1298857, _1298857)), _1298859), c_If(_1298857)), hAPP(hAPP(c_COMBC(_1298859, _1298859, tc_HOL_Obool), c_fequal), _1298863))), _1298865)), c_Groups_Oone__class_Oone(_1298857))), _1298861) = c_Groups_Oone__class_Oone(_1298857))], (27319 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298859), _1298863), _1298861)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298859, _1298857), hAPP(hAPP(c_COMBC(_1298859, _1298857, _1298857), hAPP(hAPP(c_COMBS(_1298859, _1298857, tc_fun(_1298857, _1298857)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298857, tc_fun(_1298857, _1298857)), _1298859), c_If(_1298857)), hAPP(hAPP(c_COMBC(_1298859, _1298859, tc_HOL_Obool), c_fequal), _1298863))), _1298865)), c_Groups_Oone__class_Oone(_1298857))), _1298861) = hAPP(_1298865, _1298863))]]], (10419 ^ _782476) ^ [_971883, _971885, _971887, _971889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971883, tc_HOL_Obool)), _971885), _971887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971883, tc_HOL_Obool)), _971885), hAPP(hAPP(c_Set_Oinsert(_971883), _971889), _971887))))], (50563 ^ _782476) ^ [_1804857, _1804859] : [c_Relation_Otrans(_1804857, hAPP(c_Relation_Oconverse(_1804857, _1804857), _1804859)), -(c_Relation_Otrans(_1804857, _1804859))], (14090 ^ _782476) ^ [_1044416, _1044418, _1044420, _1044422, _1044424] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044416, _1044418, hAPP(hAPP(c_Set_Oinsert(_1044416), _1044420), _1044422)), _1044424)), 14095 ^ _782476 : [(14100 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1044416), 14093 ^ [_1044416, _1044418, _1044420, _1044422, _1044424]), 14094 ^ [_1044416, _1044418, _1044420, _1044422, _1044424]))], (14098 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044416, _1044416, _1044418, 14093 ^ [_1044416, _1044418, _1044420, _1044422, _1044424], 14094 ^ [_1044416, _1044418, _1044420, _1044422, _1044424]), _1044424)))], (14096 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1044416), _1044420), _1044422) = hAPP(hAPP(c_Set_Oinsert(_1044416), 14093 ^ [_1044416, _1044418, _1044420, _1044422, _1044424]), 14094 ^ [_1044416, _1044418, _1044420, _1044422, _1044424]))]]], (10707 ^ _782476) ^ [_978450, _978452, _978454] : [class_Complete__Lattice_Ocomplete__lattice(_978450), -(c_Complete__Lattice_OSup__class_OSup(_978450, hAPP(hAPP(c_Set_Oinsert(_978450), _978452), _978454)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978450), _978452), c_Complete__Lattice_OSup__class_OSup(_978450, _978454)))], (39645 ^ _782476) ^ [_1548216, _1548218, _1548220, _1548222] : [39646 ^ _782476 : [(39647 ^ _782476) ^ [_1548291] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548216, _1548220)), hAPP(hAPP(c_Product__Type_OPair(_1548216, _1548220), _1548218), _1548291)), _1548222))]], -(hBOOL(hAPP(hAPP(c_member(_1548216), _1548218), hAPP(c_Relation_ODomain(_1548216, _1548220), _1548222))))], (39255 ^ _782476) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (5198 ^ _782476) ^ [_861911, _861913, _861915, _861917] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861917, _861913) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861915, _861911)), _861917 = _861915, _861913 = _861911], (37263 ^ _782476) ^ [_1491656, _1491658] : [_1491656 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1491658, _1491656) = 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), _1491658)))], (42273 ^ _782476) ^ [_1615084, _1615086, _1615088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1615084), _1615086)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615084, tc_HOL_Obool)), _1615088), _1615086) = hAPP(hAPP(c_Finite__Set_Ofold(_1615084, tc_fun(_1615084, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1615084, tc_HOL_Obool), tc_fun(tc_fun(_1615084, tc_HOL_Obool), tc_fun(_1615084, tc_HOL_Obool)), _1615084), hAPP(c_COMBC(tc_fun(_1615084, tc_HOL_Obool), tc_fun(_1615084, tc_HOL_Obool), tc_fun(_1615084, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1615084, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1615084, tc_fun(_1615084, tc_HOL_Obool), tc_fun(_1615084, tc_HOL_Obool)), c_Set_Oinsert(_1615084)), c_Orderings_Obot__class_Obot(tc_fun(_1615084, tc_HOL_Obool))))), _1615088), _1615086))], (46643 ^ _782476) ^ [_1718397, _1718399, _1718401, _1718403] : [46645 ^ _782476 : [(46648 ^ _782476) ^ [] : [hBOOL(hAPP(_1718401, hAPP(hAPP(c_List_Onth(_1718397), _1718399), 46644 ^ [_1718397, _1718399, _1718401, _1718403])))], (46646 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46644 ^ [_1718397, _1718399, _1718401, _1718403]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718397)), _1718399))))]], hBOOL(hAPP(hAPP(c_member(_1718397), _1718403), hAPP(c_List_Oset(_1718397), _1718399))), -(hBOOL(hAPP(_1718401, _1718403)))], (42818 ^ _782476) ^ [_1626598, _1626600, _1626602, _1626604] : [class_Rings_Olinordered__semidom(_1626598), 42824 ^ _782476 : [(42827 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626598), c_Groups_Ozero__class_Ozero(_1626598)), hAPP(_1626604, 42823 ^ [_1626598, _1626600, _1626602, _1626604])))], (42825 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626600), 42823 ^ [_1626598, _1626600, _1626602, _1626604]), _1626602)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626598), c_Groups_Ozero__class_Ozero(_1626598)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626600, _1626598), _1626604), _1626602))))], (42479 ^ _782476) ^ [_1619018, _1619020, _1619022, _1619024, _1619026] : [c_Finite__Set_Ofun__left__comm(_1619018, _1619020, _1619022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619018), _1619024)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619018, _1619020, _1619022, _1619026, _1619024), hAPP(hAPP(c_Finite__Set_Ofold(_1619018, _1619020, _1619022), _1619026), _1619024))))], (44254 ^ _782476) ^ [_1665337, _1665339, _1665341] : [-(hAPP(hAPP(c_List_Ozip(_1665337, _1665339), _1665341), c_List_Olist_ONil(_1665339)) = c_List_Olist_ONil(tc_prod(_1665337, _1665339)))], (46438 ^ _782476) ^ [_1713325, _1713327] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1713325), _1713327) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713325)), hAPP(c_Code__Numeral_Onat__of, _1713327))))], (52615 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (47093 ^ _782476) ^ [_1728182, _1728184, _1728186] : [c_List_Oconcat(_1728182, _1728184) = c_List_Oconcat(_1728182, _1728186), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728182))), _1728184) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728182))), _1728186), 47103 ^ _782476 : [(47106 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1728182), tc_List_Olist(_1728182), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728182), tc_fun(tc_List_Olist(_1728182), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728182), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1728182), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728182), tc_HOL_Obool)), tc_List_Olist(_1728182)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1728182))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1728182)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1728182))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1728182)))), 47102 ^ [_1728182, _1728184, _1728186]))], (47104 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728182), tc_List_Olist(_1728182))), 47102 ^ [_1728182, _1728184, _1728186]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1728182), tc_List_Olist(_1728182))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1728182), tc_List_Olist(_1728182)), _1728184), _1728186)))))]], -(_1728184 = _1728186)], (38933 ^ _782476) ^ [_1530800, _1530802, _1530804, _1530806, _1530808, _1530810] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530800, _1530802, _1530804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530800, _1530802), tc_HOL_Obool)), _1530806), _1530808)), _1530810) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530800, _1530804), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530800, _1530802, _1530804), _1530806), _1530810)), hAPP(hAPP(c_Relation_Orel__comp(_1530800, _1530802, _1530804), _1530808), _1530810)))], (41086 ^ _782476) ^ [_1586742, _1586744] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586742, _1586742), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1586742, _1586744)), c_Relation_OId(_1586742)) = c_Transitive__Closure_Ortrancl(_1586742, _1586744))], (34196 ^ _782476) ^ [_1430583, _1430585] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430583)))), 34199 ^ _782476 : [(34206 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430585)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430583), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430585)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430583), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430585))))], (34200 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430585))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430583), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430585)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430583))]]], (45254 ^ _782476) ^ [_1688279, _1688281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688279)), _1688281)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1688279), _1688281) = _1688281)], (9712 ^ _782476) ^ [_956634, _956636, _956638] : [class_Orderings_Oorder(_956634), 9715 ^ _782476 : [(9722 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956634), _956636), _956638))), -(c_Orderings_Obot__class_Obot(tc_fun(_956634, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956634, _956636, _956638))], (9716 ^ _782476) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_956634, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956634, _956636, _956638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956634), _956636), _956638))]]], (48363 ^ _782476) ^ [_1755407, _1755409, _1755411] : [-(c_List_OtakeWhile(_1755407, _1755409, _1755411) = hAPP(hAPP(c_List_Otake(_1755407), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755407)), c_List_OtakeWhile(_1755407, _1755409, _1755411))), _1755411))], (31053 ^ _782476) ^ [_1370461, _1370463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370461)), 31056 ^ _782476 : [(31063 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370463)), -(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), _1370463), _1370461))))], (31057 ^ _782476) ^ [] : [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), _1370463), _1370461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370463)))]]], (8178 ^ _782476) ^ [_922212, _922214, _922216, _922218] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922212, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922212, tc_fun(_922212, tc_HOL_Obool), tc_HOL_Obool), c_member(_922212)), _922214)), hAPP(hAPP(c_COMBC(_922212, tc_fun(_922212, tc_HOL_Obool), tc_HOL_Obool), c_member(_922212)), _922216)), _922218)), -(hBOOL(hAPP(hAPP(c_member(_922212), _922218), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922212, tc_HOL_Obool)), _922214), _922216))))], (48136 ^ _782476) ^ [_1750626, _1750628, _1750630] : [_1750628 = hAPP(c_List_Orev(_1750626), _1750630), -(hAPP(c_List_Orev(_1750626), _1750628) = _1750630)], (38567 ^ _782476) ^ [_1520976, _1520978, _1520980, _1520982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1520976), _1520978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1520980), _1520982)), -(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), _1520976), _1520980)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1520978), _1520982))), c_FunDef_Opair__less)))], (2940 ^ _782476) ^ [_826072, _826074, _826076, _826078] : [-(c_Nitpick_Oinverse__frac(_826078, _826074) = c_Nitpick_Oinverse__frac(_826076, _826072)), _826078 = _826076, _826074 = _826072], (35134 ^ _782476) ^ [_1446756, _1446758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446756), _1446758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446756)), c_Int_OBit0(_1446758))))], (19586 ^ _782476) ^ [_1150443, _1150445] : [19587 ^ _782476 : [(19590 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150445))], (19588 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150443))]], -(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), _1150443), _1150445))))], (38937 ^ _782476) ^ [_1530966, _1530968, _1530970, _1530972, _1530974, _1530976, _1530978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530966, _1530968), tc_HOL_Obool)), _1530970), _1530972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530968, _1530974), tc_HOL_Obool)), _1530976), _1530978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530966, _1530974), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530966, _1530968, _1530974), _1530970), _1530976)), hAPP(hAPP(c_Relation_Orel__comp(_1530966, _1530968, _1530974), _1530972), _1530978))))], (35200 ^ _782476) ^ [_1447881] : [c_Int_OBit0(_1447881) = c_Int_OPls, -(_1447881 = c_Int_OPls)], (40966 ^ _782476) ^ [_1582994] : [-(c_Transitive__Closure_Otrancl(_1582994, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582994, _1582994), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582994, _1582994), tc_HOL_Obool)))], (19360 ^ _782476) ^ [_1146760, _1146762] : [class_Groups_Olinordered__ab__group__add(_1146760), 19363 ^ _782476 : [(19370 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146760), c_Groups_Ozero__class_Ozero(_1146760)), _1146762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146760), hAPP(c_Groups_Ouminus__class_Ouminus(_1146760), _1146762)), _1146762)))], (19364 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146760), hAPP(c_Groups_Ouminus__class_Ouminus(_1146760), _1146762)), _1146762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146760), c_Groups_Ozero__class_Ozero(_1146760)), _1146762)))]]], (47309 ^ _782476) ^ [_1734534, _1734536, _1734538, _1734540, _1734542, _1734544] : [-(c_List_Ofoldr(_1734534, _1734536, _1734538, hAPP(hAPP(c_List_Olist_OCons(_1734534), _1734540), _1734542), _1734544) = hAPP(hAPP(_1734538, _1734540), c_List_Ofoldr(_1734534, _1734536, _1734538, _1734542, _1734544)))], (38957 ^ _782476) ^ [_1531506, _1531508, _1531510, _1531512] : [hAPP(hAPP(c_Relation_Orel__comp(_1531506, _1531506, _1531506), _1531508), _1531510) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531506, _1531506), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531506, _1531506, _1531506), _1531512), _1531510) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531506, _1531506), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531506, _1531506, _1531506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531506, _1531506), tc_HOL_Obool)), _1531508), _1531512)), _1531510) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531506, _1531506), tc_HOL_Obool)))], (22856 ^ _782476) ^ [_1211171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211171)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211171), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1211171)], (5930 ^ _782476) ^ [_876426, _876428, _876430, _876432] : [class_Orderings_Opreorder(_876426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876426), _876428), _876430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876426), _876430), _876432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876426), _876428), _876432)))], (1302 ^ _782476) ^ [_801951, _801953] : [-(class_Rings_Oordered__ring(_801951)), _801953 = _801951, class_Rings_Oordered__ring(_801953)], (246 ^ _782476) ^ [_786435, _786437] : [-(c_Nat__Transfer_Ois__nat(_786435)), _786437 = _786435, c_Nat__Transfer_Ois__nat(_786437)], (31141 ^ _782476) ^ [_1371839, _1371841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371839), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31144 ^ _782476 : [(31151 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371841), 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), _1371841), _1371839))))], (31145 ^ _782476) ^ [] : [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), _1371841), _1371839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371841), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (13778 ^ _782476) ^ [_1038076, _1038078, _1038080, _1038082, _1038084] : [c_Fun_Obij__betw(_1038076, _1038078, _1038080, _1038082, _1038084), -(c_Fun_Obij__betw(_1038078, _1038076, c_Fun_Othe__inv__into(_1038076, _1038078, _1038082, _1038080), _1038084, _1038082))], (7331 ^ _782476) ^ [_904842, _904844, _904846, _904848, _904850] : [hBOOL(hAPP(hAPP(c_member(_904842), _904844), c_SetInterval_Oord_OatLeastAtMost(_904842, _904846, _904848, _904850))), 7334 ^ _782476 : [(7337 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904846, _904844), _904850)))], (7335 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_904846, _904848), _904844)))]]], (16525 ^ _782476) ^ [_1093843, _1093845, _1093847, _1093849] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1093843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093843), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093843), _1093845), _1093847)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093843), _1093845), _1093849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093843), _1093847), _1093849)))], (15704 ^ _782476) ^ [_1076369, _1076371, _1076373] : [-(hAPP(c_Finite__Set_Ofold1(_1076369, _1076371), hAPP(hAPP(c_Set_Oinsert(_1076369), _1076373), c_Orderings_Obot__class_Obot(tc_fun(_1076369, tc_HOL_Obool)))) = _1076373)], (22818 ^ _782476) ^ [_1210488] : [class_Rings_Oring__1(_1210488), -(hBOOL(hAPP(hAPP(c_member(_1210488), c_Groups_Oone__class_Oone(_1210488)), c_Int_Oring__1__class_OInts(_1210488))))], (38469 ^ _782476) ^ [_1518781, _1518783] : [c_Equiv__Relations_Oequivp(_1518781, _1518783), 38472 ^ _782476 : [(38479 ^ _782476) ^ [_1518974, _1518976] : [hAPP(_1518783, _1518976) = hAPP(_1518783, _1518974), -(hBOOL(hAPP(hAPP(_1518783, _1518976), _1518974)))], (38473 ^ _782476) ^ [_1518875, _1518877] : [hBOOL(hAPP(hAPP(_1518783, _1518877), _1518875)), -(hAPP(_1518783, _1518877) = hAPP(_1518783, _1518875))]]], (36056 ^ _782476) ^ [_1463694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463694)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463694), c_Int_OMin)))], (36777 ^ _782476) ^ [_1482281, _1482283, _1482285, _1482287, _1482289, _1482291] : [36778 ^ _782476 : [(36781 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1482287, _1482283), _1482285))], (36779 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1482281, _1482283), _1482285))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482289, tc_fun(_1482291, tc_HOL_Obool))), _1482287), _1482281), _1482283), _1482285)))], (23791 ^ _782476) ^ [_1229000, _1229002, _1229004] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229000), _1229002), _1229004) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1229000), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1229000, tc_Int_Oint), _1229002), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1229004))), class_Groups_Ocomm__monoid__add(_1229000), class_Groups_Ocomm__monoid__mult(_1229000)], (35278 ^ _782476) ^ [_1449178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449178))))], (21167 ^ _782476) ^ [_1180057] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180057), _1180057)))], (26936 ^ _782476) ^ [_1291139, _1291141, _1291143, _1291145] : [class_Orderings_Olinorder(_1291139), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291139), _1291141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291139), _1291143), _1291145)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291139), _1291143), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291139), _1291141), _1291145)))], (48200 ^ _782476) ^ [_1751906, _1751908] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751906), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1751906))), c_List_Otranspose(_1751906, _1751908)))))], (43727 ^ _782476) ^ [_1653852, _1653854, _1653856] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1653852))), c_Enum_On__lists(_1653852, _1653854, _1653856)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653852)), _1653856)), _1653854))], (19424 ^ _782476) ^ [_1147844, _1147846] : [class_Groups_Olinordered__ab__group__add(_1147844), 19427 ^ _782476 : [(19434 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), c_Groups_Ozero__class_Ozero(_1147844)), _1147846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), hAPP(c_Groups_Ouminus__class_Ouminus(_1147844), _1147846)), _1147846)))], (19428 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), hAPP(c_Groups_Ouminus__class_Ouminus(_1147844), _1147846)), _1147846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), c_Groups_Ozero__class_Ozero(_1147844)), _1147846)))]]], (49094 ^ _782476) ^ [_1772091, _1772093, _1772095] : [-(c_List_Olist__ex(_1772091, _1772093, _1772095)), 49095 ^ _782476 : [(49096 ^ _782476) ^ [_1772148] : [hBOOL(hAPP(hAPP(c_member(_1772091), _1772148), hAPP(c_List_Oset(_1772091), _1772095))), hBOOL(hAPP(_1772093, _1772148))]]], (41965 ^ _782476) ^ [_1608901, _1608903, _1608905, _1608907] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608901, _1608901)), hAPP(hAPP(c_Product__Type_OPair(_1608901, _1608901), _1608903), _1608905)), c_Transitive__Closure_Otrancl(_1608901, _1608907))), 41969 ^ _782476 : [(41972 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608901, _1608901)), hAPP(hAPP(c_Product__Type_OPair(_1608901, _1608901), 41968 ^ [_1608901, _1608903, _1608905, _1608907]), _1608905)), c_Transitive__Closure_Ortrancl(_1608901, _1608907))))], (41970 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608901, _1608901)), hAPP(hAPP(c_Product__Type_OPair(_1608901, _1608901), _1608903), 41968 ^ [_1608901, _1608903, _1608905, _1608907])), _1608907)))]]], (19752 ^ _782476) ^ [_1153302, _1153304, _1153306] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1153302), _1153304)), 19755 ^ _782476 : [(19756 ^ _782476) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153302, tc_Nat_Onat), _1153306), _1153304) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19759 ^ _782476 : [(19760 ^ _782476) ^ [_1153464] : [hBOOL(hAPP(hAPP(c_member(_1153302), _1153464), _1153304)), -(hAPP(_1153306, _1153464) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19766 ^ _782476) ^ [] : [19768 ^ _782476 : [(19771 ^ _782476) ^ [] : [hAPP(_1153306, 19767 ^ [_1153302, _1153304, _1153306]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19769 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1153302), 19767 ^ [_1153302, _1153304, _1153306]), _1153304)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153302, tc_Nat_Onat), _1153306), _1153304) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (32517 ^ _782476) ^ [_1398195, _1398197, _1398199] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398195), _1398197)), 32523 ^ _782476 : [(32526 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1398199, 32522 ^ [_1398195, _1398197, _1398199])))], (32524 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398195), 32522 ^ [_1398195, _1398197, _1398199]), _1398197)))]], -(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(_1398195, tc_Nat_Onat), _1398199), _1398197))))], (49786 ^ _782476) ^ [_1787726, _1787728, _1787730, _1787732, _1787734] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787726, _1787728, _1787730), _1787732), _1787734)), -(hBOOL(hAPP(hAPP(_1787730, _1787734), _1787732)))], (51761 ^ _782476) ^ [_1831220, _1831222, _1831224, _1831226] : [class_Rings_Oidom(_1831220), 51764 ^ _782476 : [(51765 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831220), _1831222), _1831224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831220), _1831222), _1831226))), -(_1831222 = c_Groups_Ozero__class_Ozero(_1831220)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831220), _1831224), _1831226)))], (51775 ^ _782476) ^ [] : [51776 ^ _782476 : [(51779 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831220), _1831224), _1831226))], (51777 ^ _782476) ^ [] : [_1831222 = c_Groups_Ozero__class_Ozero(_1831220)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831220), _1831222), _1831224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831220), _1831222), _1831226))))]]], (50426 ^ _782476) ^ [_1801688, _1801690, _1801692, _1801694, _1801696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801688), tc_List_Olist(_1801688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801688), tc_List_Olist(_1801688)), _1801690), _1801692)), c_List_Olexord(_1801688, _1801694))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801688), tc_List_Olist(_1801688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801688), tc_List_Olist(_1801688)), _1801692), _1801696)), c_List_Olexord(_1801688, _1801694))), c_Relation_Otrans(_1801688, _1801694), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801688), tc_List_Olist(_1801688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801688), tc_List_Olist(_1801688)), _1801690), _1801696)), c_List_Olexord(_1801688, _1801694))))], (36142 ^ _782476) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (25602 ^ _782476) ^ [_1261217, _1261219, _1261221] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261217, tc_HOL_Obool)), _1261219), _1261221) = hAPP(c_Set_OCollect(_1261217), hAPP(hAPP(c_COMBS(_1261217, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261217), c_fconj), hAPP(hAPP(c_COMBC(_1261217, tc_fun(_1261217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261217)), _1261219))), hAPP(hAPP(c_COMBC(_1261217, tc_fun(_1261217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261217)), _1261221))))], (52411 ^ _782476) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (34672 ^ _782476) ^ [_1437984, _1437986] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437984), c_Int_OPls))), 34675 ^ _782476 : [(34682 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437986), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437984)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437986)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437984), _1437986)))], (34676 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437986), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437984)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437986)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437984))]]], (36170 ^ _782476) ^ [_1465449] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1465449), hAPP(c_Int_Onumber__class_Onumber__of(_1465449), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1465449)), class_Int_Onumber__ring(_1465449), class_Rings_Olinordered__idom(_1465449)], (23526 ^ _782476) ^ [_1224740, _1224742, _1224744, _1224746] : [23527 ^ _782476 : [(23530 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224744), _1224746)))], (23528 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224740), _1224742)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1224740, _1224744)), c_Sum__Type_OPlus(_1224740, _1224744, _1224742, _1224746)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37856 ^ _782476) ^ [_1503216, _1503218, _1503220] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1503216, _1503218), _1503220))), _1503216 = 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), _1503220)), _1503218)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503220)), 37863 ^ _782476 : [(37866 ^ _782476) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1503220) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37864 ^ _782476) ^ [] : [-(_1503218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 37867 ^ _782476 : [(37870 ^ _782476) ^ [] : [37871 ^ _782476 : [(37874 ^ _782476) ^ [] : [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), _1503220))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503220)), _1503218))], (37872 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503218)))]], 37879 ^ _782476 : [(37882 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1503218), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503220))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503220)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37880 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503218))]]], (37868 ^ _782476) ^ [] : [_1503218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (39330 ^ _782476) ^ [_1540404, _1540406, _1540408] : [c_Wellfounded_Owf(_1540404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540404, _1540404), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540404, _1540404), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540404, _1540404, _1540404), _1540406), _1540406)), hAPP(hAPP(c_Relation_Orel__comp(_1540404, _1540404, _1540404), _1540408), _1540406))), _1540408)), -(c_Wellfounded_Owf(_1540404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540404, _1540404), tc_HOL_Obool)), _1540406), _1540408)))], (1262 ^ _782476) ^ [_801451, _801453] : [-(class_Rings_Oordered__ring__abs(_801451)), _801453 = _801451, class_Rings_Oordered__ring__abs(_801453)], (6167 ^ _782476) ^ [_880362, _880364, _880366] : [class_Orderings_Olinorder(_880362), 6170 ^ _782476 : [(6177 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880362), _880366), _880364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880362, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880362), _880364)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880362), _880366))))], (6171 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880362, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880362), _880364)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880362), _880366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880362), _880366), _880364)))]]], (15610 ^ _782476) ^ [_1074368, _1074370, _1074372, _1074374, _1074376] : [c_Finite__Set_Ofolding__one__idem(_1074368, _1074370, _1074372), hAPP(_1074374, hAPP(hAPP(_1074370, 15615 ^ [_1074368, _1074370, _1074372, _1074374, _1074376]), 15616 ^ [_1074368, _1074370, _1074372, _1074374, _1074376])) = hAPP(hAPP(_1074370, hAPP(_1074374, 15615 ^ [_1074368, _1074370, _1074372, _1074374, _1074376])), hAPP(_1074374, 15616 ^ [_1074368, _1074370, _1074372, _1074374, _1074376])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074368), _1074376)), -(_1074376 = c_Orderings_Obot__class_Obot(tc_fun(_1074368, tc_HOL_Obool))), -(hAPP(_1074374, hAPP(_1074372, _1074376)) = hAPP(_1074372, hAPP(c_Set_Oimage(_1074368, _1074368, _1074374), _1074376)))], (3840 ^ _782476) ^ [_840128, _840130] : [_840130 = _840128, -(c_New__DSequence_Opos__not__seq(_840130) = c_New__DSequence_Opos__not__seq(_840128))], (2428 ^ _782476) ^ [_818066, _818068, _818070, _818072] : [-(c_Divides_Odivmod__int(_818072, _818068) = c_Divides_Odivmod__int(_818070, _818066)), _818072 = _818070, _818068 = _818066], (47473 ^ _782476) ^ [_1737783, _1737785] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1737783, _1737785)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1737783), hAPP(c_Nat_OSuc, _1737785)))], (22316 ^ _782476) ^ [_1201484] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1201484))], (20449 ^ _782476) ^ [_1167224, _1167226] : [_1167224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167224), _1167226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29566 ^ _782476) ^ [_1343492, _1343494, _1343496] : [class_Rings_Oring__1(_1343492), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1343492), hAPP(c_Groups_Ouminus__class_Ouminus(_1343492), _1343494)), _1343496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343492), hAPP(hAPP(c_Power_Opower__class_Opower(_1343492), hAPP(c_Groups_Ouminus__class_Ouminus(_1343492), c_Groups_Oone__class_Oone(_1343492))), _1343496)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343492), _1343494), _1343496)))], (40873 ^ _782476) ^ [_1581231, _1581233] : [_1581231 = _1581233, -(c_Random_Oinc__shift(_1581231, _1581233) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (41947 ^ _782476) ^ [_1608329, _1608331, _1608333, _1608335, _1608337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608329, _1608329)), hAPP(hAPP(c_Product__Type_OPair(_1608329, _1608329), _1608331), _1608333)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608329, _1608329), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608335)), _1608337))), 41951 ^ _782476 : [(41954 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608329, _1608329)), hAPP(hAPP(c_Product__Type_OPair(_1608329, _1608329), 41950 ^ [_1608329, _1608331, _1608333, _1608335, _1608337]), _1608333)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608329, _1608329), tc_HOL_Obool), _1608335), _1608337))))], (41952 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608329, _1608329)), hAPP(hAPP(c_Product__Type_OPair(_1608329, _1608329), _1608331), 41950 ^ [_1608329, _1608331, _1608333, _1608335, _1608337])), _1608337)))]]], (6279 ^ _782476) ^ [_882491, _882493, _882495] : [class_Orderings_Olinorder(_882491), 6282 ^ _782476 : [(6289 ^ _782476) ^ [] : [_882493 = _882495, -(hAPP(c_SetInterval_Oord__class_OlessThan(_882491), _882493) = hAPP(c_SetInterval_Oord__class_OlessThan(_882491), _882495))], (6283 ^ _782476) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_882491), _882493) = hAPP(c_SetInterval_Oord__class_OlessThan(_882491), _882495), -(_882493 = _882495)]]], (35320 ^ _782476) ^ [_1449921, _1449923] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1449921)), c_Int_OBit1(_1449923)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449921), _1449923)))], (5446 ^ _782476) ^ [_865835, _865837] : [_865837 = _865835, -(c_Orderings_Oord__class_Oless(_865837) = c_Orderings_Oord__class_Oless(_865835))], (36260 ^ _782476) ^ [_1466752] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1466752)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466752)))], (12352 ^ _782476) ^ [_1006830, _1006832, _1006834, _1006836] : [class_Orderings_Olinorder(_1006830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006830), _1006832), _1006834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006830), _1006834), _1006836)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006830, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1006830, _1006832, _1006834)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1006830, _1006834, _1006836)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1006830, _1006832, _1006836))], (21133 ^ _782476) ^ [_1179568, _1179570, _1179572] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179568), _1179570)), _1179572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179570), _1179572)))], (9849 ^ _782476) ^ [_959586, _959588, _959590, _959592, _959594] : [-(_959586 = c_Orderings_Obot__class_Obot(tc_fun(_959588, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959588, tc_fun(_959590, tc_HOL_Obool)), _959586), hAPP(hAPP(c_COMBC(_959588, tc_fun(_959590, tc_HOL_Obool), tc_fun(_959590, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959590, tc_HOL_Obool), tc_fun(tc_fun(_959590, tc_HOL_Obool), tc_fun(_959590, tc_HOL_Obool)), _959588), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959590, tc_HOL_Obool))), _959592)), _959594)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959590, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959588, tc_fun(_959590, tc_HOL_Obool)), _959586), _959592)), _959594))], (5478 ^ _782476) ^ [_866311, _866313] : [_866313 = _866311, -(c_Groups_Oplus__class_Oplus(_866313) = c_Groups_Oplus__class_Oplus(_866311))], (24698 ^ _782476) ^ [_1244151, _1244153] : [class_Rings_Oring__1(_1244151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244153)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244151), hAPP(c_Int_Onat, _1244153)) = hAPP(c_Int_Oring__1__class_Oof__int(_1244151), _1244153))], (50262 ^ _782476) ^ [_1797670, _1797672, _1797674] : [-(c_FunDef_OTHE__default(_1797672, _1797674, _1797670) = c_HOL_OThe(_1797672, _1797670)), 50263 ^ _782476 : [(50264 ^ _782476) ^ [_1797734] : [hBOOL(hAPP(_1797670, _1797734)), 50268 ^ _782476 : [(50271 ^ _782476) ^ [] : [50267 ^ [_1797670, _1797672, _1797674, _1797734] = _1797734], (50269 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1797670, 50267 ^ [_1797670, _1797672, _1797674, _1797734])))]]]]], (26828 ^ _782476) ^ [_1288989, _1288991, _1288993, _1288995] : [class_Orderings_Olinorder(_1288989), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288989), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288989), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288989), _1288991), _1288993)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288989), _1288991), _1288995))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288989), _1288991), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288989), _1288993), _1288995)))))], (44344 ^ _782476) ^ [_1666871] : [-(hAPP(c_List_Oset(_1666871), c_List_Olist_ONil(_1666871)) = c_Orderings_Obot__class_Obot(tc_fun(_1666871, tc_HOL_Obool)))], (36202 ^ _782476) ^ [_1465975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1465975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1465975)))], (24196 ^ _782476) ^ [_1235798, _1235800] : [c_Nat__Transfer_Onat__set(_1235798), c_Nat__Transfer_Onat__set(_1235800), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1235798), _1235800) = 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), _1235798)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1235800))))], (14286 ^ _782476) ^ [_1048592] : [class_Finite__Set_Ofinite(_1048592), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048592), c_Orderings_Otop__class_Otop(tc_fun(_1048592, tc_HOL_Obool)))))], (41481 ^ _782476) ^ [_1596345, _1596347] : [-(hAPP(c_Relation_OField(_1596345), hAPP(c_Relation_Oconverse(_1596345, _1596345), _1596347)) = hAPP(c_Relation_OField(_1596345), _1596347))], (35574 ^ _782476) ^ [_1454585] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1454585), _1454585)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1454585)], (36480 ^ _782476) ^ [_1475213, _1475215, _1475217, _1475219, _1475221] : [hBOOL(hAPP(hAPP(c_member(_1475213), _1475215), hAPP(c_Relation_OImage(_1475217, _1475213, _1475219), _1475221))), 36484 ^ _782476 : [(36487 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475217, _1475213)), hAPP(hAPP(c_Product__Type_OPair(_1475217, _1475213), 36483 ^ [_1475213, _1475215, _1475217, _1475219, _1475221]), _1475215)), _1475219)))], (36485 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475217), 36483 ^ [_1475213, _1475215, _1475217, _1475219, _1475221]), _1475221)))]]], (43960 ^ _782476) ^ [_1659225, _1659227, _1659229, _1659231] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659225), tc_List_Olist(_1659225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659225), tc_List_Olist(_1659225)), _1659227), _1659229)), c_List_Olistrel1(_1659225, _1659231)))), 43961 ^ _782476 : [(43962 ^ _782476) ^ [_1659358, _1659360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1659225, _1659225)), hAPP(hAPP(c_Product__Type_OPair(_1659225, _1659225), hAPP(hAPP(c_List_Onth(_1659225), _1659227), _1659358)), _1659360)), _1659231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659358), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659225)), _1659227))), _1659229 = hAPP(hAPP(c_List_Olist__update(_1659225, _1659227), _1659358), _1659360)]]], (17650 ^ _782476) ^ [_1117094, _1117096, _1117098] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117094), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117096), _1117098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117094), _1117096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117094), _1117098)))], (32640 ^ _782476) ^ [_1400542, _1400544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1400542), _1400544)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400544, _1400542) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400544), _1400542), _1400542))], (15971 ^ _782476) ^ [_1081622, _1081624] : [class_Groups_Oone(_1081622), 15974 ^ _782476 : [(15981 ^ _782476) ^ [] : [_1081624 = c_Groups_Oone__class_Oone(_1081622), -(c_Groups_Oone__class_Oone(_1081622) = _1081624)], (15975 ^ _782476) ^ [] : [c_Groups_Oone__class_Oone(_1081622) = _1081624, -(_1081624 = c_Groups_Oone__class_Oone(_1081622))]]], (5346 ^ _782476) ^ [_864219, _864221, _864223, _864225, _864227, _864229] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_864229, _864225, _864221) = c_Lazy__Sequence_Olazy__sequence_OInsert(_864227, _864223, _864219)), _864229 = _864227, _864225 = _864223, _864221 = _864219], (14136 ^ _782476) ^ [_1045704, _1045706, _1045708, _1045710] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045704), _1045706)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045708), hAPP(c_Set_Oimage(_1045704, _1045708, _1045710), _1045706))))], (47277 ^ _782476) ^ [_1732991, _1732993] : [-(c_List_Oconcat(tc_List_Olist(_1732991), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732991), tc_List_Olist(tc_List_Olist(_1732991))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1732991)), _1732991, c_List_Olist_ONil(tc_List_Olist(_1732991)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1732991), tc_List_Olist(tc_List_Olist(_1732991))), _1732991), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732991), tc_List_Olist(tc_List_Olist(_1732991)), tc_List_Olist(tc_List_Olist(_1732991))), c_List_Olist_OCons(tc_List_Olist(_1732991))), c_List_Olist_ONil(tc_List_Olist(_1732991)))))), _1732993)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732991), tc_List_Olist(_1732991)), c_List_Otl(_1732991)), hAPP(c_List_Ofilter(tc_List_Olist(_1732991), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1732991)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732991), tc_List_Olist(_1732991), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1732991)))), _1732993)))], (46428 ^ _782476) ^ [_1713148] : [-(c_Code__Numeral_OSuc__code__numeral(_1713148) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1713148))))], (49589 ^ _782476) ^ [_1782853, _1782855, _1782857, _1782859, _1782861, _1782863] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782853, _1782855, _1782857, _1782859), _1782861) = hAPP(c_Hilbert__Choice_Oinv__into(_1782853, _1782855, _1782857, _1782859), _1782863), hBOOL(hAPP(hAPP(c_member(_1782855), _1782861), hAPP(c_Set_Oimage(_1782853, _1782855, _1782859), _1782857))), hBOOL(hAPP(hAPP(c_member(_1782855), _1782863), hAPP(c_Set_Oimage(_1782853, _1782855, _1782859), _1782857))), -(_1782861 = _1782863)], (21466 ^ _782476) ^ [_1185333] : [hBOOL(hAPP(_1185333, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21467 ^ [_1185333]))), 21470 ^ _782476 : [(21471 ^ _782476) ^ [_1185433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185433)), -(hBOOL(hAPP(_1185333, _1185433)))]]], (46056 ^ _782476) ^ [_1704844, _1704846, _1704848, _1704850, _1704852, _1704854] : [-(hAPP(hAPP(c_List_Ozip(_1704844, _1704846), hAPP(hAPP(c_List_Omap(_1704848, _1704844), _1704850), _1704852)), _1704854) = hAPP(hAPP(c_List_Omap(tc_prod(_1704848, _1704846), tc_prod(_1704844, _1704846)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704848, _1704846, tc_prod(_1704844, _1704846)), hAPP(hAPP(c_COMBB(_1704844, tc_fun(_1704846, tc_prod(_1704844, _1704846)), _1704848), c_Product__Type_OPair(_1704844, _1704846)), _1704850))), hAPP(hAPP(c_List_Ozip(_1704848, _1704846), _1704852), _1704854)))], (44496 ^ _782476) ^ [_1669765, _1669767, _1669769] : [-(_1669765 = c_List_Olist_ONil(_1669767)), -(hBOOL(hAPP(hAPP(c_member(_1669767), hAPP(c_Product__Type_Ofst(_1669767, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1669767, _1669765), _1669769))), hAPP(c_List_Oset(_1669767), _1669765))))], (37692 ^ _782476) ^ [_1499829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1499829)), 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), _1499829)) = 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), _1499829))))))], (47222 ^ _782476) ^ [_1731533, _1731535, _1731537] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1731533), tc_List_Olist(_1731533)), c_List_Opartition(_1731533, _1731535, _1731537)) = hAPP(c_List_Ofilter(_1731533, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731533, c_fNot), _1731535)), _1731537))], (48492 ^ _782476) ^ [_1758156, _1758158, _1758160, _1758162] : [-(hBOOL(hAPP(_1758156, _1758158))), -(c_List_OdropWhile(_1758160, _1758156, hAPP(hAPP(c_List_Olist_OCons(_1758160), _1758158), _1758162)) = hAPP(hAPP(c_List_Olist_OCons(_1758160), _1758158), _1758162))], (22192 ^ _782476) ^ [_1199305, _1199307] : [22193 ^ _782476 : [(22196 ^ _782476) ^ [] : [_1199305 = hAPP(c_Nat_OSuc, _1199307)], (22194 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199305), _1199307))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199305), hAPP(c_Nat_OSuc, _1199307))))], (3022 ^ _782476) ^ [_827301, _827303, _827305, _827307] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827307, _827303) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827305, _827301)), _827307 = _827305, _827303 = _827301], (51384 ^ _782476) ^ [_1822100, _1822102, _1822104, _1822106, _1822108, _1822110] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1822100, _1822102, _1822104, _1822106), _1822108), _1822110) = hAPP(_1822106, hAPP(hAPP(c_Product__Type_OPair(_1822100, _1822102), _1822108), _1822110)))], (17978 ^ _782476) ^ [_1123332, _1123334] : [class_Rings_Olinordered__semidom(_1123332), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123332), c_Groups_Ozero__class_Ozero(_1123332)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123332), _1123334))))], (39110 ^ _782476) ^ [_1536223, _1536225, _1536227, _1536229] : [c_Wellfounded_Omax__extp(_1536223, _1536225, _1536227, _1536229), 39113 ^ _782476 : [(39116 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536223), _1536229)))], (39118 ^ _782476) ^ [] : [_1536229 = c_Orderings_Obot__class_Obot(tc_fun(_1536223, tc_HOL_Obool))], (39120 ^ _782476) ^ [_1536439] : [hBOOL(hAPP(hAPP(c_member(_1536223), _1536439), _1536227)), 39124 ^ _782476 : [(39127 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1536225, _1536439), 39123 ^ [_1536223, _1536225, _1536227, _1536229, _1536439])))], (39125 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536223), 39123 ^ [_1536223, _1536225, _1536227, _1536229, _1536439]), _1536229)))]]], (39114 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536223), _1536227)))]]], (27018 ^ _782476) ^ [_1293114, _1293116, _1293118] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293114, tc_Nat_Onat), _1293116), _1293118)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293114, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1293114), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1293116)), _1293118))], (25237 ^ _782476) ^ [_1254344, _1254346] : [class_Groups_Oordered__ab__group__add__abs(_1254344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254344), _1254346), c_Groups_Ozero__class_Ozero(_1254344))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254344), _1254346) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254344), _1254346))], (46124 ^ _782476) ^ [_1706756, _1706758, _1706760, _1706762] : [class_Groups_Oab__group__add(_1706756), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1706756), hAPP(c_List_Omonoid__add__class_Olistsum(_1706756), hAPP(hAPP(c_List_Omap(_1706758, _1706756), _1706760), _1706762))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1706756), hAPP(hAPP(c_List_Omap(_1706758, _1706756), hAPP(c_Fun_Ocomp(_1706756, _1706756, _1706758, c_Groups_Ouminus__class_Ouminus(_1706756)), _1706760)), _1706762)))], (17928 ^ _782476) ^ [_1122544, _1122546] : [class_Rings_Olinordered__semidom(_1122544), 17931 ^ _782476 : [(17938 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122544), c_Groups_Ozero__class_Ozero(_1122544)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122544), _1122546))))], (17932 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122544), c_Groups_Ozero__class_Ozero(_1122544)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122544), _1122546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122546)))]]], (21565 ^ _782476) ^ [_1187226, _1187228, _1187230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187226)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187228), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1187230)), 21572 ^ _782476 : [(21573 ^ _782476) ^ [_1187434] : [21575 ^ _782476 : [(21581 ^ _782476) ^ [] : [-(_1187434 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21577 ^ [_1187226, _1187228, _1187230, _1187434]), 21574 ^ [_1187226, _1187228, _1187230, _1187434]))], (21579 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21577 ^ [_1187226, _1187228, _1187230, _1187434]), _1187230)))], (21576 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21574 ^ [_1187226, _1187228, _1187230, _1187434]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1187226))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187228), _1187434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187434), _1187226))))]]], (10577 ^ _782476) ^ [_975699, _975701, _975703, _975705] : [-(hBOOL(hAPP(hAPP(c_member(_975699), _975701), _975703))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975699, tc_HOL_Obool)), _975703), hAPP(hAPP(c_Set_Oinsert(_975699), _975701), _975705)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975699, tc_HOL_Obool)), _975703), _975705))], (18442 ^ _782476) ^ [] : [-(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))))], (21981 ^ _782476) ^ [_1195998] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1195998))))], (39903 ^ _782476) ^ [_1555987, _1555989, _1555991, _1555993] : [-(hAPP(c_Set_OCollect(tc_prod(_1555987, _1555989)), hAPP(c_Product__Type_Oprod_Oprod__case(_1555987, _1555989, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1555987, tc_fun(_1555989, tc_HOL_Obool), tc_fun(_1555989, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555989, tc_HOL_Obool), tc_fun(_1555989, tc_HOL_Obool)), _1555987), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555989)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555987), c_fconj), _1555991))), _1555993))) = hAPP(hAPP(c_Product__Type_OSigma(_1555987, _1555989), hAPP(c_Set_OCollect(_1555987), _1555991)), hAPP(hAPP(c_COMBB(tc_fun(_1555989, tc_HOL_Obool), tc_fun(_1555989, tc_HOL_Obool), _1555987), c_Set_OCollect(_1555989)), _1555993)))], (19849 ^ _782476) ^ [_1155052, _1155054, _1155056] : [class_Groups_Oordered__comm__monoid__add(_1155052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155052), _1155054), c_Groups_Ozero__class_Ozero(_1155052))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155052), _1155056), c_Groups_Ozero__class_Ozero(_1155052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155052), _1155054), _1155056)), c_Groups_Ozero__class_Ozero(_1155052))))], (39495 ^ _782476) ^ [_1544356, _1544358] : [-(hAPP(c_Relation_ORange(_1544356, _1544356), c_Relation_OId__on(_1544356, _1544358)) = _1544358)], (10733 ^ _782476) ^ [_979027, _979029, _979031] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_979027, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979027, tc_HOL_Obool)), _979029), _979031)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979027, tc_HOL_Obool)), _979029), c_Complete__Lattice_OSup__class_OSup(tc_fun(_979027, tc_HOL_Obool), _979031)))], (46880 ^ _782476) ^ [_1723751, _1723753] : [c_List_Oremdups(_1723751, _1723753) = c_List_Olist_ONil(_1723751), -(_1723753 = c_List_Olist_ONil(_1723751))], (37227 ^ _782476) ^ [_1491083, _1491085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491083), _1491085)), -(c_Divides_Odivmod__nat(_1491083, _1491085) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491083))], (49689 ^ _782476) ^ [_1785254, _1785256, _1785258] : [hAPP(c_Set_Oimage(_1785254, _1785256, _1785258), c_Orderings_Otop__class_Otop(tc_fun(_1785254, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785256, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1785254, _1785256, _1785256, _1785258), c_Hilbert__Choice_Oinv__into(_1785254, _1785256, c_Orderings_Otop__class_Otop(tc_fun(_1785254, tc_HOL_Obool)), _1785258)) = c_Fun_Oid(_1785256))], (48745 ^ _782476) ^ [_1763317, _1763319, _1763321, _1763323] : [-(c_List_Oconcat(_1763317, hAPP(hAPP(c_List_Omap(_1763319, tc_List_Olist(_1763317)), _1763321), _1763323)) = c_List_Omaps(_1763319, _1763317, _1763321, _1763323))], (40047 ^ _782476) ^ [_1560982, _1560984, _1560986, _1560988] : [class_Groups_Ocomm__monoid__add(_1560982), c_Fun_Oinj__on(_1560984, _1560982, _1560986, _1560988), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560984, _1560982), _1560986), _1560988) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560982, _1560982), c_Fun_Oid(_1560982)), hAPP(c_Set_Oimage(_1560984, _1560982, _1560986), _1560988)))], (24438 ^ _782476) ^ [_1239521, _1239523, _1239525, _1239527, _1239529, _1239531] : [class_Groups_Oordered__ab__group__add(_1239521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1239523), _1239525)), 24448 ^ _782476 : [(24451 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239521), c_Groups_Ozero__class_Ozero(_1239521)), hAPP(_1239527, 24447 ^ [_1239521, _1239523, _1239525, _1239527, _1239529, _1239531])))], (24449 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1239523), 24447 ^ [_1239521, _1239523, _1239525, _1239527, _1239529, _1239531]), _1239525)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1239523, _1239521), _1239527), _1239525) = _1239529, hBOOL(hAPP(hAPP(c_member(_1239523), _1239531), _1239525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239521), hAPP(_1239527, _1239531)), _1239529)))], (47678 ^ _782476) ^ [_1741567, _1741569, _1741571] : [class_Orderings_Olinorder(_1741567), c_List_Olinorder__class_Osorted(_1741567, _1741569), -(c_List_Olinorder__class_Osorted(_1741567, c_List_Olinorder__class_Oinsort__insert__key(_1741567, _1741567, c_COMBI(_1741567), _1741571, _1741569)))], (34662 ^ _782476) ^ [] : [-(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))))))], (34024 ^ _782476) ^ [_1427524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427524), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427524)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12524 ^ _782476) ^ [_1011386, _1011388, _1011390, _1011392, _1011394, _1011396, _1011398] : [hBOOL(hAPP(hAPP(c_member(_1011386), _1011388), _1011390)), c_Nitpick_Ofold__graph_H(_1011386, _1011392, _1011394, _1011396, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011386, tc_HOL_Obool)), _1011390), hAPP(hAPP(c_Set_Oinsert(_1011386), _1011388), c_Orderings_Obot__class_Obot(tc_fun(_1011386, tc_HOL_Obool)))), _1011398), -(c_Nitpick_Ofold__graph_H(_1011386, _1011392, _1011394, _1011396, _1011390, hAPP(hAPP(_1011394, _1011388), _1011398)))], (27669 ^ _782476) ^ [_1305824, _1305826, _1305828] : [class_Orderings_Olinorder(_1305824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305824), _1305826)), -(_1305826 = c_Orderings_Obot__class_Obot(tc_fun(_1305824, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1305824, hAPP(hAPP(c_Set_Oinsert(_1305824), _1305828), _1305826)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305824), _1305828), c_Big__Operators_Olinorder__class_OMax(_1305824, _1305826)))], (34286 ^ _782476) ^ [_1431989] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1431989), c_Int_OPls) = _1431989)], (50357 ^ _782476) ^ [_1799867, _1799869, _1799871] : [c_List_Olist__ex(tc_Int_Oint, _1799867, c_List_Oupto(_1799869, _1799871)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799867), _1799869, _1799871)], (35332 ^ _782476) ^ [_1450191] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450191)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450191))))], (28802 ^ _782476) ^ [_1329703, _1329705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329703)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329703)), _1329705) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329703), _1329705)))], (43489 ^ _782476) ^ [_1646643, _1646645, _1646647, _1646649] : [hBOOL(hAPP(hAPP(c_member(_1646643), _1646645), hAPP(c_List_Oset(_1646643), c_List_Osublist(_1646643, _1646647, _1646649)))), -(hBOOL(hAPP(hAPP(c_member(_1646643), _1646645), hAPP(c_List_Oset(_1646643), _1646647))))], (14567 ^ _782476) ^ [_1053815, _1053817, _1053819, _1053821, _1053823] : [c_Finite__Set_Ofolding__one(_1053815, _1053817, _1053819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053815), _1053821)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053815), _1053823)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053815, tc_HOL_Obool)), _1053821), _1053823) = c_Orderings_Obot__class_Obot(tc_fun(_1053815, tc_HOL_Obool))), -(hAPP(hAPP(_1053817, hAPP(_1053819, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1053815, tc_HOL_Obool)), _1053821), _1053823))), hAPP(_1053819, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053815, tc_HOL_Obool)), _1053821), _1053823))) = hAPP(hAPP(_1053817, hAPP(_1053819, _1053821)), hAPP(_1053819, _1053823)))], (41156 ^ _782476) ^ [_1588436, _1588438, _1588440] : [-(c_Transitive__Closure_Ortrancl(_1588436, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588436, _1588436), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588436, _1588438)), c_Transitive__Closure_Ortrancl(_1588436, _1588440))) = c_Transitive__Closure_Ortrancl(_1588436, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588436, _1588436), tc_HOL_Obool)), _1588438), _1588440)))], (50026 ^ _782476) ^ [_1792552, _1792554, _1792556, _1792558] : [-(hAPP(hAPP(c_List_Omap(_1792552, _1792554), hAPP(c_COMBK(_1792554, _1792552), _1792556)), _1792558) = c_List_Oreplicate(_1792554, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792552)), _1792558), _1792556))], (40388 ^ _782476) ^ [_1569533, _1569535] : [c_Wellfounded_OwfP(_1569533, _1569535), -(c_Wellfounded_Oacyclic(_1569533, hAPP(c_Set_OCollect(tc_prod(_1569533, _1569533)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569533, _1569533, tc_HOL_Obool), _1569535))))], (23033 ^ _782476) ^ [_1214520, _1214522, _1214524] : [class_Groups_Ocomm__monoid__add(_1214520), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214520), _1214522), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214524))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214520), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214520), _1214522), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214524))), hAPP(_1214522, _1214524)))], (47052 ^ _782476) ^ [_1727008, _1727010] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727008)), c_List_Oconcat(_1727008, _1727010)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727008), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1727008))), _1727010)))], (34796 ^ _782476) ^ [_1440027, _1440029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1440027)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1440029)), _1440027) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1440029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1440027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (26978 ^ _782476) ^ [_1292172, _1292174, _1292176, _1292178] : [class_Orderings_Olinorder(_1292172), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292172), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292172), _1292174), _1292176)), _1292178) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292172), _1292174), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292172), _1292176), _1292178)))], (18794 ^ _782476) ^ [_1136487, _1136489, _1136491] : [class_Rings_Oordered__cancel__semiring(_1136487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136487), _1136489), c_Groups_Ozero__class_Ozero(_1136487))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136487), c_Groups_Ozero__class_Ozero(_1136487)), _1136491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136487), _1136489), _1136491)), c_Groups_Ozero__class_Ozero(_1136487))))], (21589 ^ _782476) ^ [_1187710, _1187712, _1187714, _1187716, _1187718] : [class_Groups_Oordered__comm__monoid__add(_1187710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187712), _1187714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187712, tc_HOL_Obool)), _1187716), _1187714)), 21603 ^ _782476 : [(21606 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187710), c_Groups_Ozero__class_Ozero(_1187710)), hAPP(_1187718, 21602 ^ [_1187710, _1187712, _1187714, _1187716, _1187718])))], (21604 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187712), 21602 ^ [_1187710, _1187712, _1187714, _1187716, _1187718]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1187712, tc_HOL_Obool)), _1187714), _1187716))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187710), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187712, _1187710), _1187718), _1187716)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187712, _1187710), _1187718), _1187714))))], (34488 ^ _782476) ^ [_1435101, _1435103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435101)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435103))), 34491 ^ _782476 : [(34492 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435101), _1435103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435103)))], (34498 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435101), _1435103)))]]], (23107 ^ _782476) ^ [_1216263, _1216265, _1216267] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216263), _1216265)), -(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(_1216263), _1216267)), hAPP(c_Finite__Set_Ocard(_1216263), _1216265))), hAPP(c_Finite__Set_Ocard(_1216263), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216263, tc_HOL_Obool)), _1216267), _1216265)))))], (1292 ^ _782476) ^ [_801826, _801828] : [-(class_Groups_Oab__group__add(_801826)), _801828 = _801826, class_Groups_Oab__group__add(_801828)], (20329 ^ _782476) ^ [_1164567, _1164569, _1164571, _1164573, _1164575, _1164577] : [class_Rings_Olinordered__semiring__1(_1164567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164567), _1164569), _1164571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164567), _1164573), _1164571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164567), c_Groups_Ozero__class_Ozero(_1164567)), _1164575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164567), c_Groups_Ozero__class_Ozero(_1164567)), _1164577)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164567), _1164575), _1164577) = c_Groups_Oone__class_Oone(_1164567), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164567), _1164575), _1164569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164567), _1164577), _1164573))), _1164571)))], (47453 ^ _782476) ^ [_1737431, _1737433, _1737435, _1737437] : [-(c_List_Oupt(_1737431, _1737433) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737435), _1737437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737431), _1737433)), _1737431 = _1737435, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737431), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737433) = _1737437], (18154 ^ _782476) ^ [_1125980, _1125982, _1125984] : [class_Groups_Oab__group__add(_1125980), 18157 ^ _782476 : [(18164 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125980), _1125982), _1125984) = c_Groups_Ozero__class_Ozero(_1125980), -(_1125982 = _1125984)], (18158 ^ _782476) ^ [] : [_1125982 = _1125984, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125980), _1125982), _1125984) = c_Groups_Ozero__class_Ozero(_1125980))]]], (18276 ^ _782476) ^ [_1127708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1127708)), _1127708 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9124 ^ _782476) ^ [_944093, _944095, _944097, _944099] : [9126 ^ _782476 : [(9129 ^ _782476) ^ [] : [hAPP(_944099, 9125 ^ [_944093, _944095, _944097, _944099]) = c_Orderings_Otop__class_Otop(tc_fun(_944095, tc_HOL_Obool))], (9127 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944093), 9125 ^ [_944093, _944095, _944097, _944099]), _944097)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_944093, tc_fun(_944095, tc_HOL_Obool)), _944097), _944099) = c_Orderings_Otop__class_Otop(tc_fun(_944095, tc_HOL_Obool)))], (52291 ^ _782476) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (19144 ^ _782476) ^ [_1142871, _1142873, _1142875] : [class_Rings_Olinordered__semiring__strict(_1142871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142871), c_Groups_Ozero__class_Ozero(_1142871)), _1142873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142871), _1142875), c_Groups_Ozero__class_Ozero(_1142871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142871), _1142875), _1142873)), c_Groups_Ozero__class_Ozero(_1142871))))], (7622 ^ _782476) ^ [_910474, _910476, _910478, _910480, _910482, _910484, _910486] : [7624 ^ _782476 : [(7627 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_910478, 7623 ^ [_910474, _910476, _910478, _910480, _910482, _910484, _910486]), _910480), _910482))], (7625 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910474), 7623 ^ [_910474, _910476, _910478, _910480, _910482, _910484, _910486]), _910476)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_910474, tc_fun(_910484, tc_fun(_910486, tc_HOL_Obool))), _910476), _910478), _910480), _910482)))], (37171 ^ _782476) ^ [_1490021, _1490023] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490021))), 37174 ^ _782476 : [(37181 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490023))), -(c_Divides_Odivmod__int(_1490021, _1490023) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1490021), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1490023))))], (37175 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490023)), -(c_Divides_Odivmod__int(_1490021, _1490023) = c_Divides_OnegDivAlg(_1490021, _1490023))]]], (13268 ^ _782476) ^ [_1027435, _1027437, _1027439, _1027441] : [c_Fun_Oinj__on(_1027435, _1027437, _1027439, c_Orderings_Otop__class_Otop(tc_fun(_1027435, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1027435, _1027437, _1027439), hAPP(c_Set_Oimage(_1027435, _1027437, _1027439), _1027441)) = _1027441)], (13286 ^ _782476) ^ [_1027765, _1027767, _1027769, _1027771] : [-(hAPP(c_Set_Ovimage(_1027765, _1027767, _1027769), _1027771) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1027767, tc_fun(_1027765, tc_HOL_Obool)), _1027771), hAPP(hAPP(c_COMBB(tc_fun(_1027767, tc_HOL_Obool), tc_fun(_1027765, tc_HOL_Obool), _1027767), c_Set_Ovimage(_1027765, _1027767, _1027769)), hAPP(hAPP(c_COMBC(_1027767, tc_fun(_1027767, tc_HOL_Obool), tc_fun(_1027767, tc_HOL_Obool)), c_Set_Oinsert(_1027767)), c_Orderings_Obot__class_Obot(tc_fun(_1027767, tc_HOL_Obool))))))], (35926 ^ _782476) ^ [_1461139, _1461141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461139)), -(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)))), _1461141)), 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)))), _1461139)) = 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, _1461141, _1461139))))], (6066 ^ _782476) ^ [_878520, _878522, _878524] : [class_Orderings_Olinorder(_878520), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878520), _878522), _878524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878520), _878524), _878522)))], (9885 ^ _782476) ^ [_960401, _960403, _960405, _960407, _960409] : [-(_960401 = c_Orderings_Obot__class_Obot(tc_fun(_960403, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960405, tc_HOL_Obool)), _960407), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960403, tc_fun(_960405, tc_HOL_Obool)), _960401), _960409)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960403, tc_fun(_960405, tc_HOL_Obool)), _960401), hAPP(hAPP(c_COMBB(tc_fun(_960405, tc_HOL_Obool), tc_fun(_960405, tc_HOL_Obool), _960403), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960405, tc_HOL_Obool)), _960407)), _960409)))], (21285 ^ _782476) ^ [_1182134, _1182136, _1182138, _1182140, _1182142, _1182144] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182134), _1182136)), _1182138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182140), _1182142)), _1182144), 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), _1182140), _1182142)), _1182144)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182138), _1182134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182140), _1182134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182142), _1182136)))], (24261 ^ _782476) ^ [_1236928, _1236930] : [c_Nat__Transfer_Onat__set(_1236928), c_Nat__Transfer_Onat__set(_1236930), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1236928), _1236930)))], (49928 ^ _782476) ^ [_1790826, _1790828, _1790830, _1790832, _1790834] : [c_List_Oreplicate(_1790826, _1790828, _1790830) = c_List_Oreplicate(_1790826, _1790832, _1790834), 49931 ^ _782476 : [(49934 ^ _782476) ^ [] : [-(_1790828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1790830 = _1790834)], (49932 ^ _782476) ^ [] : [-(_1790828 = _1790832)]]], (42007 ^ _782476) ^ [_1609765, _1609767, _1609769, _1609771] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609765, _1609767, _1609769), _1609771), c_Orderings_Obot__class_Obot(tc_fun(_1609765, tc_HOL_Obool))) = _1609771)], (17918 ^ _782476) ^ [_1122371, _1122373, _1122375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122371), _1122373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122373), _1122375))))], (226 ^ _782476) ^ [_786185, _786187] : [-(class_Rings_Odivision__ring(_786185)), _786187 = _786185, class_Rings_Odivision__ring(_786187)], (24092 ^ _782476) ^ [_1234102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234102)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1234102)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1234102)))], (35018 ^ _782476) ^ [_1444665, _1444667, _1444669] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444665, _1444667, _1444669), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1444667)], (45330 ^ _782476) ^ [_1689704, _1689706, _1689708] : [-(hAPP(hAPP(c_List_Odrop(_1689704), _1689706), hAPP(c_List_Otl(_1689704), _1689708)) = hAPP(c_List_Otl(_1689704), hAPP(hAPP(c_List_Odrop(_1689704), _1689706), _1689708)))], (36597 ^ _782476) ^ [_1478719, _1478721, _1478723, _1478725] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478719, _1478721), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478723), _1478725))), -(_1478721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478719), _1478721) = _1478723)], (20605 ^ _782476) ^ [_1169892, _1169894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169892), _1169894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169894))))], (29552 ^ _782476) ^ [_1343227, _1343229, _1343231, _1343233] : [class_Rings_Olinordered__semidom(_1343227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1343229), _1343231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343227), c_Groups_Oone__class_Oone(_1343227)), _1343233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343227), hAPP(hAPP(c_Power_Opower__class_Opower(_1343227), _1343233), _1343229)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343227), _1343233), _1343231))))], (31727 ^ _782476) ^ [_1382850, _1382852, _1382854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1382850, tc_HOL_Obool)), _1382852)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382850), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382850, tc_HOL_Obool), _1382852))), 31737 ^ _782476 : [(31740 ^ _782476) ^ [] : [hAPP(c_Finite__Set_Ocard(_1382850), 31736 ^ [_1382850, _1382852, _1382854]) = _1382854], (31738 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382850, tc_HOL_Obool)), 31736 ^ [_1382850, _1382852, _1382854]), _1382852)))]], 31744 ^ _782476 : [(31748 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382850, tc_HOL_Obool)), 31746 ^ [_1382850, _1382852, _1382854]), _1382852)))], (31750 ^ _782476) ^ [] : [31743 ^ [_1382850, _1382852, _1382854] = 31746 ^ [_1382850, _1382852, _1382854]], (31752 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382850, tc_HOL_Obool)), 31743 ^ [_1382850, _1382852, _1382854]), 31746 ^ [_1382850, _1382852, _1382854]) = c_Orderings_Obot__class_Obot(tc_fun(_1382850, tc_HOL_Obool))], (31745 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382850, tc_HOL_Obool)), 31743 ^ [_1382850, _1382852, _1382854]), _1382852)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1382854), hAPP(c_Finite__Set_Ocard(tc_fun(_1382850, tc_HOL_Obool)), _1382852)) = hAPP(c_Finite__Set_Ocard(_1382850), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382850, tc_HOL_Obool), _1382852)))], (22730 ^ _782476) ^ [_1208860, _1208862, _1208864, _1208866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208860), _1208862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208864), hAPP(c_Set_Oimage(_1208860, _1208864, _1208866), _1208862))), hAPP(c_Finite__Set_Ocard(_1208860), _1208862))))], (3794 ^ _782476) ^ [_839377, _839379, _839381, _839383] : [-(c_List_Omeasures(_839383, _839379) = c_List_Omeasures(_839381, _839377)), _839383 = _839381, _839379 = _839377], (3608 ^ _782476) ^ [_836492, _836494, _836496, _836498] : [-(c_List_Olinorder__class_Osorted__list__of__set(_836498, _836494) = c_List_Olinorder__class_Osorted__list__of__set(_836496, _836492)), _836498 = _836496, _836494 = _836492], (28944 ^ _782476) ^ [_1332022, _1332024, _1332026] : [class_Rings_Odivision__ring(_1332022), -(_1332024 = c_Groups_Ozero__class_Ozero(_1332022)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332022), hAPP(c_Groups_Ouminus__class_Ouminus(_1332022), _1332026)), hAPP(c_Groups_Ouminus__class_Ouminus(_1332022), _1332024)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332022), _1332026), _1332024))], (31181 ^ _782476) ^ [_1372505, _1372507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372505), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372507), _1372505)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372505), _1372507) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42433 ^ _782476) ^ [_1618157] : [class_Groups_Oab__semigroup__mult(_1618157), -(c_Finite__Set_Ofun__left__comm(_1618157, _1618157, c_Groups_Otimes__class_Otimes(_1618157)))], (52441 ^ _782476) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (9595 ^ _782476) ^ [_954628, _954630, _954632, _954634] : [-(_954628 = c_Orderings_Obot__class_Obot(tc_fun(_954630, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954630, tc_fun(_954632, tc_HOL_Obool)), _954628), hAPP(c_COMBK(tc_fun(_954632, tc_HOL_Obool), _954630), _954634)) = _954634)], (2868 ^ _782476) ^ [_824922, _824924, _824926, _824928, _824930, _824932, _824934, _824936, _824938, _824940] : [-(c_Finite__Set_Ofold__graph(_824940, _824936, _824932, _824928, _824924) = c_Finite__Set_Ofold__graph(_824938, _824934, _824930, _824926, _824922)), _824940 = _824938, _824936 = _824934, _824932 = _824930, _824928 = _824926, _824924 = _824922], (52487 ^ _782476) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52649 ^ _782476) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (31938 ^ _782476) ^ [_1387382, _1387384, _1387386, _1387388] : [class_Divides_Osemiring__div(_1387382), -(c_Divides_Odiv__class_Omod(_1387382, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387382), _1387384), _1387386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387382), _1387384), _1387388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387382), _1387384), c_Divides_Odiv__class_Omod(_1387382, _1387386, _1387388)))], (23139 ^ _782476) ^ [_1216892, _1216894] : [_1216892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216892), _1216894) = _1216894)], (21131 ^ _782476) ^ [_1179531, _1179533] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179531), _1179533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179533), _1179531))], (10083 ^ _782476) ^ [_964783, _964785] : [class_Orderings_Oorder(_964783), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964783, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964783), _964785)), hAPP(c_SetInterval_Oord__class_OatLeast(_964783), _964785)) = hAPP(hAPP(c_Set_Oinsert(_964783), _964785), c_Orderings_Obot__class_Obot(tc_fun(_964783, tc_HOL_Obool))))], (10653 ^ _782476) ^ [_977518, _977520, _977522, _977524] : [class_Orderings_Olinorder(_977518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977518), _977520), _977522)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977518, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977518, _977520), _977524)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977518, _977520), _977522)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977518, _977522), _977524))], (4504 ^ _782476) ^ [_850816, _850818, _850820, _850822] : [-(c_Wellfounded_Oaccp(_850822, _850818) = c_Wellfounded_Oaccp(_850820, _850816)), _850822 = _850820, _850818 = _850816], (46276 ^ _782476) ^ [_1710137, _1710139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710137)), hAPP(c_Code__Numeral_Oof__nat, _1710139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710137), _1710139)))], (32569 ^ _782476) ^ [_1399383, _1399385, _1399387] : [_1399385 = c_Orderings_Obot__class_Obot(tc_fun(_1399383, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399383, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399383), _1399385), _1399387))], (29936 ^ _782476) ^ [_1350479, _1350481, _1350483, _1350485] : [class_Fields_Olinordered__field(_1350479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350479), _1350481), _1350483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350479), _1350485), c_Groups_Ozero__class_Ozero(_1350479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350479), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350479), _1350483), _1350485)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350479), _1350481), _1350485))))], (19616 ^ _782476) ^ [_1150962, _1150964, _1150966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150962)), 19619 ^ _782476 : [(19626 ^ _782476) ^ [] : [_1150964 = _1150966, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150962), _1150964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150962), _1150966))], (19620 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150962), _1150964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150962), _1150966), -(_1150964 = _1150966)]]], (13232 ^ _782476) ^ [_1026477, _1026479, _1026481, _1026483] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026477, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1026479, _1026477, _1026481), hAPP(c_Set_Ovimage(_1026479, _1026477, _1026481), _1026483))), _1026483)))], (48486 ^ _782476) ^ [_1758045, _1758047, _1758049, _1758051] : [hBOOL(hAPP(_1758045, _1758047)), -(c_List_OdropWhile(_1758049, _1758045, hAPP(hAPP(c_List_Olist_OCons(_1758049), _1758047), _1758051)) = c_List_OdropWhile(_1758049, _1758045, _1758051))], (51891 ^ _782476) ^ [_1833452, _1833454, _1833456] : [51892 ^ _782476 : [(51895 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833454), _1833456))], (51893 ^ _782476) ^ [] : [_1833452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833452), _1833454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833452), _1833456))))], (38808 ^ _782476) ^ [_1526584, _1526586] : [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)), _1526584), _1526586)), 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)), _1526584), 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)), _1526586), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (16869 ^ _782476) ^ [_1101069, _1101071, _1101073, _1101075, _1101077, _1101079] : [class_Rings_Oordered__ring(_1101069), 16872 ^ _782476 : [(16879 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101069), _1101071), _1101077)), _1101073)), _1101075)), _1101079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), _1101071), _1101073)), _1101075)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), _1101077), _1101073)), _1101079))))], (16873 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), _1101071), _1101073)), _1101075)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), _1101077), _1101073)), _1101079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101069), _1101071), _1101077)), _1101073)), _1101075)), _1101079)))]]], (8729 ^ _782476) ^ [_934576, _934578, _934580, _934582, _934584] : [hBOOL(hAPP(hAPP(c_member(_934576), _934578), hAPP(c_Set_Oimage(_934580, _934576, _934582), _934584))), 8733 ^ _782476 : [(8736 ^ _782476) ^ [] : [-(_934578 = hAPP(_934582, 8732 ^ [_934576, _934578, _934580, _934582, _934584]))], (8734 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934580), 8732 ^ [_934576, _934578, _934580, _934582, _934584]), _934584)))]]], (50610 ^ _782476) ^ [_1805930, _1805932] : [c_Relation_Otrans(_1805930, _1805932), -(c_Relation_Otrans(_1805930, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1805930, _1805930), tc_HOL_Obool)), _1805932), c_Relation_OId(_1805930))))], (17588 ^ _782476) ^ [_1115882, _1115884, _1115886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115882), _1115884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115882), _1115886)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115884), _1115886))))], (41802 ^ _782476) ^ [_1604114, _1604116] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604114, _1604114), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604116) = c_Relation_OId(_1604114))], (27405 ^ _782476) ^ [_1300820, _1300822, _1300824, _1300826] : [class_Orderings_Olinorder(_1300820), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300820, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300820, _1300822, _1300824)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300820), _1300826)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300820, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300820), _1300822), _1300826), _1300824))], (24302 ^ _782476) ^ [_1237540, _1237542] : [c_Nat__Transfer_Onat__set(_1237540), c_Nat__Transfer_Onat__set(_1237542), 24309 ^ _782476 : [(24316 ^ _782476) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1237540) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1237542), -(_1237540 = _1237542)], (24310 ^ _782476) ^ [] : [_1237540 = _1237542, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1237540) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1237542))]]], (52661 ^ _782476) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (45951 ^ _782476) ^ [_1701966, _1701968, _1701970, _1701972] : [_1701972 = c_List_Olist_ONil(_1701968), -(c_List_Olist_ONil(_1701966) = hAPP(hAPP(c_List_Omap(_1701968, _1701966), _1701970), _1701972))], (40771 ^ _782476) ^ [_1579081, _1579083, _1579085, _1579087, _1579089, _1579091, _1579093, _1579095] : [class_Groups_Ocomm__monoid__add(_1579081), c_Fun_Oinj__on(_1579083, _1579085, _1579087, _1579089), _1579091 = hAPP(c_Set_Oimage(_1579083, _1579085, _1579087), _1579089), 40785 ^ _782476 : [(40788 ^ _782476) ^ [] : [hAPP(_1579093, 40784 ^ [_1579081, _1579083, _1579085, _1579087, _1579089, _1579091, _1579093, _1579095]) = hAPP(_1579095, hAPP(_1579087, 40784 ^ [_1579081, _1579083, _1579085, _1579087, _1579089, _1579091, _1579093, _1579095]))], (40786 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579083), 40784 ^ [_1579081, _1579083, _1579085, _1579087, _1579089, _1579091, _1579093, _1579095]), _1579089)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579085, _1579081), _1579095), _1579091) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579083, _1579081), _1579093), _1579089))], (46050 ^ _782476) ^ [_1704541, _1704543, _1704545, _1704547, _1704549] : [-(hAPP(hAPP(c_List_Omap(_1704541, _1704543), _1704545), hAPP(hAPP(c_List_Olist_OCons(_1704541), _1704547), _1704549)) = hAPP(hAPP(c_List_Olist_OCons(_1704543), hAPP(_1704545, _1704547)), hAPP(hAPP(c_List_Omap(_1704541, _1704543), _1704545), _1704549)))], (21277 ^ _782476) ^ [_1182015, _1182017] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1182015), _1182017))))], (1070 ^ _782476) ^ [_798721, _798723, _798725, _798727, _798729, _798731, _798733, _798735] : [-(c_Equiv__Relations_Ocongruent(_798733, _798729, _798725, _798721)), c_Equiv__Relations_Ocongruent(_798735, _798731, _798727, _798723), _798735 = _798733, _798731 = _798729, _798727 = _798725, _798723 = _798721], (48365 ^ _782476) ^ [_1755457, _1755459] : [-(c_List_OtakeWhile(_1755457, _1755459, c_List_Olist_ONil(_1755457)) = c_List_Olist_ONil(_1755457))], (30987 ^ _782476) ^ [_1369482, _1369484, _1369486, _1369488] : [class_Divides_Osemiring__div(_1369482), -(_1369484 = c_Groups_Ozero__class_Ozero(_1369482)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369482), _1369486), _1369484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369482), _1369488), _1369484)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369482), _1369486), _1369488))], (31846 ^ _782476) ^ [_1385408, _1385410, _1385412] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385408), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385410, _1385412)), _1385412) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385408), _1385410), _1385412))], (16569 ^ _782476) ^ [_1094699, _1094701, _1094703, _1094705] : [class_Groups_Oordered__ab__semigroup__add(_1094699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094699), _1094701), _1094703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094699), _1094701), _1094705)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094699), _1094703), _1094705))))], (42534 ^ _782476) ^ [_1620093, _1620095, _1620097, _1620099, _1620101, _1620103, _1620105] : [c_Finite__Set_Ofun__left__comm(_1620093, _1620095, _1620097), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620093, _1620095, _1620097, _1620099, hAPP(hAPP(c_Set_Oinsert(_1620093), _1620101), _1620103)), _1620105)), -(hBOOL(hAPP(hAPP(c_member(_1620093), _1620101), _1620103))), 42546 ^ _782476 : [(42549 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620093, _1620095, _1620097, _1620099, _1620103), 42545 ^ [_1620093, _1620095, _1620097, _1620099, _1620101, _1620103, _1620105])))], (42547 ^ _782476) ^ [] : [-(_1620105 = hAPP(hAPP(_1620097, _1620101), 42545 ^ [_1620093, _1620095, _1620097, _1620099, _1620101, _1620103, _1620105]))]]], (47389 ^ _782476) ^ [_1736320, _1736322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736320), _1736322)), -(c_List_Oupt(_1736320, _1736322) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736320), c_List_Oupt(hAPP(c_Nat_OSuc, _1736320), _1736322)))], (52227 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (24128 ^ _782476) ^ [_1234830, _1234832, _1234834, _1234836] : [-(c_Sum__Type_OPlus(_1234830, _1234832, _1234834, _1234836) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1234830, _1234832), tc_HOL_Obool))), _1234834 = c_Orderings_Obot__class_Obot(tc_fun(_1234830, tc_HOL_Obool)), _1234836 = c_Orderings_Obot__class_Obot(tc_fun(_1234832, tc_HOL_Obool))], (43049 ^ _782476) ^ [_1633984, _1633986, _1633988, _1633990] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633984), tc_List_Olist(_1633984))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633984), tc_List_Olist(_1633984)), _1633986), _1633988)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633984), c_List_Olistrel1(_1633984, _1633990)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633984)), _1633986) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633984)), _1633988))], (32801 ^ _782476) ^ [_1404214, _1404216, _1404218, _1404220, _1404222, _1404224] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404214, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404216, _1404214, _1404218), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404220, tc_fun(_1404216, tc_HOL_Obool)), _1404222), _1404224))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404220, tc_fun(_1404214, tc_HOL_Obool)), _1404222), hAPP(hAPP(c_COMBB(tc_fun(_1404216, tc_HOL_Obool), tc_fun(_1404214, tc_HOL_Obool), _1404220), c_Relation_OImage(_1404216, _1404214, _1404218)), _1404224)))))], (42734 ^ _782476) ^ [_1624514, _1624516, _1624518, _1624520, _1624522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624514, tc_HOL_Obool)), _1624516), _1624518)), 42740 ^ _782476 : [(42745 ^ _782476) ^ [] : [hBOOL(hAPP(_1624522, 42739 ^ [_1624514, _1624516, _1624518, _1624520, _1624522]))], (42743 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1624520, 42739 ^ [_1624514, _1624516, _1624518, _1624520, _1624522])))], (42741 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624514), 42739 ^ [_1624514, _1624516, _1624518, _1624520, _1624522]), _1624516)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624514, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624514, tc_HOL_Obool)), _1624516), hAPP(c_Set_OCollect(_1624514), _1624520))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624514, tc_HOL_Obool)), _1624518), hAPP(c_Set_OCollect(_1624514), _1624522)))))], (7249 ^ _782476) ^ [_903210, _903212, _903214] : [class_Orderings_Oord(_903210), 7252 ^ _782476 : [(7259 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903210), _903214), _903212)), -(hBOOL(hAPP(hAPP(c_member(_903210), _903212), hAPP(c_SetInterval_Oord__class_OatLeast(_903210), _903214))))], (7253 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903210), _903212), hAPP(c_SetInterval_Oord__class_OatLeast(_903210), _903214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903210), _903214), _903212)))]]], (8969 ^ _782476) ^ [_939346, _939348, _939350, _939352] : [hBOOL(hAPP(hAPP(c_member(_939346), _939348), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939346, tc_HOL_Obool)), _939350), _939352))), -(hBOOL(hAPP(hAPP(c_member(_939346), _939348), _939352)))], (45937 ^ _782476) ^ [_1701693, _1701695, _1701697, _1701699] : [_1701699 = c_List_Olist_ONil(_1701693), -(hAPP(hAPP(c_List_Omap(_1701693, _1701695), _1701697), _1701699) = c_List_Olist_ONil(_1701695))], (36837 ^ _782476) ^ [_1483671, _1483673, _1483675, _1483677, _1483679, _1483681] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483671, tc_fun(_1483673, tc_HOL_Obool))), _1483675), _1483677), _1483679), _1483681)), -(hBOOL(hAPP(hAPP(_1483677, _1483679), _1483681)))], (26164 ^ _782476) ^ [_1276944] : [-(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, _1276944))))))], (28067 ^ _782476) ^ [_1313285, _1313287] : [class_Orderings_Olinorder(_1313285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313285), _1313287)), -(c_Big__Operators_Olattice_OInf__fin(_1313285, c_Orderings_Oord__class_Omin(_1313285), _1313287) = hAPP(c_Finite__Set_Ofold1(_1313285, c_Orderings_Oord__class_Omin(_1313285)), _1313287))], (47041 ^ _782476) ^ [_1726754, _1726756] : [47043 ^ _782476 : [(47046 ^ _782476) ^ [] : [47042 ^ [_1726754, _1726756] = c_List_Olist_ONil(_1726754)], (47044 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726754)), 47042 ^ [_1726754, _1726756]), hAPP(c_List_Oset(tc_List_Olist(_1726754)), _1726756))))]], -(c_List_Olist_ONil(_1726754) = c_List_Oconcat(_1726754, _1726756))], (42369 ^ _782476) ^ [_1616869, _1616871, _1616873] : [class_Orderings_Olinorder(_1616869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616869), _1616871)), -(hBOOL(hAPP(hAPP(c_member(_1616869), _1616873), _1616871))), -(c_Big__Operators_Olinorder__class_OMax(_1616869, hAPP(hAPP(c_Set_Oinsert(_1616869), _1616873), _1616871)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616869, _1616869, c_Orderings_Oord__class_Omax(_1616869)), _1616873), _1616871))], (44540 ^ _782476) ^ [_1671081, _1671083, _1671085, _1671087, _1671089] : [-(_1671081 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1671083, _1671085, _1671087), _1671081), _1671089) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1671085), _1671083), tc_prod(_1671085, _1671083), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671085), _1671083), c_List_Olist_ONil(_1671085)), _1671089), hAPP(c_Product__Type_Oprod_Oprod__case(_1671085, _1671083, tc_prod(tc_List_Olist(_1671085), _1671083)), hAPP(hAPP(c_COMBC(_1671085, tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083)), tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1671085), _1671083), tc_prod(tc_List_Olist(_1671085), _1671083)), tc_fun(tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083)), tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083))), _1671085), c_COMBB(tc_prod(tc_List_Olist(_1671085), _1671083), tc_prod(tc_List_Olist(_1671085), _1671083), _1671083)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671085), tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083))), tc_fun(tc_prod(tc_List_Olist(_1671085), _1671083), tc_prod(tc_List_Olist(_1671085), _1671083)), _1671085), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1671085), _1671083, tc_prod(tc_List_Olist(_1671085), _1671083))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671085), tc_List_Olist(_1671085)), tc_fun(tc_List_Olist(_1671085), tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083))), _1671085), hAPP(c_COMBB(tc_List_Olist(_1671085), tc_fun(_1671083, tc_prod(tc_List_Olist(_1671085), _1671083)), tc_List_Olist(_1671085)), c_Product__Type_OPair(tc_List_Olist(_1671085), _1671083))), c_List_Olist_OCons(_1671085))))), hAPP(c_Lazy__Sequence_Oanamorph(_1671083, _1671085, _1671087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1671081), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1671087, _1671089)))], (12148 ^ _782476) ^ [_1003471, _1003473, _1003475] : [class_Orderings_Owellorder(_1003471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003471), _1003473), c_Orderings_Oord__class_OLeast(_1003471, _1003475))), hBOOL(hAPP(_1003475, _1003473))], (46046 ^ _782476) ^ [_1704450, _1704452] : [-(hAPP(hAPP(c_List_Omap(_1704450, _1704450), c_COMBI(_1704450)), _1704452) = _1704452)], (46418 ^ _782476) ^ [_1712971, _1712973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712971)), hAPP(c_Code__Numeral_Onat__of, _1712973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712971), _1712973)))], (37912 ^ _782476) ^ [_1504285, _1504287, _1504289, _1504291] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1504285, _1504287), _1504289), _1504291) = hAPP(c_Set_OCollect(tc_prod(_1504287, _1504287)), hAPP(c_Product__Type_Oprod_Oprod__case(_1504287, _1504287, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1504287, tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_fun(_1504287, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504287, tc_fun(tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_fun(_1504287, tc_HOL_Obool)), _1504287), c_COMBC(_1504287, tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504287, tc_prod(_1504285, _1504285)), tc_fun(_1504287, tc_fun(tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_HOL_Obool)), _1504287), hAPP(c_COMBB(tc_prod(_1504285, _1504285), tc_fun(tc_fun(tc_prod(_1504285, _1504285), tc_HOL_Obool), tc_HOL_Obool), _1504287), c_member(tc_prod(_1504285, _1504285)))), hAPP(hAPP(c_COMBC(_1504287, tc_fun(_1504287, _1504285), tc_fun(_1504287, tc_prod(_1504285, _1504285))), hAPP(hAPP(c_COMBB(tc_fun(_1504285, tc_prod(_1504285, _1504285)), tc_fun(tc_fun(_1504287, _1504285), tc_fun(_1504287, tc_prod(_1504285, _1504285))), _1504287), c_COMBB(_1504285, tc_prod(_1504285, _1504285), _1504287)), hAPP(hAPP(c_COMBB(_1504285, tc_fun(_1504285, tc_prod(_1504285, _1504285)), _1504287), c_Product__Type_OPair(_1504285, _1504285)), _1504291))), _1504291)))), _1504289))))], (42017 ^ _782476) ^ [_1609998, _1610000, _1610002, _1610004] : [class_Lattices_Osemilattice__sup(_1609998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609998), _1610000)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1609998, _1609998, c_Lattices_Osemilattice__sup__class_Osup(_1609998)), _1610002), hAPP(hAPP(c_Set_Oinsert(_1609998), _1610004), _1610000)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1609998), _1610004), hAPP(hAPP(c_Finite__Set_Ofold(_1609998, _1609998, c_Lattices_Osemilattice__sup__class_Osup(_1609998)), _1610002), _1610000)))], (39174 ^ _782476) ^ [_1537479, _1537481, _1537483, _1537485] : [c_Wellfounded_Owf(_1537479, _1537481), c_Wellfounded_Owf(_1537483, _1537485), -(c_Wellfounded_Owf(tc_prod(_1537479, _1537483), c_Wellfounded_Olex__prod(_1537479, _1537483, _1537481, _1537485)))], (26136 ^ _782476) ^ [_1276584, _1276586] : [class_Orderings_Olinorder(_1276584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276584), _1276586)), -(_1276586 = c_Orderings_Obot__class_Obot(tc_fun(_1276584, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276584), c_Big__Operators_Olinorder__class_OMin(_1276584, _1276586)), _1276586)))], (34082 ^ _782476) ^ [_1428596, _1428598] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428596)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428598)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428596), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428598))))], (44975 ^ _782476) ^ [_1681165, _1681167, _1681169, _1681171, _1681173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681165), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681167)), _1681169))), -(hAPP(hAPP(c_List_Olist__update(_1681167, hAPP(hAPP(c_List_Oappend(_1681167), _1681169), _1681171)), _1681165), _1681173) = hAPP(hAPP(c_List_Oappend(_1681167), hAPP(hAPP(c_List_Olist__update(_1681167, _1681169), _1681165), _1681173)), _1681171))], (50961 ^ _782476) ^ [_1814152, _1814154] : [50964 ^ _782476 : [(50967 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1814152, _1814152)), hAPP(hAPP(c_Product__Type_OPair(_1814152, _1814152), 50963 ^ [_1814152, _1814154]), 50962 ^ [_1814152, _1814154])), _1814154))], (50965 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1814152, _1814152)), hAPP(hAPP(c_Product__Type_OPair(_1814152, _1814152), 50962 ^ [_1814152, _1814154]), 50963 ^ [_1814152, _1814154])), _1814154)))]], -(c_Relation_Osym(_1814152, _1814154))], (43503 ^ _782476) ^ [_1647010, _1647012, _1647014] : [43505 ^ _782476 : [(43508 ^ _782476) ^ [] : [hBOOL(hAPP(_1647014, 43504 ^ [_1647010, _1647012, _1647014]))], (43506 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1647010), 43504 ^ [_1647010, _1647012, _1647014]), hAPP(c_List_Oset(_1647010), _1647012))))]], 43509 ^ _782476 : [(43510 ^ _782476) ^ [_1647194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647194), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647010)), _1647012))), -(hBOOL(hAPP(_1647014, hAPP(hAPP(c_List_Onth(_1647010), _1647012), _1647194))))]]], (40139 ^ _782476) ^ [_1563248, _1563250, _1563252, _1563254, _1563256, _1563258] : [hAPP(c_Set_Oimage(_1563248, _1563250, _1563252), c_Orderings_Otop__class_Otop(tc_fun(_1563248, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563250, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563254, _1563256, _1563258), c_Orderings_Otop__class_Otop(tc_fun(_1563254, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563256, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1563248, _1563254), tc_prod(_1563250, _1563256), c_Product__Type_Omap__pair(_1563248, _1563250, _1563254, _1563256, _1563252, _1563258)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563248, _1563254), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563250, _1563256), tc_HOL_Obool)))], (28400 ^ _782476) ^ [_1321217, _1321219, _1321221] : [class_Orderings_Olinorder(_1321217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321217), _1321219)), hBOOL(hAPP(hAPP(c_member(_1321217), _1321221), _1321219)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321217), _1321221), c_Big__Operators_Olattice_OSup__fin(_1321217, c_Orderings_Oord__class_Omax(_1321217), _1321219)) = _1321221)], (43880 ^ _782476) ^ [_1657456, _1657458, _1657460, _1657462, _1657464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657456, tc_HOL_Obool)), hAPP(c_List_Oset(_1657456), _1657458)), _1657460)), hBOOL(hAPP(hAPP(c_member(_1657456), _1657462), _1657460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657456, tc_HOL_Obool)), hAPP(c_List_Oset(_1657456), hAPP(hAPP(c_List_Olist__update(_1657456, _1657458), _1657464), _1657462))), _1657460)))], (45015 ^ _782476) ^ [_1682337, _1682339, _1682341, _1682343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682337), tc_List_Olist(_1682337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682337), tc_List_Olist(_1682337)), _1682339), _1682341)), c_List_Olistrel1(_1682337, _1682343))), 45020 ^ _782476 : [(45027 ^ _782476) ^ [] : [-(_1682341 = hAPP(hAPP(c_List_Oappend(_1682337), 45022 ^ [_1682337, _1682339, _1682341, _1682343]), hAPP(hAPP(c_List_Olist_OCons(_1682337), 45019 ^ [_1682337, _1682339, _1682341, _1682343]), 45023 ^ [_1682337, _1682339, _1682341, _1682343])))], (45025 ^ _782476) ^ [] : [-(_1682339 = hAPP(hAPP(c_List_Oappend(_1682337), 45022 ^ [_1682337, _1682339, _1682341, _1682343]), hAPP(hAPP(c_List_Olist_OCons(_1682337), 45018 ^ [_1682337, _1682339, _1682341, _1682343]), 45023 ^ [_1682337, _1682339, _1682341, _1682343])))], (45021 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682337, _1682337)), hAPP(hAPP(c_Product__Type_OPair(_1682337, _1682337), 45018 ^ [_1682337, _1682339, _1682341, _1682343]), 45019 ^ [_1682337, _1682339, _1682341, _1682343])), _1682343)))]]], (25163 ^ _782476) ^ [_1252786, _1252788] : [class_Groups_Oordered__ab__group__add__abs(_1252786), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252786), hAPP(c_Groups_Ouminus__class_Ouminus(_1252786), _1252788)), hAPP(c_Groups_Oabs__class_Oabs(_1252786), _1252788))))], (40530 ^ _782476) ^ [_1572454, _1572456, _1572458] : [hBOOL(hAPP(c_Predicate_OPowp(_1572454, _1572456), _1572458)), 40533 ^ _782476 : [(40534 ^ _782476) ^ [_1572538] : [hBOOL(hAPP(hAPP(c_member(_1572454), _1572538), _1572458)), -(hBOOL(hAPP(_1572456, _1572538)))]]], (40203 ^ _782476) ^ [_1565188, _1565190, _1565192, _1565194, _1565196, _1565198, _1565200, _1565202] : [c_Fun_Oinj__on(_1565188, _1565190, _1565192, _1565194), c_Fun_Oinj__on(_1565196, _1565198, _1565200, _1565202), -(c_Fun_Oinj__on(tc_prod(_1565188, _1565196), tc_prod(_1565190, _1565198), c_Product__Type_Omap__pair(_1565188, _1565190, _1565196, _1565198, _1565192, _1565200), hAPP(hAPP(c_Product__Type_OSigma(_1565188, _1565196), _1565194), hAPP(c_COMBK(tc_fun(_1565196, tc_HOL_Obool), _1565188), _1565202))))], (30020 ^ _782476) ^ [_1352037, _1352039, _1352041] : [class_Fields_Olinordered__field__inverse__zero(_1352037), 30023 ^ _782476 : [(30038 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352037), _1352039), _1352041)), c_Groups_Ozero__class_Ozero(_1352037)))), 30039 ^ _782476 : [(30046 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), _1352039), c_Groups_Ozero__class_Ozero(_1352037))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), c_Groups_Ozero__class_Ozero(_1352037)), _1352041))], (30040 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), c_Groups_Ozero__class_Ozero(_1352037)), _1352039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), _1352041), c_Groups_Ozero__class_Ozero(_1352037)))]]], (30024 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352037), _1352039), _1352041)), c_Groups_Ozero__class_Ozero(_1352037))), 30029 ^ _782476 : [(30032 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), _1352041), c_Groups_Ozero__class_Ozero(_1352037))))], (30030 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), c_Groups_Ozero__class_Ozero(_1352037)), _1352039)))]], 30033 ^ _782476 : [(30036 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), c_Groups_Ozero__class_Ozero(_1352037)), _1352041)))], (30034 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352037), _1352039), c_Groups_Ozero__class_Ozero(_1352037))))]]]]], (22140 ^ _782476) ^ [_1198513, _1198515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198513), hAPP(c_Nat_OSuc, _1198515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198513), _1198515))), -(_1198513 = _1198515)], (3562 ^ _782476) ^ [_835717, _835719] : [_835719 = _835717, -(c_SetInterval_Oord__class_OatMost(_835719) = c_SetInterval_Oord__class_OatMost(_835717))], (5622 ^ _782476) ^ [_868605, _868607] : [_868607 = _868605, -(tc_Option_Ooption(_868607) = tc_Option_Ooption(_868605))], (14639 ^ _782476) ^ [_1055310, _1055312, _1055314, _1055316, _1055318, _1055320, _1055322, _1055324] : [c_Finite__Set_Ofolding__image(_1055310, _1055312, _1055314, _1055316, _1055318), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055312), _1055320)), c_Fun_Oinj__on(_1055312, _1055312, _1055322, _1055320), -(hAPP(hAPP(_1055318, _1055324), hAPP(c_Set_Oimage(_1055312, _1055312, _1055322), _1055320)) = hAPP(hAPP(_1055318, hAPP(c_Fun_Ocomp(_1055312, _1055310, _1055312, _1055324), _1055322)), _1055320))], (34948 ^ _782476) ^ [_1443242, _1443244] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443242)), hAPP(c_Nat_OSuc, _1443244)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443242))), 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, _1443244))), 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)), _1443244)))))], (35610 ^ _782476) ^ [_1455211, _1455213, _1455215] : [class_Rings_Olinordered__semidom(_1455211), hAPP(hAPP(c_Power_Opower__class_Opower(_1455211), _1455213), 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(_1455211), _1455215), 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(_1455211), c_Groups_Ozero__class_Ozero(_1455211)), _1455213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455211), c_Groups_Ozero__class_Ozero(_1455211)), _1455215)), -(_1455213 = _1455215)], (47443 ^ _782476) ^ [_1737258, _1737260, _1737262, _1737264] : [c_List_Oupt(_1737258, _1737260) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737262), _1737264), 47446 ^ _782476 : [(47451 ^ _782476) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737258), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737260) = _1737264)], (47449 ^ _782476) ^ [] : [-(_1737258 = _1737262)], (47447 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737258), _1737260)))]]], (13958 ^ _782476) ^ [_1041729, _1041731, _1041733] : [c_Fun_Oinj__on(_1041729, _1041731, _1041733, c_Orderings_Otop__class_Otop(tc_fun(_1041729, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041729, _1041731, _1041733), c_Orderings_Otop__class_Otop(tc_fun(_1041729, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041731, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1041729, _1041731, _1041733, c_Orderings_Otop__class_Otop(tc_fun(_1041729, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041731, tc_HOL_Obool))))], (17634 ^ _782476) ^ [_1116756, _1116758, _1116760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116756), _1116758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116756), _1116760)), _1116758)))], (41838 ^ _782476) ^ [_1605160, _1605162, _1605164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605160, _1605160)), _1605162), c_Transitive__Closure_Otrancl(_1605160, _1605164))), 41842 ^ _782476 : [(41845 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605160, _1605160)), _1605162), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605160, _1605160), tc_HOL_Obool), 41841 ^ [_1605160, _1605162, _1605164]), _1605164))))], (41843 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41841 ^ [_1605160, _1605162, _1605164])))]]], (49454 ^ _782476) ^ [_1779680, _1779682, _1779684, _1779686] : [-(c_New__Random__Sequence_Oneg__map(_1779680, _1779682, _1779684, _1779686) = c_New__Random__Sequence_Oneg__bind(_1779680, _1779682, _1779686, hAPP(c_Fun_Ocomp(_1779682, 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(_1779682)))))), _1779680, c_New__Random__Sequence_Oneg__single(_1779682)), _1779684)))], (25564 ^ _782476) ^ [_1260094] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1260094, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260094), hAPP(c_COMBK(tc_HOL_Obool, _1260094), c_fFalse)))], (50843 ^ _782476) ^ [_1811583] : [-(c_Relation_Oantisym(_1811583, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1811583, _1811583), tc_HOL_Obool))))], (36044 ^ _782476) ^ [_1463510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463510)))], (22176 ^ _782476) ^ [_1199066, _1199068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199068)), _1199066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199066), _1199068))], (46198 ^ _782476) ^ [_1708552, _1708554, _1708556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708552), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708554)), _1708556))), -(hAPP(c_Random_Opick(_1708554, hAPP(hAPP(c_List_Omap(_1708554, tc_prod(tc_Code__Numeral_Ocode__numeral, _1708554)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1708554), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1708556)), hAPP(c_Code__Numeral_Oof__nat, _1708552)) = hAPP(hAPP(c_List_Onth(_1708554), _1708556), _1708552))], (22003 ^ _782476) ^ [_1196361, _1196363] : [hAPP(c_Nat_OSuc, _1196361) = hAPP(c_Nat_OSuc, _1196363), -(_1196361 = _1196363)], (23745 ^ _782476) ^ [_1228298, _1228300] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228298) = _1228300, 23748 ^ _782476 : [(23751 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228300)))], (23749 ^ _782476) ^ [] : [-(_1228298 = hAPP(c_Int_Onat, _1228300))]]], (46778 ^ _782476) ^ [_1721338, _1721340, _1721342, _1721344] : [_1721344 = c_List_Olist_ONil(_1721338), -(c_List_Olist__all2(_1721338, _1721340, _1721342, _1721344, c_List_Olist_ONil(_1721340)))], (26394 ^ _782476) ^ [_1281327, _1281329, _1281331, _1281333] : [class_Orderings_Olinorder(_1281327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281327), _1281329), _1281331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281327), _1281333), _1281331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281327), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281327), _1281329), _1281333)), _1281331)))], (49470 ^ _782476) ^ [_1780107, _1780109] : [-(c_List_Osplice(_1780107, c_List_Olist_ONil(_1780107), _1780109) = _1780109)], (28043 ^ _782476) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (48118 ^ _782476) ^ [_1750317, _1750319, _1750321] : [hAPP(c_List_Orev(_1750317), _1750319) = hAPP(c_List_Orev(_1750317), _1750321), -(_1750319 = _1750321)], (50337 ^ _782476) ^ [_1799521, _1799523, _1799525] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1799521, _1799523, _1799525) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799521)], (8834 ^ _782476) ^ [_936551, _936553, _936555, _936557] : [class_Lattices_Osemilattice__inf(_936551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936551), _936553), _936555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936551), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936551), _936553), _936557)), _936555)))], (25492 ^ _782476) ^ [_1258835, _1258837, _1258839] : [hBOOL(hAPP(_1258835, _1258837)), -(hBOOL(hAPP(hAPP(c_member(_1258839), _1258837), hAPP(c_Set_OCollect(_1258839), _1258835))))], (46584 ^ _782476) ^ [_1716424, _1716426, _1716428, _1716430, _1716432] : [c_List_Opartition(_1716424, _1716426, _1716428) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716424), tc_List_Olist(_1716424)), _1716430), _1716432), 46587 ^ _782476 : [(46594 ^ _782476) ^ [_1716686] : [hBOOL(hAPP(hAPP(c_member(_1716424), _1716686), hAPP(c_List_Oset(_1716424), _1716432))), hBOOL(hAPP(_1716426, _1716686))], (46588 ^ _782476) ^ [_1716577] : [hBOOL(hAPP(hAPP(c_member(_1716424), _1716577), hAPP(c_List_Oset(_1716424), _1716430))), -(hBOOL(hAPP(_1716426, _1716577)))]]], (43755 ^ _782476) ^ [_1654565, _1654567] : [class_Groups_Ocomm__monoid__add(_1654565), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654565), _1654567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1654565), hAPP(c_List_Onth(_1654565), _1654567)), 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(_1654565)), _1654567))))], (2348 ^ _782476) ^ [_816896, _816898] : [_816898 = _816896, -(c_Enum_Oenum__class_Oenum__all(_816898) = c_Enum_Oenum__class_Oenum__all(_816896))], (52127 ^ _782476) ^ [_1837864, _1837866] : [class_Lattices_Olattice(_1837864), -(class_Lattices_Osemilattice__sup(tc_fun(_1837866, _1837864)))], (48747 ^ _782476) ^ [_1763365, _1763367, _1763369] : [-(c_List_Omaps(_1763365, _1763367, _1763369, c_List_Olist_ONil(_1763365)) = c_List_Olist_ONil(_1763367))], (48124 ^ _782476) ^ [_1750412, _1750414, _1750416] : [_1750414 = _1750416, -(hAPP(c_List_Orev(_1750412), _1750414) = hAPP(c_List_Orev(_1750412), _1750416))], (40670 ^ _782476) ^ [_1576611, _1576613] : [40671 ^ _782476 : [(40672 ^ _782476) ^ [_1576657] : [hBOOL(hAPP(_1576611, _1576657))]], -(hBOOL(hAPP(_1576611, c_Hilbert__Choice_OEps(_1576613, _1576611))))], (6706 ^ _782476) ^ [_890845, _890847, _890849, _890851] : [hBOOL(hAPP(hAPP(c_member(_890845), _890847), c_Complete__Lattice_OInf__class_OInf(tc_fun(_890845, tc_HOL_Obool), _890849))), hBOOL(hAPP(hAPP(c_member(tc_fun(_890845, tc_HOL_Obool)), _890851), _890849)), -(hBOOL(hAPP(hAPP(c_member(_890845), _890847), _890851)))], (49617 ^ _782476) ^ [_1783457, _1783459, _1783461, _1783463] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783457, _1783459, c_Orderings_Otop__class_Otop(tc_fun(_1783457, tc_HOL_Obool)), _1783461), _1783463) = c_Hilbert__Choice_OEps(_1783457, hAPP(hAPP(c_COMBC(_1783457, _1783459, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783459, tc_fun(_1783459, tc_HOL_Obool), _1783457), c_fequal), _1783461)), _1783463)))], (18444 ^ _782476) ^ [_1130082, _1130084, _1130086] : [class_Groups_Ocomm__monoid__add(_1130082), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1130084, _1130082), hAPP(c_COMBK(_1130082, _1130084), c_Groups_Ozero__class_Ozero(_1130082))), _1130086) = c_Groups_Ozero__class_Ozero(_1130082))], (13220 ^ _782476) ^ [_1026028, _1026030, _1026032, _1026034, _1026036] : [-(hAPP(c_Set_Ovimage(_1026028, _1026030, _1026032), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026030, tc_HOL_Obool)), _1026034), _1026036)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026028, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026028, _1026030, _1026032), _1026034)), hAPP(c_Set_Ovimage(_1026028, _1026030, _1026032), _1026036)))], (39764 ^ _782476) ^ [_1552205, _1552207, _1552209, _1552211, _1552213, _1552215, _1552217, _1552219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552205, _1552207), tc_HOL_Obool)), _1552209), hAPP(hAPP(c_Product__Type_OSigma(_1552205, _1552207), _1552211), hAPP(c_COMBK(tc_fun(_1552207, tc_HOL_Obool), _1552205), _1552213)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552207, _1552215), tc_HOL_Obool)), _1552217), hAPP(hAPP(c_Product__Type_OSigma(_1552207, _1552215), _1552213), hAPP(c_COMBK(tc_fun(_1552215, tc_HOL_Obool), _1552207), _1552219)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552205, _1552215), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552205, _1552207, _1552215), _1552209), _1552217)), hAPP(hAPP(c_Product__Type_OSigma(_1552205, _1552215), _1552211), hAPP(c_COMBK(tc_fun(_1552215, tc_HOL_Obool), _1552205), _1552219)))))], (31486 ^ _782476) ^ [_1378262, _1378264] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378262), _1378264)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378262)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378264)))], (46524 ^ _782476) ^ [_1715209, _1715211, _1715213, _1715215] : [hBOOL(hAPP(c_List_Olistsp(_1715209, hAPP(hAPP(c_COMBS(_1715209, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715209), c_fconj), _1715211)), _1715213)), _1715215)), 46527 ^ _782476 : [(46530 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715209, _1715213), _1715215)))], (46528 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715209, _1715211), _1715215)))]]], (19684 ^ _782476) ^ [_1152159, _1152161, _1152163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152159), _1152161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152163), _1152161))), 19687 ^ _782476 : [(19690 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152159), _1152163)))], (19688 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152161)))]]], (18142 ^ _782476) ^ [_1125790, _1125792] : [class_Groups_Ogroup__add(_1125790), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125790), _1125792), c_Groups_Ozero__class_Ozero(_1125790)) = _1125792)], (17433 ^ _782476) ^ [_1113117, _1113119, _1113121, _1113123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113117), _1113119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113121), _1113119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113117), _1113123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113121), _1113123)))], (34036 ^ _782476) ^ [_1427729] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427729))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427729)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41294 ^ _782476) ^ [_1591801] : [-(c_Relation_Orefl__on(_1591801, c_Orderings_Otop__class_Otop(tc_fun(_1591801, tc_HOL_Obool)), c_Relation_OId(_1591801)))], (41995 ^ _782476) ^ [_1609523, _1609525, _1609527, _1609529, _1609531, _1609533] : [c_Finite__Set_Ofolding(_1609523, _1609525, _1609527, _1609529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609523), _1609531)), -(hAPP(hAPP(_1609529, _1609531), _1609533) = hAPP(hAPP(c_Finite__Set_Ofold(_1609523, _1609525, _1609527), _1609533), _1609531))], (51045 ^ _782476) ^ [_1815571, _1815573] : [-(c_Relation_Osym(_1815571, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1815571, _1815571), tc_HOL_Obool)), _1815573), hAPP(c_Relation_Oconverse(_1815571, _1815571), _1815573))))], (22399 ^ _782476) ^ [_1202869] : [22400 ^ _782476 : [(22401 ^ _782476) ^ [_1202911] : [_1202869 = hAPP(c_Nat_OSuc, _1202911)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202869)))], (16197 ^ _782476) ^ [_1086750, _1086752, _1086754, _1086756, _1086758] : [class_Groups_Ocomm__monoid__mult(_1086750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086752), _1086754)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086752), _1086756)), 16211 ^ _782476 : [(16214 ^ _782476) ^ [] : [hAPP(_1086758, 16210 ^ [_1086750, _1086752, _1086754, _1086756, _1086758]) = c_Groups_Oone__class_Oone(_1086750)], (16212 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086752), 16210 ^ [_1086750, _1086752, _1086754, _1086756, _1086758]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086752, tc_HOL_Obool)), _1086754), _1086756))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086750, _1086752, c_Groups_Otimes__class_Otimes(_1086750)), _1086758), c_Groups_Oone__class_Oone(_1086750)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086752, tc_HOL_Obool)), _1086754), _1086756)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086750), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086750, _1086752, c_Groups_Otimes__class_Otimes(_1086750)), _1086758), c_Groups_Oone__class_Oone(_1086750)), _1086754)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086750, _1086752, c_Groups_Otimes__class_Otimes(_1086750)), _1086758), c_Groups_Oone__class_Oone(_1086750)), _1086756)))], (32549 ^ _782476) ^ [_1398967, _1398969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1398967), _1398969)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398967, _1398969) = _1398967)], (36136 ^ _782476) ^ [_1464900] : [class_Int_Onumber__ring(_1464900), c_Int_Oiszero(_1464900, hAPP(c_Int_Onumber__class_Onumber__of(_1464900), c_Int_OMin))], (38778 ^ _782476) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (44364 ^ _782476) ^ [_1667191, _1667193] : [_1667193 = c_List_Olist_ONil(_1667191), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667191)), _1667193) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22660 ^ _782476) ^ [_1207466, _1207468, _1207470, _1207472] : [class_Groups_Ocomm__monoid__add(_1207466), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207466), _1207468), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207470)), hAPP(c_Nat_OSuc, _1207472))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207466), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207466, tc_Nat_Onat), _1207468), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207470), _1207472)))], (7954 ^ _782476) ^ [_917916, _917918, _917920, _917922, _917924] : [class_Lattices_Osemilattice__sup(_917916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917916), _917918), _917920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917916), _917922), _917924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917916), _917918), _917922)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917916), _917920), _917924))))], (40033 ^ _782476) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (46454 ^ _782476) ^ [_1713561, _1713563, _1713565, _1713567, _1713569] : [class_Groups_Omonoid__add(_1713561), class_Groups_Oordered__ab__semigroup__add(_1713561), 46464 ^ _782476 : [(46467 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713561), hAPP(_1713567, 46463 ^ [_1713561, _1713563, _1713565, _1713567, _1713569])), hAPP(_1713569, 46463 ^ [_1713561, _1713563, _1713565, _1713567, _1713569])))], (46465 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713563), 46463 ^ [_1713561, _1713563, _1713565, _1713567, _1713569]), hAPP(c_List_Oset(_1713563), _1713565))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713561), hAPP(c_List_Omonoid__add__class_Olistsum(_1713561), hAPP(hAPP(c_List_Omap(_1713563, _1713561), _1713567), _1713565))), hAPP(c_List_Omonoid__add__class_Olistsum(_1713561), hAPP(hAPP(c_List_Omap(_1713563, _1713561), _1713569), _1713565)))))], (6584 ^ _782476) ^ [_888486, _888488] : [class_Orderings_Olinorder(_888486), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888486, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888486), _888488)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888486), _888488))], (42397 ^ _782476) ^ [_1617303, _1617305, _1617307, _1617309, _1617311, _1617313] : [c_Finite__Set_Ofun__left__comm(_1617303, _1617305, _1617307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617303), _1617309)), hBOOL(hAPP(hAPP(c_member(_1617303), _1617311), _1617309)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617303, _1617305, _1617307), _1617313), _1617309) = hAPP(hAPP(_1617307, _1617311), hAPP(hAPP(c_Finite__Set_Ofold(_1617303, _1617305, _1617307), _1617313), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617303, tc_HOL_Obool)), _1617309), hAPP(hAPP(c_Set_Oinsert(_1617303), _1617311), c_Orderings_Obot__class_Obot(tc_fun(_1617303, tc_HOL_Obool)))))))], (32676 ^ _782476) ^ [_1401246, _1401248] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401246), _1401248)), _1401248) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401246), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401246, _1401248)))], (13980 ^ _782476) ^ [_1042118, _1042120, _1042122, _1042124] : [c_Fun_Obij__betw(_1042118, _1042120, _1042122, c_Orderings_Otop__class_Otop(tc_fun(_1042118, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042120, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042118, _1042120, _1042122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042118, tc_HOL_Obool)), _1042124)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042120, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1042118, _1042120, _1042122), _1042124)))], (39515 ^ _782476) ^ [_1544829, _1544831, _1544833, _1544835] : [-(hAPP(c_Relation_ORange(_1544829, _1544831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1544829, _1544831), tc_HOL_Obool)), _1544833), _1544835)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544831, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544829, _1544831), _1544833)), hAPP(c_Relation_ORange(_1544829, _1544831), _1544835)))], (38501 ^ _782476) ^ [_1519408, _1519410, _1519412] : [c_Equiv__Relations_Oequivp(_1519408, _1519410), -(hBOOL(hAPP(hAPP(_1519410, _1519412), _1519412)))], (39350 ^ _782476) ^ [_1540928, _1540930, _1540932] : [c_Wellfounded_Owf(_1540928, _1540930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540928, tc_HOL_Obool)), _1540932), hAPP(c_Relation_OImage(_1540928, _1540928, _1540930), _1540932))), -(_1540932 = c_Orderings_Obot__class_Obot(tc_fun(_1540928, tc_HOL_Obool)))], (21489 ^ _782476) ^ [_1185710, _1185712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185710)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185710), _1185712)))], (40315 ^ _782476) ^ [_1567630, _1567632, _1567634, _1567636, _1567638] : [c_Relation_Orefl__on(_1567630, _1567632, _1567634), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567630, _1567630)), hAPP(hAPP(c_Product__Type_OPair(_1567630, _1567630), _1567636), _1567638)), _1567634)), -(hBOOL(hAPP(hAPP(c_member(_1567630), _1567638), _1567632)))], (52365 ^ _782476) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (9037 ^ _782476) ^ [_940940, _940942, _940944, _940946] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940940, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940940, tc_HOL_Obool)), _940942), _940944)), _940946) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940940, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940940, tc_HOL_Obool)), _940942), _940946)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940940, tc_HOL_Obool)), _940944), _940946)))], (27155 ^ _782476) ^ [_1295812, _1295814, _1295816] : [class_Groups_Ocomm__monoid__mult(_1295812), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295814, _1295812), _1295816), c_Orderings_Obot__class_Obot(tc_fun(_1295814, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295812))], (52283 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (10811 ^ _782476) ^ [_981086, _981088, _981090] : [class_Groups_Oordered__ab__group__add(_981086), -(hAPP(c_Set_Oimage(_981086, _981086, c_Groups_Ouminus__class_Ouminus(_981086)), c_SetInterval_Oord__class_OgreaterThanLessThan(_981086, _981088, _981090)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_981086, hAPP(c_Groups_Ouminus__class_Ouminus(_981086), _981090), hAPP(c_Groups_Ouminus__class_Ouminus(_981086), _981088)))], (43743 ^ _782476) ^ [_1654413] : [c_List_Onat__list(_1654413), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654413)))], (43319 ^ _782476) ^ [_1642153, _1642155, _1642157] : [-(hAPP(hAPP(c_List_Onth(_1642153), hAPP(hAPP(c_List_Olist_OCons(_1642153), _1642155), _1642157)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1642155)], (40171 ^ _782476) ^ [_1564316, _1564318, _1564320, _1564322, _1564324, _1564326, _1564328, _1564330, _1564332, _1564334, _1564336] : [-(hAPP(c_Product__Type_Omap__pair(_1564316, _1564318, _1564320, _1564322, _1564324, _1564326), hAPP(c_Product__Type_Omap__pair(_1564328, _1564316, _1564330, _1564320, _1564332, _1564334), _1564336)) = hAPP(c_Product__Type_Omap__pair(_1564328, _1564318, _1564330, _1564322, hAPP(c_Fun_Ocomp(_1564316, _1564318, _1564328, _1564324), _1564332), hAPP(c_Fun_Ocomp(_1564320, _1564322, _1564330, _1564326), _1564334)), _1564336))], (8545 ^ _782476) ^ [_930864, _930866, _930868] : [class_Lattices_Obounded__lattice__top(_930864), 8548 ^ _782476 : [(8557 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930864), _930866), _930868) = c_Orderings_Otop__class_Otop(_930864)), _930866 = c_Orderings_Otop__class_Otop(_930864), _930868 = c_Orderings_Otop__class_Otop(_930864)], (8549 ^ _782476) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930864), _930866), _930868) = c_Orderings_Otop__class_Otop(_930864), 8552 ^ _782476 : [(8555 ^ _782476) ^ [] : [-(_930868 = c_Orderings_Otop__class_Otop(_930864))], (8553 ^ _782476) ^ [] : [-(_930866 = c_Orderings_Otop__class_Otop(_930864))]]]]], (51374 ^ _782476) ^ [_1821893, _1821895, _1821897, _1821899, _1821901] : [hBOOL(hAPP(_1821893, hAPP(hAPP(c_Product__Type_OPair(_1821895, _1821897), _1821899), _1821901))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1821895, _1821897, tc_HOL_Obool, _1821893), _1821899), _1821901)))], (47169 ^ _782476) ^ [_1730476, _1730478, _1730480] : [hAPP(c_List_Ofilter(_1730476, _1730478), _1730480) = _1730480, 47172 ^ _782476 : [(47173 ^ _782476) ^ [_1730567] : [hBOOL(hAPP(hAPP(c_member(_1730476), _1730567), hAPP(c_List_Oset(_1730476), _1730480))), -(hBOOL(hAPP(_1730478, _1730567)))]]], (23398 ^ _782476) ^ [_1221878, _1221880, _1221882, _1221884] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221878), _1221880)), hBOOL(hAPP(hAPP(c_member(_1221878), _1221882), _1221880)), -(hBOOL(hAPP(hAPP(c_member(_1221878), _1221882), _1221884))), -(hAPP(c_Finite__Set_Ocard(_1221878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221878, tc_HOL_Obool)), _1221880), hAPP(hAPP(c_Set_Oinsert(_1221878), _1221882), _1221884))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221878, tc_HOL_Obool)), _1221880), _1221884))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21448 ^ _782476) ^ [_1185015] : [21449 ^ _782476 : [(21450 ^ _782476) ^ [_1185072] : [hBOOL(hAPP(_1185015, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185072)))]], 21452 ^ _782476 : [(21455 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1185015, 21451 ^ [_1185015])))], (21453 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21451 ^ [_1185015])))]]], (43786 ^ _782476) ^ [_1655163, _1655165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655163), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1655165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1655165), _1655163)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1655165))))], (23330 ^ _782476) ^ [_1220420, _1220422, _1220424, _1220426] : [class_Groups_Ocomm__monoid__add(_1220420), 23333 ^ _782476 : [(23340 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220422), _1220424))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220420), _1220426), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220424), hAPP(c_Nat_OSuc, _1220422))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220420), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220420), _1220426), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220424), _1220422))), hAPP(_1220426, _1220422)))], (23334 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220422), _1220424)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220420), _1220426), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220424), hAPP(c_Nat_OSuc, _1220422))) = c_Groups_Ozero__class_Ozero(_1220420))]]], (49609 ^ 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hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1454001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1454001), _1454001))], (46912 ^ _782476) ^ [_1724284, _1724286] : [c_List_Oremdups(_1724284, _1724286) = _1724286, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724284)), c_List_Oremdups(_1724284, _1724286)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724284)), _1724286))], (51835 ^ _782476) ^ [_1832459, _1832461, _1832463, _1832465, _1832467] : [class_Rings_Ocomm__semiring__1(_1832459), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832459), _1832461), _1832463)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832459), _1832465), _1832467)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832459), _1832461), _1832465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832459), _1832463), _1832467))))], (4824 ^ _782476) ^ [_856056, _856058] : [_856058 = _856056, -(c_DSequence_Ounion(_856058) = c_DSequence_Ounion(_856056))], (8160 ^ _782476) ^ [_921775, _921777, _921779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921775, tc_HOL_Obool)), _921777), _921779)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921775, tc_HOL_Obool)), _921777), _921779) = _921779)], (23007 ^ _782476) ^ [_1214043] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1214043), hAPP(c_Nat_OSuc, _1214043)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1214043), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (15899 ^ _782476) ^ [_1079961, _1079963, _1079965] : [class_Lattices_Oab__semigroup__idem__mult(_1079961), hAPP(_1079963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079961), 15904 ^ [_1079961, _1079963, _1079965]), 15905 ^ [_1079961, _1079963, _1079965])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079961), hAPP(_1079963, 15904 ^ [_1079961, _1079963, _1079965])), hAPP(_1079963, 15905 ^ [_1079961, _1079963, _1079965])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079961), _1079965)), -(_1079965 = c_Orderings_Obot__class_Obot(tc_fun(_1079961, tc_HOL_Obool))), -(hAPP(_1079963, hAPP(c_Finite__Set_Ofold1(_1079961, c_Groups_Otimes__class_Otimes(_1079961)), _1079965)) = hAPP(c_Finite__Set_Ofold1(_1079961, c_Groups_Otimes__class_Otimes(_1079961)), hAPP(c_Set_Oimage(_1079961, _1079961, _1079963), _1079965)))], (34344 ^ _782476) ^ [_1432864, _1432866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1432864)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1432866)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1432864)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1432864))))], (7726 ^ _782476) ^ [_913019, _913021, _913023, _913025] : [7727 ^ _782476 : [(7730 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913019), _913021), _913025))], (7728 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913019), _913021), _913023))]], -(hBOOL(hAPP(hAPP(c_member(_913019), _913021), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913019, tc_HOL_Obool)), _913025), _913023))))], (33564 ^ _782476) ^ [_1418694, _1418696, _1418698, _1418700] : [class_Fields_Olinordered__field__inverse__zero(_1418694), class_Int_Onumber(_1418694), 33571 ^ _782476 : [(33572 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418696), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418694), _1418698), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)))), 33575 ^ _782476 : [(33582 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), c_Groups_Ozero__class_Ozero(_1418694)), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)))), 33585 ^ _782476 : [(33592 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)), c_Groups_Ozero__class_Ozero(_1418694)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418696), c_Groups_Ozero__class_Ozero(_1418694))))], (33586 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)), c_Groups_Ozero__class_Ozero(_1418694))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418694), _1418696), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)))))]]], (33576 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), c_Groups_Ozero__class_Ozero(_1418694)), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418694), _1418696), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))), _1418698)))]]], (33598 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418696), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418694), _1418698), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))))), 33601 ^ _782476 : [(33604 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418694), _1418696), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))), _1418698))], (33602 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), c_Groups_Ozero__class_Ozero(_1418694)), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))))]], 33605 ^ _782476 : [(33608 ^ _782476) ^ [] : [33609 ^ _782476 : [(33612 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418694), _1418696), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700))))], (33610 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)), c_Groups_Ozero__class_Ozero(_1418694))))]], 33613 ^ _782476 : [(33616 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), _1418696), c_Groups_Ozero__class_Ozero(_1418694)))], (33614 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)), c_Groups_Ozero__class_Ozero(_1418694)))]]], (33606 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418694), c_Groups_Ozero__class_Ozero(_1418694)), hAPP(c_Int_Onumber__class_Onumber__of(_1418694), _1418700)))]]]]], (7361 ^ _782476) ^ [_905444, _905446, _905448, _905450] : [hBOOL(hAPP(hAPP(c_member(_905444), _905446), c_SetInterval_Oord_OlessThan(_905444, _905448, _905450))), -(hBOOL(hAPP(hAPP(_905448, _905446), _905450)))], (45751 ^ _782476) ^ [_1698425, _1698427] : [-(_1698425 = c_List_Olist_ONil(_1698427)), -(c_List_Olast(_1698427, _1698425) = hAPP(hAPP(c_List_Onth(_1698427), _1698425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698427)), _1698425)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46274 ^ _782476) ^ [_1710076, _1710078] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710076)), hAPP(c_Code__Numeral_Oof__nat, _1710078)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710076), _1710078)))], (28145 ^ _782476) ^ [_1314602, _1314604, _1314606] : [class_Orderings_Olinorder(_1314602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314602), _1314604)), -(hBOOL(hAPP(hAPP(c_member(_1314602), _1314606), _1314604))), -(_1314604 = c_Orderings_Obot__class_Obot(tc_fun(_1314602, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314602, c_Orderings_Oord__class_Omin(_1314602), hAPP(hAPP(c_Set_Oinsert(_1314602), _1314606), _1314604)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314602), _1314606), c_Big__Operators_Olattice_OInf__fin(_1314602, c_Orderings_Oord__class_Omin(_1314602), _1314604)))], (52309 ^ _782476) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (8633 ^ _782476) ^ [_932550, _932552] : [class_Lattices_Osemilattice__inf(_932550), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932550), _932552), _932552) = _932552)], (34470 ^ _782476) ^ [_1434789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434789))))], (39540 ^ _782476) ^ [_1545469, _1545471, _1545473, _1545475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545469, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545471, _1545469), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1545471, _1545469), tc_HOL_Obool)), _1545473), _1545475))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545469, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545471, _1545469), _1545473)), hAPP(c_Relation_ORange(_1545471, _1545469), _1545475)))))], (7373 ^ _782476) ^ [_905689, _905691, _905693, _905695] : [hBOOL(hAPP(hAPP(c_member(_905689), _905691), c_SetInterval_Oord_OatLeast(_905689, _905693, _905695))), -(hBOOL(hAPP(hAPP(_905693, _905695), _905691)))], (10487 ^ _782476) ^ [_973616, _973618, _973620, _973622, _973624] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973616, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973618, tc_fun(_973616, tc_HOL_Obool)), _973620), _973622)), _973624) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973618, tc_fun(_973616, tc_HOL_Obool)), _973620), hAPP(hAPP(c_COMBC(_973618, tc_fun(_973616, tc_HOL_Obool), tc_fun(_973616, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973616, tc_HOL_Obool), tc_fun(tc_fun(_973616, tc_HOL_Obool), tc_fun(_973616, tc_HOL_Obool)), _973618), c_Groups_Ominus__class_Ominus(tc_fun(_973616, tc_HOL_Obool))), _973622)), _973624)))], (39963 ^ _782476) ^ [_1558094, _1558096, _1558098, _1558100, _1558102, _1558104, _1558106] : [class_Rings_Osemiring__0(_1558094), c_Fun_Oinj__on(tc_prod(_1558096, _1558098), _1558094, hAPP(c_Product__Type_Oprod_Oprod__case(_1558096, _1558098, _1558094), hAPP(hAPP(c_COMBC(_1558096, tc_fun(_1558098, _1558094), tc_fun(_1558098, _1558094)), hAPP(hAPP(c_COMBB(tc_fun(_1558094, _1558094), tc_fun(tc_fun(_1558098, _1558094), tc_fun(_1558098, _1558094)), _1558096), c_COMBB(_1558094, _1558094, _1558098)), hAPP(hAPP(c_COMBB(_1558094, tc_fun(_1558094, _1558094), _1558096), c_Groups_Otimes__class_Otimes(_1558094)), _1558100))), _1558102)), hAPP(hAPP(c_Product__Type_OSigma(_1558096, _1558098), _1558104), hAPP(c_COMBK(tc_fun(_1558098, tc_HOL_Obool), _1558096), _1558106))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1558094), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558096, _1558094), _1558100), _1558104)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558098, _1558094), _1558102), _1558106)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558094, _1558094), c_Fun_Oid(_1558094)), hAPP(c_Set_OCollect(_1558094), hAPP(hAPP(c_COMBB(tc_fun(_1558096, tc_HOL_Obool), tc_HOL_Obool, _1558094), c_HOL_OEx(_1558096)), hAPP(hAPP(c_COMBB(tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool)), tc_fun(_1558096, tc_HOL_Obool), _1558094), hAPP(c_COMBB(tc_fun(_1558098, tc_HOL_Obool), tc_HOL_Obool, _1558096), c_HOL_OEx(_1558098))), hAPP(hAPP(c_COMBC(_1558094, tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool)), tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558096, tc_fun(tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool))), tc_fun(tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool)), tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool))), _1558094), c_COMBS(_1558096, tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558096, tc_fun(_1558098, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1558096, tc_fun(tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool))), _1558094), hAPP(c_COMBB(tc_fun(_1558098, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool)), _1558096), c_COMBS(_1558098, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool)), tc_fun(_1558096, tc_fun(_1558098, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1558094), hAPP(c_COMBB(tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1558096), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558098), c_fconj))), hAPP(hAPP(c_COMBC(_1558094, tc_fun(_1558096, tc_fun(_1558098, _1558094)), tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1558098, _1558094), tc_fun(_1558098, tc_HOL_Obool)), tc_fun(tc_fun(_1558096, tc_fun(_1558098, _1558094)), tc_fun(_1558096, tc_fun(_1558098, tc_HOL_Obool))), _1558094), c_COMBB(tc_fun(_1558098, _1558094), tc_fun(_1558098, tc_HOL_Obool), _1558096)), hAPP(hAPP(c_COMBB(tc_fun(_1558094, tc_HOL_Obool), tc_fun(tc_fun(_1558098, _1558094), tc_fun(_1558098, tc_HOL_Obool)), _1558094), c_COMBB(_1558094, tc_HOL_Obool, _1558098)), c_fequal))), hAPP(hAPP(c_COMBC(_1558096, tc_fun(_1558098, _1558094), tc_fun(_1558098, _1558094)), hAPP(hAPP(c_COMBB(tc_fun(_1558094, _1558094), tc_fun(tc_fun(_1558098, _1558094), tc_fun(_1558098, _1558094)), _1558096), c_COMBB(_1558094, _1558094, _1558098)), hAPP(hAPP(c_COMBB(_1558094, tc_fun(_1558094, _1558094), _1558096), c_Groups_Otimes__class_Otimes(_1558094)), _1558100))), _1558102)))))), hAPP(hAPP(c_COMBC(_1558096, tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1558098, tc_HOL_Obool), tc_fun(_1558098, tc_HOL_Obool)), _1558096), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1558098)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558096), c_fconj), hAPP(hAPP(c_COMBC(_1558096, tc_fun(_1558096, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558096)), _1558104)))), hAPP(hAPP(c_COMBC(_1558098, tc_fun(_1558098, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558098)), _1558106))))))))], (26498 ^ _782476) ^ [_1283106, _1283108, _1283110, _1283112] : [class_Orderings_Olinorder(_1283106), 26501 ^ _782476 : [(26502 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283106), _1283108), _1283110)), _1283112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), _1283108), _1283112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), _1283110), _1283112)))], (26512 ^ _782476) ^ [] : [26513 ^ _782476 : [(26516 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), _1283110), _1283112))], (26514 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), _1283108), _1283112))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283106), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283106), _1283108), _1283110)), _1283112)))]]], (52277 ^ _782476) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (9133 ^ _782476) ^ [_944323, _944325] : [class_Orderings_Otop(_944323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944323), _944325), c_Orderings_Otop__class_Otop(_944323))))], (22552 ^ _782476) ^ [_1205367, _1205369] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205367), _1205369) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22555 ^ _782476 : [(22558 ^ _782476) ^ [] : [-(_1205369 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22556 ^ _782476) ^ [] : [-(_1205367 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (16917 ^ _782476) ^ [_1102386, _1102388, _1102390, _1102392, _1102394, _1102396] : [class_Rings_Oordered__ring(_1102386), 16920 ^ _782476 : [(16927 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102386), _1102388), _1102394)), _1102390)), _1102392)), _1102396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), _1102388), _1102390)), _1102392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), _1102394), _1102390)), _1102396))))], (16921 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), _1102388), _1102390)), _1102392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), _1102394), _1102390)), _1102396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102386), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102386), _1102388), _1102394)), _1102390)), _1102392)), _1102396)))]]], (27421 ^ _782476) ^ [_1301120, _1301122] : [class_Orderings_Olinorder(_1301120), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301120), _1301122)), -(c_Big__Operators_Olinorder__class_OMin(_1301120, _1301122) = hAPP(c_Finite__Set_Ofold1(_1301120, c_Orderings_Oord__class_Omin(_1301120)), _1301122))], (43599 ^ _782476) ^ [_1649229, _1649231, _1649233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649229), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649231)), _1649233))), -(hBOOL(hAPP(hAPP(c_member(_1649231), hAPP(hAPP(c_List_Onth(_1649231), _1649233), _1649229)), hAPP(c_List_Oset(_1649231), _1649233))))], (52347 ^ _782476) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (35528 ^ _782476) ^ [_1453752] : [class_Rings_Osemiring__1(_1453752), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453752), c_Groups_Oone__class_Oone(_1453752)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1453752))], (29230 ^ _782476) ^ [_1337352, _1337354, _1337356] : [class_Rings_Olinordered__idom(_1337352), -(hAPP(c_Groups_Oabs__class_Oabs(_1337352), hAPP(hAPP(c_Power_Opower__class_Opower(_1337352), _1337354), _1337356)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337352), hAPP(c_Groups_Oabs__class_Oabs(_1337352), _1337354)), _1337356))], (26818 ^ _782476) ^ [_1288813] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288813), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1288813)], (2202 ^ _782476) ^ [_814685, _814687, _814689, _814691] : [-(c_Nat__Transfer_Otsub(_814691, _814687) = c_Nat__Transfer_Otsub(_814689, _814685)), _814691 = _814689, _814687 = _814685], (28702 ^ _782476) ^ [_1327626, _1327628, _1327630] : [class_Orderings_Olinorder(_1327626), hAPP(_1327628, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327626), 28707 ^ [_1327626, _1327628, _1327630]), 28708 ^ [_1327626, _1327628, _1327630])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327626), hAPP(_1327628, 28707 ^ [_1327626, _1327628, _1327630])), hAPP(_1327628, 28708 ^ [_1327626, _1327628, _1327630])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327626), _1327630)), -(_1327630 = c_Orderings_Obot__class_Obot(tc_fun(_1327626, tc_HOL_Obool))), -(hAPP(_1327628, c_Big__Operators_Olattice_OSup__fin(_1327626, c_Orderings_Oord__class_Omax(_1327626), _1327630)) = c_Big__Operators_Olattice_OSup__fin(_1327626, c_Orderings_Oord__class_Omax(_1327626), hAPP(c_Set_Oimage(_1327626, _1327626, _1327628), _1327630)))], (36134 ^ _782476) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (8677 ^ _782476) ^ [_933422, _933424, _933426] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933422, tc_HOL_Obool)), _933424), _933426) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933422, tc_HOL_Obool)), _933426), _933424))], (3492 ^ _782476) ^ [_834650, _834652, _834654, _834656] : [-(c_Random_Opick(_834656, _834652) = c_Random_Opick(_834654, _834650)), _834656 = _834654, _834652 = _834650], (48337 ^ _782476) ^ [_1754975, _1754977, _1754979, _1754981, _1754983] : [-(c_List_OtakeWhile(_1754975, _1754977, hAPP(hAPP(c_List_Omap(_1754979, _1754975), _1754981), _1754983)) = hAPP(hAPP(c_List_Omap(_1754979, _1754975), _1754981), c_List_OtakeWhile(_1754979, hAPP(c_Fun_Ocomp(_1754975, tc_HOL_Obool, _1754979, _1754977), _1754981), _1754983)))], (47978 ^ _782476) ^ [_1747180, _1747182, _1747184, _1747186, _1747188] : [class_Orderings_Olinorder(_1747180), c_Fun_Oinj__on(_1747182, _1747180, _1747184, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747182, tc_HOL_Obool)), hAPP(c_List_Oset(_1747182), _1747186)), hAPP(c_List_Oset(_1747182), _1747188))), c_List_Olinorder__class_Osorted(_1747180, hAPP(hAPP(c_List_Omap(_1747182, _1747180), _1747184), _1747186)), hBOOL(hAPP(c_List_Odistinct(_1747180), hAPP(hAPP(c_List_Omap(_1747182, _1747180), _1747184), _1747186))), c_List_Olinorder__class_Osorted(_1747180, hAPP(hAPP(c_List_Omap(_1747182, _1747180), _1747184), _1747188)), hBOOL(hAPP(c_List_Odistinct(_1747180), hAPP(hAPP(c_List_Omap(_1747182, _1747180), _1747184), _1747188))), hAPP(c_List_Oset(_1747182), _1747186) = hAPP(c_List_Oset(_1747182), _1747188), -(_1747186 = _1747188)], (28163 ^ _782476) ^ [_1314851, _1314853, _1314855] : [class_Orderings_Olinorder(_1314851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314851), _1314853)), 28170 ^ _782476 : [(28177 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314851, tc_HOL_Obool)), _1314853), hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314851, c_Orderings_Oord__class_Omin(_1314851), hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), _1314853)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314851), _1314855), c_Big__Operators_Olattice_OInf__fin(_1314851, c_Orderings_Oord__class_Omin(_1314851), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314851, tc_HOL_Obool)), _1314853), hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool)))))))], (28171 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314851, tc_HOL_Obool)), _1314853), hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1314851, c_Orderings_Oord__class_Omin(_1314851), hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), _1314853)) = _1314855)]]], (50066 ^ _782476) ^ [_1793318, _1793320, _1793322] : [-(_1793318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793320), c_List_Oreplicate(_1793320, _1793318, _1793322)) = hAPP(hAPP(c_Set_Oinsert(_1793320), _1793322), c_Orderings_Obot__class_Obot(tc_fun(_1793320, tc_HOL_Obool))))], (39722 ^ _782476) ^ [_1550789, _1550791, _1550793, _1550795, _1550797, _1550799] : [class_Groups_Ocomm__monoid__add(_1550789), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550791, _1550789), hAPP(hAPP(c_COMBC(_1550791, tc_fun(_1550793, tc_HOL_Obool), _1550789), hAPP(hAPP(c_COMBB(tc_fun(_1550793, _1550789), tc_fun(tc_fun(_1550793, tc_HOL_Obool), _1550789), _1550791), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550793, _1550789)), _1550795)), _1550797)), _1550799) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1550791, _1550793), _1550789), hAPP(c_Product__Type_Oprod_Oprod__case(_1550791, _1550793, _1550789), _1550795)), hAPP(hAPP(c_Product__Type_OSigma(_1550791, _1550793), _1550799), hAPP(c_COMBK(tc_fun(_1550793, tc_HOL_Obool), _1550791), _1550797))))], (46754 ^ _782476) ^ [_1720900, _1720902, _1720904, _1720906, _1720908] : [c_List_Olist__all2(_1720900, _1720902, _1720904, _1720906, _1720908), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720900)), _1720906) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720902)), _1720908))], (48176 ^ _782476) ^ [_1751508, _1751510, _1751512, _1751514] : [hAPP(c_List_Orev(_1751508), _1751510) = hAPP(hAPP(c_List_Olist_OCons(_1751508), _1751512), _1751514), -(_1751510 = hAPP(hAPP(c_List_Oappend(_1751508), hAPP(c_List_Orev(_1751508), _1751514)), hAPP(hAPP(c_List_Olist_OCons(_1751508), _1751512), c_List_Olist_ONil(_1751508))))], (1272 ^ _782476) ^ [_801576, _801578] : [-(class_Rings_Olinordered__ring(_801576)), _801578 = _801576, class_Rings_Olinordered__ring(_801578)], (46094 ^ _782476) ^ [_1706176, _1706178, _1706180, _1706182, _1706184, _1706186] : [-(hBOOL(hAPP(hAPP(c_member(_1706176), _1706178), hAPP(c_List_Oset(_1706176), _1706180)))), -(hAPP(hAPP(c_List_Omap(_1706176, _1706182), c_Fun_Ofun__upd(_1706176, _1706182, _1706184, _1706178, _1706186)), _1706180) = hAPP(hAPP(c_List_Omap(_1706176, _1706182), _1706184), _1706180))], (9325 ^ _782476) ^ [_949377, _949379, _949381, _949383, _949385] : [9327 ^ _782476 : [(9330 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_949381), hAPP(_949383, 9326 ^ [_949377, _949379, _949381, _949383, _949385])), _949385))], (9328 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949377), 9326 ^ [_949377, _949379, _949381, _949383, _949385]), _949379)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949381, tc_HOL_Obool)), hAPP(c_Set_Oimage(_949377, _949381, _949383), _949379)), _949385)))], (12666 ^ _782476) ^ [_1014690, _1014692] : [class_Complete__Lattice_Ocomplete__lattice(_1014690), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1014690, hAPP(c_COMBK(_1014690, _1014690), _1014692)) = _1014692)], (31035 ^ _782476) ^ [_1370166, _1370168] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1370166), _1370168) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31036 ^ _782476 : [(31045 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370166), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370168), _1370166))], (31039 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370166), _1370168))], (31037 ^ _782476) ^ [] : [_1370168 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (27066 ^ _782476) ^ [_1294135, _1294137, _1294139, _1294141, _1294143] : [class_Groups_Ocomm__monoid__mult(_1294135), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294137, _1294135), hAPP(hAPP(c_COMBS(_1294137, _1294135, _1294135), hAPP(hAPP(c_COMBB(_1294135, tc_fun(_1294135, _1294135), _1294137), c_Groups_Otimes__class_Otimes(_1294135)), _1294139)), _1294141)), _1294143) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294135), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294137, _1294135), _1294139), _1294143)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294137, _1294135), _1294141), _1294143)))], (24939 ^ _782476) ^ [_1248777, _1248779] : [class_Groups_Oordered__ab__group__add__abs(_1248777), -(hAPP(c_Groups_Oabs__class_Oabs(_1248777), hAPP(c_Groups_Oabs__class_Oabs(_1248777), _1248779)) = hAPP(c_Groups_Oabs__class_Oabs(_1248777), _1248779))], (21331 ^ _782476) ^ [_1183024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1183024)), -(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)), _1183024))))], (52179 ^ _782476) ^ [_1838546, _1838548] : [class_Orderings_Otop(_1838546), -(class_Orderings_Otop(tc_fun(_1838548, _1838546)))], (8814 ^ _782476) ^ [_936211, _936213, _936215] : [class_Lattices_Osemilattice__inf(_936211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936211), _936213), _936215)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936211), _936213), _936215) = _936213)], (49444 ^ _782476) ^ [_1779323, _1779325, _1779327, _1779329, _1779331, _1779333, _1779335] : [-(c_New__Random__Sequence_Opos__decr__bind(_1779323, _1779325, _1779327, _1779329, _1779331, _1779333, _1779335) = c_New__DSequence_Opos__decr__bind(_1779323, _1779325, hAPP(hAPP(hAPP(_1779327, _1779331), _1779333), _1779335), hAPP(hAPP(c_COMBC(_1779323, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779325))), hAPP(hAPP(c_COMBC(_1779323, 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(_1779325)))), hAPP(hAPP(c_COMBC(_1779323, 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(_1779325))))), _1779329), _1779331)), _1779333)), _1779335)))], (35560 ^ _782476) ^ [_1454317, _1454319] : [class_Rings_Olinordered__idom(_1454317), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1454317), hAPP(c_Groups_Oabs__class_Oabs(_1454317), _1454319)), 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(_1454317), _1454319), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (11204 ^ _782476) ^ [_988162, _988164, _988166, _988168] : [class_Orderings_Oord(_988162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988162), _988164), _988166)), _988166 = _988168, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988162), _988164), _988168)))], (32988 ^ _782476) ^ [_1407912, _1407914, _1407916] : [class_Int_Onumber(_1407912), 32991 ^ _782476 : [(32998 ^ _782476) ^ [] : [_1407916 = hAPP(c_Int_Onumber__class_Onumber__of(_1407912), _1407914), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407912), _1407914) = _1407916)], (32992 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407912), _1407914) = _1407916, -(_1407916 = hAPP(c_Int_Onumber__class_Onumber__of(_1407912), _1407914))]]], (50024 ^ _782476) ^ [_1792483, _1792485, _1792487, _1792489] : [-(hAPP(hAPP(c_List_Oappend(_1792483), c_List_Oreplicate(_1792483, _1792485, _1792487)), hAPP(hAPP(c_List_Olist_OCons(_1792483), _1792487), _1792489)) = hAPP(hAPP(c_List_Olist_OCons(_1792483), _1792487), hAPP(hAPP(c_List_Oappend(_1792483), c_List_Oreplicate(_1792483, _1792485, _1792487)), _1792489)))], (47558 ^ _782476) ^ [_1739725, _1739727] : [class_Orderings_Olinorder(_1739725), -(c_List_Olinorder__class_Osorted(_1739725, c_List_Olinorder__class_Osort__key(_1739725, _1739725, c_COMBI(_1739725), _1739727)))], (38859 ^ _782476) ^ [_1527869] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1527869) = 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, _1527869)), 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))))))))], (47550 ^ _782476) ^ [_1739602, _1739604] : [class_Orderings_Olinorder(_1739602), -(c_List_Olinorder__class_Osorted(_1739602, hAPP(hAPP(c_List_Olist_OCons(_1739602), _1739604), c_List_Olist_ONil(_1739602))))], (40804 ^ _782476) ^ [_1580012, _1580014, _1580016, _1580018, _1580020] : [_1580012 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1580014, _1580016, _1580012, _1580018), _1580020) = hAPP(c_Product__Type_OPair(_1580014, _1580016), _1580020))], (51322 ^ _782476) ^ [_1820908, _1820910, _1820912, _1820914] : [hBOOL(hAPP(_1820908, _1820910)), hBOOL(hAPP(_1820912, _1820914)), -(hBOOL(hAPP(_1820908, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1820908) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1820912))), 51338 ^ _782476 : [(51341 ^ _782476) ^ [] : [hBOOL(hAPP(_1820912, 51335 ^ [_1820908, _1820910, _1820912, _1820914]))], (51339 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1820908, hAPP(c_Nat_OSuc, 51335 ^ [_1820908, _1820910, _1820912, _1820914]))))]], 51342 ^ _782476 : [(51345 ^ _782476) ^ [] : [hBOOL(hAPP(_1820908, hAPP(c_Nat_OSuc, 51335 ^ [_1820908, _1820910, _1820912, _1820914])))], (51343 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1820912, 51335 ^ [_1820908, _1820910, _1820912, _1820914])))]]], (50275 ^ _782476) ^ [_1797928, _1797930, _1797932] : [-(c_FunDef_OTHE__default(_1797930, _1797932, _1797928) = _1797932), 50277 ^ _782476 : [(50280 ^ _782476) ^ [_1798050] : [hBOOL(hAPP(_1797928, _1798050)), -(_1798050 = 50276 ^ [_1797928, _1797930, _1797932])], (50278 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1797928, 50276 ^ [_1797928, _1797930, _1797932])))]]], (36673 ^ _782476) ^ [_1480121, _1480123, _1480125, _1480127] : [-(hAPP(c_Relation_OImage(_1480121, _1480123, _1480125), hAPP(hAPP(c_Set_Oinsert(_1480121), _1480127), c_Orderings_Obot__class_Obot(tc_fun(_1480121, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1480123), hAPP(hAPP(c_COMBC(_1480123, tc_fun(tc_prod(_1480121, _1480123), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1480121, _1480123), tc_fun(tc_fun(tc_prod(_1480121, _1480123), tc_HOL_Obool), tc_HOL_Obool), _1480123), c_member(tc_prod(_1480121, _1480123))), hAPP(c_Product__Type_OPair(_1480121, _1480123), _1480127))), _1480125)))], (9470 ^ _782476) ^ [_952175, _952177, _952179] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952175, tc_HOL_Obool)), _952177), _952179) = c_Orderings_Obot__class_Obot(tc_fun(_952175, tc_HOL_Obool))), _952177 = c_Orderings_Obot__class_Obot(tc_fun(_952175, tc_HOL_Obool)), _952179 = c_Orderings_Obot__class_Obot(tc_fun(_952175, tc_HOL_Obool))], (32680 ^ _782476) ^ [_1401340, _1401342] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401340, _1401342) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401340), _1401342)), _1401342)))], (34300 ^ _782476) ^ [_1432192, _1432194] : [class_Int_Onumber__ring(_1432192), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432192), _1432194), hAPP(c_Int_Onumber__class_Onumber__of(_1432192), c_Int_OPls)) = _1432194)], (43025 ^ _782476) ^ [_1633174, _1633176, _1633178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633174, _1633174), tc_HOL_Obool)), _1633176), _1633178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633174), tc_List_Olist(_1633174)), tc_HOL_Obool)), c_List_Olistrel1(_1633174, _1633176)), c_List_Olistrel1(_1633174, _1633178))))], (40177 ^ _782476) ^ [_1564489, _1564491, _1564493, _1564495] : [-(c_Product__Type_Oapfst(_1564489, _1564491, _1564493, _1564495) = c_Product__Type_Omap__pair(_1564489, _1564491, _1564493, _1564493, _1564495, c_Fun_Oid(_1564493)))], (48357 ^ _782476) ^ [_1755349, _1755351, _1755353, _1755355] : [-(hBOOL(hAPP(_1755349, _1755351))), -(c_List_OtakeWhile(_1755353, _1755349, hAPP(hAPP(c_List_Olist_OCons(_1755353), _1755351), _1755355)) = c_List_Olist_ONil(_1755353))], (3674 ^ _782476) ^ [_837549, _837551] : [_837551 = _837549, -(c_Orderings_Oord__class_Omax(_837551) = c_Orderings_Oord__class_Omax(_837549))], (5744 ^ _782476) ^ [_873249, _873251] : [hAPP(_873249, 5745 ^ [_873249, _873251]) = hAPP(_873251, 5745 ^ [_873249, _873251]), -(_873249 = _873251)], (4974 ^ _782476) ^ [_858425, _858427, _858429, _858431] : [-(c_List_Olexord(_858431, _858427) = c_List_Olexord(_858429, _858425)), _858431 = _858429, _858427 = _858425], (49840 ^ _782476) ^ [_1789387, _1789389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789387), _1789389)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789387, _1789389) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (28904 ^ _782476) ^ [_1331458, _1331460] : [class_Rings_Odivision__ring(_1331458), -(_1331460 = c_Groups_Ozero__class_Ozero(_1331458)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331458), _1331460), _1331460) = c_Groups_Oone__class_Oone(_1331458))], (34248 ^ _782476) ^ [_1431413, _1431415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431413), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431415)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431415))], (34862 ^ _782476) ^ [_1441300, _1441302] : [hAPP(c_Nat_OSuc, _1441300) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441302), -(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(_1441302))), 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)), _1441300))))))], (45132 ^ _782476) ^ [_1685238, _1685240, _1685242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685238)), _1685242)), _1685240)), -(hAPP(hAPP(c_List_Odrop(_1685238), _1685240), _1685242) = c_List_Olist_ONil(_1685238))], (35020 ^ _782476) ^ [_1444699, _1444701, _1444703, _1444705] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444699, _1444701, _1444703), hAPP(c_Nat_OSuc, _1444705)) = hAPP(hAPP(_1444703, _1444705), hAPP(c_Nat_Onat_Onat__rec(_1444699, _1444701, _1444703), _1444705)))], (24604 ^ _782476) ^ [_1242522, _1242524, _1242526] : [class_Rings_Oring__1(_1242522), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1242524), _1242526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1242522), hAPP(c_Int_Oring__1__class_Oof__int(_1242522), _1242524)), hAPP(c_Int_Oring__1__class_Oof__int(_1242522), _1242526)))], (44660 ^ _782476) ^ [_1674172, _1674174, _1674176, _1674178, _1674180, _1674182] : [hAPP(hAPP(c_List_Olist_OCons(_1674172), _1674174), _1674176) = _1674178, _1674180 = hAPP(hAPP(c_List_Oappend(_1674172), _1674176), _1674182), -(hAPP(hAPP(c_List_Olist_OCons(_1674172), _1674174), _1674180) = hAPP(hAPP(c_List_Oappend(_1674172), _1674178), _1674182))], (44438 ^ _782476) ^ [_1668698, _1668700, _1668702] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668698)), -(c_List_Osublist(_1668700, hAPP(hAPP(c_List_Olist_OCons(_1668700), _1668702), c_List_Olist_ONil(_1668700)), _1668698) = hAPP(hAPP(c_List_Olist_OCons(_1668700), _1668702), c_List_Olist_ONil(_1668700)))], (17283 ^ _782476) ^ [] : [-(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)))], (13528 ^ _782476) ^ [_1032896] : [class_Lattices_Osemilattice__inf(_1032896), -(c_Finite__Set_Ofun__left__comm__idem(_1032896, _1032896, c_Lattices_Osemilattice__inf__class_Oinf(_1032896)))], (41402 ^ _782476) ^ [_1594193, _1594195, _1594197] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594193, _1594193), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1594193, _1594193), _1594195)), c_Transitive__Closure_Ortrancl(_1594193, _1594195)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594193, _1594193), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594193, _1594193)), hAPP(hAPP(c_Product__Type_OPair(_1594193, _1594193), _1594197), _1594197)), c_Transitive__Closure_Otrancl(_1594193, _1594195)))], (46342 ^ _782476) ^ [_1711448, _1711450, _1711452, _1711454] : [class_Groups_Ocomm__monoid__add(_1711448), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711448), _1711450), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711452, _1711454))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1711448), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711448), _1711450), c_List_Oupto(_1711452, _1711454))))], (13498 ^ _782476) ^ [_1032361, _1032363, _1032365, _1032367, _1032369] : [c_Finite__Set_Ofun__left__comm__idem(_1032361, _1032363, _1032365), -(hAPP(hAPP(_1032365, _1032367), hAPP(hAPP(_1032365, _1032367), _1032369)) = hAPP(hAPP(_1032365, _1032367), _1032369))], (14917 ^ _782476) ^ [_1060930, _1060932, _1060934, _1060936, _1060938, _1060940, _1060942, _1060944] : [c_Finite__Set_Ofolding__image__simple(_1060930, _1060932, _1060934, _1060936, _1060938, _1060940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060932), _1060942)), -(hBOOL(hAPP(hAPP(c_member(_1060932), _1060944), _1060942))), -(hAPP(_1060940, hAPP(hAPP(c_Set_Oinsert(_1060932), _1060944), _1060942)) = hAPP(hAPP(_1060934, hAPP(_1060938, _1060944)), hAPP(_1060940, _1060942)))], (42955 ^ _782476) ^ [_1630781, _1630783, _1630785, _1630787, _1630789, _1630791] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630781), tc_List_Olist(_1630781))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630781), tc_List_Olist(_1630781)), hAPP(hAPP(c_List_Olist_OCons(_1630781), _1630783), _1630785)), hAPP(hAPP(c_List_Olist_OCons(_1630781), _1630787), _1630789))), c_List_Olex(_1630781, _1630791))), 42960 ^ _782476 : [(42963 ^ _782476) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630781)), _1630785) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630781)), _1630789))], (42961 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630781, _1630781)), hAPP(hAPP(c_Product__Type_OPair(_1630781, _1630781), _1630783), _1630787)), _1630791)))]], 42964 ^ _782476 : [(42967 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630781), tc_List_Olist(_1630781))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630781), tc_List_Olist(_1630781)), _1630785), _1630789)), c_List_Olex(_1630781, _1630791))))], (42965 ^ _782476) ^ [] : [-(_1630783 = _1630787)]]], (25652 ^ _782476) ^ [_1262416, _1262418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262416), hAPP(c_Set_OCollect(_1262416), _1262418))), 25655 ^ _782476 : [(25662 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262416), c_Orderings_Otop__class_Otop(tc_fun(_1262416, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262416), hAPP(c_Set_OCollect(_1262416), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262416), c_fNot), _1262418)))))], (25656 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262416), hAPP(c_Set_OCollect(_1262416), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262416), c_fNot), _1262418)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262416), c_Orderings_Otop__class_Otop(tc_fun(_1262416, tc_HOL_Obool)))))]]], (44320 ^ _782476) ^ [_1666456, _1666458] : [hAPP(c_List_Oset(_1666456), _1666458) = c_Orderings_Obot__class_Obot(tc_fun(_1666456, tc_HOL_Obool)), -(_1666458 = c_List_Olist_ONil(_1666456))], (35344 ^ _782476) ^ [_1450387] : [-(c_Int_Opred(c_Int_OBit1(_1450387)) = c_Int_OBit0(_1450387))], (27511 ^ _782476) ^ [_1302969, _1302971, _1302973, _1302975] : [class_Groups_Ocomm__monoid__mult(_1302969), 27514 ^ _782476 : [(27521 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1302971), _1302973))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302971, _1302969), _1302975), _1302973) = c_Groups_Oone__class_Oone(_1302969))], (27515 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302971), _1302973)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302971, _1302969), _1302975), _1302973) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302969, _1302971, c_Groups_Otimes__class_Otimes(_1302969)), _1302975), c_Groups_Oone__class_Oone(_1302969)), _1302973))]]], (16621 ^ _782476) ^ [_1095703, _1095705, _1095707, _1095709] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095703), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095703), _1095705), _1095707)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095703), _1095709), _1095707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095703), _1095705), _1095709)))], (9921 ^ _782476) ^ [_961326, _961328, _961330, _961332, _961334] : [-(_961326 = c_Orderings_Obot__class_Obot(tc_fun(_961328, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961328, tc_fun(_961330, tc_HOL_Obool)), _961326), hAPP(hAPP(c_COMBB(tc_fun(_961330, tc_HOL_Obool), tc_fun(_961330, tc_HOL_Obool), _961328), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961330, tc_HOL_Obool)), _961332)), _961334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961330, tc_HOL_Obool)), _961332), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961328, tc_fun(_961330, tc_HOL_Obool)), _961326), _961334)))], (22276 ^ _782476) ^ [_1200834, _1200836, _1200838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200834), _1200836)), -(hBOOL(hAPP(hAPP(c_member(_1200834), _1200838), _1200836))), -(hAPP(c_Finite__Set_Ocard(_1200834), hAPP(hAPP(c_Set_Oinsert(_1200834), _1200838), _1200836)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200834), _1200836)))], (15584 ^ _782476) ^ [_1073861, _1073863, _1073865] : [class_Groups_Oab__semigroup__mult(_1073861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073861), _1073863)), -(_1073863 = c_Orderings_Obot__class_Obot(tc_fun(_1073861, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073861), _1073865)), -(_1073865 = c_Orderings_Obot__class_Obot(tc_fun(_1073861, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073861, tc_HOL_Obool)), _1073863), _1073865) = c_Orderings_Obot__class_Obot(tc_fun(_1073861, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1073861, c_Groups_Otimes__class_Otimes(_1073861)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073861, tc_HOL_Obool)), _1073863), _1073865)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073861), hAPP(c_Finite__Set_Ofold1(_1073861, c_Groups_Otimes__class_Otimes(_1073861)), _1073863)), hAPP(c_Finite__Set_Ofold1(_1073861, c_Groups_Otimes__class_Otimes(_1073861)), _1073865)))], (19130 ^ _782476) ^ [_1142616, _1142618, _1142620] : [class_Rings_Olinordered__semiring__strict(_1142616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142616), c_Groups_Ozero__class_Ozero(_1142616)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142616), _1142618), _1142620))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142616), c_Groups_Ozero__class_Ozero(_1142616)), _1142618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142616), c_Groups_Ozero__class_Ozero(_1142616)), _1142620)))], (50755 ^ _782476) ^ [_1810010, _1810012, _1810014, _1810016] : [c_Predicate_Osymp(_1810010, _1810012), hBOOL(hAPP(hAPP(_1810012, _1810014), _1810016)), -(hBOOL(hAPP(hAPP(_1810012, _1810016), _1810014)))], (22256 ^ _782476) ^ [_1200470, _1200472] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1200470, _1200472)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200472), hAPP(c_Nat_OSuc, _1200470)))], (13876 ^ _782476) ^ [_1040041, _1040043, _1040045, _1040047] : [c_Fun_Oinj__on(_1040041, _1040043, _1040045, _1040047), -(c_Fun_Obij__betw(_1040041, _1040043, _1040045, _1040047, hAPP(c_Set_Oimage(_1040041, _1040043, _1040045), _1040047)))], (17465 ^ _782476) ^ [_1113723, _1113725, _1113727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113723), _1113725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113725), _1113727))))], (590 ^ _782476) ^ [_791477, _791479] : [-(class_Lattices_Oab__semigroup__idem__mult(_791477)), _791479 = _791477, class_Lattices_Oab__semigroup__idem__mult(_791479)], (41861 ^ _782476) ^ [_1605707, _1605709, _1605711, _1605713, _1605715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605707, _1605707)), hAPP(hAPP(c_Product__Type_OPair(_1605707, _1605707), _1605709), _1605711)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605707, _1605707), tc_HOL_Obool), _1605713), _1605715))), 41866 ^ _782476 : [(41869 ^ _782476) ^ [] : [-(_1605709 = _1605711)], (41867 ^ _782476) ^ [] : [-(_1605713 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41872 ^ _782476 : [(41877 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605707, _1605707)), hAPP(hAPP(c_Product__Type_OPair(_1605707, _1605707), 41870 ^ [_1605707, _1605709, _1605711, _1605713, _1605715]), _1605711)), _1605715)))], (41875 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605707, _1605707)), hAPP(hAPP(c_Product__Type_OPair(_1605707, _1605707), _1605709), 41870 ^ [_1605707, _1605709, _1605711, _1605713, _1605715])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605707, _1605707), tc_HOL_Obool), 41871 ^ [_1605707, _1605709, _1605711, _1605713, _1605715]), _1605715))))], (41873 ^ _782476) ^ [] : [-(_1605713 = hAPP(c_Nat_OSuc, 41871 ^ [_1605707, _1605709, _1605711, _1605713, _1605715]))]]], (29840 ^ _782476) ^ [_1348761, _1348763, _1348765, _1348767] : [class_Fields_Olinordered__field__inverse__zero(_1348761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348761), _1348763), _1348765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348761), _1348767), c_Groups_Ozero__class_Ozero(_1348761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348761), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348761), _1348765), _1348767)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348761), _1348763), _1348767))))], (41847 ^ _782476) ^ [_1605358, _1605360, _1605362] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605358, _1605358)), _1605360), c_Transitive__Closure_Otrancl(_1605358, _1605362)))), 41848 ^ _782476 : [(41849 ^ _782476) ^ [_1605437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605437)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605358, _1605358)), _1605360), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605358, _1605358), tc_HOL_Obool), _1605437), _1605362)))]]], (19504 ^ _782476) ^ [_1149194, _1149196] : [class_Groups_Ogroup__add(_1149194), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149194), hAPP(c_Groups_Ouminus__class_Ouminus(_1149194), _1149196)), _1149196) = c_Groups_Ozero__class_Ozero(_1149194))], (46118 ^ _782476) ^ [_1706615, _1706617] : [class_Groups_Oordered__ab__group__add__abs(_1706615), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706615), hAPP(c_Groups_Oabs__class_Oabs(_1706615), hAPP(c_List_Omonoid__add__class_Olistsum(_1706615), _1706617))), hAPP(c_List_Omonoid__add__class_Olistsum(_1706615), hAPP(hAPP(c_List_Omap(_1706615, _1706615), c_Groups_Oabs__class_Oabs(_1706615)), _1706617)))))], (8705 ^ _782476) ^ [_934094] : [-(hAPP(c_Set_OPow(_934094), c_Orderings_Otop__class_Otop(tc_fun(_934094, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934094, tc_HOL_Obool), tc_HOL_Obool)))], (33918 ^ _782476) ^ [_1425610, _1425612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425610), _1425612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425610)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425612))))], (10974 ^ _782476) ^ [_984819, _984821, _984823, _984825] : [c_Orderings_Oorder__class_Omono(tc_fun(_984819, tc_HOL_Obool), tc_fun(_984819, tc_HOL_Obool), _984821), hBOOL(hAPP(hAPP(c_member(_984819), _984823), _984825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984819, tc_HOL_Obool)), _984825), hAPP(_984821, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984819, tc_HOL_Obool)), _984825), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984819, tc_HOL_Obool), _984821))))), -(hBOOL(hAPP(hAPP(c_member(_984819), _984823), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984819, tc_HOL_Obool), _984821))))], (47064 ^ _782476) ^ [_1727308, _1727310] : [class_Orderings_Olinorder(_1727308), -(c_List_Olinorder__class_Osort__key(_1727308, _1727308, c_COMBI(_1727308), _1727310) = hAPP(c_List_Ofoldl(tc_List_Olist(_1727308), _1727308, hAPP(c_COMBC(_1727308, tc_List_Olist(_1727308), tc_List_Olist(_1727308)), c_List_Olinorder__class_Oinsort__key(_1727308, _1727308, c_COMBI(_1727308))), c_List_Olist_ONil(_1727308)), _1727310))], (49886 ^ _782476) ^ [_1790064, _1790066, _1790068] : [_1790066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1790064) = c_List_Oreplicate(_1790064, _1790066, _1790068))], (13342 ^ _782476) ^ [_1028989, _1028991, _1028993, _1028995, _1028997, _1028999] : [hBOOL(hAPP(hAPP(c_member(_1028989), _1028991), _1028993)), 13345 ^ _782476 : [(13352 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028989), _1028995), _1028993))), -(hAPP(c_Set_Ovimage(_1028997, _1028989, hAPP(hAPP(c_COMBC(_1028997, _1028989, _1028989), hAPP(hAPP(c_COMBC(_1028997, _1028989, tc_fun(_1028989, _1028989)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028989, tc_fun(_1028989, _1028989)), _1028997), c_If(_1028989)), hAPP(hAPP(c_COMBC(_1028997, tc_fun(_1028997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028997)), _1028999))), _1028991)), _1028995)), _1028993) = _1028999)], (13346 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1028989), _1028995), _1028993)), -(hAPP(c_Set_Ovimage(_1028997, _1028989, hAPP(hAPP(c_COMBC(_1028997, _1028989, _1028989), hAPP(hAPP(c_COMBC(_1028997, _1028989, tc_fun(_1028989, _1028989)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028989, tc_fun(_1028989, _1028989)), _1028997), c_If(_1028989)), hAPP(hAPP(c_COMBC(_1028997, tc_fun(_1028997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028997)), _1028999))), _1028991)), _1028995)), _1028993) = c_Orderings_Otop__class_Otop(tc_fun(_1028997, tc_HOL_Obool)))]]], (22922 ^ _782476) ^ [_1212290, _1212292, _1212294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212290), _1212292)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212294), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212292), _1212290))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212294), _1212290)), hAPP(c_Nat_OSuc, _1212292)))], (44737 ^ _782476) ^ [_1675874, _1675876, _1675878, _1675880, _1675882] : [-(hAPP(hAPP(c_List_Oappend(_1675874), _1675876), _1675878) = hAPP(hAPP(c_List_Oappend(_1675874), _1675880), _1675882)), 44738 ^ _782476 : [(44745 ^ _782476) ^ [_1676098] : [hAPP(hAPP(c_List_Oappend(_1675874), _1675876), _1676098) = _1675880, _1675878 = hAPP(hAPP(c_List_Oappend(_1675874), _1676098), _1675882)], (44739 ^ _782476) ^ [_1675986] : [_1675876 = hAPP(hAPP(c_List_Oappend(_1675874), _1675880), _1675986), hAPP(hAPP(c_List_Oappend(_1675874), _1675986), _1675878) = _1675882]]], (9114 ^ _782476) ^ [_943864, _943866, _943868, _943870] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943864, tc_fun(_943866, tc_HOL_Obool)), _943868), _943870) = c_Orderings_Otop__class_Otop(tc_fun(_943866, tc_HOL_Obool)), 9117 ^ _782476 : [(9118 ^ _782476) ^ [_943980] : [hBOOL(hAPP(hAPP(c_member(_943864), _943980), _943868)), -(hAPP(_943870, _943980) = c_Orderings_Otop__class_Otop(tc_fun(_943866, tc_HOL_Obool)))]]], (22334 ^ _782476) ^ [_1201815, _1201817, _1201819, _1201821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201815), _1201817)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201819), _1201821)), 22341 ^ _782476 : [(22348 ^ _782476) ^ [] : [hAPP(c_Finite__Set_Ocard(_1201815), _1201817) = hAPP(c_Finite__Set_Ocard(_1201819), _1201821), -(c_Fun_Obij__betw(_1201815, _1201819, 22351 ^ [_1201815, _1201817, _1201819, _1201821], _1201817, _1201821))], (22342 ^ _782476) ^ [] : [22343 ^ _782476 : [(22344 ^ _782476) ^ [_1202004] : [c_Fun_Obij__betw(_1201815, _1201819, _1202004, _1201817, _1201821)]], -(hAPP(c_Finite__Set_Ocard(_1201815), _1201817) = hAPP(c_Finite__Set_Ocard(_1201819), _1201821))]]], (34444 ^ _782476) ^ [_1434391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434391), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434391))], (32819 ^ _782476) ^ [_1404759, _1404761, _1404763, _1404765, _1404767] : [-(hAPP(c_Relation_OImage(_1404759, _1404761, _1404763), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404759, tc_HOL_Obool)), _1404765), _1404767)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404761, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404759, _1404761, _1404763), _1404765)), hAPP(c_Relation_OImage(_1404759, _1404761, _1404763), _1404767)))], (9524 ^ _782476) ^ [_953229, _953231, _953233, _953235, _953237] : [class_Orderings_Oorder(_953229), class_Orderings_Oorder(_953231), c_Orderings_Oorder__class_Omono(_953231, _953229, _953233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953231), _953235), _953237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953229), hAPP(_953233, _953235)), hAPP(_953233, _953237))))], (27050 ^ _782476) ^ [_1293847] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1293847) = c_Orderings_Oord__class_Omax(_1293847)), class_Lattices_Osemilattice__sup(_1293847), class_Orderings_Olinorder(_1293847)], (21391 ^ _782476) ^ [_1184103, _1184105] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184103) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184105), -(_1184103 = _1184105)], (13012 ^ _782476) ^ [_1021109, _1021111, _1021113, _1021115] : [c_Fun_Oinj__on(_1021109, _1021111, _1021113, c_Orderings_Otop__class_Otop(tc_fun(_1021109, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021111, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021109, _1021111, _1021113), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021109, tc_HOL_Obool)), _1021115))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021111, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021109, _1021111, _1021113), _1021115)))))], (41495 ^ _782476) ^ [_1596592, _1596594, _1596596, _1596598, _1596600] : [-(hAPP(c_Relation_Oconverse(_1596592, _1596594), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596596, tc_fun(tc_prod(_1596592, _1596594), tc_HOL_Obool)), _1596598), _1596600)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596596, tc_fun(tc_prod(_1596594, _1596592), tc_HOL_Obool)), _1596598), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1596592, _1596594), tc_HOL_Obool), tc_fun(tc_prod(_1596594, _1596592), tc_HOL_Obool), _1596596), c_Relation_Oconverse(_1596592, _1596594)), _1596600)))], (51382 ^ _782476) ^ [_1822059, _1822061, _1822063, _1822065] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1822059, _1822061, _1822063), c_Product__Type_Ocurry(_1822059, _1822061, _1822063, _1822065)) = _1822065)], (30422 ^ _782476) ^ [_1359174, _1359176, _1359178, _1359180] : [class_Fields_Olinordered__field(_1359174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359174), c_Groups_Ozero__class_Ozero(_1359174)), _1359176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359174), _1359178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359174), _1359180), _1359176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359174), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359174), _1359178), _1359176)), _1359180)))], (21457 ^ _782476) ^ [_1185176] : [21459 ^ _782476 : [(21462 ^ _782476) ^ [] : [hBOOL(hAPP(_1185176, 21458 ^ [_1185176]))], (21460 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21458 ^ [_1185176])))]], 21463 ^ _782476 : [(21464 ^ _782476) ^ [_1185303] : [-(hBOOL(hAPP(_1185176, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185303))))]]], (36146 ^ _782476) ^ [_1465033, _1465035] : [class_Int_Onumber__ring(_1465033), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465033), hAPP(c_Int_Onumber__class_Onumber__of(_1465033), c_Int_OMin)), _1465035) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465033), _1465035))], (9452 ^ _782476) ^ [_951805, _951807, _951809, _951811] : [_951811 = c_Orderings_Obot__class_Obot(tc_fun(_951805, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_951805, _951807, _951809), _951811) = c_Orderings_Obot__class_Obot(tc_fun(_951807, tc_HOL_Obool)))], (1352 ^ _782476) ^ [_802576, _802578] : [-(class_Int_Oring__char__0(_802576)), _802578 = _802576, class_Int_Oring__char__0(_802578)], (50521 ^ _782476) ^ [_1804166, _1804168] : [-(hBOOL(hAPP(_1804168, 50528 ^ [_1804166, _1804168]))), 50522 ^ _782476 : [(50523 ^ _782476) ^ [_1804227] : [hBOOL(hAPP(hAPP(c_member(_1804166), _1804227), c_Orderings_Otop__class_Otop(tc_fun(_1804166, tc_HOL_Obool)))), hBOOL(hAPP(_1804168, _1804227))]]], (4354 ^ _782476) ^ [_848617, _848619, _848621, _848623] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848623, _848619) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848621, _848617)), _848623 = _848621, _848619 = _848617], (20916 ^ _782476) ^ [_1175703, _1175705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175703)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175705))))], (35372 ^ _782476) ^ [_1450800] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1450800)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1450800)), 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))))], (17894 ^ _782476) ^ [_1121941, _1121943, _1121945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121941), _1121943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121943), _1121945))))], (50200 ^ _782476) ^ [_1796333, _1796335, _1796337] : [c_List_Olist__ex1(_1796333, _1796335, _1796337), 50204 ^ _782476 : [(50209 ^ _782476) ^ [_1796579] : [-(_1796579 = 50203 ^ [_1796333, _1796335, _1796337]), hBOOL(hAPP(hAPP(c_member(_1796333), _1796579), hAPP(c_List_Oset(_1796333), _1796337))), hBOOL(hAPP(_1796335, _1796579))], (50207 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1796335, 50203 ^ [_1796333, _1796335, _1796337])))], (50205 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796333), 50203 ^ [_1796333, _1796335, _1796337]), hAPP(c_List_Oset(_1796333), _1796337))))]]], (40885 ^ _782476) ^ [_1581355, _1581357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1581355)), -(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(_1581355), _1581357))), _1581355)))], (4726 ^ _782476) ^ [_854461, _854463, _854465, _854467, _854469, _854471, _854473, _854475, _854477, _854479] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854479, _854475, _854471, _854467, _854463) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854477, _854473, _854469, _854465, _854461)), _854479 = _854477, _854475 = _854473, _854471 = _854469, _854467 = _854465, _854463 = _854461], (24150 ^ _782476) ^ [_1235192, _1235194] : [c_Nat__Transfer_Ois__nat(_1235192), c_Nat__Transfer_Ois__nat(_1235194), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235192), _1235194)))], (28436 ^ _782476) ^ [_1321819, _1321821, _1321823] : [class_Orderings_Olinorder(_1321819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321819), _1321821)), -(hBOOL(hAPP(hAPP(c_member(_1321819), _1321823), _1321821))), -(_1321821 = c_Orderings_Obot__class_Obot(tc_fun(_1321819, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321819, c_Orderings_Oord__class_Omax(_1321819), hAPP(hAPP(c_Set_Oinsert(_1321819), _1321823), _1321821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321819), _1321823), c_Big__Operators_Olattice_OSup__fin(_1321819, c_Orderings_Oord__class_Omax(_1321819), _1321821)))], (48693 ^ _782476) ^ [_1762393, _1762395, _1762397, _1762399] : [-(_1762393 = _1762395), -(hAPP(c_List_OremoveAll(_1762397, _1762393), hAPP(hAPP(c_List_Olist_OCons(_1762397), _1762395), _1762399)) = hAPP(hAPP(c_List_Olist_OCons(_1762397), _1762395), hAPP(c_List_OremoveAll(_1762397, _1762393), _1762399)))], (17421 ^ _782476) ^ [_1112888, _1112890, _1112892] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112888), _1112890)), _1112892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112890), _1112892)))], (3568 ^ _782476) ^ [_835802, _835804, _835806, _835808, _835810, _835812, _835814, _835816] : [-(c_List_Olinorder__class_Osort__key(_835816, _835812, _835808, _835804) = c_List_Olinorder__class_Osort__key(_835814, _835810, _835806, _835802)), _835816 = _835814, _835812 = _835810, _835808 = _835806, _835804 = _835802], (37746 ^ _782476) ^ [_1500952, _1500954, _1500956, _1500958, _1500960] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500952, _1500954, _1500956), _1500958), _1500960) = hAPP(hAPP(_1500958, hAPP(c_Product__Type_Ofst(_1500952, _1500954), _1500960)), hAPP(c_Product__Type_Osnd(_1500952, _1500954), _1500960)))], (42383 ^ _782476) ^ [_1617083, _1617085, _1617087] : [class_Orderings_Olinorder(_1617083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617083), _1617085)), -(hBOOL(hAPP(hAPP(c_member(_1617083), _1617087), _1617085))), -(c_Big__Operators_Olattice_OInf__fin(_1617083, c_Orderings_Oord__class_Omin(_1617083), hAPP(hAPP(c_Set_Oinsert(_1617083), _1617087), _1617085)) = hAPP(hAPP(c_Finite__Set_Ofold(_1617083, _1617083, c_Orderings_Oord__class_Omin(_1617083)), _1617087), _1617085))], (47479 ^ _782476) ^ [_1737893, _1737895, _1737897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737893), _1737895)), _1737897)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1737893, _1737897)), _1737895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737893), _1737895))], (14008 ^ _782476) ^ [_1042799, _1042801, _1042803, _1042805] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042799, _1042801, hAPP(hAPP(c_Set_Oinsert(_1042799), _1042803), c_Orderings_Obot__class_Obot(tc_fun(_1042799, tc_HOL_Obool)))), _1042805)), -(_1042803 = _1042805)], (34954 ^ _782476) ^ [_1443498, _1443500, _1443502, _1443504, _1443506] : [-(hAPP(c_Nat_Onat_Onat__rec(_1443498, _1443500, _1443502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443504)), _1443506)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443498), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443504))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443498, _1443498), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443498, tc_fun(_1443498, _1443498)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443498, tc_fun(_1443498, _1443498)), tc_Int_Oint), c_If(_1443498)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1443498, _1443500, _1443502), _1443506))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443498, _1443498), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1443498, _1443498), tc_Int_Oint), _1443502), 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)), _1443506))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443498, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1443498, _1443500, _1443502)), 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)), _1443506))))))], (30436 ^ _782476) ^ [_1359443, _1359445, _1359447, _1359449] : [class_Fields_Olinordered__field(_1359443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359443), c_Groups_Ozero__class_Ozero(_1359443)), _1359445)), 30443 ^ _782476 : [(30450 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359443), _1359447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359443), _1359449), _1359445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359443), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359443), _1359447), _1359445)), _1359449)))], (30444 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359443), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359443), _1359447), _1359445)), _1359449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359443), _1359447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359443), _1359449), _1359445))))]]], (36000 ^ _782476) ^ [_1462951] : [c_Int_OMin = c_Int_OBit0(_1462951)], (30863 ^ _782476) ^ [_1367580, _1367582] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367580)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367582)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367580), _1367582))], (34312 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10651 ^ _782476) ^ [_977434, _977436, _977438, _977440] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977434, tc_HOL_Obool)), _977436), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977434, tc_HOL_Obool)), _977438), _977440)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977434, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977434, tc_HOL_Obool)), _977436), _977438)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977434, tc_HOL_Obool)), _977436), _977440)))], (39730 ^ _782476) ^ [_1551113, _1551115, _1551117, _1551119] : [hAPP(hAPP(c_Product__Type_OSigma(_1551113, _1551115), _1551117), hAPP(c_COMBK(tc_fun(_1551115, tc_HOL_Obool), _1551113), _1551119)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551113, _1551115), tc_HOL_Obool)), -(_1551117 = c_Orderings_Obot__class_Obot(tc_fun(_1551113, tc_HOL_Obool))), -(_1551119 = c_Orderings_Obot__class_Obot(tc_fun(_1551115, tc_HOL_Obool)))], (46886 ^ _782476) ^ [_1723838, _1723840] : [_1723840 = c_List_Olist_ONil(_1723838), -(c_List_Oremdups(_1723838, _1723840) = c_List_Olist_ONil(_1723838))], (19280 ^ _782476) ^ [_1145339, _1145341, _1145343] : [class_Rings_Osemiring__1(_1145339), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145341), _1145343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145339), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145339), _1145341)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145339), _1145343)))], (43892 ^ _782476) ^ [_1657755, _1657757, _1657759, _1657761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657755), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657757)), _1657759))), -(hAPP(hAPP(c_List_Onth(_1657757), hAPP(hAPP(c_List_Olist__update(_1657757, _1657759), _1657755), _1657761)), _1657755) = _1657761)], (9057 ^ _782476) ^ [_941698, _941700, _941702, _941704, _941706, _941708] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941698, tc_fun(_941700, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941702, _941698, _941704), _941706)), _941708) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941702, tc_fun(_941700, tc_HOL_Obool)), _941706), hAPP(hAPP(c_COMBB(_941698, tc_fun(_941700, tc_HOL_Obool), _941702), _941708), _941704)))], (1642 ^ _782476) ^ [_806201, _806203] : [-(class_Groups_Oordered__comm__monoid__add(_806201)), _806203 = _806201, class_Groups_Oordered__comm__monoid__add(_806203)], (10255 ^ _782476) ^ [_968243, _968245, _968247, _968249] : [hBOOL(hAPP(hAPP(c_member(_968243), _968245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968243, tc_HOL_Obool)), _968247), _968249))), -(hBOOL(hAPP(hAPP(c_member(_968243), _968245), _968247)))], (8440 ^ _782476) ^ [_928643, _928645] : [class_Groups_Oordered__ab__group__add(_928643), -(hAPP(c_Set_Oimage(_928643, _928643, c_Groups_Ouminus__class_Ouminus(_928643)), hAPP(c_SetInterval_Oord__class_OlessThan(_928643), _928645)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_928643), hAPP(c_Groups_Ouminus__class_Ouminus(_928643), _928645)))], (33926 ^ _782476) ^ [_1425762, _1425764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425762)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425762), _1425764)))], (20529 ^ _782476) ^ [_1168703, _1168705, _1168707] : [class_Rings_Osemiring__1(_1168703), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1168703, _1168705, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168707) = _1168707)], (52101 ^ _782476) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (41370 ^ _782476) ^ [_1593471, _1593473] : [-(c_Relation_Orefl__on(_1593471, c_Orderings_Otop__class_Otop(tc_fun(_1593471, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593471, _1593471), tc_HOL_Obool)), _1593473), c_Relation_OId(_1593471))))], (50668 ^ _782476) ^ [_1807845, _1807847, _1807849, _1807851] : [class_Complete__Lattice_Ocomplete__lattice(_1807845), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1807847, _1807845), _1807849), _1807851) = c_Complete__Lattice_OInf__class_OInf(_1807845, hAPP(c_Set_OCollect(_1807845), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807847, _1807845), tc_HOL_Obool), tc_HOL_Obool, _1807845), c_HOL_OEx(tc_fun(_1807847, _1807845))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807847, _1807845), tc_HOL_Obool), tc_fun(tc_fun(_1807847, _1807845), tc_HOL_Obool), _1807845), hAPP(c_COMBS(tc_fun(_1807847, _1807845), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, 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_1042059, _1042061, _1042063, _1042065] : [-(hBOOL(hAPP(hAPP(c_member(_1042055), _1042057), _1042059))), -(hAPP(c_Fun_Ooverride__on(_1042055, _1042061, _1042063, _1042065, _1042059), _1042057) = hAPP(_1042063, _1042057))], (25498 ^ _782476) ^ [_1258942, _1258944, _1258946] : [25499 ^ _782476 : [(25502 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258942), hAPP(c_Set_OCollect(_1258942), _1258946)))], (25500 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258942), hAPP(c_Set_OCollect(_1258942), _1258944)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1258942), hAPP(c_Set_OCollect(_1258942), hAPP(hAPP(c_COMBS(_1258942, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1258942), c_fconj), _1258944)), _1258946)))))], (36164 ^ _782476) ^ [_1465352] : [class_Int_Onumber__ring(_1465352), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1465352), c_Groups_Oone__class_Oone(_1465352)) = hAPP(c_Int_Onumber__class_Onumber__of(_1465352), c_Int_OMin))], (10037 ^ _782476) ^ [_963637, _963639, _963641, _963643, _963645] : [class_Orderings_Oorder(_963637), c_Orderings_Oorder__class_Omono(_963637, tc_fun(_963639, tc_HOL_Obool), _963641), -(c_Orderings_Oorder__class_Omono(_963637, tc_fun(_963639, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_963637, tc_fun(_963639, tc_HOL_Obool), tc_fun(_963639, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963639, tc_HOL_Obool), tc_fun(tc_fun(_963639, tc_HOL_Obool), tc_fun(_963639, tc_HOL_Obool)), _963637), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963639, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_963637, tc_fun(_963639, tc_HOL_Obool), tc_fun(_963639, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963639, tc_HOL_Obool), tc_fun(tc_fun(_963639, tc_HOL_Obool), tc_fun(_963639, tc_HOL_Obool)), _963637), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963639, tc_HOL_Obool))), _963641)), _963643))), _963645)))], (26684 ^ _782476) ^ [_1286335, _1286337, _1286339, _1286341] : [class_Orderings_Olinorder(_1286335), 26687 ^ _782476 : [(26696 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286335), _1286337), _1286339)), _1286341))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), _1286337), _1286341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), _1286339), _1286341))], (26688 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286335), _1286337), _1286339)), _1286341)), 26691 ^ _782476 : [(26694 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), _1286339), _1286341)))], (26692 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286335), _1286337), _1286341)))]]]]], (52337 ^ _782476) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (40101 ^ _782476) ^ [_1562322, _1562324, _1562326, _1562328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562322), _1562324)), 40107 ^ _782476 : [(40110 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562326), hAPP(_1562328, 40106 ^ [_1562322, _1562324, _1562326, _1562328])))], (40108 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562322), 40106 ^ [_1562322, _1562324, _1562326, _1562328]), _1562324)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1562322, _1562326)), hAPP(hAPP(c_Product__Type_OSigma(_1562322, _1562326), _1562324), _1562328)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562322, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1562326, tc_HOL_Obool), tc_Nat_Onat, _1562322), c_Finite__Set_Ocard(_1562326)), _1562328)), _1562324))], (6507 ^ _782476) ^ [_887012, _887014, _887016, _887018, _887020, _887022] : [hBOOL(hAPP(hAPP(_887016, hAPP(_887018, _887020)), hAPP(_887018, _887022))), -(c_Predicate_Oinv__imagep(_887012, _887014, _887016, _887018, _887020, _887022))], (8172 ^ _782476) ^ [_922015, _922017, _922019] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922015, tc_HOL_Obool)), _922017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922015, tc_HOL_Obool)), _922019), _922017))))], (35526 ^ _782476) ^ [_1453720] : [-(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)))), _1453720) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1453720)))], (6417 ^ _782476) ^ [_884933, _884935, _884937, _884939, _884941] : [6419 ^ _782476 : [(6422 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884933, tc_HOL_Obool)), _884935), hAPP(_884941, 6418 ^ [_884933, _884935, _884937, _884939, _884941])))], (6420 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884937), 6418 ^ [_884933, _884935, _884937, _884939, _884941]), _884939)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884933, tc_HOL_Obool)), _884935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884937, tc_fun(_884933, tc_HOL_Obool)), _884939), _884941))))], (26030 ^ _782476) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10964 ^ _782476) ^ [_984606, _984608, _984610] : [class_Orderings_Olinorder(_984606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984606), _984608), _984610)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984606, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984606), _984608), c_Orderings_Obot__class_Obot(tc_fun(_984606, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_984606, _984608, _984610)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984606, _984608), _984610))], (9498 ^ _782476) ^ [_952786, _952788, _952790] : [9500 ^ _782476 : [(9506 ^ _782476) ^ [] : [-(9499 ^ [_952786, _952788, _952790] = 9502 ^ [_952786, _952788, _952790])], (9504 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952786), 9502 ^ [_952786, _952788, _952790]), _952790)))], (9501 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952786), 9499 ^ [_952786, _952788, _952790]), _952788)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952786, tc_HOL_Obool)), _952788), _952790) = c_Orderings_Obot__class_Obot(tc_fun(_952786, tc_HOL_Obool)))], (38857 ^ _782476) ^ [_1527817, _1527819] : [-(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), _1527817), _1527819)), 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), _1527817), _1527819))], (1942 ^ _782476) ^ [_809951, _809953] : [-(class_Power_Opower(_809951)), _809953 = _809951, class_Power_Opower(_809953)], (18290 ^ _782476) ^ [_1127911] : [-(_1127911 = 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)), _1127911)))], (21337 ^ _782476) ^ [_1183109] : [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)), _1183109))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1183109)))], (11588 ^ _782476) ^ [_993988, _993990, _993992] : [class_Orderings_Oorder(_993988), -(_993990 = _993992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993988), _993992), _993990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993988), _993992), _993990)))], (34282 ^ _782476) ^ [_1431937] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1431937) = c_Int_OPls)], (52385 ^ _782476) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (50135 ^ _782476) ^ [_1794755, _1794757, _1794759] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794755, _1794757), _1794759) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794755, tc_Lazy__Sequence_Olazy__sequence(_1794755)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794755, tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1794755, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat)), _1794755), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1794755), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1794755)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1794755, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794755), tc_Nat_Onat)), _1794755), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1794755))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1794755), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1794757))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794755, _1794757))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1794755), _1794759)))], (15498 ^ _782476) ^ [_1072069, _1072071, _1072073, _1072075] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1072069), _1072071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072069, tc_HOL_Obool)), _1072071), _1072073)), hBOOL(hAPP(_1072075, c_Orderings_Obot__class_Obot(tc_fun(_1072069, tc_HOL_Obool)))), 15513 ^ _782476 : [(15514 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1072069), 15512 ^ [_1072069, _1072071, _1072073, _1072075])))], (15518 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1072069), 15511 ^ [_1072069, _1072071, _1072073, _1072075]), 15512 ^ [_1072069, _1072071, _1072073, _1072075]))], (15522 ^ _782476) ^ [] : [hBOOL(hAPP(_1072075, hAPP(hAPP(c_Set_Oinsert(_1072069), 15511 ^ [_1072069, _1072071, _1072073, _1072075]), 15512 ^ [_1072069, _1072071, _1072073, _1072075])))], (15520 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1072075, 15512 ^ [_1072069, _1072071, _1072073, _1072075])))], (15516 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072069), 15511 ^ [_1072069, _1072071, _1072073, _1072075]), _1072073)))]], -(hBOOL(hAPP(_1072075, _1072071)))], (8539 ^ _782476) ^ [_930721, _930723, _930725, _930727] : [class_Lattices_Osemilattice__inf(_930721), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930721), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930721), _930723), _930725)), _930727) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930721), _930723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930721), _930725), _930727)))], (3680 ^ _782476) ^ [_837634, _837636, _837638, _837640] : [-(c_List_Otranspose(_837640, _837636) = c_List_Otranspose(_837638, _837634)), _837640 = _837638, _837636 = _837634], (28978 ^ _782476) ^ [_1332658, _1332660, _1332662, _1332664] : [class_Rings_Ocomm__semiring__1(_1332658), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332658), hAPP(hAPP(c_Power_Opower__class_Opower(_1332658), _1332660), _1332662)), hAPP(hAPP(c_Power_Opower__class_Opower(_1332658), _1332660), _1332664)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332658), _1332660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332662), _1332664)))], (10739 ^ _782476) ^ [_979219, _979221, _979223] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_979219, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979219, tc_HOL_Obool)), _979221), _979223)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979219, tc_HOL_Obool)), _979221), c_Complete__Lattice_OInf__class_OInf(tc_fun(_979219, tc_HOL_Obool), _979223)))], (45529 ^ _782476) ^ [_1693826, _1693828, _1693830] : [class_Orderings_Olinorder(_1693826), -(c_Big__Operators_Olinorder__class_OMax(_1693826, hAPP(c_List_Oset(_1693826), hAPP(hAPP(c_List_Olist_OCons(_1693826), _1693828), _1693830))) = hAPP(c_List_Ofoldl(_1693826, _1693826, c_Orderings_Oord__class_Omax(_1693826), _1693828), _1693830))], (8945 ^ _782476) ^ [_938810, _938812, _938814, _938816] : [class_Lattices_Odistrib__lattice(_938810), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938810), _938812), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938810), _938814), _938816)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938810), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938810), _938812), _938814)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938810), _938812), _938816)))], (14763 ^ _782476) ^ [_1058090, _1058092, _1058094, _1058096, _1058098, _1058100, _1058102, _1058104] : [c_Finite__Set_Ofolding__image(_1058090, _1058092, _1058094, _1058096, _1058098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058092), _1058100)), -(hAPP(hAPP(_1058098, hAPP(hAPP(c_COMBS(_1058092, _1058090, _1058090), hAPP(hAPP(c_COMBB(_1058090, tc_fun(_1058090, _1058090), _1058092), _1058094), _1058102)), _1058104)), _1058100) = hAPP(hAPP(_1058094, hAPP(hAPP(_1058098, _1058102), _1058100)), hAPP(hAPP(_1058098, _1058104), _1058100)))], (15726 ^ _782476) ^ [_1076813, _1076815, _1076817, _1076819] : [c_Finite__Set_Ofolding__one(_1076813, _1076815, _1076817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076813), _1076819)), -(hAPP(_1076817, _1076819) = hAPP(c_Finite__Set_Ofold1(_1076813, _1076815), _1076819))], (29206 ^ _782476) ^ [_1336830, _1336832] : [class_Groups_Omonoid__mult(_1336830), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336830), c_Groups_Oone__class_Oone(_1336830)), _1336832) = c_Groups_Oone__class_Oone(_1336830))], (13222 ^ _782476) ^ [_1026102, _1026104, _1026106, _1026108, _1026110] : [-(hAPP(c_Set_Ovimage(_1026102, _1026104, _1026106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026104, tc_HOL_Obool)), _1026108), _1026110)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026102, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026102, _1026104, _1026106), _1026108)), hAPP(c_Set_Ovimage(_1026102, _1026104, _1026106), _1026110)))], (46408 ^ _782476) ^ [_1712801] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1712801)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712801))], (21011 ^ _782476) ^ [_1177375, _1177377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177377), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177375), _1177377))), -(_1177375 = _1177377)], (45003 ^ _782476) ^ [_1681895, _1681897, _1681899, _1681901, _1681903, _1681905, _1681907] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681895, _1681895)), hAPP(hAPP(c_Product__Type_OPair(_1681895, _1681895), _1681897), _1681899)), _1681901)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681895), tc_List_Olist(_1681895))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681895), tc_List_Olist(_1681895)), hAPP(hAPP(c_List_Oappend(_1681895), _1681903), hAPP(hAPP(c_List_Olist_OCons(_1681895), _1681897), _1681905))), hAPP(hAPP(c_List_Oappend(_1681895), _1681903), hAPP(hAPP(c_List_Olist_OCons(_1681895), _1681899), _1681907)))), c_List_Olexord(_1681895, _1681901))))], (11512 ^ _782476) ^ [_992931, _992933, _992935] : [class_Orderings_Oorder(_992931), 11515 ^ _782476 : [(11516 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992931), _992933), _992935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992931), _992933), _992935))), -(_992933 = _992935)], (11526 ^ _782476) ^ [] : [11527 ^ _782476 : [(11530 ^ _782476) ^ [] : [_992933 = _992935], (11528 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992931), _992933), _992935))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992931), _992933), _992935)))]]], (49625 ^ _782476) ^ [_1783656, _1783658, _1783660, _1783662, _1783664] : [c_Fun_Oinj__on(_1783656, _1783658, _1783660, _1783662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783656, tc_HOL_Obool)), _1783664), _1783662)), -(hAPP(c_Set_Oimage(_1783658, _1783656, c_Hilbert__Choice_Oinv__into(_1783656, _1783658, _1783662, _1783660)), hAPP(c_Set_Oimage(_1783656, _1783658, _1783660), _1783664)) = _1783664)], (2298 ^ _782476) ^ [_816119, _816121, _816123, _816125, _816127, _816129] : [-(c_Nat_Onat_Onat__rec(_816129, _816125, _816121) = c_Nat_Onat_Onat__rec(_816127, _816123, _816119)), _816129 = _816127, _816125 = _816123, _816121 = _816119], (32131 ^ _782476) ^ [_1390988, _1390990] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390988, _1390990)), _1390990) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13240 ^ _782476) ^ [_1026673, _1026675, _1026677, _1026679] : [-(hAPP(c_Set_Ovimage(_1026673, _1026675, _1026677), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1026675, tc_HOL_Obool), _1026679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1026675, tc_HOL_Obool), tc_fun(_1026673, tc_HOL_Obool)), _1026679), c_Set_Ovimage(_1026673, _1026675, _1026677)))], (7579 ^ _782476) ^ [_909557, _909559, _909561] : [class_Lattices_Oboolean__algebra(_909557), 7582 ^ _782476 : [(7589 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909557), _909561), _909559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909557), hAPP(c_Groups_Ouminus__class_Ouminus(_909557), _909559)), hAPP(c_Groups_Ouminus__class_Ouminus(_909557), _909561))))], (7583 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909557), hAPP(c_Groups_Ouminus__class_Ouminus(_909557), _909559)), hAPP(c_Groups_Ouminus__class_Ouminus(_909557), _909561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909557), _909561), _909559)))]]], (4782 ^ _782476) ^ [_855369, _855371] : [_855371 = _855369, -(c_Code__Numeral_OSuc__code__numeral(_855371) = c_Code__Numeral_OSuc__code__numeral(_855369))], (26470 ^ _782476) ^ [_1282636, _1282638, _1282640] : [class_Orderings_Olinorder(_1282636), 26473 ^ _782476 : [(26480 ^ _782476) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282636), _1282638), _1282640) = _1282640, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282636), _1282638), _1282640)))], (26474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282636), _1282638), _1282640)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282636), _1282638), _1282640) = _1282640)]]], (52639 ^ _782476) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (46954 ^ _782476) ^ [_1725069, _1725071, _1725073] : [-(hBOOL(hAPP(hAPP(c_member(_1725069), _1725071), hAPP(c_List_Oset(_1725069), _1725073)))), -(c_List_Oremdups(_1725069, hAPP(hAPP(c_List_Olist_OCons(_1725069), _1725071), _1725073)) = hAPP(hAPP(c_List_Olist_OCons(_1725069), _1725071), c_List_Oremdups(_1725069, _1725073)))], (7816 ^ _782476) ^ [_914952, _914954, _914956] : [class_Lattices_Osemilattice__sup(_914952), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914952), _914954), _914956) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914952), _914956), _914954))], (50911 ^ _782476) ^ [_1812962, _1812964] : [c_Relation_Oantisym(_1812962, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812962, _1812962), tc_HOL_Obool)), _1812964), c_Relation_OId(_1812962))), -(c_Relation_Oantisym(_1812962, _1812964))], (42931 ^ _782476) ^ [_1630287, _1630289, _1630291, _1630293, _1630295] : [hAPP(hAPP(c_List_Olist_OCons(_1630287), _1630289), _1630291) = hAPP(hAPP(c_List_Olist_OCons(_1630287), _1630293), _1630295), 42934 ^ _782476 : [(42937 ^ _782476) ^ [] : [-(_1630291 = _1630295)], (42935 ^ _782476) ^ [] : [-(_1630289 = _1630293)]]], (39501 ^ _782476) ^ [_1544535, _1544537] : [-(hAPP(c_Relation_ORange(_1544535, _1544537), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544535, _1544537), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1544537, tc_HOL_Obool)))], (15216 ^ _782476) ^ [_1066939, _1066941, _1066943] : [class_Lattices_Olattice(_1066939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066939), _1066941)), hBOOL(hAPP(hAPP(c_member(_1066939), _1066943), _1066941)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066939), _1066943), c_Big__Operators_Olattice__class_OSup__fin(_1066939, _1066941)) = _1066943)], (3188 ^ _782476) ^ [_829904, _829906, _829908, _829910] : [-(c_Finite__Set_Ofold1(_829910, _829906) = c_Finite__Set_Ofold1(_829908, _829904)), _829910 = _829908, _829906 = _829904], (23927 ^ _782476) ^ [_1231131, _1231133] : [hBOOL(hAPP(_1231131, hAPP(c_Int_Onat, _1231133))), 23930 ^ _782476 : [(23937 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231133), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1231131, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23931 ^ _782476) ^ [_1231231] : [_1231133 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231231), -(hBOOL(hAPP(_1231131, _1231231)))]]], (47226 ^ _782476) ^ [_1731633, _1731635] : [-(c_List_Otranspose(_1731633, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1731633)), c_List_Olist_ONil(_1731633)), _1731635)) = c_List_Otranspose(_1731633, _1731635))], (9744 ^ _782476) ^ [_957072, _957074, _957076] : [class_Orderings_Oorder(_957072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957072), _957074), _957076)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957072, _957076), _957074) = c_Orderings_Obot__class_Obot(tc_fun(_957072, tc_HOL_Obool)))], (13802 ^ _782476) ^ [_1038594, _1038596, _1038598, _1038600, _1038602] : [c_Fun_Oinj__on(_1038594, _1038596, _1038598, c_Orderings_Otop__class_Otop(tc_fun(_1038594, tc_HOL_Obool))), c_Fun_Oinj__on(_1038600, _1038594, _1038602, c_Orderings_Otop__class_Otop(tc_fun(_1038600, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1038600, _1038596, hAPP(c_Fun_Ocomp(_1038594, _1038596, _1038600, _1038598), _1038602), c_Orderings_Otop__class_Otop(tc_fun(_1038600, tc_HOL_Obool))))], (36370 ^ _782476) ^ [_1468763, _1468765] : [class_Int_Onumber__ring(_1468763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1468765)), -(hBOOL(hAPP(hAPP(c_member(_1468763), hAPP(c_Int_Onumber__class_Onumber__of(_1468763), _1468765)), c_Nat_Osemiring__1__class_ONats(_1468763))))], (10719 ^ _782476) ^ [_978742, _978744, _978746] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978742, tc_HOL_Obool)), _978744), _978746) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978742, tc_HOL_Obool)), _978744), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978742, tc_HOL_Obool)), _978746)))], (22624 ^ _782476) ^ [_1206767, _1206769, _1206771] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206767), _1206769)), hBOOL(hAPP(hAPP(c_member(_1206767), _1206771), _1206769)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1206767), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206767, tc_HOL_Obool)), _1206769), hAPP(hAPP(c_Set_Oinsert(_1206767), _1206771), c_Orderings_Obot__class_Obot(tc_fun(_1206767, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1206767), _1206769))], (6680 ^ _782476) ^ [_890407, _890409, _890411, _890413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890407, tc_HOL_Obool)), _890409), _890411)), hBOOL(hAPP(hAPP(c_member(_890407), _890413), _890409)), -(hBOOL(hAPP(hAPP(c_member(_890407), _890413), _890411)))], (7519 ^ _782476) ^ [_908518, _908520] : [class_Lattices_Oboolean__algebra(_908518), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908518), hAPP(c_Groups_Ouminus__class_Ouminus(_908518), _908520)) = _908520)], (1902 ^ _782476) ^ [_809451, _809453] : [-(class_Orderings_Oorder(_809451)), _809453 = _809451, class_Orderings_Oorder(_809453)], (41541 ^ _782476) ^ [_1597854, _1597856, _1597858, _1597860, _1597862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597854, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597856, _1597854, _1597858), _1597860)), _1597862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597856, tc_HOL_Obool)), _1597860), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597856, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597854, _1597856, hAPP(c_Relation_Oconverse(_1597856, _1597854), _1597858)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597854, tc_HOL_Obool)), _1597862))))))], (25670 ^ _782476) ^ [_1262786, _1262788] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262786, tc_HOL_Obool)), _1262788) = hAPP(c_Set_OCollect(_1262786), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262786), c_fNot), hAPP(hAPP(c_COMBC(_1262786, tc_fun(_1262786, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262786)), _1262788))))], (30456 ^ _782476) ^ [_1359824, _1359826, _1359828, _1359830] : [class_Fields_Olinordered__field(_1359824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359824), c_Groups_Ozero__class_Ozero(_1359824)), _1359826)), 30463 ^ _782476 : [(30470 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359824), _1359828), _1359826)), _1359830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359824), _1359828), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359824), _1359830), _1359826))))], (30464 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359824), _1359828), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359824), _1359830), _1359826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359824), _1359828), _1359826)), _1359830)))]]], (32217 ^ _782476) ^ [_1392693, _1392695] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392693, _1392695) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392693, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392695)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47279 ^ _782476) ^ [_1733143, _1733145, _1733147, _1733149] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733143)), c_List_Otranspose__rel(_1733143)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733143)), hAPP(hAPP(c_List_Olist_OCons(_1733143), _1733145), _1733147)), _1733149))), -(c_List_Otranspose(_1733143, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733143)), hAPP(hAPP(c_List_Olist_OCons(_1733143), _1733145), _1733147)), _1733149)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733143)), hAPP(hAPP(c_List_Olist_OCons(_1733143), _1733145), c_List_Oconcat(_1733143, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733143), tc_List_Olist(_1733143)), c_List_Olist_Olist__case(tc_List_Olist(_1733143), _1733143, c_List_Olist_ONil(_1733143), hAPP(hAPP(c_COMBB(tc_List_Olist(_1733143), tc_fun(tc_List_Olist(_1733143), tc_List_Olist(_1733143)), _1733143), c_COMBK(tc_List_Olist(_1733143), tc_List_Olist(_1733143))), hAPP(hAPP(c_COMBC(_1733143, tc_List_Olist(_1733143), tc_List_Olist(_1733143)), c_List_Olist_OCons(_1733143)), c_List_Olist_ONil(_1733143))))), _1733149)))), c_List_Otranspose(_1733143, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733143)), _1733147), c_List_Oconcat(tc_List_Olist(_1733143), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733143), tc_List_Olist(tc_List_Olist(_1733143))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1733143)), _1733143, c_List_Olist_ONil(tc_List_Olist(_1733143)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1733143), tc_List_Olist(tc_List_Olist(_1733143))), _1733143), hAPP(hAPP(c_COMBC(tc_List_Olist(_1733143), tc_List_Olist(tc_List_Olist(_1733143)), tc_List_Olist(tc_List_Olist(_1733143))), c_List_Olist_OCons(tc_List_Olist(_1733143))), c_List_Olist_ONil(tc_List_Olist(_1733143)))))), _1733149))))))], (26574 ^ _782476) ^ [_1284447, _1284449, _1284451] : [class_Orderings_Olinorder(_1284447), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284447), _1284449), _1284451)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284447), _1284451), _1284449) = _1284449)], (45106 ^ _782476) ^ [_1684698, _1684700] : [-(hAPP(hAPP(c_List_Odrop(_1684698), _1684700), c_List_Olist_ONil(_1684698)) = c_List_Olist_ONil(_1684698))], (13454 ^ _782476) ^ [_1031709, _1031711, _1031713, _1031715] : [-(c_Partial__Function_Omk__less(_1031709, _1031711, _1031713, _1031715)), hBOOL(hAPP(hAPP(_1031711, _1031713), _1031715)), -(hBOOL(hAPP(hAPP(_1031711, _1031715), _1031713)))], (17784 ^ _782476) ^ [_1119553, _1119555] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119553), _1119555) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119553 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119555 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (49695 ^ _782476) ^ [_1785403, _1785405, _1785407] : [hAPP(c_Fun_Ocomp(_1785403, _1785405, _1785405, _1785407), c_Hilbert__Choice_Oinv__into(_1785403, _1785405, c_Orderings_Otop__class_Otop(tc_fun(_1785403, tc_HOL_Obool)), _1785407)) = c_Fun_Oid(_1785405), -(hAPP(c_Set_Oimage(_1785403, _1785405, _1785407), c_Orderings_Otop__class_Otop(tc_fun(_1785403, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785405, tc_HOL_Obool)))], (34532 ^ _782476) ^ [_1435831, _1435833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435831)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435831), _1435833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435831), c_Int_OPls)))], (44266 ^ _782476) ^ [_1665537, _1665539] : [-(c_List_Olistrelp(_1665537, _1665539, c_List_Olist_ONil(_1665537), c_List_Olist_ONil(_1665537)))], (52475 ^ _782476) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (44869 ^ _782476) ^ [_1678520, _1678522, _1678524] : [_1678522 = c_List_Olist_ONil(_1678520), -(hAPP(hAPP(c_List_Oappend(_1678520), _1678522), _1678524) = _1678524)], (24006 ^ _782476) ^ [_1232548, _1232550, _1232552] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232548, tc_Nat_Onat), _1232550), _1232552) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232548, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1232548), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232550)), _1232552)))], (52229 ^ _782476) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (13986 ^ _782476) ^ [_1042285, _1042287, _1042289, _1042291] : [-(c_Fun_Ooverride__on(_1042285, _1042287, _1042289, _1042291, c_Orderings_Obot__class_Obot(tc_fun(_1042285, tc_HOL_Obool))) = _1042289)], (47204 ^ _782476) ^ [_1731188, _1731190, _1731192, _1731194] : [-(hBOOL(hAPP(_1731188, _1731190))), -(hAPP(c_List_Ofilter(_1731192, _1731188), hAPP(hAPP(c_List_Olist_OCons(_1731192), _1731190), _1731194)) = hAPP(c_List_Ofilter(_1731192, _1731188), _1731194))], (4376 ^ _782476) ^ [_848936, _848938] : [_848938 = _848936, -(c_Lazy__Sequence_Osingle(_848938) = c_Lazy__Sequence_Osingle(_848936))], (43780 ^ _782476) ^ [_1655034, _1655036, _1655038] : [class_Groups_Omonoid__add(_1655034), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1655034), hAPP(hAPP(c_List_Olist_OCons(_1655034), _1655036), _1655038)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655034), _1655036), hAPP(c_List_Omonoid__add__class_Olistsum(_1655034), _1655038)))], (26084 ^ _782476) ^ [_1275831] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275831), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52755 ^ _782476) ^ [_1844604, _1844606] : [-(hBOOL(_1844604)), -(hBOOL(hAPP(hAPP(c_fimplies, _1844604), _1844606)))], (5006 ^ _782476) ^ [_858893, _858895, _858897, _858899] : [-(c_Complete__Lattice_OSup__class_OSup(_858899, _858895) = c_Complete__Lattice_OSup__class_OSup(_858897, _858893)), _858899 = _858897, _858895 = _858893], (47118 ^ _782476) ^ [_1729399, _1729401, _1729403] : [-(hAPP(c_List_Ofilter(_1729399, _1729401), c_List_Oconcat(_1729399, _1729403)) = c_List_Oconcat(_1729399, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729399), tc_List_Olist(_1729399)), c_List_Ofilter(_1729399, _1729401)), _1729403)))], (48391 ^ _782476) ^ [_1755996, _1755998] : [-(_1755996 = c_List_Olist_ONil(_1755998)), hBOOL(hAPP(c_List_Odistinct(_1755998), _1755996)), -(c_List_OtakeWhile(_1755998, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1755998), c_fNot), hAPP(hAPP(c_COMBC(_1755998, _1755998, tc_HOL_Obool), c_fequal), c_List_Olast(_1755998, _1755996))), _1755996) = c_List_Obutlast(_1755998, _1755996))], (14142 ^ _782476) ^ [_1045815, _1045817, _1045819] : [14143 ^ _782476 : [(14146 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045815), _1045819))], (14144 ^ _782476) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045815), _1045817))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045815), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045815, tc_HOL_Obool)), _1045817), _1045819))))], (25476 ^ _782476) ^ [_1258539, _1258541] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258539), _1258541)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1258539, 25479 ^ [_1258539, _1258541], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1258539), _1258541)), _1258541))], (47421 ^ _782476) ^ [_1736861, _1736863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736861), _1736863)), -(c_List_Oupt(_1736863, _1736861) = c_List_Olist_ONil(tc_Nat_Onat))], (32453 ^ _782476) ^ [_1397058, _1397060] : [-(_1397058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32456 ^ _782476 : [(32463 ^ _782476) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397060, _1397058) = 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), _1397060)), _1397058) = 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), _1397060), _1397058))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32457 ^ _782476) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397060, _1397058) = 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), _1397060)), _1397058) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397060), _1397058)))]]], (1992 ^ _782476) ^ [_810576, _810578] : [-(class_Nat_Osize(_810576)), _810578 = _810576, class_Nat_Osize(_810578)], (5793 ^ _782476) ^ [_874050, _874052, _874054, _874056] : [class_Orderings_Oord(_874050), 5796 ^ _782476 : [(5803 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874050), hAPP(_874054, 5804 ^ [_874050, _874052, _874054, _874056])), hAPP(_874056, 5804 ^ [_874050, _874052, _874054, _874056]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874052, _874050)), _874054), _874056)))], (5797 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874052, _874050)), _874054), _874056)), 5800 ^ _782476 : [(5801 ^ _782476) ^ [_874207] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874050), hAPP(_874054, _874207)), hAPP(_874056, _874207))))]]]]], (43499 ^ _782476) ^ [_1646894, _1646896, _1646898] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646894, tc_HOL_Obool)), hAPP(c_List_Oset(_1646894), c_List_Osublist(_1646894, _1646896, _1646898))), hAPP(c_List_Oset(_1646894), _1646896))))], (15698 ^ _782476) ^ [_1076250, _1076252, _1076254, _1076256] : [_1076250 = c_Finite__Set_Ofold1(_1076252, _1076254), -(hAPP(_1076250, hAPP(hAPP(c_Set_Oinsert(_1076252), _1076256), c_Orderings_Obot__class_Obot(tc_fun(_1076252, tc_HOL_Obool)))) = _1076256)], (17640 ^ _782476) ^ [_1116867, _1116869] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116867), _1116869)), _1116869) = _1116867)], (34084 ^ _782476) ^ [_1428645] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428645))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428645) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38413 ^ _782476) ^ [_1516772, _1516774, _1516776, _1516778, _1516780, _1516782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516772, _1516774)), hAPP(hAPP(c_Product__Type_OPair(_1516772, _1516774), _1516776), _1516778)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516772, _1516774), tc_HOL_Obool), _1516780))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1516772, _1516774), tc_HOL_Obool), tc_fun(tc_prod(_1516772, _1516774), tc_HOL_Obool), _1516780), 38424 ^ _782476 : [(38427 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(_1516782, 38422 ^ [_1516772, _1516774, _1516776, _1516778, _1516780, _1516782]), 38423 ^ [_1516772, _1516774, _1516776, _1516778, _1516780, _1516782]))], (38425 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516772, _1516774)), hAPP(hAPP(c_Product__Type_OPair(_1516772, _1516774), 38422 ^ [_1516772, _1516774, _1516776, _1516778, _1516780, _1516782]), 38423 ^ [_1516772, _1516774, _1516776, _1516778, _1516780, _1516782])), hAPP(_1516780, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516772, _1516774), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516772, _1516774), tc_HOL_Obool), _1516780)), hAPP(c_Set_OCollect(tc_prod(_1516772, _1516774)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516772, _1516774, tc_HOL_Obool), _1516782)))))))]], -(hBOOL(hAPP(hAPP(_1516782, _1516776), _1516778)))], (31598 ^ _782476) ^ [_1380314, _1380316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380314)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380314), _1380316)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380314)), hAPP(c_Int_Onat, _1380316)))], (32547 ^ _782476) ^ [_1398924, _1398926] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398924), _1398926) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398924, _1398926)), _1398926))], (39038 ^ _782476) ^ [_1533824, _1533826, _1533828, _1533830, _1533832, _1533834, _1533836] : [c_Typedef_Otype__definition(_1533824, _1533826, _1533828, _1533830, _1533832), 39041 ^ _782476 : [(39048 ^ _782476) ^ [] : [_1533834 = _1533836, -(hAPP(_1533828, _1533834) = hAPP(_1533828, _1533836))], (39042 ^ _782476) ^ [] : [hAPP(_1533828, _1533834) = hAPP(_1533828, _1533836), -(_1533834 = _1533836)]]], (47228 ^ _782476) ^ [_1731676, _1731678, _1731680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731678))), c_List_Otranspose(_1731678, _1731680)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1731678)), c_List_Otranspose(_1731678, _1731680)), _1731676) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731678), _1731678), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731678), tc_Nat_Onat, _1731678), c_List_Onth(_1731678)), _1731676)), hAPP(c_List_Ofilter(tc_List_Olist(_1731678), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731678)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731676)), c_Nat_Osize__class_Osize(tc_List_Olist(_1731678)))), _1731680)))], (14473 ^ _782476) ^ [_1052026, _1052028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052026), c_Orderings_Otop__class_Otop(tc_fun(_1052026, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1052026, _1052026, _1052028), c_Orderings_Otop__class_Otop(tc_fun(_1052026, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052026, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1052026, _1052026, _1052028, c_Orderings_Otop__class_Otop(tc_fun(_1052026, tc_HOL_Obool))))], (9446 ^ _782476) ^ [_951694, _951696, _951698, _951700] : [hAPP(c_Set_Oimage(_951694, _951696, _951698), _951700) = c_Orderings_Obot__class_Obot(tc_fun(_951696, tc_HOL_Obool)), -(_951700 = c_Orderings_Obot__class_Obot(tc_fun(_951694, tc_HOL_Obool)))], (10375 ^ _782476) ^ [_970647, _970649, _970651] : [c_Orderings_Obot__class_Obot(tc_fun(_970647, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_970647), _970649), _970651)], (22482 ^ _782476) ^ [_1204160, _1204162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204160), _1204162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204160)), _1204162)))], (11912 ^ _782476) ^ [_999354, _999356, _999358, _999360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999354, tc_HOL_Obool)), _999356), _999358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999354, tc_HOL_Obool)), _999358), _999360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999354, tc_HOL_Obool)), _999356), _999360)))], (38851 ^ _782476) ^ [] : [-(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))))))], (26906 ^ _782476) ^ [_1290478, _1290480, _1290482] : [class_Orderings_Olinorder(_1290478), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290478), _1290480), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290478), _1290480), _1290482)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290478), _1290480), _1290482))], (36743 ^ _782476) ^ [_1481745, _1481747] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481745), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36746 ^ _782476 : [(36755 ^ _782476) ^ [] : [-(c_Nitpick_Onorm__frac(_1481747, _1481745) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1481747), _1481745)), 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), _1481747))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481745)))), -(_1481747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1481745 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36747 ^ _782476) ^ [] : [36748 ^ _782476 : [(36751 ^ _782476) ^ [] : [_1481745 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36749 ^ _782476) ^ [] : [_1481747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1481747, _1481745) = 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)))]]], (43109 ^ _782476) ^ [_1635929, _1635931, _1635933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1635929, _1635929), tc_HOL_Obool)), _1635931), _1635933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1635929), tc_List_Olist(_1635929)), tc_HOL_Obool)), c_List_Olistrel(_1635929, _1635931)), c_List_Olistrel(_1635929, _1635933))))], (34076 ^ _782476) ^ [_1428542, _1428544] : [-(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), _1428542)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428544), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428542))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25742 ^ _782476) ^ [_1265430, _1265432, _1265434, _1265436, _1265438, _1265440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265430), _1265432)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265434), _1265436)), 25752 ^ _782476 : [(25755 ^ _782476) ^ [] : [hAPP(c_Finite__Set_Ocard(_1265430), hAPP(c_Set_OCollect(_1265430), hAPP(hAPP(c_COMBS(_1265430, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265430), c_fconj), hAPP(hAPP(c_COMBC(_1265430, tc_fun(_1265430, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265430)), _1265432))), hAPP(hAPP(c_COMBC(_1265430, _1265434, tc_HOL_Obool), _1265438), 25751 ^ [_1265430, _1265432, _1265434, _1265436, _1265438, _1265440])))) = _1265440], (25753 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1265434), 25751 ^ [_1265430, _1265432, _1265434, _1265436, _1265438, _1265440]), _1265436)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1265430, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1265434, tc_HOL_Obool), tc_Nat_Onat, _1265430), c_Finite__Set_Ocard(_1265434)), hAPP(hAPP(c_COMBB(tc_fun(_1265434, tc_HOL_Obool), tc_fun(_1265434, tc_HOL_Obool), _1265430), c_Set_OCollect(_1265434)), hAPP(hAPP(c_COMBB(tc_fun(_1265434, tc_HOL_Obool), tc_fun(_1265434, tc_HOL_Obool), _1265430), hAPP(c_COMBS(_1265434, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265434), c_fconj), hAPP(hAPP(c_COMBC(_1265434, tc_fun(_1265434, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265434)), _1265436)))), _1265438)))), _1265432) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1265440), hAPP(c_Finite__Set_Ocard(_1265434), _1265436)))], (16885 ^ _782476) ^ [_1101508, _1101510, _1101512, _1101514, _1101516, _1101518] : [class_Rings_Oordered__ring(_1101508), 16888 ^ _782476 : [(16895 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101508), _1101514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101508), _1101516), _1101510)), _1101512)), _1101518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), _1101510), _1101512)), _1101514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), _1101516), _1101512)), _1101518))))], (16889 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), _1101510), _1101512)), _1101514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), _1101516), _1101512)), _1101518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101508), _1101514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101508), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101508), _1101516), _1101510)), _1101512)), _1101518))))]]], (15748 ^ _782476) ^ [_1077175, _1077177] : [class_Lattices_Olattice(_1077175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077175), _1077177)), -(c_Big__Operators_Olattice__class_OInf__fin(_1077175, _1077177) = hAPP(c_Finite__Set_Ofold1(_1077175, c_Lattices_Osemilattice__inf__class_Oinf(_1077175)), _1077177))], (9480 ^ _782476) ^ [_952362, _952364] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952362, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952362, tc_HOL_Obool))), _952364) = c_Orderings_Obot__class_Obot(tc_fun(_952362, tc_HOL_Obool)))], (35490 ^ _782476) ^ [_1453176, _1453178] : [class_Rings_Oring__1__no__zero__divisors(_1453176), 35493 ^ _782476 : [(35500 ^ _782476) ^ [] : [_1453178 = c_Groups_Ozero__class_Ozero(_1453176), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453176), _1453178), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453176))], (35494 ^ _782476) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1453176), _1453178), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453176), -(_1453178 = c_Groups_Ozero__class_Ozero(_1453176))]]], (42155 ^ _782476) ^ [_1612895, _1612897, _1612899, _1612901] : [class_Orderings_Olinorder(_1612895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612895), _1612897)), hBOOL(hAPP(hAPP(c_member(_1612895), _1612899), _1612897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612895), hAPP(hAPP(c_Finite__Set_Ofold(_1612895, _1612895, c_Orderings_Oord__class_Omin(_1612895)), _1612901), _1612897)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1612895), _1612899), _1612901))))], (38718 ^ _782476) ^ [_1524033] : [-(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)), _1524033), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (9458 ^ _782476) ^ [_951922, _951924] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951922, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_951922, tc_HOL_Obool))), _951924) = _951924)], (46512 ^ _782476) ^ [_1714939, _1714941, _1714943, _1714945] : [hBOOL(hAPP(c_List_Olistsp(_1714939, _1714941), _1714943)), hBOOL(hAPP(c_List_Olistsp(_1714939, _1714945), _1714943)), -(hBOOL(hAPP(c_List_Olistsp(_1714939, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714939, tc_HOL_Obool)), _1714941), _1714945)), _1714943)))], (41744 ^ _782476) ^ [_1602696, _1602698, _1602700] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602696, _1602696)), _1602698), c_Transitive__Closure_Ortrancl(_1602696, _1602700))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602696, _1602696)), _1602698), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1602696, _1602696), 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(_1602696, _1602696), tc_HOL_Obool), tc_fun(tc_prod(_1602696, _1602696), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1602696, _1602696), tc_HOL_Obool)), _1602700)))))], (42459 ^ _782476) ^ [_1618616, _1618618, _1618620, _1618622, _1618624, _1618626] : [c_Finite__Set_Ofun__left__comm(_1618616, _1618618, _1618620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618616), _1618622)), -(hAPP(hAPP(_1618620, _1618624), hAPP(hAPP(c_Finite__Set_Ofold(_1618616, _1618618, _1618620), _1618626), _1618622)) = hAPP(hAPP(c_Finite__Set_Ofold(_1618616, _1618618, _1618620), hAPP(hAPP(_1618620, _1618624), _1618626)), _1618622))], (12752 ^ _782476) ^ [_1016142, _1016144, _1016146, _1016148, _1016150] : [c_Fun_Oinj__on(_1016142, _1016144, _1016146, c_Orderings_Otop__class_Otop(tc_fun(_1016142, tc_HOL_Obool))), 12755 ^ _782476 : [(12762 ^ _782476) ^ [] : [_1016148 = _1016150, -(hAPP(_1016146, _1016148) = hAPP(_1016146, _1016150))], (12756 ^ _782476) ^ [] : [hAPP(_1016146, _1016148) = hAPP(_1016146, _1016150), -(_1016148 = _1016150)]]], (25588 ^ _782476) ^ [_1260699, _1260701, _1260703] : [-(hAPP(c_Set_OCollect(_1260699), hAPP(hAPP(c_COMBS(_1260699, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260699), c_fdisj), _1260701)), _1260703)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260699, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260699), _1260701)), hAPP(c_Set_OCollect(_1260699), _1260703)))], (25995 ^ _782476) ^ [_1274216, _1274218] : [25996 ^ _782476 : [(25997 ^ _782476) ^ [_1274280, _1274282] : [_1274218 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274216, _1274280), 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)), _1274282)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274216), _1274218)))], (27897 ^ _782476) ^ [_1309895, _1309897, _1309899] : [class_Orderings_Olinorder(_1309895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309895), _1309897)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309895), _1309899)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309895, tc_HOL_Obool)), _1309897), _1309899) = c_Orderings_Obot__class_Obot(tc_fun(_1309895, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309895), c_Big__Operators_Olinorder__class_OMax(_1309895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309895, tc_HOL_Obool)), _1309897), _1309899))), c_Big__Operators_Olinorder__class_OMax(_1309895, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309895, tc_HOL_Obool)), _1309897), _1309899))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309895), c_Big__Operators_Olinorder__class_OMax(_1309895, _1309897)), c_Big__Operators_Olinorder__class_OMax(_1309895, _1309899)))], (39020 ^ _782476) ^ [_1533497, _1533499, _1533501, _1533503, _1533505] : [c_Typedef_Otype__definition(_1533497, _1533499, _1533501, _1533503, _1533505), -(hAPP(c_Set_Oimage(_1533497, _1533499, _1533501), c_Orderings_Otop__class_Otop(tc_fun(_1533497, tc_HOL_Obool))) = _1533505)], (9085 ^ _782476) ^ [_942842, _942844, _942846, _942848, _942850, _942852, _942854] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942842, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942844, tc_fun(_942842, tc_HOL_Obool)), _942846), _942848)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942850, tc_fun(_942842, tc_HOL_Obool)), _942852), _942854)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942844, tc_fun(_942842, tc_HOL_Obool)), _942846), hAPP(hAPP(c_COMBB(tc_fun(_942850, tc_fun(_942842, tc_HOL_Obool)), tc_fun(_942842, tc_HOL_Obool), _942844), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942850, tc_fun(_942842, tc_HOL_Obool)), _942852)), hAPP(hAPP(c_COMBC(_942844, tc_fun(_942850, tc_fun(_942842, tc_HOL_Obool)), tc_fun(_942850, tc_fun(_942842, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_942842, tc_HOL_Obool), tc_fun(_942842, tc_HOL_Obool)), tc_fun(tc_fun(_942850, tc_fun(_942842, tc_HOL_Obool)), tc_fun(_942850, tc_fun(_942842, tc_HOL_Obool))), _942844), c_COMBB(tc_fun(_942842, tc_HOL_Obool), tc_fun(_942842, tc_HOL_Obool), _942850)), hAPP(hAPP(c_COMBB(tc_fun(_942842, tc_HOL_Obool), tc_fun(tc_fun(_942842, tc_HOL_Obool), tc_fun(_942842, tc_HOL_Obool)), _942844), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942842, tc_HOL_Obool))), _942848))), _942854))))], (32048 ^ _782476) ^ [_1389569, _1389571, _1389573] : [class_Divides_Osemiring__div(_1389569), -(c_Divides_Odiv__class_Omod(_1389569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389569), _1389571), _1389573), _1389573) = c_Groups_Ozero__class_Ozero(_1389569))], (1632 ^ _782476) ^ [_806076, _806078] : [-(class_Groups_Oordered__ab__semigroup__add(_806076)), _806078 = _806076, class_Groups_Oordered__ab__semigroup__add(_806078)], (39953 ^ _782476) ^ [_1557861, _1557863, _1557865] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557861), _1557863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557861, _1557861), tc_HOL_Obool)), _1557865), hAPP(hAPP(c_Product__Type_OSigma(_1557861, _1557861), _1557863), hAPP(c_COMBK(tc_fun(_1557861, tc_HOL_Obool), _1557861), _1557863)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1557861, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1557861), _1557863), _1557865))))], (43681 ^ _782476) ^ [_1652606, _1652608, _1652610, _1652612] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652606, _1652606)), hAPP(hAPP(c_Product__Type_OPair(_1652606, _1652606), _1652608), _1652610)), hAPP(c_List_Oset(tc_prod(_1652606, _1652606)), hAPP(hAPP(c_List_Ozip(_1652606, _1652606), _1652612), _1652612))))), hBOOL(hAPP(hAPP(c_member(_1652606), _1652608), hAPP(c_List_Oset(_1652606), _1652612))), _1652608 = _1652610], (3996 ^ _782476) ^ [_842708, _842710, _842712, _842714, _842716, _842718, _842720, _842722, _842724, _842726, _842728, _842730, _842732, _842734] : [-(c_New__Random__Sequence_Opos__decr__bind(_842734, _842730, _842726, _842722, _842718, _842714, _842710) = c_New__Random__Sequence_Opos__decr__bind(_842732, _842728, _842724, _842720, _842716, _842712, _842708)), _842734 = _842732, _842730 = _842728, _842726 = _842724, _842722 = _842720, _842718 = _842716, _842714 = _842712, _842710 = _842708], (6199 ^ _782476) ^ [_880946, _880948, _880950] : [class_Orderings_Oorder(_880946), 6202 ^ _782476 : [(6209 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880946), _880950), _880948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880946, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880946), _880948)), hAPP(c_SetInterval_Oord__class_OatLeast(_880946), _880950))))], (6203 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880946, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880946), _880948)), hAPP(c_SetInterval_Oord__class_OatLeast(_880946), _880950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880946), _880950), _880948)))]]], (25279 ^ _782476) ^ [_1255039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255039)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1255039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29488 ^ _782476) ^ [_1342012, _1342014, _1342016] : [class_Rings_Olinordered__semidom(_1342012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342012), c_Groups_Oone__class_Oone(_1342012)), _1342014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342012), c_Groups_Oone__class_Oone(_1342012)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342012), _1342014), hAPP(c_Nat_OSuc, _1342016)))))], (52463 ^ _782476) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (5278 ^ _782476) ^ [_863181, _863183, _863185, _863187] : [-(c_Transitive__Closure_Ortrancl(_863187, _863183) = c_Transitive__Closure_Ortrancl(_863185, _863181)), _863187 = _863185, _863183 = _863181], (34272 ^ _782476) ^ [_1431821] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1431821), c_Int_OPls) = _1431821)], (6752 ^ _782476) ^ [_891782, _891784, _891786, _891788, _891790, _891792] : [hBOOL(hAPP(hAPP(c_member(_891782), _891784), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891786, tc_fun(_891782, tc_HOL_Obool)), _891788), _891790))), hBOOL(hAPP(hAPP(c_member(_891786), _891792), _891788)), -(hBOOL(hAPP(hAPP(c_member(_891782), _891784), hAPP(_891790, _891792))))], (68 ^ _782476) ^ [_783550, _783552, _783554, _783556, _783558, _783560, _783562, _783564, _783566, _783568, _783570, _783572] : [-(c_Nitpick_Ofold__graph_H(_783570, _783566, _783562, _783558, _783554, _783550)), c_Nitpick_Ofold__graph_H(_783572, _783568, _783564, _783560, _783556, _783552), _783572 = _783570, _783568 = _783566, _783564 = _783562, _783560 = _783558, _783556 = _783554, _783552 = _783550], (18324 ^ _782476) ^ [_1128360] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128360)))], (12626 ^ _782476) ^ [_1013716, _1013718, _1013720, _1013722] : [c_Fun_Oinj__on(_1013716, _1013718, _1013720, c_Orderings_Otop__class_Otop(tc_fun(_1013716, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1013716, tc_fun(_1013722, _1013718), hAPP(hAPP(c_COMBB(_1013718, tc_fun(_1013722, _1013718), _1013716), c_COMBK(_1013718, _1013722)), _1013720), c_Orderings_Otop__class_Otop(tc_fun(_1013716, tc_HOL_Obool))))], (50931 ^ _782476) ^ [_1813474, _1813476] : [c_Relation_Osym(_1813474, _1813476), c_Relation_Otrans(_1813474, _1813476), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1813474, _1813474), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1813474, _1813474, _1813474), hAPP(c_Relation_Oconverse(_1813474, _1813474), _1813476)), _1813476)), _1813476)))], (8703 ^ _782476) ^ [_934052] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_934052, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934052, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_934052, tc_HOL_Obool)))], (24634 ^ _782476) ^ [_1243121, _1243123] : [class_Rings_Olinordered__idom(_1243121), 24637 ^ _782476 : [(24644 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243121), c_Groups_Ozero__class_Ozero(_1243121)), hAPP(c_Int_Oring__1__class_Oof__int(_1243121), _1243123))))], (24638 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243121), c_Groups_Ozero__class_Ozero(_1243121)), hAPP(c_Int_Oring__1__class_Oof__int(_1243121), _1243123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243123)))]]], (4190 ^ _782476) ^ [_845957, _845959, _845961, _845963] : [-(c_New__DSequence_Opos__single(_845963, _845959) = c_New__DSequence_Opos__single(_845961, _845957)), _845963 = _845961, _845959 = _845957], (22218 ^ _782476) ^ [_1199788, _1199790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199788), hAPP(c_Nat_OSuc, _1199790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199788), _1199790))), -(_1199788 = hAPP(c_Nat_OSuc, _1199790))], (28966 ^ _782476) ^ [_1332432, _1332434, _1332436] : [class_Rings_Ocomm__semiring__1(_1332432), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332432), _1332434), hAPP(c_Nat_OSuc, _1332436)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332432), _1332434), hAPP(hAPP(c_Power_Opower__class_Opower(_1332432), _1332434), _1332436)))], (41014 ^ _782476) ^ [_1584158, _1584160, _1584162, _1584164, _1584166] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584158, _1584158)), hAPP(hAPP(c_Product__Type_OPair(_1584158, _1584158), _1584160), _1584162)), _1584164)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584158, _1584158)), hAPP(hAPP(c_Product__Type_OPair(_1584158, _1584158), _1584162), _1584166)), _1584164)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584158, _1584158)), hAPP(hAPP(c_Product__Type_OPair(_1584158, _1584158), _1584160), _1584166)), c_Transitive__Closure_Otrancl(_1584158, _1584164))))], (41194 ^ _782476) ^ [_1589438, _1589440] : [-(c_Relation_Orefl__on(_1589438, c_Orderings_Otop__class_Otop(tc_fun(_1589438, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589438, _1589440)))], (8679 ^ _782476) ^ [_933471, _933473] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933471, tc_HOL_Obool)), _933473), _933473) = _933473)], (43447 ^ _782476) ^ [_1645450, _1645452, _1645454, _1645456] : [-(hAPP(hAPP(c_List_Otake(_1645450), _1645452), hAPP(hAPP(c_List_Otake(_1645450), _1645454), _1645456)) = hAPP(hAPP(c_List_Otake(_1645450), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1645452), _1645454)), _1645456))], (10279 ^ _782476) ^ [_968776, _968778, _968780] : [hBOOL(hAPP(hAPP(c_member(_968776), _968778), _968780)), -(hAPP(hAPP(c_Set_Oinsert(_968776), _968778), _968780) = _968780)], (34352 ^ _782476) ^ [_1433021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433021), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433021)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3978 ^ _782476) ^ [_842407, _842409, _842411, _842413, _842415, _842417, _842419, _842421] : [-(c_New__DSequence_Oneg__bind(_842421, _842417, _842413, _842409) = c_New__DSequence_Oneg__bind(_842419, _842415, _842411, _842407)), _842421 = _842419, _842417 = _842415, _842413 = _842411, _842409 = _842407], (10217 ^ _782476) ^ [_967478, _967480, _967482, _967484, _967486] : [class_Groups_Oordered__ab__group__add(_967478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967478), _967480), _967482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967478), _967484), _967486), 10224 ^ _782476 : [(10231 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967478), _967484), _967486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967478), _967480), _967482)))], (10225 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967478), _967480), _967482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967478), _967484), _967486)))]]], (1492 ^ _782476) ^ [_804326, _804328] : [-(class_Lattices_Odistrib__lattice(_804326)), _804328 = _804326, class_Lattices_Odistrib__lattice(_804328)], (50543 ^ _782476) ^ [_1804563, _1804565] : [c_Relation_Otrans(_1804563, _1804565), -(c_Relation_Otrans(tc_List_Olist(_1804563), c_List_Olexord(_1804563, _1804565)))], (17293 ^ _782476) ^ [_1110990, _1110992] : [-(_1110990 = _1110992), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110990), _1110992))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110992), _1110990)))], (8363 ^ _782476) ^ [_926993, _926995, _926997] : [class_Complete__Lattice_Ocomplete__lattice(_926993), 8369 ^ _782476 : [(8372 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926993), _926997), 8368 ^ [_926993, _926995, _926997]))], (8370 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926993), 8368 ^ [_926993, _926995, _926997]), _926995)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926993), _926997), c_Complete__Lattice_OInf__class_OInf(_926993, _926995))))], (22355 ^ _782476) ^ [_1202184, _1202186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202184), hAPP(c_Nat_OSuc, _1202186))), -(_1202184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22363 ^ _782476 : [(22366 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22362 ^ [_1202184, _1202186]), _1202186)))], (22364 ^ _782476) ^ [] : [-(_1202184 = hAPP(c_Nat_OSuc, 22362 ^ [_1202184, _1202186]))]]], (30408 ^ _782476) ^ [_1358905, _1358907, _1358909, _1358911] : [class_Fields_Olinordered__field(_1358905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358905), c_Groups_Ozero__class_Ozero(_1358905)), _1358907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358905), _1358909), _1358907)), _1358911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358905), _1358909), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358905), _1358911), _1358907))))], (43731 ^ _782476) ^ [_1654130, _1654132, _1654134, _1654136] : [-(hAPP(c_List_Oset(tc_prod(_1654130, _1654132)), c_Enum_Oproduct(_1654130, _1654132, _1654134, _1654136)) = hAPP(hAPP(c_Product__Type_OSigma(_1654130, _1654132), hAPP(c_List_Oset(_1654130), _1654134)), hAPP(c_COMBK(tc_fun(_1654132, tc_HOL_Obool), _1654130), hAPP(c_List_Oset(_1654132), _1654136))))], (44881 ^ _782476) ^ [_1678720, _1678722, _1678724, _1678726] : [-(hAPP(hAPP(c_List_Onth(_1678720), hAPP(hAPP(c_List_Oappend(_1678720), _1678722), hAPP(hAPP(c_List_Olist_OCons(_1678720), _1678724), _1678726))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678720)), _1678722)) = _1678724)], (32746 ^ _782476) ^ [_1402919, _1402921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1402919)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402919), _1402921)), _1402919) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (40720 ^ _782476) ^ [_1577741, _1577743, _1577745, _1577747] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1577741, tc_HOL_Obool), tc_fun(_1577741, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1577741, tc_HOL_Obool), tc_fun(_1577741, tc_HOL_Obool)), _1577743), _1577745)), c_Wellfounded_Omax__ext(_1577741, _1577747))), 40723 ^ _782476 : [(40726 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577741), _1577745)))], (40728 ^ _782476) ^ [] : [_1577745 = c_Orderings_Obot__class_Obot(tc_fun(_1577741, tc_HOL_Obool))], (40730 ^ _782476) ^ [_1578035] : [hBOOL(hAPP(hAPP(c_member(_1577741), _1578035), _1577743)), 40734 ^ _782476 : [(40737 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577741, _1577741)), hAPP(hAPP(c_Product__Type_OPair(_1577741, _1577741), _1578035), 40733 ^ [_1577741, _1577743, _1577745, _1577747, _1578035])), _1577747)))], (40735 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577741), 40733 ^ [_1577741, _1577743, _1577745, _1577747, _1578035]), _1577745)))]]], (40724 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577741), _1577743)))]]], (44757 ^ _782476) ^ [_1676384, _1676386, _1676388, _1676390, _1676392, _1676394] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676384)), _1676386) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676388)), _1676390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676384)), _1676392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676388)), _1676394), -(hAPP(hAPP(c_List_Ozip(_1676384, _1676388), hAPP(hAPP(c_List_Oappend(_1676384), _1676386), _1676392)), hAPP(hAPP(c_List_Oappend(_1676388), _1676390), _1676394)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1676384, _1676388)), hAPP(hAPP(c_List_Ozip(_1676384, _1676388), _1676386), _1676390)), hAPP(hAPP(c_List_Ozip(_1676384, _1676388), _1676392), _1676394)))], (11726 ^ _782476) ^ [_995998, _996000, _996002, _996004] : [class_Orderings_Oorder(_995998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995998), _996000), _996002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995998), _996004), _996000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995998), _996004), _996002)))], (16763 ^ _782476) ^ [_1098680, _1098682, _1098684] : [class_Rings_Ocomm__ring__1(_1098680), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1098680), _1098682), _1098684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098680), _1098682), hAPP(c_Groups_Ouminus__class_Ouminus(_1098680), _1098684)))], (48707 ^ _782476) ^ [_1762550, _1762552, _1762554] : [hBOOL(hAPP(c_List_Odistinct(_1762550), _1762552)), -(c_List_Oremove1(_1762550, _1762554, _1762552) = hAPP(c_List_OremoveAll(_1762550, _1762554), _1762552))], (35188 ^ _782476) ^ [_1447713] : [c_Int_OPls = c_Int_OBit0(_1447713), -(c_Int_OPls = _1447713)], (41581 ^ _782476) ^ [_1598891, _1598893, _1598895, _1598897, _1598899, _1598901] : [c_Relation_Osingle__valued(_1598891, _1598893, hAPP(c_Relation_Oconverse(_1598893, _1598891), _1598895)), -(_1598897 = c_Orderings_Obot__class_Obot(tc_fun(_1598899, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1598893, _1598891, _1598895), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598899, tc_fun(_1598893, tc_HOL_Obool)), _1598897), _1598901)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598899, tc_fun(_1598891, tc_HOL_Obool)), _1598897), hAPP(hAPP(c_COMBB(tc_fun(_1598893, tc_HOL_Obool), tc_fun(_1598891, tc_HOL_Obool), _1598899), c_Relation_OImage(_1598893, _1598891, _1598895)), _1598901)))], (43348 ^ _782476) ^ [_1642881] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1642881)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1642881), tc_HOL_Obool))))], (19604 ^ _782476) ^ [_1150758, _1150760] : [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), _1150758), _1150760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150760), _1150758)))], (39653 ^ _782476) ^ [_1548447, _1548449, _1548451, _1548453] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548447, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548447, _1548449), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1548447, _1548449), tc_HOL_Obool)), _1548451), _1548453))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1548447, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548447, _1548449), _1548451)), hAPP(c_Relation_ODomain(_1548447, _1548449), _1548453)))))], (20357 ^ _782476) ^ [_1165192, _1165194, _1165196, _1165198] : [class_Groups_Ocomm__monoid__add(_1165192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165194), _1165196)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165194, _1165192), _1165198), _1165196) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165192, _1165194, c_Groups_Oplus__class_Oplus(_1165192)), _1165198), c_Groups_Ozero__class_Ozero(_1165192)), _1165196))], (11232 ^ _782476) ^ [_988600, _988602, _988604, _988606] : [class_Orderings_Opreorder(_988600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988600), _988602), _988604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988600), _988604), _988606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988600), _988602), _988606)))], (19376 ^ _782476) ^ [_1147028, _1147030] : [class_Groups_Oordered__ab__group__add(_1147028), 19379 ^ _782476 : [(19386 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147028), c_Groups_Ozero__class_Ozero(_1147028)), _1147030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147028), hAPP(c_Groups_Ouminus__class_Ouminus(_1147028), _1147030)), c_Groups_Ozero__class_Ozero(_1147028))))], (19380 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147028), hAPP(c_Groups_Ouminus__class_Ouminus(_1147028), _1147030)), c_Groups_Ozero__class_Ozero(_1147028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147028), c_Groups_Ozero__class_Ozero(_1147028)), _1147030)))]]], (26380 ^ _782476) ^ [_1281078, _1281080, _1281082, _1281084] : [class_Orderings_Olinorder(_1281078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281078), _1281080), _1281082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281078), _1281084), _1281082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281078), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281078), _1281080), _1281084)), _1281082)))], (3586 ^ _782476) ^ [_836103, _836105, _836107, _836109, _836111, _836113, _836115, _836117, _836119, _836121] : [-(c_List_Olinorder__class_Oinsort__insert__key(_836121, _836117, _836113, _836109, _836105) = c_List_Olinorder__class_Oinsort__insert__key(_836119, _836115, _836111, _836107, _836103)), _836121 = _836119, _836117 = _836115, _836113 = _836111, _836109 = _836107, _836105 = _836103], (44450 ^ _782476) ^ [_1668881] : [-(c_List_Olists(_1668881, c_Orderings_Obot__class_Obot(tc_fun(_1668881, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1668881)), c_List_Olist_ONil(_1668881)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1668881), tc_HOL_Obool))))], (46354 ^ _782476) ^ [_1711788, _1711790] : [-(c_Random_Oselect__weight(_1711788, _1711790) = 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(_1711788, 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, _1711788), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711788)), _1711790)))), hAPP(hAPP(c_COMBB(_1711788, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711788, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711788, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1711788, _1711790))))], (37028 ^ _782476) ^ [_1487685, _1487687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1487685)), 37031 ^ _782476 : [(37038 ^ _782476) ^ [] : [-(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), _1487687), _1487685)))), -(c_Divides_OnegDivAlg(_1487687, _1487685) = hAPP(c_Divides_Oadjust(_1487685), c_Divides_OnegDivAlg(_1487687, 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)))), _1487685))))], (37032 ^ _782476) ^ [] : [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), _1487687), _1487685))), -(c_Divides_OnegDivAlg(_1487687, _1487685) = 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), _1487687), _1487685)))]]], (40025 ^ _782476) ^ [_1560558, _1560560, _1560562, _1560564, _1560566, _1560568, _1560570] : [hAPP(c_Fun_Ocomp(_1560558, _1560560, _1560562, _1560564), _1560566) = hAPP(c_Fun_Ocomp(_1560560, _1560560, _1560562, c_Fun_Oid(_1560560)), _1560568), -(hAPP(_1560564, hAPP(_1560566, _1560570)) = hAPP(_1560568, _1560570))], (35824 ^ _782476) ^ [_1459023, _1459025, _1459027] : [class_Rings_Olinordered__idom(_1459023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459023), c_Groups_Ozero__class_Ozero(_1459023)), hAPP(hAPP(c_Power_Opower__class_Opower(_1459023), _1459025), 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)))), _1459027)))))], (52323 ^ _782476) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (23362 ^ _782476) ^ [] : [-(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))))], (29158 ^ _782476) ^ [_1335962, _1335964] : [29159 ^ _782476 : [(29162 ^ _782476) ^ [] : [_1335962 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29160 ^ _782476) ^ [] : [_1335964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335962), _1335964) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35112 ^ _782476) ^ [_1446347, _1446349] : [c_Int_OBit0(_1446347) = c_Int_OBit1(_1446349)], (47307 ^ _782476) ^ [_1734497, _1734499, _1734501, _1734503] : [-(c_List_Ofoldr(_1734497, _1734499, _1734501, c_List_Olist_ONil(_1734497), _1734503) = _1734503)], (52653 ^ _782476) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (9093 ^ _782476) ^ [_943242, _943244, _943246, _943248, _943250] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943242, tc_fun(_943244, tc_HOL_Obool)), _943246), hAPP(hAPP(c_COMBS(_943242, tc_fun(_943244, tc_HOL_Obool), tc_fun(_943244, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_943244, tc_HOL_Obool), tc_fun(tc_fun(_943244, tc_HOL_Obool), tc_fun(_943244, tc_HOL_Obool)), _943242), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943244, tc_HOL_Obool))), _943248)), _943250)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943244, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943242, tc_fun(_943244, tc_HOL_Obool)), _943246), _943248)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943242, tc_fun(_943244, tc_HOL_Obool)), _943246), _943250)))], (52121 ^ _782476) ^ [_1837785, _1837787] : [class_Lattices_Obounded__lattice(_1837785), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1837787, _1837785)))], (8390 ^ _782476) ^ [_927514, _927516, _927518] : [class_Complete__Lattice_Ocomplete__lattice(_927514), 8396 ^ _782476 : [(8399 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927514), 8395 ^ [_927514, _927516, _927518]), _927518))], (8397 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927514), 8395 ^ [_927514, _927516, _927518]), _927516)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927514), c_Complete__Lattice_OSup__class_OSup(_927514, _927516)), _927518)))], (45965 ^ _782476) ^ [_1702378, _1702380, _1702382] : [class_Groups_Omonoid__add(_1702378), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702378), hAPP(hAPP(c_List_Omap(_1702380, _1702378), hAPP(c_COMBK(_1702378, _1702380), c_Groups_Ozero__class_Ozero(_1702378))), _1702382)) = c_Groups_Ozero__class_Ozero(_1702378))], (38873 ^ _782476) ^ [_1528341, _1528343, _1528345, _1528347] : [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), _1528341), _1528343)), 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), _1528345), _1528347)), 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), _1528341), _1528347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528345), _1528343))))], (36332 ^ _782476) ^ [_1468017, _1468019, _1468021, _1468023] : [-(c_Nitpick_Oprod(_1468017, _1468019, _1468021, _1468023) = hAPP(c_Set_OCollect(tc_prod(_1468017, _1468019)), hAPP(c_Product__Type_Oprod_Oprod__case(_1468017, _1468019, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468017, tc_fun(_1468019, tc_HOL_Obool), tc_fun(_1468019, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1468019, tc_HOL_Obool), tc_fun(_1468019, tc_HOL_Obool)), _1468017), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1468019)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468017), c_fconj), hAPP(hAPP(c_COMBC(_1468017, tc_fun(_1468017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468017)), _1468021)))), hAPP(hAPP(c_COMBC(_1468019, tc_fun(_1468019, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468019)), _1468023)))))], (11812 ^ _782476) ^ [_997539, _997541, _997543] : [class_Groups_Oordered__ab__group__add(_997539), 11815 ^ _782476 : [(11822 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997539), _997543), _997541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997539), hAPP(c_Groups_Ouminus__class_Ouminus(_997539), _997541)), hAPP(c_Groups_Ouminus__class_Ouminus(_997539), _997543))))], (11816 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997539), hAPP(c_Groups_Ouminus__class_Ouminus(_997539), _997541)), hAPP(c_Groups_Ouminus__class_Ouminus(_997539), _997543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997539), _997543), _997541)))]]], (6137 ^ _782476) ^ [_879844, _879846, _879848, _879850, _879852, _879854] : [hBOOL(hAPP(hAPP(_879848, hAPP(_879850, _879852)), hAPP(_879850, _879854))), -(c_Predicate_Oinv__imagep(_879844, _879846, _879848, _879850, _879852, _879854))], (9043 ^ _782476) ^ [_941192, _941194, _941196, _941198] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941192, tc_HOL_Obool)), _941194), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941192, tc_HOL_Obool)), _941196), _941198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941192, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941192, tc_HOL_Obool)), _941194), _941196)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941192, tc_HOL_Obool)), _941194), _941198)))], (11612 ^ _782476) ^ [_994364, _994366, _994368] : [class_Orderings_Opreorder(_994364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994364), _994366), _994368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994364), _994366), _994368)))], (39758 ^ _782476) ^ [_1551897, _1551899, _1551901, _1551903, _1551905] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551897, _1551899), _1551901), hAPP(hAPP(c_COMBS(_1551897, tc_fun(_1551899, tc_HOL_Obool), tc_fun(_1551899, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551899, tc_HOL_Obool), tc_fun(tc_fun(_1551899, tc_HOL_Obool), tc_fun(_1551899, tc_HOL_Obool)), _1551897), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1551899, tc_HOL_Obool))), _1551903)), _1551905)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551897, _1551899), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551897, _1551899), _1551901), _1551903)), hAPP(hAPP(c_Product__Type_OSigma(_1551897, _1551899), _1551901), _1551905)))], (48512 ^ _782476) ^ [_1758516, _1758518, _1758520, _1758522, _1758524] : [c_List_OdropWhile(_1758516, _1758518, _1758520) = hAPP(hAPP(c_List_Olist_OCons(_1758516), _1758522), _1758524), 48515 ^ _782476 : [(48518 ^ _782476) ^ [] : [hBOOL(hAPP(_1758518, _1758522))], (48516 ^ _782476) ^ [] : [-(_1758520 = hAPP(hAPP(c_List_Oappend(_1758516), c_List_OtakeWhile(_1758516, _1758518, _1758520)), hAPP(hAPP(c_List_Olist_OCons(_1758516), _1758522), _1758524)))]]], (40549 ^ _782476) ^ [_1572817] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572817, tc_HOL_Obool) = c_Set_OBall(_1572817))], (21173 ^ _782476) ^ [_1180165, _1180167] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1180165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180167), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1180165, _1180167))], (32682 ^ _782476) ^ [_1401387, _1401389, _1401391, _1401393] : [c_Fun_Oinj__on(_1401387, tc_fun(tc_fun(_1401387, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1401387, tc_fun(tc_prod(_1401387, _1401387), tc_HOL_Obool), tc_fun(tc_fun(_1401387, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401387, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1401387, _1401387), tc_HOL_Obool), tc_fun(tc_fun(_1401387, tc_HOL_Obool), tc_HOL_Obool)), _1401387), c_Equiv__Relations_Oquotient(_1401387)), hAPP(hAPP(c_COMBC(_1401387, tc_fun(_1401387, tc_HOL_Obool), tc_fun(_1401387, tc_HOL_Obool)), c_Set_Oinsert(_1401387)), c_Orderings_Obot__class_Obot(tc_fun(_1401387, tc_HOL_Obool))))), _1401389), _1401391), hBOOL(hAPP(hAPP(c_member(_1401387), _1401393), _1401391)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401387), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401387, tc_HOL_Obool)), _1401391), hAPP(hAPP(c_Set_Oinsert(_1401387), _1401393), c_Orderings_Obot__class_Obot(tc_fun(_1401387, tc_HOL_Obool))))), _1401389) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1401387, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401387), _1401391), _1401389)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401387), hAPP(hAPP(c_Set_Oinsert(_1401387), _1401393), c_Orderings_Obot__class_Obot(tc_fun(_1401387, tc_HOL_Obool)))), _1401389)))], (16139 ^ _782476) ^ [_1085490, _1085492, _1085494, _1085496, _1085498] : [class_Groups_Oab__group__add(_1085490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085492), _1085494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1085492, tc_HOL_Obool)), _1085496), _1085494)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085492, _1085490), _1085498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085492, tc_HOL_Obool)), _1085494), _1085496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085490), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085492, _1085490), _1085498), _1085494)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085492, _1085490), _1085498), _1085496)))], (44815 ^ _782476) ^ [_1677568, _1677570, _1677572] : [_1677572 = c_List_Olist_ONil(_1677570), -(_1677568 = hAPP(hAPP(c_List_Oappend(_1677570), _1677568), _1677572))], (25518 ^ _782476) ^ [_1259368, _1259370] : [-(hBOOL(hAPP(_1259370, 25519 ^ [_1259368, _1259370]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1259368, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259368), _1259370))], (6110 ^ _782476) ^ [_879314, _879316, _879318] : [class_Orderings_Owellorder(_879314), hBOOL(hAPP(_879316, _879318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879314), c_Orderings_Oord__class_OLeast(_879314, _879316)), _879318)))], (43001 ^ _782476) ^ [_1632469, _1632471, _1632473, _1632475, _1632477, _1632479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632469, _1632469)), hAPP(hAPP(c_Product__Type_OPair(_1632469, _1632469), _1632471), _1632473)), c_Transitive__Closure_Ortrancl(_1632469, _1632475))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632469), tc_List_Olist(_1632469))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632469), tc_List_Olist(_1632469)), _1632477), _1632479)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632469), c_List_Olistrel1(_1632469, _1632475)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632469), tc_List_Olist(_1632469))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632469), tc_List_Olist(_1632469)), hAPP(hAPP(c_List_Olist_OCons(_1632469), _1632471), _1632477)), hAPP(hAPP(c_List_Olist_OCons(_1632469), _1632473), _1632479))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632469), c_List_Olistrel1(_1632469, _1632475)))))], (40891 ^ _782476) ^ [_1581477, _1581479] : [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), _1581477), _1581479)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581477), _1581479)))], (4830 ^ _782476) ^ [_856141, _856143, _856145, _856147, _856149, _856151, _856153, _856155] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856155, _856151, _856147, _856143) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856153, _856149, _856145, _856141)), _856155 = _856153, _856151 = _856149, _856147 = _856145, _856143 = _856141], (1026 ^ _782476) ^ [_797983, _797985, _797987, _797989] : [-(c_Equiv__Relations_Oequivp(_797987, _797983)), c_Equiv__Relations_Oequivp(_797989, _797985), _797989 = _797987, _797985 = _797983], (9364 ^ _782476) ^ [_950261] : [c_Orderings_Otop__class_Otop(tc_fun(_950261, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_950261, tc_HOL_Obool))], (22170 ^ _782476) ^ [_1199021, _1199023] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199021), _1199023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199023)), _1199021)))], (42127 ^ _782476) ^ [_1612361, _1612363, _1612365, _1612367] : [class_Lattices_Osemilattice__sup(_1612361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612361), _1612363)), hBOOL(hAPP(hAPP(c_member(_1612361), _1612365), _1612363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1612361), _1612365), _1612367)), hAPP(hAPP(c_Finite__Set_Ofold(_1612361, _1612361, c_Lattices_Osemilattice__sup__class_Osup(_1612361)), _1612367), _1612363))))], (7025 ^ _782476) ^ [_898189, _898191, _898193] : [hAPP(hAPP(c_COMBC(_898189, tc_fun(_898189, tc_HOL_Obool), tc_HOL_Obool), c_member(_898189)), _898191) = hAPP(hAPP(c_COMBC(_898189, tc_fun(_898189, tc_HOL_Obool), tc_HOL_Obool), c_member(_898189)), _898193), -(_898191 = _898193)], (7179 ^ _782476) ^ [_901832, _901834, _901836, _901838, _901840] : [hBOOL(hAPP(hAPP(c_member(_901832), _901834), _901836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901838, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_901832, tc_fun(_901838, tc_HOL_Obool)), _901836), _901840)), hAPP(_901840, _901834))))], (10988 ^ _782476) ^ [_985126, _985128, _985130, _985132, _985134] : [_985126 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_985128, tc_HOL_Obool), _985130), c_Orderings_Oorder__class_Omono(tc_fun(_985128, tc_HOL_Obool), tc_fun(_985128, tc_HOL_Obool), _985130), hBOOL(hAPP(hAPP(c_member(_985128), _985132), _985134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985128, tc_HOL_Obool)), _985134), hAPP(_985130, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985128, tc_HOL_Obool)), _985134), _985126)))), -(hBOOL(hAPP(hAPP(c_member(_985128), _985132), _985126)))], (6971 ^ _782476) ^ [_896751, _896753, _896755] : [hBOOL(hAPP(_896755, _896753)), -(hBOOL(hAPP(hAPP(c_member(_896751), _896753), _896755)))], (9175 ^ _782476) ^ [_945238, _945240, _945242] : [class_Groups_Oordered__ab__group__add(_945238), -(hAPP(c_Set_Oimage(_945238, _945238, c_Groups_Ouminus__class_Ouminus(_945238)), c_SetInterval_Oord__class_OatLeastAtMost(_945238, _945240, _945242)) = c_SetInterval_Oord__class_OatLeastAtMost(_945238, hAPP(c_Groups_Ouminus__class_Ouminus(_945238), _945242), hAPP(c_Groups_Ouminus__class_Ouminus(_945238), _945240)))], (24328 ^ _782476) ^ [_1237894, _1237896] : [c_Nat__Transfer_Onat__set(_1237894), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1237896), _1237894)), -(c_Nat__Transfer_Ois__nat(_1237896))], (5526 ^ _782476) ^ [_867037, _867039] : [_867039 = _867037, -(c_Set_Oinsert(_867039) = c_Set_Oinsert(_867037))], (5830 ^ _782476) ^ [_874766, _874768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874766, tc_HOL_Obool)), _874768), _874768)))], (6530 ^ _782476) ^ [_887418, _887420, _887422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887418, tc_HOL_Obool)), _887420), _887422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887418, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_887418), _887420)), hAPP(c_Set_OPow(_887418), _887422))))], (19722 ^ _782476) ^ [_1152853, _1152855] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1152853), _1152855)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24979 ^ _782476) ^ [_1249419] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249419)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249419))], (52407 ^ _782476) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (13512 ^ _782476) ^ [_1032637, _1032639, _1032641, _1032643] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032637, _1032639, _1032641, _1032643, c_Orderings_Obot__class_Obot(tc_fun(_1032637, tc_HOL_Obool))), _1032643)))], (16255 ^ _782476) ^ [_1088014, _1088016, _1088018, _1088020, _1088022] : [class_Groups_Ocomm__monoid__add(_1088014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088016), _1088018)), hBOOL(hAPP(hAPP(c_member(_1088016), _1088020), _1088018)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088016, _1088014), _1088022), _1088018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088014), hAPP(_1088022, _1088020)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088016, _1088014), _1088022), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088016, tc_HOL_Obool)), _1088018), hAPP(hAPP(c_Set_Oinsert(_1088016), _1088020), c_Orderings_Obot__class_Obot(tc_fun(_1088016, tc_HOL_Obool)))))))], (32135 ^ _782476) ^ [_1391047] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391047, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1391047)], (13588 ^ _782476) ^ [_1034041, _1034043, _1034045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1034041, tc_HOL_Obool)), _1034043), _1034045)), -(hBOOL(hAPP(hAPP(c_member(_1034041), 13591 ^ [_1034041, _1034043, _1034045]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1034041, tc_HOL_Obool)), _1034045), _1034043))))], (38610 ^ _782476) ^ [_1521902, _1521904, _1521906, _1521908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521902), _1521904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521906), _1521908)), -(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), _1521902), _1521906)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521904), _1521908))), c_FunDef_Opair__leq)))], (26614 ^ _782476) ^ [_1285127, _1285129, _1285131, _1285133] : [class_Orderings_Olinorder(_1285127), 26617 ^ _782476 : [(26626 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285127), _1285131), _1285133)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), _1285131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), _1285133))], (26618 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285127), _1285131), _1285133))), 26621 ^ _782476 : [(26624 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), _1285133)))], (26622 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285127), _1285129), _1285131)))]]]]], (32119 ^ _782476) ^ [_1390807, _1390809] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390807), _1390809) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390807, _1390809) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (16709 ^ _782476) ^ [_1097525, _1097527, _1097529] : [class_Groups_Ogroup__add(_1097525), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097525), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097525), _1097527), _1097529)), _1097529) = _1097527)], (26882 ^ _782476) ^ [_1290026, _1290028, _1290030] : [class_Orderings_Olinorder(_1290026), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290026), _1290028), _1290030) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290026), _1290030), _1290028))], (14503 ^ _782476) ^ [_1052617, _1052619, _1052621, _1052623] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052617), _1052619)), c_Fun_Oinj__on(_1052621, _1052617, _1052623, c_Orderings_Otop__class_Otop(tc_fun(_1052621, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052621), hAPP(c_Set_Ovimage(_1052621, _1052617, _1052623), _1052619))))], (4442 ^ _782476) ^ [_849893, _849895] : [_849895 = _849893, -(c_Orderings_Oord__class_Omin(_849895) = c_Orderings_Oord__class_Omin(_849893))], (6772 ^ _782476) ^ [_892220, _892222, _892224, _892226, _892228, _892230] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892220, tc_fun(_892222, tc_HOL_Obool)), _892224), _892226), _892228)), -(hBOOL(hAPP(hAPP(_892226, _892230), _892228))), hBOOL(hAPP(hAPP(c_member(_892220), _892230), _892224))], (50871 ^ _782476) ^ [_1812032, _1812034] : [c_Relation_Oantisym(_1812032, _1812034), 50874 ^ _782476 : [(50875 ^ _782476) ^ [_1812144, _1812146] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1812032, _1812032)), hAPP(hAPP(c_Product__Type_OPair(_1812032, _1812032), _1812146), _1812144)), _1812034)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1812032, _1812032)), hAPP(hAPP(c_Product__Type_OPair(_1812032, _1812032), _1812144), _1812146)), _1812034)), -(_1812146 = _1812144)]]], (28251 ^ _782476) ^ [_1316730, _1316732, _1316734] : [class_Orderings_Olinorder(_1316730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316730), _1316732)), -(_1316732 = c_Orderings_Obot__class_Obot(tc_fun(_1316730, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316730), _1316734)), -(_1316734 = c_Orderings_Obot__class_Obot(tc_fun(_1316730, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316730), c_Big__Operators_Olattice_OInf__fin(_1316730, c_Orderings_Oord__class_Omin(_1316730), _1316732)), c_Big__Operators_Olattice_OInf__fin(_1316730, c_Orderings_Oord__class_Omin(_1316730), _1316734)) = c_Big__Operators_Olattice_OInf__fin(_1316730, c_Orderings_Oord__class_Omin(_1316730), hAPP(c_Set_OCollect(_1316730), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_HOL_Obool), tc_HOL_Obool, _1316730), c_HOL_OEx(_1316730)), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool)), tc_fun(_1316730, tc_HOL_Obool), _1316730), hAPP(c_COMBB(tc_fun(_1316730, tc_HOL_Obool), tc_HOL_Obool, _1316730), c_HOL_OEx(_1316730))), hAPP(hAPP(c_COMBC(_1316730, tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool)), tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_fun(tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool))), tc_fun(tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool)), tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool))), _1316730), c_COMBS(_1316730, tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_fun(_1316730, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1316730, tc_fun(tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool))), _1316730), hAPP(c_COMBB(tc_fun(_1316730, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool)), _1316730), c_COMBS(_1316730, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool)), tc_fun(_1316730, tc_fun(_1316730, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1316730), hAPP(c_COMBB(tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1316730), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316730), c_fconj))), hAPP(hAPP(c_COMBC(_1316730, tc_fun(_1316730, tc_fun(_1316730, _1316730)), tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1316730, _1316730), tc_fun(_1316730, tc_HOL_Obool)), tc_fun(tc_fun(_1316730, tc_fun(_1316730, _1316730)), tc_fun(_1316730, tc_fun(_1316730, tc_HOL_Obool))), _1316730), c_COMBB(tc_fun(_1316730, _1316730), tc_fun(_1316730, tc_HOL_Obool), _1316730)), hAPP(hAPP(c_COMBB(tc_fun(_1316730, tc_HOL_Obool), tc_fun(tc_fun(_1316730, _1316730), tc_fun(_1316730, tc_HOL_Obool)), _1316730), c_COMBB(_1316730, tc_HOL_Obool, _1316730)), c_fequal))), c_Orderings_Oord__class_Omax(_1316730)))))), hAPP(hAPP(c_COMBC(_1316730, tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1316730, tc_HOL_Obool), tc_fun(_1316730, tc_HOL_Obool)), _1316730), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1316730)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316730), c_fconj), hAPP(hAPP(c_COMBC(_1316730, tc_fun(_1316730, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316730)), _1316732)))), hAPP(hAPP(c_COMBC(_1316730, tc_fun(_1316730, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316730)), _1316734))))))))], (5178 ^ _782476) ^ [_861613, _861615, _861617, _861619] : [-(c_Orderings_Oord__class_OLeast(_861619, _861615) = c_Orderings_Oord__class_OLeast(_861617, _861613)), _861619 = _861617, _861615 = _861613], (18822 ^ _782476) ^ [_1136997, _1136999, _1137001] : [class_Rings_Oordered__cancel__semiring(_1136997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136997), c_Groups_Ozero__class_Ozero(_1136997)), _1136999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136997), _1137001), c_Groups_Ozero__class_Ozero(_1136997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136997), _1136999), _1137001)), c_Groups_Ozero__class_Ozero(_1136997))))], (36994 ^ _782476) ^ [_1487106, _1487108] : [36995 ^ _782476 : [(36998 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487108), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36996 ^ _782476) ^ [] : [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), _1487106), _1487108)))]], -(c_Divides_OnegDivAlg(_1487106, _1487108) = 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), _1487106), _1487108)))], (2228 ^ _782476) ^ [_815068, _815070, _815072, _815074] : [-(c_Orderings_Oord_Omax(_815074, _815070) = c_Orderings_Oord_Omax(_815072, _815068)), _815074 = _815072, _815070 = _815068], (3208 ^ _782476) ^ [_830202, _830204, _830206, _830208] : [-(c_Big__Operators_Olattice__class_OInf__fin(_830208, _830204) = c_Big__Operators_Olattice__class_OInf__fin(_830206, _830202)), _830208 = _830206, _830204 = _830202], (40213 ^ _782476) ^ [_1565415, _1565417, _1565419, _1565421, _1565423, _1565425, _1565427, _1565429] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565415, _1565417)), _1565419), hAPP(c_Set_Oimage(tc_prod(_1565421, _1565423), tc_prod(_1565415, _1565417), c_Product__Type_Omap__pair(_1565421, _1565415, _1565423, _1565417, _1565425, _1565427)), _1565429))), 40218 ^ _782476 : [(40221 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565421, _1565423)), hAPP(hAPP(c_Product__Type_OPair(_1565421, _1565423), 40216 ^ [_1565415, _1565417, _1565419, _1565421, _1565423, _1565425, _1565427, _1565429]), 40217 ^ [_1565415, _1565417, _1565419, _1565421, _1565423, _1565425, _1565427, _1565429])), _1565429)))], (40219 ^ _782476) ^ [] : [-(_1565419 = hAPP(hAPP(c_Product__Type_OPair(_1565415, _1565417), hAPP(_1565425, 40216 ^ [_1565415, _1565417, _1565419, _1565421, _1565423, _1565425, _1565427, _1565429])), hAPP(_1565427, 40217 ^ [_1565415, _1565417, _1565419, _1565421, _1565423, _1565425, _1565427, _1565429])))]]], (41296 ^ _782476) ^ [] : [-(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))))], (26816 ^ _782476) ^ [_1288787] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288787) = _1288787)], (10015 ^ _782476) ^ [_963178, _963180] : [-(hBOOL(hAPP(hAPP(c_member(_963178), _963180), c_Orderings_Otop__class_Otop(tc_fun(_963178, tc_HOL_Obool)))))], (50833 ^ _782476) ^ [_1811422, _1811424] : [c_Relation_Otrans(_1811422, _1811424), c_Relation_Oantisym(_1811422, _1811424), -(c_Relation_Otrans(_1811422, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1811422, _1811422), tc_HOL_Obool)), _1811424), c_Relation_OId(_1811422))))], (14166 ^ _782476) ^ [_1046303, _1046305, _1046307, _1046309] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046307), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1046303, tc_fun(_1046307, tc_HOL_Obool)), _1046305), _1046309)))), 14167 ^ _782476 : [(14168 ^ _782476) ^ [_1046377] : [hBOOL(hAPP(hAPP(c_member(_1046303), _1046377), _1046305)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046307), hAPP(_1046309, _1046377)))]]], (13766 ^ _782476) ^ [_1037866, _1037868, _1037870, _1037872, _1037874] : [c_Fun_Obij__betw(_1037866, _1037868, _1037870, _1037872, _1037874), -(c_Fun_Oinj__on(_1037866, _1037868, _1037870, _1037872))], (13230 ^ _782476) ^ [_1026393, _1026395, _1026397, _1026399, _1026401, _1026403] : [-(hAPP(c_Set_Ovimage(_1026393, _1026395, _1026397), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026399, tc_fun(_1026395, tc_HOL_Obool)), _1026401), _1026403)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026399, tc_fun(_1026393, tc_HOL_Obool)), _1026401), hAPP(hAPP(c_COMBB(tc_fun(_1026395, tc_HOL_Obool), tc_fun(_1026393, tc_HOL_Obool), _1026399), c_Set_Ovimage(_1026393, _1026395, _1026397)), _1026403)))], (10639 ^ _782476) ^ [_977088, _977090, _977092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977088, tc_HOL_Obool)), _977090), _977092)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977088, tc_HOL_Obool)), _977090), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977088, tc_HOL_Obool)), _977092), _977090)) = _977092)], (52705 ^ _782476) ^ [_1843988] : [-(hBOOL(_1843988)), -(hBOOL(hAPP(c_fNot, _1843988)))], (46294 ^ _782476) ^ [_1710490, _1710492, _1710494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1710490), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710492), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1710492)), _1710494)))), -(hBOOL(hAPP(hAPP(c_member(_1710492), hAPP(c_Random_Opick(_1710492, _1710494), _1710490)), hAPP(c_List_Oset(_1710492), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710492), _1710492), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1710492)), _1710494)))))], (52023 ^ _782476) ^ [_1836164, _1836166] : [_1836164 = _1836166, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836164, _1836166) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1836164), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (36922 ^ _782476) ^ [_1485424, _1485426, _1485428, _1485430, _1485432, _1485434, _1485436, _1485438] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485424, _1485426, _1485428), _1485430), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485432, _1485434, tc_prod(_1485424, _1485426)), _1485436), _1485438)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485432, _1485434, _1485428), hAPP(hAPP(c_COMBB(tc_fun(_1485434, tc_prod(_1485424, _1485426)), tc_fun(_1485434, _1485428), _1485432), hAPP(c_COMBB(tc_prod(_1485424, _1485426), _1485428, _1485434), hAPP(c_Product__Type_Oprod_Oprod__case(_1485424, _1485426, _1485428), _1485430))), _1485436)), _1485438))], (9051 ^ _782476) ^ [_941408, _941410, _941412, _941414, _941416] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941408, tc_fun(_941410, tc_HOL_Obool)), _941412), hAPP(hAPP(c_COMBS(_941408, tc_fun(_941410, tc_HOL_Obool), tc_fun(_941410, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_941410, tc_HOL_Obool), tc_fun(tc_fun(_941410, tc_HOL_Obool), tc_fun(_941410, tc_HOL_Obool)), _941408), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941410, tc_HOL_Obool))), _941414)), _941416)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941410, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941410, tc_HOL_Obool), hAPP(c_Set_Oimage(_941408, tc_fun(_941410, tc_HOL_Obool), _941414), _941412))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941410, tc_HOL_Obool), hAPP(c_Set_Oimage(_941408, tc_fun(_941410, tc_HOL_Obool), _941416), _941412))))], (34230 ^ _782476) ^ [_1431154, _1431156] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431154)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431154)), _1431156) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431154)), _1431156)))], (36392 ^ _782476) ^ [_1469284, _1469286, _1469288, _1469290] : [hAPP(hAPP(c_COMBC(_1469284, tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_fun(_1469286, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469286, tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_fun(_1469286, tc_HOL_Obool)), _1469284), c_COMBC(_1469286, tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469286, tc_prod(_1469284, _1469286)), tc_fun(_1469286, tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), _1469284), hAPP(c_COMBB(tc_prod(_1469284, _1469286), tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool), _1469286), c_member(tc_prod(_1469284, _1469286)))), c_Product__Type_OPair(_1469284, _1469286)))), _1469288) = hAPP(hAPP(c_COMBC(_1469284, tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_fun(_1469286, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469286, tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_fun(_1469286, tc_HOL_Obool)), _1469284), c_COMBC(_1469286, tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469286, tc_prod(_1469284, _1469286)), tc_fun(_1469286, tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool)), _1469284), hAPP(c_COMBB(tc_prod(_1469284, _1469286), tc_fun(tc_fun(tc_prod(_1469284, _1469286), tc_HOL_Obool), tc_HOL_Obool), _1469286), c_member(tc_prod(_1469284, _1469286)))), c_Product__Type_OPair(_1469284, _1469286)))), _1469290), -(_1469288 = _1469290)], (41489 ^ _782476) ^ [_1596495, _1596497, _1596499] : [c_Relation_Orefl__on(_1596495, _1596497, _1596499), -(c_Relation_Orefl__on(_1596495, _1596497, hAPP(c_Relation_Oconverse(_1596495, _1596495), _1596499)))], (27106 ^ _782476) ^ [_1294949, _1294951, _1294953, _1294955] : [class_Rings_Ocomm__semiring__1(_1294949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294951), _1294953)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294951, _1294949), _1294955), _1294953) = c_Groups_Ozero__class_Ozero(_1294949)), 27115 ^ _782476 : [(27116 ^ _782476) ^ [_1295130] : [hBOOL(hAPP(hAPP(c_member(_1294951), _1295130), _1294953)), hAPP(_1294955, _1295130) = c_Groups_Ozero__class_Ozero(_1294949)]]], (49164 ^ _782476) ^ [_1773722, _1773724, _1773726] : [c_List_Olist__all(_1773722, _1773724, _1773726), 49167 ^ _782476 : [(49168 ^ _782476) ^ [_1773811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773811), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773722)), _1773726))), -(hBOOL(hAPP(_1773724, hAPP(hAPP(c_List_Onth(_1773722), _1773726), _1773811))))]]], (48058 ^ _782476) ^ [_1748952] : [-(hAPP(c_List_Orev(_1748952), c_List_Olist_ONil(_1748952)) = c_List_Olist_ONil(_1748952))], (49532 ^ _782476) ^ [_1781505, _1781507, _1781509] : [c_Fun_Obij__betw(_1781505, _1781507, _1781509, c_Orderings_Otop__class_Otop(tc_fun(_1781505, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781507, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1781507, _1781505, c_Hilbert__Choice_Oinv__into(_1781505, _1781507, c_Orderings_Otop__class_Otop(tc_fun(_1781505, tc_HOL_Obool)), _1781509), c_Orderings_Otop__class_Otop(tc_fun(_1781507, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781505, tc_HOL_Obool))))], (22046 ^ _782476) ^ [_1197085, _1197087] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197085), _1197087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197087), hAPP(c_Nat_OSuc, _1197085))))], (50182 ^ _782476) ^ [_1795930] : [-(c_List_Omember(_1795930) = c_List_Oset(_1795930))], (35742 ^ _782476) ^ [_1457356, _1457358, _1457360] : [class_Rings_Oring__1(_1457356), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457356), hAPP(c_Groups_Ouminus__class_Ouminus(_1457356), _1457358)), 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)))), _1457360)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1457356), _1457358), 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)))), _1457360)))], (45559 ^ _782476) ^ [_1694567, _1694569] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1694567), hAPP(c_List_Oset(tc_Nat_Onat), _1694569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1694567), 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)), _1694569))))], (43299 ^ _782476) ^ [_1641535, _1641537, _1641539, _1641541] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641535), tc_List_Olist(_1641535))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641535), tc_List_Olist(_1641535)), _1641537), _1641539)), c_List_Olistrel(_1641535, _1641541)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641535)), _1641537) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641535)), _1641539), 43305 ^ _782476 : [(43308 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1641535, _1641535)), hAPP(hAPP(c_Product__Type_OPair(_1641535, _1641535), hAPP(hAPP(c_List_Onth(_1641535), _1641537), 43304 ^ [_1641535, _1641537, _1641539, _1641541])), hAPP(hAPP(c_List_Onth(_1641535), _1641539), 43304 ^ [_1641535, _1641537, _1641539, _1641541]))), _1641541))], (43306 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43304 ^ [_1641535, _1641537, _1641539, _1641541]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641535)), _1641537))))]]], (16751 ^ _782476) ^ [_1098404, _1098406, _1098408] : [class_Rings_Ocomm__semiring__1(_1098404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098404), _1098406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098404), _1098408), _1098406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098404), _1098408), c_Groups_Oone__class_Oone(_1098404))), _1098406))], (20455 ^ _782476) ^ [_1167307, _1167309] : [-(_1167307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167307), _1167309) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1167309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167307), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1167309)))], (32133 ^ _782476) ^ [_1391021] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391021), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52255 ^ _782476) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12690 ^ _782476) ^ [_1015096, _1015098, _1015100, _1015102, _1015104, _1015106] : [c_Fun_Oinj__on(_1015096, _1015098, _1015100, _1015102), hBOOL(hAPP(hAPP(c_member(_1015096), _1015104), _1015102)), hBOOL(hAPP(hAPP(c_member(_1015096), _1015106), _1015102)), 12701 ^ _782476 : [(12708 ^ _782476) ^ [] : [_1015104 = _1015106, -(hAPP(_1015100, _1015104) = hAPP(_1015100, _1015106))], (12702 ^ _782476) ^ [] : [hAPP(_1015100, _1015104) = hAPP(_1015100, _1015106), -(_1015104 = _1015106)]]], (16315 ^ _782476) ^ [_1089502, _1089504, _1089506, _1089508, _1089510] : [class_Groups_Ocomm__monoid__add(_1089502), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089502), _1089504), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089506), _1089508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089510), _1089508))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089502), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089502, tc_Nat_Onat), _1089504), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089508))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089506, _1089510)))], (34724 ^ _782476) ^ [_1438855, _1438857] : [class_Int_Onumber__ring(_1438855), class_Rings_Olinordered__idom(_1438855), 34731 ^ _782476 : [(34738 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438855), c_Groups_Oone__class_Oone(_1438855)), hAPP(c_Int_Onumber__class_Onumber__of(_1438855), _1438857))))], (34732 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438855), c_Groups_Oone__class_Oone(_1438855)), hAPP(c_Int_Onumber__class_Onumber__of(_1438855), _1438857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438857)))]]], (2812 ^ _782476) ^ [_824084, _824086, _824088, _824090, _824092, _824094] : [-(c_Random_Ominus__shift(_824094, _824090, _824086) = c_Random_Ominus__shift(_824092, _824088, _824084)), _824094 = _824092, _824090 = _824088, _824086 = _824084], (4282 ^ _782476) ^ [_847389, _847391, _847393, _847395, _847397, _847399, _847401, _847403] : [-(c_Lazy__Sequence_Oproduct(_847403, _847399, _847395, _847391) = c_Lazy__Sequence_Oproduct(_847401, _847397, _847393, _847389)), _847403 = _847401, _847399 = _847397, _847395 = _847393, _847391 = _847389], (47556 ^ _782476) ^ [_1739697, _1739699] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1739697, _1739699)))], (50553 ^ _782476) ^ [_1804706, _1804708] : [c_Relation_Otrans(_1804706, _1804708), -(c_Transitive__Closure_Otrancl(_1804706, _1804708) = _1804708)], (13534 ^ _782476) ^ [_1032974, _1032976, _1032978, _1032980, _1032982, _1032984, _1032986] : [-(hBOOL(hAPP(hAPP(c_member(_1032974), _1032976), _1032978))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032974, _1032980, _1032982, _1032984, _1032978), _1032986)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032974, _1032980, _1032982, _1032984, hAPP(hAPP(c_Set_Oinsert(_1032974), _1032976), _1032978)), hAPP(hAPP(_1032982, _1032976), _1032986))))], (46444 ^ _782476) ^ [_1713435, _1713437] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713435), _1713437) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1713435), _1713437))], (26900 ^ _782476) ^ [_1290353, _1290355, _1290357] : [class_Orderings_Olinorder(_1290353), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290353), _1290355), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290353), _1290355), _1290357)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290353), _1290355), _1290357))], (35478 ^ _782476) ^ [_1452972] : [class_Int_Onumber__ring(_1452972), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452972), c_Groups_Oone__class_Oone(_1452972)), c_Groups_Oone__class_Oone(_1452972)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452972), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (52231 ^ _782476) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (10721 ^ _782476) ^ [_978799, _978801] : [class_Complete__Lattice_Ocomplete__lattice(_978799), -(c_Complete__Lattice_OInf__class_OInf(_978799, hAPP(hAPP(c_Set_Oinsert(_978799), _978801), c_Orderings_Obot__class_Obot(tc_fun(_978799, tc_HOL_Obool)))) = _978801)], (17427 ^ _782476) ^ [_1113006, _1113008, _1113010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113006), _1113008)), _1113010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113006), _1113010)))], (20860 ^ _782476) ^ [_1174857, _1174859] : [-(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), _1174857))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174859))))], (7651 ^ _782476) ^ [_911122, _911124, _911126, _911128, _911130] : [7653 ^ _782476 : [(7656 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911126, tc_HOL_Obool)), _911128), hAPP(_911130, 7652 ^ [_911122, _911124, _911126, _911128, _911130])))], (7654 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911122), 7652 ^ [_911122, _911124, _911126, _911128, _911130]), _911124)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911126, tc_HOL_Obool)), _911128), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911122, tc_fun(_911126, tc_HOL_Obool)), _911124), _911130))))], (35142 ^ _782476) ^ [_1446906, _1446908] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1446906)), _1446908) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446906), _1446908)))], (13609 ^ _782476) ^ [_1034574, _1034576, _1034578, _1034580, _1034582, _1034584] : [hBOOL(hAPP(hAPP(c_member(_1034574), _1034576), _1034578)), -(hAPP(c_Fun_Ooverride__on(_1034574, _1034580, _1034582, _1034584, _1034578), _1034576) = hAPP(_1034584, _1034576))], (6333 ^ _782476) ^ [_883423, _883425, _883427, _883429, _883431, _883433] : [class_Complete__Lattice_Ocomplete__lattice(_883423), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883425, _883423), _883427), hAPP(hAPP(c_COMBB(tc_fun(_883429, _883423), _883423, _883425), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883429, _883423), _883431)), _883433)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883429, _883423), _883431), hAPP(hAPP(c_COMBB(tc_fun(_883425, _883423), _883423, _883429), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883425, _883423), _883427)), hAPP(c_COMBC(_883425, _883429, _883423), _883433))))], (49964 ^ _782476) ^ [_1791424, _1791426, _1791428, _1791430] : [49972 ^ _782476 : [(49975 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1791430, 49971 ^ [_1791424, _1791426, _1791428, _1791430])))], (49973 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791424), 49971 ^ [_1791424, _1791426, _1791428, _1791430]), hAPP(c_List_Oset(_1791424), c_List_Oreplicate(_1791424, _1791426, _1791428)))))]], hBOOL(hAPP(_1791430, _1791428)), -(_1791426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49079 ^ _782476) ^ [_1771824, _1771826, _1771828] : [c_List_Olist__ex(_1771824, _1771826, _1771828), -(c_List_Olist__ex(_1771824, _1771826, hAPP(c_List_Orev(_1771824), _1771828)))], (31856 ^ _782476) ^ [_1385637, _1385639, _1385641, _1385643, _1385645, _1385647] : [class_Divides_Osemiring__div(_1385637), c_Divides_Odiv__class_Omod(_1385637, _1385639, _1385641) = c_Divides_Odiv__class_Omod(_1385637, _1385643, _1385641), c_Divides_Odiv__class_Omod(_1385637, _1385645, _1385641) = c_Divides_Odiv__class_Omod(_1385637, _1385647, _1385641), -(c_Divides_Odiv__class_Omod(_1385637, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385637), _1385639), _1385645), _1385641) = c_Divides_Odiv__class_Omod(_1385637, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385637), _1385643), _1385647), _1385641))], (41605 ^ _782476) ^ [_1599389, _1599391, _1599393, _1599395, _1599397] : [c_Relation_Osingle__valued(_1599389, _1599391, _1599393), c_Relation_Osingle__valued(_1599391, _1599395, _1599397), -(c_Relation_Osingle__valued(_1599389, _1599395, hAPP(hAPP(c_Relation_Orel__comp(_1599389, _1599391, _1599395), _1599393), _1599397)))], (17624 ^ _782476) ^ [_1116569, _1116571, _1116573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116569), _1116571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116569), _1116573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116573), _1116571)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116573), _1116569))))], (360 ^ _782476) ^ [_787976, _787978, _787980, _787982] : [-(c_Wellfounded_OwfP(_787980, _787976)), c_Wellfounded_OwfP(_787982, _787978), _787982 = _787980, _787978 = _787976], (14483 ^ _782476) ^ [_1052221, _1052223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052221), c_Orderings_Otop__class_Otop(tc_fun(_1052221, tc_HOL_Obool)))), c_Fun_Oinj__on(_1052221, _1052221, _1052223, c_Orderings_Otop__class_Otop(tc_fun(_1052221, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1052221, _1052221, _1052223), c_Orderings_Otop__class_Otop(tc_fun(_1052221, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052221, tc_HOL_Obool)))], (22770 ^ _782476) ^ [_1209593, _1209595, _1209597, _1209599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1209593), hAPP(c_Set_Oimage(_1209595, _1209593, _1209597), _1209599))), hAPP(c_Finite__Set_Ocard(_1209595), _1209599))), c_Fun_Oinj__on(_1209595, _1209593, _1209597, _1209599)], (13340 ^ _782476) ^ [_1028868, _1028870, _1028872, _1028874, _1028876] : [-(hAPP(c_Fun_Othe__inv__into(_1028868, _1028870, _1028872, _1028874), _1028876) = c_HOL_OThe(_1028868, hAPP(hAPP(c_COMBS(_1028868, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1028868), c_fconj), hAPP(hAPP(c_COMBC(_1028868, tc_fun(_1028868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028868)), _1028872))), hAPP(hAPP(c_COMBC(_1028868, _1028870, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1028870, tc_fun(_1028870, tc_HOL_Obool), _1028868), c_fequal), _1028874)), _1028876))))], (1712 ^ _782476) ^ [_807076, _807078] : [-(class_Groups_Oab__semigroup__mult(_807076)), _807078 = _807076, class_Groups_Oab__semigroup__mult(_807078)], (32595 ^ _782476) ^ [_1399899, _1399901] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399899, _1399901)) = _1399901), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399899), _1399901) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399899, _1399901)))], (1212 ^ _782476) ^ [_800826, _800828] : [-(class_Rings_Oring__1__no__zero__divisors(_800826)), _800828 = _800826, class_Rings_Oring__1__no__zero__divisors(_800828)], (36565 ^ _782476) ^ [_1477505, _1477507, _1477509, _1477511, _1477513, _1477515] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477505, tc_fun(_1477507, tc_fun(_1477509, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477505, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_fun(_1477507, tc_fun(_1477509, tc_HOL_Obool)), _1477505), hAPP(c_COMBC(_1477507, tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_fun(_1477509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477509, tc_fun(tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_fun(_1477509, tc_HOL_Obool)), _1477507), c_COMBC(_1477509, tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477509, tc_prod(_1477507, _1477509)), tc_fun(_1477509, tc_fun(tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_HOL_Obool)), _1477507), hAPP(c_COMBB(tc_prod(_1477507, _1477509), tc_fun(tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool), tc_HOL_Obool), _1477509), c_member(tc_prod(_1477507, _1477509)))), c_Product__Type_OPair(_1477507, _1477509))))), _1477511)), _1477513), _1477515)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477507, _1477509)), hAPP(hAPP(c_Product__Type_OPair(_1477507, _1477509), _1477513), _1477515)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477505, tc_fun(tc_prod(_1477507, _1477509), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477505, tc_HOL_Obool))), _1477511))))], (1842 ^ _782476) ^ [_808701, _808703] : [-(class_Orderings_Olinorder(_808701)), _808703 = _808701, class_Orderings_Olinorder(_808703)], (12015 ^ _782476) ^ [_1001106, _1001108, _1001110] : [class_Complete__Lattice_Ocomplete__lattice(_1001106), class_Orderings_Olinorder(_1001106), 12022 ^ _782476 : [(12032 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001106), c_Complete__Lattice_OInf__class_OInf(_1001106, _1001108)), _1001110))), 12033 ^ _782476 : [(12034 ^ _782476) ^ [_1001412] : [hBOOL(hAPP(hAPP(c_member(_1001106), _1001412), _1001108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001106), _1001412), _1001110))]]], (12023 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001106), c_Complete__Lattice_OInf__class_OInf(_1001106, _1001108)), _1001110)), 12027 ^ _782476 : [(12030 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001106), 12026 ^ [_1001106, _1001108, _1001110]), _1001110)))], (12028 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001106), 12026 ^ [_1001106, _1001108, _1001110]), _1001108)))]]]]], (11036 ^ _782476) ^ [_985867, _985869, _985871] : [class_Orderings_Olinorder(_985867), 11039 ^ _782476 : [(11040 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985867), _985869), _985871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985867), _985871), _985869))), -(_985869 = _985871)], (11050 ^ _782476) ^ [] : [11051 ^ _782476 : [(11054 ^ _782476) ^ [] : [_985869 = _985871], (11052 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985867), _985871), _985869))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985867), _985869), _985871))]]], (39214 ^ _782476) ^ [] : [-(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)))))], (31834 ^ _782476) ^ [_1385226, _1385228, _1385230] : [-(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, _1385226, _1385228)), _1385230), _1385228) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1385226), _1385230), _1385228))], (5660 ^ _782476) ^ [_869158, _869160, _869162, _869164] : [-(c_COMBK(_869164, _869160) = c_COMBK(_869162, _869158)), _869164 = _869162, _869160 = _869158], (35848 ^ _782476) ^ [_1459586, _1459588] : [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), _1459586))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459588))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459586))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459588)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459586)))], (1012 ^ _782476) ^ [_797790, _797792, _797794, _797796] : [-(c_Wellfounded_Owf(_797794, _797790)), c_Wellfounded_Owf(_797796, _797792), _797796 = _797794, _797792 = _797790], (45342 ^ _782476) ^ [_1689971, _1689973, _1689975] : [hBOOL(hAPP(c_List_Odistinct(_1689971), hAPP(c_List_Orotate(_1689971, _1689973), _1689975))), -(hBOOL(hAPP(c_List_Odistinct(_1689971), _1689975)))], (20932 ^ _782476) ^ [_1176013] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176013), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1176013)], (34294 ^ _782476) ^ [_1432105] : [class_Int_Onumber__ring(_1432105), -(c_Groups_Ozero__class_Ozero(_1432105) = hAPP(c_Int_Onumber__class_Onumber__of(_1432105), c_Int_OPls))], (9837 ^ _782476) ^ [_959253, _959255, _959257, _959259, _959261] : [-(_959253 = c_Orderings_Obot__class_Obot(tc_fun(_959255, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959255, tc_fun(_959257, tc_HOL_Obool)), _959253), hAPP(hAPP(c_COMBB(tc_fun(_959257, tc_HOL_Obool), tc_fun(_959257, tc_HOL_Obool), _959255), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959257, tc_HOL_Obool)), _959259)), _959261)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959257, tc_HOL_Obool)), _959259), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959255, tc_fun(_959257, tc_HOL_Obool)), _959253), _959261)))], (47377 ^ _782476) ^ [_1736163, _1736165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736163), _1736165)), -(c_List_Oupt(_1736163, _1736165) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736163), c_List_Oupt(hAPP(c_Nat_OSuc, _1736163), _1736165)))], (5578 ^ _782476) ^ [_867897, _867899, _867901, _867903, _867905, _867907, _867909, _867911, _867913, _867915] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_867915, _867911, _867907, _867903, _867899) = c_SetInterval_Oord_OgreaterThanAtMost(_867913, _867909, _867905, _867901, _867897)), _867915 = _867913, _867911 = _867909, _867907 = _867905, _867903 = _867901, _867899 = _867897], (27487 ^ _782476) ^ [_1302499, _1302501, _1302503, _1302505, _1302507] : [class_Groups_Ocomm__monoid__mult(_1302499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302501), _1302503)), c_Fun_Oinj__on(_1302501, _1302501, _1302505, _1302503), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302501, _1302499), _1302507), hAPP(c_Set_Oimage(_1302501, _1302501, _1302505), _1302503)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302501, _1302499), hAPP(c_Fun_Ocomp(_1302501, _1302499, _1302501, _1302507), _1302505)), _1302503))], (11844 ^ _782476) ^ [_998105, _998107, _998109] : [class_Groups_Oordered__ab__group__add(_998105), 11847 ^ _782476 : [(11854 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998105), _998109), hAPP(c_Groups_Ouminus__class_Ouminus(_998105), _998107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998105), _998107), hAPP(c_Groups_Ouminus__class_Ouminus(_998105), _998109))))], (11848 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998105), _998107), hAPP(c_Groups_Ouminus__class_Ouminus(_998105), _998109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998105), _998109), hAPP(c_Groups_Ouminus__class_Ouminus(_998105), _998107))))]]], (47437 ^ _782476) ^ [_1737179, _1737181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737179)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737181)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737179), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737181)) = c_List_Olist_ONil(tc_Nat_Onat))], (34956 ^ _782476) ^ [_1443650, _1443652] : [class_Int_Onumber__ring(_1443650), 34959 ^ _782476 : [(34966 ^ _782476) ^ [] : [c_Int_Oiszero(_1443650, hAPP(c_Int_Onumber__class_Onumber__of(_1443650), 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), _1443652)))), -(c_Groups_Oone__class_Oone(_1443650) = hAPP(c_Int_Onumber__class_Onumber__of(_1443650), _1443652))], (34960 ^ _782476) ^ [] : [c_Groups_Oone__class_Oone(_1443650) = hAPP(c_Int_Onumber__class_Onumber__of(_1443650), _1443652), -(c_Int_Oiszero(_1443650, hAPP(c_Int_Onumber__class_Onumber__of(_1443650), 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), _1443652)))))]]], (48421 ^ _782476) ^ [_1756592, _1756594, _1756596] : [hBOOL(hAPP(c_List_Odistinct(_1756592), _1756594)), hBOOL(hAPP(hAPP(c_member(_1756592), _1756596), hAPP(c_List_Oset(_1756592), _1756594))), -(c_List_OtakeWhile(_1756592, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756592), c_fNot), hAPP(hAPP(c_COMBC(_1756592, _1756592, tc_HOL_Obool), c_fequal), _1756596)), hAPP(c_List_Orev(_1756592), _1756594)) = hAPP(c_List_Orev(_1756592), hAPP(c_List_Otl(_1756592), c_List_OdropWhile(_1756592, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756592), c_fNot), hAPP(hAPP(c_COMBC(_1756592, _1756592, tc_HOL_Obool), c_fequal), _1756596)), _1756594))))], (44196 ^ _782476) ^ [_1664245, _1664247, _1664249] : [-(hBOOL(hAPP(hAPP(c_member(_1664245), _1664247), hAPP(c_List_Oset(_1664245), _1664249)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664245)), c_List_Oremove1(_1664245, _1664247, _1664249)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664245)), _1664249))], (22937 ^ _782476) ^ [_1212591, _1212593] : [22938 ^ _782476 : [(22939 ^ _782476) ^ [_1212647] : [_1212593 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212591), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212647)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212591), _1212593)))], (9139 ^ _782476) ^ [_944416, _944418] : [class_Lattices_Obounded__lattice__top(_944416), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944416), _944418), c_Orderings_Otop__class_Otop(_944416)) = c_Orderings_Otop__class_Otop(_944416))], (51582 ^ _782476) ^ [_1827897, _1827899, _1827901] : [c_List_Oall__interval__nat(_1827897, _1827899, _1827901), 51585 ^ _782476 : [(51586 ^ _782476) ^ [_1827977] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1827977), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1827899), _1827901))), -(hBOOL(hAPP(_1827897, _1827977)))]]], (10893 ^ _782476) ^ [_983138, _983140, _983142, _983144] : [class_Orderings_Oorder(_983138), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983138, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983138, _983140, _983142)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_983138, _983142), _983144)) = c_Orderings_Obot__class_Obot(tc_fun(_983138, tc_HOL_Obool)))], (45236 ^ _782476) ^ [_1687854, _1687856, _1687858, _1687860] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1687856), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687854)), hAPP(hAPP(c_List_Olist_OCons(_1687856), _1687858), _1687860)) = hAPP(hAPP(c_List_Olist_OCons(_1687856), _1687858), _1687860))], (28123 ^ _782476) ^ [_1314235, _1314237, _1314239] : [class_Orderings_Olinorder(_1314235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314235), _1314237)), -(_1314237 = c_Orderings_Obot__class_Obot(tc_fun(_1314235, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314235), _1314239)), -(_1314239 = c_Orderings_Obot__class_Obot(tc_fun(_1314235, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314235, c_Orderings_Oord__class_Omin(_1314235), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314235, tc_HOL_Obool)), _1314237), _1314239)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314235), c_Big__Operators_Olattice_OInf__fin(_1314235, c_Orderings_Oord__class_Omin(_1314235), _1314237)), c_Big__Operators_Olattice_OInf__fin(_1314235, c_Orderings_Oord__class_Omin(_1314235), _1314239)))], (41771 ^ _782476) ^ [_1603247, _1603249, _1603251, _1603253] : [-(hAPP(_1603247, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603249, _1603249), _1603251), _1603247), _1603253)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603249, _1603249), _1603251), _1603247), hAPP(_1603247, _1603253)))], (44158 ^ _782476) ^ [_1663519, _1663521, _1663523, _1663525] : [-(c_List_Oremove1(_1663519, _1663521, c_List_Oremove1(_1663519, _1663523, _1663525)) = c_List_Oremove1(_1663519, _1663523, c_List_Oremove1(_1663519, _1663521, _1663525)))], (50480 ^ _782476) ^ [_1803008, _1803010] : [50483 ^ _782476 : [(50489 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1803008, _1803008)), hAPP(hAPP(c_Product__Type_OPair(_1803008, _1803008), 50481 ^ [_1803008, _1803010]), 50485 ^ [_1803008, _1803010])), _1803010))], (50487 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1803008, _1803008)), hAPP(hAPP(c_Product__Type_OPair(_1803008, _1803008), 50482 ^ [_1803008, _1803010]), 50485 ^ [_1803008, _1803010])), _1803010)))], (50484 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1803008, _1803008)), hAPP(hAPP(c_Product__Type_OPair(_1803008, _1803008), 50481 ^ [_1803008, _1803010]), 50482 ^ [_1803008, _1803010])), _1803010)))]], -(c_Relation_Otrans(_1803008, _1803010))], (46009 ^ _782476) ^ [_1703644, _1703646, _1703648, _1703650, _1703652] : [46011 ^ _782476 : [(46014 ^ _782476) ^ [] : [hAPP(_1703648, 46010 ^ [_1703644, _1703646, _1703648, _1703650, _1703652]) = hAPP(_1703652, 46010 ^ [_1703644, _1703646, _1703648, _1703650, _1703652])], (46012 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703644), 46010 ^ [_1703644, _1703646, _1703648, _1703650, _1703652]), hAPP(c_List_Oset(_1703644), _1703650))))]], -(hAPP(hAPP(c_List_Omap(_1703644, _1703646), _1703648), _1703650) = hAPP(hAPP(c_List_Omap(_1703644, _1703646), _1703652), _1703650))], (34500 ^ _782476) ^ [_1435304, _1435306] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435304)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435306)))), 34503 ^ _782476 : [(34506 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435306))], (34504 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435304), _1435306)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435304), _1435306))], (46360 ^ _782476) ^ [_1712006] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1712006)) = _1712006)], (18246 ^ _782476) ^ [_1127310, _1127312] : [class_Groups_Ogroup__add(_1127310), 18249 ^ _782476 : [(18256 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1127310) = _1127312, -(c_Groups_Ozero__class_Ozero(_1127310) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127310), _1127312))], (18250 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1127310) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127310), _1127312), -(c_Groups_Ozero__class_Ozero(_1127310) = _1127312)]]], (17746 ^ _782476) ^ [_1118915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118915), _1118915)))))], (46568 ^ _782476) ^ [_1716104, _1716106, _1716108, _1716110] : [-(hBOOL(hAPP(c_List_Olistsp(_1716104, _1716106), hAPP(hAPP(c_List_Oappend(_1716104), _1716108), _1716110)))), hBOOL(hAPP(c_List_Olistsp(_1716104, _1716106), _1716108)), hBOOL(hAPP(c_List_Olistsp(_1716104, _1716106), _1716110))], (13722 ^ _782476) ^ [_1036964, _1036966, _1036968, _1036970, _1036972, _1036974, _1036976, _1036978] : [c_Fun_Obij__betw(_1036964, _1036966, _1036968, _1036970, _1036972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036964, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1036974, _1036964, _1036976), _1036978)), _1036970)), 13729 ^ _782476 : [(13736 ^ _782476) ^ [] : [c_Fun_Obij__betw(_1036974, _1036966, hAPP(c_Fun_Ocomp(_1036964, _1036966, _1036974, _1036968), _1036976), _1036978, _1036972), -(c_Fun_Obij__betw(_1036974, _1036964, _1036976, _1036978, _1036970))], (13730 ^ _782476) ^ [] : [c_Fun_Obij__betw(_1036974, _1036964, _1036976, _1036978, _1036970), -(c_Fun_Obij__betw(_1036974, _1036966, hAPP(c_Fun_Ocomp(_1036964, _1036966, _1036974, _1036968), _1036976), _1036978, _1036972))]]], (35076 ^ _782476) ^ [_1445600, _1445602] : [class_Int_Onumber__ring(_1445600), 35079 ^ _782476 : [(35086 ^ _782476) ^ [] : [c_Int_Oiszero(_1445600, hAPP(c_Int_Onumber__class_Onumber__of(_1445600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445602), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445600), _1445602) = c_Groups_Ozero__class_Ozero(_1445600))], (35080 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445600), _1445602) = c_Groups_Ozero__class_Ozero(_1445600), -(c_Int_Oiszero(_1445600, hAPP(c_Int_Onumber__class_Onumber__of(_1445600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445602), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (5102 ^ _782476) ^ [_860429, _860431] : [_860431 = _860429, -(c_Lattices_Osemilattice__sup__class_Osup(_860431) = c_Lattices_Osemilattice__sup__class_Osup(_860429))], (46718 ^ _782476) ^ [_1720217, _1720219, _1720221, _1720223, _1720225, _1720227, _1720229] : [c_List_Olist__all2(_1720217, _1720219, _1720221, hAPP(hAPP(c_List_Olist_OCons(_1720217), _1720223), _1720225), hAPP(hAPP(c_List_Olist_OCons(_1720219), _1720227), _1720229)), 46721 ^ _782476 : [(46724 ^ _782476) ^ [] : [-(c_List_Olist__all2(_1720217, _1720219, _1720221, _1720225, _1720229))], (46722 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(_1720221, _1720223), _1720227)))]]], (40792 ^ _782476) ^ [_1579573, _1579575, _1579577, _1579579, _1579581, _1579583, _1579585] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579573, _1579575, _1579577, _1579579), _1579581), _1579583), _1579585) = hAPP(hAPP(_1579583, hAPP(c_Product__Type_Ofst(_1579575, _1579577), hAPP(_1579581, _1579585))), hAPP(c_Product__Type_Osnd(_1579575, _1579577), hAPP(_1579581, _1579585))))], (30238 ^ _782476) ^ [_1355646, _1355648, _1355650, _1355652, _1355654] : [class_Fields_Olinordered__field(_1355646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355646), c_Groups_Ozero__class_Ozero(_1355646)), _1355648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355646), _1355648), _1355650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355646), c_Groups_Ozero__class_Ozero(_1355646)), _1355652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355646), _1355652), _1355654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355646), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355646), _1355648), _1355654)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355646), _1355650), _1355652))))], (7792 ^ _782476) ^ [_914484, _914486, _914488] : [class_Lattices_Olattice(_914484), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914484), _914486), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914484), _914486), _914488)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914484), _914486), _914488))], (25247 ^ _782476) ^ [_1254509, _1254511] : [class_Groups_Oordered__ab__group__add__abs(_1254509), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254509), hAPP(c_Groups_Ouminus__class_Ouminus(_1254509), hAPP(c_Groups_Oabs__class_Oabs(_1254509), _1254511))), c_Groups_Ozero__class_Ozero(_1254509))))], (28061 ^ _782476) ^ [_1313172, _1313174] : [class_Orderings_Olinorder(_1313172), -(c_Big__Operators_Olattice_OInf__fin(_1313172, c_Orderings_Oord__class_Omin(_1313172), hAPP(hAPP(c_Set_Oinsert(_1313172), _1313174), c_Orderings_Obot__class_Obot(tc_fun(_1313172, tc_HOL_Obool)))) = _1313174)], (32776 ^ _782476) ^ [_1403611, _1403613, _1403615, _1403617] : [hBOOL(hAPP(hAPP(c_member(_1403611), _1403613), _1403615)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1403611, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403611, _1403611, _1403617), hAPP(hAPP(c_Set_Oinsert(_1403611), _1403613), c_Orderings_Obot__class_Obot(tc_fun(_1403611, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403611), _1403615), _1403617))))], (46300 ^ _782476) ^ [_1710681, _1710683, _1710685, _1710687, _1710689] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710681)), _1710683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710685)), _1710687), 46303 ^ _782476 : [(46312 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1710681, _1710685), _1710683), _1710687) = _1710689), hAPP(hAPP(c_List_Omap(tc_prod(_1710681, _1710685), _1710681), c_Product__Type_Ofst(_1710681, _1710685)), _1710689) = _1710683, hAPP(hAPP(c_List_Omap(tc_prod(_1710681, _1710685), _1710685), c_Product__Type_Osnd(_1710681, _1710685)), _1710689) = _1710687], (46304 ^ _782476) ^ [] : [hAPP(hAPP(c_List_Ozip(_1710681, _1710685), _1710683), _1710687) = _1710689, 46307 ^ _782476 : [(46310 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710681, _1710685), _1710685), c_Product__Type_Osnd(_1710681, _1710685)), _1710689) = _1710687)], (46308 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710681, _1710685), _1710681), c_Product__Type_Ofst(_1710681, _1710685)), _1710689) = _1710683)]]]]], (45364 ^ _782476) ^ [_1690412] : [-(hAPP(c_List_Otl(_1690412), c_List_Olist_ONil(_1690412)) = c_List_Olist_ONil(_1690412))], (27941 ^ _782476) ^ [_1310720, _1310722, _1310724] : [class_Orderings_Olinorder(_1310720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310720), _1310722)), 27948 ^ _782476 : [(27955 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310720, tc_HOL_Obool)), _1310722), hAPP(hAPP(c_Set_Oinsert(_1310720), _1310724), c_Orderings_Obot__class_Obot(tc_fun(_1310720, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310720, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1310720, hAPP(hAPP(c_Set_Oinsert(_1310720), _1310724), _1310722)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310720), _1310724), c_Big__Operators_Olinorder__class_OMin(_1310720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310720, tc_HOL_Obool)), _1310722), hAPP(hAPP(c_Set_Oinsert(_1310720), _1310724), c_Orderings_Obot__class_Obot(tc_fun(_1310720, tc_HOL_Obool)))))))], (27949 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310720, tc_HOL_Obool)), _1310722), hAPP(hAPP(c_Set_Oinsert(_1310720), _1310724), c_Orderings_Obot__class_Obot(tc_fun(_1310720, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310720, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310720, hAPP(hAPP(c_Set_Oinsert(_1310720), _1310724), _1310722)) = _1310724)]]], (7716 ^ _782476) ^ [_912889, _912891, _912893, _912895] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912889, tc_HOL_Obool)), _912891), _912893), _912895)), -(hBOOL(hAPP(_912891, _912895))), -(hBOOL(hAPP(_912893, _912895)))], (51458 ^ _782476) ^ [_1823577, _1823579, _1823581, _1823583] : [c_Equiv__Relations_Oequivp(_1823577, _1823579), 51464 ^ _782476 : [(51467 ^ _782476) ^ [] : [hBOOL(hAPP(_1823583, 51463 ^ [_1823577, _1823579, _1823581, _1823583]))], (51465 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1823581, 51463 ^ [_1823577, _1823579, _1823581, _1823583])))]], 51470 ^ _782476 : [(51471 ^ _782476) ^ [_1823836] : [hBOOL(hAPP(_1823581, _1823836))]], 51473 ^ _782476 : [(51476 ^ _782476) ^ [] : [-(hBOOL(hAPP(_1823583, 51472 ^ [_1823577, _1823579, _1823581, _1823583])))], (51474 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1823577), 51472 ^ [_1823577, _1823579, _1823581, _1823583]), c_Quotient_ORespects(_1823577, _1823579))))]]], (6977 ^ _782476) ^ [_896850, _896852] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896850, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896850, tc_HOL_Obool)), _896852)) = _896852)], (32575 ^ _782476) ^ [_1399524, _1399526, _1399528] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399524), _1399526), _1399528) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399524, tc_HOL_Obool), tc_HOL_Obool)), -(_1399526 = c_Orderings_Obot__class_Obot(tc_fun(_1399524, tc_HOL_Obool)))], (26546 ^ _782476) ^ [_1283949, _1283951, _1283953, _1283955] : [class_Orderings_Olinorder(_1283949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283949), _1283951), _1283953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283949), _1283951), _1283955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283949), _1283951), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283949), _1283953), _1283955))))], (9444 ^ _782476) ^ [_951629, _951631, _951633] : [-(hAPP(c_Set_Oimage(_951629, _951631, _951633), c_Orderings_Obot__class_Obot(tc_fun(_951629, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_951631, tc_HOL_Obool)))], (6796 ^ _782476) ^ [_892856, _892858, _892860, _892862, _892864, _892866] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892856, tc_fun(_892858, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892860, tc_fun(_892856, tc_HOL_Obool)), _892862), _892864)), _892866) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892860, tc_fun(_892858, tc_HOL_Obool)), _892862), hAPP(hAPP(c_COMBC(_892860, tc_fun(_892856, tc_fun(_892858, tc_HOL_Obool)), tc_fun(_892858, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892856, tc_HOL_Obool), tc_fun(tc_fun(_892856, tc_fun(_892858, tc_HOL_Obool)), tc_fun(_892858, tc_HOL_Obool)), _892860), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892856, tc_fun(_892858, tc_HOL_Obool))), _892864)), _892866)))], (24271 ^ _782476) ^ [_1237063, _1237065] : [c_Nat__Transfer_Onat__set(_1237063), c_Nat__Transfer_Onat__set(_1237065), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1237063), _1237065)))], (20061 ^ _782476) ^ [_1159106, _1159108, _1159110, _1159112] : [class_Rings_Olinordered__semiring__strict(_1159106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159106), _1159108), _1159110)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159106), _1159108), _1159112))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159106), c_Groups_Ozero__class_Ozero(_1159106)), _1159108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159106), _1159110), _1159112)))], (51446 ^ _782476) ^ [_1823381, _1823383, _1823385] : [hBOOL(hAPP(c_Quotient_ORespects(_1823381, _1823383), _1823385)), -(hBOOL(hAPP(hAPP(_1823383, _1823385), _1823385)))], (3008 ^ _782476) ^ [_827080, _827082, _827084, _827086, _827088, _827090] : [-(c_Product__Type_Ointernal__split(_827090, _827086, _827082) = c_Product__Type_Ointernal__split(_827088, _827084, _827080)), _827090 = _827088, _827086 = _827084, _827082 = _827080], (46560 ^ _782476) ^ [_1715955, _1715957, _1715959, _1715961] : [hBOOL(hAPP(c_List_Olistsp(_1715955, _1715957), hAPP(hAPP(c_List_Oappend(_1715955), _1715959), _1715961))), 46563 ^ _782476 : [(46566 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715955, _1715957), _1715961)))], (46564 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715955, _1715957), _1715959)))]]], (39829 ^ _782476) ^ [_1554206, _1554208, _1554210, _1554212, _1554214, _1554216] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554206, _1554208)), hAPP(hAPP(c_Product__Type_OPair(_1554206, _1554208), _1554210), _1554212)), hAPP(hAPP(c_Product__Type_OSigma(_1554206, _1554208), _1554214), _1554216))), -(hBOOL(hAPP(hAPP(c_member(_1554208), _1554212), hAPP(_1554216, _1554210))))], (17367 ^ _782476) ^ [_1112025, _1112027, _1112029] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112025), _1112027) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112025), _1112029), -(_1112027 = _1112029)], (38541 ^ _782476) ^ [_1520188, _1520190, _1520192, _1520194, _1520196, _1520198, _1520200] : [-(hAPP(c_Product__Type_Oapfst(_1520188, _1520190, _1520192, _1520194), hAPP(c_Product__Type_Oapsnd(_1520196, _1520192, _1520188, _1520198), _1520200)) = hAPP(hAPP(c_Product__Type_OPair(_1520190, _1520192), hAPP(_1520194, hAPP(c_Product__Type_Ofst(_1520188, _1520196), _1520200))), hAPP(_1520198, hAPP(c_Product__Type_Osnd(_1520188, _1520196), _1520200))))], (38911 ^ _782476) ^ [_1529628, _1529630, _1529632, _1529634, _1529636] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529628, _1529630, _1529632), _1529634), _1529636) = hAPP(c_Set_OCollect(tc_prod(_1529628, _1529632)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529628, _1529632, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1529632, tc_fun(_1529630, tc_HOL_Obool)), tc_fun(_1529632, tc_HOL_Obool), _1529628), hAPP(c_COMBB(tc_fun(_1529630, tc_HOL_Obool), tc_HOL_Obool, _1529632), c_HOL_OEx(_1529630))), hAPP(hAPP(c_COMBC(_1529628, tc_fun(_1529632, tc_fun(_1529630, tc_HOL_Obool)), tc_fun(_1529632, tc_fun(_1529630, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529630, tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), tc_fun(tc_fun(_1529632, tc_fun(_1529630, tc_HOL_Obool)), tc_fun(_1529632, tc_fun(_1529630, tc_HOL_Obool))), _1529628), c_COMBB(tc_fun(_1529630, tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool), _1529632)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529630, tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), _1529628), c_COMBS(_1529630, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_HOL_Obool), tc_fun(_1529630, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529628), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529630), c_fconj)), hAPP(hAPP(c_COMBC(_1529628, tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_fun(tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), _1529628), c_COMBC(_1529630, tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_prod(_1529628, _1529630)), tc_fun(_1529630, tc_fun(tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_HOL_Obool)), _1529628), hAPP(c_COMBB(tc_prod(_1529628, _1529630), tc_fun(tc_fun(tc_prod(_1529628, _1529630), tc_HOL_Obool), tc_HOL_Obool), _1529630), c_member(tc_prod(_1529628, _1529630)))), c_Product__Type_OPair(_1529628, _1529630)))), _1529634))))), hAPP(hAPP(c_COMBC(_1529632, tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_fun(tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_fun(_1529630, tc_HOL_Obool)), _1529632), c_COMBC(_1529630, tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529630, tc_prod(_1529630, _1529632)), tc_fun(_1529630, tc_fun(tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_HOL_Obool)), _1529632), hAPP(c_COMBB(tc_prod(_1529630, _1529632), tc_fun(tc_fun(tc_prod(_1529630, _1529632), tc_HOL_Obool), tc_HOL_Obool), _1529630), c_member(tc_prod(_1529630, _1529632)))), hAPP(c_COMBC(_1529630, _1529632, tc_prod(_1529630, _1529632)), c_Product__Type_OPair(_1529630, _1529632))))), _1529636))))))], (44624 ^ _782476) ^ [_1673348, _1673350, _1673352, _1673354, _1673356] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673348), _1673350), _1673352) = hAPP(hAPP(c_List_Oappend(_1673348), _1673354), _1673356)), 44625 ^ _782476 : [(44632 ^ _782476) ^ [_1673531] : [hAPP(hAPP(c_List_Olist_OCons(_1673348), _1673350), _1673531) = _1673354, _1673352 = hAPP(hAPP(c_List_Oappend(_1673348), _1673531), _1673356)], (44626 ^ _782476) ^ [] : [_1673354 = c_List_Olist_ONil(_1673348), hAPP(hAPP(c_List_Olist_OCons(_1673348), _1673350), _1673352) = _1673356]]], (3502 ^ _782476) ^ [_834799, _834801] : [_834801 = _834799, -(c_List_Otranspose__rel(_834801) = c_List_Otranspose__rel(_834799))], (45144 ^ _782476) ^ [_1685486, _1685488, _1685490, _1685492] : [-(hAPP(hAPP(c_List_Odrop(_1685486), _1685488), hAPP(hAPP(c_List_Oappend(_1685486), _1685490), _1685492)) = hAPP(hAPP(c_List_Oappend(_1685486), hAPP(hAPP(c_List_Odrop(_1685486), _1685488), _1685490)), hAPP(hAPP(c_List_Odrop(_1685486), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685488), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685486)), _1685490))), _1685492)))], (9512 ^ _782476) ^ [_952988] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_952988, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952988, tc_HOL_Obool)))], (18262 ^ _782476) ^ [_1127542] : [class_Groups_Ogroup__add(_1127542), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127542), c_Groups_Ozero__class_Ozero(_1127542)) = c_Groups_Ozero__class_Ozero(_1127542))], (24951 ^ _782476) ^ [_1248989, _1248991] : [class_Rings_Olinordered__idom(_1248989), -(hAPP(c_Groups_Oabs__class_Oabs(_1248989), _1248991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248989), _1248991), c_Groups_Osgn__class_Osgn(_1248989, _1248991)))], (26852 ^ _782476) ^ [_1289517, _1289519] : [class_Orderings_Olinorder(_1289517), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289517), _1289519), _1289519) = _1289519)], (44432 ^ _782476) ^ [_1668640, _1668642] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668640), _1668642))), -(c_List_Oupto(_1668640, _1668642) = c_List_Olist_ONil(tc_Int_Oint))], (10781 ^ _782476) ^ [_980282, _980284, _980286, _980288, _980290] : [-(_980282 = c_Orderings_Obot__class_Obot(tc_fun(_980284, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980284, tc_fun(_980286, tc_HOL_Obool)), _980282), hAPP(hAPP(c_COMBB(tc_fun(_980286, tc_HOL_Obool), tc_fun(_980286, tc_HOL_Obool), _980284), hAPP(c_Set_Oinsert(_980286), _980288)), _980290)) = hAPP(hAPP(c_Set_Oinsert(_980286), _980288), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980284, tc_fun(_980286, tc_HOL_Obool)), _980282), _980290)))], (37964 ^ _782476) ^ [_1506291, _1506293, _1506295] : [c_Equiv__Relations_Oequiv(_1506291, _1506293, _1506295), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1506291, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506291), _1506293), _1506295)) = _1506293)], (6455 ^ _782476) ^ [_885886, _885888, _885890, _885892, _885894] : [class_Complete__Lattice_Ocomplete__lattice(_885886), 6458 ^ _782476 : [(6459 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885886), _885888), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885890, _885886), _885892), _885894))), 6462 ^ _782476 : [(6463 ^ _782476) ^ [_886067] : [hBOOL(hAPP(hAPP(c_member(_885890), _886067), _885892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885886), _885888), hAPP(_885894, _886067))))]]], (6469 ^ _782476) ^ [] : [6471 ^ _782476 : [(6474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885886), _885888), hAPP(_885894, 6470 ^ [_885886, _885888, _885890, _885892, _885894])))], (6472 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885890), 6470 ^ [_885886, _885888, _885890, _885892, _885894]), _885892)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885886), _885888), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885890, _885886), _885892), _885894))))]]], (10749 ^ _782476) ^ [_979574, _979576, _979578, _979580] : [_979574 = c_Orderings_Obot__class_Obot(tc_fun(_979576, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_979576, _979578, hAPP(c_COMBK(_979578, _979576), _979580)), _979574) = c_Orderings_Obot__class_Obot(tc_fun(_979578, tc_HOL_Obool)))], (43942 ^ _782476) ^ [_1658777, _1658779, _1658781, _1658783] : [-(_1658777 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658779)), _1658781)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1658779, hAPP(hAPP(c_List_Olist__update(_1658779, _1658781), _1658777), _1658783)) = hAPP(hAPP(c_List_Olist__update(_1658779, c_List_Obutlast(_1658779, _1658781)), _1658777), _1658783))], (52485 ^ _782476) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (15330 ^ _782476) ^ [_1068634, _1068636, _1068638] : [class_Lattices_Olattice(_1068634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068634), _1068636)), 15337 ^ _782476 : [(15344 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068634, tc_HOL_Obool)), _1068636), hAPP(hAPP(c_Set_Oinsert(_1068634), _1068638), c_Orderings_Obot__class_Obot(tc_fun(_1068634, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068634, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068634, hAPP(hAPP(c_Set_Oinsert(_1068634), _1068638), _1068636)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068634), _1068638), c_Big__Operators_Olattice__class_OSup__fin(_1068634, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068634, tc_HOL_Obool)), _1068636), hAPP(hAPP(c_Set_Oinsert(_1068634), _1068638), c_Orderings_Obot__class_Obot(tc_fun(_1068634, tc_HOL_Obool)))))))], (15338 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068634, tc_HOL_Obool)), _1068636), hAPP(hAPP(c_Set_Oinsert(_1068634), _1068638), c_Orderings_Obot__class_Obot(tc_fun(_1068634, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068634, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1068634, hAPP(hAPP(c_Set_Oinsert(_1068634), _1068638), _1068636)) = _1068638)]]], (29396 ^ _782476) ^ [_1340312, _1340314, _1340316] : [class_Rings_Olinordered__idom(_1340312), -(hAPP(c_Groups_Oabs__class_Oabs(_1340312), hAPP(hAPP(c_Power_Opower__class_Opower(_1340312), hAPP(c_Groups_Ouminus__class_Ouminus(_1340312), _1340314)), _1340316)) = hAPP(c_Groups_Oabs__class_Oabs(_1340312), hAPP(hAPP(c_Power_Opower__class_Opower(_1340312), _1340314), _1340316)))], (906 ^ _782476) ^ [_796287, _796289, _796291, _796293, _796295, _796297] : [-(c_Equiv__Relations_Oequiv(_796295, _796291, _796287)), c_Equiv__Relations_Oequiv(_796297, _796293, _796289), _796297 = _796295, _796293 = _796291, _796289 = _796287], (14032 ^ _782476) ^ [_1043293, _1043295, _1043297] : [class_Rings_Oring(_1043293), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043293), hAPP(c_Groups_Ouminus__class_Ouminus(_1043293), _1043295)), _1043297) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043293), _1043295), hAPP(c_Groups_Ouminus__class_Ouminus(_1043293), _1043297)))], (40978 ^ _782476) ^ [_1583238, _1583240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583238, _1583238)), _1583240)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583238, _1583238)), c_Transitive__Closure_Otrancl(_1583238, _1583240))))], (37665 ^ _782476) ^ [_1499285, _1499287] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499285, _1499285)), hAPP(hAPP(c_Product__Type_OPair(_1499285, _1499285), 37666 ^ [_1499285, _1499287]), 37666 ^ [_1499285, _1499287])), _1499287))), -(c_Relation_Oirrefl(_1499285, _1499287))], (1110 ^ _782476) ^ [_799343, _799345, _799347, _799349, _799351, _799353] : [-(c_List_Olist__ex(_799351, _799347, _799343)), c_List_Olist__ex(_799353, _799349, _799345), _799353 = _799351, _799349 = _799347, _799345 = _799343], (45493 ^ _782476) ^ [_1693064, _1693066, _1693068, _1693070, _1693072] : [c_Finite__Set_Ofun__left__comm__idem(_1693064, _1693066, _1693068), -(hAPP(hAPP(c_Finite__Set_Ofold(_1693064, _1693066, _1693068), _1693070), hAPP(c_List_Oset(_1693064), _1693072)) = hAPP(c_List_Ofoldl(_1693066, _1693064, hAPP(c_COMBC(_1693064, _1693066, _1693066), _1693068), _1693070), _1693072))], (38278 ^ _782476) ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395] : [c_Equiv__Relations_Oequiv(_1513383, _1513385, _1513387), c_Equiv__Relations_Ocongruent(_1513383, tc_fun(_1513389, tc_HOL_Obool), _1513387, _1513391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513383, tc_fun(_1513389, tc_HOL_Obool)), _1513393), _1513391) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513383, tc_fun(_1513389, tc_HOL_Obool)), _1513395), _1513391), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513383, tc_HOL_Obool)), _1513393), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513383), _1513385), _1513387))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513383, tc_HOL_Obool)), _1513395), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513383), _1513385), _1513387))), 38300 ^ _782476 : [(38304 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513383), 38302 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395]), _1513385)))], (38306 ^ _782476) ^ [] : [-(hAPP(_1513391, 38299 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395]) = hAPP(_1513391, 38302 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395]))], (38308 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513383, _1513383)), hAPP(hAPP(c_Product__Type_OPair(_1513383, _1513383), 38299 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395]), 38302 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395])), _1513387))], (38301 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513383), 38299 ^ [_1513383, _1513385, _1513387, _1513389, _1513391, _1513393, _1513395]), _1513385)))]], -(_1513393 = _1513395)], (37505 ^ _782476) ^ [_1496137, _1496139, _1496141, _1496143, _1496145] : [hAPP(c_Product__Type_Osnd(_1496137, _1496139), hAPP(hAPP(c_Product__Type_OPair(_1496137, _1496139), _1496141), _1496143)) = _1496145, -(_1496143 = _1496145)], (2184 ^ _782476) ^ [_814384, _814386, _814388, _814390, _814392, _814394, _814396, _814398] : [-(c_Sum__Type_OPlus(_814398, _814394, _814390, _814386) = c_Sum__Type_OPlus(_814396, _814392, _814388, _814384)), _814398 = _814396, _814394 = _814392, _814390 = _814388, _814386 = _814384], (36330 ^ _782476) ^ [_1467897, _1467899] : [-(c_Fun_Oinj__on(tc_fun(_1467897, _1467899), tc_fun(tc_prod(_1467897, _1467899), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1467897, _1467899), tc_HOL_Obool), tc_fun(tc_prod(_1467897, _1467899), tc_HOL_Obool), tc_fun(_1467897, _1467899)), c_Set_OCollect(tc_prod(_1467897, _1467899))), hAPP(hAPP(c_COMBB(tc_fun(_1467897, tc_fun(_1467899, tc_HOL_Obool)), tc_fun(tc_prod(_1467897, _1467899), tc_HOL_Obool), tc_fun(_1467897, _1467899)), c_Product__Type_Oprod_Oprod__case(_1467897, _1467899, tc_HOL_Obool)), hAPP(c_COMBB(_1467899, tc_fun(_1467899, tc_HOL_Obool), _1467897), hAPP(c_COMBC(_1467899, _1467899, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1467897, _1467899), tc_HOL_Obool))))], (25197 ^ _782476) ^ [_1253374, _1253376, _1253378] : [class_Rings_Olinordered__idom(_1253374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253374), c_Groups_Ozero__class_Ozero(_1253374)), _1253376)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253374), hAPP(c_Groups_Oabs__class_Oabs(_1253374), _1253378)), _1253376) = hAPP(c_Groups_Oabs__class_Oabs(_1253374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253374), _1253378), _1253376)))], (20289 ^ _782476) ^ [_1163519, _1163521, _1163523, _1163525, _1163527] : [class_Groups_Ocomm__monoid__add(_1163519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163521), _1163523)), 20296 ^ _782476 : [(20303 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163521), _1163525), _1163523))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163521, _1163519), hAPP(hAPP(c_COMBC(_1163521, _1163519, _1163519), hAPP(hAPP(c_COMBS(_1163521, _1163519, tc_fun(_1163519, _1163519)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163519, tc_fun(_1163519, _1163519)), _1163521), c_If(_1163519)), hAPP(c_fequal, _1163525))), _1163527)), c_Groups_Ozero__class_Ozero(_1163519))), _1163523) = c_Groups_Ozero__class_Ozero(_1163519))], (20297 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1163521), _1163525), _1163523)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163521, _1163519), hAPP(hAPP(c_COMBC(_1163521, _1163519, _1163519), hAPP(hAPP(c_COMBS(_1163521, _1163519, tc_fun(_1163519, _1163519)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163519, tc_fun(_1163519, _1163519)), _1163521), c_If(_1163519)), hAPP(c_fequal, _1163525))), _1163527)), c_Groups_Ozero__class_Ozero(_1163519))), _1163523) = hAPP(_1163527, _1163525))]]], (50040 ^ _782476) ^ [_1792865, _1792867, _1792869, _1792871] : [-(hBOOL(hAPP(hAPP(c_member(_1792865), _1792867), hAPP(c_List_Oset(_1792865), c_List_Oreplicate(_1792865, _1792869, _1792871))))), _1792867 = _1792871, -(_1792869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50174 ^ _782476) ^ [_1795765, _1795767, _1795769, _1795771] : [50175 ^ _782476 : [(50178 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795765), _1795769), _1795771))], (50176 ^ _782476) ^ [] : [_1795767 = _1795771]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1795765), hAPP(hAPP(c_List_Olist_OCons(_1795765), _1795767), _1795769)), _1795771)))], (44704 ^ _782476) ^ [_1675159, _1675161, _1675163, _1675165] : [_1675161 = _1675165, -(hAPP(hAPP(c_List_Oappend(_1675159), _1675161), _1675163) = hAPP(hAPP(c_List_Oappend(_1675159), _1675165), _1675163))], (52439 ^ _782476) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (28992 ^ _782476) ^ [_1332967, _1332969, _1332971] : [class_Rings_Oring__1(_1332967), hBOOL(hAPP(hAPP(c_member(_1332967), _1332969), c_Int_Oring__1__class_OInts(_1332967))), -(hBOOL(hAPP(hAPP(c_member(_1332967), hAPP(hAPP(c_Power_Opower__class_Opower(_1332967), _1332969), _1332971)), c_Int_Oring__1__class_OInts(_1332967))))], (26096 ^ _782476) ^ [_1276007] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1276007)), -(hAPP(c_Int_Onat, _1276007) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2422 ^ _782476) ^ [_817981, _817983] : [_817983 = _817981, -(c_Nat_Onat_Onat__size(_817983) = c_Nat_Onat_Onat__size(_817981))], (17075 ^ _782476) ^ [_1106216, _1106218, _1106220, _1106222, _1106224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106216), _1106218)), 17078 ^ _782476 : [(17085 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106222), 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), _1106218), _1106216)), _1106220)), _1106224))), -(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), _1106216), _1106220)), _1106222)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106218), _1106220)), _1106224))))], (17079 ^ _782476) ^ [] : [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), _1106216), _1106220)), _1106222)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106218), _1106220)), _1106224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106222), 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), _1106218), _1106216)), _1106220)), _1106224))))]]], (35670 ^ _782476) ^ [_1456224, _1456226, _1456228] : [class_Rings_Olinordered__idom(_1456224), 35673 ^ _782476 : [(35682 ^ _782476) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456224), hAPP(hAPP(c_Power_Opower__class_Opower(_1456224), _1456226), 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(_1456224), _1456228), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456224)), _1456226 = c_Groups_Ozero__class_Ozero(_1456224), _1456228 = c_Groups_Ozero__class_Ozero(_1456224)], (35674 ^ _782476) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456224), hAPP(hAPP(c_Power_Opower__class_Opower(_1456224), _1456226), 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(_1456224), _1456228), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456224), 35677 ^ _782476 : [(35680 ^ _782476) ^ [] : [-(_1456228 = c_Groups_Ozero__class_Ozero(_1456224))], (35678 ^ _782476) ^ [] : [-(_1456226 = c_Groups_Ozero__class_Ozero(_1456224))]]]]], (51013 ^ _782476) ^ [_1815077] : [-(c_Relation_Osym(_1815077, c_Relation_OId(_1815077)))], (29200 ^ _782476) ^ [_1336689, _1336691, _1336693] : [class_Groups_Omonoid__mult(_1336689), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336689), hAPP(hAPP(c_Power_Opower__class_Opower(_1336689), _1336691), _1336693)), _1336691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336689), _1336691), hAPP(hAPP(c_Power_Opower__class_Opower(_1336689), _1336691), _1336693)))], (42859 ^ _782476) ^ [_1627479, _1627481] : [-(c_List_Olenlex(_1627479, _1627481) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1627479)), tc_List_Olist(_1627479)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1627479), c_Wellfounded_Oless__than, c_List_Olex(_1627479, _1627481))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627479), tc_List_Olist(_1627479), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627479))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1627479), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627479))), tc_List_Olist(_1627479)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1627479))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627479)))), c_COMBI(tc_List_Olist(_1627479)))))], (36334 ^ _782476) ^ [_1468154, _1468156] : [_1468154 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1468154, _1468156) = _1468156)], (35060 ^ _782476) ^ [_1445341, _1445343] : [class_Int_Onumber__ring(_1445341), 35063 ^ _782476 : [(35070 ^ _782476) ^ [] : [c_Int_Oiszero(_1445341, hAPP(c_Int_Onumber__class_Onumber__of(_1445341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445343)))), -(c_Groups_Ozero__class_Ozero(_1445341) = hAPP(c_Int_Onumber__class_Onumber__of(_1445341), _1445343))], (35064 ^ _782476) ^ [] : [c_Groups_Ozero__class_Ozero(_1445341) = hAPP(c_Int_Onumber__class_Onumber__of(_1445341), _1445343), -(c_Int_Oiszero(_1445341, hAPP(c_Int_Onumber__class_Onumber__of(_1445341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445343)))))]]], (10143 ^ _782476) ^ [_966054, _966056, _966058, _966060] : [hBOOL(hAPP(hAPP(c_member(_966054), _966056), _966058)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966054, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_966054), _966056), _966060)), _966058) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966054, tc_HOL_Obool)), _966060), _966058))], (51580 ^ _782476) ^ [_1827833, _1827835, _1827837, _1827839] : [-(hAPP(c_Lazy__Sequence_Obind(_1827833, _1827835, _1827837), _1827839) = c_Lazy__Sequence_Oflat(_1827835, c_Lazy__Sequence_Omap(_1827833, tc_Lazy__Sequence_Olazy__sequence(_1827835), _1827839, _1827837)))], (11358 ^ _782476) ^ [_990539, _990541, _990543, _990545, _990547] : [class_Orderings_Oorder(_990539), 11361 ^ _782476 : [(11382 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990539, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990539, _990541, _990543)), c_SetInterval_Oord__class_OatLeastAtMost(_990539, _990545, _990547)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990545), _990547)), 11385 ^ _782476 : [(11388 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990545), _990541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990543), _990547)), 11395 ^ _782476 : [(11398 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990539), _990543), _990547))], (11396 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990539), _990545), _990541))]]], (11386 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990541), _990543)))]]], (11362 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990539, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990539, _990541, _990543)), c_SetInterval_Oord__class_OatLeastAtMost(_990539, _990545, _990547))), 11365 ^ _782476 : [(11366 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990541), _990543)), 11369 ^ _782476 : [(11374 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990539), _990545), _990541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990539), _990543), _990547)))], (11372 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990543), _990547)))], (11370 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990545), _990541)))]]], (11380 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990539), _990545), _990547)))]]]]], (41244 ^ _782476) ^ [_1590655, _1590657, _1590659, _1590661] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590655, _1590655)), hAPP(hAPP(c_Product__Type_OPair(_1590655, _1590655), _1590657), _1590659)), c_Transitive__Closure_Ortrancl(_1590655, _1590661))), -(_1590657 = _1590659), 41251 ^ _782476 : [(41254 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590655, _1590655)), hAPP(hAPP(c_Product__Type_OPair(_1590655, _1590655), _1590657), _1590659)), c_Transitive__Closure_Otrancl(_1590655, _1590661))))], (41252 ^ _782476) ^ [] : [_1590657 = _1590659]]], (13750 ^ _782476) ^ [_1037524, _1037526, _1037528, _1037530] : [c_Fun_Obij__betw(_1037524, _1037526, _1037528, _1037530, c_Orderings_Obot__class_Obot(tc_fun(_1037526, tc_HOL_Obool))), -(_1037530 = c_Orderings_Obot__class_Obot(tc_fun(_1037524, tc_HOL_Obool)))], (18470 ^ _782476) ^ [_1130547, _1130549, _1130551] : [class_Rings_Olinordered__semidom(_1130547), 18473 ^ _782476 : [(18480 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130549), _1130551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130547), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130547), _1130549)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130547), _1130551))))], (18474 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130547), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130547), _1130549)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130547), _1130551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130549), _1130551)))]]], (42097 ^ _782476) ^ [_1611706, _1611708, _1611710, _1611712, _1611714] : [class_Complete__Lattice_Ocomplete__lattice(_1611706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611708), _1611710)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1611706), _1611712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611708, _1611706), _1611710), _1611714)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611708, _1611706, hAPP(hAPP(c_COMBB(_1611706, tc_fun(_1611706, _1611706), _1611708), c_Lattices_Osemilattice__sup__class_Osup(_1611706)), _1611714)), _1611712), _1611710))], (48749 ^ _782476) ^ [_1763401, _1763403, _1763405, _1763407, _1763409] : [-(c_List_Omaps(_1763401, _1763403, _1763405, hAPP(hAPP(c_List_Olist_OCons(_1763401), _1763407), _1763409)) = hAPP(hAPP(c_List_Oappend(_1763403), hAPP(_1763405, _1763407)), c_List_Omaps(_1763401, _1763403, _1763405, _1763409)))], (7397 ^ _782476) ^ [_906158, _906160, _906162] : [class_Lattices_Oboolean__algebra(_906158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906158), _906160), _906162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906158), hAPP(c_Groups_Ouminus__class_Ouminus(_906158), _906162)), hAPP(c_Groups_Ouminus__class_Ouminus(_906158), _906160))))], (35178 ^ _782476) ^ [_1447563, _1447565] : [_1447563 = _1447565, -(c_Int_OBit0(_1447563) = c_Int_OBit0(_1447565))], (2802 ^ _782476) ^ [_823935, _823937, _823939, _823941] : [-(c_Random_Olog(_823941, _823937) = c_Random_Olog(_823939, _823935)), _823941 = _823939, _823937 = _823935], (38768 ^ _782476) ^ [_1525095, _1525097, _1525099, _1525101, _1525103, _1525105] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool)), _1525097), _1525099)), c_Wellfounded_Omax__ext(_1525095, _1525101))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool)), _1525103), _1525105)), c_Wellfounded_Omax__ext(_1525095, _1525101))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525095, tc_HOL_Obool), tc_fun(_1525095, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525095, tc_HOL_Obool)), _1525097), _1525103)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525095, tc_HOL_Obool)), _1525099), _1525105))), c_Wellfounded_Omax__ext(_1525095, _1525101))))], (11468 ^ _782476) ^ [_992238, _992240, _992242] : [class_Orderings_Oorder(_992238), 11471 ^ _782476 : [(11480 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992238), _992240), _992242))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992238), _992240), _992242)), -(_992240 = _992242)], (11472 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992238), _992240), _992242)), 11475 ^ _782476 : [(11478 ^ _782476) ^ [] : [_992240 = _992242], (11476 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992238), _992240), _992242)))]]]]], (18102 ^ _782476) ^ [_1125200, _1125202, _1125204] : [class_Rings_Ono__zero__divisors(_1125200), -(_1125202 = c_Groups_Ozero__class_Ozero(_1125200)), -(_1125204 = c_Groups_Ozero__class_Ozero(_1125200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125200), _1125202), _1125204) = c_Groups_Ozero__class_Ozero(_1125200)], (44609 ^ _782476) ^ [_1673055, _1673057, _1673059, _1673061, _1673063] : [hAPP(hAPP(c_List_Olist_OCons(_1673055), _1673057), _1673059) = hAPP(hAPP(c_List_Oappend(_1673055), _1673061), _1673063), 44614 ^ _782476 : [(44617 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673055), _1673057), _1673059) = _1673063)], (44615 ^ _782476) ^ [] : [-(_1673061 = c_List_Olist_ONil(_1673055))]], 44619 ^ _782476 : [(44622 ^ _782476) ^ [] : [-(_1673059 = hAPP(hAPP(c_List_Oappend(_1673055), 44618 ^ [_1673055, _1673057, _1673059, _1673061, _1673063]), _1673063))], (44620 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673055), _1673057), 44618 ^ [_1673055, _1673057, _1673059, _1673061, _1673063]) = _1673061)]]], (25566 ^ _782476) ^ [_1260151, _1260153, _1260155] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1260151), hAPP(c_Set_OCollect(_1260151), hAPP(hAPP(c_COMBS(_1260151, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260151), c_fdisj), _1260153)), _1260155)))), 25569 ^ _782476 : [(25572 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260151), hAPP(c_Set_OCollect(_1260151), _1260155))))], (25570 ^ _782476) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260151), hAPP(c_Set_OCollect(_1260151), _1260153))))]]], (17183 ^ _782476) ^ [_1108914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1108914)), 17187 ^ _782476 : [(17188 ^ _782476) ^ [_1108994] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1108994), _1108914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108994), 17186 ^ [_1108914])))]]], (9187 ^ _782476) ^ [_945575, _945577, _945579, _945581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945575, tc_HOL_Obool)), _945581), _945577)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945575, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945575, tc_HOL_Obool)), _945577), _945579)), _945581) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945575, tc_HOL_Obool)), _945577), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945575, tc_HOL_Obool)), _945579), _945581)))], (45372 ^ _782476) ^ [_1690557, _1690559, _1690561] : [_1690561 = c_List_Olist_ONil(_1690557), -(hAPP(c_List_Orotate(_1690557, _1690559), _1690561) = c_List_Olist_ONil(_1690557))], (20241 ^ _782476) ^ [_1162522, _1162524, _1162526, _1162528, _1162530, _1162532, _1162534, _1162536, _1162538, _1162540, _1162542] : [hAPP(_1162522, hAPP(_1162524, _1162526)) = hAPP(_1162528, hAPP(_1162530, _1162532)), -(hAPP(hAPP(c_Fun_Ocomp(_1162534, _1162536, _1162538, _1162522), _1162524), _1162526) = hAPP(hAPP(c_Fun_Ocomp(_1162540, _1162536, _1162542, _1162528), _1162530), _1162532))], (22824 ^ _782476) ^ [_1210583, _1210585] : [class_Rings_Oring__1(_1210583), hBOOL(hAPP(hAPP(c_member(_1210583), _1210585), c_Int_Oring__1__class_OInts(_1210583))), -(hBOOL(hAPP(hAPP(c_member(_1210583), hAPP(c_Groups_Ouminus__class_Ouminus(_1210583), _1210585)), c_Int_Oring__1__class_OInts(_1210583))))], (6979 ^ _782476) ^ [_896891, _896893] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_896891, tc_HOL_Obool)), _896893), hAPP(c_Set_OPow(_896891), _896893))))], (47817 ^ _782476) ^ [_1744004, _1744006, _1744008] : [class_Orderings_Olinorder(_1744004), 47820 ^ _782476 : [(47839 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744004, hAPP(hAPP(c_List_Oappend(_1744004), _1744006), _1744008))), c_List_Olinorder__class_Osorted(_1744004, _1744006), c_List_Olinorder__class_Osorted(_1744004, _1744008), 47849 ^ _782476 : [(47855 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744004), 47848 ^ [_1744004, _1744006, _1744008]), 47851 ^ [_1744004, _1744006, _1744008]))], (47853 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744004), 47851 ^ [_1744004, _1744006, _1744008]), hAPP(c_List_Oset(_1744004), _1744008))))], (47850 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744004), 47848 ^ [_1744004, _1744006, _1744008]), hAPP(c_List_Oset(_1744004), _1744006))))]]], (47821 ^ _782476) ^ [] : [c_List_Olinorder__class_Osorted(_1744004, hAPP(hAPP(c_List_Oappend(_1744004), _1744006), _1744008)), 47824 ^ _782476 : [(47829 ^ _782476) ^ [_1744240] : [hBOOL(hAPP(hAPP(c_member(_1744004), _1744240), hAPP(c_List_Oset(_1744004), _1744006))), 47832 ^ _782476 : [(47833 ^ _782476) ^ [_1744350] : [hBOOL(hAPP(hAPP(c_member(_1744004), _1744350), hAPP(c_List_Oset(_1744004), _1744008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744004), _1744240), _1744350)))]]], (47827 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744004, _1744008))], (47825 ^ _782476) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744004, _1744006))]]]]], (8657 ^ _782476) ^ [_932922, _932924, _932926, _932928] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932922, tc_HOL_Obool)), _932924), _932926), _932928)), -(hBOOL(hAPP(_932926, _932928)))], (5336 ^ _782476) ^ [_864070, _864072, _864074, _864076] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_864076, _864072) = c_SetInterval_Oord__class_OatLeastLessThan(_864074, _864070)), _864076 = _864074, _864072 = _864070], (39431 ^ _782476) ^ [_1542979, _1542981, _1542983, _1542985] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542979), _1542981)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542979), _1542983)), -(_1542983 = c_Orderings_Obot__class_Obot(tc_fun(_1542979, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1542979, tc_HOL_Obool), tc_fun(_1542979, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1542979, tc_HOL_Obool), tc_fun(_1542979, tc_HOL_Obool)), _1542981), _1542983)), c_Wellfounded_Omax__ext(_1542979, _1542985)))), 39445 ^ _782476 : [(39448 ^ _782476) ^ [_1543384] : [hBOOL(hAPP(hAPP(c_member(_1542979), _1543384), _1542983)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1542979, _1542979)), hAPP(hAPP(c_Product__Type_OPair(_1542979, _1542979), 39444 ^ [_1542979, _1542981, _1542983, _1542985]), _1543384)), _1542985))], (39446 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542979), 39444 ^ [_1542979, _1542981, _1542983, _1542985]), _1542981)))]]], (32229 ^ _782476) ^ [_1392854, _1392856] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392854, _1392856) = 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), _1392854), _1392856) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6732 ^ _782476) ^ [_891368, _891370, _891372, _891374, _891376, _891378] : [hBOOL(hAPP(hAPP(c_member(_891368), _891370), _891372)), hBOOL(hAPP(hAPP(c_member(_891374), _891376), hAPP(_891378, _891370))), -(hBOOL(hAPP(hAPP(c_member(_891374), _891376), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891368, tc_fun(_891374, tc_HOL_Obool)), _891372), _891378))))], (7037 ^ _782476) ^ [_898489, _898491, _898493, _898495, _898497] : [hBOOL(hAPP(hAPP(c_member(_898489), _898491), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898493, tc_fun(_898489, tc_HOL_Obool)), _898495), _898497))), 7040 ^ _782476 : [(7041 ^ _782476) ^ [_898613] : [hBOOL(hAPP(hAPP(c_member(_898493), _898613), _898495)), -(hBOOL(hAPP(hAPP(c_member(_898489), _898491), hAPP(_898497, _898613))))]]], (19566 ^ _782476) ^ [_1150194, _1150196, _1150198, _1150200] : [class_Groups_Ocomm__monoid__add(_1150194), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150196), _1150198))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150196, _1150194), _1150200), _1150198) = c_Groups_Ozero__class_Ozero(_1150194))], (32809 ^ _782476) ^ [_1404520, _1404522, _1404524, _1404526, _1404528, _1404530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1404520, _1404522), tc_HOL_Obool)), _1404524), _1404526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404520, tc_HOL_Obool)), _1404528), _1404530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404522, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404520, _1404522, _1404524), _1404528)), hAPP(c_Relation_OImage(_1404520, _1404522, _1404526), _1404530))))], (36068 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (25085 ^ _782476) ^ [_1251202, _1251204, _1251206, _1251208, _1251210] : [class_Rings_Olinordered__idom(_1251202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251202), hAPP(c_Groups_Oabs__class_Oabs(_1251202), _1251204)), _1251206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251202), hAPP(c_Groups_Oabs__class_Oabs(_1251202), _1251208)), _1251210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251202), hAPP(c_Groups_Oabs__class_Oabs(_1251202), _1251204)), hAPP(c_Groups_Oabs__class_Oabs(_1251202), _1251208))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251202), _1251206), _1251210))))], (11298 ^ _782476) ^ [_989636, _989638, _989640, _989642, _989644] : [-(hAPP(c_Fun_Ofun__upd(_989636, _989638, _989640, _989642, _989644), _989642) = _989644)], (50495 ^ _782476) ^ [_1803612, _1803614] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803612, tc_HOL_Obool), _1803614) = hAPP(c_Set_OCollect(_1803612), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803612, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1803612), c_HOL_OEx(tc_fun(_1803612, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803612, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803612, tc_HOL_Obool), tc_HOL_Obool), _1803612), hAPP(c_COMBS(tc_fun(_1803612, 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(_1803612, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1803612, tc_HOL_Obool), tc_fun(tc_fun(_1803612, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1803612, tc_HOL_Obool))), _1803614)))), c_member(_1803612)))))], (50351 ^ _782476) ^ [_1799758, _1799760, _1799762] : [c_List_Oall__interval__int(_1799758, _1799760, _1799762), -(c_List_Olist__all(tc_Int_Oint, _1799758, c_List_Oupto(_1799760, _1799762)))], (6542 ^ _782476) ^ [_887712, _887714, _887716, _887718, _887720] : [class_Complete__Lattice_Ocomplete__lattice(_887712), hBOOL(hAPP(hAPP(c_member(_887714), _887716), _887718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887714, _887712), _887718), _887720)), hAPP(_887720, _887716))))], (2538 ^ _782476) ^ [_819823, _819825, _819827, _819829] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819829, _819825) = c_Inductive_Ocomplete__lattice__class_Olfp(_819827, _819823)), _819829 = _819827, _819825 = _819823], (32251 ^ _782476) ^ [_1393295, _1393297] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393295, _1393297) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393295), _1393297)), _1393297)))], (38108 ^ _782476) ^ [_1509300, _1509302, _1509304, _1509306, _1509308] : [c_Equiv__Relations_Oequiv(_1509300, _1509302, _1509304), hBOOL(hAPP(hAPP(c_member(_1509300), _1509306), _1509302)), hBOOL(hAPP(hAPP(c_member(_1509300), _1509308), _1509302)), 38119 ^ _782476 : [(38126 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509300, _1509300)), hAPP(hAPP(c_Product__Type_OPair(_1509300, _1509300), _1509306), _1509308)), _1509304)), -(hAPP(c_Relation_OImage(_1509300, _1509300, _1509304), hAPP(hAPP(c_Set_Oinsert(_1509300), _1509306), c_Orderings_Obot__class_Obot(tc_fun(_1509300, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509300, _1509300, _1509304), hAPP(hAPP(c_Set_Oinsert(_1509300), _1509308), c_Orderings_Obot__class_Obot(tc_fun(_1509300, tc_HOL_Obool)))))], (38120 ^ _782476) ^ [] : [hAPP(c_Relation_OImage(_1509300, _1509300, _1509304), hAPP(hAPP(c_Set_Oinsert(_1509300), _1509306), c_Orderings_Obot__class_Obot(tc_fun(_1509300, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509300, _1509300, _1509304), hAPP(hAPP(c_Set_Oinsert(_1509300), _1509308), c_Orderings_Obot__class_Obot(tc_fun(_1509300, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509300, _1509300)), hAPP(hAPP(c_Product__Type_OPair(_1509300, _1509300), _1509306), _1509308)), _1509304)))]]], (14429 ^ _782476) ^ [_1051298, _1051300, _1051302, _1051304, _1051306] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051298), hAPP(c_Set_Oimage(_1051300, _1051298, _1051302), c_Orderings_Otop__class_Otop(tc_fun(_1051300, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051304), hAPP(c_Set_Oimage(_1051300, _1051304, hAPP(hAPP(c_COMBB(_1051298, _1051304, _1051300), _1051306), _1051302)), c_Orderings_Otop__class_Otop(tc_fun(_1051300, tc_HOL_Obool))))))], (47275 ^ _782476) ^ [_1732911, _1732913, _1732915] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732911)), hAPP(c_List_Ofilter(_1732911, _1732913), _1732915)) = 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(_1732911)), _1732915)))), hAPP(hAPP(c_COMBB(_1732911, tc_HOL_Obool, tc_Nat_Onat), _1732913), hAPP(c_List_Onth(_1732911), _1732915))))))], (45499 ^ _782476) ^ [_1693209, _1693211] : [class_Complete__Lattice_Ocomplete__lattice(_1693209), -(c_Complete__Lattice_OSup__class_OSup(_1693209, hAPP(c_List_Oset(_1693209), _1693211)) = hAPP(c_List_Ofoldl(_1693209, _1693209, c_Lattices_Osemilattice__sup__class_Osup(_1693209), c_Orderings_Obot__class_Obot(_1693209)), _1693211))], (43376 ^ _782476) ^ [_1643402, _1643404, _1643406, _1643408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643402), tc_List_Olist(_1643402))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643402), tc_List_Olist(_1643402)), _1643404), _1643406)), c_List_Olexord(_1643402, _1643408))), 43381 ^ _782476 : [(43384 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643402)), _1643404)), _1643406) = _1643404)], (43382 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643402)), _1643404)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643402)), _1643406))))]], 43386 ^ _782476 : [(43391 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643402, _1643402)), hAPP(hAPP(c_Product__Type_OPair(_1643402, _1643402), hAPP(hAPP(c_List_Onth(_1643402), _1643404), 43385 ^ [_1643402, _1643404, _1643406, _1643408])), hAPP(hAPP(c_List_Onth(_1643402), _1643406), 43385 ^ [_1643402, _1643404, _1643406, _1643408]))), _1643408)))], (43389 ^ _782476) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643402), 43385 ^ [_1643402, _1643404, _1643406, _1643408]), _1643404) = hAPP(hAPP(c_List_Otake(_1643402), 43385 ^ [_1643402, _1643404, _1643406, _1643408]), _1643406))], (43387 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43385 ^ [_1643402, _1643404, _1643406, _1643408]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643402)), _1643404)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643402)), _1643406)))))]]], (6445 ^ _782476) ^ [_885741, _885743, _885745] : [class_Orderings_Owellorder(_885741), hBOOL(hAPP(_885743, _885745)), -(hBOOL(hAPP(_885743, c_Orderings_Oord__class_OLeast(_885741, _885743))))], (29362 ^ _782476) ^ [_1339638, _1339640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1339638)), -(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), _1339638), _1339640))))], (44212 ^ _782476) ^ [_1664537, _1664539, _1664541, _1664543] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664537) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1664539), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664537)), hAPP(hAPP(c_List_Olist_OCons(_1664539), _1664541), _1664543)) = c_List_Olist_ONil(_1664539))], (48530 ^ _782476) ^ [_1758911, _1758913, _1758915] : [-(c_List_OdropWhile(_1758911, _1758913, _1758915) = hAPP(hAPP(c_List_Odrop(_1758911), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758911)), c_List_OtakeWhile(_1758911, _1758913, _1758915))), _1758915))], (44476 ^ _782476) ^ [_1669363, _1669365] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1669363), tc_List_Olist(_1669363), c_List_Olistrel(_1669363, _1669365)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669363)), c_List_Olist_ONil(_1669363)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669363), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669363)), c_List_Olist_ONil(_1669363)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669363), tc_HOL_Obool))))], (38395 ^ _782476) ^ [_1516491] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1516491)], (34218 ^ _782476) ^ [_1430970, _1430972] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430970)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430970)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430972)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430970)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430972))))], (6562 ^ _782476) ^ [_888094, _888096, _888098, _888100, _888102] : [class_Orderings_Olinorder(_888094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888094, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888094, _888096), _888098)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888094, _888100), _888102))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888094), _888098), _888096))), 6573 ^ _782476 : [(6576 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888094), _888098), _888102)))], (6574 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888094), _888100), _888096)))]]], (49446 ^ _782476) ^ [_1779434, _1779436] : [-(hAPP(c_New__DSequence_Opos__empty(_1779434), _1779436) = c_Lazy__Sequence_Oempty(_1779434))], (32157 ^ _782476) ^ [_1391558, _1391560, _1391562, _1391564] : [class_Divides_Osemiring__div(_1391558), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391558), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391558), _1391560), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391558), _1391562), _1391560))), c_Divides_Odiv__class_Omod(_1391558, _1391562, _1391560))), _1391564) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391558), _1391562), _1391564))], (45799 ^ _782476) ^ [_1699087, _1699089, _1699091] : [-(_1699087 = c_List_Olist_ONil(_1699089)), -(c_List_Olast(_1699089, hAPP(hAPP(c_List_Olist_OCons(_1699089), _1699091), _1699087)) = c_List_Olast(_1699089, _1699087))], (19096 ^ _782476) ^ [_1141980, _1141982, _1141984, _1141986] : [class_Rings_Olinordered__ring__strict(_1141980), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141980), _1141982), c_Groups_Ozero__class_Ozero(_1141980))), 19103 ^ _782476 : [(19110 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141980), _1141986), _1141984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141980), _1141982), _1141984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141980), _1141982), _1141986))))], (19104 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141980), _1141982), _1141984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141980), _1141982), _1141986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141980), _1141986), _1141984)))]]], (36152 ^ _782476) ^ [_1465144, _1465146] : [class_Int_Onumber__ring(_1465144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465144), _1465146), hAPP(c_Int_Onumber__class_Onumber__of(_1465144), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465144), _1465146))], (42503 ^ _782476) ^ [_1619457, _1619459, _1619461, _1619463, _1619465, _1619467] : [c_Finite__Set_Ofun__left__comm(_1619457, _1619459, _1619461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619457), _1619463)), -(hBOOL(hAPP(hAPP(c_member(_1619457), _1619465), _1619463))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619457, _1619459, _1619461), _1619467), hAPP(hAPP(c_Set_Oinsert(_1619457), _1619465), _1619463)) = hAPP(hAPP(_1619461, _1619465), hAPP(hAPP(c_Finite__Set_Ofold(_1619457, _1619459, _1619461), _1619467), _1619463)))], (32401 ^ _782476) ^ [_1396166, _1396168, _1396170, _1396172] : [_1396166 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396168), _1396170)), _1396172), -(_1396168 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396166, _1396168) = _1396172), 32408 ^ _782476 : [(32411 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396172), _1396168))], (32409 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396168)))]], 32416 ^ _782476 : [(32419 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396168), _1396172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396172), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32417 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396168))]]], (45260 ^ _782476) ^ [_1688390, _1688392, _1688394, _1688396, _1688398] : [-(hAPP(hAPP(c_List_Ozip(_1688390, _1688392), _1688394), hAPP(hAPP(c_List_Oappend(_1688392), _1688396), _1688398)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688390, _1688392)), hAPP(hAPP(c_List_Ozip(_1688390, _1688392), hAPP(hAPP(c_List_Otake(_1688390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688392)), _1688396)), _1688394)), _1688396)), hAPP(hAPP(c_List_Ozip(_1688390, _1688392), hAPP(hAPP(c_List_Odrop(_1688390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688392)), _1688396)), _1688394)), _1688398)))], (46906 ^ _782476) ^ [_1724171, _1724173] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724171)), c_List_Oremdups(_1724171, _1724173)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724171)), _1724173), -(c_List_Oremdups(_1724171, _1724173) = _1724173)], (9083 ^ _782476) ^ [_942733, _942735, _942737, _942739, _942741] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942733, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942735, tc_fun(_942733, tc_HOL_Obool)), _942737), _942739)), _942741) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942735, tc_fun(_942733, tc_HOL_Obool)), _942737), hAPP(hAPP(c_COMBC(_942735, tc_fun(_942733, tc_HOL_Obool), tc_fun(_942733, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942733, tc_HOL_Obool), tc_fun(tc_fun(_942733, tc_HOL_Obool), tc_fun(_942733, tc_HOL_Obool)), _942735), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942733, tc_HOL_Obool))), _942739)), _942741)))], (10335 ^ _782476) ^ [_969798, _969800] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969798, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_969798, tc_HOL_Obool))), _969800) = c_Orderings_Obot__class_Obot(tc_fun(_969798, tc_HOL_Obool)))], (41668 ^ _782476) ^ [_1600751, _1600753, _1600755, _1600757, _1600759, _1600761] : [c_Relation_Osingle__valued(_1600751, _1600753, _1600755), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600751, _1600753)), hAPP(hAPP(c_Product__Type_OPair(_1600751, _1600753), _1600757), _1600759)), _1600755)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600751, _1600753)), hAPP(hAPP(c_Product__Type_OPair(_1600751, _1600753), _1600757), _1600761)), _1600755)), -(_1600759 = _1600761)], (27373 ^ _782476) ^ [_1300128, _1300130, _1300132, _1300134, _1300136] : [class_Lattices_Osemilattice__inf(_1300128), class_Orderings_Olinorder(_1300130), c_Orderings_Oorder__class_Omono(_1300130, _1300128, _1300132), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300128), hAPP(_1300132, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300130), _1300134), _1300136))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300128), hAPP(_1300132, _1300134)), hAPP(_1300132, _1300136)))))], (22042 ^ _782476) ^ [_1197015] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1197015)], (49223 ^ _782476) ^ [_1774960, _1774962, _1774964] : [c_List_Olist__all(_1774960, _1774962, hAPP(c_List_Orev(_1774960), _1774964)), -(c_List_Olist__all(_1774960, _1774962, _1774964))], (30318 ^ _782476) ^ [_1357170, _1357172, _1357174] : [class_Fields_Olinordered__field(_1357170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357170), _1357172), c_Groups_Ozero__class_Ozero(_1357170))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357170), _1357174), c_Groups_Ozero__class_Ozero(_1357170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357170), c_Groups_Ozero__class_Ozero(_1357170)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357170), _1357172), _1357174))))], (48471 ^ _782476) ^ [_1757735, _1757737, _1757739] : [48473 ^ _782476 : [(48476 ^ _782476) ^ [] : [hBOOL(hAPP(_1757737, 48472 ^ [_1757735, _1757737, _1757739]))], (48474 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757735), 48472 ^ [_1757735, _1757737, _1757739]), hAPP(c_List_Oset(_1757735), _1757739))))]], -(c_List_OdropWhile(_1757735, _1757737, _1757739) = c_List_Olist_ONil(_1757735))], (36090 ^ _782476) ^ [_1464235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464235))))], (45589 ^ _782476) ^ [_1695300, _1695302, _1695304, _1695306] : [class_Orderings_Olinorder(_1695300), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695302, _1695300, _1695304), _1695306), c_List_Olist_ONil(_1695302)) = hAPP(hAPP(c_List_Olist_OCons(_1695302), _1695306), c_List_Olist_ONil(_1695302)))], (40031 ^ _782476) ^ [_1560699, _1560701] : [-(c_Product__Type_Oapfst(_1560699, _1560699, _1560701, c_Fun_Oid(_1560699)) = c_Fun_Oid(tc_prod(_1560699, _1560701)))], (31950 ^ _782476) ^ [_1387668, _1387670, _1387672, _1387674] : [class_Divides_Osemiring__div(_1387668), -(c_Divides_Odiv__class_Omod(_1387668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387668), _1387670), _1387672), _1387674) = c_Divides_Odiv__class_Omod(_1387668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387668), c_Divides_Odiv__class_Omod(_1387668, _1387670, _1387674)), _1387672), _1387674))], (9087 ^ _782476) ^ [_943045, _943047, _943049, _943051, _943053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943045, tc_HOL_Obool)), hAPP(c_Set_Oimage(_943047, _943045, _943049), _943051)), _943053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_943045, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_943047, tc_HOL_Obool), tc_fun(_943045, tc_HOL_Obool), c_Set_Oimage(_943047, _943045, _943049)), hAPP(c_Set_OPow(_943047), _943051))), hAPP(c_Set_OPow(_943045), _943053))))], (43792 ^ _782476) ^ [_1655284, _1655286, _1655288, _1655290] : [43794 ^ _782476 : [(43797 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1655288, 43793 ^ [_1655284, _1655286, _1655288, _1655290])), hAPP(_1655290, 43793 ^ [_1655284, _1655286, _1655288, _1655290])))], (43795 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655284), 43793 ^ [_1655284, _1655286, _1655288, _1655290]), hAPP(c_List_Oset(_1655284), _1655286))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1655284, _1655288, _1655286)), c_List_Olist_Olist__size(_1655284, _1655290, _1655286))))], (11802 ^ _782476) ^ [_997360, _997362, _997364, _997366] : [class_Lattices_Osemilattice__inf(_997360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997360), _997362), _997364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997360), _997366), _997362)), _997364)))], (19730 ^ _782476) ^ [_1153004, _1153006] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153004), _1153006) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153004), _1153006)))], (52333 ^ _782476) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (5066 ^ _782476) ^ [_859897, _859899, _859901, _859903] : [-(c_Relation_Oinv__image(_859903, _859899) = c_Relation_Oinv__image(_859901, _859897)), _859903 = _859901, _859899 = _859897], (45360 ^ _782476) ^ [_1690322, _1690324, _1690326] : [-(hAPP(c_List_Oset(_1690322), hAPP(c_List_Orotate(_1690322, _1690324), _1690326)) = hAPP(c_List_Oset(_1690322), _1690326))], (17355 ^ _782476) ^ [_1111803, _1111805, _1111807] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111803), _1111805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111807), _1111805), -(_1111803 = _1111807)], (374 ^ _782476) ^ [_788169, _788171, _788173, _788175] : [-(c_Relation_Oirrefl(_788173, _788169)), c_Relation_Oirrefl(_788175, _788171), _788175 = _788173, _788171 = _788169], (43846 ^ _782476) ^ [_1656636, _1656638, _1656640, _1656642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656636)), _1656638)), _1656640)), -(hAPP(hAPP(c_List_Olist__update(_1656636, _1656638), _1656640), _1656642) = _1656638)], (49073 ^ _782476) ^ [_1771735, _1771737, _1771739] : [c_List_Olist__ex(_1771735, _1771737, hAPP(c_List_Orev(_1771735), _1771739)), -(c_List_Olist__ex(_1771735, _1771737, _1771739))], (39802 ^ _782476) ^ [_1553493, _1553495, _1553497, _1553499, _1553501] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553493, _1553495), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553493, tc_HOL_Obool)), _1553497), _1553499)), hAPP(c_COMBK(tc_fun(_1553495, tc_HOL_Obool), _1553493), _1553501)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553493, _1553495), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553493, _1553495), _1553497), hAPP(c_COMBK(tc_fun(_1553495, tc_HOL_Obool), _1553493), _1553501))), hAPP(hAPP(c_Product__Type_OSigma(_1553493, _1553495), _1553499), hAPP(c_COMBK(tc_fun(_1553495, tc_HOL_Obool), _1553493), _1553501))))], (37750 ^ _782476) ^ [_1501112, _1501114, _1501116, _1501118, _1501120] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501112, _1501114, _1501116), _1501118), _1501120) = hAPP(hAPP(_1501118, hAPP(c_Product__Type_Ofst(_1501112, _1501114), _1501120)), hAPP(c_Product__Type_Osnd(_1501112, _1501114), _1501120)))], (11782 ^ _782476) ^ [_997002, _997004, _997006, _997008] : [class_Lattices_Osemilattice__sup(_997002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997002), _997004), _997006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997002), _997004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997002), _997008), _997006))))], (25831 ^ _782476) ^ [_1267760, _1267762] : [-(hAPP(c_Set_OPow(_1267760), _1267762) = hAPP(c_Set_OCollect(tc_fun(_1267760, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267760, tc_HOL_Obool), tc_fun(_1267760, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267760, tc_HOL_Obool))), _1267762)))], (28023 ^ _782476) ^ [_1312304] : [class_Orderings_Oord(_1312304), -(c_Orderings_Oord__class_Omin(_1312304) = c_Orderings_Oord_Omin(_1312304, c_Orderings_Oord__class_Oless__eq(_1312304)))], (44781 ^ _782476) ^ [_1677011, _1677013, _1677015] : [-(_1677011 = c_List_Olist_ONil(_1677013)), -(c_List_Obutlast(_1677013, hAPP(hAPP(c_List_Oappend(_1677013), _1677015), _1677011)) = hAPP(hAPP(c_List_Oappend(_1677013), _1677015), c_List_Obutlast(_1677013, _1677011)))], (17900 ^ _782476) ^ [_1122052, _1122054, _1122056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122052), _1122054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122056), _1122054))))], (32345 ^ _782476) ^ [_1395124, _1395126, _1395128, _1395130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395126), _1395128)), -(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), _1395128), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395130, _1395124))), _1395126))))], (39497 ^ _782476) ^ [_1544390, _1544392, _1544394, _1544396] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544390, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1544390, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544392, _1544390), _1544394)), hAPP(c_Relation_ORange(_1544392, _1544390), _1544396))), hAPP(c_Relation_ORange(_1544392, _1544390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1544392, _1544390), tc_HOL_Obool)), _1544394), _1544396)))))], (19925 ^ _782476) ^ [_1156492, _1156494, _1156496, _1156498, _1156500] : [class_Rings_Olinordered__semiring__strict(_1156492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156492), _1156494), _1156496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156492), _1156498), _1156500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156492), c_Groups_Ozero__class_Ozero(_1156492)), _1156494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156492), c_Groups_Ozero__class_Ozero(_1156492)), _1156498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156492), _1156494), _1156498)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156492), _1156496), _1156500))))], (42293 ^ _782476) ^ [_1615573, _1615575, _1615577, _1615579] : [class_Complete__Lattice_Ocomplete__lattice(_1615573), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615575), _1615577)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615575, _1615573), _1615577), _1615579) = hAPP(hAPP(c_Finite__Set_Ofold(_1615575, _1615573, hAPP(hAPP(c_COMBB(_1615573, tc_fun(_1615573, _1615573), _1615575), c_Lattices_Osemilattice__sup__class_Osup(_1615573)), _1615579)), c_Orderings_Obot__class_Obot(_1615573)), _1615577))], (17812 ^ _782476) ^ [_1120007, _1120009, _1120011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120007), _1120009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120007), _1120011)), 17819 ^ _782476 : [(17826 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120009), _1120011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120009), _1120007)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120011), _1120007))))], (17820 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120009), _1120007)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120011), _1120007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120009), _1120011)))]]], (49254 ^ _782476) ^ [_1775555, _1775557, _1775559, _1775561] : [c_List_Olist__all(_1775555, _1775557, hAPP(hAPP(c_List_Oappend(_1775555), _1775559), _1775561)), 49257 ^ _782476 : [(49260 ^ _782476) ^ [] : [-(c_List_Olist__all(_1775555, _1775557, _1775561))], (49258 ^ _782476) ^ [] : [-(c_List_Olist__all(_1775555, _1775557, _1775559))]]], (21425 ^ _782476) ^ [_1184652, _1184654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184654)), -(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), _1184652), _1184654))))], (52579 ^ _782476) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (938 ^ _782476) ^ [_796749, _796751, _796753, _796755] : [-(c_Relation_Osym(_796753, _796749)), c_Relation_Osym(_796755, _796751), _796755 = _796753, _796751 = _796749], (9897 ^ _782476) ^ [_960660, _960662, _960664, _960666, _960668] : [-(_960660 = c_Orderings_Obot__class_Obot(tc_fun(_960662, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960664, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960662, tc_fun(_960664, tc_HOL_Obool)), _960660), _960666)), _960668) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960662, tc_fun(_960664, tc_HOL_Obool)), _960660), hAPP(hAPP(c_COMBC(_960662, tc_fun(_960664, tc_HOL_Obool), tc_fun(_960664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960664, tc_HOL_Obool), tc_fun(tc_fun(_960664, tc_HOL_Obool), tc_fun(_960664, tc_HOL_Obool)), _960662), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960664, tc_HOL_Obool))), _960666)), _960668)))], (7208 ^ _782476) ^ [_902413, _902415, _902417] : [class_Complete__Lattice_Ocomplete__lattice(_902413), 7211 ^ _782476 : [(7212 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902413), _902415), c_Complete__Lattice_OInf__class_OInf(_902413, _902417))), 7215 ^ _782476 : [(7216 ^ _782476) ^ [_902571] : [hBOOL(hAPP(hAPP(c_member(_902413), _902571), _902417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902413), _902415), _902571)))]]], (7222 ^ _782476) ^ [] : [7224 ^ _782476 : [(7227 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902413), _902415), 7223 ^ [_902413, _902415, _902417]))], (7225 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902413), 7223 ^ [_902413, _902415, _902417]), _902417)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902413), _902415), c_Complete__Lattice_OInf__class_OInf(_902413, _902417))))]]], (22240 ^ _782476) ^ [_1200124, _1200126] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200124)), hAPP(c_Nat_OSuc, _1200126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200124), _1200126))], (24190 ^ _782476) ^ [_1235719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235719)), -(c_Nat__Transfer_Ois__nat(_1235719))], (7031 ^ _782476) ^ [_898324, _898326, _898328] : [_898326 = _898328, -(hAPP(hAPP(c_COMBC(_898324, tc_fun(_898324, tc_HOL_Obool), tc_HOL_Obool), c_member(_898324)), _898326) = hAPP(hAPP(c_COMBC(_898324, tc_fun(_898324, tc_HOL_Obool), tc_HOL_Obool), c_member(_898324)), _898328))], (14276 ^ _782476) ^ [_1048423, _1048425, _1048427] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048423), _1048425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048423, tc_HOL_Obool)), _1048427), _1048425)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048423), _1048427)))], (44398 ^ _782476) ^ [_1667800, _1667802] : [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(_1667800)), _1667802))), _1667802 = c_List_Olist_ONil(_1667800)], (13112 ^ _782476) ^ [_1023503, _1023505, _1023507, _1023509, _1023511, _1023513, _1023515, _1023517] : [c_Fun_Oinj__on(_1023503, _1023505, _1023507, _1023509), 13118 ^ _782476 : [(13121 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023503, tc_HOL_Obool)), hAPP(_1023515, 13117 ^ [_1023503, _1023505, _1023507, _1023509, _1023511, _1023513, _1023515, _1023517])), _1023509))], (13119 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1023511), 13117 ^ [_1023503, _1023505, _1023507, _1023509, _1023511, _1023513, _1023515, _1023517]), _1023513)))]], hBOOL(hAPP(hAPP(c_member(_1023511), _1023517), _1023513)), -(hAPP(c_Set_Oimage(_1023503, _1023505, _1023507), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023511, tc_fun(_1023503, tc_HOL_Obool)), _1023513), _1023515)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023511, tc_fun(_1023505, tc_HOL_Obool)), _1023513), hAPP(hAPP(c_COMBB(tc_fun(_1023503, tc_HOL_Obool), tc_fun(_1023505, tc_HOL_Obool), _1023511), c_Set_Oimage(_1023503, _1023505, _1023507)), _1023515)))], (21973 ^ _782476) ^ [_1195858] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195858), hAPP(c_Nat_OSuc, _1195858))))], (40369 ^ _782476) ^ [_1569065, _1569067] : [c_Relation_Orefl__on(_1569065, c_Orderings_Otop__class_Otop(tc_fun(_1569065, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569065, _1569065)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569065, _1569065, tc_HOL_Obool), _1569067))), -(c_Predicate_Oreflp(_1569065, _1569067))], (18836 ^ _782476) ^ [_1137252, _1137254, _1137256] : [class_Rings_Oordered__cancel__semiring(_1137252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137252), c_Groups_Ozero__class_Ozero(_1137252)), _1137254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137252), c_Groups_Ozero__class_Ozero(_1137252)), _1137256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137252), c_Groups_Ozero__class_Ozero(_1137252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137252), _1137254), _1137256))))], (33906 ^ _782476) ^ [_1425420, _1425422] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425420)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425420)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425422)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425420)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425422))))], (32968 ^ _782476) ^ [_1407617, _1407619, _1407621] : [class_Int_Onumber__ring(_1407617), class_Int_Oring__char__0(_1407617), 32975 ^ _782476 : [(32982 ^ _782476) ^ [] : [_1407619 = _1407621, -(hAPP(c_Int_Onumber__class_Onumber__of(_1407617), _1407619) = hAPP(c_Int_Onumber__class_Onumber__of(_1407617), _1407621))], (32976 ^ _782476) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407617), _1407619) = hAPP(c_Int_Onumber__class_Onumber__of(_1407617), _1407621), -(_1407619 = _1407621)]]], (7047 ^ _782476) ^ [_898732, _898734, _898736, _898738, _898740] : [7049 ^ _782476 : [(7052 ^ _782476) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898732), _898734), hAPP(_898740, 7048 ^ [_898732, _898734, _898736, _898738, _898740])))], (7050 ^ _782476) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898736), 7048 ^ [_898732, _898734, _898736, _898738, _898740]), _898738)))]], -(hBOOL(hAPP(hAPP(c_member(_898732), _898734), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898736, tc_fun(_898732, tc_HOL_Obool)), _898738), _898740))))], (8074 ^ _782476) ^ [_920001, _920003, _920005] : [class_Lattices_Osemilattice__sup(_920001), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920001), _920003), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920001), _920005), _920003))))]], input).
% 45.17/44.02  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)],start(52781 ^ 0)).
% 45.17/44.02  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, v_ts), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G)],extension(5767 ^ 1,bind([[_873645, _873647, _873649, _873651], [t_a, v_G, v_ts, v_Ga]]))).
% 45.17/44.02  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, v_ts)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G))],extension(5751 ^ 2,bind([[_873375, _873377, _873379], [t_a, v_ts, v_G]]))).
% 45.17/44.02  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G)))],extension(52777 ^ 3)).
% 45.17/44.02  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(5751 ^ 2,bind([[_873375, _873377, _873379], [t_a, v_G, v_Ga]]))).
% 45.17/44.02  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(52779 ^ 3)).
% 45.17/44.02  %-----------------------------------------------------
% 45.17/44.02  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------