%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW345+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:26:00 EDT 2023

% Result   : Theorem 45.12s 44.02s
% Output   : Proof 45.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW345+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 22:36:15 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 45.12/44.02  
% 45.12/44.02  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.12/44.02  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.12/44.02  %-----------------------------------------------------
% 45.12/44.02  ncf(matrix, plain, [(51705 ^ _2062483) ^ [] : [v_R(v_Z, v_s_H)], !, (7502 ^ _779571) ^ [_903840, _903842, _903844, _903846, _903848] : [c_Sum__Type_OSumr(_903840, _903842, _903844, _903846) = c_Sum__Type_OSumr(_903840, _903842, _903844, _903848), -(_903846 = _903848)], (10444 ^ _779571) ^ [_953433, _953435, _953437, _953439, _953441] : [class_Orderings_Oord(_953433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953435, _953433)), _953437), _953439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953433), hAPP(_953437, _953441)), hAPP(_953439, _953441))))], (6031 ^ _779571) ^ [_876709, _876711, _876713, _876715] : [c_Com_Ocom_OSemi(_876709, _876711) = c_Com_Ocom_OWhile(_876713, _876715)], (44514 ^ _779571) ^ [_1651558] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651558, tc_HOL_Obool) = c_Set_OBall(_1651558))], (39561 ^ _779571) ^ [_1525566, _1525568, _1525570, _1525572, _1525574, _1525576] : [hBOOL(hAPP(hAPP(c_member(_1525566), _1525568), _1525570)), 39564 ^ _779571 : [(39571 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525566), _1525572), _1525570))), -(hAPP(c_Set_Ovimage(_1525574, _1525566, hAPP(hAPP(c_COMBC(_1525574, _1525566, _1525566), hAPP(hAPP(c_COMBC(_1525574, _1525566, tc_fun(_1525566, _1525566)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525566, tc_fun(_1525566, _1525566)), _1525574), c_If(_1525566)), hAPP(hAPP(c_COMBC(_1525574, tc_fun(_1525574, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525574)), _1525576))), _1525568)), _1525572)), _1525570) = _1525576)], (39565 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525566), _1525572), _1525570)), -(hAPP(c_Set_Ovimage(_1525574, _1525566, hAPP(hAPP(c_COMBC(_1525574, _1525566, _1525566), hAPP(hAPP(c_COMBC(_1525574, _1525566, tc_fun(_1525566, _1525566)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525566, tc_fun(_1525566, _1525566)), _1525574), c_If(_1525566)), hAPP(hAPP(c_COMBC(_1525574, tc_fun(_1525574, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525574)), _1525576))), _1525568)), _1525572)), _1525570) = c_Orderings_Otop__class_Otop(tc_fun(_1525574, tc_HOL_Obool)))]]], (49144 ^ _779571) ^ [_1765700, _1765702] : [class_Groups_Omonoid__add(_1765700), -(hAPP(c_List_Ofoldl(_1765700, _1765700, c_Groups_Oplus__class_Oplus(_1765700), c_Groups_Ozero__class_Ozero(_1765700)), _1765702) = c_List_Ofoldr(_1765700, _1765700, c_Groups_Oplus__class_Oplus(_1765700), _1765702, c_Groups_Ozero__class_Ozero(_1765700)))], (40116 ^ _779571) ^ [_1538926, _1538928, _1538930, _1538932, _1538934] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538926, _1538928), _1538930), hAPP(hAPP(c_COMBS(_1538926, tc_fun(_1538928, tc_HOL_Obool), tc_fun(_1538928, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538928, tc_HOL_Obool), tc_fun(tc_fun(_1538928, tc_HOL_Obool), tc_fun(_1538928, tc_HOL_Obool)), _1538926), c_Groups_Ominus__class_Ominus(tc_fun(_1538928, tc_HOL_Obool))), _1538932)), _1538934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1538926, _1538928), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1538926, _1538928), _1538930), _1538932)), hAPP(hAPP(c_Product__Type_OSigma(_1538926, _1538928), _1538930), _1538934)))], (13803 ^ _779571) ^ [_1011495, _1011497, _1011499] : [class_Divides_Osemiring__div(_1011495), -(c_Divides_Odiv__class_Omod(_1011495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011495), _1011497), _1011499), _1011499) = c_Groups_Ozero__class_Ozero(_1011495))], (36164 ^ _779571) ^ [_1450514, _1450516, _1450518, _1450520] : [-(hBOOL(hAPP(hAPP(c_member(_1450514), _1450516), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450514, tc_HOL_Obool)), _1450518), _1450520)))), hBOOL(hAPP(hAPP(c_member(_1450514), _1450516), _1450518)), hBOOL(hAPP(hAPP(c_member(_1450514), _1450516), _1450520))], (22466 ^ _779571) ^ [_1167984, _1167986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167984)), hAPP(c_Nat_OSuc, _1167986))), -(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(_1167984))), 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)), _1167986)))))], (19287 ^ _779571) ^ [_1110353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1110353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1110353)))], (31782 ^ _779571) ^ [_1356331, _1356333, _1356335, _1356337, _1356339] : [class_Groups_Oab__group__add(_1356331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356333), _1356335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356333, tc_HOL_Obool)), _1356337), _1356335)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356333, _1356331), _1356339), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356333, tc_HOL_Obool)), _1356335), _1356337)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356331), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356333, _1356331), _1356339), _1356335)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356333, _1356331), _1356339), _1356337)))], (34202 ^ _779571) ^ [_1405000, _1405002, _1405004] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1405000), _1405002), _1405004) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1405000), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1405000, tc_Int_Oint), _1405002), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1405004))), class_Groups_Ocomm__monoid__add(_1405000), class_Groups_Ocomm__monoid__mult(_1405000)], (10325 ^ _779571) ^ [_951560] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951560), _951560)))))], (28064 ^ _779571) ^ [_1276929, _1276931] : [class_Lattices_Osemilattice__sup(_1276929), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276929), _1276931), _1276931) = _1276931)], (37748 ^ _779571) ^ [_1487093, _1487095, _1487097, _1487099, _1487101, _1487103] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487093, tc_fun(_1487095, tc_HOL_Obool))), _1487097), _1487099), _1487101), _1487103)), -(hBOOL(hAPP(hAPP(_1487099, _1487101), _1487103)))], (20045 ^ _779571) ^ [_1124160, _1124162, _1124164, _1124166] : [class_Rings_Odivision__ring(_1124160), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124160), _1124162), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124160), _1124164), _1124166)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124160), _1124162), _1124164)), _1124166))], (43074 ^ _779571) ^ [_1617391, _1617393] : [-(c_Transitive__Closure_Ortrancl(_1617391, _1617393) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1617391, _1617391), tc_HOL_Obool)), c_Relation_OId(_1617391)), hAPP(hAPP(c_Relation_Orel__comp(_1617391, _1617391, _1617391), c_Transitive__Closure_Ortrancl(_1617391, _1617393)), _1617393)))], (1042 ^ _779571) ^ [_795364, _795366] : [-(class_Rings_Olinordered__semiring__1(_795364)), _795366 = _795364, class_Rings_Olinordered__semiring__1(_795366)], (47322 ^ _779571) ^ [_1721164, _1721166] : [-(c_List_Osublist(_1721164, c_List_Olist_ONil(_1721164), _1721166) = c_List_Olist_ONil(_1721164))], (40508 ^ _779571) ^ [_1548659, _1548661, _1548663] : [class_Orderings_Olinorder(_1548659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548659), _1548661)), -(_1548661 = c_Orderings_Obot__class_Obot(tc_fun(_1548659, tc_HOL_Obool))), 40519 ^ _779571 : [(40520 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1548659), _1548663), hAPP(c_Finite__Set_Ofold1(_1548659, c_Orderings_Oord__class_Omin(_1548659)), _1548661))), 40523 ^ _779571 : [(40524 ^ _779571) ^ [_1548952] : [hBOOL(hAPP(hAPP(c_member(_1548659), _1548952), _1548661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1548659), _1548663), _1548952)))]]], (40530 ^ _779571) ^ [] : [40532 ^ _779571 : [(40535 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1548659), _1548663), 40531 ^ [_1548659, _1548661, _1548663]))], (40533 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1548659), 40531 ^ [_1548659, _1548661, _1548663]), _1548661)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1548659), _1548663), hAPP(c_Finite__Set_Ofold1(_1548659, c_Orderings_Oord__class_Omin(_1548659)), _1548661))))]]], (11418 ^ _779571) ^ [_969051, _969053] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969051), _969053))))], (9738 ^ _779571) ^ [_941517, _941519, _941521] : [class_Rings_Olinordered__semiring__strict(_941517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941517), _941519), c_Groups_Ozero__class_Ozero(_941517))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941517), c_Groups_Ozero__class_Ozero(_941517)), _941521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941517), _941519), _941521)), c_Groups_Ozero__class_Ozero(_941517))))], (17189 ^ _779571) ^ [_1075120, _1075122, _1075124] : [class_Rings_Olinordered__semidom(_1075120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075120), c_Groups_Ozero__class_Ozero(_1075120)), _1075122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075120), _1075122), c_Groups_Oone__class_Oone(_1075120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075120), hAPP(hAPP(c_Power_Opower__class_Opower(_1075120), _1075122), hAPP(c_Nat_OSuc, _1075124))), c_Groups_Oone__class_Oone(_1075120))))], (8496 ^ _779571) ^ [_920283, _920285, _920287] : [class_Orderings_Oorder(_920283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920283), _920285), _920287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920283), _920287), _920285))], (13416 ^ _779571) ^ [_1004367] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004367), _1004367)))], (24821 ^ _779571) ^ [_1213429, _1213431, _1213433, _1213435, _1213437] : [_1213429 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1213431, _1213433, _1213435, _1213437), _1213429) = c_Lazy__Sequence_Ohit__bound(_1213433))], (35860 ^ _779571) ^ [] : [-(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))], (40154 ^ _779571) ^ [_1540168, _1540170, _1540172, _1540174, _1540176, _1540178] : [class_Groups_Ocomm__monoid__mult(_1540168), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1540170, _1540168), hAPP(hAPP(c_COMBC(_1540170, tc_fun(_1540172, tc_HOL_Obool), _1540168), hAPP(hAPP(c_COMBB(tc_fun(_1540172, _1540168), tc_fun(tc_fun(_1540172, tc_HOL_Obool), _1540168), _1540170), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1540172, _1540168)), _1540174)), _1540176)), _1540178) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1540170, _1540172), _1540168), hAPP(c_Product__Type_Oprod_Oprod__case(_1540170, _1540172, _1540168), _1540174)), hAPP(hAPP(c_Product__Type_OSigma(_1540170, _1540172), _1540178), hAPP(c_COMBK(tc_fun(_1540172, tc_HOL_Obool), _1540170), _1540176))))], (22370 ^ _779571) ^ [_1165767, _1165769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1165767), _1165769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1165767)), hAPP(c_Code__Numeral_Oof__nat, _1165769))))], (5026 ^ _779571) ^ [_857260, _857262, _857264, _857266, _857268, _857270] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_857270, _857266, _857262) = c_SetInterval_Oord__class_OgreaterThanLessThan(_857268, _857264, _857260)), _857270 = _857268, _857266 = _857264, _857262 = _857260], (14514 ^ _779571) ^ [_1024375, _1024377] : [14515 ^ _779571 : [(14516 ^ _779571) ^ [_1024424] : [_1024375 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024377), _1024424)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024375, _1024377) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44826 ^ _779571) ^ [_1660199, _1660201, _1660203, _1660205, _1660207] : [class_Complete__Lattice_Ocomplete__lattice(_1660199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660201), _1660203)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1660199), _1660205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660201, _1660199), _1660203), _1660207)) = hAPP(hAPP(c_Finite__Set_Ofold(_1660201, _1660199, hAPP(hAPP(c_COMBB(_1660199, tc_fun(_1660199, _1660199), _1660201), c_Lattices_Osemilattice__inf__class_Oinf(_1660199)), _1660207)), _1660205), _1660203))], (32016 ^ _779571) ^ [_1361804, _1361806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1361804, _1361806)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1361804, _1361806), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1361806), c_Orderings_Otop__class_Otop(tc_fun(_1361806, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1361804), c_Orderings_Otop__class_Otop(tc_fun(_1361804, tc_HOL_Obool)))))], (22548 ^ _779571) ^ [_1169808, _1169810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1169808)), 22551 ^ _779571 : [(22558 ^ _779571) ^ [] : [-(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), _1169810), _1169808)))), -(c_Divides_OnegDivAlg(_1169810, _1169808) = hAPP(c_Divides_Oadjust(_1169808), c_Divides_OnegDivAlg(_1169810, 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)))), _1169808))))], (22552 ^ _779571) ^ [] : [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), _1169810), _1169808))), -(c_Divides_OnegDivAlg(_1169810, _1169808) = 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), _1169810), _1169808)))]]], (30116 ^ _779571) ^ [_1319394, _1319396, _1319398, _1319400] : [hBOOL(hAPP(hAPP(c_member(_1319394), _1319396), _1319398)), -(hBOOL(hAPP(hAPP(c_member(_1319394), _1319396), hAPP(hAPP(c_Set_Oinsert(_1319394), _1319400), _1319398))))], (29722 ^ _779571) ^ [_1310949, _1310951, _1310953, _1310955, _1310957] : [-(_1310949 = c_Orderings_Obot__class_Obot(tc_fun(_1310951, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310951, tc_fun(_1310953, tc_HOL_Obool)), _1310949), hAPP(hAPP(c_COMBB(tc_fun(_1310953, tc_HOL_Obool), tc_fun(_1310953, tc_HOL_Obool), _1310951), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310953, tc_HOL_Obool)), _1310955)), _1310957)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310953, tc_HOL_Obool)), _1310955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310951, tc_fun(_1310953, tc_HOL_Obool)), _1310949), _1310957)))], (8966 ^ _779571) ^ [_928216, _928218, _928220] : [class_Rings_Ocomm__semiring__1(_928216), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928216), _928218), _928220) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928216), _928220), _928218))], (7550 ^ _779571) ^ [_904752, _904754, _904756, _904758] : [class_Groups_Oordered__cancel__ab__semigroup__add(_904752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904752), _904754), _904756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904752), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904752), _904758), _904754)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904752), _904758), _904756))))], (45031 ^ _779571) ^ [_1664949, _1664951, _1664953] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1664949, tc_HOL_Obool)), _1664951), _1664953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664949, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1664949, tc_HOL_Obool), _1664953)), _1664951)))], (51569 ^ _779571) ^ [_1813054, _1813056] : [-(hAPP(c_COMBI(_1813054), _1813056) = _1813056)], (45963 ^ _779571) ^ [_1686113, _1686115, _1686117, _1686119, _1686121] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1686113), tc_List_Olist(_1686115), tc_List_Olist(_1686117), hAPP(c_List_Omap(_1686113, _1686115), _1686119)), hAPP(c_List_Omap(_1686117, _1686113), _1686121)) = hAPP(c_List_Omap(_1686117, _1686115), hAPP(c_Fun_Ocomp(_1686113, _1686115, _1686117, _1686119), _1686121)))], (34043 ^ _779571) ^ [_1401559, _1401561, _1401563, _1401565, _1401567, _1401569] : [hBOOL(hAPP(hAPP(c_member(_1401559), _1401561), _1401563)), -(hAPP(c_Set_Oimage(_1401559, _1401565, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1401559, _1401565), _1401567), _1401561), _1401569)), _1401563) = hAPP(hAPP(c_Set_Oinsert(_1401565), _1401569), hAPP(c_Set_Oimage(_1401559, _1401565, _1401567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401559, tc_HOL_Obool)), _1401563), hAPP(hAPP(c_Set_Oinsert(_1401559), _1401561), c_Orderings_Obot__class_Obot(tc_fun(_1401559, tc_HOL_Obool)))))))], (35406 ^ _779571) ^ [_1431947, _1431949] : [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)), _1431947), 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)), _1431949), 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)), _1431947), _1431949)), c_Int_Ointrel)))], (21923 ^ _779571) ^ [_1157832, _1157834, _1157836, _1157838] : [class_Fields_Olinordered__field__inverse__zero(_1157832), class_Int_Onumber(_1157832), 21930 ^ _779571 : [(21931 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157832), _1157836), _1157838))), 21934 ^ _779571 : [(21941 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), c_Groups_Ozero__class_Ozero(_1157832)), _1157838))), 21944 ^ _779571 : [(21951 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), _1157838), c_Groups_Ozero__class_Ozero(_1157832)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), c_Groups_Ozero__class_Ozero(_1157832))))], (21945 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), _1157838), c_Groups_Ozero__class_Ozero(_1157832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), _1157836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), _1157838))))]]], (21935 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), c_Groups_Ozero__class_Ozero(_1157832)), _1157838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), _1157838)), _1157836)))]]], (21957 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157832), _1157836), _1157838)))), 21960 ^ _779571 : [(21963 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), _1157838)), _1157836))], (21961 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), c_Groups_Ozero__class_Ozero(_1157832)), _1157838)))]], 21964 ^ _779571 : [(21967 ^ _779571) ^ [] : [21968 ^ _779571 : [(21971 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), _1157836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), _1157838)))], (21969 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), _1157838), c_Groups_Ozero__class_Ozero(_1157832))))]], 21972 ^ _779571 : [(21975 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157832), hAPP(c_Int_Onumber__class_Onumber__of(_1157832), _1157834)), c_Groups_Ozero__class_Ozero(_1157832)))], (21973 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), _1157838), c_Groups_Ozero__class_Ozero(_1157832)))]]], (21965 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157832), c_Groups_Ozero__class_Ozero(_1157832)), _1157838))]]]]], (46927 ^ _779571) ^ [_1711338, _1711340, _1711342, _1711344, _1711346, _1711348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1711338, _1711338)), hAPP(hAPP(c_Product__Type_OPair(_1711338, _1711338), _1711340), _1711342)), _1711344)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711338), tc_List_Olist(_1711338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711338), tc_List_Olist(_1711338)), _1711346), _1711348)), c_List_Olistrel(_1711338, _1711344))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711338), tc_List_Olist(_1711338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711338), tc_List_Olist(_1711338)), hAPP(hAPP(c_List_Olist_OCons(_1711338), _1711340), _1711346)), hAPP(hAPP(c_List_Olist_OCons(_1711338), _1711342), _1711348))), c_List_Olistrel(_1711338, _1711344))))], (29596 ^ _779571) ^ [_1308395, _1308397, _1308399] : [class_Orderings_Oorder(_1308395), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308395), _1308397), _1308399)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1308395, _1308399, _1308397) = c_Orderings_Obot__class_Obot(tc_fun(_1308395, tc_HOL_Obool)))], (40220 ^ _779571) ^ [_1542222, _1542224, _1542226, _1542228, _1542230, _1542232] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542222, _1542224)), hAPP(hAPP(c_Product__Type_OPair(_1542222, _1542224), _1542226), _1542228)), hAPP(hAPP(c_Product__Type_OSigma(_1542222, _1542224), _1542230), _1542232))), -(hBOOL(hAPP(hAPP(c_member(_1542222), _1542226), _1542230)))], (9490 ^ _779571) ^ [_937122, _937124] : [class_Rings_Olinordered__idom(_937122), 9493 ^ _779571 : [(9500 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937122), _937124), c_Groups_Ozero__class_Ozero(_937122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937122), _937124), hAPP(c_Groups_Ouminus__class_Ouminus(_937122), _937124))))], (9494 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937122), _937124), hAPP(c_Groups_Ouminus__class_Ouminus(_937122), _937124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937122), _937124), c_Groups_Ozero__class_Ozero(_937122))))]]], (5891 ^ _779571) ^ [_874101, _874103, _874105, _874107, _874109] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_874101, _874103), _874105, _874107, _874109)), 5892 ^ _779571 : [(5899 ^ _779571) ^ [] : [hBOOL(hAPP(_874101, _874105)), 5902 ^ _779571 : [(5903 ^ _779571) ^ [_874311] : [c_Natural_Oevaln(_874103, _874105, _874107, _874311), c_Natural_Oevaln(c_Com_Ocom_OWhile(_874101, _874103), _874311, _874107, _874109)]]], (5893 ^ _779571) ^ [] : [_874109 = _874105, -(hBOOL(hAPP(_874101, _874105)))]]], (28325 ^ _779571) ^ [_1282254, _1282256] : [c_Nat__Transfer_Ois__nat(_1282254), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1282254, _1282256)))], (14381 ^ _779571) ^ [_1022284, _1022286] : [class_Divides_Osemiring__div(_1022284), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1022284), _1022286), c_Groups_Ozero__class_Ozero(_1022284)) = c_Groups_Ozero__class_Ozero(_1022284))], (43060 ^ _779571) ^ [_1617033, _1617035, _1617037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1617033, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1617033, _1617033, _1617035), _1617037)), _1617037)), -(hAPP(c_Relation_OImage(_1617033, _1617033, c_Transitive__Closure_Ortrancl(_1617033, _1617035)), _1617037) = _1617037)], (9330 ^ _779571) ^ [_934032] : [class_Rings_Ozero__neq__one(_934032), c_Groups_Oone__class_Oone(_934032) = c_Groups_Ozero__class_Ozero(_934032)], (21581 ^ _779571) ^ [_1151151, _1151153, _1151155, _1151157] : [class_Fields_Olinordered__field(_1151151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151151), _1151153), _1151155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151151), c_Groups_Ozero__class_Ozero(_1151151)), _1151157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151151), c_Groups_Ozero__class_Ozero(_1151151)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151151), _1151155), _1151153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151151), _1151157), _1151155)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151151), _1151157), _1151153))))], (15538 ^ _779571) ^ [_1042885, _1042887, _1042889] : [hBOOL(hAPP(_1042885, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042887), _1042889)))), 15541 ^ _779571 : [(15548 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042887), _1042889)), -(hBOOL(hAPP(_1042885, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15542 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042889), _1042887)), -(hBOOL(hAPP(_1042885, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042887)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042889)))))]]], (40439 ^ _779571) ^ [_1547341, _1547343, _1547345] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547341), _1547343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547341, _1547341), tc_HOL_Obool)), _1547345), hAPP(hAPP(c_Product__Type_OSigma(_1547341, _1547341), _1547343), hAPP(c_COMBK(tc_fun(_1547341, tc_HOL_Obool), _1547341), _1547343)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1547341, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1547341), _1547343), _1547345))))], (29916 ^ _779571) ^ [_1314852, _1314854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314852), _1314854))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1314854, _1314852) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1314854), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1314854), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1314852)))], (51539 ^ _779571) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (11094 ^ _779571) ^ [_963714, _963716, _963718, _963720] : [class_Groups_Oordered__ab__semigroup__add(_963714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963714), _963716), _963718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963714), _963716), _963720)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963714), _963718), _963720))))], (23885 ^ _779571) ^ [_1194832, _1194834, _1194836] : [-(hAPP(hAPP(c_Product__Type_OPair(_1194832, _1194834), hAPP(c_Product__Type_Ofst(_1194832, _1194834), _1194836)), hAPP(c_Product__Type_Osnd(_1194832, _1194834), _1194836)) = _1194836)], (1452 ^ _779571) ^ [_800489, _800491] : [-(class_Rings_Oordered__cancel__semiring(_800489)), _800491 = _800489, class_Rings_Oordered__cancel__semiring(_800491)], (19197 ^ _779571) ^ [_1108758, _1108760] : [c_Int_OBit1(_1108758) = c_Int_OBit0(_1108760)], (16929 ^ _779571) ^ [_1070068, _1070070, _1070072] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1070068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070070), _1070072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1070068), _1070070)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1070068), _1070072)))], (40407 ^ _779571) ^ [_1546243, _1546245, _1546247, _1546249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1546243), _1546245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1546243, _1546243), tc_HOL_Obool)), _1546247), hAPP(hAPP(c_Product__Type_OSigma(_1546243, _1546243), _1546245), hAPP(c_COMBK(tc_fun(_1546243, tc_HOL_Obool), _1546243), _1546245)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1546243, tc_HOL_Obool)), _1546249), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1546243), _1546245), _1546247))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1546243), _1546249)))], (22660 ^ _779571) ^ [_1171691, _1171693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171691)), 22663 ^ _779571 : [(22670 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171693), _1171691))), -(c_Divides_OposDivAlg(_1171693, _1171691) = hAPP(c_Divides_Oadjust(_1171691), c_Divides_OposDivAlg(_1171693, 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)))), _1171691))))], (22664 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171693), _1171691)), -(c_Divides_OposDivAlg(_1171693, _1171691) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171693))]]], (43359 ^ _779571) ^ [_1624295, _1624297, _1624299, _1624301] : [-(hAPP(c_Relation_Oconverse(_1624295, _1624297), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1624295, _1624297), tc_HOL_Obool)), _1624299), _1624301)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1624297, _1624295), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1624295, _1624297), _1624299)), hAPP(c_Relation_Oconverse(_1624295, _1624297), _1624301)))], (18765 ^ _779571) ^ [_1101475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101475), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1101475)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (3246 ^ _779571) ^ [_829334, _829336, _829338, _829340, _829342, _829344, _829346, _829348, _829350, _829352] : [-(c_SetInterval_Oord_OatLeastLessThan(_829352, _829348, _829344, _829340, _829336) = c_SetInterval_Oord_OatLeastLessThan(_829350, _829346, _829342, _829338, _829334)), _829352 = _829350, _829348 = _829346, _829344 = _829342, _829340 = _829338, _829336 = _829334], (43094 ^ _779571) ^ [_1617893, _1617895] : [-(hAPP(c_Relation_ODomain(_1617893, _1617893), c_Transitive__Closure_Ortrancl(_1617893, _1617895)) = c_Orderings_Otop__class_Otop(tc_fun(_1617893, tc_HOL_Obool)))], (35561 ^ _779571) ^ [] : [-(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))], (49006 ^ _779571) ^ [_1762722, _1762724, _1762726] : [-(hAPP(c_List_Otl(_1762722), hAPP(hAPP(c_List_Olist_OCons(_1762722), _1762724), _1762726)) = _1762726)], (46201 ^ _779571) ^ [_1692062, _1692064, _1692066, _1692068] : [-(hBOOL(hAPP(c_List_Odistinct(_1692062), hAPP(hAPP(c_List_Omap(_1692064, _1692062), _1692066), _1692068)))), hBOOL(hAPP(c_List_Odistinct(_1692064), _1692068)), c_Fun_Oinj__on(_1692064, _1692062, _1692066, hAPP(c_List_Oset(_1692064), _1692068))], (31377 ^ _779571) ^ [_1346753, _1346755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346753), _1346755)), 31380 ^ _779571 : [(31387 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346753), c_Orderings_Otop__class_Otop(tc_fun(_1346753, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346753), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1346753, tc_HOL_Obool)), _1346755))))], (31381 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346753), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1346753, tc_HOL_Obool)), _1346755))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346753), c_Orderings_Otop__class_Otop(tc_fun(_1346753, tc_HOL_Obool)))))]]], (35016 ^ _779571) ^ [_1423311, _1423313, _1423315, _1423317] : [_1423311 = _1423313, hBOOL(hAPP(hAPP(c_member(_1423315), _1423311), _1423317)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1423315, _1423315)), hAPP(hAPP(c_Product__Type_OPair(_1423315, _1423315), _1423311), _1423313)), c_Relation_OId__on(_1423315, _1423317))))], (27700 ^ _779571) ^ [_1269947, _1269949, _1269951, _1269953] : [27701 ^ _779571 : [(27704 ^ _779571) ^ [] : [hBOOL(hAPP(_1269951, _1269949))], (27702 ^ _779571) ^ [] : [hBOOL(hAPP(_1269947, _1269949))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269953, tc_HOL_Obool)), _1269951), _1269947), _1269949)))], (6554 ^ _779571) ^ [_886533] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _886533)], (19101 ^ _779571) ^ [_1107116, _1107118] : [class_Rings_Osemiring__1(_1107116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1107118)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1107116), 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)))), _1107118))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107116), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1107116), hAPP(c_Int_Onat, _1107118))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1107116), hAPP(c_Int_Onat, _1107118))))], (40897 ^ _779571) ^ [_1557812, _1557814, _1557816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557812), _1557814)), 40903 ^ _779571 : [(40906 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1557816, 40902 ^ [_1557812, _1557814, _1557816])))], (40904 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557812), 40902 ^ [_1557812, _1557814, _1557816]), _1557814)))]], -(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(_1557812, tc_Nat_Onat), _1557816), _1557814))))], (44345 ^ _779571) ^ [_1646697, _1646699, _1646701, _1646703, _1646705, _1646707, _1646709] : [c_Finite__Set_Ofun__left__comm(_1646697, _1646699, _1646701), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1646697, _1646699, _1646701, _1646703, _1646705), _1646707)), hBOOL(hAPP(hAPP(c_member(_1646697), _1646709), _1646705)), 44357 ^ _779571 : [(44360 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1646697, _1646699, _1646701, _1646703, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1646697, tc_HOL_Obool)), _1646705), hAPP(hAPP(c_Set_Oinsert(_1646697), _1646709), c_Orderings_Obot__class_Obot(tc_fun(_1646697, tc_HOL_Obool))))), 44356 ^ [_1646697, _1646699, _1646701, _1646703, _1646705, _1646707, _1646709])))], (44358 ^ _779571) ^ [] : [-(_1646707 = hAPP(hAPP(_1646701, _1646709), 44356 ^ [_1646697, _1646699, _1646701, _1646703, _1646705, _1646707, _1646709]))]]], (23107 ^ _779571) ^ [_1180361, _1180363, _1180365, _1180367, _1180369, _1180371] : [_1180361 = _1180363, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180365, _1180367, _1180369), _1180371), _1180361) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180365, _1180367, _1180369), _1180371), _1180363))], (46241 ^ _779571) ^ [_1692929, _1692931, _1692933, _1692935, _1692937] : [hBOOL(hAPP(c_List_Odistinct(_1692929), hAPP(hAPP(c_List_Omap(tc_prod(_1692929, _1692931), _1692929), c_Product__Type_Ofst(_1692929, _1692931)), _1692933))), 46244 ^ _779571 : [(46251 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1692929, _1692931)), hAPP(hAPP(c_Product__Type_OPair(_1692929, _1692931), _1692935), _1692937)), hAPP(c_List_Oset(tc_prod(_1692929, _1692931)), _1692933))), -(hAPP(c_Map_Omap__of(_1692929, _1692931, _1692933), _1692935) = hAPP(c_Option_Ooption_OSome(_1692931), _1692937))], (46245 ^ _779571) ^ [] : [hAPP(c_Map_Omap__of(_1692929, _1692931, _1692933), _1692935) = hAPP(c_Option_Ooption_OSome(_1692931), _1692937), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1692929, _1692931)), hAPP(hAPP(c_Product__Type_OPair(_1692929, _1692931), _1692935), _1692937)), hAPP(c_List_Oset(tc_prod(_1692929, _1692931)), _1692933))))]]], (16361 ^ _779571) ^ [_1059411, _1059413, _1059415] : [class_Int_Onumber__ring(_1059411), class_Int_Oring__char__0(_1059411), 16368 ^ _779571 : [(16375 ^ _779571) ^ [] : [_1059413 = _1059415, -(hAPP(c_Int_Onumber__class_Onumber__of(_1059411), _1059413) = hAPP(c_Int_Onumber__class_Onumber__of(_1059411), _1059415))], (16369 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1059411), _1059413) = hAPP(c_Int_Onumber__class_Onumber__of(_1059411), _1059415), -(_1059413 = _1059415)]]], (4820 ^ _779571) ^ [_854045, _854047, _854049, _854051, _854053, _854055] : [-(c_List_Opartition(_854055, _854051, _854047) = c_List_Opartition(_854053, _854049, _854045)), _854055 = _854053, _854051 = _854049, _854047 = _854045], (28016 ^ _779571) ^ [_1275993, _1275995, _1275997, _1275999] : [class_Lattices_Osemilattice__sup(_1275993), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275993), _1275995), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275993), _1275997), _1275999)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275993), _1275997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275993), _1275995), _1275999)))], (6788 ^ _779571) ^ [_891356, _891358, _891360, _891362] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_891356)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_891356), _891358), _891360), _891362)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18223 ^ _779571) ^ [_1092821, _1092823] : [class_Int_Onumber__ring(_1092821), -(hAPP(c_Int_Onumber__class_Onumber__of(_1092821), c_Int_Osucc(_1092823)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092821), c_Groups_Oone__class_Oone(_1092821)), hAPP(c_Int_Onumber__class_Onumber__of(_1092821), _1092823)))], (18375 ^ _779571) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (43156 ^ _779571) ^ [_1619377, _1619379, _1619381, _1619383, _1619385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619377, _1619377)), hAPP(hAPP(c_Product__Type_OPair(_1619377, _1619377), _1619379), _1619381)), _1619383)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1619377, _1619377)), hAPP(hAPP(c_Product__Type_OPair(_1619377, _1619377), _1619381), _1619385)), c_Transitive__Closure_Ortrancl(_1619377, _1619383))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619377, _1619377)), hAPP(hAPP(c_Product__Type_OPair(_1619377, _1619377), _1619379), _1619385)), c_Transitive__Closure_Otrancl(_1619377, _1619383))))], (44684 ^ _779571) ^ [_1656278, _1656280, _1656282, _1656284, _1656286] : [-(_1656278 = c_Orderings_Obot__class_Obot(tc_fun(_1656280, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656282, tc_HOL_Obool)), _1656284), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656280, tc_fun(_1656282, tc_HOL_Obool)), _1656278), _1656286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656280, tc_fun(_1656282, tc_HOL_Obool)), _1656278), hAPP(hAPP(c_COMBB(tc_fun(_1656282, tc_HOL_Obool), tc_fun(_1656282, tc_HOL_Obool), _1656280), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656282, tc_HOL_Obool)), _1656284)), _1656286)))], (660 ^ _779571) ^ [_789779, _789781, _789783, _789785, _789787, _789789] : [-(c_Relation_Ototal__on(_789787, _789783, _789779)), c_Relation_Ototal__on(_789789, _789785, _789781), _789789 = _789787, _789785 = _789783, _789781 = _789779], (32069 ^ _779571) ^ [_1362946, _1362948, _1362950, _1362952] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1362946, tc_fun(_1362948, tc_HOL_Obool))), _1362950), _1362952))], (12183 ^ _779571) ^ [_982742, _982744] : [class_Rings_Olinordered__semidom(_982742), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982742), c_Groups_Ozero__class_Ozero(_982742)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_982742), _982744))))], (24667 ^ _779571) ^ [_1210347, _1210349] : [_1210347 = _1210349, -(hAPP(c_Code__Numeral_Onat__of, _1210347) = hAPP(c_Code__Numeral_Onat__of, _1210349))], (22580 ^ _779571) ^ [_1170429, _1170431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1170431, _1170429) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170431), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170429)))], (23147 ^ _779571) ^ [_1181196, _1181198] : [-(_1181196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23150 ^ _779571 : [(23157 ^ _779571) ^ [] : [-(_1181198 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1181196, _1181198) = 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, _1181198))), 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, _1181196)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1181198))), c_Divides_Opdivmod(_1181196, _1181198)), 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), _1181198))))), c_Divides_Opdivmod(_1181196, _1181198)))))], (23151 ^ _779571) ^ [] : [_1181198 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1181196, _1181198) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181196))]]], (7021 ^ _779571) ^ [_895291, _895293] : [class_Groups_Ocomm__monoid__add(_895291), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895291), _895293), c_Groups_Ozero__class_Ozero(_895291)) = _895293)], (50461 ^ _779571) ^ [_1793148, _1793150] : [class_Orderings_Olinorder(_1793148), 50464 ^ _779571 : [(50465 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1793148, _1793150), 50468 ^ _779571 : [(50469 ^ _779571) ^ [_1793319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1793319), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793148)), _1793150))), 50472 ^ _779571 : [(50473 ^ _779571) ^ [_1793436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1793436), _1793319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793148), hAPP(hAPP(c_List_Onth(_1793148), _1793150), _1793436)), hAPP(hAPP(c_List_Onth(_1793148), _1793150), _1793319))))]]]]], (50479 ^ _779571) ^ [] : [50481 ^ _779571 : [(50487 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793148), hAPP(hAPP(c_List_Onth(_1793148), _1793150), 50483 ^ [_1793148, _1793150])), hAPP(hAPP(c_List_Onth(_1793148), _1793150), 50480 ^ [_1793148, _1793150])))], (50485 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50483 ^ [_1793148, _1793150]), 50480 ^ [_1793148, _1793150])))], (50482 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50480 ^ [_1793148, _1793150]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793148)), _1793150))))]], -(c_List_Olinorder__class_Osorted(_1793148, _1793150))]]], (380 ^ _779571) ^ [_785265, _785267, _785269, _785271, _785273, _785275, _785277, _785279, _785281, _785283] : [-(c_Typedef_Otype__definition(_785281, _785277, _785273, _785269, _785265)), c_Typedef_Otype__definition(_785283, _785279, _785275, _785271, _785267), _785283 = _785281, _785279 = _785277, _785275 = _785273, _785271 = _785269, _785267 = _785265], (28429 ^ _779571) ^ [_1284520] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1284520) = 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), _1284520))))], (42884 ^ _779571) ^ [_1611811, _1611813, _1611815, _1611817, _1611819] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611811, _1611811)), hAPP(hAPP(c_Product__Type_OPair(_1611811, _1611811), _1611813), _1611815)), c_Transitive__Closure_Otrancl(_1611811, _1611817))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1611811, _1611811)), hAPP(hAPP(c_Product__Type_OPair(_1611811, _1611811), _1611815), _1611819)), c_Transitive__Closure_Otrancl(_1611811, _1611817))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611811, _1611811)), hAPP(hAPP(c_Product__Type_OPair(_1611811, _1611811), _1611813), _1611819)), c_Transitive__Closure_Otrancl(_1611811, _1611817))))], (9896 ^ _779571) ^ [_944432, _944434] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944432)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944434), 9899 ^ _779571 : [(9902 ^ _779571) ^ [] : [-(_944434 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9900 ^ _779571) ^ [] : [-(_944432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42791 ^ _779571) ^ [_1609855, _1609857, _1609859] : [c_Wellfounded_Owf(_1609855, _1609857), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609855, _1609855)), hAPP(hAPP(c_Product__Type_OPair(_1609855, _1609855), hAPP(_1609859, hAPP(c_Nat_OSuc, 42794 ^ [_1609855, _1609857, _1609859]))), hAPP(_1609859, 42794 ^ [_1609855, _1609857, _1609859]))), _1609857))], (41531 ^ _779571) ^ [_1576820, _1576822, _1576824] : [class_Lattices_Odistrib__lattice(_1576820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576820), _1576822)), -(_1576822 = c_Orderings_Obot__class_Obot(tc_fun(_1576820, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576820), _1576824)), -(_1576824 = c_Orderings_Obot__class_Obot(tc_fun(_1576820, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576820), c_Big__Operators_Olattice__class_OSup__fin(_1576820, _1576822)), c_Big__Operators_Olattice__class_OSup__fin(_1576820, _1576824)) = c_Big__Operators_Olattice__class_OSup__fin(_1576820, hAPP(c_Set_OCollect(_1576820), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_HOL_Obool), tc_HOL_Obool, _1576820), c_HOL_OEx(_1576820)), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool)), tc_fun(_1576820, tc_HOL_Obool), _1576820), hAPP(c_COMBB(tc_fun(_1576820, tc_HOL_Obool), tc_HOL_Obool, _1576820), c_HOL_OEx(_1576820))), hAPP(hAPP(c_COMBC(_1576820, tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool)), tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_fun(tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool))), tc_fun(tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool)), tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool))), _1576820), c_COMBS(_1576820, tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_fun(_1576820, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1576820, tc_fun(tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool))), _1576820), hAPP(c_COMBB(tc_fun(_1576820, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool)), _1576820), c_COMBS(_1576820, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool)), tc_fun(_1576820, tc_fun(_1576820, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1576820), hAPP(c_COMBB(tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1576820), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576820), c_fconj))), hAPP(hAPP(c_COMBC(_1576820, tc_fun(_1576820, tc_fun(_1576820, _1576820)), tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1576820, _1576820), tc_fun(_1576820, tc_HOL_Obool)), tc_fun(tc_fun(_1576820, tc_fun(_1576820, _1576820)), tc_fun(_1576820, tc_fun(_1576820, tc_HOL_Obool))), _1576820), c_COMBB(tc_fun(_1576820, _1576820), tc_fun(_1576820, tc_HOL_Obool), _1576820)), hAPP(hAPP(c_COMBB(tc_fun(_1576820, tc_HOL_Obool), tc_fun(tc_fun(_1576820, _1576820), tc_fun(_1576820, tc_HOL_Obool)), _1576820), c_COMBB(_1576820, tc_HOL_Obool, _1576820)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1576820)))))), hAPP(hAPP(c_COMBC(_1576820, tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1576820, tc_HOL_Obool), tc_fun(_1576820, tc_HOL_Obool)), _1576820), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1576820)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576820), c_fconj), hAPP(hAPP(c_COMBC(_1576820, tc_fun(_1576820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576820)), _1576822)))), hAPP(hAPP(c_COMBC(_1576820, tc_fun(_1576820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576820)), _1576824))))))))], (8173 ^ _779571) ^ [_915079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _915079)), -(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), _915079))))], (45923 ^ _779571) ^ [_1685305, _1685307, _1685309] : [c_Fun_Oinj__on(tc_List_Olist(_1685305), tc_List_Olist(_1685307), hAPP(c_List_Omap(_1685305, _1685307), _1685309), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1685305), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1685305, _1685307, _1685309, c_Orderings_Otop__class_Otop(tc_fun(_1685305, tc_HOL_Obool))))], (10259 ^ _779571) ^ [_950442, _950444, _950446, _950448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950442), _950444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950446), _950448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950442), _950446)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950444), _950448))))], (47270 ^ _779571) ^ [_1720219, _1720221] : [_1720221 = c_List_Olist_ONil(_1720219), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720219)), _1720221) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39451 ^ _779571) ^ [_1523026, _1523028, _1523030, _1523032, _1523034] : [hBOOL(hAPP(hAPP(c_member(_1523026), _1523028), hAPP(c_Set_Ovimage(_1523026, _1523030, _1523032), _1523034))), -(hBOOL(hAPP(hAPP(c_member(_1523030), hAPP(_1523032, _1523028)), _1523034)))], (12442 ^ _779571) ^ [_987313] : [12444 ^ _779571 : [(12447 ^ _779571) ^ [] : [hBOOL(hAPP(_987313, hAPP(c_Int_Onat, 12443 ^ [_987313])))], (12445 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12443 ^ [_987313])))]], 12448 ^ _779571 : [(12449 ^ _779571) ^ [_987446] : [-(hBOOL(hAPP(_987313, _987446)))]]], (50864 ^ _779571) ^ [_1803126, _1803128, _1803130] : [class_Orderings_Olinorder(_1803126), c_List_Olinorder__class_Osorted(_1803126, hAPP(c_List_Orev(_1803126), _1803128)), 50871 ^ _779571 : [(50878 ^ _779571) ^ [] : [-(_1803128 = c_List_Olist_ONil(_1803126)), -(c_List_Ofoldr(_1803126, _1803126, c_Orderings_Oord__class_Omax(_1803126), _1803128, _1803130) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1803126), hAPP(hAPP(c_List_Onth(_1803126), _1803128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1803130))], (50872 ^ _779571) ^ [] : [_1803128 = c_List_Olist_ONil(_1803126), -(c_List_Ofoldr(_1803126, _1803126, c_Orderings_Oord__class_Omax(_1803126), _1803128, _1803130) = _1803130)]]], (49732 ^ _779571) ^ [_1778616, _1778618, _1778620] : [hAPP(c_List_Ofilter(_1778616, _1778618), _1778620) = _1778620, 49735 ^ _779571 : [(49736 ^ _779571) ^ [_1778707] : [hBOOL(hAPP(hAPP(c_member(_1778616), _1778707), hAPP(c_List_Oset(_1778616), _1778620))), -(hBOOL(hAPP(_1778618, _1778707)))]]], (22448 ^ _779571) ^ [_1167525, _1167527] : [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(_1167525))), 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)), _1167527)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167525)), hAPP(c_Nat_OSuc, _1167527))))], (18351 ^ _779571) ^ [_1094720] : [class_Int_Onumber__ring(_1094720), -(hAPP(c_Int_Onumber__class_Onumber__of(_1094720), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1094720))], (31474 ^ _779571) ^ [_1349256] : [-(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)), _1349256))))], (5090 ^ _779571) ^ [_858242, _858244] : [_858244 = _858242, -(c_Lattices_Osemilattice__sup__class_Osup(_858244) = c_Lattices_Osemilattice__sup__class_Osup(_858242))], (18085 ^ _779571) ^ [_1090851, _1090853] : [class_Rings_Osemiring__1(_1090851), 18088 ^ _779571 : [(18095 ^ _779571) ^ [] : [_1090853 = c_Groups_Ozero__class_Ozero(_1090851), -(c_Int_Oiszero(_1090851, _1090853))], (18089 ^ _779571) ^ [] : [c_Int_Oiszero(_1090851, _1090853), -(_1090853 = c_Groups_Ozero__class_Ozero(_1090851))]]], (51367 ^ _779571) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (28357 ^ _779571) ^ [_1282844, _1282846, _1282848, _1282850] : [class_Orderings_Olinorder(_1282844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282844), _1282846), _1282848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282844), _1282848), _1282850)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282844, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1282844, _1282846, _1282848)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1282844, _1282848, _1282850)) = c_SetInterval_Oord__class_OatLeastAtMost(_1282844, _1282846, _1282850))], (6361 ^ _779571) ^ [_882741, _882743, _882745, _882747, _882749] : [c_Com_Ocom_OLocal(_882741, _882743, _882745) = c_Com_Ocom_OWhile(_882747, _882749)], (10708 ^ _779571) ^ [_957852, _957854, _957856] : [10709 ^ _779571 : [(10712 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957852), _957856))], (10710 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957854)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957852), _957854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957856), _957854))))], (29043 ^ _779571) ^ [_1297672, _1297674] : [class_Orderings_Otop(_1297672), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297672), _1297674), c_Orderings_Otop__class_Otop(_1297672))))], (15868 ^ _779571) ^ [_1049279, _1049281] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049279), hAPP(c_Nat_OSuc, _1049281)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049279), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1049281))], (39098 ^ _779571) ^ [_1515165, _1515167, _1515169, _1515171, _1515173, _1515175] : [c_Typedef_Otype__definition(_1515165, _1515167, _1515169, _1515171, _1515173), hBOOL(hAPP(hAPP(c_member(_1515167), _1515175), _1515173)), -(hAPP(_1515169, hAPP(_1515171, _1515175)) = _1515175)], (49590 ^ _779571) ^ [_1775567, _1775569, _1775571, _1775573] : [-(hAPP(hAPP(c_List_Omap(_1775567, _1775569), _1775571), c_List_Obutlast(_1775567, _1775573)) = c_List_Obutlast(_1775569, hAPP(hAPP(c_List_Omap(_1775567, _1775569), _1775571), _1775573)))], (14036 ^ _779571) ^ [_1015536, _1015538, _1015540] : [-(hBOOL(hAPP(_1015536, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1015538, _1015540)))), 14039 ^ _779571 : [(14042 ^ _779571) ^ [] : [hBOOL(hAPP(_1015536, _1015538))], (14040 ^ _779571) ^ [] : [-(_1015540 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14045 ^ _779571 : [(14046 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1015540)))], (14052 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14048 ^ [_1015536, _1015538, _1015540]), _1015540)))], (14056 ^ _779571) ^ [] : [hBOOL(hAPP(_1015536, 14048 ^ [_1015536, _1015538, _1015540]))], (14054 ^ _779571) ^ [] : [-(_1015538 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015540), 14047 ^ [_1015536, _1015538, _1015540])), 14048 ^ [_1015536, _1015538, _1015540]))], (14050 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14048 ^ [_1015536, _1015538, _1015540])))]], 14057 ^ _779571 : [(14058 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015540), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14064 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14060 ^ [_1015536, _1015538, _1015540]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14068 ^ _779571) ^ [] : [hBOOL(hAPP(_1015536, 14060 ^ [_1015536, _1015538, _1015540]))], (14066 ^ _779571) ^ [] : [-(_1015538 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015540), 14059 ^ [_1015536, _1015538, _1015540])), 14060 ^ [_1015536, _1015538, _1015540]))], (14062 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015540), 14060 ^ [_1015536, _1015538, _1015540])))]]], (50258 ^ _779571) ^ [_1789376] : [-(c_List_Oupt(_1789376, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (18121 ^ _779571) ^ [_1091300, _1091302] : [class_Int_Onumber__ring(_1091300), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091300), _1091302), hAPP(c_Int_Onumber__class_Onumber__of(_1091300), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1091300), _1091302))], (23097 ^ _779571) ^ [_1180192, _1180194, _1180196, _1180198, _1180200, _1180202] : [hAPP(hAPP(c_Product__Type_OPair(_1180192, _1180194), _1180196), _1180198) = hAPP(hAPP(c_Product__Type_OPair(_1180192, _1180194), _1180200), _1180202), 23100 ^ _779571 : [(23103 ^ _779571) ^ [] : [-(_1180198 = _1180202)], (23101 ^ _779571) ^ [] : [-(_1180196 = _1180200)]]], (31964 ^ _779571) ^ [_1360583, _1360585, _1360587, _1360589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360583), _1360585)), hBOOL(hAPP(hAPP(c_member(_1360583), _1360587), _1360585)), -(hBOOL(hAPP(hAPP(c_member(_1360583), _1360587), _1360589))), -(hAPP(c_Finite__Set_Ocard(_1360583), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360583, tc_HOL_Obool)), _1360585), hAPP(hAPP(c_Set_Oinsert(_1360583), _1360587), _1360589))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1360583), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360583, tc_HOL_Obool)), _1360585), _1360589))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47224 ^ _779571) ^ [_1719394, _1719396, _1719398] : [-(hAPP(hAPP(c_List_Omap(_1719394, _1719396), _1719398), c_List_Olist_ONil(_1719394)) = c_List_Olist_ONil(_1719396))], (29926 ^ _779571) ^ [_1315099, _1315101, _1315103, _1315105, _1315107] : [c_Hoare__Mirabelle_Ohoare__derivs(_1315099, _1315101, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315099)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315099), _1315103), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1315105))), _1315107)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315099), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1315099, _1315101, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315099)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315099), _1315103), hAPP(c_Com_Ocom_OBODY, _1315105)), _1315107)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315099), tc_HOL_Obool)))))], (27652 ^ _779571) ^ [_1268708, _1268710] : [class_Groups_Oordered__ab__group__add(_1268708), -(hAPP(c_Set_Oimage(_1268708, _1268708, c_Groups_Ouminus__class_Ouminus(_1268708)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1268708), _1268710)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1268708), hAPP(c_Groups_Ouminus__class_Ouminus(_1268708), _1268710)))], (13946 ^ _779571) ^ [_1013922, _1013924] : [class_Lattices_Oab__semigroup__idem__mult(_1013922), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013922), _1013924), _1013924) = _1013924)], (42868 ^ _779571) ^ [_1611496, _1611498] : [-(hAPP(c_Relation_ODomain(_1611496, _1611496), c_Transitive__Closure_Otrancl(_1611496, _1611498)) = hAPP(c_Relation_ODomain(_1611496, _1611496), _1611498))], (27209 ^ _779571) ^ [_1259386, _1259388, _1259390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259386)), 27212 ^ _779571 : [(27213 ^ _779571) ^ [_1259520] : [27215 ^ _779571 : [(27221 ^ _779571) ^ [] : [-(_1259520 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27217 ^ [_1259386, _1259388, _1259390, _1259520]), 27214 ^ [_1259386, _1259388, _1259390, _1259520]))], (27219 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27217 ^ [_1259386, _1259388, _1259390, _1259520]), _1259388)))], (27216 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27214 ^ [_1259386, _1259388, _1259390, _1259520]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1259386))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259520), _1259390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1259520), _1259386)), _1259390)))]]], (44718 ^ _779571) ^ [_1657435, _1657437, _1657439, _1657441, _1657443] : [-(hAPP(c_Relation_Oconverse(_1657435, _1657437), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657439, tc_fun(tc_prod(_1657435, _1657437), tc_HOL_Obool)), _1657441), _1657443)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657439, tc_fun(tc_prod(_1657437, _1657435), tc_HOL_Obool)), _1657441), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1657435, _1657437), tc_HOL_Obool), tc_fun(tc_prod(_1657437, _1657435), tc_HOL_Obool), _1657439), c_Relation_Oconverse(_1657435, _1657437)), _1657443)))], (19863 ^ _779571) ^ [_1120653] : [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, _1120653, 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, _1120653, 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))], (36786 ^ _779571) ^ [_1464220, _1464222, _1464224, _1464226, _1464228] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464220, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1464222, _1464220, _1464224), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464222, tc_HOL_Obool)), _1464226), _1464228))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464220, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1464222, _1464220, _1464224), _1464226)), hAPP(c_Relation_OImage(_1464222, _1464220, _1464224), _1464228)))))], (9250 ^ _779571) ^ [_932827, _932829, _932831] : [class_Groups_Ogroup__add(_932827), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932827), hAPP(c_Groups_Ouminus__class_Ouminus(_932827), _932829)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932827), _932829), _932831)) = _932831)], (43427 ^ _779571) ^ [_1625812, _1625814, _1625816, _1625818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625812, _1625812)), hAPP(hAPP(c_Product__Type_OPair(_1625812, _1625812), _1625814), _1625816)), hAPP(c_Relation_Oconverse(_1625812, _1625812), c_Transitive__Closure_Otrancl(_1625812, _1625818)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625812, _1625812)), hAPP(hAPP(c_Product__Type_OPair(_1625812, _1625812), _1625814), _1625816)), c_Transitive__Closure_Otrancl(_1625812, hAPP(c_Relation_Oconverse(_1625812, _1625812), _1625818)))))], (35195 ^ _779571) ^ [_1427365, _1427367, _1427369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427365, tc_HOL_Obool)), _1427367), _1427369)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1427365, tc_HOL_Obool)), _1427367), hAPP(c_Set_OPow(_1427365), _1427369))))], (19425 ^ _779571) ^ [_1112744, _1112746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112744), _1112746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112744)), c_Int_OBit1(_1112746))))], (39182 ^ _779571) ^ [_1516993, _1516995, _1516997, _1516999, _1517001, _1517003] : [c_Fun_Oinj__on(_1516993, _1516995, _1516997, _1516999), hAPP(_1516997, _1517001) = _1517003, hBOOL(hAPP(hAPP(c_member(_1516993), _1517001), _1516999)), -(hAPP(c_Fun_Othe__inv__into(_1516993, _1516995, _1516999, _1516997), _1517003) = _1517001)], (27484 ^ _779571) ^ [_1265324, _1265326] : [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)), _1265324)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1265324), _1265326)))], (47783 ^ _779571) ^ [_1732429, _1732431, _1732433, _1732435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732429), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732431)), _1732433))), -(hBOOL(hAPP(hAPP(c_member(_1732431), _1732435), hAPP(c_List_Oset(_1732431), hAPP(hAPP(c_List_Olist__update(_1732431, _1732433), _1732429), _1732435)))))], (49895 ^ _779571) ^ [_1782778, _1782780, _1782782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782778), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1782780))), c_List_Otranspose(_1782780, _1782782)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1782780)), c_List_Otranspose(_1782780, _1782782)), _1782778) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1782780), _1782780), hAPP(hAPP(c_COMBC(tc_List_Olist(_1782780), tc_Nat_Onat, _1782780), c_List_Onth(_1782780)), _1782778)), hAPP(c_List_Ofilter(tc_List_Olist(_1782780), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1782780)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782778)), c_Nat_Osize__class_Osize(tc_List_Olist(_1782780)))), _1782782)))], (22192 ^ _779571) ^ [_1162546] : [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), _1162546))), 22195 ^ _779571 : [(22202 ^ _779571) ^ [] : [-(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), _1162546))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162546)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162546)), 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), _1162546)))))], (22196 ^ _779571) ^ [] : [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), _1162546)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162546)) = 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), _1162546))))]]], (6357 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (47398 ^ _779571) ^ [_1722525, _1722527, _1722529, _1722531, _1722533] : [_1722525 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1722527, _1722529, _1722531, _1722525), _1722533) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722529), _1722527), c_List_Olist_ONil(_1722529)), _1722533))], (27878 ^ _779571) ^ [_1273266, _1273268, _1273270] : [class_Lattices_Osemilattice__sup(_1273266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273266), _1273268), _1273270)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273266), _1273268), _1273270) = _1273270)], (6909 ^ _779571) ^ [_893587, _893589] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _893587)), _893589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893587), hAPP(c_Nat_OSuc, _893589)))], (47727 ^ _779571) ^ [_1731182, _1731184, _1731186, _1731188, _1731190] : [-(hAPP(hAPP(c_List_Olist__update(_1731182, hAPP(hAPP(c_List_Olist_OCons(_1731182), _1731184), _1731186)), _1731188), _1731190) = c_Nat_Onat_Onat__case(tc_List_Olist(_1731182), hAPP(hAPP(c_List_Olist_OCons(_1731182), _1731190), _1731186), hAPP(hAPP(c_COMBB(tc_List_Olist(_1731182), tc_List_Olist(_1731182), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1731182), _1731184)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1731182, tc_List_Olist(_1731182)), c_List_Olist__update(_1731182, _1731186)), _1731190)), _1731188))], (16893 ^ _779571) ^ [_1069296, _1069298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069296)), -(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), _1069296), _1069298))))], (51567 ^ _779571) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (8366 ^ _779571) ^ [_918335, _918337, _918339] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918335), _918337)), _918339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918337), _918339)))], (48321 ^ _779571) ^ [_1745206, _1745208, _1745210, _1745212] : [-(c_Map_Omap__upds(_1745206, _1745208, _1745210, c_List_Olist_ONil(_1745206), _1745212) = _1745210)], (7924 ^ _779571) ^ [_911049, _911051] : [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), _911049), _911051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _911049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _911051)))], (51299 ^ _779571) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (36768 ^ _779571) ^ [_1463713, _1463715, _1463717, _1463719] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463713, tc_HOL_Obool)), _1463715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463713, tc_HOL_Obool)), _1463717), _1463719)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463713, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463713, tc_HOL_Obool)), _1463715), _1463717)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463713, tc_HOL_Obool)), _1463715), _1463719)))], (768 ^ _779571) ^ [_791401, _791403, _791405, _791407] : [-(c_Wellfounded_Owf(_791405, _791401)), c_Wellfounded_Owf(_791407, _791403), _791407 = _791405, _791403 = _791401], (49887 ^ _779571) ^ [_1782466, _1782468] : [-(c_List_Otranspose(_1782466, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1782466)), c_List_Olist_ONil(_1782466)), _1782468)) = c_List_Otranspose(_1782466, _1782468))], (28583 ^ _779571) ^ [_1287115, _1287117, _1287119] : [class_Orderings_Oorder(_1287115), 28586 ^ _779571 : [(28593 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287115), _1287117), _1287119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287115, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287115), _1287117)), hAPP(c_SetInterval_Oord__class_OatMost(_1287115), _1287119))))], (28587 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287115, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287115), _1287117)), hAPP(c_SetInterval_Oord__class_OatMost(_1287115), _1287119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287115), _1287117), _1287119)))]]], (5320 ^ _779571) ^ [_861805, _861807, _861809, _861811] : [-(c_Product__Type_Ofst(_861811, _861807) = c_Product__Type_Ofst(_861809, _861805)), _861811 = _861809, _861807 = _861805], (32147 ^ _779571) ^ [_1364527, _1364529] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1364527), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1364529)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364527), _1364529)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364529), _1364527)))], (16443 ^ _779571) ^ [_1060679, _1060681, _1060683] : [class_Groups_Oordered__ab__group__add__abs(_1060679), -(hAPP(c_Groups_Oabs__class_Oabs(_1060679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060679), hAPP(c_Groups_Oabs__class_Oabs(_1060679), _1060681)), hAPP(c_Groups_Oabs__class_Oabs(_1060679), _1060683))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060679), hAPP(c_Groups_Oabs__class_Oabs(_1060679), _1060681)), hAPP(c_Groups_Oabs__class_Oabs(_1060679), _1060683)))], (36772 ^ _779571) ^ [_1463881, _1463883, _1463885] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463881, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463881, tc_HOL_Obool)), _1463883), _1463885)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463881, tc_HOL_Obool)), _1463883), _1463885)) = _1463883)], (24329 ^ _779571) ^ [_1203720, _1203722, _1203724, _1203726] : [class_Orderings_Olinorder(_1203720), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203720), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203720), _1203722), _1203724)), _1203726) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203720), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203720), _1203722), _1203726)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203720), _1203724), _1203726)))], (18919 ^ _779571) ^ [_1104011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1104011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1104011))))], (19483 ^ _779571) ^ [_1113769] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1113769)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1113769)))], (13218 ^ _779571) ^ [_1000823, _1000825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000825)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1000823)), hAPP(c_Int_Onat, _1000825)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1000823), _1000825)))], (22418 ^ _779571) ^ [_1166928] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1166928))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1166928)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6383 ^ _779571) ^ [_883414, _883416, _883418, _883420, _883422] : [c_Com_Ocom_OSemi(_883414, _883416) = c_Com_Ocom_OCall(_883418, _883420, _883422)], (2768 ^ _779571) ^ [_821549, _821551] : [_821551 = _821549, -(c_Lazy__Sequence_Ohit__bound(_821551) = c_Lazy__Sequence_Ohit__bound(_821549))], (17965 ^ _779571) ^ [_1088741, _1088743] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088741))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088741)), _1088743) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088743))], (29035 ^ _779571) ^ [_1297420, _1297422] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297420, tc_HOL_Obool)), _1297422), c_Orderings_Otop__class_Otop(tc_fun(_1297420, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1297420, tc_HOL_Obool)))], (29099 ^ _779571) ^ [_1298743, _1298745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1298743), hAPP(c_Nat_OSuc, _1298745))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298743, hAPP(c_Nat_OSuc, _1298745)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298745)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298743, _1298745)))], (46098 ^ _779571) ^ [_1689665, _1689667, _1689669, _1689671, _1689673] : [c_Fun_Oinj__on(_1689665, _1689667, _1689669, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689665, tc_HOL_Obool)), hAPP(c_List_Oset(_1689665), _1689671)), hAPP(c_List_Oset(_1689665), _1689673))), 46101 ^ _779571 : [(46108 ^ _779571) ^ [] : [_1689671 = _1689673, -(hAPP(hAPP(c_List_Omap(_1689665, _1689667), _1689669), _1689671) = hAPP(hAPP(c_List_Omap(_1689665, _1689667), _1689669), _1689673))], (46102 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Omap(_1689665, _1689667), _1689669), _1689671) = hAPP(hAPP(c_List_Omap(_1689665, _1689667), _1689669), _1689673), -(_1689671 = _1689673)]]], (48744 ^ _779571) ^ [_1756965, _1756967, _1756969, _1756971] : [hBOOL(hAPP(hAPP(c_member(_1756965), _1756967), hAPP(c_List_Oset(_1756965), hAPP(hAPP(c_List_Odrop(_1756965), _1756969), _1756971)))), -(hBOOL(hAPP(hAPP(c_member(_1756965), _1756967), hAPP(c_List_Oset(_1756965), _1756971))))], (3806 ^ _779571) ^ [_838276, _838278, _838280, _838282, _838284, _838286, _838288, _838290] : [-(c_New__Random__Sequence_Opos__bind(_838290, _838286, _838282, _838278) = c_New__Random__Sequence_Opos__bind(_838288, _838284, _838280, _838276)), _838290 = _838288, _838286 = _838284, _838282 = _838280, _838278 = _838276], (48752 ^ _779571) ^ [_1757150, _1757152, _1757154] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1757150, tc_HOL_Obool)), hAPP(c_List_Oset(_1757150), hAPP(hAPP(c_List_Odrop(_1757150), _1757152), _1757154))), hAPP(c_List_Oset(_1757150), _1757154))))], (29268 ^ _779571) ^ [_1302682, _1302684, _1302686] : [class_Orderings_Obot(_1302682), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1302684, _1302682)), _1302686) = c_Orderings_Obot__class_Obot(_1302682))], (42301 ^ _779571) ^ [_1598452, _1598454, _1598456, _1598458, _1598460] : [-(hAPP(c_Relation_ODomain(_1598452, _1598454), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1598452, _1598454)), hAPP(hAPP(c_Product__Type_OPair(_1598452, _1598454), _1598456), _1598458)), _1598460)) = hAPP(hAPP(c_Set_Oinsert(_1598452), _1598456), hAPP(c_Relation_ODomain(_1598452, _1598454), _1598460)))], (42303 ^ _779571) ^ [_1598523, _1598525, _1598527, _1598529] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598523, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1598523, _1598525), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1598523, _1598525), tc_HOL_Obool)), _1598527), _1598529))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598523, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1598523, _1598525), _1598527)), hAPP(c_Relation_ODomain(_1598523, _1598525), _1598529)))))], (7985 ^ _779571) ^ [_912063, _912065] : [-(c_Option_Ooption_Ooption__size(_912063, _912065, c_Option_Ooption_ONone(_912063)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17027 ^ _779571) ^ [_1072049, _1072051] : [class_Groups_Oordered__ab__group__add__abs(_1072049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072049), _1072051), c_Groups_Ozero__class_Ozero(_1072049))), -(hAPP(c_Groups_Oabs__class_Oabs(_1072049), _1072051) = hAPP(c_Groups_Ouminus__class_Ouminus(_1072049), _1072051))], (19371 ^ _779571) ^ [_1111829] : [-(c_Int_Opred(c_Int_OBit1(_1111829)) = c_Int_OBit0(_1111829))], (2532 ^ _779571) ^ [_817871, _817873, _817875, _817877] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817877, _817873) = c_Code__Numeral_Odiv__mod__code__numeral(_817875, _817871)), _817877 = _817875, _817873 = _817871], (2890 ^ _779571) ^ [_823570, _823572, _823574, _823576, _823578, _823580] : [-(c_Nitpick_Oplus__frac(_823580, _823576, _823572) = c_Nitpick_Oplus__frac(_823578, _823574, _823570)), _823580 = _823578, _823576 = _823574, _823572 = _823570], (24635 ^ _779571) ^ [_1209813, _1209815] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1209813), hAPP(c_Nat_OSuc, _1209815)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1209815), 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)), _1209815)), _1209813))], (47649 ^ _779571) ^ [_1729414, _1729416, _1729418, _1729420] : [-(hAPP(c_List_Oset(tc_prod(_1729414, _1729416)), hAPP(hAPP(c_List_Ozip(_1729414, _1729416), _1729418), _1729420)) = hAPP(c_Set_OCollect(tc_prod(_1729414, _1729416)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1729414, _1729416)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1729414, _1729416), 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(_1729414, _1729416)), 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(_1729414, _1729416)), 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(_1729414, _1729416), tc_fun(tc_Nat_Onat, tc_prod(_1729414, _1729416)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1729414, _1729416), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1729414, _1729416)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1729414, _1729416)), c_COMBB(tc_prod(_1729414, _1729416), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1729416, tc_prod(_1729414, _1729416)), hAPP(hAPP(c_COMBB(_1729414, tc_fun(_1729416, tc_prod(_1729414, _1729416)), tc_Nat_Onat), c_Product__Type_OPair(_1729414, _1729416)), hAPP(c_List_Onth(_1729414), _1729418))), hAPP(c_List_Onth(_1729416), _1729420)))))), 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(_1729414)), _1729418)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729416)), _1729420)))))))], (24673 ^ _779571) ^ [_1210453, _1210455] : [hAPP(c_Code__Numeral_Onat__of, _1210453) = hAPP(c_Code__Numeral_Onat__of, _1210455), -(_1210453 = _1210455)], (12263 ^ _779571) ^ [_984218, _984220, _984222] : [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, _984218)), _984220)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984218)), _984222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984220), _984222)))], (14634 ^ _779571) ^ [_1026416, _1026418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1026416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1026418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026418), _1026416)), _1026418)))], (14369 ^ _779571) ^ [_1022046, _1022048, _1022050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022046), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1022048, _1022050)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022046), _1022048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022046), _1022050)))], (22103 ^ _779571) ^ [] : [-(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))], (25842 ^ _779571) ^ [_1232178, _1232180] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232178), _1232180)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1232180), _1232178))))], (43401 ^ _779571) ^ [_1625165, _1625167, _1625169] : [-(hAPP(c_Relation_ORange(_1625165, _1625167), hAPP(c_Relation_Oconverse(_1625167, _1625165), _1625169)) = hAPP(c_Relation_ODomain(_1625167, _1625165), _1625169))], (15140 ^ _779571) ^ [_1035453, _1035455, _1035457] : [class_Divides_Osemiring__div(_1035453), -(_1035455 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035453), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1035453), _1035455), _1035457)), _1035457)), c_Divides_Odiv__class_Omod(_1035453, _1035455, _1035457)))], (38739 ^ _779571) ^ [_1507559, _1507561, _1507563, _1507565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507559), _1507561)), hAPP(c_Finite__Set_Ocard(_1507563), hAPP(c_Set_Oimage(_1507559, _1507563, _1507565), _1507561)) = hAPP(c_Finite__Set_Ocard(_1507559), _1507561), -(c_Fun_Oinj__on(_1507559, _1507563, _1507565, _1507561))], (714 ^ _779571) ^ [_790594, _790596, _790598, _790600, _790602, _790604] : [-(c_Finite__Set_Ofolding__one__idem(_790602, _790598, _790594)), c_Finite__Set_Ofolding__one__idem(_790604, _790600, _790596), _790604 = _790602, _790600 = _790598, _790596 = _790594], (13112 ^ _779571) ^ [_999208, _999210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999210)), 13119 ^ _779571 : [(13126 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _999208), _999210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _999208)), hAPP(c_Int_Onat, _999210))))], (13120 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _999208)), hAPP(c_Int_Onat, _999210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _999208), _999210)))]]], (40306 ^ _779571) ^ [_1544177, _1544179, _1544181, _1544183] : [_1544177 = c_Orderings_Obot__class_Obot(tc_fun(_1544179, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1544179, _1544181), _1544181, c_Product__Type_Osnd(_1544179, _1544181)), hAPP(hAPP(c_Product__Type_OSigma(_1544179, _1544181), _1544177), hAPP(c_COMBK(tc_fun(_1544181, tc_HOL_Obool), _1544179), _1544183))) = c_Orderings_Obot__class_Obot(tc_fun(_1544181, tc_HOL_Obool)))], (23451 ^ _779571) ^ [_1186638, _1186640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186638), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186640), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186638, _1186640) = 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), _1186638), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186640)))))], (51531 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (12606 ^ _779571) ^ [_990104, _990106, _990108] : [class_Groups_Oordered__comm__monoid__add(_990104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990104), _990106), c_Groups_Ozero__class_Ozero(_990104))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990104), _990108), c_Groups_Ozero__class_Ozero(_990104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990104), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_990104), _990106), _990108)), c_Groups_Ozero__class_Ozero(_990104))))], (47039 ^ _779571) ^ [_1715039, _1715041, _1715043] : [class_Groups_Omonoid__add(_1715039), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715039), hAPP(hAPP(c_List_Olist_OCons(_1715039), _1715041), _1715043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1715039), _1715041), hAPP(c_List_Omonoid__add__class_Olistsum(_1715039), _1715043)))], (18561 ^ _779571) ^ [_1097970, _1097972] : [class_Int_Onumber__ring(_1097970), class_Rings_Olinordered__idom(_1097970), 18568 ^ _779571 : [(18575 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097972), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097970), hAPP(c_Int_Onumber__class_Onumber__of(_1097970), _1097972)), c_Groups_Ozero__class_Ozero(_1097970))))], (18569 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097970), hAPP(c_Int_Onumber__class_Onumber__of(_1097970), _1097972)), c_Groups_Ozero__class_Ozero(_1097970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097972), c_Int_OPls)))]]], (23815 ^ _779571) ^ [_1193446, _1193448] : [class_Orderings_Olinorder(_1193446), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193446), _1193448), _1193448) = _1193448)], (23461 ^ _779571) ^ [_1186825, _1186827, _1186829, _1186831, _1186833] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186825, _1186827), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1186829), _1186831))), -(_1186827 = 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), _1186833), _1186825), _1186827), 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), _1186833), _1186829)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186833), _1186831)), _1186827))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186833), _1186831), _1186827)))))], (40210 ^ _779571) ^ [_1541985, _1541987, _1541989, _1541991, _1541993, _1541995] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541985, _1541987)), hAPP(hAPP(c_Product__Type_OPair(_1541985, _1541987), _1541989), _1541991)), hAPP(hAPP(c_Product__Type_OSigma(_1541985, _1541987), _1541993), _1541995)))), hBOOL(hAPP(hAPP(c_member(_1541985), _1541989), _1541993)), hBOOL(hAPP(hAPP(c_member(_1541987), _1541991), hAPP(_1541995, _1541989)))], (39218 ^ _779571) ^ [_1517659, _1517661, _1517663, _1517665] : [c_Fun_Oinj__on(_1517659, _1517661, _1517663, _1517665), -(hAPP(c_Set_Oimage(_1517661, _1517659, c_Fun_Othe__inv__into(_1517659, _1517661, _1517665, _1517663)), hAPP(c_Set_Oimage(_1517659, _1517661, _1517663), _1517665)) = _1517665)], (32424 ^ _779571) ^ [_1370390, _1370392, _1370394, _1370396, _1370398, _1370400, _1370402, _1370404] : [c_Finite__Set_Ofolding__image__simple(_1370390, _1370392, _1370394, _1370396, _1370398, _1370400), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370392), _1370402)), hBOOL(hAPP(hAPP(c_member(_1370392), _1370404), _1370402)), -(hAPP(_1370400, _1370402) = hAPP(hAPP(_1370394, hAPP(_1370398, _1370404)), hAPP(_1370400, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370392, tc_HOL_Obool)), _1370402), hAPP(hAPP(c_Set_Oinsert(_1370392), _1370404), c_Orderings_Obot__class_Obot(tc_fun(_1370392, tc_HOL_Obool)))))))], (34837 ^ _779571) ^ [] : [-(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)))))], (50578 ^ _779571) ^ [_1796110, _1796112] : [-(c_List_Oconcat(_1796110, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796110), tc_List_Olist(_1796110)), c_List_Olist_Olist__case(tc_List_Olist(_1796110), _1796110, c_List_Olist_ONil(_1796110), hAPP(hAPP(c_COMBB(tc_List_Olist(_1796110), tc_fun(tc_List_Olist(_1796110), tc_List_Olist(_1796110)), _1796110), c_COMBK(tc_List_Olist(_1796110), tc_List_Olist(_1796110))), hAPP(hAPP(c_COMBC(_1796110, tc_List_Olist(_1796110), tc_List_Olist(_1796110)), c_List_Olist_OCons(_1796110)), c_List_Olist_ONil(_1796110))))), _1796112)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796110), _1796110), c_List_Ohd(_1796110)), hAPP(c_List_Ofilter(tc_List_Olist(_1796110), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1796110)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1796110), tc_List_Olist(_1796110), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1796110)))), _1796112)))], (25912 ^ _779571) ^ [_1233525, _1233527, _1233529] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233525), _1233527)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233525), _1233529)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233525), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1233527), _1233529))))], (19925 ^ _779571) ^ [_1121906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1121906)), -(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), _1121906), 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)))))))], (9888 ^ _779571) ^ [_944276, _944278] : [class_Rings_Olinordered__semidom(_944276), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944276), _944278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944276), _944278), c_Groups_Oone__class_Oone(_944276)))))], (7189 ^ _779571) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29938 ^ _779571) ^ [_1315581, _1315583, _1315585, _1315587, _1315589, _1315591] : [c_Hoare__Mirabelle_Ohoare__derivs(_1315581, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315581), tc_HOL_Obool)), _1315583), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1315581), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581))), hAPP(hAPP(c_COMBB(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1315581)), _1315585)), c_Com_Ocom_OBODY)), _1315587)), _1315589)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1315581), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581))), hAPP(hAPP(c_COMBB(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1315581, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1315581))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1315581)), _1315585)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1315587)), _1315589)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1315591), _1315589)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1315581, _1315583, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315581)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315581), hAPP(_1315585, _1315591)), hAPP(c_Com_Ocom_OBODY, _1315591)), hAPP(_1315587, _1315591))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315581), tc_HOL_Obool)))))], (35661 ^ _779571) ^ [_1438862, _1438864, _1438866, _1438868, _1438870, _1438872] : [c_Finite__Set_Ofolding(_1438862, _1438864, _1438866, _1438868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438862), _1438870)), -(hAPP(_1438868, hAPP(hAPP(c_Set_Oinsert(_1438862), _1438872), _1438870)) = hAPP(c_Fun_Ocomp(_1438864, _1438864, _1438864, hAPP(_1438868, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1438862, tc_HOL_Obool)), _1438870), hAPP(hAPP(c_Set_Oinsert(_1438862), _1438872), c_Orderings_Obot__class_Obot(tc_fun(_1438862, tc_HOL_Obool)))))), hAPP(_1438866, _1438872)))], (40971 ^ _779571) ^ [_1559385, _1559387] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1559385))), -(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)), _1559385))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1559387)))) = 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)), _1559385))), 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, _1559387))))))], (41764 ^ _779571) ^ [_1585674, _1585676, _1585678, _1585680, _1585682, _1585684, _1585686] : [c_Predicate_Opred__comp(_1585674, _1585676, _1585678, hAPP(hAPP(c_COMBC(_1585674, tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_fun(_1585676, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585676, tc_fun(tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_fun(_1585676, tc_HOL_Obool)), _1585674), c_COMBC(_1585676, tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585676, tc_prod(_1585674, _1585676)), tc_fun(_1585676, tc_fun(tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_HOL_Obool)), _1585674), hAPP(c_COMBB(tc_prod(_1585674, _1585676), tc_fun(tc_fun(tc_prod(_1585674, _1585676), tc_HOL_Obool), tc_HOL_Obool), _1585676), c_member(tc_prod(_1585674, _1585676)))), c_Product__Type_OPair(_1585674, _1585676)))), _1585680), hAPP(hAPP(c_COMBC(_1585676, tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_fun(_1585678, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585678, tc_fun(tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_fun(_1585678, tc_HOL_Obool)), _1585676), c_COMBC(_1585678, tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585678, tc_prod(_1585676, _1585678)), tc_fun(_1585678, tc_fun(tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_HOL_Obool)), _1585676), hAPP(c_COMBB(tc_prod(_1585676, _1585678), tc_fun(tc_fun(tc_prod(_1585676, _1585678), tc_HOL_Obool), tc_HOL_Obool), _1585678), c_member(tc_prod(_1585676, _1585678)))), c_Product__Type_OPair(_1585676, _1585678)))), _1585682), _1585684, _1585686), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585674, _1585678)), hAPP(hAPP(c_Product__Type_OPair(_1585674, _1585678), _1585684), _1585686)), hAPP(hAPP(c_Relation_Orel__comp(_1585674, _1585676, _1585678), _1585680), _1585682))))], (29626 ^ _779571) ^ [_1308956, _1308958, _1308960, _1308962, _1308964] : [-(_1308956 = c_Orderings_Obot__class_Obot(tc_fun(_1308958, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1308960), _1308962), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308958, tc_fun(_1308960, tc_HOL_Obool)), _1308956), _1308964)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308958, tc_fun(_1308960, tc_HOL_Obool)), _1308956), hAPP(hAPP(c_COMBB(tc_fun(_1308960, tc_HOL_Obool), tc_fun(_1308960, tc_HOL_Obool), _1308958), hAPP(c_Set_Oinsert(_1308960), _1308962)), _1308964)))], (13910 ^ _779571) ^ [_1013325, _1013327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013325), _1013327)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013325, _1013327) = _1013325)], (18389 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (50053 ^ _779571) ^ [_1785938, _1785940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1785938), _1785940)), -(c_List_Oupt(_1785938, hAPP(c_Nat_OSuc, _1785940)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1785938, _1785940)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1785940), c_List_Olist_ONil(tc_Nat_Onat))))], (7027 ^ _779571) ^ [_895386, _895388, _895390] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_895386), 7030 ^ _779571 : [(7037 ^ _779571) ^ [] : [_895390 = c_Groups_Ozero__class_Ozero(_895386), -(_895388 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895386), _895388), _895390))], (7031 ^ _779571) ^ [] : [_895388 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895386), _895388), _895390), -(_895390 = c_Groups_Ozero__class_Ozero(_895386))]]], (19323 ^ _779571) ^ [_1110971, _1110973] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1110971)), c_Int_OBit0(_1110973)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110971), _1110973)))], (18145 ^ _779571) ^ [_1091716] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1091716), hAPP(c_Int_Onumber__class_Onumber__of(_1091716), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1091716)), class_Int_Onumber__ring(_1091716), class_Rings_Olinordered__idom(_1091716)], (46340 ^ _779571) ^ [_1694950, _1694952, _1694954, _1694956] : [-(c_List_Oremove1(_1694950, _1694952, c_List_Oremove1(_1694950, _1694954, _1694956)) = c_List_Oremove1(_1694950, _1694954, c_List_Oremove1(_1694950, _1694952, _1694956)))], (36616 ^ _779571) ^ [_1459743, _1459745, _1459747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459743, tc_HOL_Obool)), _1459745), _1459747)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459743, tc_HOL_Obool)), _1459747), _1459745) = _1459745)], (40170 ^ _779571) ^ [_1540868, _1540870, _1540872, _1540874] : [_1540868 = c_Finite__Set_Ofold1(_1540870, _1540872), -(hAPP(_1540868, hAPP(hAPP(c_Set_Oinsert(_1540870), _1540874), c_Orderings_Obot__class_Obot(tc_fun(_1540870, tc_HOL_Obool)))) = _1540874)], (7244 ^ _779571) ^ [_899355, _899357, _899359, _899361, _899363] : [-(c_Sum__Type_Osum_Osum__size(_899355, _899357, _899359, _899361, hAPP(c_Sum__Type_OInr(_899357, _899355), _899363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_899361, _899363)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34979 ^ _779571) ^ [_1422408, _1422410] : [c_Relation_Oirrefl(_1422408, _1422410), 34982 ^ _779571 : [(34983 ^ _779571) ^ [_1422490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1422408, _1422408)), hAPP(hAPP(c_Product__Type_OPair(_1422408, _1422408), _1422490), _1422490)), _1422410))]]], (51505 ^ _779571) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (1810 ^ _779571) ^ [_805008, _805010, _805012, _805014] : [-(v_Q(_805012, _805008)), v_Q(_805014, _805010), _805014 = _805012, _805010 = _805008], (30941 ^ _779571) ^ [_1336586, _1336588, _1336590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336586), _1336588)), 30944 ^ _779571 : [(30951 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336586), _1336590), _1336588))), -(hAPP(c_Finite__Set_Ocard(_1336586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336586, tc_HOL_Obool)), _1336588), hAPP(hAPP(c_Set_Oinsert(_1336586), _1336590), c_Orderings_Obot__class_Obot(tc_fun(_1336586, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1336586), _1336588))], (30945 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1336586), _1336590), _1336588)), -(hAPP(c_Finite__Set_Ocard(_1336586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336586, tc_HOL_Obool)), _1336588), hAPP(hAPP(c_Set_Oinsert(_1336586), _1336590), c_Orderings_Obot__class_Obot(tc_fun(_1336586, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1336586), _1336588)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (43096 ^ _779571) ^ [_1617932, _1617934, _1617936] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1617932, _1617934, _1617934), _1617936), c_Relation_OId(_1617934)) = _1617936)], (36490 ^ _779571) ^ [_1457533, _1457535, _1457537, _1457539] : [class_Lattices_Osemilattice__inf(_1457533), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457533), _1457535), _1457537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457533), _1457535), _1457539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457533), _1457535), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457533), _1457537), _1457539))))], (17387 ^ _779571) ^ [_1078632, _1078634, _1078636] : [class_Rings_Olinordered__idom(_1078632), -(hAPP(c_Groups_Oabs__class_Oabs(_1078632), hAPP(hAPP(c_Power_Opower__class_Opower(_1078632), _1078634), _1078636)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1078632), hAPP(c_Groups_Oabs__class_Oabs(_1078632), _1078634)), _1078636))], (40865 ^ _779571) ^ [_1556752, _1556754, _1556756, _1556758, _1556760, _1556762] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1556752, _1556754), _1556752, tc_prod(_1556756, _1556758), c_Product__Type_Ofst(_1556752, _1556754)), c_Product__Type_Omap__pair(_1556756, _1556752, _1556758, _1556754, _1556760, _1556762)) = hAPP(c_Fun_Ocomp(_1556756, _1556752, tc_prod(_1556756, _1556758), _1556760), c_Product__Type_Ofst(_1556756, _1556758)))], (36780 ^ _779571) ^ [_1464076, _1464078] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1464076), _1464078) = 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)), _1464076)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1464078))))], (17721 ^ _779571) ^ [_1084796, _1084798, _1084800, _1084802] : [class_Rings_Olinordered__semidom(_1084796), hAPP(hAPP(c_Power_Opower__class_Opower(_1084796), _1084798), _1084800) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084796), _1084802), _1084800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084796), c_Groups_Ozero__class_Ozero(_1084796)), _1084798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084796), c_Groups_Ozero__class_Ozero(_1084796)), _1084802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1084800)), -(_1084798 = _1084802)], (51463 ^ _779571) ^ [_1812022, _1812024] : [-(class_Finite__Set_Ofinite(tc_prod(_1812022, _1812024))), class_Finite__Set_Ofinite(_1812022), class_Finite__Set_Ofinite(_1812024)], (43260 ^ _779571) ^ [_1621705, _1621707, _1621709, _1621711] : [-(c_Wellfounded_Oacyclic(_1621705, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1621705, _1621705)), hAPP(hAPP(c_Product__Type_OPair(_1621705, _1621705), _1621707), _1621709)), _1621711))), c_Wellfounded_Oacyclic(_1621705, _1621711), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621705, _1621705)), hAPP(hAPP(c_Product__Type_OPair(_1621705, _1621705), _1621709), _1621707)), c_Transitive__Closure_Ortrancl(_1621705, _1621711))))], (16887 ^ _779571) ^ [_1069127, _1069129, _1069131, _1069133] : [class_Int_Onumber__ring(_1069127), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069127), hAPP(c_Int_Onumber__class_Onumber__of(_1069127), _1069129)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069127), hAPP(c_Int_Onumber__class_Onumber__of(_1069127), _1069131)), _1069133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069127), hAPP(c_Int_Onumber__class_Onumber__of(_1069127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069129), _1069131))), _1069133))], (11715 ^ _779571) ^ [_974285, _974287, _974289, _974291] : [class_Groups_Oordered__comm__monoid__add(_974285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974285), c_Groups_Ozero__class_Ozero(_974285)), _974287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974285), _974289), _974291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974285), _974289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974285), _974287), _974291))))], (13735 ^ _779571) ^ [_1010057, _1010059, _1010061, _1010063] : [class_Divides_Osemiring__div(_1010057), -(c_Divides_Odiv__class_Omod(_1010057, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010057), _1010059), _1010061), _1010063) = c_Divides_Odiv__class_Omod(_1010057, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010057), c_Divides_Odiv__class_Omod(_1010057, _1010059, _1010063)), c_Divides_Odiv__class_Omod(_1010057, _1010061, _1010063)), _1010063))], (41089 ^ _779571) ^ [_1561973] : [class_Lattices_Osemilattice__sup(_1561973), -(c_Finite__Set_Ofun__left__comm__idem(_1561973, _1561973, c_Lattices_Osemilattice__sup__class_Osup(_1561973)))], (25416 ^ _779571) ^ [_1224843, _1224845] : [_1224843 = _1224845, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224843), _1224845)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224845), _1224843)))], (7009 ^ _779571) ^ [_895101, _895103] : [class_Groups_Omonoid__add(_895101), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895101), _895103), c_Groups_Ozero__class_Ozero(_895101)) = _895103)], (22478 ^ _779571) ^ [_1168244, _1168246] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1168244)), hAPP(c_Code__Numeral_Oof__nat, _1168246)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168244), _1168246)))], (14435 ^ _779571) ^ [_1023201, _1023203] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023201, _1023203)) = _1023203), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1023201), _1023203) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023201, _1023203)))], (15584 ^ _779571) ^ [_1043732, _1043734, _1043736] : [class_Groups_Oordered__ab__group__add(_1043732), 15587 ^ _779571 : [(15594 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043732), _1043734), _1043736)), c_Groups_Ozero__class_Ozero(_1043732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043732), _1043734), _1043736)))], (15588 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043732), _1043734), _1043736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043732), _1043734), _1043736)), c_Groups_Ozero__class_Ozero(_1043732))))]]], (8370 ^ _779571) ^ [_918437, _918439] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918437), _918439) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918439), _918437))], (47580 ^ _779571) ^ [_1727493, _1727495, _1727497] : [-(hBOOL(hAPP(hAPP(c_member(_1727493), _1727495), hAPP(c_List_Oset(_1727493), _1727497)))), 47581 ^ _779571 : [(47582 ^ _779571) ^ [_1727567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727493)), _1727497))), hAPP(hAPP(c_List_Onth(_1727493), _1727497), _1727567) = _1727495]]], (28959 ^ _779571) ^ [] : [-(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))))], (44802 ^ _779571) ^ [] : [-(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)))], (40654 ^ _779571) ^ [_1551294, _1551296, _1551298, _1551300, _1551302, _1551304] : [-(hAPP(c_Set_Ovimage(_1551294, tc_prod(_1551296, _1551298), _1551300), hAPP(hAPP(c_Product__Type_OSigma(_1551296, _1551298), _1551302), hAPP(c_COMBK(tc_fun(_1551298, tc_HOL_Obool), _1551296), _1551304))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551294, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1551294, _1551296, hAPP(c_Fun_Ocomp(tc_prod(_1551296, _1551298), _1551296, _1551294, c_Product__Type_Ofst(_1551296, _1551298)), _1551300)), _1551302)), hAPP(c_Set_Ovimage(_1551294, _1551298, hAPP(c_Fun_Ocomp(tc_prod(_1551296, _1551298), _1551298, _1551294, c_Product__Type_Osnd(_1551296, _1551298)), _1551300)), _1551304)))], (15344 ^ _779571) ^ [_1039203, _1039205, _1039207, _1039209] : [class_Divides_Oring__div(_1039203), -(c_Divides_Odiv__class_Omod(_1039203, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039203), _1039205), _1039207), _1039209) = c_Divides_Odiv__class_Omod(_1039203, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039203), _1039205), c_Divides_Odiv__class_Omod(_1039203, _1039207, _1039209)), _1039209))], (45074 ^ _779571) ^ [_1665788, _1665790, _1665792] : [class_Complete__Lattice_Ocomplete__lattice(_1665788), class_Orderings_Olinorder(_1665788), 45081 ^ _779571 : [(45091 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665788), c_Complete__Lattice_OInf__class_OInf(_1665788, _1665790)), _1665792))), 45092 ^ _779571 : [(45093 ^ _779571) ^ [_1666094] : [hBOOL(hAPP(hAPP(c_member(_1665788), _1666094), _1665790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665788), _1666094), _1665792))]]], (45082 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665788), c_Complete__Lattice_OInf__class_OInf(_1665788, _1665790)), _1665792)), 45086 ^ _779571 : [(45089 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665788), 45085 ^ [_1665788, _1665790, _1665792]), _1665792)))], (45087 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665788), 45085 ^ [_1665788, _1665790, _1665792]), _1665790)))]]]]], (24959 ^ _779571) ^ [_1216887, _1216889, _1216891, _1216893, _1216895, _1216897] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1216887, _1216889, _1216891, _1216893), _1216895), _1216897) = hAPP(_1216893, hAPP(hAPP(c_Product__Type_OPair(_1216887, _1216889), _1216895), _1216897)))], (12083 ^ _779571) ^ [_981095] : [class_Rings_Olinordered__semidom(_981095), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981095), c_Groups_Ozero__class_Ozero(_981095)), c_Groups_Oone__class_Oone(_981095))))], (22184 ^ _779571) ^ [_1162417] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1162417)], (20033 ^ _779571) ^ [_1123824, _1123826, _1123828, _1123830] : [class_Rings_Odivision__ring(_1123824), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123824), _1123826), _1123828)), _1123830) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123824), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123824), _1123826), _1123830)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123824), _1123828), _1123830)))], (28461 ^ _779571) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (31335 ^ _779571) ^ [_1346063, _1346065, _1346067, _1346069] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346063, tc_HOL_Obool)), _1346065), _1346069))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346063, tc_HOL_Obool)), _1346065), hAPP(hAPP(c_Set_Oinsert(_1346063), _1346067), _1346069)))))], (30054 ^ _779571) ^ [_1318120, _1318122, _1318124, _1318126] : [hBOOL(hAPP(hAPP(c_member(_1318120), _1318122), _1318124)), -(hBOOL(hAPP(hAPP(c_member(_1318120), _1318122), _1318126))), -(hBOOL(hAPP(hAPP(c_member(_1318120), _1318122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318120, tc_HOL_Obool)), _1318124), _1318126))))], (23507 ^ _779571) ^ [_1187775, _1187777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1187775), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187777), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187775), _1187777) = 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), _1187775), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187777)))))], (36174 ^ _779571) ^ [_1450717, _1450719, _1450721, _1450723] : [hBOOL(hAPP(hAPP(c_member(_1450717), _1450719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450717, tc_HOL_Obool)), _1450721), _1450723))), -(hBOOL(hAPP(hAPP(c_member(_1450717), _1450719), _1450721)))], (13759 ^ _779571) ^ [_1010621, _1010623, _1010625, _1010627, _1010629, _1010631] : [class_Divides_Osemiring__div(_1010621), c_Divides_Odiv__class_Omod(_1010621, _1010623, _1010625) = c_Divides_Odiv__class_Omod(_1010621, _1010627, _1010625), c_Divides_Odiv__class_Omod(_1010621, _1010629, _1010625) = c_Divides_Odiv__class_Omod(_1010621, _1010631, _1010625), -(c_Divides_Odiv__class_Omod(_1010621, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010621), _1010623), _1010629), _1010625) = c_Divides_Odiv__class_Omod(_1010621, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010621), _1010627), _1010631), _1010625))], (46624 ^ _779571) ^ [_1702530, _1702532, _1702534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1702530), _1702532)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1702530)), hAPP(c_Set_OCollect(tc_List_Olist(_1702530)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1702530), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1702530)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1702530), tc_fun(_1702530, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1702530, tc_HOL_Obool), tc_fun(tc_fun(_1702530, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1702530)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1702530, tc_HOL_Obool))), c_List_Oset(_1702530))), _1702532))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1702530), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1702530)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1702530)))), _1702534))))))], (15554 ^ _779571) ^ [_1043174, _1043176, _1043178] : [-(hBOOL(hAPP(_1043174, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043176), _1043178))))), 15557 ^ _779571 : [(15560 ^ _779571) ^ [] : [hBOOL(hAPP(_1043174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1043176)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1043178))))], (15558 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043178), _1043176)))]], 15561 ^ _779571 : [(15564 ^ _779571) ^ [] : [hBOOL(hAPP(_1043174, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15562 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043176), _1043178)))]]], (51519 ^ _779571) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (46035 ^ _779571) ^ [_1688128, _1688130, _1688132, _1688134, _1688136, _1688138] : [-(hAPP(hAPP(c_Option_Omap(_1688128, _1688130), _1688132), hAPP(hAPP(c_Option_Omap(_1688134, _1688128), _1688136), _1688138)) = hAPP(hAPP(c_Option_Omap(_1688134, _1688130), hAPP(c_Fun_Ocomp(_1688128, _1688130, _1688134, _1688132), _1688136)), _1688138))], (9752 ^ _779571) ^ [_941772, _941774, _941776] : [class_Rings_Olinordered__ring__strict(_941772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941772), _941774), c_Groups_Ozero__class_Ozero(_941772))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941772), _941776), c_Groups_Ozero__class_Ozero(_941772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941772), c_Groups_Ozero__class_Ozero(_941772)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941772), _941774), _941776))))], (47051 ^ _779571) ^ [_1715399, _1715401, _1715403, _1715405, _1715407] : [class_Rings_Osemiring__0(_1715399), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715399), hAPP(hAPP(c_List_Omap(_1715401, _1715399), hAPP(hAPP(c_COMBC(_1715401, _1715399, _1715399), hAPP(hAPP(c_COMBB(_1715399, tc_fun(_1715399, _1715399), _1715401), c_Groups_Otimes__class_Otimes(_1715399)), _1715403)), _1715405)), _1715407)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1715399), hAPP(c_List_Omonoid__add__class_Olistsum(_1715399), hAPP(hAPP(c_List_Omap(_1715401, _1715399), _1715403), _1715407))), _1715405))], (48104 ^ _779571) ^ [_1740018, _1740020, _1740022] : [-(hAPP(hAPP(c_List_Oappend(_1740018), _1740020), _1740022) = c_List_Olist_ONil(_1740018)), _1740020 = c_List_Olist_ONil(_1740018), _1740022 = c_List_Olist_ONil(_1740018)], (39745 ^ _779571) ^ [_1529654, _1529656, _1529658, _1529660, _1529662] : [hAPP(_1529654, _1529656) = hAPP(c_Option_Ooption_OSome(_1529658), _1529660), -(hAPP(hAPP(c_Set_Oinsert(_1529662), _1529656), c_Map_Odom(_1529662, _1529658, _1529654)) = c_Map_Odom(_1529662, _1529658, _1529654))], (49106 ^ _779571) ^ [_1764783, _1764785, _1764787] : [class_Groups_Omonoid__add(_1764783), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1764783), _1764785), hAPP(c_List_Ofoldl(_1764783, _1764783, c_Groups_Oplus__class_Oplus(_1764783), c_Groups_Ozero__class_Ozero(_1764783)), _1764787)) = hAPP(c_List_Ofoldl(_1764783, _1764783, c_Groups_Oplus__class_Oplus(_1764783), _1764785), _1764787))], (46462 ^ _779571) ^ [_1698521, _1698523, _1698525, _1698527] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1698521, _1698523))), hAPP(hAPP(c_List_Ozip(_1698521, _1698523), _1698525), _1698527)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698521)), _1698525)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698523)), _1698527)))], (51601 ^ _779571) ^ [_1813577] : [-(hBOOL(_1813577)), -(hBOOL(hAPP(c_fNot, _1813577)))], (47845 ^ _779571) ^ [_1733829, _1733831, _1733833, _1733835, _1733837, _1733839] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733829), tc_List_Olist(_1733829))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733829), tc_List_Olist(_1733829)), hAPP(hAPP(c_List_Olist_OCons(_1733829), _1733831), _1733833)), hAPP(hAPP(c_List_Olist_OCons(_1733829), _1733835), _1733837))), c_List_Olexord(_1733829, _1733839)))), 47846 ^ _779571 : [(47849 ^ _779571) ^ [] : [_1733831 = _1733835, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733829), tc_List_Olist(_1733829))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733829), tc_List_Olist(_1733829)), _1733833), _1733837)), c_List_Olexord(_1733829, _1733839)))], (47847 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1733829, _1733829)), hAPP(hAPP(c_Product__Type_OPair(_1733829, _1733829), _1733831), _1733835)), _1733839))]]], (41235 ^ _779571) ^ [_1565616, _1565618, _1565620, _1565622, _1565624] : [-(c_Map_Odom(_1565616, _1565618, hAPP(hAPP(c_COMBS(_1565616, tc_Option_Ooption(_1565618), tc_Option_Ooption(_1565618)), hAPP(hAPP(c_COMBS(_1565616, tc_Option_Ooption(_1565618), tc_fun(tc_Option_Ooption(_1565618), tc_Option_Ooption(_1565618))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1565618), tc_fun(tc_Option_Ooption(_1565618), tc_Option_Ooption(_1565618))), _1565616), c_If(tc_Option_Ooption(_1565618))), _1565620)), _1565622)), _1565624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565616, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565616, tc_HOL_Obool)), c_Map_Odom(_1565616, _1565618, _1565622)), hAPP(c_Set_OCollect(_1565616), _1565620))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565616, tc_HOL_Obool)), c_Map_Odom(_1565616, _1565618, _1565624)), hAPP(c_Set_OCollect(_1565616), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565616), c_fNot), _1565620)))))], (51081 ^ _779571) ^ [_1808135, _1808137] : [class_Lattices_Obounded__lattice(_1808135), -(class_Lattices_Obounded__lattice__top(tc_fun(_1808137, _1808135)))], (50011 ^ _779571) ^ [_1785147, _1785149, _1785151, _1785153] : [class_Orderings_Olinorder(_1785147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1785147), _1785149), _1785151)), c_List_Olinorder__class_Osorted(_1785147, hAPP(hAPP(c_List_Olist_OCons(_1785147), _1785151), _1785153)), -(c_List_Olinorder__class_Osorted(_1785147, hAPP(hAPP(c_List_Olist_OCons(_1785147), _1785149), hAPP(hAPP(c_List_Olist_OCons(_1785147), _1785151), _1785153))))], (33785 ^ _779571) ^ [_1396590, _1396592, _1396594] : [class_Orderings_Olinorder(_1396590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396590), _1396592)), -(_1396592 = c_Orderings_Obot__class_Obot(tc_fun(_1396590, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1396590, c_Orderings_Oord__class_Omax(_1396590), hAPP(hAPP(c_Set_Oinsert(_1396590), _1396594), _1396592)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1396590), _1396594), c_Big__Operators_Olattice_OSup__fin(_1396590, c_Orderings_Oord__class_Omax(_1396590), _1396592)))], (19739 ^ _779571) ^ [_1118050, _1118052, _1118054] : [class_Rings_Ocomm__semiring__1(_1118050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118050), _1118052), 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)))), _1118054)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118050), hAPP(hAPP(c_Power_Opower__class_Opower(_1118050), _1118052), _1118054)), hAPP(hAPP(c_Power_Opower__class_Opower(_1118050), _1118052), _1118054)))], (3366 ^ _779571) ^ [_831302, _831304] : [_831304 = _831302, -(c_Int_Oring__1__class_OInts(_831304) = c_Int_Oring__1__class_OInts(_831302))], (10104 ^ _779571) ^ [_947940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _947940), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_947940 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 10107 ^ [_947940]))))], (29158 ^ _779571) ^ [_1300436, _1300438, _1300440, _1300442, _1300444] : [hAPP(hAPP(c_Set_Oinsert(_1300436), _1300438), hAPP(hAPP(c_Set_Oinsert(_1300436), _1300440), c_Orderings_Obot__class_Obot(tc_fun(_1300436, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1300436), _1300442), hAPP(hAPP(c_Set_Oinsert(_1300436), _1300444), c_Orderings_Obot__class_Obot(tc_fun(_1300436, tc_HOL_Obool)))), 29163 ^ _779571 : [(29166 ^ _779571) ^ [] : [-(_1300440 = _1300444)], (29164 ^ _779571) ^ [] : [-(_1300438 = _1300442)]], 29167 ^ _779571 : [(29170 ^ _779571) ^ [] : [-(_1300440 = _1300442)], (29168 ^ _779571) ^ [] : [-(_1300438 = _1300444)]]], (19147 ^ _779571) ^ [_1107961, _1107963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1107961)), c_Int_OBit0(_1107963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107961), _1107963)))], (36932 ^ _779571) ^ [_1467531, _1467533, _1467535] : [class_Orderings_Oorder(_1467531), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467531, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1467531, _1467533), _1467535)), hAPP(c_SetInterval_Oord__class_OatLeast(_1467531), _1467535)) = c_Orderings_Obot__class_Obot(tc_fun(_1467531, tc_HOL_Obool)))], (6159 ^ _779571) ^ [_879050, _879052, _879054, _879056] : [class_Rings_Osemiring__1(_879050), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_879050, _879052, hAPP(c_Nat_OSuc, _879054), _879056) = c_Nat_Osemiring__1__class_Oof__nat__aux(_879050, _879052, _879054, hAPP(_879052, _879056)))], (6406 ^ _779571) ^ [_883947, _883949, _883951] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_883947, _883949, 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c_List_Oconcat(_1798795, _1798797)) = c_List_Oconcat(_1798795, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798795), tc_List_Olist(_1798795)), c_List_Orev(_1798795)), hAPP(c_List_Orev(tc_List_Olist(_1798795)), _1798797))))], (24567 ^ _779571) ^ [_1208141, _1208143, _1208145, _1208147, _1208149, _1208151] : [-(hAPP(c_Product__Type_Oapfst(_1208141, _1208143, _1208145, _1208147), hAPP(hAPP(c_Product__Type_OPair(_1208141, _1208145), _1208149), _1208151)) = hAPP(hAPP(c_Product__Type_OPair(_1208143, _1208145), hAPP(_1208147, _1208149)), _1208151))], (36262 ^ _779571) ^ [_1452893, _1452895] : [class_Lattices_Obounded__lattice__bot(_1452893), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452893), c_Orderings_Obot__class_Obot(_1452893)), _1452895) = c_Orderings_Obot__class_Obot(_1452893))], (36668 ^ _779571) ^ [_1461432, _1461434] : [class_Lattices_Oboolean__algebra(_1461432), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461432), _1461434), 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_1257787)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257781, _1257783), _1257785)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257781, _1257785), _1257787))], (41890 ^ _779571) ^ [_1589197, _1589199] : [c_Wellfounded_Owf(_1589197, _1589199), -(c_Wellfounded_Owf(tc_fun(_1589197, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1589197, _1589199)))], (51117 ^ _779571) ^ [_1808609, _1808611] : [class_Orderings_Opreorder(_1808609), -(class_Orderings_Opreorder(tc_fun(_1808611, _1808609)))], (26480 ^ _779571) ^ [_1244642, _1244644, _1244646, _1244648] : [class_Rings_Ocomm__semiring__1(_1244642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244642), c_Groups_Oone__class_Oone(_1244642)), c_Groups_Oone__class_Oone(_1244642))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244642), hAPP(hAPP(c_COMBB(_1244642, _1244642, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1244642), _1244644)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1244642, _1244642), hAPP(hAPP(c_COMBB(_1244642, tc_fun(_1244642, _1244642), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1244642)), c_Nat_Osemiring__1__class_Oof__nat(_1244642))), _1244646))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1244648))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244642), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244642), _1244648)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244642), _1244644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244642), _1244644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244642), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1244648), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1244646)))))], (15870 ^ _779571) ^ [_1049325] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1049325)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1049325)], (4562 ^ _779571) ^ [_850182, _850184] : [_850184 = _850182, -(c_Fun_Oid(_850184) = c_Fun_Oid(_850182))], (11208 ^ _779571) ^ [_965649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965649), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_965649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35000 ^ _779571) ^ [_1422949] : [-(hAPP(c_Relation_OField(_1422949), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1422949, _1422949), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1422949, tc_HOL_Obool)))], (18001 ^ _779571) ^ [_1089245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089245)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1089245) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1089245), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (39417 ^ _779571) ^ [_1522132, _1522134, _1522136, _1522138, _1522140] : [-(hAPP(c_Set_Ovimage(_1522132, _1522134, _1522136), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522134, tc_HOL_Obool)), _1522138), _1522140)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522132, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522132, _1522134, _1522136), _1522138)), hAPP(c_Set_Ovimage(_1522132, _1522134, _1522136), _1522140)))], (42102 ^ _779571) ^ [_1593641, _1593643, _1593645] : [-(hAPP(c_Relation_ORange(_1593641, _1593643), hAPP(c_Set_OCollect(tc_prod(_1593641, _1593643)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593641, _1593643, tc_HOL_Obool), _1593645))) = hAPP(c_Set_OCollect(_1593643), hAPP(hAPP(c_COMBB(tc_fun(_1593641, tc_HOL_Obool), tc_HOL_Obool, _1593643), c_HOL_OEx(_1593641)), hAPP(c_COMBC(_1593641, _1593643, tc_HOL_Obool), _1593645))))], (7379 ^ _779571) ^ [_902120, _902122, _902124, _902126, _902128] : [-(hAPP(c_Sum__Type_OSumr(_902120, _902122, _902124, _902126), hAPP(c_Sum__Type_OInr(_902120, _902124), _902128)) = hAPP(_902126, _902128))], (51325 ^ _779571) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (45797 ^ _779571) ^ [_1682380, _1682382, _1682384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1682380), _1682382)), -(c_Smallcheck_Osmall_H(_1682384, _1682380, _1682382) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (8056 ^ _779571) ^ [_913069, _913071, _913073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913069), _913071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913073), _913071))))], (42904 ^ _779571) ^ [_1612351, _1612353, _1612355, _1612357, _1612359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612351, _1612351)), hAPP(hAPP(c_Product__Type_OPair(_1612351, _1612351), _1612353), _1612355)), _1612357)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1612351, _1612351)), hAPP(hAPP(c_Product__Type_OPair(_1612351, _1612351), _1612355), _1612359)), c_Transitive__Closure_Otrancl(_1612351, _1612357))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612351, _1612351)), hAPP(hAPP(c_Product__Type_OPair(_1612351, _1612351), _1612353), _1612359)), c_Transitive__Closure_Otrancl(_1612351, _1612357))))], (19587 ^ _779571) ^ [] : [-(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)))))], (9474 ^ _779571) ^ [_936854, _936856] : [class_Groups_Olinordered__ab__group__add(_936854), 9477 ^ _779571 : [(9484 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936854), c_Groups_Ozero__class_Ozero(_936854)), _936856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936854), hAPP(c_Groups_Ouminus__class_Ouminus(_936854), _936856)), _936856)))], (9478 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936854), hAPP(c_Groups_Ouminus__class_Ouminus(_936854), _936856)), _936856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936854), c_Groups_Ozero__class_Ozero(_936854)), _936856)))]]], (7949 ^ _779571) ^ [_911428, _911430] : [7950 ^ _779571 : [(7951 ^ _779571) ^ [_911481] : [_911430 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911428), _911481))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911428), _911430)))], (29388 ^ _779571) ^ [_1304967, _1304969, _1304971] : [class_Groups_Ocomm__monoid__add(_1304967), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304969, _1304967), _1304971), c_Orderings_Obot__class_Obot(tc_fun(_1304969, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1304967))], (45945 ^ _779571) ^ [_1685747, _1685749, _1685751] : [c_Fun_Oinj__on(tc_List_Olist(_1685747), tc_List_Olist(_1685749), hAPP(c_List_Omap(_1685747, _1685749), _1685751), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1685747), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1685747, _1685749, _1685751, c_Orderings_Otop__class_Otop(tc_fun(_1685747, tc_HOL_Obool))))], (44648 ^ _779571) ^ [_1655433, _1655435, _1655437, _1655439, _1655441, _1655443] : [hBOOL(hAPP(hAPP(c_member(_1655433), _1655435), _1655437)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655433, tc_fun(_1655439, tc_HOL_Obool)), _1655437), hAPP(hAPP(c_COMBB(tc_fun(_1655439, tc_HOL_Obool), tc_fun(_1655439, tc_HOL_Obool), _1655433), hAPP(c_Set_Oinsert(_1655439), _1655441)), _1655443)) = hAPP(hAPP(c_Set_Oinsert(_1655439), _1655441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655433, tc_fun(_1655439, tc_HOL_Obool)), _1655437), _1655443)))], (15886 ^ _779571) ^ [_1049646, _1049648, _1049650, _1049652, _1049654, _1049656] : [class_Rings_Oordered__ring(_1049646), 15889 ^ _779571 : [(15896 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049646), _1049648), _1049654)), _1049650)), _1049652)), _1049656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), _1049648), _1049650)), _1049652)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), _1049654), _1049650)), _1049656))))], (15890 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), _1049648), _1049650)), _1049652)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), _1049654), _1049650)), _1049656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049646), _1049648), _1049654)), _1049650)), _1049652)), _1049656)))]]], (22376 ^ _779571) ^ [_1165893, _1165895] : [hAPP(c_Nat_OSuc, _1165893) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1165895), -(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(_1165895))), 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)), _1165893))))))], (17487 ^ _779571) ^ [_1080317, _1080319, _1080321, _1080323] : [class_Rings_Olinordered__semidom(_1080317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080317), c_Groups_Oone__class_Oone(_1080317)), _1080319)), 17494 ^ _779571 : [(17501 ^ _779571) ^ [] : [_1080321 = _1080323, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1080317), _1080319), _1080321) = hAPP(hAPP(c_Power_Opower__class_Opower(_1080317), _1080319), _1080323))], (17495 ^ _779571) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1080317), _1080319), _1080321) = hAPP(hAPP(c_Power_Opower__class_Opower(_1080317), _1080319), _1080323), -(_1080321 = _1080323)]]], (47187 ^ _779571) ^ [_1718746] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1718746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 47190 ^ _779571 : [(47191 ^ _779571) ^ [_1718821] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1718821), hAPP(c_List_Oset(tc_Nat_Onat), _1718746))), -(_1718821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22278 ^ _779571) ^ [_1163904, _1163906, _1163908, _1163910, _1163912] : [class_Groups_Ominus(_1163904), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1163906, _1163904)), _1163908), _1163910), _1163912) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163904), hAPP(_1163908, _1163912)), hAPP(_1163910, _1163912)))], (40863 ^ _779571) ^ [_1556681, _1556683, _1556685, _1556687, _1556689, _1556691] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1556681, _1556683), _1556683, tc_prod(_1556685, _1556687), c_Product__Type_Osnd(_1556681, _1556683)), c_Product__Type_Omap__pair(_1556685, _1556681, _1556687, _1556683, _1556689, _1556691)) = hAPP(c_Fun_Ocomp(_1556687, _1556683, tc_prod(_1556685, _1556687), _1556691), c_Product__Type_Osnd(_1556685, _1556687)))], (13524 ^ _779571) ^ [] : [-(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))))], (3116 ^ _779571) ^ [_827341, _827343, _827345, _827347] : [-(c_Divides_Odivmod__nat__rel(_827347, _827343) = c_Divides_Odivmod__nat__rel(_827345, _827341)), _827347 = _827345, _827343 = _827341], (6132 ^ _779571) ^ [_878488] : [_878488 = hAPP(c_Nat_OSuc, _878488)], (24993 ^ _779571) ^ [_1217723, _1217725, _1217727, _1217729] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1217723), _1217725), _1217727), _1217729) = 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(_1217723)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1217723), _1217725)))], (49060 ^ _779571) ^ [_1763866, _1763868, _1763870] : [-(c_List_Orotate(_1763866, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1763868), _1763870)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1763866), tc_List_Olist(_1763866), tc_List_Olist(_1763866), c_List_Orotate(_1763866, _1763868)), c_List_Orotate(_1763866, _1763870)))], (29480 ^ _779571) ^ [_1306535, _1306537, _1306539] : [class_Orderings_Oorder(_1306535), 29483 ^ _779571 : [(29490 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306535), _1306537), _1306539))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306535, _1306537), _1306539) = c_Orderings_Obot__class_Obot(tc_fun(_1306535, tc_HOL_Obool)))], (29484 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306535, _1306537), _1306539) = c_Orderings_Obot__class_Obot(tc_fun(_1306535, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306535), _1306537), _1306539))]]], (51249 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (17819 ^ _779571) ^ [_1086350] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086350), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30997 ^ _779571) ^ [_1337629] : [class_Finite__Set_Ofinite(_1337629), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337629), c_Orderings_Otop__class_Otop(tc_fun(_1337629, tc_HOL_Obool)))))], (5462 ^ _779571) ^ [_863992, _863994, _863996, _863998] : [-(c_List_Omap(_863998, _863994) = c_List_Omap(_863996, _863992)), _863998 = _863996, _863994 = _863992], (47340 ^ _779571) ^ [_1721503, _1721505, _1721507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721503), tc_List_Olist(_1721503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721503), tc_List_Olist(_1721503)), _1721505), c_List_Olist_ONil(_1721503))), c_List_Olex(_1721503, _1721507)))], (18357 ^ _779571) ^ [_1094807, _1094809] : [class_Int_Onumber__ring(_1094807), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094807), hAPP(c_Int_Onumber__class_Onumber__of(_1094807), c_Int_OPls)), _1094809) = _1094809)], (23235 ^ _779571) ^ [_1183274, _1183276, _1183278] : [-(hAPP(c_Product__Type_Osnd(_1183274, _1183276), _1183278) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183274, _1183276, _1183276), hAPP(c_COMBK(tc_fun(_1183276, _1183276), _1183274), c_COMBI(_1183276))), _1183278))], (42552 ^ _779571) ^ [_1604607, _1604609] : [hBOOL(hAPP(_1604607, c_Hilbert__Choice_OEps(_1604609, _1604607))), -(hBOOL(hAPP(_1604607, 42555 ^ [_1604607, _1604609])))], (546 ^ _779571) ^ [_788036, _788038, _788040, _788042] : [-(c_Predicate_Oreflp(_788040, _788036)), c_Predicate_Oreflp(_788042, _788038), _788042 = _788040, _788038 = _788036], (11120 ^ _779571) ^ [_964216, _964218, _964220, _964222] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_964216), 11123 ^ _779571 : [(11130 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964216), _964218), _964222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964216), _964218), _964220)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964216), _964222), _964220))))], (11124 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964216), _964218), _964220)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964216), _964222), _964220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964216), _964218), _964222)))]]], (41007 ^ _779571) ^ [_1560260, _1560262, _1560264, _1560266] : [-(hAPP(c_Set_OCollect(tc_prod(_1560260, _1560262)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560260, _1560262, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1560260, tc_fun(_1560262, tc_HOL_Obool), tc_fun(_1560262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1560262, tc_HOL_Obool), tc_fun(_1560262, tc_HOL_Obool)), _1560260), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560262)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560260), c_fconj), _1560264))), _1560266))) = hAPP(hAPP(c_Product__Type_OSigma(_1560260, _1560262), hAPP(c_Set_OCollect(_1560260), _1560264)), hAPP(c_COMBK(tc_fun(_1560262, tc_HOL_Obool), _1560260), hAPP(c_Set_OCollect(_1560262), _1560266))))], (43925 ^ _779571) ^ [_1638586, _1638588, _1638590, _1638592] : [class_Orderings_Olinorder(_1638586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638586), _1638588)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1638586, _1638586, c_Orderings_Oord__class_Omin(_1638586)), _1638590), hAPP(hAPP(c_Set_Oinsert(_1638586), _1638592), _1638588)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1638586), _1638592), hAPP(hAPP(c_Finite__Set_Ofold(_1638586, _1638586, c_Orderings_Oord__class_Omin(_1638586)), _1638590), _1638588)))], (334 ^ _779571) ^ [_784594, _784596] : [-(class_Fields_Ofield(_784594)), _784596 = _784594, class_Fields_Ofield(_784596)], (49353 ^ _779571) ^ [_1770576, _1770578, _1770580] : [49355 ^ _779571 : [(49358 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1770576), 49354 ^ [_1770576, _1770578, _1770580]), _1770580))], (49356 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770576), 49354 ^ [_1770576, _1770578, _1770580]), hAPP(c_List_Oset(_1770576), _1770578))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770576)), _1770578), c_List_Olists(_1770576, _1770580))))], (51187 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (7754 ^ _779571) ^ [_907981, _907983, _907985, _907987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907981), _907983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907985), _907987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _907981), _907985)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _907983), _907987))))], (32177 ^ _779571) ^ [_1365104, _1365106] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1365104), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1365106)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1365106), _1365104)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1365104), _1365106)))], (45929 ^ _779571) ^ [_1685436, _1685438, _1685440, _1685442, _1685444] : [c_Fun_Oinj__on(_1685436, _1685438, _1685440, c_Orderings_Otop__class_Otop(tc_fun(_1685436, tc_HOL_Obool))), 45932 ^ _779571 : [(45939 ^ _779571) ^ [] : [_1685442 = _1685444, -(hAPP(hAPP(c_List_Omap(_1685436, _1685438), _1685440), _1685442) = hAPP(hAPP(c_List_Omap(_1685436, _1685438), _1685440), _1685444))], (45933 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Omap(_1685436, _1685438), _1685440), _1685442) = hAPP(hAPP(c_List_Omap(_1685436, _1685438), _1685440), _1685444), -(_1685442 = _1685444)]]], (25782 ^ _779571) ^ [_1231103, _1231105, _1231107] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231103), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231105, _1231107))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231103), _1231107)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231103), _1231105)))], (33165 ^ _779571) ^ [_1384056, _1384058, _1384060] : [class_Lattices_Olattice(_1384056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384056), _1384058)), 33172 ^ _779571 : [(33179 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384056, tc_HOL_Obool)), _1384058), hAPP(hAPP(c_Set_Oinsert(_1384056), _1384060), c_Orderings_Obot__class_Obot(tc_fun(_1384056, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1384056, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1384056, hAPP(hAPP(c_Set_Oinsert(_1384056), _1384060), _1384058)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1384056), _1384060), c_Big__Operators_Olattice__class_OSup__fin(_1384056, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384056, tc_HOL_Obool)), _1384058), hAPP(hAPP(c_Set_Oinsert(_1384056), _1384060), c_Orderings_Obot__class_Obot(tc_fun(_1384056, tc_HOL_Obool)))))))], (33173 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384056, tc_HOL_Obool)), _1384058), hAPP(hAPP(c_Set_Oinsert(_1384056), _1384060), c_Orderings_Obot__class_Obot(tc_fun(_1384056, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1384056, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1384056, hAPP(hAPP(c_Set_Oinsert(_1384056), _1384060), _1384058)) = _1384060)]]], (6365 ^ _779571) ^ [_882859, _882861, _882863, _882865, _882867] : [c_Com_Ocom_OWhile(_882859, _882861) = c_Com_Ocom_OLocal(_882863, _882865, _882867)], (45576 ^ _779571) ^ [_1677383, _1677385, _1677387, _1677389, _1677391, _1677393, _1677395] : [c_Finite__Set_Ofolding__image__simple__idem(_1677383, _1677385, _1677387, _1677389, _1677391, _1677393), -(hAPP(hAPP(_1677387, _1677395), _1677395) = _1677395)], (37174 ^ _779571) ^ [_1473067, _1473069, _1473071, _1473073, _1473075] : [c_Finite__Set_Ofolding__one(_1473067, _1473069, _1473071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473067), _1473073)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473067), _1473075)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473067, tc_HOL_Obool)), _1473073), _1473075) = c_Orderings_Obot__class_Obot(tc_fun(_1473067, tc_HOL_Obool))), -(hAPP(hAPP(_1473069, hAPP(_1473071, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473067, tc_HOL_Obool)), _1473073), _1473075))), hAPP(_1473071, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473067, tc_HOL_Obool)), _1473073), _1473075))) = hAPP(hAPP(_1473069, hAPP(_1473071, _1473073)), hAPP(_1473071, _1473075)))], (42278 ^ _779571) ^ [_1597883, _1597885, _1597887, _1597889] : [-(hAPP(c_Relation_ODomain(_1597883, _1597885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1597883, _1597885), tc_HOL_Obool)), _1597887), _1597889)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597883, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597883, _1597885), _1597887)), hAPP(c_Relation_ODomain(_1597883, _1597885), _1597889)))], (11777 ^ _779571) ^ [_975422, _975424, _975426] : [class_Rings_Oordered__ring(_975422), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975422), c_Groups_Ozero__class_Ozero(_975422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975422), _975424), _975426)))), 11782 ^ _779571 : [(11789 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975422), _975424), c_Groups_Ozero__class_Ozero(_975422))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975422), _975426), c_Groups_Ozero__class_Ozero(_975422)))], (11783 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975422), c_Groups_Ozero__class_Ozero(_975422)), _975424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975422), c_Groups_Ozero__class_Ozero(_975422)), _975426))]]], (48325 ^ _779571) ^ [_1745280, _1745282, _1745284] : [-(c_List_Osublist(_1745280, _1745282, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1745284)) = hAPP(hAPP(c_List_Otake(_1745280), _1745284), _1745282))], (41287 ^ _779571) ^ [_1567499, _1567501, _1567503, _1567505, _1567507] : [-(c_Map_Odom(_1567499, _1567501, c_Fun_Ooverride__on(_1567499, tc_Option_Ooption(_1567501), _1567503, _1567505, _1567507)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567499, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567499, tc_HOL_Obool)), c_Map_Odom(_1567499, _1567501, _1567503)), hAPP(c_Set_OCollect(_1567499), hAPP(hAPP(c_COMBC(_1567499, tc_fun(_1567499, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567499)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567499, tc_HOL_Obool)), _1567507), c_Map_Odom(_1567499, _1567501, _1567505)))))), hAPP(c_Set_OCollect(_1567499), hAPP(hAPP(c_COMBC(_1567499, tc_fun(_1567499, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567499)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567499, tc_HOL_Obool)), _1567507), c_Map_Odom(_1567499, _1567501, _1567505))))))], (43080 ^ _779571) ^ [_1617543, _1617545, _1617547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617543, _1617543), tc_HOL_Obool)), c_Relation_OId(_1617543)), _1617545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617543, _1617543), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1617543, _1617543, _1617543), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1617543, _1617543), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1617543, _1617547)), _1617545)), _1617547)), _1617545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617543, _1617543), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1617543, _1617547)), _1617545)))], (35279 ^ _779571) ^ [_1429483, _1429485, _1429487, _1429489, _1429491] : [c_Finite__Set_Ofolding__one__idem(_1429483, _1429485, _1429487), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429483), _1429489)), -(_1429489 = c_Orderings_Obot__class_Obot(tc_fun(_1429483, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429483), _1429491)), -(_1429491 = c_Orderings_Obot__class_Obot(tc_fun(_1429483, tc_HOL_Obool))), -(hAPP(_1429487, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1429483, tc_HOL_Obool)), _1429489), _1429491)) = hAPP(hAPP(_1429485, hAPP(_1429487, _1429489)), hAPP(_1429487, _1429491)))], (39364 ^ _779571) ^ [_1520895, _1520897, _1520899, _1520901, _1520903, _1520905, _1520907] : [c_Big__Operators_Ocomm__monoid__big(_1520895, _1520897, _1520899, _1520901, _1520903), 39367 ^ _779571 : [(39374 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520897), _1520905))), -(hAPP(hAPP(_1520903, _1520907), _1520905) = _1520901)], (39368 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520897), _1520905)), -(hAPP(hAPP(_1520903, _1520907), _1520905) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1520895, _1520897, _1520899), _1520907), _1520901), _1520905))]]], (44071 ^ _779571) ^ [_1641535, _1641537, _1641539] : [class_Orderings_Olinorder(_1641535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641535), _1641537)), -(c_Big__Operators_Olinorder__class_OMin(_1641535, hAPP(hAPP(c_Set_Oinsert(_1641535), _1641539), _1641537)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641535, _1641535, c_Orderings_Oord__class_Omin(_1641535)), _1641539), _1641537))], (5502 ^ _779571) ^ [_864596, _864598] : [_864598 = _864596, -(c_List_Oembed__list(_864598) = c_List_Oembed__list(_864596))], (29452 ^ _779571) ^ [_1306076, _1306078, _1306080] : [-(hAPP(hAPP(c_Set_Oinsert(_1306076), _1306078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306076, tc_HOL_Obool)), _1306080), hAPP(hAPP(c_Set_Oinsert(_1306076), _1306078), c_Orderings_Obot__class_Obot(tc_fun(_1306076, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1306076), _1306078), _1306080))], (7464 ^ _779571) ^ [_903427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903427), _903427))], (42307 ^ _779571) ^ [_1598687, _1598689] : [-(hAPP(c_Relation_OField(_1598687), _1598689) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598687, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1598687, _1598687), _1598689)), hAPP(c_Relation_ORange(_1598687, _1598687), _1598689)))], (49931 ^ _779571) ^ [_1783767, _1783769] : [class_Orderings_Olinorder(_1783767), -(c_List_Olinorder__class_Osorted(_1783767, hAPP(hAPP(c_List_Olist_OCons(_1783767), _1783769), c_List_Olist_ONil(_1783767))))], (18933 ^ _779571) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (366 ^ _779571) ^ [_785072, _785074, _785076, _785078] : [-(c_Equiv__Relations_Oequivp(_785076, _785072)), c_Equiv__Relations_Oequivp(_785078, _785074), _785078 = _785076, _785074 = _785072], (31868 ^ _779571) ^ [_1358321, _1358323, _1358325, _1358327, _1358329] : [class_Groups_Ocomm__monoid__add(_1358321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358323), _1358325)), hBOOL(hAPP(hAPP(c_member(_1358323), _1358327), _1358325)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358323, _1358321), _1358329), _1358325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1358321), hAPP(_1358329, _1358327)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358323, _1358321), _1358329), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358323, tc_HOL_Obool)), _1358325), hAPP(hAPP(c_Set_Oinsert(_1358323), _1358327), c_Orderings_Obot__class_Obot(tc_fun(_1358323, tc_HOL_Obool)))))))], (25922 ^ _779571) ^ [_1233700, _1233702, _1233704, _1233706, _1233708, _1233710] : [class_Groups_Ocomm__monoid__add(_1233700), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233702, _1233700), hAPP(hAPP(c_COMBC(_1233702, tc_fun(_1233704, tc_HOL_Obool), _1233700), hAPP(hAPP(c_COMBB(tc_fun(_1233704, _1233700), tc_fun(tc_fun(_1233704, tc_HOL_Obool), _1233700), _1233702), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233704, _1233700)), _1233706)), _1233708)), _1233710) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233704, _1233700), hAPP(hAPP(c_COMBC(_1233704, tc_fun(_1233702, tc_HOL_Obool), _1233700), hAPP(hAPP(c_COMBB(tc_fun(_1233702, _1233700), tc_fun(tc_fun(_1233702, tc_HOL_Obool), _1233700), _1233704), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233702, _1233700)), hAPP(c_COMBC(_1233702, _1233704, _1233700), _1233706))), _1233710)), _1233708))], (13833 ^ _779571) ^ [_1012050, _1012052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012050, _1012052)), _1012050)))], (4744 ^ _779571) ^ [_852909, _852911, _852913, _852915] : [-(c_Wellfounded_Oacc(_852915, _852911) = c_Wellfounded_Oacc(_852913, _852909)), _852915 = _852913, _852911 = _852909], (43522 ^ _779571) ^ [_1628365, _1628367, _1628369] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628365, _1628365), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1628367)), _1628369) = hAPP(hAPP(c_Relation_Orel__comp(_1628365, _1628365, _1628365), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628365, _1628365), tc_HOL_Obool), _1628367), _1628369)), _1628369))], (15724 ^ _779571) ^ [_1046522, _1046524, _1046526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046522), _1046526)), _1046524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046524), _1046526))))], (33225 ^ _779571) ^ [_1385440, _1385442] : [class_Lattices_Olattice(_1385440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385440), _1385442)), -(_1385442 = c_Orderings_Obot__class_Obot(tc_fun(_1385440, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1385440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1385440), 33238 ^ [_1385440, _1385442]), 33239 ^ [_1385440, _1385442])), hAPP(hAPP(c_Set_Oinsert(_1385440), 33238 ^ [_1385440, _1385442]), hAPP(hAPP(c_Set_Oinsert(_1385440), 33239 ^ [_1385440, _1385442]), c_Orderings_Obot__class_Obot(tc_fun(_1385440, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1385440), c_Big__Operators_Olattice__class_OSup__fin(_1385440, _1385442)), _1385442)))], (48784 ^ _779571) ^ [_1757809, _1757811] : [_1757811 = c_List_Olist_ONil(_1757809), -(hAPP(c_List_Orotate1(_1757809), _1757811) = c_List_Olist_ONil(_1757809))], (16397 ^ _779571) ^ [_1059947, _1059949] : [class_Groups_Oordered__ab__group__add__abs(_1059947), -(hAPP(c_Groups_Oabs__class_Oabs(_1059947), hAPP(c_Groups_Oabs__class_Oabs(_1059947), _1059949)) = hAPP(c_Groups_Oabs__class_Oabs(_1059947), _1059949))], (38841 ^ _779571) ^ [_1509665, _1509667, _1509669, _1509671, _1509673] : [class_Groups_Ocomm__monoid__add(_1509665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509667), _1509669)), c_Fun_Oinj__on(_1509667, _1509667, _1509671, _1509669), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509667, _1509665), _1509673), hAPP(c_Set_Oimage(_1509667, _1509667, _1509671), _1509669)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509667, _1509665), hAPP(c_Fun_Ocomp(_1509667, _1509665, _1509667, _1509673), _1509671)), _1509669))], (17075 ^ _779571) ^ [_1072916, _1072918, _1072920] : [class_Int_Onumber__ring(_1072916), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1072916), hAPP(c_Int_Onumber__class_Onumber__of(_1072916), _1072918)), hAPP(c_Int_Onumber__class_Onumber__of(_1072916), _1072920)) = hAPP(c_Int_Onumber__class_Onumber__of(_1072916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072918), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1072920))))], (28423 ^ _779571) ^ [_1283999, _1284001, _1284003, _1284005, _1284007] : [c_Hoare__Mirabelle_Ohoare__derivs(_1283999, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1283999), tc_HOL_Obool)), _1284001), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1283999), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), hAPP(hAPP(c_COMBB(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1283999)), _1284003)), c_Com_Ocom_OBODY)), _1284005)), _1284007)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1283999), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), hAPP(hAPP(c_COMBB(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1283999)), _1284003)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1284005)), _1284007)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1283999, _1284001, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1283999), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), hAPP(hAPP(c_COMBB(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1283999, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1283999))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1283999)), _1284003)), c_Com_Ocom_OBODY)), _1284005)), _1284007)))], (26738 ^ _779571) ^ [_1249815, _1249817, _1249819, _1249821] : [class_Orderings_Oorder(_1249815), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1249815, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249817), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249819), _1249821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249815), hAPP(_1249817, _1249819)), hAPP(_1249817, _1249821))))], (37856 ^ _779571) ^ [_1489874, _1489876, _1489878] : [-(c_Relation_Orefl__on(_1489874, _1489876, _1489878)), 37860 ^ _779571 : [(37863 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1489874, _1489874, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1489874, tc_fun(_1489874, tc_HOL_Obool), tc_fun(_1489874, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1489874, tc_HOL_Obool), tc_fun(_1489874, tc_HOL_Obool)), _1489874), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1489874)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1489874), c_fconj), hAPP(hAPP(c_COMBC(_1489874, tc_fun(_1489874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1489874)), _1489876)))), hAPP(hAPP(c_COMBC(_1489874, tc_fun(_1489874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1489874)), _1489876))), 37859 ^ [_1489874, _1489876, _1489878]))], (37861 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1489874, _1489874)), 37859 ^ [_1489874, _1489876, _1489878]), _1489878)))]], 37865 ^ _779571 : [(37868 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1489874, _1489874)), hAPP(hAPP(c_Product__Type_OPair(_1489874, _1489874), 37864 ^ [_1489874, _1489876, _1489878]), 37864 ^ [_1489874, _1489876, _1489878])), _1489878))], (37866 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489874), 37864 ^ [_1489874, _1489876, _1489878]), _1489876)))]]], (7998 ^ _779571) ^ [_912296, _912298] : [hAPP(c_Option_Ooption_OSome(_912296), _912298) = c_Option_Ooption_ONone(_912296)], (11819 ^ _779571) ^ [_976221, _976223, _976225, _976227, _976229] : [class_Rings_Oordered__semiring(_976221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976221), _976223), _976225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976221), _976227), _976229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976221), c_Groups_Ozero__class_Ozero(_976221)), _976223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976221), c_Groups_Ozero__class_Ozero(_976221)), _976227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976221), _976223), _976227)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976221), _976225), _976229))))], (40252 ^ _779571) ^ [_1542981, _1542983, _1542985, _1542987, _1542989, _1542991] : [hBOOL(hAPP(hAPP(c_member(_1542981), _1542983), _1542985)), 40255 ^ _779571 : [(40262 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542987, tc_HOL_Obool)), _1542989), _1542991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542987, _1542981), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1542987, _1542981), _1542989), hAPP(c_COMBK(tc_fun(_1542981, tc_HOL_Obool), _1542987), _1542985))), hAPP(hAPP(c_Product__Type_OSigma(_1542987, _1542981), _1542991), hAPP(c_COMBK(tc_fun(_1542981, tc_HOL_Obool), _1542987), _1542985)))))], (40256 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542987, _1542981), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1542987, _1542981), _1542989), hAPP(c_COMBK(tc_fun(_1542981, tc_HOL_Obool), _1542987), _1542985))), hAPP(hAPP(c_Product__Type_OSigma(_1542987, _1542981), _1542991), hAPP(c_COMBK(tc_fun(_1542981, tc_HOL_Obool), _1542987), _1542985)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542987, tc_HOL_Obool)), _1542989), _1542991)))]]], (45283 ^ _779571) ^ [_1670551, _1670553] : [class_Complete__Lattice_Ocomplete__lattice(_1670551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670551), _1670553)), -(_1670553 = c_Orderings_Obot__class_Obot(tc_fun(_1670551, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1670551, _1670553) = c_Complete__Lattice_OInf__class_OInf(_1670551, _1670553))], (47751 ^ _779571) ^ [_1731839, _1731841, _1731843, _1731845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731839), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731841)), _1731843))), 47754 ^ _779571 : [(47761 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Onth(_1731841), _1731843), _1731839) = _1731845, -(hAPP(hAPP(c_List_Olist__update(_1731841, _1731843), _1731839), _1731845) = _1731843)], (47755 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1731841, _1731843), _1731839), _1731845) = _1731843, -(hAPP(hAPP(c_List_Onth(_1731841), _1731843), _1731839) = _1731845)]]], (14590 ^ _779571) ^ [_1025675, _1025677] : [class_Divides_Osemiring__div(_1025675), -(_1025677 = c_Groups_Ozero__class_Ozero(_1025675)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025675), _1025677), _1025677) = c_Groups_Oone__class_Oone(_1025675))], (6329 ^ _779571) ^ [_882256, _882258] : [hBOOL(hAPP(c_Com_OWT, _882256)), hBOOL(hAPP(c_Com_OWT, _882258)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_882256, _882258))))], (19251 ^ _779571) ^ [_1109702, _1109704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1109702)), c_Int_OBit1(_1109704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109702), _1109704)))], (36282 ^ _779571) ^ [_1453391, _1453393, _1453395, _1453397] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453391, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453391, tc_HOL_Obool)), _1453393), _1453395)), _1453397) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453391, tc_HOL_Obool)), _1453393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453391, tc_HOL_Obool)), _1453395), _1453397)))], (34316 ^ _779571) ^ [_1406940, _1406942, _1406944] : [class_Groups_Ocomm__monoid__add(_1406940), class_Groups_Ocomm__monoid__mult(_1406940), c_Nat__Transfer_Onat__set(_1406942), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1406940), _1406944), _1406942) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1406940), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1406940, tc_Nat_Onat), _1406944), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1406942)))], (19019 ^ _779571) ^ [_1105470, _1105472] : [class_Int_Onumber__ring(_1105470), class_Rings_Olinordered__idom(_1105470), 19026 ^ _779571 : [(19033 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1105472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105470), c_Groups_Oone__class_Oone(_1105470)), hAPP(c_Int_Onumber__class_Onumber__of(_1105470), _1105472))))], (19027 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105470), c_Groups_Oone__class_Oone(_1105470)), hAPP(c_Int_Onumber__class_Onumber__of(_1105470), _1105472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1105472)))]]], (41109 ^ _779571) ^ [_1562297, _1562299, _1562301] : [hBOOL(hAPP(_1562301, _1562299)), -(hBOOL(hAPP(hAPP(c_member(_1562297), _1562299), hAPP(c_Set_OCollect(_1562297), _1562301))))], (8732 ^ _779571) ^ [_923744, _923746] : [-(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, _923744)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923746))))], (36276 ^ _779571) ^ [_1453166, _1453168, _1453170, _1453172, _1453174] : [-(c_Map_Orestrict__map(_1453166, _1453168, c_Map_Orestrict__map(_1453166, _1453168, _1453170, _1453172), _1453174) = c_Map_Orestrict__map(_1453166, _1453168, _1453170, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453166, tc_HOL_Obool)), _1453172), _1453174)))], (21111 ^ _779571) ^ [_1142903, _1142905, _1142907, _1142909, _1142911] : [class_Fields_Ofield(_1142903), -(_1142905 = c_Groups_Ozero__class_Ozero(_1142903)), -(_1142907 = c_Groups_Ozero__class_Ozero(_1142903)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142903), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142903), _1142909), _1142905)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142903), _1142911), _1142907)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142903), _1142909), _1142907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142903), _1142911), _1142905))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142903), _1142905), _1142907)))], (51269 ^ _779571) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (42860 ^ _779571) ^ [_1611329, _1611331, _1611333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611329, _1611329)), _1611331), _1611333)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611329, _1611329)), _1611331), c_Transitive__Closure_Otrancl(_1611329, _1611333))))], (36318 ^ _779571) ^ [_1454196, _1454198] : [class_Lattices_Osemilattice__inf(_1454196), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454196), _1454198), _1454198) = _1454198)], (19887 ^ _779571) ^ [_1121151, _1121153, _1121155] : [class_Rings_Olinordered__idom(_1121151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121151), c_Groups_Ozero__class_Ozero(_1121151)), hAPP(hAPP(c_Power_Opower__class_Opower(_1121151), _1121153), 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)))), _1121155))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121151), c_Groups_Ozero__class_Ozero(_1121151)), _1121153)))], (45141 ^ _779571) ^ [_1667541, _1667543, _1667545] : [-(hAPP(c_Relation_ODomain(_1667541, _1667543), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1667541, _1667543), tc_HOL_Obool), _1667545)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1667541, _1667543), tc_HOL_Obool), tc_fun(_1667541, tc_HOL_Obool)), _1667545), c_Relation_ODomain(_1667541, _1667543)))], (49654 ^ _779571) ^ [_1776805, _1776807] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776805)), c_List_Obutlast(_1776805, _1776807)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776805)), _1776807)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42375 ^ _779571) ^ [_1600957, _1600959] : [c_Wellfounded_Owf(_1600957, _1600959), -(c_Wellfounded_Oacyclic(_1600957, _1600959))], (18599 ^ _779571) ^ [_1098593, _1098595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098593), c_Int_OPls))), 18602 ^ _779571 : [(18609 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098595), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098593)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098595)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098593), _1098595)))], (18603 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098595), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098593)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098595)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098593))]]], (30345 ^ _779571) ^ [_1323791, _1323793, _1323795] : [hAPP(hAPP(c_COMBC(_1323791, tc_fun(_1323791, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323791)), _1323793) = hAPP(hAPP(c_COMBC(_1323791, tc_fun(_1323791, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323791)), _1323795), -(_1323793 = _1323795)], (18401 ^ _779571) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (45559 ^ _779571) ^ [_1677062, _1677064] : [-(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)))), _1677062)) = 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)))), _1677064))), 45561 ^ _779571 : [(45564 ^ _779571) ^ [] : [45565 ^ _779571 : [(45568 ^ _779571) ^ [] : [hBOOL(hAPP(_1677064, 45560 ^ [_1677062, _1677064]))], (45566 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1677062, 45560 ^ [_1677062, _1677064])))]], 45569 ^ _779571 : [(45572 ^ _779571) ^ [] : [hBOOL(hAPP(_1677062, 45560 ^ [_1677062, _1677064]))], (45570 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1677064, 45560 ^ [_1677062, _1677064])))]]], (45562 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 45560 ^ [_1677062, _1677064])))]]], (38693 ^ _779571) ^ [_1506505, _1506507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506505), c_Orderings_Otop__class_Otop(tc_fun(_1506505, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1506505, _1506505, _1506507), c_Orderings_Otop__class_Otop(tc_fun(_1506505, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1506505, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1506505, _1506505, _1506507, c_Orderings_Otop__class_Otop(tc_fun(_1506505, tc_HOL_Obool))))], (18945 ^ _779571) ^ [_1104325, _1104327] : [class_Groups_Omonoid__mult(_1104325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104325), _1104327), 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(_1104325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104325), _1104327), _1104327)), _1104327))], (16989 ^ _779571) ^ [_1071378, _1071380, _1071382] : [class_Groups_Oordered__ab__group__add__abs(_1071378), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071378), hAPP(c_Groups_Oabs__class_Oabs(_1071378), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071378), _1071380), _1071382))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071378), hAPP(c_Groups_Oabs__class_Oabs(_1071378), _1071380)), hAPP(c_Groups_Oabs__class_Oabs(_1071378), _1071382)))))], (23521 ^ _779571) ^ [_1188055] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1188055), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2242 ^ _779571) ^ [_813330, _813332, _813334, _813336, _813338, _813340, _813342, _813344] : [-(c_Sum__Type_OSumr(_813344, _813340, _813336, _813332) = c_Sum__Type_OSumr(_813342, _813338, _813334, _813330)), _813344 = _813342, _813340 = _813338, _813336 = _813334, _813332 = _813330], (48966 ^ _779571) ^ [_1762171, _1762173] : [-(_1762171 = c_List_Olist_ONil(_1762173)), -(hBOOL(hAPP(hAPP(c_member(_1762173), hAPP(c_List_Ohd(_1762173), _1762171)), hAPP(c_List_Oset(_1762173), _1762171))))], (39128 ^ _779571) ^ [_1515816, _1515818, _1515820, _1515822, _1515824, _1515826] : [c_Fun_Oinj__on(_1515816, _1515818, _1515820, _1515822), hBOOL(hAPP(hAPP(c_member(_1515818), _1515824), hAPP(c_Set_Oimage(_1515816, _1515818, _1515820), _1515822))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515816, tc_HOL_Obool)), _1515822), _1515826)), -(hBOOL(hAPP(hAPP(c_member(_1515816), hAPP(c_Fun_Othe__inv__into(_1515816, _1515818, _1515822, _1515820), _1515824)), _1515826)))], (16268 ^ _779571) ^ [_1057671, _1057673, _1057675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057671)), 16274 ^ _779571 : [(16277 ^ _779571) ^ [] : [hBOOL(hAPP(_1057673, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16273 ^ [_1057671, _1057673, _1057675]), _1057671)))], (16275 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1057673, 16273 ^ [_1057671, _1057673, _1057675])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057675)), 16282 ^ _779571 : [(16283 ^ _779571) ^ [_1057960] : [hBOOL(hAPP(_1057673, _1057960)), -(hBOOL(hAPP(_1057673, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1057960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057675), _1057671)))))]]], (15214 ^ _779571) ^ [_1036884, _1036886, _1036888] : [class_Rings_Oring__1(_1036884), -(hAPP(c_Int_Oring__1__class_Oof__int(_1036884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036886), _1036888)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1036884), hAPP(c_Int_Oring__1__class_Oof__int(_1036884), _1036886)), hAPP(c_Int_Oring__1__class_Oof__int(_1036884), _1036888)))], (44710 ^ _779571) ^ [_1657057, _1657059, _1657061, _1657063, _1657065] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657057, tc_HOL_Obool)), _1657059), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657061, tc_fun(_1657057, tc_HOL_Obool)), _1657063), _1657065)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657061, tc_fun(_1657057, tc_HOL_Obool)), _1657063), hAPP(hAPP(c_COMBB(tc_fun(_1657057, tc_HOL_Obool), tc_fun(_1657057, tc_HOL_Obool), _1657061), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657057, tc_HOL_Obool)), _1657059)), _1657065)))], (50234 ^ _779571) ^ [_1789037, _1789039] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1789037, _1789039))))], (25870 ^ _779571) ^ [_1232706, _1232708, _1232710] : [class_Rings_Ocomm__ring__1(_1232706), 25873 ^ _779571 : [(25880 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232706), _1232708), _1232710)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232706), hAPP(c_Groups_Ouminus__class_Ouminus(_1232706), _1232708)), _1232710)))], (25874 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232706), hAPP(c_Groups_Ouminus__class_Ouminus(_1232706), _1232708)), _1232710)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232706), _1232708), _1232710)))]]], (18119 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (48546 ^ _779571) ^ [_1751183, _1751185, _1751187, _1751189, _1751191, _1751193] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751183), tc_List_Olist(_1751183))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751183), tc_List_Olist(_1751183)), hAPP(hAPP(c_List_Oappend(_1751183), _1751185), _1751191)), hAPP(hAPP(c_List_Oappend(_1751183), _1751187), _1751193))), c_List_Olistrel1(_1751183, _1751189)))), 48547 ^ _779571 : [(48554 ^ _779571) ^ [] : [_1751185 = _1751187, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751183), tc_List_Olist(_1751183))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751183), tc_List_Olist(_1751183)), _1751191), _1751193)), c_List_Olistrel1(_1751183, _1751189)))], (48548 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751183), tc_List_Olist(_1751183))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751183), tc_List_Olist(_1751183)), _1751185), _1751187)), c_List_Olistrel1(_1751183, _1751189))), _1751191 = _1751193]]], (3840 ^ _779571) ^ [_838811, _838813, _838815, _838817] : [-(c_Lazy__Sequence_Ohb__single(_838817, _838813) = c_Lazy__Sequence_Ohb__single(_838815, _838811)), _838817 = _838815, _838813 = _838811], (4452 ^ _779571) ^ [_848457, _848459, _848461, _848463, _848465, _848467] : [-(c_Set_Oimage(_848467, _848463, _848459) = c_Set_Oimage(_848465, _848461, _848457)), _848467 = _848465, _848463 = _848461, _848459 = _848457], (40871 ^ _779571) ^ [_1556935, _1556937, _1556939, _1556941, _1556943, _1556945, _1556947] : [-(hAPP(c_Product__Type_Osnd(_1556935, _1556937), hAPP(c_Product__Type_Omap__pair(_1556939, _1556935, _1556941, _1556937, _1556943, _1556945), _1556947)) = hAPP(_1556945, hAPP(c_Product__Type_Osnd(_1556939, _1556941), _1556947)))], (14818 ^ _779571) ^ [_1029321, _1029323, _1029325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029321), _1029323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029321), _1029325)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029323), _1029325))))], (14357 ^ _779571) ^ [_1021813, _1021815, _1021817] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021815), _1021817)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021813), _1021815)), _1021817))], (42845 ^ _779571) ^ [_1611023, _1611025] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611023, _1611023)), hAPP(hAPP(c_Product__Type_OPair(_1611023, _1611023), 42846 ^ [_1611023, _1611025]), 42846 ^ [_1611023, _1611025])), c_Transitive__Closure_Otrancl(_1611023, _1611025)))), -(c_Wellfounded_Oacyclic(_1611023, _1611025))], (25808 ^ _779571) ^ [_1231559, _1231561] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231559), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231561))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231559), _1231561)))], (28878 ^ _779571) ^ [_1293709, _1293711, _1293713, _1293715, _1293717, _1293719] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293709, tc_fun(_1293711, tc_HOL_Obool)), _1293713), hAPP(hAPP(c_COMBC(_1293709, tc_fun(_1293715, tc_fun(_1293711, tc_HOL_Obool)), tc_fun(_1293711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293715, tc_HOL_Obool), tc_fun(tc_fun(_1293715, tc_fun(_1293711, tc_HOL_Obool)), tc_fun(_1293711, tc_HOL_Obool)), _1293709), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293715, tc_fun(_1293711, tc_HOL_Obool))), _1293717)), _1293719)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293715, tc_fun(_1293711, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293709, tc_fun(_1293715, tc_HOL_Obool)), _1293713), _1293717)), _1293719))], (10014 ^ _779571) ^ [_946338, _946340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946338)), hAPP(c_Int_Onat, _946340))), 10017 ^ _779571 : [(10020 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946338), _946340)))], (10018 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946340)))]]], (26182 ^ _779571) ^ [_1239267, _1239269, _1239271, _1239273, _1239275] : [class_Divides_Osemiring__div(_1239267), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239267), _1239269), _1239271)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239267), _1239273), _1239275)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239267), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239267), _1239271), _1239269)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239267), _1239275), _1239273)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239267), _1239271), _1239275)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239267), _1239269), _1239273)))], (18741 ^ _779571) ^ [_1101119] : [c_Int_OMin = _1101119, -(c_Int_OMin = c_Int_OBit1(_1101119))], (47418 ^ _779571) ^ [_1723462, _1723464, _1723466, _1723468, _1723470, _1723472] : [-(hAPP(c_List_Olist_Olist__case(_1723462, _1723464, _1723466, _1723468), hAPP(hAPP(c_List_Olist_OCons(_1723464), _1723470), _1723472)) = hAPP(hAPP(_1723468, _1723470), _1723472))], (12207 ^ _779571) ^ [_983156, _983158, _983160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983156), _983158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983156), _983160))), 12210 ^ _779571 : [(12213 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983158), _983160)))], (12211 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983156)))]]], (48808 ^ _779571) ^ [_1758410, _1758412, _1758414, _1758416] : [-(hAPP(hAPP(c_List_Oappend(_1758410), _1758412), _1758414) = _1758416), _1758412 = hAPP(hAPP(c_List_Otake(_1758410), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758410)), _1758412)), _1758416), _1758414 = hAPP(hAPP(c_List_Odrop(_1758410), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758410)), _1758412)), _1758416)], (33025 ^ _779571) ^ [_1381862, _1381864, _1381866] : [class_Orderings_Olinorder(_1381862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381862), _1381864)), -(_1381864 = c_Orderings_Obot__class_Obot(tc_fun(_1381862, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1381862, hAPP(hAPP(c_Set_Oinsert(_1381862), _1381866), _1381864)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1381862), _1381866), c_Big__Operators_Olinorder__class_OMax(_1381862, _1381864)))], (2638 ^ _779571) ^ [_819564, _819566, _819568, _819570] : [-(c_Orderings_Oord_Omin(_819570, _819566) = c_Orderings_Oord_Omin(_819568, _819564)), _819570 = _819568, _819566 = _819564], (13164 ^ _779571) ^ [_999989, _999991] : [-(_999989 = hAPP(c_Int_Onat, _999991)), 13167 ^ _779571 : [(13170 ^ _779571) ^ [] : [_999991 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _999989)], (13168 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999991)))]], 13171 ^ _779571 : [(13174 ^ _779571) ^ [] : [_999989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13172 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999991))]]], (32765 ^ _779571) ^ [_1377314, _1377316, _1377318] : [class_Lattices_Olattice(_1377314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377314), _1377316)), hBOOL(hAPP(hAPP(c_member(_1377314), _1377318), _1377316)), 32776 ^ _779571 : [(32783 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377314, tc_HOL_Obool)), _1377316), hAPP(hAPP(c_Set_Oinsert(_1377314), _1377318), c_Orderings_Obot__class_Obot(tc_fun(_1377314, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377314, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1377314, _1377316) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1377314), _1377318), c_Big__Operators_Olattice__class_OSup__fin(_1377314, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377314, tc_HOL_Obool)), _1377316), hAPP(hAPP(c_Set_Oinsert(_1377314), _1377318), c_Orderings_Obot__class_Obot(tc_fun(_1377314, tc_HOL_Obool)))))))], (32777 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377314, tc_HOL_Obool)), _1377316), hAPP(hAPP(c_Set_Oinsert(_1377314), _1377318), c_Orderings_Obot__class_Obot(tc_fun(_1377314, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377314, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1377314, _1377316) = _1377318)]]], (6649 ^ _779571) ^ [_888357, _888359, _888361, _888363, _888365] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_888357, _888359, _888361)), _888363), _888365)), 6654 ^ _779571 : [(6657 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888359), _888363), _888365)))], (6655 ^ _779571) ^ [] : [-(hBOOL(hAPP(_888357, _888363)))]], 6658 ^ _779571 : [(6661 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888361), _888363), _888365)))], (6659 ^ _779571) ^ [] : [hBOOL(hAPP(_888357, _888363))]]], (24651 ^ _779571) ^ [_1210123] : [-(_1210123 = 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, _1210123)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1210123))))], (33615 ^ _779571) ^ [_1393258, _1393260, _1393262, _1393264] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1393258, _1393260)), c_Sum__Type_OPlus(_1393258, _1393260, _1393262, _1393264)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393258), _1393262)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393260), _1393264))], (34662 ^ _779571) ^ [_1414680, _1414682, _1414684, _1414686, _1414688, _1414690] : [-(hBOOL(hAPP(hAPP(c_member(_1414680), _1414682), _1414684))), -(c_Map_Orestrict__map(_1414680, _1414686, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414680, tc_Option_Ooption(_1414686)), _1414688), _1414682), _1414690), _1414684) = c_Map_Orestrict__map(_1414680, _1414686, _1414688, _1414684))], (48323 ^ _779571) ^ [_1745243, _1745245, _1745247, _1745249] : [-(c_Map_Omap__upds(_1745243, _1745245, _1745247, _1745249, c_List_Olist_ONil(_1745245)) = _1745247)], (18797 ^ _779571) ^ [_1102014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1102014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1102014)))], (42321 ^ _779571) ^ [_1599149, _1599151] : [c_Wellfounded_Owf(_1599149, _1599151), -(c_Wellfounded_OwfP(_1599149, hAPP(hAPP(c_COMBC(_1599149, tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_fun(_1599149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599149, tc_fun(tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_fun(_1599149, tc_HOL_Obool)), _1599149), c_COMBC(_1599149, tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599149, tc_prod(_1599149, _1599149)), tc_fun(_1599149, tc_fun(tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_HOL_Obool)), _1599149), hAPP(c_COMBB(tc_prod(_1599149, _1599149), tc_fun(tc_fun(tc_prod(_1599149, _1599149), tc_HOL_Obool), tc_HOL_Obool), _1599149), c_member(tc_prod(_1599149, _1599149)))), c_Product__Type_OPair(_1599149, _1599149)))), _1599151)))], (36286 ^ _779571) ^ [_1453548, _1453550] : [c_Nat__Transfer_Onat__set(_1453548), c_Nat__Transfer_Onat__set(_1453550), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1453548), _1453550)))], (9114 ^ _779571) ^ [_930574] : [class_Groups_Ogroup__add(_930574), -(hAPP(c_Groups_Ouminus__class_Ouminus(_930574), c_Groups_Ozero__class_Ozero(_930574)) = c_Groups_Ozero__class_Ozero(_930574))], (50182 ^ _779571) ^ [_1788216, _1788218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1788216), _1788218)), -(c_List_Oupt(_1788216, _1788218) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1788216), c_List_Oupt(hAPP(c_Nat_OSuc, _1788216), _1788218)))], (35488 ^ _779571) ^ [_1434113, _1434115, _1434117, _1434119, _1434121, _1434123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1434113, _1434115), tc_HOL_Obool)), _1434117), _1434119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434113, tc_HOL_Obool)), _1434121), _1434123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434115, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1434113, _1434115, _1434117), _1434121)), hAPP(c_Relation_OImage(_1434113, _1434115, _1434119), _1434123))))], (862 ^ _779571) ^ [_792886, _792888] : [-(class_Lattices_Oab__semigroup__idem__mult(_792886)), _792888 = _792886, class_Lattices_Oab__semigroup__idem__mult(_792888)], (38277 ^ _779571) ^ [_1498693, _1498695, _1498697, _1498699, _1498701, _1498703] : [c_Fun_Oinj__on(_1498693, _1498695, _1498697, _1498699), hAPP(_1498697, _1498701) = hAPP(_1498697, _1498703), hBOOL(hAPP(hAPP(c_member(_1498693), _1498701), _1498699)), hBOOL(hAPP(hAPP(c_member(_1498693), _1498703), _1498699)), -(_1498701 = _1498703)], (16493 ^ _779571) ^ [_1061725, _1061727, _1061729, _1061731] : [class_Rings_Ocomm__semiring__1(_1061725), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1061725), hAPP(hAPP(c_Power_Opower__class_Opower(_1061725), _1061727), _1061729)), _1061731) = hAPP(hAPP(c_Power_Opower__class_Opower(_1061725), _1061727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061729), _1061731)))], (16551 ^ _779571) ^ [_1062759, _1062761] : [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), _1062759)), _1062761))), _1062759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1062761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38785 ^ _779571) ^ [_1508544, _1508546, _1508548, _1508550, _1508552, _1508554] : [class_Groups_Ocomm__monoid__add(_1508544), c_Fun_Oinj__on(_1508546, _1508548, _1508550, _1508552), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1508548, _1508544), _1508554), hAPP(c_Set_Oimage(_1508546, _1508548, _1508550), _1508552)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1508546, _1508544), hAPP(c_Fun_Ocomp(_1508548, _1508544, _1508546, _1508554), _1508550)), _1508552))], (43317 ^ _779571) ^ [_1623175] : [-(hAPP(c_Relation_Oconverse(_1623175, _1623175), c_Relation_OId(_1623175)) = c_Relation_OId(_1623175))], (16899 ^ _779571) ^ [_1069393, _1069395, _1069397, _1069399] : [class_Int_Onumber__ring(_1069393), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069393), hAPP(c_Int_Onumber__class_Onumber__of(_1069393), _1069395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069393), hAPP(c_Int_Onumber__class_Onumber__of(_1069393), _1069397)), _1069399)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069393), hAPP(c_Int_Onumber__class_Onumber__of(_1069393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069395), _1069397))), _1069399))], (9516 ^ _779571) ^ [_937551, _937553] : [class_Groups_Oab__group__add(_937551), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937551), hAPP(c_Groups_Ouminus__class_Ouminus(_937551), _937553)), _937553) = c_Groups_Ozero__class_Ozero(_937551))], (20095 ^ _779571) ^ [_1125260, _1125262] : [c_Nat__Transfer_Ois__nat(_1125260), c_Nat__Transfer_Ois__nat(_1125262), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125260), _1125262)))], (42500 ^ _779571) ^ [_1603256, _1603258, _1603260] : [c_Wellfounded_OwfP(_1603256, hAPP(_1603258, 42501 ^ [_1603256, _1603258, _1603260])), 42508 ^ _779571 : [(42511 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603256, tc_HOL_Obool)), c_Predicate_ODomainP(_1603256, _1603256, hAPP(_1603258, 42506 ^ [_1603256, _1603258, _1603260]))), c_Predicate_ORangeP(_1603256, _1603256, hAPP(_1603258, 42507 ^ [_1603256, _1603258, _1603260]))) = c_Orderings_Obot__class_Obot(tc_fun(_1603256, tc_HOL_Obool))], (42509 ^ _779571) ^ [] : [hAPP(_1603258, 42506 ^ [_1603256, _1603258, _1603260]) = hAPP(_1603258, 42507 ^ [_1603256, _1603258, _1603260])]], -(c_Wellfounded_OwfP(_1603256, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1603260, tc_fun(_1603256, tc_fun(_1603256, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1603260, tc_HOL_Obool))), _1603258)))], (24121 ^ _779571) ^ [_1199700, _1199702, _1199704] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199700, tc_HOL_Obool)), _1199702) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199700, tc_HOL_Obool)), _1199704), -(_1199702 = _1199704)], (8292 ^ _779571) ^ [_917219, _917221] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917219)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917221)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _917219), _917221)))], (35498 ^ _779571) ^ [_1434352, _1434354, _1434356, _1434358, _1434360] : [-(hAPP(c_Relation_OImage(_1434352, _1434354, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1434352, _1434354), tc_HOL_Obool)), _1434356), _1434358)), _1434360) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434354, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1434352, _1434354, _1434356), _1434360)), hAPP(c_Relation_OImage(_1434352, _1434354, _1434358), _1434360)))], (25186 ^ _779571) ^ [_1221151, _1221153] : [class_Rings_Ocomm__semiring__1(_1221151), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221151), c_Groups_Ozero__class_Ozero(_1221151)), _1221153)), -(_1221153 = c_Groups_Ozero__class_Ozero(_1221151))], (2054 ^ _779571) ^ [_810096, _810098, _810100, _810102, _810104, _810106, _810108, _810110, _810112, _810114] : [-(c_Nitpick_Opair__box_Opair__box__size(_810114, _810110, _810106, _810102, _810098) = c_Nitpick_Opair__box_Opair__box__size(_810112, _810108, _810104, _810100, _810096)), _810114 = _810112, _810110 = _810108, _810106 = _810104, _810102 = _810100, _810098 = _810096], (44456 ^ _779571) ^ [_1649526, _1649528, _1649530, _1649532, _1649534] : [class_Complete__Lattice_Ocomplete__lattice(_1649526), class_Orderings_Olinorder(_1649526), 44463 ^ _779571 : [(44473 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1649526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649528, _1649526), _1649530), _1649532)), _1649534))), 44474 ^ _779571 : [(44475 ^ _779571) ^ [_1649874] : [hBOOL(hAPP(hAPP(c_member(_1649528), _1649874), _1649530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1649526), hAPP(_1649532, _1649874)), _1649534))]]], (44464 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1649526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649528, _1649526), _1649530), _1649532)), _1649534)), 44468 ^ _779571 : [(44471 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1649526), hAPP(_1649532, 44467 ^ [_1649526, _1649528, _1649530, _1649532, _1649534])), _1649534)))], (44469 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1649528), 44467 ^ [_1649526, _1649528, _1649530, _1649532, _1649534]), _1649530)))]]]]], (2842 ^ _779571) ^ [_822680, _822682, _822684, _822686, _822688, _822690, _822692, _822694, _822696, _822698, _822700, _822702, _822704, _822706] : [-(c_New__Random__Sequence_Opos__decr__bind(_822706, _822702, _822698, _822694, _822690, _822686, _822682) = c_New__Random__Sequence_Opos__decr__bind(_822704, _822700, _822696, _822692, _822688, _822684, _822680)), _822706 = _822704, _822702 = _822700, _822698 = _822696, _822694 = _822692, _822690 = _822688, _822686 = _822684, _822682 = _822680], (12948 ^ _779571) ^ [_996460, _996462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996462), _996460))))], (29114 ^ _779571) ^ [_1299314, _1299316, _1299318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299314), _1299316)), -(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)), _1299314)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299318), _1299316)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1299318), _1299314)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1299316), _1299314)))], (48431 ^ _779571) ^ [_1747825, _1747827, _1747829, _1747831] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1747825) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1747827), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1747825)), hAPP(hAPP(c_List_Olist_OCons(_1747827), _1747829), _1747831)) = hAPP(hAPP(c_List_Olist_OCons(_1747827), _1747829), hAPP(hAPP(c_List_Otake(_1747827), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1747825)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1747831)))], (3702 ^ _779571) ^ [_836596, _836598] : [_836598 = _836596, -(c_Wellfounded_Ofinite__psubset(_836598) = c_Wellfounded_Ofinite__psubset(_836596))], (30375 ^ _779571) ^ [_1324392, _1324394, _1324396] : [hBOOL(hAPP(_1324396, _1324394)), -(hBOOL(hAPP(hAPP(c_member(_1324392), _1324394), _1324396)))], (28250 ^ _779571) ^ [_1280839, _1280841] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1280839), _1280841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1280841), _1280839))], (23295 ^ _779571) ^ [_1184079, _1184081, _1184083] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184079, _1184079), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184081), _1184083))), -(_1184079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1184081 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (28156 ^ _779571) ^ [_1279005, _1279007] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279005, tc_HOL_Obool)), _1279007), _1279007) = _1279007)], (49243 ^ _779571) ^ [_1767805, _1767807, _1767809, _1767811, _1767813] : [hBOOL(hAPP(hAPP(c_member(_1767805), _1767807), hAPP(c_List_Oset(_1767805), _1767809))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767811), hAPP(_1767813, _1767807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767811), c_List_Olist_Olist__size(_1767805, _1767813, _1767809))))], (48120 ^ _779571) ^ [_1740294, _1740296, _1740298] : [_1740298 = c_List_Olist_ONil(_1740296), -(_1740294 = hAPP(hAPP(c_List_Oappend(_1740296), _1740298), _1740294))], (49058 ^ _779571) ^ [_1763836] : [-(c_List_Orotate(_1763836, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1763836)))], (1682 ^ _779571) ^ [_803364, _803366] : [-(class_Rings_Omult__zero(_803364)), _803366 = _803364, class_Rings_Omult__zero(_803366)], (43999 ^ _779571) ^ [_1640169, _1640171, _1640173, _1640175] : [class_Lattices_Osemilattice__inf(_1640169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640169), _1640171)), hBOOL(hAPP(hAPP(c_member(_1640169), _1640173), _1640171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1640169), hAPP(hAPP(c_Finite__Set_Ofold(_1640169, _1640169, c_Lattices_Osemilattice__inf__class_Oinf(_1640169)), _1640175), _1640171)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1640169), _1640173), _1640175))))], (45153 ^ _779571) ^ [_1667891, _1667893, _1667895] : [class_Complete__Lattice_Ocomplete__lattice(_1667891), hBOOL(hAPP(hAPP(c_member(_1667891), _1667893), _1667895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667891), _1667893), c_Complete__Lattice_OSup__class_OSup(_1667891, _1667895))))], (16659 ^ _779571) ^ [_1064646, _1064648, _1064650] : [class_Groups_Oordered__ab__group__add__abs(_1064646), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064646), hAPP(c_Groups_Oabs__class_Oabs(_1064646), _1064648)), hAPP(c_Groups_Oabs__class_Oabs(_1064646), _1064650))), hAPP(c_Groups_Oabs__class_Oabs(_1064646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064646), _1064648), _1064650)))))], (19667 ^ _779571) ^ [_1116955, _1116957] : [class_Rings_Olinordered__idom(_1116955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116955), hAPP(hAPP(c_Power_Opower__class_Opower(_1116955), _1116957), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1116955)))], (45131 ^ _779571) ^ [_1667148, _1667150, _1667152, _1667154] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667148, tc_fun(_1667150, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667148, tc_HOL_Obool), _1667152)), _1667154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1667148, tc_HOL_Obool), tc_fun(_1667150, tc_HOL_Obool)), _1667152), hAPP(hAPP(c_COMBC(tc_fun(_1667148, tc_HOL_Obool), tc_fun(_1667148, tc_fun(_1667150, tc_HOL_Obool)), tc_fun(_1667150, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667148, tc_fun(_1667150, tc_HOL_Obool))), _1667154)))], (19869 ^ _779571) ^ [_1120744] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1120744, 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, _1120744, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21561 ^ _779571) ^ [_1150770, _1150772, _1150774, _1150776] : [class_Fields_Olinordered__field(_1150770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150770), _1150772), c_Groups_Ozero__class_Ozero(_1150770))), 21568 ^ _779571 : [(21575 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150770), _1150776), _1150772)), _1150774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150770), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150770), _1150774), _1150772)), _1150776)))], (21569 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150770), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150770), _1150774), _1150772)), _1150776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150770), _1150776), _1150772)), _1150774)))]]], (19305 ^ _779571) ^ [_1110641, _1110643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110641), _1110643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110641)), c_Int_OBit0(_1110643))))], (24337 ^ _779571) ^ [_1203905] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1203905), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1203905)], (6432 ^ _779571) ^ [_884398, _884400, _884402, _884404, _884406, _884408, _884410, _884412, _884414, _884416, _884418] : [-(c_Com_Ocom_Ocom__rec(_884398, _884400, _884402, _884404, _884406, _884408, _884410, _884412, _884414, c_Com_Ocom_OAss(_884416, _884418)) = hAPP(hAPP(_884402, _884416), _884418))], (23227 ^ _779571) ^ [_1183065, _1183067, _1183069, _1183071, _1183073, _1183075] : [hAPP(_1183071, hAPP(c_Product__Type_Osnd(_1183069, _1183065), _1183073)) = hAPP(_1183075, hAPP(c_Product__Type_Osnd(_1183069, _1183065), _1183073)), -(hAPP(c_Product__Type_Oapsnd(_1183065, _1183067, _1183069, _1183071), _1183073) = hAPP(c_Product__Type_Oapsnd(_1183065, _1183067, _1183069, _1183075), _1183073))], (5330 ^ _779571) ^ [_861954, _861956] : [_861956 = _861954, -(c_Orderings_Oord__class_Oless__eq(_861956) = c_Orderings_Oord__class_Oless__eq(_861954))], (46464 ^ _779571) ^ [_1698589, _1698591, _1698593, _1698595, _1698597] : [class_Orderings_Olinorder(_1698589), -(hAPP(c_List_Oset(_1698591), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698591, _1698589, _1698593), _1698595), _1698597)) = hAPP(hAPP(c_Set_Oinsert(_1698591), _1698595), hAPP(c_List_Oset(_1698591), _1698597)))], (41732 ^ _779571) ^ [_1584270, _1584272, _1584274, _1584276] : [hAPP(hAPP(c_Relation_Orel__comp(_1584270, _1584270, _1584270), _1584272), _1584274) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1584270, _1584270), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584270, _1584270, _1584270), _1584272), _1584276) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1584270, _1584270), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1584270, _1584270, _1584270), _1584272), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584270, _1584270), tc_HOL_Obool)), _1584274), _1584276)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1584270, _1584270), tc_HOL_Obool)))], (6375 ^ _779571) ^ [_883175, _883177, _883179, _883181, _883183, _883185] : [c_Com_Ocom_OCall(_883175, _883177, _883179) = c_Com_Ocom_OCond(_883181, _883183, _883185)], (45907 ^ _779571) ^ [_1685001, _1685003, _1685005, _1685007, _1685009, _1685011] : [hAPP(_1685001, _1685003) = c_Option_Ooption_ONone(_1685005), -(c_Map_Omap__comp(_1685005, _1685007, _1685009, _1685011, _1685001, _1685003) = c_Option_Ooption_ONone(_1685007))], (43683 ^ _779571) ^ [_1632547, _1632549] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632547, _1632547)), hAPP(hAPP(c_Product__Type_OPair(_1632547, _1632547), 43684 ^ [_1632547, _1632549]), 43684 ^ [_1632547, _1632549])), c_Transitive__Closure_Otrancl(_1632547, _1632549)))), -(c_Wellfounded_Oacyclic(_1632547, _1632549))], (31494 ^ _779571) ^ [_1350695, _1350697] : [hAPP(c_Finite__Set_Ocard(_1350695), _1350697) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1350697 = c_Orderings_Obot__class_Obot(tc_fun(_1350695, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350695), _1350697))], (6438 ^ _779571) ^ [_884553, _884555] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _884553), _884555)), -(_884555 = _884553)], (18953 ^ _779571) ^ [_1104466] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1104466))) = 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)))), _1104466))], (23187 ^ _779571) ^ [_1182108, _1182110, _1182112] : [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), _1182108), _1182110))), -(hBOOL(hAPP(hAPP(_1182112, _1182108), _1182110))), 23194 ^ _779571 : [(23197 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23193 ^ [_1182108, _1182110, _1182112]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1182112, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23192 ^ [_1182108, _1182110, _1182112])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23193 ^ [_1182108, _1182110, _1182112]))))], (23203 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1182112, 23192 ^ [_1182108, _1182110, _1182112]), 23193 ^ [_1182108, _1182110, _1182112]))], (23195 ^ _779571) ^ [] : [-(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), 23192 ^ [_1182108, _1182110, _1182112]), 23193 ^ [_1182108, _1182110, _1182112]))))]]], (44934 ^ _779571) ^ [_1662569, _1662571, _1662573, _1662575] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1662569, tc_HOL_Obool), tc_fun(_1662571, tc_HOL_Obool)), _1662573), hAPP(hAPP(c_COMBC(tc_fun(_1662569, tc_HOL_Obool), tc_fun(_1662569, tc_fun(_1662571, tc_HOL_Obool)), tc_fun(_1662571, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662569, tc_fun(_1662571, tc_HOL_Obool))), _1662575)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662569, tc_fun(_1662571, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662569, tc_HOL_Obool), _1662573)), _1662575))], (29262 ^ _779571) ^ [_1302554, _1302556] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302554, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1302554, tc_HOL_Obool))), _1302556) = c_Orderings_Obot__class_Obot(tc_fun(_1302554, tc_HOL_Obool)))], (19821 ^ _779571) ^ [_1119649, _1119651, _1119653] : [class_Int_Onumber__ring(_1119649), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119649), _1119651), _1119653)), 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(_1119649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119649), hAPP(hAPP(c_Power_Opower__class_Opower(_1119649), _1119651), 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(_1119649), _1119653), 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(_1119649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119649), hAPP(c_Int_Onumber__class_Onumber__of(_1119649), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1119651)), _1119653)))], (40318 ^ _779571) ^ [_1544412, _1544414, _1544416] : [-(hAPP(c_Finite__Set_Ofold1(_1544412, _1544414), _1544416) = c_HOL_OThe(_1544412, c_Finite__Set_Ofold1Set(_1544412, _1544414, _1544416)))], (43274 ^ _779571) ^ [_1622107, _1622109] : [-(c_Relation_Oirrefl(_1622107, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1622107, _1622107), tc_HOL_Obool)), _1622109), c_Relation_OId(_1622107))))], (50584 ^ _779571) ^ [_1796341, _1796343] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796341)), c_List_Oconcat(_1796341, _1796343)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796341), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1796341))), _1796343)))], (1192 ^ _779571) ^ [_797239, _797241] : [-(class_Rings_Oring__1(_797239)), _797241 = _797239, class_Rings_Oring__1(_797241)], (31283 ^ _779571) ^ [_1345230] : [c_Nat__Transfer_Onat__set(_1345230), 31286 ^ _779571 : [(31293 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1345230))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1345230)))], (31287 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1345230)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1345230))))]]], (15242 ^ _779571) ^ [_1037484, _1037486, _1037488, _1037490, _1037492] : [class_Groups_Oordered__ab__group__add(_1037484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037484), _1037486), _1037488) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037484), _1037490), _1037492), 15249 ^ _779571 : [(15256 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037484), _1037490), _1037492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037484), _1037486), _1037488)))], (15250 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037484), _1037486), _1037488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037484), _1037490), _1037492)))]]], (782 ^ _779571) ^ [_791594, _791596, _791598, _791600, _791602, _791604, _791606, _791608, _791610, _791612, _791614, _791616] : [-(c_Finite__Set_Ofolding__image__simple__idem(_791614, _791610, _791606, _791602, _791598, _791594)), c_Finite__Set_Ofolding__image__simple__idem(_791616, _791612, _791608, _791604, _791600, _791596), _791616 = _791614, _791612 = _791610, _791608 = _791606, _791604 = _791602, _791600 = _791598, _791596 = _791594], (14524 ^ _779571) ^ [_1024540, _1024542] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024540, _1024542)), _1024542) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48924 ^ _779571) ^ [_1761435, _1761437, _1761439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761437)), _1761439))), -(hAPP(hAPP(c_List_Oappend(_1761437), hAPP(hAPP(c_List_Otake(_1761437), _1761435), _1761439)), hAPP(hAPP(c_List_Olist_OCons(_1761437), hAPP(c_List_Ohd(_1761437), hAPP(hAPP(c_List_Odrop(_1761437), _1761435), _1761439))), c_List_Olist_ONil(_1761437))) = hAPP(hAPP(c_List_Otake(_1761437), hAPP(c_Nat_OSuc, _1761435)), _1761439))], (12726 ^ _779571) ^ [_992396, _992398, _992400, _992402, _992404] : [class_Rings_Olinordered__semiring__strict(_992396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992396), _992398), _992400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992396), _992402), _992404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992396), c_Groups_Ozero__class_Ozero(_992396)), _992398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992396), c_Groups_Ozero__class_Ozero(_992396)), _992402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992396), _992398), _992402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992396), _992400), _992404))))], (45163 ^ _779571) ^ [_1668056] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668056, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1668056, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1668056, tc_HOL_Obool)))], (45876 ^ _779571) ^ [_1684273, _1684275, _1684277] : [c_Fun_Oinj__on(_1684273, _1684275, _1684277, c_Orderings_Otop__class_Otop(tc_fun(_1684273, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1684273), tc_List_Olist(_1684275), hAPP(c_List_Omap(_1684273, _1684275), _1684277), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1684273), tc_HOL_Obool))))], (46807 ^ _779571) ^ [_1708764, _1708766, _1708768, _1708770, _1708772, _1708774] : [-(hAPP(hAPP(c_List_Ozip(_1708764, _1708766), hAPP(hAPP(c_List_Olist_OCons(_1708764), _1708768), _1708770)), hAPP(hAPP(c_List_Olist_OCons(_1708766), _1708772), _1708774)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1708764, _1708766)), hAPP(hAPP(c_Product__Type_OPair(_1708764, _1708766), _1708768), _1708772)), hAPP(hAPP(c_List_Ozip(_1708764, _1708766), _1708770), _1708774)))], (9268 ^ _779571) ^ [_933144, _933146] : [class_Rings_Omult__zero(_933144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933144), c_Groups_Ozero__class_Ozero(_933144)), _933146) = c_Groups_Ozero__class_Ozero(_933144))], (44392 ^ _779571) ^ [_1647746, _1647748, _1647750, _1647752, _1647754, _1647756] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647746, tc_fun(_1647748, tc_HOL_Obool)), _1647750), _1647752), _1647754)), hBOOL(hAPP(hAPP(c_member(_1647746), _1647756), _1647750)), -(hBOOL(hAPP(hAPP(_1647752, _1647756), _1647754)))], (2832 ^ _779571) ^ [_822531, _822533, _822535, _822537] : [-(c_Nitpick_OAbs__Frac(_822537, _822533) = c_Nitpick_OAbs__Frac(_822535, _822531)), _822537 = _822535, _822533 = _822531], (22460 ^ _779571) ^ [_1167818, _1167820] : [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(_1167820))), 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), _1167818)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167820))))], (9066 ^ _779571) ^ [_929874] : [class_Rings_Osemiring__1(_929874), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929874), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_929874))], (28700 ^ _779571) ^ [_1289418, _1289420, _1289422] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1289418, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1289420)), _1289422) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289418, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1289418, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1289420)), _1289422)), hAPP(_1289422, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7744 ^ _779571) ^ [_907800, _907802, _907804, _907806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907800), _907802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _907804), _907802) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _907800), _907806), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907804), _907806)))], (49638 ^ _779571) ^ [_1776391, _1776393, _1776395, _1776397] : [49639 ^ _779571 : [(49642 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1776391), _1776393), hAPP(c_List_Oset(_1776391), c_List_Obutlast(_1776391, _1776397))))], (49640 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1776391), _1776393), hAPP(c_List_Oset(_1776391), c_List_Obutlast(_1776391, _1776395))))]], -(hBOOL(hAPP(hAPP(c_member(_1776391), _1776393), hAPP(c_List_Oset(_1776391), c_List_Obutlast(_1776391, hAPP(hAPP(c_List_Oappend(_1776391), _1776395), _1776397))))))], (38881 ^ _779571) ^ [_1510437, _1510439, _1510441, _1510443, _1510445] : [class_Groups_Ocomm__monoid__mult(_1510437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510439), _1510441)), c_Fun_Oinj__on(_1510439, _1510439, _1510443, _1510441), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1510439, _1510437), _1510445), hAPP(c_Set_Oimage(_1510439, _1510439, _1510443), _1510441)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1510439, _1510437), hAPP(c_Fun_Ocomp(_1510439, _1510437, _1510439, _1510445), _1510443)), _1510441))], (48536 ^ _779571) ^ [_1750856, _1750858, _1750860, _1750862] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750856), tc_List_Olist(_1750856))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750856), tc_List_Olist(_1750856)), _1750858), _1750860)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750856), c_List_Olistrel1(_1750856, _1750862)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750856)), _1750858) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750856)), _1750860))], (27970 ^ _779571) ^ [_1274884, _1274886, _1274888] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274884, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274884, tc_HOL_Obool)), _1274886), _1274888)), _1274888) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274884, tc_HOL_Obool)), _1274886), _1274888))], (37555 ^ _779571) ^ [_1481252, _1481254, _1481256, _1481258, _1481260, _1481262] : [c_Equiv__Relations_Ocongruent(_1481252, _1481254, _1481256, _1481258), hBOOL(hAPP(hAPP(c_member(tc_prod(_1481252, _1481252)), hAPP(hAPP(c_Product__Type_OPair(_1481252, _1481252), _1481260), _1481262)), _1481256)), -(hAPP(_1481258, _1481260) = hAPP(_1481258, _1481262))], (24945 ^ _779571) ^ [_1216490, _1216492, _1216494, _1216496, _1216498, _1216500, _1216502] : [hBOOL(hAPP(hAPP(_1216490, hAPP(c_Product__Type_Osnd(_1216492, _1216494), _1216496)), hAPP(c_Product__Type_Ofst(_1216492, _1216494), _1216496))), 24952 ^ _779571 : [(24955 ^ _779571) ^ [] : [hBOOL(hAPP(_1216498, hAPP(hAPP(_1216500, 24950 ^ [_1216490, _1216492, _1216494, _1216496, _1216498, _1216500, _1216502]), 24951 ^ [_1216490, _1216492, _1216494, _1216496, _1216498, _1216500, _1216502])))], (24953 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1216490, 24951 ^ [_1216490, _1216492, _1216494, _1216496, _1216498, _1216500, _1216502]), 24950 ^ [_1216490, _1216492, _1216494, _1216496, _1216498, _1216500, _1216502])))]], -(hBOOL(hAPP(_1216498, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1216492, _1216494, _1216502), _1216500), _1216496))))], (6249 ^ _779571) ^ [_880906, _880908, _880910, _880912, _880914, _880916] : [c_Com_Ocom_OLocal(_880906, _880908, _880910) = c_Com_Ocom_OLocal(_880912, _880914, _880916), 6252 ^ _779571 : [(6257 ^ _779571) ^ [] : [-(_880910 = _880916)], (6255 ^ _779571) ^ [] : [-(_880908 = _880914)], (6253 ^ _779571) ^ [] : [-(_880906 = _880912)]]], (17565 ^ _779571) ^ [_1081857, _1081859, _1081861, _1081863] : [class_Rings_Olinordered__semidom(_1081857), hAPP(hAPP(c_Power_Opower__class_Opower(_1081857), _1081859), hAPP(c_Nat_OSuc, _1081861)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1081857), _1081863), hAPP(c_Nat_OSuc, _1081861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081857), c_Groups_Ozero__class_Ozero(_1081857)), _1081859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081857), c_Groups_Ozero__class_Ozero(_1081857)), _1081863)), -(_1081859 = _1081863)], (22484 ^ _779571) ^ [_1168560, _1168562, _1168564] : [class_Int_Onumber__ring(_1168560), 22487 ^ _779571 : [(22494 ^ _779571) ^ [] : [-(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), _1168562)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168560), _1168564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168562))) = c_Groups_Oone__class_Oone(_1168560))], (22488 ^ _779571) ^ [] : [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), _1168562))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168560), _1168564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168562))) = hAPP(hAPP(c_HOL_OLet(_1168560, _1168560), hAPP(hAPP(c_Power_Opower__class_Opower(_1168560), _1168564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168562))), hAPP(hAPP(c_COMBS(_1168560, _1168560, _1168560), hAPP(hAPP(c_COMBB(_1168560, tc_fun(_1168560, _1168560), _1168560), c_Groups_Otimes__class_Otimes(_1168560)), hAPP(c_Groups_Otimes__class_Otimes(_1168560), _1168564))), c_COMBI(_1168560))))]]], (46470 ^ _779571) ^ [_1698726, _1698728, _1698730, _1698732, _1698734] : [class_Orderings_Olinorder(_1698726), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698728)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698728, _1698726, _1698730), _1698732), _1698734)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698728)), _1698734)))], (39769 ^ _779571) ^ [_1530182, _1530184, _1530186] : [_1530186 = hAPP(c_COMBK(tc_Option_Ooption(_1530184), _1530182), c_Option_Ooption_ONone(_1530184)), -(c_Map_Odom(_1530182, _1530184, _1530186) = c_Orderings_Obot__class_Obot(tc_fun(_1530182, tc_HOL_Obool)))], (2130 ^ _779571) ^ [_811412, _811414, _811416, _811418, _811420, _811422, _811424, _811426, _811428, _811430] : [-(c_Nitpick_Opair__box_Opair__box__case(_811430, _811426, _811422, _811418, _811414) = c_Nitpick_Opair__box_Opair__box__case(_811428, _811424, _811420, _811416, _811412)), _811430 = _811428, _811426 = _811424, _811422 = _811420, _811418 = _811416, _811414 = _811412], (23849 ^ _779571) ^ [_1194108, _1194110, _1194112, _1194114] : [-(_1194108 = _1194110), hAPP(c_Product__Type_Ofst(_1194112, _1194114), _1194108) = hAPP(c_Product__Type_Ofst(_1194112, _1194114), _1194110), hAPP(c_Product__Type_Osnd(_1194112, _1194114), _1194108) = hAPP(c_Product__Type_Osnd(_1194112, _1194114), _1194110)], (10662 ^ _779571) ^ [_957022, _957024] : [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), _957022), _957024))), 10665 ^ _779571 : [(10668 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _957024)))], (10666 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _957022)))]]], (1362 ^ _779571) ^ [_799364, _799366] : [-(class_Smallcheck_Osmall(_799364)), _799366 = _799364, class_Smallcheck_Osmall(_799366)], (1062 ^ _779571) ^ [_795614, _795616] : [-(class_Rings_Oordered__ring__abs(_795614)), _795616 = _795614, class_Rings_Oordered__ring__abs(_795616)], (42593 ^ _779571) ^ [_1605273, _1605275, _1605277] : [-(c_Hilbert__Choice_OEps(tc_prod(_1605273, _1605275), _1605277) = c_Hilbert__Choice_OEps(tc_prod(_1605273, _1605275), hAPP(c_Product__Type_Oprod_Oprod__case(_1605273, _1605275, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1605275, tc_prod(_1605273, _1605275)), tc_fun(_1605275, tc_HOL_Obool), _1605273), hAPP(c_COMBB(tc_prod(_1605273, _1605275), tc_HOL_Obool, _1605275), _1605277)), c_Product__Type_OPair(_1605273, _1605275)))))], (3170 ^ _779571) ^ [_828136, _828138, _828140, _828142] : [-(c_Com_Ocom_OSemi(_828142, _828138) = c_Com_Ocom_OSemi(_828140, _828136)), _828142 = _828140, _828138 = _828136], (23407 ^ _779571) ^ [_1185980, _1185982] : [23408 ^ _779571 : [(23411 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185982), _1185980))], (23409 ^ _779571) ^ [] : [_1185980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1185982, _1185980) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185982))], (24015 ^ _779571) ^ [_1197657, _1197659, _1197661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197657, tc_HOL_Obool)), _1197659), _1197661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197657, tc_HOL_Obool)), _1197659), _1197661))), -(_1197659 = _1197661)], (40799 ^ _779571) ^ [_1554946, _1554948, _1554950] : [class_Lattices_Oab__semigroup__idem__mult(_1554946), hAPP(_1554948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1554946), 40804 ^ [_1554946, _1554948, _1554950]), 40805 ^ [_1554946, _1554948, _1554950])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1554946), hAPP(_1554948, 40804 ^ [_1554946, _1554948, _1554950])), hAPP(_1554948, 40805 ^ [_1554946, _1554948, _1554950])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554946), _1554950)), -(_1554950 = c_Orderings_Obot__class_Obot(tc_fun(_1554946, tc_HOL_Obool))), -(hAPP(_1554948, hAPP(c_Finite__Set_Ofold1(_1554946, c_Groups_Otimes__class_Otimes(_1554946)), _1554950)) = hAPP(c_Finite__Set_Ofold1(_1554946, c_Groups_Otimes__class_Otimes(_1554946)), hAPP(c_Set_Oimage(_1554946, _1554946, _1554948), _1554950)))], (25952 ^ _779571) ^ [_1234635, _1234637, _1234639, _1234641, _1234643, _1234645, _1234647] : [class_Rings_Osemiring__0(_1234635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234635), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234637, _1234635), _1234639), _1234641)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234643, _1234635), _1234645), _1234647)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234637, _1234635), hAPP(hAPP(c_COMBC(_1234637, tc_fun(_1234643, tc_HOL_Obool), _1234635), hAPP(hAPP(c_COMBB(tc_fun(_1234643, _1234635), tc_fun(tc_fun(_1234643, tc_HOL_Obool), _1234635), _1234637), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234643, _1234635)), hAPP(hAPP(c_COMBC(_1234637, tc_fun(_1234643, _1234635), tc_fun(_1234643, _1234635)), hAPP(hAPP(c_COMBB(tc_fun(_1234635, _1234635), tc_fun(tc_fun(_1234643, _1234635), tc_fun(_1234643, _1234635)), _1234637), c_COMBB(_1234635, _1234635, _1234643)), hAPP(hAPP(c_COMBB(_1234635, tc_fun(_1234635, _1234635), _1234637), c_Groups_Otimes__class_Otimes(_1234635)), _1234639))), _1234645))), _1234647)), _1234641))], (9848 ^ _779571) ^ [_943563, _943565, _943567] : [class_Rings_Olinordered__ring__strict(_943563), 9851 ^ _779571 : [(9860 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943563), _943565), _943565)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943563), _943567), _943567)) = c_Groups_Ozero__class_Ozero(_943563)), _943565 = c_Groups_Ozero__class_Ozero(_943563), _943567 = c_Groups_Ozero__class_Ozero(_943563)], (9852 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943563), _943565), _943565)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943563), _943567), _943567)) = c_Groups_Ozero__class_Ozero(_943563), 9855 ^ _779571 : [(9858 ^ _779571) ^ [] : [-(_943567 = c_Groups_Ozero__class_Ozero(_943563))], (9856 ^ _779571) ^ [] : [-(_943565 = c_Groups_Ozero__class_Ozero(_943563))]]]]], (16405 ^ _779571) ^ [_1060088, _1060090, _1060092] : [class_Groups_Oordered__ab__group__add__abs(_1060088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060088), hAPP(c_Groups_Oabs__class_Oabs(_1060088), _1060090)), _1060092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060088), _1060090), _1060092)))], (39779 ^ _779571) ^ [_1530395, _1530397, _1530399, _1530401, _1530403] : [hAPP(_1530395, _1530397) = c_Option_Ooption_ONone(_1530399), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530401, tc_HOL_Obool)), c_Map_Odom(_1530401, _1530399, _1530395)), hAPP(hAPP(c_Set_Oinsert(_1530401), _1530397), _1530403)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530401, tc_HOL_Obool)), c_Map_Odom(_1530401, _1530399, _1530395)), _1530403))], (50918 ^ _779571) ^ [_1804744, _1804746, _1804748, _1804750] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1804744), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1804744))), _1804746))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1804748), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804744))), c_List_Otranspose(_1804744, _1804746)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1804750), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804744))), hAPP(c_List_Ofilter(tc_List_Olist(_1804744), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1804744)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1804748)), c_Nat_Osize__class_Osize(tc_List_Olist(_1804744)))), _1804746)))), -(hAPP(hAPP(c_List_Onth(_1804744), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1804744)), c_List_Otranspose(_1804744, _1804746)), _1804748)), _1804750) = hAPP(hAPP(c_List_Onth(_1804744), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1804744)), _1804746), _1804750)), _1804748))], (31082 ^ _779571) ^ [_1339306, _1339308] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1339306)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1339308))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1339306), _1339308)))], (9302 ^ _779571) ^ [_933640, _933642, _933644] : [class_Rings_Ono__zero__divisors(_933640), -(_933642 = c_Groups_Ozero__class_Ozero(_933640)), -(_933644 = c_Groups_Ozero__class_Ozero(_933640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933640), _933642), _933644) = c_Groups_Ozero__class_Ozero(_933640)], (46498 ^ _779571) ^ [_1699317] : [class_Orderings_Olinorder(_1699317), -(c_Finite__Set_Ofun__left__comm(_1699317, tc_List_Olist(_1699317), c_List_Olinorder__class_Oinsort__key(_1699317, _1699317, c_COMBI(_1699317))))], (49842 ^ _779571) ^ [_1780887, _1780889, _1780891, _1780893] : [-(c_List_Opartition(_1780887, _1780889, hAPP(hAPP(c_List_Olist_OCons(_1780887), _1780891), _1780893)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1780887), tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1780887), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1780887), tc_fun(tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), tc_fun(tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), tc_List_Olist(_1780887)), c_COMBS(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_fun(tc_List_Olist(_1780887), tc_fun(tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), tc_List_Olist(_1780887)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_fun(tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_List_Olist(_1780887)), hAPP(c_If(tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), hAPP(_1780889, _1780891)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1780887), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_List_Olist(_1780887)), c_Product__Type_OPair(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), hAPP(c_List_Olist_OCons(_1780887), _1780891))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1780887), tc_fun(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887))), tc_fun(tc_fun(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_fun(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), tc_List_Olist(_1780887)), c_COMBB(tc_List_Olist(_1780887), tc_prod(tc_List_Olist(_1780887), tc_List_Olist(_1780887)), tc_List_Olist(_1780887))), c_Product__Type_OPair(tc_List_Olist(_1780887), tc_List_Olist(_1780887)))), hAPP(c_List_Olist_OCons(_1780887), _1780891)))), c_List_Opartition(_1780887, _1780889, _1780893)))], (33595 ^ _779571) ^ [_1392835, _1392837, _1392839, _1392841] : [-(c_Sum__Type_OPlus(_1392835, _1392837, _1392839, _1392841) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1392835, _1392837), tc_HOL_Obool))), _1392839 = c_Orderings_Obot__class_Obot(tc_fun(_1392835, tc_HOL_Obool)), _1392841 = c_Orderings_Obot__class_Obot(tc_fun(_1392837, tc_HOL_Obool))], (45143 ^ _779571) ^ [_1667604, _1667606, _1667608] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667604, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1667604, tc_HOL_Obool)), _1667606), _1667608)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667604, tc_HOL_Obool)), _1667606), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667604, tc_HOL_Obool), _1667608)))], (3388 ^ _779571) ^ [_831621, _831623, _831625, _831627] : [-(c_Predicate_OPowp(_831627, _831623) = c_Predicate_OPowp(_831625, _831621)), _831627 = _831625, _831623 = _831621], (6782 ^ _779571) ^ [_891224, _891226] : [c_Com_Ocom_OAss(_891224, _891226) = c_Com_Ocom_OSKIP], (45874 ^ _779571) ^ [_1684218, _1684220, _1684222, _1684224, _1684226, _1684228] : [-(c_Map_Omap__comp(_1684218, _1684220, _1684222, _1684224, _1684226, _1684228) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1684220), _1684218, c_Option_Ooption_ONone(_1684220), _1684224), hAPP(_1684226, _1684228)))], (46761 ^ _779571) ^ [_1706908, _1706910, _1706912, _1706914, _1706916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706908), tc_List_Olist(_1706908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706908), tc_List_Olist(_1706908)), _1706910), _1706912)), c_List_Olistrel(_1706908, c_Transitive__Closure_Ortrancl(_1706908, _1706914)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706908), tc_List_Olist(_1706908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706908), tc_List_Olist(_1706908)), _1706912), _1706916)), c_List_Olistrel(_1706908, c_Transitive__Closure_Ortrancl(_1706908, _1706914)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706908), tc_List_Olist(_1706908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706908), tc_List_Olist(_1706908)), _1706910), _1706916)), c_List_Olistrel(_1706908, c_Transitive__Closure_Ortrancl(_1706908, _1706914)))))], (20081 ^ _779571) ^ [_1124944, _1124946, _1124948, _1124950] : [class_Fields_Ofield__inverse__zero(_1124944), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124944), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124944), _1124946), _1124948)), _1124950) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124944), hAPP(hAPP(c_Power_Opower__class_Opower(_1124944), _1124946), _1124950)), hAPP(hAPP(c_Power_Opower__class_Opower(_1124944), _1124948), _1124950)))], (51261 ^ _779571) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (34023 ^ _779571) ^ [_1401052, _1401054, _1401056, _1401058] : [c_Finite__Set_Ofolding__one(_1401052, _1401054, _1401056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401052), _1401058)), -(_1401058 = c_Orderings_Obot__class_Obot(tc_fun(_1401052, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1401052), hAPP(hAPP(_1401054, 34036 ^ [_1401052, _1401054, _1401056, _1401058]), 34037 ^ [_1401052, _1401054, _1401056, _1401058])), hAPP(hAPP(c_Set_Oinsert(_1401052), 34036 ^ [_1401052, _1401054, _1401056, _1401058]), hAPP(hAPP(c_Set_Oinsert(_1401052), 34037 ^ [_1401052, _1401054, _1401056, _1401058]), c_Orderings_Obot__class_Obot(tc_fun(_1401052, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1401052), hAPP(_1401056, _1401058)), _1401058)))], (31558 ^ _779571) ^ [_1351803, _1351805, _1351807, _1351809] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351803), _1351805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1351807), hAPP(c_Set_Oimage(_1351803, _1351807, _1351809), _1351805))), hAPP(c_Finite__Set_Ocard(_1351803), _1351805))))], (48778 ^ _779571) ^ [_1757718, _1757720] : [hAPP(c_List_Orotate1(_1757718), _1757720) = c_List_Olist_ONil(_1757718), -(_1757720 = c_List_Olist_ONil(_1757718))], (37355 ^ _779571) ^ [_1477213, _1477215, _1477217] : [class_Orderings_Olinorder(_1477213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477213), _1477215)), -(_1477215 = c_Orderings_Obot__class_Obot(tc_fun(_1477213, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477213), _1477217)), -(_1477217 = c_Orderings_Obot__class_Obot(tc_fun(_1477213, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477213, tc_HOL_Obool)), _1477215), _1477217) = c_Orderings_Obot__class_Obot(tc_fun(_1477213, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1477213, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477213, tc_HOL_Obool)), _1477215), _1477217)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1477213), c_Big__Operators_Olinorder__class_OMin(_1477213, _1477215)), c_Big__Operators_Olinorder__class_OMin(_1477213, _1477217)))], (18895 ^ _779571) ^ [_1103621] : [class_Int_Onumber__ring(_1103621), -(hAPP(c_Int_Onumber__class_Onumber__of(_1103621), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1103621))], (51585 ^ _779571) ^ [_1813370, _1813372] : [_1813370 = _1813372, -(hBOOL(hAPP(hAPP(c_fequal, _1813370), _1813372)))], (29900 ^ _779571) ^ [_1314510, _1314512, _1314514] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314510, _1314512, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314510)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314510), _1314514), c_Com_Ocom_OSKIP), _1314514)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314510), tc_HOL_Obool)))))], (13990 ^ _779571) ^ [_1014659, _1014661, _1014663] : [hBOOL(hAPP(_1014659, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1014661, _1014663))), 13993 ^ _779571 : [(14018 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014663), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14021 ^ _779571 : [(14022 ^ _779571) ^ [_1015281, _1015283] : [-(hBOOL(hAPP(_1014659, _1015281))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014663), _1015281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015281), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1014661 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014663), _1015283)), _1015281)]]], (14000 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014663)), 14003 ^ _779571 : [(14004 ^ _779571) ^ [_1014989, _1014991] : [-(hBOOL(hAPP(_1014659, _1014989))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014989), _1014663)), _1014661 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014663), _1014991)), _1014989)]]], (13994 ^ _779571) ^ [] : [_1014663 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1014659, _1014661)))]]], (46076 ^ _779571) ^ [_1689117, _1689119, _1689121, _1689123] : [_1689123 = c_Option_Ooption_ONone(_1689117), -(hAPP(hAPP(c_Option_Omap(_1689117, _1689119), _1689121), _1689123) = c_Option_Ooption_ONone(_1689119))], (45973 ^ _779571) ^ [_1686458, _1686460, _1686462, _1686464, _1686466] : [-(c_Map_Omap__comp(_1686458, _1686460, _1686462, hAPP(c_COMBK(tc_Option_Ooption(_1686460), _1686458), c_Option_Ooption_ONone(_1686460)), _1686464, _1686466) = c_Option_Ooption_ONone(_1686460))], (24899 ^ _779571) ^ [_1215246, _1215248, _1215250, _1215252, _1215254, _1215256] : [hBOOL(hAPP(hAPP(_1215246, _1215248), _1215250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215252, tc_fun(_1215254, tc_HOL_Obool))), _1215246), _1215256)), -(hBOOL(hAPP(hAPP(_1215256, _1215248), _1215250)))], (23891 ^ _779571) ^ [_1194976, _1194978] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1194976, _1194978) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1194976, _1194978)))], (51417 ^ _779571) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (8130 ^ _779571) ^ [_914284] : [_914284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914284) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (49366 ^ _779571) ^ [_1770924, _1770926, _1770928] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770924)), _1770926), c_List_Olists(_1770924, c_Wellfounded_Oacc(_1770924, _1770928)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770924)), _1770926), c_Wellfounded_Oacc(tc_List_Olist(_1770924), c_List_Olistrel1(_1770924, _1770928)))))], (14072 ^ _779571) ^ [_1016248, _1016250, _1016252, _1016254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016250), _1016252)), -(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), _1016252), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016254, _1016248))), _1016250))))], (18729 ^ _779571) ^ [_1100955] : [c_Int_OPls = c_Int_OBit1(_1100955)], (13246 ^ _779571) ^ [_1001291, _1001293] : [class_Rings_Olinordered__idom(_1001291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001291), c_Groups_Ozero__class_Ozero(_1001291)), _1001293)), -(c_Groups_Osgn__class_Osgn(_1001291, _1001293) = c_Groups_Oone__class_Oone(_1001291))], (45977 ^ _779571) ^ [_1686585, _1686587, _1686589, _1686591, _1686593, _1686595] : [c_Map_Omap__comp(_1686585, _1686587, _1686589, _1686591, _1686593, _1686595) = c_Option_Ooption_ONone(_1686587), -(hAPP(_1686593, _1686595) = c_Option_Ooption_ONone(_1686585)), 45985 ^ _779571 : [(45988 ^ _779571) ^ [] : [-(hAPP(_1686591, 45984 ^ [_1686585, _1686587, _1686589, _1686591, _1686593, _1686595]) = c_Option_Ooption_ONone(_1686587))], (45986 ^ _779571) ^ [] : [-(hAPP(_1686593, _1686595) = hAPP(c_Option_Ooption_OSome(_1686585), 45984 ^ [_1686585, _1686587, _1686589, _1686591, _1686593, _1686595]))]]], (14345 ^ _779571) ^ [_1021585, _1021587, _1021589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1021585), _1021587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021585), _1021589)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021587), _1021589))))], (32973 ^ _779571) ^ [_1381037, _1381039] : [class_Int_Oring__char__0(_1381037), hBOOL(hAPP(hAPP(c_member(_1381037), _1381039), c_Int_Oring__1__class_OInts(_1381037))), 32980 ^ _779571 : [(32987 ^ _779571) ^ [] : [_1381039 = c_Groups_Ozero__class_Ozero(_1381037), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1381037), _1381039), _1381039) = c_Groups_Ozero__class_Ozero(_1381037))], (32981 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1381037), _1381039), _1381039) = c_Groups_Ozero__class_Ozero(_1381037), -(_1381039 = c_Groups_Ozero__class_Ozero(_1381037))]]], (29264 ^ _779571) ^ [_1302600, _1302602] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302600, tc_HOL_Obool)), _1302602), c_Orderings_Obot__class_Obot(tc_fun(_1302600, tc_HOL_Obool))) = _1302602)], (15872 ^ _779571) ^ [_1049357, _1049359] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049357), _1049359)), _1049359) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049357), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1049357, _1049359)))], (42213 ^ _779571) ^ [_1596637, _1596639] : [c_Wellfounded_Owf(_1596637, hAPP(c_Set_OCollect(tc_prod(_1596637, _1596637)), hAPP(c_Product__Type_Oprod_Oprod__case(_1596637, _1596637, tc_HOL_Obool), _1596639))), -(c_Wellfounded_OwfP(_1596637, _1596639))], (29774 ^ _779571) ^ [_1311934, _1311936] : [_1311934 = _1311936, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1311934, _1311936) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1311934), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (50776 ^ _779571) ^ [_1800430, _1800432] : [-(_1800430 = c_List_Olist_ONil(_1800432)), -(c_List_Olast(_1800432, hAPP(c_List_Orev(_1800432), _1800430)) = hAPP(c_List_Ohd(_1800432), _1800430))], (14622 ^ _779571) ^ [_1026180, _1026182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1026180)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026180), _1026182)), _1026180) = _1026182)], (29984 ^ _779571) ^ [_1316783, _1316785, _1316787, _1316789, _1316791, _1316793, _1316795, _1316797] : [hBOOL(hAPP(hAPP(c_member(_1316783), _1316785), _1316787)), hBOOL(hAPP(hAPP(hAPP(_1316789, _1316785), _1316791), _1316793)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1316783, tc_fun(_1316795, tc_fun(_1316797, tc_HOL_Obool))), _1316787), _1316789), _1316791), _1316793)))], (40168 ^ _779571) ^ [_1540822, _1540824, _1540826] : [-(hAPP(c_Finite__Set_Ofold1(_1540822, _1540824), hAPP(hAPP(c_Set_Oinsert(_1540822), _1540826), c_Orderings_Obot__class_Obot(tc_fun(_1540822, tc_HOL_Obool)))) = _1540826)], (46292 ^ _779571) ^ [_1694111] : [c_List_Onat__list(_1694111), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1694111)))], (41211 ^ _779571) ^ [_1564503, _1564505, _1564507, _1564509] : [-(hAPP(c_Set_Ovimage(_1564503, _1564505, _1564507), _1564509) = hAPP(c_Set_OCollect(_1564503), hAPP(hAPP(c_COMBC(_1564503, tc_fun(_1564505, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1564505, tc_fun(tc_fun(_1564505, tc_HOL_Obool), tc_HOL_Obool), _1564503), c_member(_1564505)), _1564507)), _1564509)))], (28052 ^ _779571) ^ [_1276729, _1276731, _1276733] : [class_Lattices_Osemilattice__sup(_1276729), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276729), _1276731), _1276733) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276729), _1276733), _1276731))], (9428 ^ _779571) ^ [_936086] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936086)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936086))], (36354 ^ _779571) ^ [_1454830, _1454832, _1454834] : [class_Lattices_Olattice(_1454830), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454830), _1454832), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454830), _1454832), _1454834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454830), _1454832), _1454834))], (35671 ^ _779571) ^ [_1439117, _1439119, _1439121, _1439123, _1439125, _1439127, _1439129, _1439131, _1439133, _1439135, _1439137] : [c_Finite__Set_Ofolding(_1439117, _1439119, _1439121, _1439123), -(hAPP(c_Fun_Ocomp(_1439125, _1439127, _1439129, _1439131), hAPP(c_Fun_Ocomp(_1439133, _1439125, _1439129, _1439135), _1439137)) = hAPP(c_Fun_Ocomp(_1439133, _1439127, _1439129, hAPP(c_Fun_Ocomp(_1439125, _1439127, _1439133, _1439131), _1439135)), _1439137))], (51259 ^ _779571) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (42341 ^ _779571) ^ [_1600261, _1600263, _1600265, _1600267] : [hBOOL(hAPP(hAPP(c_member(_1600261), _1600263), hAPP(c_Relation_ODomain(_1600261, _1600265), _1600267))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600261, _1600265)), hAPP(hAPP(c_Product__Type_OPair(_1600261, _1600265), _1600263), 42344 ^ [_1600261, _1600263, _1600265, _1600267])), _1600267)))], (9554 ^ _779571) ^ [_938158, _938160] : [class_Rings_Olinordered__ring(_938158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938158), _938160), _938160)), c_Groups_Ozero__class_Ozero(_938158)))], (18371 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17361 ^ _779571) ^ [_1078072, _1078074, _1078076, _1078078] : [class_Groups_Ocomm__monoid__mult(_1078072), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078072), _1078074), _1078076)), _1078078) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078072), hAPP(hAPP(c_Power_Opower__class_Opower(_1078072), _1078074), _1078078)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078072), _1078076), _1078078)))], (14734 ^ _779571) ^ [_1027935, _1027937, _1027939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027937), _1027939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027935), _1027939)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027935), _1027937))))], (38994 ^ _779571) ^ [_1513281, _1513283, _1513285, _1513287, _1513289] : [c_Typedef_Otype__definition(_1513281, _1513283, _1513285, _1513287, _1513289), -(hAPP(c_Set_Oimage(_1513283, _1513281, _1513287), _1513289) = c_Orderings_Otop__class_Otop(tc_fun(_1513281, tc_HOL_Obool)))], (34055 ^ _779571) ^ [_1401847, _1401849, _1401851, _1401853, _1401855, _1401857] : [class_Groups_Ocomm__monoid__mult(_1401847), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401849), _1401851)), 34062 ^ _779571 : [(34069 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401849), _1401853), _1401851))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401849, _1401847), hAPP(hAPP(c_COMBC(_1401849, _1401847, _1401847), hAPP(hAPP(c_COMBS(_1401849, _1401847, tc_fun(_1401847, _1401847)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401847, tc_fun(_1401847, _1401847)), _1401849), c_If(_1401847)), hAPP(hAPP(c_COMBC(_1401849, _1401849, tc_HOL_Obool), c_fequal), _1401853))), _1401855)), _1401857)), _1401851) = hAPP(hAPP(c_Power_Opower__class_Opower(_1401847), _1401857), hAPP(c_Finite__Set_Ocard(_1401849), _1401851)))], (34063 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1401849), _1401853), _1401851)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401849, _1401847), hAPP(hAPP(c_COMBC(_1401849, _1401847, _1401847), hAPP(hAPP(c_COMBS(_1401849, _1401847, tc_fun(_1401847, _1401847)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401847, tc_fun(_1401847, _1401847)), _1401849), c_If(_1401847)), hAPP(hAPP(c_COMBC(_1401849, _1401849, tc_HOL_Obool), c_fequal), _1401853))), _1401855)), _1401857)), _1401851) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401847), hAPP(_1401855, _1401853)), hAPP(hAPP(c_Power_Opower__class_Opower(_1401847), _1401857), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1401849), _1401851)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (43554 ^ _779571) ^ [_1629082, _1629084, _1629086, _1629088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629082, _1629082)), hAPP(hAPP(c_Product__Type_OPair(_1629082, _1629082), _1629084), _1629086)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629082, _1629082), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629088))), -(_1629084 = _1629086)], (27526 ^ _779571) ^ [_1266172, _1266174, _1266176] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1266172), _1266174), _1266176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1266172), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1266172, tc_Int_Oint), _1266174), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1266176))), class_Groups_Ocomm__monoid__add(_1266172), class_Groups_Ocomm__monoid__mult(_1266172)], (12578 ^ _779571) ^ [_989596, _989598, _989600, _989602] : [class_Groups_Oordered__comm__monoid__add(_989596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989596), c_Groups_Ozero__class_Ozero(_989596)), _989598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989596), _989600), _989602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989596), _989600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989596), _989598), _989602))))], (48182 ^ _779571) ^ [_1741464, _1741466, _1741468] : [-(hBOOL(hAPP(c_List_Odistinct(_1741464), hAPP(hAPP(c_List_Oappend(_1741464), _1741466), _1741468)))), hBOOL(hAPP(c_List_Odistinct(_1741464), _1741466)), hBOOL(hAPP(c_List_Odistinct(_1741464), _1741468)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1741464, tc_HOL_Obool)), hAPP(c_List_Oset(_1741464), _1741466)), hAPP(c_List_Oset(_1741464), _1741468)) = c_Orderings_Obot__class_Obot(tc_fun(_1741464, tc_HOL_Obool))], (41346 ^ _779571) ^ [_1569277, _1569279, _1569281, _1569283] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1569277, _1569279), _1569281), _1569283) = hAPP(c_Set_OCollect(tc_prod(_1569279, _1569279)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569279, _1569279, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1569279, tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_fun(_1569279, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569279, tc_fun(tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_fun(_1569279, tc_HOL_Obool)), _1569279), c_COMBC(_1569279, tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569279, tc_prod(_1569277, _1569277)), tc_fun(_1569279, tc_fun(tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_HOL_Obool)), _1569279), hAPP(c_COMBB(tc_prod(_1569277, _1569277), tc_fun(tc_fun(tc_prod(_1569277, _1569277), tc_HOL_Obool), tc_HOL_Obool), _1569279), c_member(tc_prod(_1569277, _1569277)))), hAPP(hAPP(c_COMBC(_1569279, tc_fun(_1569279, _1569277), tc_fun(_1569279, tc_prod(_1569277, _1569277))), hAPP(hAPP(c_COMBB(tc_fun(_1569277, tc_prod(_1569277, _1569277)), tc_fun(tc_fun(_1569279, _1569277), tc_fun(_1569279, tc_prod(_1569277, _1569277))), _1569279), c_COMBB(_1569277, tc_prod(_1569277, _1569277), _1569279)), hAPP(hAPP(c_COMBB(_1569277, tc_fun(_1569277, tc_prod(_1569277, _1569277)), _1569279), c_Product__Type_OPair(_1569277, _1569277)), _1569283))), _1569283)))), _1569281))))], (34869 ^ _779571) ^ [_1419485, _1419487] : [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), _1419485), _1419487)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1419485), _1419487)))], (9424 ^ _779571) ^ [_936005, _936007, _936009] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _936005), _936007)), _936009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _936005), _936009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _936007), _936009)))], (35509 ^ _779571) ^ [_1434669, _1434671, _1434673, _1434675, _1434677] : [-(hBOOL(hAPP(hAPP(c_member(_1434669), _1434671), hAPP(c_Relation_OImage(_1434673, _1434669, _1434675), _1434677)))), 35510 ^ _779571 : [(35511 ^ _779571) ^ [_1434755] : [hBOOL(hAPP(hAPP(c_member(_1434673), _1434755), _1434677)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1434673, _1434669)), hAPP(hAPP(c_Product__Type_OPair(_1434673, _1434669), _1434755), _1434671)), _1434675))]]], (6097 ^ _779571) ^ [_877848, _877850, _877852, _877854, _877856] : [c_Com_Ocom_OCond(_877848, _877850, _877852) = c_Com_Ocom_OWhile(_877854, _877856)], (14351 ^ _779571) ^ [_1021708, _1021710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021708), _1021710)), _1021708)))], (32667 ^ _779571) ^ [_1375557, _1375559] : [32668 ^ _779571 : [(32671 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375559), _1375557))], (32669 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375557), _1375559)))]], -(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)))), _1375557, _1375559))], (43586 ^ _779571) ^ [_1630031, _1630033, _1630035] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630031, _1630031)), _1630033), c_Transitive__Closure_Otrancl(_1630031, _1630035))), 43590 ^ _779571 : [(43593 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630031, _1630031)), _1630033), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630031, _1630031), tc_HOL_Obool), 43589 ^ [_1630031, _1630033, _1630035]), _1630035))))], (43591 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 43589 ^ [_1630031, _1630033, _1630035])))]]], (18133 ^ _779571) ^ [_1091522] : [class_Int_Onumber__ring(_1091522), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1091522), c_Groups_Oone__class_Oone(_1091522)) = hAPP(c_Int_Onumber__class_Onumber__of(_1091522), c_Int_OMin))], (43445 ^ _779571) ^ [_1626413, _1626415, _1626417, _1626419, _1626421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626415, tc_HOL_Obool)), _1626419), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1626415, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1626413, _1626415, hAPP(c_Relation_Oconverse(_1626415, _1626413), _1626417)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1626413, tc_HOL_Obool)), _1626421))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626413, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1626415, _1626413, _1626417), _1626419)), _1626421)))], (46382 ^ _779571) ^ [_1695815, _1695817] : [-(hAPP(hAPP(c_List_Ozip(_1695815, _1695815), _1695817), _1695817) = hAPP(hAPP(c_List_Omap(_1695815, tc_prod(_1695815, _1695815)), hAPP(hAPP(c_COMBS(_1695815, _1695815, tc_prod(_1695815, _1695815)), c_Product__Type_OPair(_1695815, _1695815)), c_COMBI(_1695815))), _1695817))], (45107 ^ _779571) ^ [_1666357, _1666359] : [class_Complete__Lattice_Ocomplete__lattice(_1666357), -(c_Complete__Lattice_OInf__class_OInf(_1666357, _1666359) = c_Complete__Lattice_OSup__class_OSup(_1666357, hAPP(c_Set_OCollect(_1666357), hAPP(hAPP(c_COMBB(tc_fun(_1666357, tc_HOL_Obool), tc_HOL_Obool, _1666357), c_HOL_OAll(_1666357)), hAPP(hAPP(c_COMBB(tc_fun(_1666357, tc_HOL_Obool), tc_fun(_1666357, tc_HOL_Obool), _1666357), hAPP(c_COMBS(_1666357, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1666357), c_fimplies), hAPP(hAPP(c_COMBC(_1666357, tc_fun(_1666357, tc_HOL_Obool), tc_HOL_Obool), c_member(_1666357)), _1666359)))), c_Orderings_Oord__class_Oless__eq(_1666357))))))], (36662 ^ _779571) ^ [_1461259, _1461261, _1461263, _1461265] : [class_Lattices_Olattice(_1461259), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1461259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461259), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461259), _1461261), _1461263)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461259), _1461261), _1461265))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461259), _1461261), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461259), _1461263), _1461265)))))], (39821 ^ _779571) ^ [_1531326, _1531328, _1531330, _1531332, _1531334] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1531326, _1531326, _1531328, _1531330, _1531332), _1531334)), -(hBOOL(hAPP(hAPP(c_member(_1531326), _1531330), _1531332))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1531326, _1531328, hAPP(hAPP(c_Set_Oinsert(_1531326), _1531330), _1531332)), _1531334)))], (29948 ^ _779571) ^ [_1316112] : [-(hAPP(c_Int_Onat, _1316112) = 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, _1316112)), 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)))))))], (15356 ^ _779571) ^ [_1039473, _1039475, _1039477, _1039479] : [class_Divides_Oring__div(_1039473), -(c_Divides_Odiv__class_Omod(_1039473, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039473), _1039475), _1039477), _1039479) = c_Divides_Odiv__class_Omod(_1039473, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039473), c_Divides_Odiv__class_Omod(_1039473, _1039475, _1039479)), c_Divides_Odiv__class_Omod(_1039473, _1039477, _1039479)), _1039479))], (41966 ^ _779571) ^ [_1590559] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1590559)))], (35008 ^ _779571) ^ [_1423135, _1423137, _1423139] : [-(hAPP(c_Relation_OField(_1423135), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1423135, _1423135), tc_HOL_Obool)), _1423137), _1423139)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423135, tc_HOL_Obool)), hAPP(c_Relation_OField(_1423135), _1423137)), hAPP(c_Relation_OField(_1423135), _1423139)))], (1052 ^ _779571) ^ [_795489, _795491] : [-(class_Groups_Oordered__ab__group__add(_795489)), _795491 = _795489, class_Groups_Oordered__ab__group__add(_795491)], (44804 ^ _779571) ^ [_1659696, _1659698, _1659700, _1659702, _1659704] : [_1659696 = c_Orderings_Obot__class_Obot(tc_fun(_1659698, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659698, tc_fun(_1659700, tc_HOL_Obool)), _1659696), hAPP(hAPP(c_COMBB(tc_fun(_1659700, tc_HOL_Obool), tc_fun(_1659700, tc_HOL_Obool), _1659698), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659700, tc_HOL_Obool)), _1659702)), _1659704)) = c_Orderings_Otop__class_Otop(tc_fun(_1659700, tc_HOL_Obool)))], (47127 ^ _779571) ^ [_1717352, _1717354, _1717356, _1717358, _1717360] : [class_Groups_Ocomm__monoid__add(_1717352), hBOOL(hAPP(hAPP(c_member(_1717354), _1717356), hAPP(c_List_Oset(_1717354), _1717358))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717352), hAPP(hAPP(c_List_Omap(_1717354, _1717352), _1717360), _1717358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1717352), hAPP(_1717360, _1717356)), hAPP(c_List_Omonoid__add__class_Olistsum(_1717352), hAPP(hAPP(c_List_Omap(_1717354, _1717352), _1717360), c_List_Oremove1(_1717354, _1717356, _1717358)))))], (51389 ^ _779571) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (24717 ^ _779571) ^ [_1211210] : [-(hAPP(c_Code__Numeral_Onat__of, _1211210) = c_Code__Numeral_Onat__of__aux(_1211210, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6981 ^ _779571) ^ [_894670, _894672] : [class_Rings_Ocomm__semiring__1(_894670), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894670), c_Groups_Ozero__class_Ozero(_894670)), _894672) = _894672)], (28702 ^ _779571) ^ [_1289511, _1289513, _1289515, _1289517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289511, _1289513)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289515, _1289517))), 28705 ^ _779571 : [(28706 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289511), _1289513)), 28709 ^ _779571 : [(28714 ^ _779571) ^ [] : [28715 ^ _779571 : [(28718 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289511), _1289515))], (28716 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289515), _1289511)))]], 28719 ^ _779571 : [(28722 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289517), _1289513))], (28720 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289513), _1289517)))]]], (28712 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289513), _1289517)))], (28710 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289515), _1289511)))]]], (28724 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289515), _1289517)))]]], (34931 ^ _779571) ^ [_1421363, _1421365, _1421367, _1421369, _1421371, _1421373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1421369, _1421369)), hAPP(hAPP(c_Product__Type_OPair(_1421369, _1421369), hAPP(_1421373, _1421365)), hAPP(_1421373, _1421367))), _1421371)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1421363, _1421363)), hAPP(hAPP(c_Product__Type_OPair(_1421363, _1421363), _1421365), _1421367)), hAPP(hAPP(c_Relation_Oinv__image(_1421369, _1421363), _1421371), _1421373))))], (6500 ^ _779571) ^ [_885596, _885598, _885600, _885602, _885604] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885596), _885598), _885600)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885602), _885600), _885604)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_885596, _885602)), _885598), _885604)))], (46288 ^ _779571) ^ [_1694015, _1694017] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1694015), _1694017) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1694015, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1694017), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43485 ^ _779571) ^ [_1627388, _1627390, _1627392] : [c_Relation_Ototal__on(_1627388, _1627390, _1627392), -(c_Relation_Ototal__on(_1627388, _1627390, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1627388, _1627388), tc_HOL_Obool)), _1627392), c_Relation_OId(_1627388))))], (15784 ^ _779571) ^ [_1047633, _1047635, _1047637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047633), _1047635)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047637), _1047635)), _1047633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047635), _1047633)))], (25728 ^ _779571) ^ [_1230133, _1230135, _1230137, _1230139] : [class_Rings_Odvd(_1230133), _1230135 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230133), _1230137), _1230139), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230133), _1230137), _1230135)))], (44774 ^ _779571) ^ [_1659083, _1659085, _1659087, _1659089, _1659091] : [-(_1659083 = c_Orderings_Obot__class_Obot(tc_fun(_1659085, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659087, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659085, tc_fun(_1659087, tc_HOL_Obool)), _1659083), _1659089)), _1659091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659085, tc_fun(_1659087, tc_HOL_Obool)), _1659083), hAPP(hAPP(c_COMBC(_1659085, tc_fun(_1659087, tc_HOL_Obool), tc_fun(_1659087, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659087, tc_HOL_Obool), tc_fun(tc_fun(_1659087, tc_HOL_Obool), tc_fun(_1659087, tc_HOL_Obool)), _1659085), c_Groups_Ominus__class_Ominus(tc_fun(_1659087, tc_HOL_Obool))), _1659089)), _1659091)))], (36950 ^ _779571) ^ [_1467932, _1467934, _1467936, _1467938] : [class_Orderings_Olinorder(_1467932), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467932, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1467932), _1467934)), c_SetInterval_Oord__class_OatLeastAtMost(_1467932, _1467936, _1467938)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467932, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1467932), _1467934), _1467936), _1467938))], (14532 ^ _779571) ^ [_1024747, _1024749] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024747, _1024749)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1024747), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1024749)))], (46861 ^ _779571) ^ [_1709945, _1709947, _1709949] : [hAPP(hAPP(c_List_Olist_OCons(_1709945), _1709947), _1709949) = _1709949], (19919 ^ _779571) ^ [_1121783, _1121785] : [class_Int_Onumber__ring(_1121783), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121783), hAPP(c_Int_Onumber__class_Onumber__of(_1121783), 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)))), _1121785))) = hAPP(c_Int_Onumber__class_Onumber__of(_1121783), c_Int_OMin))], (26942 ^ _779571) ^ [_1254071, _1254073] : [26950 ^ _779571 : [(26953 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1254073, 26949 ^ [_1254071, _1254073])))], (26951 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26949 ^ [_1254071, _1254073]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1254071))))]], 26943 ^ _779571 : [(26944 ^ _779571) ^ [_1254140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1254140), _1254071)), hBOOL(hAPP(_1254073, _1254140))]]], (9930 ^ _779571) ^ [_945004, _945006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _945006), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945004), _945006))), -(_945004 = _945006)], (24055 ^ _779571) ^ [_1198379, _1198381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198379), 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)), _1198381)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198379), _1198381) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1198379, _1198381)))], (40196 ^ _779571) ^ [_1541526, _1541528, _1541530, _1541532, _1541534] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1541526, _1541528), _1541530), hAPP(hAPP(c_COMBS(_1541526, tc_fun(_1541528, tc_HOL_Obool), tc_fun(_1541528, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541528, tc_HOL_Obool), tc_fun(tc_fun(_1541528, tc_HOL_Obool), tc_fun(_1541528, tc_HOL_Obool)), _1541526), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541528, tc_HOL_Obool))), _1541532)), _1541534)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1541526, _1541528), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1541526, _1541528), _1541530), _1541532)), hAPP(hAPP(c_Product__Type_OSigma(_1541526, _1541528), _1541530), _1541534)))], (15696 ^ _779571) ^ [_1045999, _1046001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045999), _1046001)), hAPP(c_Nat_OSuc, _1045999))))], (11639 ^ _779571) ^ [_972993, _972995] : [class_Groups_Olinordered__ab__group__add(_972993), 11642 ^ _779571 : [(11649 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), c_Groups_Ozero__class_Ozero(_972993)), _972995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), c_Groups_Ozero__class_Ozero(_972993)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972993), _972995), _972995))))], (11643 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), c_Groups_Ozero__class_Ozero(_972993)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972993), _972995), _972995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), c_Groups_Ozero__class_Ozero(_972993)), _972995)))]]], (24691 ^ _779571) ^ [_1210731, _1210733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1210731), _1210733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210731)), hAPP(c_Code__Numeral_Onat__of, _1210733))))], (24749 ^ _779571) ^ [_1211777, _1211779] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1211777, _1211779) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1211777), hAPP(c_Code__Numeral_Onat__of, _1211779))))], (31488 ^ _779571) ^ [_1350073, _1350075, _1350077, _1350079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool)), _1350077), _1350079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350073, tc_fun(_1350075, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1350073, tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_fun(_1350075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350075, tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_fun(_1350075, tc_HOL_Obool)), _1350073), c_COMBC(_1350075, tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350075, tc_prod(_1350073, _1350075)), tc_fun(_1350075, tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), _1350073), hAPP(c_COMBB(tc_prod(_1350073, _1350075), tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool), _1350075), c_member(tc_prod(_1350073, _1350075)))), c_Product__Type_OPair(_1350073, _1350075)))), _1350077)), hAPP(hAPP(c_COMBC(_1350073, tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_fun(_1350075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350075, tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_fun(_1350075, tc_HOL_Obool)), _1350073), c_COMBC(_1350075, tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350075, tc_prod(_1350073, _1350075)), tc_fun(_1350075, tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool)), _1350073), hAPP(c_COMBB(tc_prod(_1350073, _1350075), tc_fun(tc_fun(tc_prod(_1350073, _1350075), tc_HOL_Obool), tc_HOL_Obool), _1350075), c_member(tc_prod(_1350073, _1350075)))), c_Product__Type_OPair(_1350073, _1350075)))), _1350079))))], (39481 ^ _779571) ^ [_1523691, _1523693, _1523695, _1523697] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523691, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1523693, _1523691, _1523695), hAPP(c_Set_Ovimage(_1523693, _1523691, _1523695), _1523697))), _1523697)))], (4628 ^ _779571) ^ [_851169, _851171, _851173, _851175] : [-(c_Big__Operators_Olattice__class_OInf__fin(_851175, _851171) = c_Big__Operators_Olattice__class_OInf__fin(_851173, _851169)), _851175 = _851173, _851171 = _851169], (20593 ^ _779571) ^ [_1133559, _1133561] : [class_Rings_Odivision__ring(_1133559), -(_1133561 = c_Groups_Ozero__class_Ozero(_1133559)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133559), _1133561), _1133561) = c_Groups_Oone__class_Oone(_1133559))], (51551 ^ _779571) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (45347 ^ _779571) ^ [_1672096, _1672098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1672096, tc_HOL_Obool)), _1672098)), 45353 ^ _779571 : [(45356 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1672096), 45352 ^ [_1672096, _1672098]))], (45354 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1672096, tc_HOL_Obool)), 45352 ^ [_1672096, _1672098]), _1672098)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1672096), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672096, tc_HOL_Obool), _1672098))))], (3708 ^ _779571) ^ [_836681, _836683] : [_836683 = _836681, -(c_Int_Oint__ge__less__than(_836683) = c_Int_Oint__ge__less__than(_836681))], (20573 ^ _779571) ^ [_1133257, _1133259, _1133261] : [class_Rings_Odivision__ring(_1133257), -(_1133259 = c_Groups_Ozero__class_Ozero(_1133257)), 20580 ^ _779571 : [(20587 ^ _779571) ^ [] : [_1133261 = _1133259, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133257), _1133261), _1133259) = c_Groups_Oone__class_Oone(_1133257))], (20581 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133257), _1133261), _1133259) = c_Groups_Oone__class_Oone(_1133257), -(_1133261 = _1133259)]]], (51337 ^ _779571) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (3152 ^ _779571) ^ [_827881, _827883] : [_827883 = _827881, -(c_Divides_Odiv__class_Odiv(_827883) = c_Divides_Odiv__class_Odiv(_827881))], (11268 ^ _779571) ^ [_966666, _966668, _966670] : [class_Groups_Oordered__ab__group__add(_966666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966666), _966668), _966670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966666), hAPP(c_Groups_Ouminus__class_Ouminus(_966666), _966670)), hAPP(c_Groups_Ouminus__class_Ouminus(_966666), _966668))))], (35261 ^ _779571) ^ [_1428990, _1428992, _1428994] : [hBOOL(hAPP(c_Predicate_OPowp(_1428990, hAPP(hAPP(c_COMBC(_1428990, tc_fun(_1428990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1428990)), _1428992)), _1428994)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1428990, tc_HOL_Obool)), _1428994), hAPP(c_Set_OPow(_1428990), _1428992))))], (26768 ^ _779571) ^ [_1250484, _1250486] : [class_Rings_Ocomm__semiring__1(_1250484), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250484), c_Groups_Oone__class_Oone(_1250484)), c_Groups_Oone__class_Oone(_1250484))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1250484), c_Nat_Osemiring__1__class_Oof__nat(_1250484)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1250486))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250484), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1250484), _1250486)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250484), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1250484), _1250486)), c_Groups_Oone__class_Oone(_1250484))))], (6847 ^ _779571) ^ [_892523, _892525, _892527] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892523), _892525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892527), _892525), -(_892523 = _892527)], (15866 ^ _779571) ^ [_1049239, _1049241] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049239), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1049241)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049239), _1049241))], (1092 ^ _779571) ^ [_795989, _795991] : [-(class_Groups_Oab__group__add(_795989)), _795991 = _795989, class_Groups_Oab__group__add(_795991)], (32211 ^ _779571) ^ [_1365726, _1365728, _1365730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365726)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1365728), _1365730)), 32218 ^ _779571 : [(32219 ^ _779571) ^ [_1365916] : [32221 ^ _779571 : [(32227 ^ _779571) ^ [] : [-(_1365916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32223 ^ [_1365726, _1365728, _1365730, _1365916]), 32220 ^ [_1365726, _1365728, _1365730, _1365916]))], (32225 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32223 ^ [_1365726, _1365728, _1365730, _1365916]), _1365730)))], (32222 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32220 ^ [_1365726, _1365728, _1365730, _1365916]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1365726))))]], -(_1365916 = _1365728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1365916), _1365726) = _1365728]]], (30447 ^ _779571) ^ [_1325630, _1325632, _1325634, _1325636, _1325638, _1325640] : [hBOOL(hAPP(hAPP(c_member(_1325630), _1325632), c_SetInterval_Oord_OatLeastLessThan(_1325630, _1325634, _1325636, _1325638, _1325640))), 30450 ^ _779571 : [(30453 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1325636, _1325632), _1325640)))], (30451 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1325634, _1325638), _1325632)))]]], (34136 ^ _779571) ^ [_1403729, _1403731, _1403733] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403729, tc_Nat_Onat), _1403731), _1403733)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403729, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1403729), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1403731)), _1403733))], (26985 ^ _779571) ^ [_1254991, _1254993] : [26993 ^ _779571 : [(26996 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1254993, 26992 ^ [_1254991, _1254993])))], (26994 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26992 ^ [_1254991, _1254993]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254991))))]], 26986 ^ _779571 : [(26987 ^ _779571) ^ [_1255059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255059), _1254991)), hBOOL(hAPP(_1254993, _1255059))]]], (18871 ^ _779571) ^ [_1103187, _1103189] : [class_Int_Onumber__ring(_1103187), -(hAPP(c_Int_Onumber__class_Onumber__of(_1103187), c_Int_OBit1(_1103189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103187), c_Groups_Oone__class_Oone(_1103187)), hAPP(c_Int_Onumber__class_Onumber__of(_1103187), _1103189))), hAPP(c_Int_Onumber__class_Onumber__of(_1103187), _1103189)))], (26112 ^ _779571) ^ [_1237896, _1237898, _1237900] : [class_Orderings_Olinorder(_1237896), 26115 ^ _779571 : [(26122 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237896), _1237898), _1237900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1237896, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1237896), _1237898)), hAPP(c_SetInterval_Oord__class_OlessThan(_1237896), _1237900))))], (26116 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1237896, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1237896), _1237898)), hAPP(c_SetInterval_Oord__class_OlessThan(_1237896), _1237900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237896), _1237898), _1237900)))]]], (10646 ^ _779571) ^ [_956730, _956732, _956734] : [class_Rings_Olinordered__idom(_956730), 10649 ^ _779571 : [(10656 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956732), _956734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956730), hAPP(c_Int_Oring__1__class_Oof__int(_956730), _956732)), hAPP(c_Int_Oring__1__class_Oof__int(_956730), _956734))))], (10650 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956730), hAPP(c_Int_Oring__1__class_Oof__int(_956730), _956732)), hAPP(c_Int_Oring__1__class_Oof__int(_956730), _956734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956732), _956734)))]]], (30656 ^ _779571) ^ [_1330299, _1330301, _1330303, _1330305, _1330307] : [-(hBOOL(hAPP(hAPP(c_member(_1330299), _1330301), c_SetInterval_Oord_OgreaterThanLessThan(_1330299, _1330303, _1330305, _1330307)))), hBOOL(hAPP(hAPP(_1330303, _1330305), _1330301)), hBOOL(hAPP(hAPP(_1330303, _1330301), _1330307))], (47877 ^ _779571) ^ [_1734812, _1734814, _1734816] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734812)), hAPP(hAPP(c_List_Oappend(_1734812), _1734814), _1734816)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734812)), _1734814)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734812)), _1734816)))], (37028 ^ _779571) ^ [_1469639, _1469641, _1469643, _1469645, _1469647] : [class_Groups_Ocomm__monoid__mult(_1469639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469641), _1469643)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469641), _1469645)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469639), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1469641, _1469639), _1469647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469641, tc_HOL_Obool)), _1469643), _1469645))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1469641, _1469639), _1469647), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469641, tc_HOL_Obool)), _1469643), _1469645))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469639), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1469641, _1469639), _1469647), _1469643)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1469641, _1469639), _1469647), _1469645)))], (29404 ^ _779571) ^ [_1305250, _1305252, _1305254] : [-(hAPP(hAPP(c_Set_Oinsert(_1305250), _1305252), _1305254) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305250, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1305250), _1305252), c_Orderings_Obot__class_Obot(tc_fun(_1305250, tc_HOL_Obool)))), _1305254))], (41960 ^ _779571) ^ [_1590460, _1590462, _1590464] : [c_Wellfounded_Owf(_1590460, _1590462), -(hBOOL(hAPP(hAPP(c_member(_1590460), _1590464), c_Wellfounded_Oacc(_1590460, _1590462))))], (28268 ^ _779571) ^ [_1281209, _1281211, _1281213, _1281215] : [class_Orderings_Olinorder(_1281209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281209), _1281211), _1281213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281209), _1281213), _1281215)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281209, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1281209, _1281211, _1281213)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1281209, _1281213, _1281215)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1281209, _1281211), _1281215))], (41915 ^ _779571) ^ [_1589702, _1589704, _1589706] : [c_Wellfounded_Owf(_1589702, _1589704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589702, _1589702), tc_HOL_Obool)), _1589706), _1589704)), -(c_Wellfounded_Owf(_1589702, _1589706))], (2626 ^ _779571) ^ [_819394, _819396] : [_819396 = _819394, -(c_Lazy__Sequence_Ohb__not__seq(_819396) = c_Lazy__Sequence_Ohb__not__seq(_819394))], (39785 ^ _779571) ^ [_1530564, _1530566, _1530568, _1530570, _1530572] : [class_Groups_Oab__semigroup__mult(_1530564), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530564, _1530564, c_Groups_Otimes__class_Otimes(_1530564), _1530566, _1530568), _1530570)), -(hBOOL(hAPP(hAPP(c_member(_1530564), _1530566), _1530568))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530564, _1530564, c_Groups_Otimes__class_Otimes(_1530564), _1530572, hAPP(hAPP(c_Set_Oinsert(_1530564), _1530566), _1530568)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1530564), _1530572), _1530570))))], (15424 ^ _779571) ^ [_1040685, _1040687] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040685), _1040687))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1040685, _1040687) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040685), _1040687), _1040687))], (17799 ^ _779571) ^ [_1086081, _1086083] : [-(c_Nitpick_Oint__lcm(_1086081, _1086083) = 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), _1086081)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1086083)))))], (46310 ^ _779571) ^ [_1694422, _1694424, _1694426] : [-(hBOOL(hAPP(hAPP(c_member(_1694422), _1694424), hAPP(c_List_Oset(_1694422), _1694426)))), -(c_List_Oremove1(_1694422, _1694424, _1694426) = _1694426)], (43282 ^ _779571) ^ [_1622268, _1622270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622268), _1622270)), -(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), _1622268), _1622270)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (49008 ^ _779571) ^ [_1762762, _1762764, _1762766, _1762768] : [-(hAPP(hAPP(c_List_Omap(_1762762, _1762764), _1762766), hAPP(c_List_Otl(_1762762), _1762768)) = hAPP(c_List_Otl(_1762764), hAPP(hAPP(c_List_Omap(_1762762, _1762764), _1762766), _1762768)))], (39709 ^ _779571) ^ [_1529026, _1529028, _1529030, _1529032] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529026, _1529028, _1529030, _1529032, c_Orderings_Obot__class_Obot(tc_fun(_1529026, tc_HOL_Obool))), _1529032)))], (25792 ^ _779571) ^ [_1231274, _1231276, _1231278] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231274), _1231276)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231274), _1231278)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231274), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231276, _1231278))))], (4728 ^ _779571) ^ [_852675, _852677, _852679, _852681] : [-(c_List_Olistrel(_852681, _852677) = c_List_Olistrel(_852679, _852675)), _852681 = _852679, _852677 = _852675], (36756 ^ _779571) ^ [_1463337, _1463339, _1463341, _1463343] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463337, tc_HOL_Obool)), _1463339), _1463341)), _1463343) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463337, tc_HOL_Obool)), _1463339), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463337, tc_HOL_Obool)), _1463341), _1463343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463337, tc_HOL_Obool)), _1463343), _1463339)))], (41453 ^ _779571) ^ [_1573777, _1573779, _1573781] : [class_Groups_Olinordered__ab__semigroup__add(_1573777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573777), _1573779)), -(_1573779 = c_Orderings_Obot__class_Obot(tc_fun(_1573777, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1573777), _1573781), c_Big__Operators_Olinorder__class_OMax(_1573777, _1573779)) = c_Big__Operators_Olinorder__class_OMax(_1573777, hAPP(c_Set_OCollect(_1573777), hAPP(hAPP(c_COMBB(tc_fun(_1573777, tc_HOL_Obool), tc_HOL_Obool, _1573777), c_HOL_OEx(_1573777)), hAPP(hAPP(c_COMBC(_1573777, tc_fun(_1573777, tc_HOL_Obool), tc_fun(_1573777, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573777, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1573777, tc_HOL_Obool), tc_fun(_1573777, tc_HOL_Obool)), _1573777), c_COMBS(_1573777, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573777, tc_HOL_Obool), tc_fun(_1573777, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1573777), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573777), c_fconj)), hAPP(hAPP(c_COMBC(_1573777, tc_fun(_1573777, _1573777), tc_fun(_1573777, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573777, tc_HOL_Obool), tc_fun(tc_fun(_1573777, _1573777), tc_fun(_1573777, tc_HOL_Obool)), _1573777), c_COMBB(_1573777, tc_HOL_Obool, _1573777)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1573777), _1573781))))), hAPP(hAPP(c_COMBC(_1573777, tc_fun(_1573777, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573777)), _1573779))))))], (4370 ^ _779571) ^ [_847166, _847168, _847170, _847172, _847174, _847176, _847178, _847180] : [-(c_Lazy__Sequence_Oanamorph(_847180, _847176, _847172, _847168) = c_Lazy__Sequence_Oanamorph(_847178, _847174, _847170, _847166)), _847180 = _847178, _847176 = _847174, _847172 = _847170, _847168 = _847166], (8556 ^ _779571) ^ [_921215, _921217, _921219] : [class_Orderings_Oorder(_921215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921215), _921217), _921219)), _921217 = _921219], (31950 ^ _779571) ^ [_1360228, _1360230, _1360232, _1360234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360228), _1360230)), hBOOL(hAPP(hAPP(c_member(_1360228), _1360232), _1360230)), hBOOL(hAPP(hAPP(c_member(_1360228), _1360234), _1360230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1360228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360228, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360228, tc_HOL_Obool)), _1360230), hAPP(hAPP(c_Set_Oinsert(_1360228), _1360232), c_Orderings_Obot__class_Obot(tc_fun(_1360228, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1360228), _1360234), c_Orderings_Obot__class_Obot(tc_fun(_1360228, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1360228), _1360230))))], (23289 ^ _779571) ^ [_1184035, _1184037] : [-(_1184035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184037, _1184035), c_Divides_Odivmod__int(_1184037, _1184035))))], (51281 ^ _779571) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (18247 ^ _779571) ^ [_1093192] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093192), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093192)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1093192)))], (26358 ^ _779571) ^ [_1242544, _1242546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242544), _1242546)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1242546), _1242544))], (50690 ^ _779571) ^ [_1798643] : [-(hAPP(c_List_Orev(_1798643), c_List_Olist_ONil(_1798643)) = c_List_Olist_ONil(_1798643))], (32085 ^ _779571) ^ [_1363278, _1363280, _1363282] : [_1363278 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1363280, _1363280), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1363280, _1363280), tc_HOL_Obool)), _1363278), _1363282)))], (49177 ^ _779571) ^ [_1766302, _1766304, _1766306, _1766308, _1766310] : [c_Finite__Set_Ofun__left__comm__idem(_1766302, _1766304, _1766306), -(hAPP(hAPP(c_Finite__Set_Ofold(_1766302, _1766304, _1766306), _1766308), hAPP(c_List_Oset(_1766302), _1766310)) = hAPP(c_List_Ofoldl(_1766304, _1766302, hAPP(c_COMBC(_1766302, _1766304, _1766304), _1766306), _1766308), _1766310))], (44446 ^ _779571) ^ [_1648990, _1648992, _1648994, _1648996, _1648998, _1649000] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648990, tc_fun(_1648992, tc_HOL_Obool)), _1648994), hAPP(hAPP(c_COMBC(_1648990, tc_fun(_1648996, tc_fun(_1648992, tc_HOL_Obool)), tc_fun(_1648992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648996, tc_HOL_Obool), tc_fun(tc_fun(_1648996, tc_fun(_1648992, tc_HOL_Obool)), tc_fun(_1648992, tc_HOL_Obool)), _1648990), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648996, tc_fun(_1648992, tc_HOL_Obool))), _1648998)), _1649000)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648996, tc_fun(_1648992, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648990, tc_fun(_1648996, tc_HOL_Obool)), _1648994), _1648998)), _1649000))], (48818 ^ _779571) ^ [_1758625, _1758627, _1758629, _1758631] : [-(hAPP(hAPP(c_List_Odrop(_1758625), _1758627), hAPP(hAPP(c_List_Olist_OCons(_1758625), _1758629), _1758631)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1758625), hAPP(hAPP(c_List_Olist_OCons(_1758625), _1758629), _1758631), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1758625), tc_List_Olist(_1758625)), c_List_Odrop(_1758625)), _1758631), _1758627))], (18115 ^ _779571) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35791 ^ _779571) ^ [_1442154, _1442156, _1442158] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1442154, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442154), _1442156), _1442158), -(_1442156 = c_Orderings_Obot__class_Obot(tc_fun(_1442154, tc_HOL_Obool)))], (7059 ^ _779571) ^ [_895868] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _895868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_895868)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28381 ^ _779571) ^ [_1283304] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1283304) = 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)), _1283304)))], (28815 ^ _779571) ^ [_1291779, _1291781, _1291783, _1291785, _1291787] : [class_Complete__Lattice_Ocomplete__lattice(_1291779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291781, tc_HOL_Obool)), _1291783), _1291785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291779), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291781, _1291779), _1291783), _1291787)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291781, _1291779), _1291785), _1291787))))], (6037 ^ _779571) ^ [_876877, _876879, _876881, _876883] : [c_Com_Ocom_OWhile(_876877, _876879) = c_Com_Ocom_OWhile(_876881, _876883), 6040 ^ _779571 : [(6043 ^ _779571) ^ [] : [-(_876879 = _876883)], (6041 ^ _779571) ^ [] : [-(_876877 = _876881)]]], (11729 ^ _779571) ^ [_974538, _974540, _974542, _974544] : [class_Groups_Oordered__comm__monoid__add(_974538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974538), c_Groups_Ozero__class_Ozero(_974538)), _974540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974538), _974542), _974544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974538), _974542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974538), _974544), _974540))))], (2522 ^ _779571) ^ [_817722, _817724, _817726, _817728] : [-(c_Divides_Opdivmod(_817728, _817724) = c_Divides_Opdivmod(_817726, _817722)), _817728 = _817726, _817724 = _817722], (6901 ^ _779571) ^ [_893446] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893446), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _893446)], (15918 ^ _779571) ^ [_1050524, _1050526, _1050528, _1050530, _1050532, _1050534] : [class_Rings_Oordered__ring(_1050524), 15921 ^ _779571 : [(15928 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050524), _1050526), _1050532)), _1050528)), _1050530)), _1050534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), _1050526), _1050528)), _1050530)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), _1050532), _1050528)), _1050534))))], (15922 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), _1050526), _1050528)), _1050530)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), _1050532), _1050528)), _1050534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050524), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050524), _1050526), _1050532)), _1050528)), _1050530)), _1050534)))]]], (40124 ^ _779571) ^ [_1539305, _1539307, _1539309, _1539311, _1539313, _1539315] : [class_Groups_Ocomm__monoid__add(_1539305), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539307, _1539305), hAPP(hAPP(c_COMBC(_1539307, tc_fun(_1539309, tc_HOL_Obool), _1539305), hAPP(hAPP(c_COMBB(tc_fun(_1539309, _1539305), tc_fun(tc_fun(_1539309, tc_HOL_Obool), _1539305), _1539307), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539309, _1539305)), _1539311)), _1539313)), _1539315) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1539307, _1539309), _1539305), hAPP(c_Product__Type_Oprod_Oprod__case(_1539307, _1539309, _1539305), _1539311)), hAPP(hAPP(c_Product__Type_OSigma(_1539307, _1539309), _1539315), hAPP(c_COMBK(tc_fun(_1539309, tc_HOL_Obool), _1539307), _1539313))))], (14854 ^ _779571) ^ [_1029947, _1029949, _1029951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029947)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029951), _1029947)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029949), _1029951)), _1029947))], (50431 ^ _779571) ^ [_1792651, _1792653] : [class_Orderings_Olinorder(_1792651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792651), _1792653)), 50438 ^ _779571 : [(50443 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1792651), c_List_Olinorder__class_Osorted__list__of__set(_1792651, _1792653))))], (50441 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1792651, c_List_Olinorder__class_Osorted__list__of__set(_1792651, _1792653)))], (50439 ^ _779571) ^ [] : [-(hAPP(c_List_Oset(_1792651), c_List_Olinorder__class_Osorted__list__of__set(_1792651, _1792653)) = _1792653)]]], (11589 ^ _779571) ^ [_972159, _972161] : [class_Rings_Olinordered__idom(_972159), 11592 ^ _779571 : [(11599 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972159), c_Groups_Ozero__class_Ozero(_972159)), hAPP(c_Int_Oring__1__class_Oof__int(_972159), _972161))))], (11593 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972159), c_Groups_Ozero__class_Ozero(_972159)), hAPP(c_Int_Oring__1__class_Oof__int(_972159), _972161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972161)))]]], (12912 ^ _779571) ^ [_995880, _995882] : [class_Rings_Olinordered__idom(_995880), 12915 ^ _779571 : [(12922 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995880), c_Groups_Ozero__class_Ozero(_995880)), _995882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995880), c_Groups_Ozero__class_Ozero(_995880)), c_Groups_Osgn__class_Osgn(_995880, _995882))))], (12916 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995880), c_Groups_Ozero__class_Ozero(_995880)), c_Groups_Osgn__class_Osgn(_995880, _995882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995880), c_Groups_Ozero__class_Ozero(_995880)), _995882)))]]], (29542 ^ _779571) ^ [_1307558, _1307560] : [_1307560 = c_Orderings_Obot__class_Obot(tc_fun(_1307558, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307558, tc_HOL_Obool)), _1307560), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307558, tc_HOL_Obool)), _1307560))))], (48722 ^ _779571) ^ [_1756448, _1756450, _1756452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756448)), _1756450)), _1756452)), -(hAPP(hAPP(c_List_Odrop(_1756448), _1756452), _1756450) = c_List_Olist_ONil(_1756448))], (10301 ^ _779571) ^ [_951199, _951201] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951199), _951201) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951201), _951199))], (34455 ^ _779571) ^ [_1409992, _1409994, _1409996, _1409998, _1410000] : [class_Groups_Ocomm__monoid__mult(_1409992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409994), _1409996)), -(hBOOL(hAPP(hAPP(c_member(_1409994), _1409998), _1409996))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409994, _1409992), _1410000), hAPP(hAPP(c_Set_Oinsert(_1409994), _1409998), _1409996)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409992), hAPP(_1410000, _1409998)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409994, _1409992), _1410000), _1409996)))], (4202 ^ _779571) ^ [_844488, _844490, _844492, _844494] : [-(c_Option_Omap(_844494, _844490) = c_Option_Omap(_844492, _844488)), _844494 = _844492, _844490 = _844488], (20675 ^ _779571) ^ [_1134805, _1134807, _1134809] : [class_Fields_Olinordered__field(_1134805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134805), _1134807), c_Groups_Ozero__class_Ozero(_1134805))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134805), _1134809), c_Groups_Ozero__class_Ozero(_1134805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134805), c_Groups_Ozero__class_Ozero(_1134805)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134805), _1134807), _1134809))))], (4322 ^ _779571) ^ [_846410, _846412] : [_846412 = _846410, -(c_Nat_Osemiring__1__class_Oof__nat(_846412) = c_Nat_Osemiring__1__class_Oof__nat(_846410))], (31195 ^ _779571) ^ [_1341549] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1341549)), -(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)), _1341549))))], (47388 ^ _779571) ^ [_1722361, _1722363, _1722365] : [-(_1722361 = c_List_Olist_ONil(_1722363)), -(hBOOL(hAPP(hAPP(c_member(_1722363), hAPP(c_Product__Type_Ofst(_1722363, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1722363, _1722361), _1722365))), hAPP(c_List_Oset(_1722363), _1722361))))], (48425 ^ _779571) ^ [_1747702, _1747704, _1747706, _1747708] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1747702) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1747704), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1747702)), hAPP(hAPP(c_List_Olist_OCons(_1747704), _1747706), _1747708)) = c_List_Olist_ONil(_1747704))], (51377 ^ _779571) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (27968 ^ _779571) ^ [_1274800, _1274802, _1274804, _1274806] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274800, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274800, tc_HOL_Obool)), _1274802), _1274804)), _1274806) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274800, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274800, tc_HOL_Obool)), _1274802), _1274806)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274800, tc_HOL_Obool)), _1274804), _1274806)))], (44712 ^ _779571) ^ [_1657147, _1657149, _1657151, _1657153, _1657155] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657147, tc_fun(_1657149, tc_HOL_Obool)), _1657151), hAPP(hAPP(c_COMBC(_1657147, tc_fun(_1657149, tc_HOL_Obool), tc_fun(_1657149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657149, tc_HOL_Obool), tc_fun(tc_fun(_1657149, tc_HOL_Obool), tc_fun(_1657149, tc_HOL_Obool)), _1657147), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657149, tc_HOL_Obool))), _1657153)), _1657155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657149, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657147, tc_fun(_1657149, tc_HOL_Obool)), _1657151), _1657153)), _1657155))], (38319 ^ _779571) ^ [_1499403, _1499405, _1499407, _1499409, _1499411, _1499413] : [c_Fun_Oinj__on(_1499403, _1499405, _1499407, _1499409), -(_1499411 = _1499413), hBOOL(hAPP(hAPP(c_member(_1499403), _1499411), _1499409)), hBOOL(hAPP(hAPP(c_member(_1499403), _1499413), _1499409)), hAPP(_1499407, _1499411) = hAPP(_1499407, _1499413)], (6875 ^ _779571) ^ [_893051, _893053] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893051), _893053) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893053), _893051))], (4944 ^ _779571) ^ [_855961, _855963, _855965, _855967] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_855967, _855963) = c_SetInterval_Oord__class_OatLeastLessThan(_855965, _855961)), _855967 = _855965, _855963 = _855961], (30979 ^ _779571) ^ [_1337290, _1337292, _1337294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337290), _1337292)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337290), hAPP(hAPP(c_Set_Oinsert(_1337290), _1337294), _1337292))))], (15706 ^ _779571) ^ [_1046185, _1046187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046185), _1046187)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046185), _1046187) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49777 ^ _779571) ^ [_1779431, _1779433, _1779435] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1779431), tc_List_Olist(_1779431)), c_List_Opartition(_1779431, _1779433, _1779435)) = hAPP(c_List_Ofilter(_1779431, _1779433), _1779435))], (28617 ^ _779571) ^ [_1287790, _1287792] : [class_Orderings_Olinorder(_1287790), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1287790, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287790), _1287792)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287790), _1287792))], (47432 ^ _779571) ^ [_1723873, _1723875, _1723877] : [-(hAPP(hAPP(c_List_Onth(_1723873), hAPP(hAPP(c_List_Olist_OCons(_1723873), _1723875), _1723877)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1723875)], (9442 ^ _779571) ^ [_936306, _936308] : [class_Groups_Oordered__ab__group__add(_936306), 9445 ^ _779571 : [(9452 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936306), _936308), c_Groups_Ozero__class_Ozero(_936306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936306), c_Groups_Ozero__class_Ozero(_936306)), hAPP(c_Groups_Ouminus__class_Ouminus(_936306), _936308))))], (9446 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936306), c_Groups_Ozero__class_Ozero(_936306)), hAPP(c_Groups_Ouminus__class_Ouminus(_936306), _936308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936306), _936308), c_Groups_Ozero__class_Ozero(_936306))))]]], (21617 ^ _779571) ^ [_1151869, _1151871, _1151873, _1151875] : [class_Fields_Olinordered__field__inverse__zero(_1151869), class_Int_Onumber(_1151869), 21624 ^ _779571 : [(21625 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151869), _1151871), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))), _1151875)), 21628 ^ _779571 : [(21635 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)))), 21638 ^ _779571 : [(21645 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)), c_Groups_Ozero__class_Ozero(_1151869)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151875)))], (21639 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)), c_Groups_Ozero__class_Ozero(_1151869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))), _1151871)))]]], (21629 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)))))]]], (21651 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151869), _1151871), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))), _1151875))), 21654 ^ _779571 : [(21657 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))))], (21655 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))))]], 21658 ^ _779571 : [(21661 ^ _779571) ^ [] : [21662 ^ _779571 : [(21665 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873))), _1151871))], (21663 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)), c_Groups_Ozero__class_Ozero(_1151869))))]], 21666 ^ _779571 : [(21669 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151875))], (21667 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)), c_Groups_Ozero__class_Ozero(_1151869)))]]], (21659 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), hAPP(c_Int_Onumber__class_Onumber__of(_1151869), _1151873)))]]]]], (6446 ^ _779571) ^ [_884664, _884666, _884668] : [-(hBOOL(hAPP(_884664, _884666))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884664, _884668)), _884666), _884666)))], (51257 ^ _779571) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (10932 ^ _779571) ^ [_961211, _961213, _961215] : [class_Orderings_Olinorder(_961211), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961211), _961213), _961215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961211), _961215), _961213)))], (7345 ^ _779571) ^ [_901461, _901463, _901465, _901467] : [hAPP(c_Sum__Type_OInr(_901461, _901463), _901465) = hAPP(c_Sum__Type_OInr(_901461, _901463), _901467), -(_901465 = _901467)], (8546 ^ _779571) ^ [_921055, _921057, _921059] : [class_Orderings_Opreorder(_921055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921055), _921057), _921059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921055), _921059), _921057))], (18309 ^ _779571) ^ [_1094183, _1094185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094183), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094183)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094185)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11346 ^ _779571) ^ [_967971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967971)), _967971))], (8344 ^ _779571) ^ [_917998, _918000] : [_917998 = _918000, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917998) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918000))], (45047 ^ _779571) ^ [_1665328, _1665330, _1665332] : [class_Complete__Lattice_Ocomplete__lattice(_1665328), class_Orderings_Olinorder(_1665328), 45054 ^ _779571 : [(45064 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665328), _1665330), c_Complete__Lattice_OSup__class_OSup(_1665328, _1665332)))), 45065 ^ _779571 : [(45066 ^ _779571) ^ [_1665634] : [hBOOL(hAPP(hAPP(c_member(_1665328), _1665634), _1665332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665328), _1665330), _1665634))]]], (45055 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665328), _1665330), c_Complete__Lattice_OSup__class_OSup(_1665328, _1665332))), 45059 ^ _779571 : [(45062 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665328), _1665330), 45058 ^ [_1665328, _1665330, _1665332])))], (45060 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665328), 45058 ^ [_1665328, _1665330, _1665332]), _1665332)))]]]]], (34531 ^ _779571) ^ [_1411627, _1411629, _1411631, _1411633, _1411635] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1411627)), hAPP(c_Set_Oimage(_1411629, tc_Option_Ooption(_1411627), _1411631), c_Orderings_Otop__class_Otop(tc_fun(_1411629, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1411627)), hAPP(c_Set_Oimage(_1411629, tc_Option_Ooption(_1411627), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1411629, tc_Option_Ooption(_1411627)), _1411631), _1411633), hAPP(c_Option_Ooption_OSome(_1411627), _1411635))), c_Orderings_Otop__class_Otop(tc_fun(_1411629, tc_HOL_Obool))))))], (51441 ^ _779571) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (48616 ^ _779571) ^ [_1753359, _1753361, _1753363, _1753365, _1753367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1753359, _1753359)), hAPP(hAPP(c_Product__Type_OPair(_1753359, _1753359), _1753361), _1753363)), _1753365)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753359), tc_List_Olist(_1753359))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753359), tc_List_Olist(_1753359)), hAPP(hAPP(c_List_Olist_OCons(_1753359), _1753361), _1753367)), hAPP(hAPP(c_List_Olist_OCons(_1753359), _1753363), _1753367))), c_List_Olistrel1(_1753359, _1753365))))], (21087 ^ _779571) ^ [_1142478, _1142480, _1142482, _1142484] : [class_Fields_Ofield(_1142478), -(_1142480 = c_Groups_Ozero__class_Ozero(_1142478)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142478), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142478), _1142482), _1142480)), _1142484) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142478), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142478), _1142482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142478), _1142480), _1142484))), _1142480))], (49800 ^ _779571) ^ [_1779853, _1779855, _1779857] : [-(c_List_Opartition(_1779853, _1779855, _1779857) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1779853), tc_List_Olist(_1779853)), hAPP(c_List_Ofilter(_1779853, _1779855), _1779857)), hAPP(c_List_Ofilter(_1779853, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1779853, c_fNot), _1779855)), _1779857)))], (26264 ^ _779571) ^ [_1240936, _1240938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240938)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240936), _1240938)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240938), _1240936)), -(_1240936 = _1240938)], (30006 ^ _779571) ^ [_1317195, _1317197, _1317199, _1317201] : [30007 ^ _779571 : [(30010 ^ _779571) ^ [] : [_1317197 = _1317201], (30008 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1317195), _1317197), _1317199))]], -(hBOOL(hAPP(hAPP(c_member(_1317195), _1317197), hAPP(hAPP(c_Set_Oinsert(_1317195), _1317201), _1317199))))], (48447 ^ _779571) ^ [_1748193, _1748195, _1748197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748195)), _1748197))), -(hAPP(hAPP(c_List_Otake(_1748195), hAPP(c_Nat_OSuc, _1748193)), _1748197) = hAPP(hAPP(c_List_Oappend(_1748195), hAPP(hAPP(c_List_Otake(_1748195), _1748193), _1748197)), hAPP(hAPP(c_List_Olist_OCons(_1748195), hAPP(hAPP(c_List_Onth(_1748195), _1748197), _1748193)), c_List_Olist_ONil(_1748195))))], (13849 ^ _779571) ^ [_1012298, _1012300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012298), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012298), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012300, _1012298))))], (7375 ^ _779571) ^ [_902023, _902025, _902027, _902029, _902031, _902033] : [-(c_Sum__Type_Osum_Osum__rec(_902023, _902025, _902027, _902029, _902031, hAPP(c_Sum__Type_OInr(_902027, _902023), _902033)) = hAPP(_902031, _902033))], (44091 ^ _779571) ^ [_1641905, _1641907, _1641909] : [class_Orderings_Olinorder(_1641905), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641905), _1641907)), -(c_Big__Operators_Olattice_OInf__fin(_1641905, c_Orderings_Oord__class_Omin(_1641905), hAPP(hAPP(c_Set_Oinsert(_1641905), _1641909), _1641907)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641905, _1641905, c_Orderings_Oord__class_Omin(_1641905)), _1641909), _1641907))], (46570 ^ _779571) ^ [_1700895, _1700897, _1700899, _1700901, _1700903] : [class_Orderings_Olinorder(_1700895), 46573 ^ _779571 : [(46582 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1700897), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700897, _1700895, _1700899), _1700901), _1700903)))), -(hBOOL(hAPP(hAPP(c_member(_1700897), _1700901), hAPP(c_List_Oset(_1700897), _1700903)))), hBOOL(hAPP(c_List_Odistinct(_1700897), _1700903))], (46574 ^ _779571) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1700897), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700897, _1700895, _1700899), _1700901), _1700903))), 46577 ^ _779571 : [(46580 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1700897), _1700903)))], (46578 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1700897), _1700901), hAPP(c_List_Oset(_1700897), _1700903)))]]]]], (51641 ^ _779571) ^ [_1814099, _1814101] : [hBOOL(hAPP(hAPP(c_fdisj, _1814099), _1814101)), -(hBOOL(_1814099)), -(hBOOL(_1814101))], (38259 ^ _779571) ^ [_1498363, _1498365, _1498367] : [-(c_Fun_Oinj__on(_1498363, _1498365, _1498367, c_Orderings_Obot__class_Obot(tc_fun(_1498363, tc_HOL_Obool))))], (19245 ^ _779571) ^ [_1109598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1109598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1109598))))], (13148 ^ _779571) ^ [_999797, _999799] : [_999797 = hAPP(c_Int_Onat, _999799), 13151 ^ _779571 : [(13158 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999799))), -(_999797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13152 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999799)), -(_999799 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _999797))]]], (41328 ^ _779571) ^ [_1568766, _1568768] : [-(c_Fun_Oinj__on(tc_fun(_1568766, _1568768), tc_fun(tc_prod(_1568766, _1568768), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1568766, _1568768), tc_HOL_Obool), tc_fun(tc_prod(_1568766, _1568768), tc_HOL_Obool), tc_fun(_1568766, _1568768)), c_Set_OCollect(tc_prod(_1568766, _1568768))), hAPP(hAPP(c_COMBB(tc_fun(_1568766, tc_fun(_1568768, tc_HOL_Obool)), tc_fun(tc_prod(_1568766, _1568768), tc_HOL_Obool), tc_fun(_1568766, _1568768)), c_Product__Type_Oprod_Oprod__case(_1568766, _1568768, tc_HOL_Obool)), hAPP(c_COMBB(_1568768, tc_fun(_1568768, tc_HOL_Obool), _1568766), hAPP(c_COMBC(_1568768, _1568768, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1568766, _1568768), tc_HOL_Obool))))], (42469 ^ _779571) ^ [_1602625, _1602627] : [42471 ^ _779571 : [(42474 ^ _779571) ^ [] : [hBOOL(hAPP(_1602625, hAPP(c_Int_OAbs__Integ, 42470 ^ [_1602625, _1602627])))], (42472 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42470 ^ [_1602625, _1602627]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1602625, _1602627)))], (51221 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (24803 ^ _779571) ^ [_1213034, _1213036, _1213038] : [-(c_Nitpick_Oplus__frac(_1213034, _1213036, _1213038) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1213034), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1213034), _1213036), hAPP(c_Nitpick_Odenom(_1213034), _1213038))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1213034), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1213034), tc_Int_Oint), c_Nitpick_Ofrac(_1213034)), 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(_1213034), _1213036))), 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(_1213034), _1213036))))), 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(_1213034), _1213038))), 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(_1213034), _1213038)))))), c_COMBI(tc_Int_Oint))))], (17301 ^ _779571) ^ [_1077022, _1077024] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077022)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077024)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077022), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077024))))], (8600 ^ _779571) ^ [_921755, _921757, _921759] : [class_Orderings_Olinorder(_921755), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921755), _921757), _921759))), -(_921757 = _921759), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921755), _921759), _921757)))], (15098 ^ _779571) ^ [_1034721, _1034723] : [-(_1034721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15101 ^ _779571 : [(15108 ^ _779571) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034723, _1034721) = 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), _1034723)), _1034721) = 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), _1034723), _1034721))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15102 ^ _779571) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034723, _1034721) = 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), _1034723)), _1034721) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034723), _1034721)))]]], (20921 ^ _779571) ^ [_1139493, _1139495, _1139497, _1139499] : [class_Fields_Olinordered__field(_1139493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139493), c_Groups_Ozero__class_Ozero(_1139493)), _1139495)), 20928 ^ _779571 : [(20935 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139493), _1139497), _1139495)), _1139499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139493), _1139497), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139493), _1139499), _1139495))))], (20929 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139493), _1139497), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139493), _1139499), _1139495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139493), _1139497), _1139495)), _1139499)))]]], (31776 ^ _779571) ^ [_1356214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1356214), c_Orderings_Otop__class_Otop(tc_fun(_1356214, 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(_1356214), c_Orderings_Otop__class_Otop(tc_fun(_1356214, tc_HOL_Obool))))))], (35010 ^ _779571) ^ [_1423202, _1423204] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1423202, _1423202)), _1423204)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1423202), hAPP(c_Relation_OField(_1423202), _1423204))))], (29107 ^ _779571) ^ [_1298972, _1298974, _1298976, _1298978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298972, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29108 ^ [_1298972, _1298974, _1298976, _1298978])), _1298974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298972, 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), 29108 ^ [_1298972, _1298974, _1298976, _1298978]), _1298976))), _1298978))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298972, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1298974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298972, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1298978))))], (18759 ^ _779571) ^ [_1101380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1101380)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101380), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19437 ^ _779571) ^ [_1112967, _1112969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112967), _1112969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1112967)), c_Int_OBit0(_1112969))))], (35551 ^ _779571) ^ [_1435800, _1435802, _1435804, _1435806] : [-(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), _1435800), _1435802)), 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), _1435804), _1435806)), 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), _1435800), _1435804)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1435802), _1435806))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1435800), _1435806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1435802), _1435804)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (39056 ^ _779571) ^ [_1514473, _1514475, _1514477, _1514479, _1514481, _1514483, _1514485] : [c_Typedef_Otype__definition(_1514473, _1514475, _1514477, _1514479, _1514481), 39059 ^ _779571 : [(39066 ^ _779571) ^ [] : [_1514483 = _1514485, -(hAPP(_1514477, _1514483) = hAPP(_1514477, _1514485))], (39060 ^ _779571) ^ [] : [hAPP(_1514477, _1514483) = hAPP(_1514477, _1514485), -(_1514483 = _1514485)]]], (27642 ^ _779571) ^ [_1268502] : [-(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)), _1268502)) = hAPP(c_Int_Onat, _1268502))], (38531 ^ _779571) ^ [_1503458, _1503460, _1503462, _1503464, _1503466] : [c_Fun_Oinj__on(_1503458, _1503460, _1503462, c_Orderings_Otop__class_Otop(tc_fun(_1503458, tc_HOL_Obool))), 38534 ^ _779571 : [(38541 ^ _779571) ^ [] : [_1503464 = _1503466, -(hAPP(c_Set_Oimage(_1503458, _1503460, _1503462), _1503464) = hAPP(c_Set_Oimage(_1503458, _1503460, _1503462), _1503466))], (38535 ^ _779571) ^ [] : [hAPP(c_Set_Oimage(_1503458, _1503460, _1503462), _1503464) = hAPP(c_Set_Oimage(_1503458, _1503460, _1503462), _1503466), -(_1503464 = _1503466)]]], (13084 ^ _779571) ^ [_998645] : [-(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), _998645))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44444 ^ _779571) ^ [_1648900, _1648902, _1648904, _1648906, _1648908] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648900, tc_fun(_1648902, tc_HOL_Obool)), _1648904), hAPP(hAPP(c_COMBB(tc_fun(_1648902, tc_HOL_Obool), tc_fun(_1648902, tc_HOL_Obool), _1648900), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648902, tc_HOL_Obool)), _1648906)), _1648908)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648902, tc_HOL_Obool)), _1648906), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648900, tc_fun(_1648902, tc_HOL_Obool)), _1648904), _1648908)))], (244 ^ _779571) ^ [_783177, _783179] : [-(class_Fields_Ofield__inverse__zero(_783177)), _783179 = _783177, class_Fields_Ofield__inverse__zero(_783179)], (36762 ^ _779571) ^ [_1463522, _1463524, _1463526, _1463528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463522, tc_HOL_Obool)), _1463528), _1463524)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463522, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463522, tc_HOL_Obool)), _1463524), _1463526)), _1463528) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463522, tc_HOL_Obool)), _1463524), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463522, tc_HOL_Obool)), _1463526), _1463528)))], (17931 ^ _779571) ^ [_1088246] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088246)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088246)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088246))], (30742 ^ _779571) ^ [_1332073, _1332075, _1332077, _1332079] : [hBOOL(hAPP(hAPP(c_member(_1332075), _1332079), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332073, tc_fun(_1332075, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1332073, tc_HOL_Obool))), _1332077))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332073, tc_fun(_1332075, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1332073, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1332075, tc_HOL_Obool), tc_fun(_1332075, tc_HOL_Obool), _1332073), hAPP(c_COMBC(_1332075, tc_fun(_1332075, tc_HOL_Obool), tc_HOL_Obool), c_member(_1332075))), _1332077)), _1332079)))], (51549 ^ _779571) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (43985 ^ _779571) ^ [_1639902, _1639904, _1639906, _1639908] : [class_Lattices_Osemilattice__sup(_1639902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639902), _1639904)), hBOOL(hAPP(hAPP(c_member(_1639902), _1639906), _1639904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1639902), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1639902), _1639906), _1639908)), hAPP(hAPP(c_Finite__Set_Ofold(_1639902, _1639902, c_Lattices_Osemilattice__sup__class_Osup(_1639902)), _1639908), _1639904))))], (16525 ^ _779571) ^ [_1062297, _1062299] : [class_Int_Onumber__ring(_1062297), -(hAPP(c_Int_Onumber__class_Onumber__of(_1062297), _1062299) = hAPP(c_Int_Oring__1__class_Oof__int(_1062297), _1062299))], (42423 ^ _779571) ^ [_1601704, _1601706, _1601708, _1601710, _1601712] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1601704), _1601706), _1601708), _1601710), _1601712) = c_New__DSequence_Opos__single(_1601704, _1601706))], (38337 ^ _779571) ^ [_1499716, _1499718, _1499720, _1499722, _1499724] : [c_Fun_Oinj__on(_1499716, _1499718, _1499720, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499716, tc_HOL_Obool)), _1499722), _1499724)), 38340 ^ _779571 : [(38347 ^ _779571) ^ [] : [_1499722 = _1499724, -(hAPP(c_Set_Oimage(_1499716, _1499718, _1499720), _1499722) = hAPP(c_Set_Oimage(_1499716, _1499718, _1499720), _1499724))], (38341 ^ _779571) ^ [] : [hAPP(c_Set_Oimage(_1499716, _1499718, _1499720), _1499722) = hAPP(c_Set_Oimage(_1499716, _1499718, _1499720), _1499724), -(_1499722 = _1499724)]]], (48172 ^ _779571) ^ [_1741247, _1741249, _1741251] : [hBOOL(hAPP(c_List_Odistinct(_1741247), hAPP(hAPP(c_List_Oappend(_1741247), _1741249), _1741251))), 48175 ^ _779571 : [(48180 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1741247, tc_HOL_Obool)), hAPP(c_List_Oset(_1741247), _1741249)), hAPP(c_List_Oset(_1741247), _1741251)) = c_Orderings_Obot__class_Obot(tc_fun(_1741247, tc_HOL_Obool)))], (48178 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1741247), _1741251)))], (48176 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1741247), _1741249)))]]], (18457 ^ _779571) ^ [] : [-(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))))], (5012 ^ _779571) ^ [_857039, _857041, _857043, _857045, _857047, _857049] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_857049, _857045, _857041) = c_SetInterval_Oord__class_OgreaterThanAtMost(_857047, _857043, _857039)), _857049 = _857047, _857045 = _857043, _857041 = _857039], (43367 ^ _779571) ^ [_1624479, _1624481, _1624483] : [c_Relation_Orefl__on(_1624479, _1624481, _1624483), -(c_Relation_Orefl__on(_1624479, _1624481, hAPP(c_Relation_Oconverse(_1624479, _1624479), _1624483)))], (48301 ^ _779571) ^ [_1744914, _1744916, _1744918] : [hAPP(hAPP(c_List_Otake(_1744914), _1744916), _1744918) = c_List_Olist_ONil(_1744914), -(_1744916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1744918 = c_List_Olist_ONil(_1744914))], (5795 ^ _779571) ^ [_872408, _872410, _872412, _872414, _872416, _872418] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_872408, _872410, _872412), _872414, _872416, _872418), 5800 ^ _779571 : [(5803 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_872410, _872414, _872416, _872418))], (5801 ^ _779571) ^ [] : [-(hBOOL(hAPP(_872408, _872414)))]], 5804 ^ _779571 : [(5807 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_872412, _872414, _872416, _872418))], (5805 ^ _779571) ^ [] : [hBOOL(hAPP(_872408, _872414))]]], (19597 ^ _779571) ^ [_1115749, _1115751] : [class_Rings_Olinordered__idom(_1115749), -(hAPP(c_Groups_Oabs__class_Oabs(_1115749), hAPP(hAPP(c_Power_Opower__class_Opower(_1115749), _1115751), 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(_1115749), _1115751), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (9316 ^ _779571) ^ [_933860, _933862, _933864] : [class_Rings_Ono__zero__divisors(_933860), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933860), _933862), _933864) = c_Groups_Ozero__class_Ozero(_933860), -(_933862 = c_Groups_Ozero__class_Ozero(_933860)), -(_933864 = c_Groups_Ozero__class_Ozero(_933860))], (38171 ^ _779571) ^ [_1496031, _1496033, _1496035, _1496037, _1496039, _1496041] : [c_Finite__Set_Ofolding__idem(_1496031, _1496033, _1496035, _1496037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496031), _1496039)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496031), _1496041)), -(hAPP(_1496037, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496031, tc_HOL_Obool)), _1496039), _1496041)) = hAPP(c_Fun_Ocomp(_1496033, _1496033, _1496033, hAPP(_1496037, _1496039)), hAPP(_1496037, _1496041)))], (28463 ^ _779571) ^ [_1285099, _1285101, _1285103, _1285105] : [c_Hoare__Mirabelle_Ohoare__derivs(_1285099, _1285101, _1285103), c_Hoare__Mirabelle_Ohoare__derivs(_1285099, _1285105, _1285101), -(c_Hoare__Mirabelle_Ohoare__derivs(_1285099, _1285105, _1285103))], (29552 ^ _779571) ^ [_1307765] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307765), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (46404 ^ _779571) ^ [_1696685, _1696687, _1696689, _1696691, _1696693, _1696695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696685, _1696687)), hAPP(hAPP(c_Product__Type_OPair(_1696685, _1696687), _1696689), _1696691)), hAPP(c_List_Oset(tc_prod(_1696685, _1696687)), hAPP(hAPP(c_List_Ozip(_1696685, _1696687), _1696693), _1696695)))), -(hBOOL(hAPP(hAPP(c_member(_1696685), _1696689), hAPP(c_List_Oset(_1696685), _1696693))))], (49325 ^ _779571) ^ [_1769933, _1769935, _1769937, _1769939] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769933)), hAPP(hAPP(c_List_Olist_OCons(_1769933), _1769935), _1769937)), c_List_Olists(_1769933, _1769939))), 49328 ^ _779571 : [(49331 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769933)), _1769937), c_List_Olists(_1769933, _1769939))))], (49329 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769933), _1769935), _1769939)))]]], (49132 ^ _779571) ^ [_1765472] : [class_Groups_Omonoid__add(_1765472), -(c_List_Omonoid__add__class_Olistsum(_1765472) = c_List_Ofoldl(_1765472, _1765472, c_Groups_Oplus__class_Oplus(_1765472), c_Groups_Ozero__class_Ozero(_1765472)))], (21135 ^ _779571) ^ [_1143328, _1143330, _1143332, _1143334] : [class_Fields_Ofield(_1143328), -(_1143330 = c_Groups_Ozero__class_Ozero(_1143328)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1143328), _1143332), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143328), _1143334), _1143330)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1143328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143328), _1143330), _1143332)), _1143334)), _1143330))], (36582 ^ _779571) ^ [_1459098, _1459100, _1459102] : [class_Lattices_Osemilattice__inf(_1459098), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459098), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459098), _1459100), _1459102)), _1459102)))], (51273 ^ _779571) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (22791 ^ _779571) ^ [_1174576, _1174578, _1174580] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1174576, _1174578), _1174580)), 22794 ^ _779571 : [(22795 ^ _779571) ^ [_1174661] : [hBOOL(hAPP(hAPP(_1174578, _1174661), _1174580)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1174576, _1174578), _1174661)))]]], (27055 ^ _779571) ^ [_1256283, _1256285, _1256287, _1256289, _1256291] : [class_Orderings_Olinorder(_1256283), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256283, _1256285), _1256287) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256283, _1256289), _1256291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256283), _1256285), _1256287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256283), _1256289), _1256291)), -(_1256285 = _1256289)], (12420 ^ _779571) ^ [_986937] : [-(hBOOL(hAPP(_986937, 12427 ^ [_986937]))), 12421 ^ _779571 : [(12422 ^ _779571) ^ [_986989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986989)), hBOOL(hAPP(_986937, hAPP(c_Int_Onat, _986989)))]]], (4804 ^ _779571) ^ [_853811, _853813] : [_853813 = _853811, -(c_Orderings_Obot__class_Obot(_853813) = c_Orderings_Obot__class_Obot(_853811))], (23779 ^ _779571) ^ [_1192692, _1192694, _1192696, _1192698] : [class_Orderings_Olinorder(_1192692), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192692), _1192694), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192692), _1192696), _1192698)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192692), _1192696), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192692), _1192694), _1192698)))], (36236 ^ _779571) ^ [_1452418, _1452420, _1452422] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452418, tc_HOL_Obool)), _1452420), _1452422) = c_Orderings_Obot__class_Obot(tc_fun(_1452418, tc_HOL_Obool)), 36239 ^ _779571 : [(36240 ^ _779571) ^ [_1452542] : [hBOOL(hAPP(hAPP(c_member(_1452418), _1452542), _1452420)), 36243 ^ _779571 : [(36244 ^ _779571) ^ [_1452632] : [hBOOL(hAPP(hAPP(c_member(_1452418), _1452632), _1452422)), _1452542 = _1452632]]]]], (15742 ^ _779571) ^ [_1046819, _1046821, _1046823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046819), _1046821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046819), _1046823)), 15749 ^ _779571 : [(15756 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046821), _1046823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046821), _1046819)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046823), _1046819))))], (15750 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046821), _1046819)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046823), _1046819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046821), _1046823)))]]], (1242 ^ _779571) ^ [_797864, _797866] : [-(class_Complete__Lattice_Ocomplete__lattice(_797864)), _797866 = _797864, class_Complete__Lattice_Ocomplete__lattice(_797866)], (5482 ^ _779571) ^ [_864290, _864292, _864294, _864296, _864298, _864300] : [-(c_List_OtakeWhile(_864300, _864296, _864292) = c_List_OtakeWhile(_864298, _864294, _864290)), _864300 = _864298, _864296 = _864294, _864292 = _864290], (41718 ^ _779571) ^ [_1583887, _1583889, _1583891, _1583893] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583887, _1583889, _1583891), _1583893), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583889, _1583891), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583887, _1583891), tc_HOL_Obool)))], (45951 ^ _779571) ^ [_1685874, _1685876, _1685878] : [c_Fun_Oinj__on(_1685874, _1685876, _1685878, c_Orderings_Otop__class_Otop(tc_fun(_1685874, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1685874), tc_List_Olist(_1685876), hAPP(c_List_Omap(_1685874, _1685876), _1685878), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1685874), tc_HOL_Obool))))], (47871 ^ _779571) ^ [_1734637, _1734639, _1734641, _1734643, _1734645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734637), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734639)), _1734641))), -(hAPP(hAPP(c_List_Olist__update(_1734639, hAPP(hAPP(c_List_Oappend(_1734639), _1734641), _1734643)), _1734637), _1734645) = hAPP(hAPP(c_List_Oappend(_1734639), hAPP(hAPP(c_List_Olist__update(_1734639, _1734641), _1734637), _1734645)), _1734643))], (6369 ^ _779571) ^ [_882980, _882982, _882984, _882986, _882988, _882990] : [c_Com_Ocom_OLocal(_882980, _882982, _882984) = c_Com_Ocom_OCond(_882986, _882988, _882990)], (49923 ^ _779571) ^ [_1783587, _1783589, _1783591] : [-(c_List_Osublist(_1783587, _1783589, _1783591) = hAPP(hAPP(c_List_Omap(tc_prod(_1783587, tc_Nat_Onat), _1783587), c_Product__Type_Ofst(_1783587, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1783587, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1783587, 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(_1783587, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1783587, tc_Nat_Onat))), _1783591)), hAPP(hAPP(c_List_Ozip(_1783587, tc_Nat_Onat), _1783589), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783587)), _1783589))))))], (46376 ^ _779571) ^ [_1695694, _1695696, _1695698, _1695700] : [hBOOL(hAPP(c_List_Odistinct(_1695694), _1695696)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1695698, _1695694)), hAPP(hAPP(c_List_Ozip(_1695698, _1695694), _1695700), _1695696))))], (12964 ^ _779571) ^ [_996718] : [_996718 = 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), _996718)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6784 ^ _779571) ^ [_891252, _891254, _891256, _891258, _891260, _891262, _891264, _891266, _891268, _891270] : [-(c_Com_Ocom_Ocom__rec(_891252, _891254, _891256, _891258, _891260, _891262, _891264, _891266, _891268, hAPP(c_Com_Ocom_OBODY, _891270)) = hAPP(_891266, _891270))], (39497 ^ _779571) ^ [_1524126, _1524128, _1524130, _1524132, _1524134] : [-(hAPP(c_Set_Ovimage(_1524126, _1524128, _1524130), hAPP(hAPP(c_Set_Oinsert(_1524128), _1524132), _1524134)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524126, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1524126, _1524128, _1524130), hAPP(hAPP(c_Set_Oinsert(_1524128), _1524132), c_Orderings_Obot__class_Obot(tc_fun(_1524128, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1524126, _1524128, _1524130), _1524134)))], (17423 ^ _779571) ^ [_1079304, _1079306, _1079308] : [class_Rings_Olinordered__semidom(_1079304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079304), c_Groups_Ozero__class_Ozero(_1079304)), _1079306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079304), c_Groups_Ozero__class_Ozero(_1079304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079304), _1079306), _1079308))))], (15950 ^ _779571) ^ [_1051402, _1051404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051402), hAPP(c_Nat_OSuc, _1051404))), _1051402)))], (5520 ^ _779571) ^ [_864851, _864853, _864855, _864857] : [-(c_List_Oremdups(_864857, _864853) = c_List_Oremdups(_864855, _864851)), _864857 = _864855, _864853 = _864851], (47636 ^ _779571) ^ [_1728970, _1728972, _1728974, _1728976] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728970), tc_List_Olist(_1728970))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1728970), tc_List_Olist(_1728970)), _1728972), _1728974)), c_List_Olistrel(_1728970, _1728976)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728970)), _1728972) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728970)), _1728974), 47642 ^ _779571 : [(47645 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1728970, _1728970)), hAPP(hAPP(c_Product__Type_OPair(_1728970, _1728970), hAPP(hAPP(c_List_Onth(_1728970), _1728972), 47641 ^ [_1728970, _1728972, _1728974, _1728976])), hAPP(hAPP(c_List_Onth(_1728970), _1728974), 47641 ^ [_1728970, _1728972, _1728974, _1728976]))), _1728976))], (47643 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47641 ^ [_1728970, _1728972, _1728974, _1728976]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728970)), _1728972))))]]], (19589 ^ _779571) ^ [] : [-(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)))))], (21367 ^ _779571) ^ [] : [-(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))], (51557 ^ _779571) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (33669 ^ _779571) ^ [_1394404, _1394406, _1394408] : [class_Orderings_Olinorder(_1394404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394404), _1394406)), hBOOL(hAPP(hAPP(c_member(_1394404), _1394408), _1394406)), 33680 ^ _779571 : [(33687 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394404, tc_HOL_Obool)), _1394406), hAPP(hAPP(c_Set_Oinsert(_1394404), _1394408), c_Orderings_Obot__class_Obot(tc_fun(_1394404, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1394404, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1394404, c_Orderings_Oord__class_Omax(_1394404), _1394406) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1394404), _1394408), c_Big__Operators_Olattice_OSup__fin(_1394404, c_Orderings_Oord__class_Omax(_1394404), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394404, tc_HOL_Obool)), _1394406), hAPP(hAPP(c_Set_Oinsert(_1394404), _1394408), c_Orderings_Obot__class_Obot(tc_fun(_1394404, tc_HOL_Obool)))))))], (33681 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394404, tc_HOL_Obool)), _1394406), hAPP(hAPP(c_Set_Oinsert(_1394404), _1394408), c_Orderings_Obot__class_Obot(tc_fun(_1394404, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1394404, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1394404, c_Orderings_Oord__class_Omax(_1394404), _1394406) = _1394408)]]], (51701 ^ _779571) ^ [] : [-(c_Natural_Oevaln(v_c, v_s, v_n, v_s1))], (28961 ^ _779571) ^ [_1295851, _1295853, _1295855] : [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), _1295851), _1295853))), -(hBOOL(hAPP(hAPP(_1295855, _1295851), _1295853))), 28968 ^ _779571 : [(28971 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 28966 ^ [_1295851, _1295853, _1295855]), 28967 ^ [_1295851, _1295853, _1295855])), -(hBOOL(hAPP(hAPP(_1295855, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28966 ^ [_1295851, _1295853, _1295855]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 28967 ^ [_1295851, _1295853, _1295855])))], (28977 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1295855, 28966 ^ [_1295851, _1295853, _1295855]), 28967 ^ [_1295851, _1295853, _1295855]))], (28969 ^ _779571) ^ [] : [-(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), 28966 ^ [_1295851, _1295853, _1295855]), 28967 ^ [_1295851, _1295853, _1295855]))))]]], (7658 ^ _779571) ^ [_906472, _906474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906472), _906474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _906472)), hAPP(c_Nat_OSuc, _906474))))], (5118 ^ _779571) ^ [_858646, _858648, _858650, _858652, _858654, _858656, _858658, _858660] : [-(c_List_Ofoldl(_858660, _858656, _858652, _858648) = c_List_Ofoldl(_858658, _858654, _858650, _858646)), _858660 = _858658, _858656 = _858654, _858652 = _858650, _858648 = _858646], (23185 ^ _779571) ^ [_1181993, _1181995] : [-(c_Divides_Odivmod__int__rel(_1181993, _1181995) = 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, _1181993))), 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), _1181995)))))), 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)), _1181995))), 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)), _1181995))))), 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)), _1181995)))), 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), _1181995))), 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))))))))], (3624 ^ _779571) ^ [_835369, _835371] : [_835371 = _835369, -(c_Int_Oring__1__class_Oof__int(_835371) = c_Int_Oring__1__class_Oof__int(_835369))], (51561 ^ _779571) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (35231 ^ _779571) ^ [_1428229, _1428231, _1428233, _1428235, _1428237] : [hAPP(c_Set_Oimage(_1428229, _1428231, _1428233), _1428235) = _1428237, -(hAPP(c_Set_Oimage(tc_fun(_1428229, tc_HOL_Obool), tc_fun(_1428231, tc_HOL_Obool), c_Set_Oimage(_1428229, _1428231, _1428233)), hAPP(c_Set_OPow(_1428229), _1428235)) = hAPP(c_Set_OPow(_1428231), _1428237))], (39990 ^ _779571) ^ [_1535661, _1535663, _1535665, _1535667, _1535669, _1535671] : [c_Hoare__Mirabelle_Ohoare__derivs(_1535661, _1535663, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1535661)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1535661), _1535665), _1535667), _1535669)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1535661), tc_HOL_Obool)))), 39997 ^ _779571 : [(40000 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1535665, 39995 ^ [_1535661, _1535663, _1535665, _1535667, _1535669, _1535671]), 39996 ^ [_1535661, _1535663, _1535665, _1535667, _1535669, _1535671]))], (39998 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1535671, 39995 ^ [_1535661, _1535663, _1535665, _1535667, _1535669, _1535671]), 39996 ^ [_1535661, _1535663, _1535665, _1535667, _1535669, _1535671])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1535661, _1535663, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1535661)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1535661), _1535671), _1535667), _1535669)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1535661), tc_HOL_Obool)))))], (16849 ^ _779571) ^ [_1068371, _1068373, _1068375, _1068377] : [class_Rings_Ocomm__semiring__1(_1068371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068371), hAPP(hAPP(c_Power_Opower__class_Opower(_1068371), _1068373), _1068375)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068371), _1068373), _1068377)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1068371), _1068373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068375), _1068377)))], (30606 ^ _779571) ^ [_1329274, _1329276, _1329278, _1329280, _1329282] : [_1329274 = hAPP(_1329276, _1329278), -(hBOOL(hAPP(hAPP(c_member(_1329280), _1329274), hAPP(c_Set_Oimage(_1329282, _1329280, _1329276), c_Orderings_Otop__class_Otop(tc_fun(_1329282, tc_HOL_Obool))))))], (23939 ^ _779571) ^ [_1196213, _1196215, _1196217] : [_1196213 = _1196215, 23942 ^ _779571 : [(23945 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196217, tc_HOL_Obool)), _1196215), _1196213)))], (23943 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196217, tc_HOL_Obool)), _1196213), _1196215)))]]], (29256 ^ _779571) ^ [_1302447, _1302449, _1302451] : [hBOOL(hAPP(hAPP(c_member(_1302449), _1302447), c_Orderings_Obot__class_Obot(tc_fun(_1302449, tc_HOL_Obool)))), -(hBOOL(hAPP(_1302451, _1302447)))], (49293 ^ _779571) ^ [_1769201, _1769203, _1769205] : [c_Relation_Orefl__on(_1769201, _1769203, _1769205), -(c_Relation_Orefl__on(tc_List_Olist(_1769201), c_List_Olists(_1769201, _1769203), c_List_Olistrel(_1769201, _1769205)))], (23921 ^ _779571) ^ [_1195744, _1195746, _1195748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195744, tc_HOL_Obool)), _1195746), _1195748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195744, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195744, tc_HOL_Obool)), _1195748)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195744, tc_HOL_Obool)), _1195746))))], (45750 ^ _779571) ^ [_1680978, _1680980, _1680982, _1680984] : [c_Fun_Oinj__on(_1680978, tc_Option_Ooption(_1680980), c_Map_Omap__add(_1680978, _1680980, _1680982, _1680984), c_Map_Odom(_1680978, _1680980, _1680984)), -(c_Fun_Oinj__on(_1680978, tc_Option_Ooption(_1680980), _1680984, c_Map_Odom(_1680978, _1680980, _1680984)))], (11573 ^ _779571) ^ [_971897, _971899] : [class_Rings_Olinordered__idom(_971897), 11576 ^ _779571 : [(11583 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _971899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971897), hAPP(c_Int_Oring__1__class_Oof__int(_971897), _971899)), c_Groups_Ozero__class_Ozero(_971897))))], (11577 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971897), hAPP(c_Int_Oring__1__class_Oof__int(_971897), _971899)), c_Groups_Ozero__class_Ozero(_971897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _971899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4120 ^ _779571) ^ [_843087, _843089, _843091, _843093, _843095, _843097] : [-(c_Smallcheck_Ofull__small_H(_843097, _843093, _843089) = c_Smallcheck_Ofull__small_H(_843095, _843091, _843087)), _843097 = _843095, _843093 = _843091, _843089 = _843087], (51617 ^ _779571) ^ [_1813751, _1813753] : [hBOOL(hAPP(hAPP(c_fconj, _1813751), _1813753)), -(hBOOL(_1813751))], (15736 ^ _779571) ^ [_1046696, _1046698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046696), _1046698)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046698)), _1046696) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046698), _1046696)))], (39401 ^ _779571) ^ [_1521706, _1521708, _1521710, _1521712] : [c_Fun_Oinj__on(_1521706, _1521708, _1521710, c_Orderings_Otop__class_Otop(tc_fun(_1521706, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521706, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521706, _1521708, _1521710), hAPP(hAPP(c_Set_Oinsert(_1521708), _1521712), c_Orderings_Obot__class_Obot(tc_fun(_1521708, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1521706), c_HOL_OThe(_1521706, hAPP(hAPP(c_COMBC(_1521706, _1521708, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1521708, tc_fun(_1521708, tc_HOL_Obool), _1521706), c_fequal), _1521710)), _1521712))), c_Orderings_Obot__class_Obot(tc_fun(_1521706, tc_HOL_Obool))))))], (22250 ^ _779571) ^ [_1163503, _1163505] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1163503), _1163505))), -(c_Quickcheck_Obeyond(_1163503, _1163505) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (5691 ^ _779571) ^ [_870213, _870215, _870217, _870219, _870221] : [c_Hoare__Mirabelle_Otriple__valid(_870213, _870215, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_870213), _870217), _870219), _870221)), 5694 ^ _779571 : [(5695 ^ _779571) ^ [_870334, _870336] : [hBOOL(hAPP(hAPP(_870217, _870336), _870334)), 5698 ^ _779571 : [(5699 ^ _779571) ^ [_870424] : [c_Natural_Oevaln(_870219, _870334, _870215, _870424), -(hBOOL(hAPP(hAPP(_870221, _870336), _870424)))]]]]], (43528 ^ _779571) ^ [_1628559, _1628561, _1628563, _1628565] : [-(hAPP(hAPP(c_Nat_Ocompow(_1628559, _1628559), _1628561), hAPP(hAPP(c_Nat_Ocompow(_1628559, _1628559), _1628563), _1628565)) = hAPP(hAPP(c_Nat_Ocompow(_1628559, _1628559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1628563), _1628561)), _1628565))], (18699 ^ _779571) ^ [_1100393, _1100395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100393), _1100395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1100393)), c_Int_OBit1(_1100395))))], (50987 ^ _779571) ^ [_1806424, _1806426, _1806428] : [class_Orderings_Olinorder(_1806424), c_List_Olinorder__class_Osorted(_1806424, _1806426), -(c_List_Olinorder__class_Osorted(_1806424, c_List_OtakeWhile(_1806424, _1806428, _1806426)))], (30736 ^ _779571) ^ [_1331854, _1331856, _1331858, _1331860] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331854, tc_fun(_1331856, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1331854, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1331856, tc_HOL_Obool), tc_fun(_1331856, tc_HOL_Obool), _1331854), hAPP(c_COMBC(_1331856, tc_fun(_1331856, tc_HOL_Obool), tc_HOL_Obool), c_member(_1331856))), _1331858)), _1331860)), -(hBOOL(hAPP(hAPP(c_member(_1331856), _1331860), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331854, tc_fun(_1331856, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1331854, tc_HOL_Obool))), _1331858))))], (45969 ^ _779571) ^ [_1686323, _1686325, _1686327, _1686329, _1686331, _1686333] : [-(hAPP(hAPP(c_List_Omap(_1686323, _1686325), _1686327), hAPP(hAPP(c_List_Omap(_1686329, _1686323), _1686331), _1686333)) = hAPP(hAPP(c_List_Omap(_1686329, _1686325), hAPP(c_Fun_Ocomp(_1686323, _1686325, _1686329, _1686327), _1686331)), _1686333))], (48140 ^ _779571) ^ [_1740662, _1740664, _1740666] : [c_List_Olist_ONil(_1740662) = hAPP(hAPP(c_List_Oappend(_1740662), _1740664), _1740666), 48143 ^ _779571 : [(48146 ^ _779571) ^ [] : [-(_1740666 = c_List_Olist_ONil(_1740662))], (48144 ^ _779571) ^ [] : [-(_1740664 = c_List_Olist_ONil(_1740662))]]], (10283 ^ _779571) ^ [_950945, _950947] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950945), _950947) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10286 ^ _779571 : [(10289 ^ _779571) ^ [] : [-(_950947 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10287 ^ _779571) ^ [] : [-(_950945 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (36198 ^ _779571) ^ [_1451297, _1451299, _1451301, _1451303] : [class_Lattices_Odistrib__lattice(_1451297), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451297), _1451299), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451297), _1451301), _1451303)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451297), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451297), _1451299), _1451301)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451297), _1451299), _1451303)))], (36774 ^ _779571) ^ [_1463941, _1463943, _1463945, _1463947] : [class_Orderings_Oorder(_1463941), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463941, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1463941, _1463943), _1463945)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1463941, _1463945), _1463947)) = c_Orderings_Obot__class_Obot(tc_fun(_1463941, tc_HOL_Obool)))], (36462 ^ _779571) ^ [_1457013, _1457015, _1457017, _1457019, _1457021] : [class_Lattices_Osemilattice__inf(_1457013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457013), _1457015), _1457017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457013), _1457019), _1457021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457013), _1457015), _1457019)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457013), _1457017), _1457021))))], (10698 ^ _779571) ^ [_957675, _957677, _957679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957675), _957677)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957679), _957677))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957675), _957679)))], (41067 ^ _779571) ^ [_1561663, _1561665] : [-(hBOOL(hAPP(_1561665, 41068 ^ [_1561663, _1561665]))), -(hAPP(c_Set_OCollect(_1561663), _1561665) = c_Orderings_Obot__class_Obot(tc_fun(_1561663, tc_HOL_Obool)))], (27648 ^ _779571) ^ [_1268619, _1268621] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1268619), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1268621) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1268619, _1268621))], (28852 ^ _779571) ^ [_1292817, _1292819, _1292821, _1292823, _1292825] : [28854 ^ _779571 : [(28860 ^ _779571) ^ [] : [hBOOL(hAPP(_1292825, 28856 ^ [_1292817, _1292819, _1292821, _1292823, _1292825]))], (28858 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292817), 28856 ^ [_1292817, _1292819, _1292821, _1292823, _1292825]), hAPP(_1292823, 28853 ^ [_1292817, _1292819, _1292821, _1292823, _1292825]))))], (28855 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292819), 28853 ^ [_1292817, _1292819, _1292821, _1292823, _1292825]), _1292821)))]], 28861 ^ _779571 : [(28862 ^ _779571) ^ [_1293127] : [hBOOL(hAPP(hAPP(c_member(_1292817), _1293127), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292819, tc_fun(_1292817, tc_HOL_Obool)), _1292821), _1292823))), -(hBOOL(hAPP(_1292825, _1293127)))]]], (33303 ^ _779571) ^ [_1386904, _1386906, _1386908] : [class_Orderings_Olinorder(_1386904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386904), _1386906)), hBOOL(hAPP(hAPP(c_member(_1386904), _1386908), _1386906)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1386904), _1386908), c_Big__Operators_Olinorder__class_OMin(_1386904, _1386906)) = c_Big__Operators_Olinorder__class_OMin(_1386904, _1386906))], (43004 ^ _779571) ^ [_1615651, _1615653, _1615655, _1615657, _1615659] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615651, _1615651)), hAPP(hAPP(c_Product__Type_OPair(_1615651, _1615651), _1615653), _1615655)), c_Transitive__Closure_Ortrancl(_1615651, _1615657))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615651, _1615651)), hAPP(hAPP(c_Product__Type_OPair(_1615651, _1615651), _1615655), _1615659)), _1615657)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615651, _1615651)), hAPP(hAPP(c_Product__Type_OPair(_1615651, _1615651), _1615653), _1615659)), c_Transitive__Closure_Ortrancl(_1615651, _1615657))))], (44382 ^ _779571) ^ [_1647523, _1647525, _1647527, _1647529, _1647531, _1647533, _1647535, _1647537] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647523, tc_fun(_1647525, tc_fun(_1647527, tc_HOL_Obool))), _1647529), _1647531), _1647533), _1647535)), hBOOL(hAPP(hAPP(c_member(_1647523), _1647537), _1647529)), -(hBOOL(hAPP(hAPP(hAPP(_1647531, _1647537), _1647533), _1647535)))], (46997 ^ _779571) ^ [_1714069, _1714071, _1714073] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714069)), c_List_Osublist(_1714069, _1714071, _1714073)) = 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(_1714069)), _1714071)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1714073)))))], (7959 ^ _779571) ^ [_911626, _911628] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _911626) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _911628), -(hBOOL(hAPP(c_Com_OWT, _911628)))], (3914 ^ _779571) ^ [_839934, _839936] : [_839936 = _839934, -(c_Rings_Odvd__class_Odvd(_839936) = c_Rings_Odvd__class_Odvd(_839934))], (19111 ^ _779571) ^ [_1107332, _1107334] : [c_Int_OBit0(_1107332) = c_Int_OBit0(_1107334), -(_1107332 = _1107334)], (49798 ^ _779571) ^ [_1779818, _1779820] : [-(hAPP(c_List_Ofilter(_1779818, _1779820), c_List_Olist_ONil(_1779818)) = c_List_Olist_ONil(_1779818))], (39160 ^ _779571) ^ [_1516546, _1516548, _1516550, _1516552, _1516554] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516546, _1516548, _1516550), _1516552), _1516554), c_Orderings_Obot__class_Obot(tc_fun(_1516548, tc_HOL_Obool))) = _1516554)], (32993 ^ _779571) ^ [_1381348, _1381350, _1381352] : [class_Orderings_Olinorder(_1381348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381348, tc_HOL_Obool)), _1381350), _1381352)), -(_1381350 = c_Orderings_Obot__class_Obot(tc_fun(_1381348, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381348), _1381352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381348), c_Big__Operators_Olinorder__class_OMax(_1381348, _1381350)), c_Big__Operators_Olinorder__class_OMax(_1381348, _1381352))))], (39858 ^ _779571) ^ [_1532509, _1532511, _1532513] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1532509, _1532511, c_Orderings_Obot__class_Obot(tc_fun(_1532509, tc_HOL_Obool))), _1532513))], (49273 ^ _779571) ^ [_1768675, _1768677, _1768679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1768675, _1768675), tc_HOL_Obool)), _1768677), hAPP(hAPP(c_Product__Type_OSigma(_1768675, _1768675), _1768679), hAPP(c_COMBK(tc_fun(_1768675, tc_HOL_Obool), _1768675), _1768679)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1768675), tc_List_Olist(_1768675)), tc_HOL_Obool)), c_List_Olistrel(_1768675, _1768677)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1768675), tc_List_Olist(_1768675)), c_List_Olists(_1768675, _1768679)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1768675), tc_HOL_Obool), tc_List_Olist(_1768675)), c_List_Olists(_1768675, _1768679))))))], (16164 ^ _779571) ^ [_1055803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1055803)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055803), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1055803)], (1752 ^ _779571) ^ [_804239, _804241] : [-(class_Int_Onumber(_804239)), _804241 = _804239, class_Int_Onumber(_804241)], (36514 ^ _779571) ^ [_1457943, _1457945, _1457947] : [class_Lattices_Osemilattice__inf(_1457943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457943), _1457945), _1457947)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457943), _1457945), _1457947) = _1457945)], (50744 ^ _779571) ^ [_1799807, _1799809, _1799811] : [hAPP(c_List_Orev(_1799807), _1799809) = hAPP(c_List_Orev(_1799807), _1799811), -(_1799809 = _1799811)], (36204 ^ _779571) ^ [_1451456, _1451458, _1451460, _1451462] : [class_Lattices_Odistrib__lattice(_1451456), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451456), _1451458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451456), _1451460), _1451462)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451456), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451456), _1451458), _1451460)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451456), _1451458), _1451462)))], (46558 ^ _779571) ^ [_1700581, _1700583, _1700585, _1700587] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700581)), _1700583) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700585)), _1700587), -(hAPP(hAPP(c_List_Omap(tc_prod(_1700581, _1700585), _1700581), c_Product__Type_Ofst(_1700581, _1700585)), hAPP(hAPP(c_List_Ozip(_1700581, _1700585), _1700583), _1700587)) = _1700583)], (24311 ^ _779571) ^ [_1203243, _1203245, _1203247, _1203249] : [class_Orderings_Olinorder(_1203243), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203243), _1203245), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203243), _1203247), _1203249)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203243), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203243), _1203245), _1203247)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203243), _1203245), _1203249)))], (20519 ^ _779571) ^ [_1132371, _1132373, _1132375, _1132377] : [class_Rings_Odivision__ring(_1132371), -(_1132373 = c_Groups_Ozero__class_Ozero(_1132371)), _1132375 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132371), _1132377), _1132373), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132371), _1132375), _1132373) = _1132377)], (47292 ^ _779571) ^ [_1720588, _1720590] : [_1720590 = c_List_Olist_ONil(_1720588), -(c_Orderings_Obot__class_Obot(tc_fun(_1720588, tc_HOL_Obool)) = hAPP(c_List_Oset(_1720588), _1720590))], (17235 ^ _779571) ^ [_1075996] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1075996) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38673 ^ _779571) ^ [_1506131, _1506133, _1506135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506131), _1506133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1506131, tc_HOL_Obool)), _1506133), hAPP(c_Set_Oimage(_1506131, _1506131, _1506135), _1506133))), -(c_Fun_Oinj__on(_1506131, _1506131, _1506135, _1506133))], (4508 ^ _779571) ^ [_849349, _849351, _849353, _849355] : [-(c_Relation_Oconverse(_849355, _849351) = c_Relation_Oconverse(_849353, _849349)), _849355 = _849353, _849351 = _849349], (40867 ^ _779571) ^ [_1556823, _1556825, _1556827, _1556829, _1556831, _1556833, _1556835, _1556837] : [-(hAPP(c_Product__Type_Omap__pair(_1556823, _1556825, _1556827, _1556829, _1556831, _1556833), hAPP(hAPP(c_Product__Type_OPair(_1556823, _1556827), _1556835), _1556837)) = hAPP(hAPP(c_Product__Type_OPair(_1556825, _1556829), hAPP(_1556831, _1556835)), hAPP(_1556833, _1556837)))], (7264 ^ _779571) ^ [_899797, _899799, _899801, _899803, _899805, _899807] : [c_Nitpick_Opair__box_OPairBox(_899797, _899799, _899801, _899803) = c_Nitpick_Opair__box_OPairBox(_899797, _899799, _899805, _899807), 7267 ^ _779571 : [(7270 ^ _779571) ^ [] : [-(_899803 = _899807)], (7268 ^ _779571) ^ [] : [-(_899801 = _899805)]]], (18037 ^ _779571) ^ [_1089961, _1089963, _1089965] : [18039 ^ _779571 : [(18042 ^ _779571) ^ [] : [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(_1089963, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18038 ^ [_1089961, _1089963, _1089965]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1089963, 18038 ^ [_1089961, _1089963, _1089965])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18040 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18038 ^ [_1089961, _1089963, _1089965]), _1089961)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1089963, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1089965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089965), hAPP(_1089963, _1089961))), 18052 ^ _779571 : [(18055 ^ _779571) ^ [] : [-(hAPP(_1089963, 18051 ^ [_1089961, _1089963, _1089965]) = _1089965)], (18053 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18051 ^ [_1089961, _1089963, _1089965]), _1089961)))]]], (13920 ^ _779571) ^ [_1013476, _1013478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013476)), 13923 ^ _779571 : [(13926 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013478, _1013476)), _1013476)))], (13924 ^ _779571) ^ [] : [-(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, _1013478, _1013476))))]]], (49616 ^ _779571) ^ [_1776048, _1776050, _1776052] : [-(_1776048 = c_List_Olist_ONil(_1776050)), -(c_List_Obutlast(_1776050, hAPP(hAPP(c_List_Olist_OCons(_1776050), _1776052), _1776048)) = hAPP(hAPP(c_List_Olist_OCons(_1776050), _1776052), c_List_Obutlast(_1776050, _1776048)))], (49850 ^ _779571) ^ [_1781585, _1781587, _1781589, _1781591, _1781593, _1781595] : [hAPP(c_Map_Omap__of(_1781585, _1781587, _1781589), _1781591) = hAPP(c_Option_Ooption_OSome(_1781587), _1781593), hBOOL(hAPP(hAPP(_1781595, _1781591), _1781593)), -(hAPP(c_Map_Omap__of(_1781585, _1781587, hAPP(c_List_Ofilter(tc_prod(_1781585, _1781587), hAPP(c_Product__Type_Oprod_Oprod__case(_1781585, _1781587, tc_HOL_Obool), _1781595)), _1781589)), _1781591) = hAPP(c_Option_Ooption_OSome(_1781587), _1781593))], (27898 ^ _779571) ^ [_1273588, _1273590, _1273592, _1273594] : [class_Lattices_Osemilattice__sup(_1273588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273588), _1273590), _1273592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273588), _1273594), _1273592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273588), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273588), _1273590), _1273594)), _1273592)))], (32235 ^ _779571) ^ [_1366197, _1366199, _1366201, _1366203] : [hBOOL(hAPP(hAPP(c_member(_1366197), _1366199), c_SetInterval_Oord_OgreaterThan(_1366197, _1366201, _1366203))), -(hBOOL(hAPP(hAPP(_1366201, _1366203), _1366199)))], (7680 ^ _779571) ^ [_906815, _906817] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906815), _906817))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906815), hAPP(c_Nat_OSuc, _906817))), -(_906817 = _906815)], (44287 ^ _779571) ^ [_1645604, _1645606, _1645608, _1645610, _1645612, _1645614] : [c_Finite__Set_Ofun__left__comm(_1645604, _1645606, _1645608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645604), _1645610)), -(hAPP(hAPP(_1645608, _1645612), hAPP(hAPP(c_Finite__Set_Ofold(_1645604, _1645606, _1645608), _1645614), _1645610)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645604, _1645606, _1645608), hAPP(hAPP(_1645608, _1645612), _1645614)), _1645610))], (32157 ^ _779571) ^ [_1364720, _1364722, _1364724, _1364726] : [hBOOL(hAPP(hAPP(c_member(_1364720), _1364722), c_SetInterval_Oord_OlessThan(_1364720, _1364724, _1364726))), -(hBOOL(hAPP(hAPP(_1364724, _1364722), _1364726)))], (47348 ^ _779571) ^ [_1721688, _1721690] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1721688), _1721690))), -(c_List_Oupto(_1721688, _1721690) = c_List_Olist_ONil(tc_Int_Oint))], (50586 ^ _779571) ^ [_1796394, _1796396, _1796398] : [-(hAPP(c_List_Orev(_1796394), hAPP(hAPP(c_List_Olist_OCons(_1796394), _1796396), _1796398)) = hAPP(hAPP(c_List_Oappend(_1796394), hAPP(c_List_Orev(_1796394), _1796398)), hAPP(hAPP(c_List_Olist_OCons(_1796394), _1796396), c_List_Olist_ONil(_1796394))))], (30957 ^ _779571) ^ [_1336950, _1336952] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1336950), _1336952))))], (49718 ^ _779571) ^ [_1778308, _1778310, _1778312] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778308)), hAPP(c_List_Ofilter(_1778308, _1778310), _1778312))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778308)), hAPP(c_List_Ofilter(_1778308, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1778308), c_fNot), _1778310)), _1778312))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778308)), _1778312))], (40330 ^ _779571) ^ [_1544609, _1544611] : [class_Lattices_Olattice(_1544609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544609), _1544611)), -(c_Big__Operators_Olattice__class_OInf__fin(_1544609, _1544611) = hAPP(c_Finite__Set_Ofold1(_1544609, c_Lattices_Osemilattice__inf__class_Oinf(_1544609)), _1544611))], (43540 ^ _779571) ^ [_1628836, _1628838, _1628840] : [c_Relation_Ototal__on(_1628836, _1628838, hAPP(c_Relation_Oconverse(_1628836, _1628836), _1628840)), -(c_Relation_Ototal__on(_1628836, _1628838, _1628840))], (47264 ^ _779571) ^ [_1720128, _1720130] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720128)), _1720130) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1720130 = c_List_Olist_ONil(_1720128))], (49431 ^ _779571) ^ [_1772468, _1772470, _1772472] : [-(_1772468 = c_List_Olist_ONil(_1772470)), -(c_List_Olast(_1772470, hAPP(hAPP(c_List_Oappend(_1772470), _1772472), _1772468)) = c_List_Olast(_1772470, _1772468))], (44836 ^ _779571) ^ [_1660430, _1660432] : [class_Complete__Lattice_Ocomplete__lattice(_1660430), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660430), _1660432)), -(c_Complete__Lattice_OInf__class_OInf(_1660430, _1660432) = hAPP(hAPP(c_Finite__Set_Ofold(_1660430, _1660430, c_Lattices_Osemilattice__inf__class_Oinf(_1660430)), c_Orderings_Otop__class_Otop(_1660430)), _1660432))], (50318 ^ _779571) ^ [_1790396, _1790398] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1790396, _1790398)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1790396), hAPP(c_Nat_OSuc, _1790398)))], (50770 ^ _779571) ^ [_1800383, _1800385] : [-(_1800383 = c_List_Olist_ONil(_1800385)), -(hAPP(c_List_Ohd(_1800385), hAPP(c_List_Orev(_1800385), _1800383)) = c_List_Olast(_1800385, _1800383))], (29704 ^ _779571) ^ [_1310428, _1310430, _1310432, _1310434, _1310436] : [_1310428 = c_Orderings_Obot__class_Obot(tc_fun(_1310430, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310430, tc_fun(_1310432, tc_HOL_Obool)), _1310428), hAPP(hAPP(c_COMBC(_1310430, tc_fun(_1310432, tc_HOL_Obool), tc_fun(_1310432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310432, tc_HOL_Obool), tc_fun(tc_fun(_1310432, tc_HOL_Obool), tc_fun(_1310432, tc_HOL_Obool)), _1310430), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310432, tc_HOL_Obool))), _1310434)), _1310436)) = c_Orderings_Obot__class_Obot(tc_fun(_1310432, tc_HOL_Obool)))], (18669 ^ _779571) ^ [_1099886, _1099888] : [c_Int_OBit1(_1099886) = c_Int_OBit1(_1099888), -(_1099886 = _1099888)], (33717 ^ _779571) ^ [_1395452, _1395454] : [class_Orderings_Olinorder(_1395452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395452), _1395454)), -(_1395454 = c_Orderings_Obot__class_Obot(tc_fun(_1395452, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395452), c_Big__Operators_Olattice_OInf__fin(_1395452, c_Orderings_Oord__class_Omin(_1395452), _1395454)), c_Big__Operators_Olattice_OSup__fin(_1395452, c_Orderings_Oord__class_Omax(_1395452), _1395454))))], (7085 ^ _779571) ^ [_896221, _896223, _896225, _896227] : [class_Groups_Ocancel__semigroup__add(_896221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896221), _896223), _896225) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896221), _896227), _896225), -(_896223 = _896227)], (17299 ^ _779571) ^ [_1076979, _1076981] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076979)), _1076981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076979), _1076981)))], (28545 ^ _779571) ^ [_1286437] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286437)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1286437))], (43915 ^ _779571) ^ [_1638363, _1638365, _1638367, _1638369] : [class_Lattices_Osemilattice__inf(_1638363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638363), _1638365)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1638363, _1638363, c_Lattices_Osemilattice__inf__class_Oinf(_1638363)), _1638367), hAPP(hAPP(c_Set_Oinsert(_1638363), _1638369), _1638365)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1638363), _1638369), hAPP(hAPP(c_Finite__Set_Ofold(_1638363, _1638363, c_Lattices_Osemilattice__inf__class_Oinf(_1638363)), _1638367), _1638365)))], (16355 ^ _779571) ^ [_1059310, _1059312] : [class_Int_Onumber__ring(_1059310), -(hAPP(c_Int_Oring__1__class_Oof__int(_1059310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1059312)) = hAPP(c_Int_Onumber__class_Onumber__of(_1059310), _1059312))], (48512 ^ _779571) ^ [_1750058, _1750060] : [-(c_List_Olistrel1(_1750058, hAPP(c_Relation_Oconverse(_1750058, _1750058), _1750060)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1750058), tc_List_Olist(_1750058)), c_List_Olistrel1(_1750058, _1750060)))], (41975 ^ _779571) ^ [_1590802, _1590804] : [41977 ^ _779571 : [(41978 ^ _779571) ^ [_1590827] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590802, _1590802)), hAPP(hAPP(c_Product__Type_OPair(_1590802, _1590802), hAPP(41976 ^ [_1590802, _1590804], hAPP(c_Nat_OSuc, _1590827))), hAPP(41976 ^ [_1590802, _1590804], _1590827))), _1590804)))]], -(c_Wellfounded_Owf(_1590802, _1590804))], (9458 ^ _779571) ^ [_936580, _936582] : [class_Groups_Oordered__ab__group__add(_936580), 9461 ^ _779571 : [(9468 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), c_Groups_Ozero__class_Ozero(_936580)), _936582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), hAPP(c_Groups_Ouminus__class_Ouminus(_936580), _936582)), c_Groups_Ozero__class_Ozero(_936580))))], (9462 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), hAPP(c_Groups_Ouminus__class_Ouminus(_936580), _936582)), c_Groups_Ozero__class_Ozero(_936580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936580), c_Groups_Ozero__class_Ozero(_936580)), _936582)))]]], (19875 ^ _779571) ^ [_1120841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1120841)), -(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), _1120841), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (15520 ^ _779571) ^ [_1042466, _1042468, _1042470] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042466), _1042468)), _1042470) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042466), _1042470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042468), _1042470)))], (47218 ^ _779571) ^ [_1719285, _1719287, _1719289, _1719291] : [_1719291 = c_List_Olist_ONil(_1719287), -(c_List_Olist_ONil(_1719285) = hAPP(hAPP(c_List_Omap(_1719287, _1719285), _1719289), _1719291))], (5732 ^ _779571) ^ [_871129, _871131, _871133] : [c_Hoare__Mirabelle_Ohoare__valids(_871129, _871131, _871133), 5735 ^ _779571 : [(5736 ^ _779571) ^ [_871238] : [5738 ^ _779571 : [(5741 ^ _779571) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_871129, _871238, 5737 ^ [_871129, _871131, _871133, _871238])], (5739 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871129)), 5737 ^ [_871129, _871131, _871133, _871238]), _871131)))]], 5742 ^ _779571 : [(5743 ^ _779571) ^ [_871410] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871129)), _871410), _871133)), -(c_Hoare__Mirabelle_Otriple__valid(_871129, _871238, _871410))]]]]], (23909 ^ _779571) ^ [_1195451, _1195453, _1195455, _1195457, _1195459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195451, tc_HOL_Obool)), _1195453), _1195455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195451, tc_HOL_Obool)), _1195457), _1195459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195451, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195451, tc_HOL_Obool)), _1195453), _1195459)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195451, tc_HOL_Obool)), _1195455), _1195457))))], (31732 ^ _779571) ^ [_1355440, _1355442, _1355444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1355440), _1355442)), 31735 ^ _779571 : [(31742 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1355440), _1355444), _1355442))), -(hAPP(c_Finite__Set_Ocard(_1355440), hAPP(hAPP(c_Set_Oinsert(_1355440), _1355444), _1355442)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1355440), _1355442)))], (31736 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1355440), _1355444), _1355442)), -(hAPP(c_Finite__Set_Ocard(_1355440), hAPP(hAPP(c_Set_Oinsert(_1355440), _1355444), _1355442)) = hAPP(c_Finite__Set_Ocard(_1355440), _1355442))]]], (822 ^ _779571) ^ [_792264, _792266, _792268, _792270, _792272, _792274] : [-(c_Finite__Set_Ofun__left__comm(_792272, _792268, _792264)), c_Finite__Set_Ofun__left__comm(_792274, _792270, _792266), _792274 = _792272, _792270 = _792268, _792266 = _792264], (45791 ^ _779571) ^ [_1682018, _1682020, _1682022, _1682024] : [-(c_Map_Omap__add(_1682018, _1682020, _1682022, c_Map_Omap__of(_1682018, _1682020, _1682024)) = c_List_Ofoldr(tc_prod(_1682018, _1682020), tc_fun(_1682018, tc_Option_Ooption(_1682020)), hAPP(c_Product__Type_Oprod_Oprod__case(_1682018, _1682020, tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), hAPP(hAPP(c_COMBC(_1682018, tc_fun(_1682020, tc_Option_Ooption(_1682020)), tc_fun(_1682020, tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1682020), tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), tc_fun(tc_fun(_1682020, tc_Option_Ooption(_1682020)), tc_fun(_1682020, tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020))))), _1682018), c_COMBB(tc_Option_Ooption(_1682020), tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020))), _1682020)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(tc_Option_Ooption(_1682020), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), tc_fun(tc_Option_Ooption(_1682020), tc_fun(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), _1682018), c_COMBC(tc_fun(_1682018, tc_Option_Ooption(_1682020)), tc_Option_Ooption(_1682020), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), hAPP(c_COMBC(tc_fun(_1682018, tc_Option_Ooption(_1682020)), _1682018, tc_fun(tc_Option_Ooption(_1682020), tc_fun(_1682018, tc_Option_Ooption(_1682020)))), c_Fun_Ofun__upd(_1682018, tc_Option_Ooption(_1682020)))))), c_Option_Ooption_OSome(_1682020))), _1682024, _1682022))], (31265 ^ _779571) ^ [_1344319, _1344321, _1344323, _1344325, _1344327, _1344329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1344319, _1344321)), hAPP(hAPP(c_Product__Type_OPair(_1344319, _1344321), _1344327), _1344329)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool)), _1344323), _1344325))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1344319, tc_fun(_1344321, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1344319, tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_fun(_1344321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344321, tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_fun(_1344321, tc_HOL_Obool)), _1344319), c_COMBC(_1344321, tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344321, tc_prod(_1344319, _1344321)), tc_fun(_1344321, tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), _1344319), hAPP(c_COMBB(tc_prod(_1344319, _1344321), tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool), _1344321), c_member(tc_prod(_1344319, _1344321)))), c_Product__Type_OPair(_1344319, _1344321)))), _1344323)), hAPP(hAPP(c_COMBC(_1344319, tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_fun(_1344321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344321, tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_fun(_1344321, tc_HOL_Obool)), _1344319), c_COMBC(_1344321, tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344321, tc_prod(_1344319, _1344321)), tc_fun(_1344321, tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool)), _1344319), hAPP(c_COMBB(tc_prod(_1344319, _1344321), tc_fun(tc_fun(tc_prod(_1344319, _1344321), tc_HOL_Obool), tc_HOL_Obool), _1344321), c_member(tc_prod(_1344319, _1344321)))), c_Product__Type_OPair(_1344319, _1344321)))), _1344325)), _1344327), _1344329)))], (15490 ^ _779571) ^ [_1041844, _1041846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041844), _1041846)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041846), _1041844)) = _1041844)], (41033 ^ _779571) ^ [_1561005] : [class_Lattices_Osemilattice__inf(_1561005), -(c_Finite__Set_Ofun__left__comm__idem(_1561005, _1561005, c_Lattices_Osemilattice__inf__class_Oinf(_1561005)))], (29886 ^ _779571) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34676 ^ _779571) ^ [_1415051, _1415053, _1415055, _1415057, _1415059] : [-(c_Map_Orestrict__map(_1415051, _1415053, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415051, tc_Option_Ooption(_1415053)), _1415055), _1415057), hAPP(c_Option_Ooption_OSome(_1415053), _1415059)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1415051, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1415051), _1415057), c_Orderings_Obot__class_Obot(tc_fun(_1415051, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1415051, _1415053, _1415055, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1415051, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1415051), _1415057), c_Orderings_Obot__class_Obot(tc_fun(_1415051, tc_HOL_Obool))))))], (43066 ^ _779571) ^ [_1617166, _1617168, _1617170, _1617172] : [43067 ^ _779571 : [(43070 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617166, _1617166)), _1617168), c_Transitive__Closure_Ortrancl(_1617166, _1617172)))], (43068 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617166, _1617166)), _1617168), c_Transitive__Closure_Ortrancl(_1617166, _1617170)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617166, _1617166)), _1617168), c_Transitive__Closure_Ortrancl(_1617166, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1617166, _1617166), tc_HOL_Obool)), _1617170), _1617172)))))], (51373 ^ _779571) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (16509 ^ _779571) ^ [_1062057, _1062059] : [class_Int_Onumber__ring(_1062057), 16512 ^ _779571 : [(16519 ^ _779571) ^ [] : [-(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), _1062059)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1062057), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062059)) = c_Groups_Ozero__class_Ozero(_1062057))], (16513 ^ _779571) ^ [] : [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), _1062059))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1062057), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062059)) = hAPP(c_Int_Onumber__class_Onumber__of(_1062057), _1062059))]]], (28903 ^ _779571) ^ [_1294322, _1294324, _1294326, _1294328, _1294330] : [class_Complete__Lattice_Ocomplete__lattice(_1294322), class_Orderings_Olinorder(_1294322), 28910 ^ _779571 : [(28920 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294322), _1294324), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294326, _1294322), _1294328), _1294330)))), 28921 ^ _779571 : [(28922 ^ _779571) ^ [_1294670] : [hBOOL(hAPP(hAPP(c_member(_1294326), _1294670), _1294328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294322), _1294324), hAPP(_1294330, _1294670)))]]], (28911 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294322), _1294324), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294326, _1294322), _1294328), _1294330))), 28915 ^ _779571 : [(28918 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294322), _1294324), hAPP(_1294330, 28914 ^ [_1294322, _1294324, _1294326, _1294328, _1294330]))))], (28916 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294326), 28914 ^ [_1294322, _1294324, _1294326, _1294328, _1294330]), _1294328)))]]]]], (9426 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (344 ^ _779571) ^ [_784719, _784721, _784723, _784725, _784727, _784729, _784731, _784733] : [-(c_Finite__Set_Ofolding__idem(_784731, _784727, _784723, _784719)), c_Finite__Set_Ofolding__idem(_784733, _784729, _784725, _784721), _784733 = _784731, _784729 = _784727, _784725 = _784723, _784721 = _784719], (45511 ^ _779571) ^ [_1675774, _1675776] : [c_Wellfounded_Owf(_1675774, _1675776), 45514 ^ _779571 : [(45515 ^ _779571) ^ [_1675906] : [45516 ^ _779571 : [(45517 ^ _779571) ^ [_1676011] : [hBOOL(hAPP(hAPP(c_member(_1675774), _1676011), _1675906))]], 45519 ^ _779571 : [(45522 ^ _779571) ^ [_1676133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1675774, _1675774)), hAPP(hAPP(c_Product__Type_OPair(_1675774, _1675774), _1676133), 45518 ^ [_1675774, _1675776, _1675906])), _1675776)), hBOOL(hAPP(hAPP(c_member(_1675774), _1676133), _1675906))], (45520 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675774), 45518 ^ [_1675774, _1675776, _1675906]), _1675906)))]]]]], (24519 ^ _779571) ^ [_1207153, _1207155, _1207157, _1207159] : [class_Orderings_Olinorder(_1207153), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207153), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207153), _1207155), _1207157)), _1207159) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207153), _1207155), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207153), _1207157), _1207159)))], (16220 ^ _779571) ^ [_1056930, _1056932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1056930)), 16223 ^ _779571 : [(16230 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056932), _1056930))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1056932), _1056930) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056932), _1056930)), _1056930)))], (16224 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056932), _1056930)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1056932), _1056930) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50047 ^ _779571) ^ [_1785786, _1785788, _1785790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1785786), _1785788)), -(c_List_Oupt(_1785786, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1785788), _1785790)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1785786, _1785788)), c_List_Oupt(_1785788, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1785788), _1785790))))], (51411 ^ _779571) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (5562 ^ _779571) ^ [_865468, _865470] : [_865470 = _865468, -(c_List_Oset(_865470) = c_List_Oset(_865468))], (42126 ^ _779571) ^ [_1594191, _1594193, _1594195, _1594197] : [-(hAPP(c_Relation_ORange(_1594191, _1594193), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1594191, _1594193), tc_HOL_Obool)), _1594195), _1594197)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1594193, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594191, _1594193), _1594195)), hAPP(c_Relation_ORange(_1594191, _1594193), _1594197)))], (14092 ^ _779571) ^ [_1016593, _1016595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016593))), -(c_SMT_Oz3mod(_1016595, _1016593) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016595, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016593)))], (36230 ^ _779571) ^ [_1452224, _1452226, _1452228, _1452230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452224, tc_HOL_Obool)), _1452226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452224, tc_HOL_Obool)), _1452228), _1452230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452224, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452224, tc_HOL_Obool)), _1452226), _1452228)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452224, tc_HOL_Obool)), _1452226), _1452230)))], (27123 ^ _779571) ^ [_1257419, _1257421, _1257423, _1257425] : [class_Groups_Ocomm__monoid__add(_1257419), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257419), _1257421), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1257423)), hAPP(c_Nat_OSuc, _1257425))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257419), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1257419, tc_Nat_Onat), _1257421), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257423), _1257425)))], (43736 ^ _779571) ^ [_1633750, _1633752, _1633754] : [c_Relation_Osingle__valued(_1633750, _1633750, _1633752), -(c_Relation_Osingle__valued(_1633750, _1633750, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1633750, _1633750), tc_HOL_Obool), _1633754), _1633752)))], (41080 ^ _779571) ^ [_1561843, _1561845] : [-(hBOOL(hAPP(_1561845, 41081 ^ [_1561843, _1561845]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1561843, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561843), _1561845))], (8048 ^ _779571) ^ [_912936, _912938, _912940] : [_912938 = _912940, -(hAPP(c_Option_Ooption_OSome(_912936), _912938) = hAPP(c_Option_Ooption_OSome(_912936), _912940))], (18667 ^ _779571) ^ [_1099822, _1099824] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1099822)))), _1099824) = 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)))), _1099822)), _1099824))], (36396 ^ _779571) ^ [_1455795, _1455797, _1455799, _1455801] : [class_Lattices_Osemilattice__inf(_1455795), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455795), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455795), _1455797), _1455799)), _1455801) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455795), _1455797), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455795), _1455799), _1455801)))], (14186 ^ _779571) ^ [_1018411, _1018413, _1018415] : [hBOOL(hAPP(_1018411, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018413), _1018415))), 14189 ^ _779571 : [(14214 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018415), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14217 ^ _779571 : [(14218 ^ _779571) ^ [_1019075] : [-(hBOOL(hAPP(_1018411, _1019075))), 14219 ^ _779571 : [(14220 ^ _779571) ^ [_1019149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018415), _1019149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019149), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1018413 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018415), _1019075)), _1019149)]]]]], (14196 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018415)), 14199 ^ _779571 : [(14200 ^ _779571) ^ [_1018745] : [-(hBOOL(hAPP(_1018411, _1018745))), 14201 ^ _779571 : [(14202 ^ _779571) ^ [_1018816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018816), _1018415)), _1018413 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018415), _1018745)), _1018816)]]]]], (14190 ^ _779571) ^ [] : [_1018415 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1018411, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10964 ^ _779571) ^ [_961629, _961631, _961633] : [class_Orderings_Opreorder(_961629), 10967 ^ _779571 : [(10976 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961629), _961631), _961633))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961629), _961631), _961633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961629), _961633), _961631)))], (10968 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961629), _961631), _961633)), 10971 ^ _779571 : [(10974 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961629), _961633), _961631))], (10972 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961629), _961631), _961633)))]]]]], (24679 ^ _779571) ^ [_1210538, _1210540] : [_1210538 = _1210540, -(hAPP(c_Code__Numeral_Onat__of, _1210538) = hAPP(c_Code__Numeral_Onat__of, _1210540))], (22188 ^ _779571) ^ [_1162476, _1162478, _1162480, _1162482] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1162476, _1162478, _1162480, c_Code__Numeral_OSuc__code__numeral(_1162482)) = hAPP(_1162480, _1162482))], (45231 ^ _779571) ^ [_1669493, _1669495, _1669497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669493, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669493, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1669493, tc_HOL_Obool), tc_HOL_Obool)), _1669495), _1669497))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669493, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669493, tc_HOL_Obool), _1669495)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669493, tc_HOL_Obool), _1669497)))))], (7177 ^ _779571) ^ [_898001, _898003, _898005, _898007] : [class_Rings_Ocomm__semiring__1(_898001), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898001), _898003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898001), _898005), _898007)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898001), _898005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898001), _898003), _898007)))], (21097 ^ _779571) ^ [_1142656, _1142658, _1142660, _1142662, _1142664] : [class_Fields_Ofield(_1142656), -(_1142658 = c_Groups_Ozero__class_Ozero(_1142656)), -(_1142660 = c_Groups_Ozero__class_Ozero(_1142656)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142656), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142656), _1142662), _1142658)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142656), _1142664), _1142660)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142656), _1142662), _1142660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142656), _1142664), _1142658))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142656), _1142658), _1142660)))], (44297 ^ _779571) ^ [_1645823, _1645825, _1645827, _1645829, _1645831, _1645833] : [c_Finite__Set_Ofun__left__comm(_1645823, _1645825, _1645827), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1645823, _1645825, _1645827, _1645829, _1645831), _1645833)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1645823, _1645825, _1645827), _1645829), _1645831) = _1645833)], (43582 ^ _779571) ^ [_1629907, _1629909, _1629911, _1629913] : [-(hAPP(hAPP(c_Nat_Ocompow(_1629907, _1629907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1629909), _1629911)), _1629913) = hAPP(c_Fun_Ocomp(_1629907, _1629907, _1629907, hAPP(hAPP(c_Nat_Ocompow(_1629907, _1629907), _1629909), _1629913)), hAPP(hAPP(c_Nat_Ocompow(_1629907, _1629907), _1629911), _1629913)))], (22624 ^ _779571) ^ [_1171102, _1171104] : [22625 ^ _779571 : [(22628 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171104), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22626 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171102), _1171104))]], -(c_Divides_OposDivAlg(_1171102, _1171104) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171102))], (29798 ^ _779571) ^ [_1312417, _1312419] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312417), _1312419))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1312417), hAPP(c_Nat_OSuc, _1312419)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (49866 ^ _779571) ^ [_1782010, _1782012, _1782014] : [-(c_List_Omap__filter(_1782010, _1782012, _1782014, c_List_Olist_ONil(_1782010)) = c_List_Olist_ONil(_1782012))], (6758 ^ _779571) ^ [_890592, _890594, _890596, _890598] : [c_Com_Ocom_OAss(_890592, _890594) = c_Com_Ocom_OWhile(_890596, _890598)], (5472 ^ _779571) ^ [_864141, _864143, _864145, _864147] : [-(c_List_Ofilter(_864147, _864143) = c_List_Ofilter(_864145, _864141)), _864147 = _864145, _864143 = _864141], (6718 ^ _779571) ^ [_889682, _889684, _889686, _889688] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_889682, _889684)), _889686), _889688))), 6719 ^ _779571 : [(6720 ^ _779571) ^ [_889750] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889682), _889686), _889750)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889684), _889750), _889688))]]], (50688 ^ _779571) ^ [_1798611] : [-(c_List_Oconcat(_1798611, c_List_Olist_ONil(tc_List_Olist(_1798611))) = c_List_Olist_ONil(_1798611))], (38451 ^ _779571) ^ [_1502038, _1502040, _1502042, _1502044] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502038), hAPP(c_Set_Oimage(_1502040, _1502038, _1502042), _1502044))), c_Fun_Oinj__on(_1502040, _1502038, _1502042, _1502044), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502040), _1502044)))], (51307 ^ _779571) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (13472 ^ _779571) ^ [_1005246, _1005248, _1005250] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005246), _1005248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005246), _1005250), -(_1005246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1005248 = _1005250)], (39114 ^ _779571) ^ [_1515453, _1515455, _1515457, _1515459, _1515461, _1515463, _1515465] : [c_Fun_Oinj__on(_1515453, _1515455, _1515457, hAPP(c_Set_Oimage(_1515459, _1515453, _1515461), _1515463)), c_Fun_Oinj__on(_1515459, _1515453, _1515461, _1515463), hBOOL(hAPP(hAPP(c_member(_1515455), _1515465), hAPP(c_Set_Oimage(_1515453, _1515455, _1515457), hAPP(c_Set_Oimage(_1515459, _1515453, _1515461), _1515463)))), -(hAPP(c_Fun_Othe__inv__into(_1515459, _1515455, _1515463, hAPP(c_Fun_Ocomp(_1515453, _1515455, _1515459, _1515457), _1515461)), _1515465) = hAPP(hAPP(c_Fun_Ocomp(_1515453, _1515459, _1515455, c_Fun_Othe__inv__into(_1515459, _1515453, _1515463, _1515461)), c_Fun_Othe__inv__into(_1515453, _1515455, hAPP(c_Set_Oimage(_1515459, _1515453, _1515461), _1515463), _1515457)), _1515465))], (9042 ^ _779571) ^ [_929442, _929444] : [class_Groups_Ogroup__add(_929442), -(hAPP(c_Groups_Ouminus__class_Ouminus(_929442), hAPP(c_Groups_Ouminus__class_Ouminus(_929442), _929444)) = _929444)], (49219 ^ _779571) ^ [_1767193, _1767195, _1767197] : [class_Orderings_Olinorder(_1767193), -(c_Big__Operators_Olattice_OInf__fin(_1767193, c_Orderings_Oord__class_Omin(_1767193), hAPP(c_List_Oset(_1767193), hAPP(hAPP(c_List_Olist_OCons(_1767193), _1767195), _1767197))) = hAPP(c_List_Ofoldl(_1767193, _1767193, c_Orderings_Oord__class_Omin(_1767193), _1767195), _1767197))], (43355 ^ _779571) ^ [_1624215, _1624217] : [-(hAPP(c_Relation_OField(_1624215), hAPP(c_Relation_Oconverse(_1624215, _1624215), _1624217)) = hAPP(c_Relation_OField(_1624215), _1624217))], (20107 ^ _779571) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47549 ^ _779571) ^ [_1726744, _1726746, _1726748, _1726750, _1726752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726744), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726746)), _1726748))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726744), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726750)), _1726752))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1726746, _1726750)), hAPP(hAPP(c_List_Ozip(_1726746, _1726750), _1726748), _1726752)), _1726744) = hAPP(hAPP(c_Product__Type_OPair(_1726746, _1726750), hAPP(hAPP(c_List_Onth(_1726746), _1726748), _1726744)), hAPP(hAPP(c_List_Onth(_1726750), _1726752), _1726744)))], (49716 ^ _779571) ^ [_1778245, _1778247, _1778249, _1778251] : [-(hAPP(c_List_Ofilter(_1778245, _1778247), hAPP(hAPP(c_List_Oappend(_1778245), _1778249), _1778251)) = hAPP(hAPP(c_List_Oappend(_1778245), hAPP(c_List_Ofilter(_1778245, _1778247), _1778249)), hAPP(c_List_Ofilter(_1778245, _1778247), _1778251)))], (24751 ^ _779571) ^ [_1211819] : [-(c_Nitpick_Oone__frac(_1211819) = c_Nitpick_OAbs__Frac(_1211819, 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))))], (22152 ^ _779571) ^ [_1161974, _1161976] : [_1161974 = _1161976, -(c_Random_Oinc__shift(_1161974, _1161976) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (39419 ^ _779571) ^ [_1522206, _1522208, _1522210] : [-(hAPP(c_Set_Ovimage(_1522206, _1522208, _1522210), c_Orderings_Otop__class_Otop(tc_fun(_1522208, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522206, tc_HOL_Obool)))], (49889 ^ _779571) ^ [_1782509, _1782511, _1782513, _1782515] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1782509, tc_Nat_Onat), _1782509), c_Product__Type_Ofst(_1782509, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1782509, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1782509, tc_Nat_Onat)), _1782511), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1782509, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1782509, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1782509, tc_Nat_Onat), _1782513), _1782515))) = hAPP(hAPP(c_List_Omap(tc_prod(_1782509, tc_Nat_Onat), _1782509), c_Product__Type_Ofst(_1782509, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1782509, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1782509, tc_Nat_Onat)), _1782511), c_Product__Type_Osnd(_1782509, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1782509, tc_Nat_Onat), _1782513), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1782515)))))], (44412 ^ _779571) ^ [_1648144, _1648146, _1648148, _1648150, _1648152, _1648154] : [hBOOL(hAPP(hAPP(c_member(_1648144), _1648146), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648148, tc_fun(_1648144, tc_HOL_Obool)), _1648150), _1648152))), hBOOL(hAPP(hAPP(c_member(_1648148), _1648154), _1648150)), -(hBOOL(hAPP(hAPP(c_member(_1648144), _1648146), hAPP(_1648152, _1648154))))], (14375 ^ _779571) ^ [_1022185, _1022187] : [class_Divides_Osemiring__div(_1022185), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1022185), c_Groups_Ozero__class_Ozero(_1022185)), _1022187) = c_Groups_Ozero__class_Ozero(_1022185))], (13980 ^ _779571) ^ [_1014466, _1014468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1014466), _1014468)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1014466, _1014468) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1014466), _1014468))], (33097 ^ _779571) ^ [_1383047, _1383049, _1383051] : [class_Orderings_Olinorder(_1383047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383047), _1383049)), -(_1383049 = c_Orderings_Obot__class_Obot(tc_fun(_1383047, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383047), _1383051)), -(_1383051 = c_Orderings_Obot__class_Obot(tc_fun(_1383047, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1383047, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1383047, tc_HOL_Obool)), _1383049), _1383051)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1383047), c_Big__Operators_Olinorder__class_OMax(_1383047, _1383049)), c_Big__Operators_Olinorder__class_OMax(_1383047, _1383051)))], (24883 ^ _779571) ^ [_1214837, _1214839, _1214841, _1214843] : [-(c_New__Random__Sequence_Opos__empty(_1214837, _1214839, _1214841, _1214843) = c_New__DSequence_Opos__empty(_1214837))], (36980 ^ _779571) ^ [_1468583, _1468585, _1468587] : [class_Orderings_Oorder(_1468583), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468583, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1468583, _1468585, _1468587)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1468583), _1468587)) = c_Orderings_Obot__class_Obot(tc_fun(_1468583, tc_HOL_Obool)))], (33625 ^ _779571) ^ [_1393437, _1393439, _1393441, _1393443] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393437), _1393439)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393441), _1393443)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1393437, _1393441)), c_Sum__Type_OPlus(_1393437, _1393441, _1393439, _1393443))))], (18331 ^ _779571) ^ [_1094456] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094456), c_Int_OPls) = _1094456)], (32004 ^ _779571) ^ [_1361528, _1361530, _1361532, _1361534, _1361536] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1361528, _1361530, _1361532), _1361534), _1361536)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361528, _1361530)), hAPP(hAPP(c_Product__Type_OPair(_1361528, _1361530), _1361534), _1361536)), _1361532)))], (3146 ^ _779571) ^ [_827796, _827798] : [_827798 = _827796, -(c_DSequence_Osingle(_827798) = c_DSequence_Osingle(_827796))], (27107 ^ _779571) ^ [_1257138, _1257140, _1257142, _1257144, _1257146] : [class_Orderings_Olinorder(_1257138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257138, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257138, _1257140), _1257142)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257138, _1257144), _1257146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257138), _1257142), _1257140))), 27118 ^ _779571 : [(27121 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257138), _1257142), _1257146)))], (27119 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257138), _1257144), _1257140)))]]], (17843 ^ _779571) ^ [_1086649, _1086651, _1086653, _1086655] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1086649, _1086651, _1086653), _1086655), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1086651)], (43560 ^ _779571) ^ [_1629225, _1629227, _1629229, _1629231, _1629233, _1629235] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629225, _1629225)), hAPP(hAPP(c_Product__Type_OPair(_1629225, _1629225), _1629227), _1629229)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629225, _1629225), tc_HOL_Obool), _1629231), _1629233))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1629225, _1629225)), hAPP(hAPP(c_Product__Type_OPair(_1629225, _1629225), _1629229), _1629235)), _1629233)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629225, _1629225)), hAPP(hAPP(c_Product__Type_OPair(_1629225, _1629225), _1629227), _1629235)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629225, _1629225), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1629231)), _1629233))))], (16843 ^ _779571) ^ [_1068276, _1068278] : [class_Rings_Ocomm__semiring__1(_1068276), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1068276), _1068278), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1068276))], (51157 ^ _779571) ^ [_1809133, _1809135] : [class_Orderings_Obot(_1809133), -(class_Orderings_Obot(tc_fun(_1809135, _1809133)))], (11310 ^ _779571) ^ [_967409, _967411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967409), _967411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967409)), hAPP(c_Nat_OSuc, _967411))))], (6762 ^ _779571) ^ [_890701, _890703, _890705, _890707, _890709] : [c_Com_Ocom_OAss(_890701, _890703) = c_Com_Ocom_OCond(_890705, _890707, _890709)], (622 ^ _779571) ^ [_789268, _789270] : [-(c_Nitpick_Ounknown(_789268)), _789270 = _789268, c_Nitpick_Ounknown(_789270)], (14520 ^ _779571) ^ [_1024485] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024485), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36228 ^ _779571) ^ [_1452140, _1452142, _1452144, _1452146] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452140, tc_HOL_Obool)), _1452142), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452140, tc_HOL_Obool)), _1452144), _1452146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452140, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452140, tc_HOL_Obool)), _1452142), _1452144)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452140, tc_HOL_Obool)), _1452142), _1452146)))], (48 ^ _779571) ^ [_780217, _780219] : [-(class_Rings_Odivision__ring__inverse__zero(_780217)), _780219 = _780217, class_Rings_Odivision__ring__inverse__zero(_780219)], (22716 ^ _779571) ^ [_1173078, _1173080, _1173082, _1173084, _1173086] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1173078, _1173080), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1173082), _1173084))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173080)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173086), _1173078), _1173080), 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), _1173086), _1173082)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173086), _1173084)), _1173080))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173086), _1173084), _1173080)))))], (1492 ^ _779571) ^ [_800989, _800991] : [-(class_Rings_Olinordered__semidom(_800989)), _800991 = _800989, class_Rings_Olinordered__semidom(_800991)], (15674 ^ _779571) ^ [_1045636, _1045638] : [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), _1045636), _1045638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045638), _1045636)))], (26680 ^ _779571) ^ [_1248786, _1248788, _1248790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248786)), 26683 ^ _779571 : [(26690 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248788), _1248790)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248786), _1248788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248786), _1248790))))], (26684 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248786), _1248788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248786), _1248790))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248788), _1248790)))]]], (24525 ^ _779571) ^ [_1207296, _1207298, _1207300, _1207302] : [class_Orderings_Olinorder(_1207296), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207296), _1207298), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207296), _1207300), _1207302)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207296), _1207300), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207296), _1207298), _1207302)))], (1462 ^ _779571) ^ [_800614, _800616] : [-(class_Rings_Oordered__comm__semiring(_800614)), _800616 = _800614, class_Rings_Oordered__comm__semiring(_800616)], (49012 ^ _779571) ^ [_1762880, _1762882, _1762884] : [-(hAPP(c_List_Oset(_1762880), hAPP(c_List_Orotate(_1762880, _1762882), _1762884)) = hAPP(c_List_Oset(_1762880), _1762884))], (3584 ^ _779571) ^ [_834679, _834681, _834683, _834685, _834687, _834689, _834691, _834693, _834695, _834697] : [-(c_Fun_Ooverride__on(_834697, _834693, _834689, _834685, _834681) = c_Fun_Ooverride__on(_834695, _834691, _834687, _834683, _834679)), _834697 = _834695, _834693 = _834691, _834689 = _834687, _834685 = _834683, _834681 = _834679], (46012 ^ _779571) ^ [_1687440, _1687442, _1687444, _1687446] : [-(hAPP(c_List_Oset(_1687440), hAPP(hAPP(c_List_Omap(_1687442, _1687440), _1687444), _1687446)) = hAPP(c_Set_Oimage(_1687442, _1687440, _1687444), hAPP(c_List_Oset(_1687442), _1687446)))], (19215 ^ _779571) ^ [_1109099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1109099)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109099), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8516 ^ _779571) ^ [_920603, _920605, _920607] : [class_Orderings_Oorder(_920603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920603), _920605), _920607)), _920607 = _920605], (18637 ^ _779571) ^ [_1099254, _1099256] : [class_Int_Onumber__ring(_1099254), 18640 ^ _779571 : [(18647 ^ _779571) ^ [] : [c_Int_Oiszero(_1099254, hAPP(c_Int_Onumber__class_Onumber__of(_1099254), 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), _1099256)))), -(c_Groups_Oone__class_Oone(_1099254) = hAPP(c_Int_Onumber__class_Onumber__of(_1099254), _1099256))], (18641 ^ _779571) ^ [] : [c_Groups_Oone__class_Oone(_1099254) = hAPP(c_Int_Onumber__class_Onumber__of(_1099254), _1099256), -(c_Int_Oiszero(_1099254, hAPP(c_Int_Onumber__class_Onumber__of(_1099254), 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), _1099256)))))]]], (49372 ^ _779571) ^ [_1771067, _1771069, _1771071, _1771073] : [49373 ^ _779571 : [(49374 ^ _779571) ^ [_1771164, _1771166] : [_1771067 = hAPP(hAPP(c_List_Olist_OCons(_1771069), _1771166), _1771164)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1771069), tc_List_Olist(_1771069))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771069), tc_List_Olist(_1771069)), _1771071), hAPP(hAPP(c_List_Oappend(_1771069), _1771071), _1771067))), c_List_Olexord(_1771069, _1771073))))], (6709 ^ _779571) ^ [_889504, _889506, _889508, _889510] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_889504, _889506)), _889508), _889510)), 6713 ^ _779571 : [(6716 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889506), 6712 ^ [_889504, _889506, _889508, _889510]), _889510)))], (6714 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889504), _889508), 6712 ^ [_889504, _889506, _889508, _889510])))]]], (22222 ^ _779571) ^ [_1163076, _1163078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1163076), _1163078)), -(c_Divides_Odivmod__nat(_1163078, _1163076) = 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), _1163078), _1163076)), _1163076))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1163078), _1163076), _1163076)))], (10622 ^ _779571) ^ [_956283, _956285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956283)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956283), _956285)))], (5634 ^ _779571) ^ [_866540, _866542, _866544, _866546, _866548, _866550] : [-(c_COMBC(_866550, _866546, _866542) = c_COMBC(_866548, _866544, _866540)), _866550 = _866548, _866546 = _866544, _866542 = _866540], (35803 ^ _779571) ^ [_1442394, _1442396] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442394), c_Orderings_Obot__class_Obot(tc_fun(_1442394, tc_HOL_Obool))), _1442396) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1442394, tc_HOL_Obool), tc_HOL_Obool)))], (2406 ^ _779571) ^ [_815896, _815898, _815900, _815902, _815904, _815906, _815908, _815910] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_815910, _815906, _815902, _815898) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_815908, _815904, _815900, _815896)), _815910 = _815908, _815906 = _815904, _815902 = _815900, _815898 = _815896], (24119 ^ _779571) ^ [_1199628, _1199630, _1199632, _1199634, _1199636, _1199638] : [-(c_Product__Type_Oprod_Oprod__rec(_1199628, _1199630, _1199632, _1199634, hAPP(hAPP(c_Product__Type_OPair(_1199628, _1199630), _1199636), _1199638)) = hAPP(hAPP(_1199634, _1199636), _1199638))], (48886 ^ _779571) ^ [_1760384, _1760386, _1760388, _1760390] : [-(hAPP(c_List_Orotate1(_1760384), c_List_Olist_ONil(_1760384)) = c_List_Olist_ONil(_1760384))], (10750 ^ _779571) ^ [_958562, _958564, _958566, _958568] : [class_Orderings_Opreorder(_958562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958562), _958564), _958566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958562), _958566), _958568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958562), _958564), _958568)))], (44255 ^ _779571) ^ [_1644970, _1644972, _1644974, _1644976, _1644978, _1644980] : [c_Finite__Set_Ofun__left__comm(_1644970, _1644972, _1644974), -(hAPP(hAPP(_1644974, _1644976), hAPP(hAPP(_1644974, _1644978), _1644980)) = hAPP(hAPP(_1644974, _1644978), hAPP(hAPP(_1644974, _1644976), _1644980)))], (15146 ^ _779571) ^ [_1035586, _1035588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035588)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1035586)), hAPP(c_Int_Onat, _1035588)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1035586, _1035588)))], (34162 ^ _779571) ^ [_1404270, _1404272, _1404274, _1404276, _1404278, _1404280] : [_1404270 = _1404272, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404274, _1404276), _1404278), _1404272), _1404280), _1404270) = _1404280)], (27986 ^ _779571) ^ [_1275278, _1275280, _1275282, _1275284] : [class_Lattices_Osemilattice__sup(_1275278), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275278), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275278), _1275280), _1275282)), _1275284) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275278), _1275280), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275278), _1275282), _1275284)))], (41213 ^ _779571) ^ [_1564575, _1564577, _1564579] : [-(hAPP(c_Set_OCollect(_1564575), hAPP(hAPP(c_COMBS(_1564575, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564575), c_fimplies), _1564577)), _1564579)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564575, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1564575, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1564575), _1564577))), hAPP(c_Set_OCollect(_1564575), _1564579)))], (26696 ^ _779571) ^ [_1249068, _1249070] : [-(_1249068 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249070), _1249068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1249070)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1249068))))], (44505 ^ _779571) ^ [_1651310, _1651312, _1651314, _1651316, _1651318] : [44507 ^ _779571 : [(44510 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1651310), _1651312), hAPP(_1651318, 44506 ^ [_1651310, _1651312, _1651314, _1651316, _1651318])))], (44508 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1651314), 44506 ^ [_1651310, _1651312, _1651314, _1651316, _1651318]), _1651316)))]], -(hBOOL(hAPP(hAPP(c_member(_1651310), _1651312), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651314, tc_fun(_1651310, tc_HOL_Obool)), _1651316), _1651318))))], (8426 ^ _779571) ^ [_919174, _919176, _919178, _919180] : [class_Orderings_Opreorder(_919174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919174), _919176), _919178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919174), _919178), _919180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919174), _919176), _919180)))], (23361 ^ _779571) ^ [_1184979, _1184981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184981)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184979, _1184981) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1184979, _1184981)))], (45712 ^ _779571) ^ [_1680211, _1680213, _1680215, _1680217, _1680219, _1680221] : [hAPP(c_Map_Omap__add(_1680211, _1680213, _1680215, _1680217), _1680219) = hAPP(c_Option_Ooption_OSome(_1680213), _1680221), -(hAPP(_1680217, _1680219) = hAPP(c_Option_Ooption_OSome(_1680213), _1680221)), 45719 ^ _779571 : [(45722 ^ _779571) ^ [] : [-(hAPP(_1680215, _1680219) = hAPP(c_Option_Ooption_OSome(_1680213), _1680221))], (45720 ^ _779571) ^ [] : [-(hAPP(_1680217, _1680219) = c_Option_Ooption_ONone(_1680213))]]], (29021 ^ _779571) ^ [_1297084, _1297086, _1297088, _1297090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297084, tc_HOL_Obool)), _1297086), _1297088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297084, tc_HOL_Obool)), _1297086), hAPP(hAPP(c_Set_Oinsert(_1297084), _1297090), _1297088))))], (5186 ^ _779571) ^ [_859708, _859710, _859712, _859714] : [-(c_List_Olist__update(_859714, _859710) = c_List_Olist__update(_859712, _859708)), _859714 = _859712, _859710 = _859708], (432 ^ _779571) ^ [_786155, _786157, _786159, _786161, _786163, _786165, _786167, _786169, _786171, _786173] : [-(c_Big__Operators_Ocomm__monoid__big(_786171, _786167, _786163, _786159, _786155)), c_Big__Operators_Ocomm__monoid__big(_786173, _786169, _786165, _786161, _786157), _786173 = _786171, _786169 = _786167, _786165 = _786163, _786161 = _786159, _786157 = _786155], (14860 ^ _779571) ^ [_1030078, _1030080, _1030082] : [-(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), _1030078), _1030080)), _1030082)), _1030080) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1030082), _1030080))], (32647 ^ _779571) ^ [_1375222, _1375224] : [class_Int_Onumber__ring(_1375222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1375224)), -(hBOOL(hAPP(hAPP(c_member(_1375222), hAPP(c_Int_Onumber__class_Onumber__of(_1375222), _1375224)), c_Nat_Osemiring__1__class_ONats(_1375222))))], (9808 ^ _779571) ^ [_942834, _942836, _942838, _942840] : [class_Rings_Olinordered__ring__strict(_942834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942834), _942836), _942838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942834), _942840), c_Groups_Ozero__class_Ozero(_942834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942834), _942838), _942840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942834), _942836), _942840))))], (6283 ^ _779571) ^ [_881523, _881525] : [hBOOL(hAPP(c_Com_OWT, _881523)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_881525, _881523))))], (17903 ^ _779571) ^ [_1087686, _1087688, _1087690] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087686))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087686)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087688)), _1087690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087688)), _1087690))], (8748 ^ _779571) ^ [_924057, _924059, _924061] : [class_Rings_Ocomm__semiring__1(_924057), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924057), _924059), _924061)), _924061) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924057), _924059), c_Groups_Oone__class_Oone(_924057))), _924061))], (36524 ^ _779571) ^ [_1458104, _1458106, _1458108, _1458110] : [class_Lattices_Osemilattice__inf(_1458104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458104), _1458106), _1458108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458104), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458104), _1458110), _1458106)), _1458108)))], (11334 ^ _779571) ^ [_967811, _967813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967811), _967813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967813)), _967811)))], (23221 ^ _779571) ^ [_1182916, _1182918, _1182920, _1182922, _1182924, _1182926] : [hAPP(c_Product__Type_Oapsnd(_1182916, _1182918, _1182920, _1182922), _1182924) = hAPP(c_Product__Type_Oapsnd(_1182916, _1182918, _1182920, _1182926), _1182924), -(hAPP(_1182922, hAPP(c_Product__Type_Osnd(_1182920, _1182916), _1182924)) = hAPP(_1182926, hAPP(c_Product__Type_Osnd(_1182920, _1182916), _1182924)))], (28829 ^ _779571) ^ [_1292206, _1292208, _1292210, _1292212, _1292214, _1292216] : [class_Complete__Lattice_Ocomplete__lattice(_1292206), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292208, tc_fun(_1292210, _1292206)), _1292212), _1292214), _1292216) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292208, _1292206), _1292212), hAPP(hAPP(c_COMBC(_1292208, _1292210, _1292206), _1292214), _1292216)))], (28152 ^ _779571) ^ [_1278896, _1278898, _1278900] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278896, tc_HOL_Obool)), _1278898), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278896, tc_HOL_Obool)), _1278898), _1278900)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278896, tc_HOL_Obool)), _1278898), _1278900))], (24637 ^ _779571) ^ [_1209861, _1209863, _1209865, _1209867, _1209869, _1209871, _1209873] : [-(hAPP(c_Product__Type_Oapfst(_1209861, _1209863, _1209865, _1209867), hAPP(c_Product__Type_Oapsnd(_1209869, _1209865, _1209861, _1209871), _1209873)) = hAPP(hAPP(c_Product__Type_OPair(_1209863, _1209865), hAPP(_1209867, hAPP(c_Product__Type_Ofst(_1209861, _1209869), _1209873))), hAPP(_1209871, hAPP(c_Product__Type_Osnd(_1209861, _1209869), _1209873))))], (29093 ^ _779571) ^ [_1298638, _1298640] : [class_Lattices_Oboolean__algebra(_1298638), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1298638), _1298640), hAPP(c_Groups_Ouminus__class_Ouminus(_1298638), _1298640)) = c_Orderings_Otop__class_Otop(_1298638))], (3564 ^ _779571) ^ [_834373, _834375] : [_834375 = _834373, -(c_Hoare__Mirabelle_Otriple_Otriple(_834375) = c_Hoare__Mirabelle_Otriple_Otriple(_834373))], (32026 ^ _779571) ^ [_1361979, _1361981] : [c_Nitpick_Orefl_H(_1361979, _1361981), 32029 ^ _779571 : [(32030 ^ _779571) ^ [_1362057] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361979, _1361979)), hAPP(hAPP(c_Product__Type_OPair(_1361979, _1361979), _1362057), _1362057)), _1361981)))]]], (9168 ^ _779571) ^ [_931355, _931357] : [class_Groups_Olinordered__ab__group__add(_931355), 9171 ^ _779571 : [(9178 ^ _779571) ^ [] : [_931357 = c_Groups_Ozero__class_Ozero(_931355), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931355), _931357) = _931357)], (9172 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_931355), _931357) = _931357, -(_931357 = c_Groups_Ozero__class_Ozero(_931355))]]], (39733 ^ _779571) ^ [_1529475, _1529477, _1529479, _1529481] : [-(hAPP(_1529481, _1529477) = c_Option_Ooption_ONone(_1529479)), -(hBOOL(hAPP(hAPP(c_member(_1529475), _1529477), c_Map_Odom(_1529475, _1529479, _1529481))))], (19207 ^ _779571) ^ [_1108943, _1108945] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1108943)), c_Int_OBit0(_1108945)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1108943), _1108945)))], (42155 ^ _779571) ^ [_1595016, _1595018, _1595020, _1595022] : [hBOOL(hAPP(c_Predicate_ORangeP(_1595016, _1595018, hAPP(hAPP(c_COMBC(_1595016, tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_fun(_1595018, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595018, tc_fun(tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_fun(_1595018, tc_HOL_Obool)), _1595016), c_COMBC(_1595018, tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595018, tc_prod(_1595016, _1595018)), tc_fun(_1595018, tc_fun(tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_HOL_Obool)), _1595016), hAPP(c_COMBB(tc_prod(_1595016, _1595018), tc_fun(tc_fun(tc_prod(_1595016, _1595018), tc_HOL_Obool), tc_HOL_Obool), _1595018), c_member(tc_prod(_1595016, _1595018)))), c_Product__Type_OPair(_1595016, _1595018)))), _1595020)), _1595022)), -(hBOOL(hAPP(hAPP(c_member(_1595018), _1595022), hAPP(c_Relation_ORange(_1595016, _1595018), _1595020))))], (23999 ^ _779571) ^ [_1197323, _1197325, _1197327, _1197329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197323, tc_HOL_Obool)), _1197325), _1197327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197323, tc_HOL_Obool)), _1197327), _1197329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197323, tc_HOL_Obool)), _1197325), _1197329)))], (5196 ^ _779571) ^ [_859857, _859859] : [_859859 = _859857, -(c_Groups_Ominus__class_Ominus(_859859) = c_Groups_Ominus__class_Ominus(_859857))], (23821 ^ _779571) ^ [_1193537, _1193539, _1193541] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1193537), _1193539)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1193541), _1193539)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1193537), _1193541)), _1193539))], (4016 ^ _779571) ^ [_841431, _841433] : [_841433 = _841431, -(c_HOL_OAll(_841433) = c_HOL_OAll(_841431))], (36608 ^ _779571) ^ [_1459574, _1459576, _1459578] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459574, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459574, tc_HOL_Obool)), _1459576), _1459578)), _1459578)))], (24053 ^ _779571) ^ [_1198334, _1198336] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1198334), hAPP(c_Nat_OSuc, _1198336)) = 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)), _1198336)), _1198334))], (28034 ^ _779571) ^ [_1276386, _1276388, _1276390] : [class_Lattices_Osemilattice__sup(_1276386), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276386), _1276388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276386), _1276388), _1276390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276386), _1276388), _1276390))], (44942 ^ _779571) ^ [_1662863, _1662865, _1662867] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662863, tc_HOL_Obool)), _1662865), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1662863, tc_HOL_Obool), _1662867)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1662863, tc_HOL_Obool), tc_fun(_1662863, tc_HOL_Obool)), _1662867), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662863, tc_HOL_Obool)), _1662865)))], (29003 ^ _779571) ^ [_1296678, _1296680, _1296682, _1296684] : [29004 ^ _779571 : [(29007 ^ _779571) ^ [] : [hBOOL(hAPP(_1296682, _1296684))], (29005 ^ _779571) ^ [] : [_1296680 = _1296684]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1296678), _1296680), _1296682), _1296684)))], (41616 ^ _779571) ^ [_1581031, _1581033] : [-(hAPP(c_Fun_Oid(_1581031), _1581033) = _1581033)], (6883 ^ _779571) ^ [_893192, _893194] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893192), _893194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6886 ^ _779571 : [(6889 ^ _779571) ^ [] : [-(_893194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6887 ^ _779571) ^ [] : [-(_893192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19577 ^ _779571) ^ [_1115398] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1115398), 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), _1115398), _1115398))], (20481 ^ _779571) ^ [_1131692, _1131694, _1131696, _1131698, _1131700] : [class_Fields_Ofield(_1131692), -(_1131694 = c_Groups_Ozero__class_Ozero(_1131692)), -(_1131696 = c_Groups_Ozero__class_Ozero(_1131692)), 20492 ^ _779571 : [(20499 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131692), _1131698), _1131696) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131692), _1131700), _1131694), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131692), _1131698), _1131694) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131692), _1131700), _1131696))], (20493 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131692), _1131698), _1131694) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131692), _1131700), _1131696), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131692), _1131698), _1131696) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131692), _1131700), _1131694))]]], (12215 ^ _779571) ^ [_983305, _983307, _983309] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983305), _983307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983305), _983309)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983307), _983309))], (15502 ^ _779571) ^ [_1042078, _1042080, _1042082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042078), _1042080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042082), _1042080)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042082), _1042078))))], (22586 ^ _779571) ^ [_1170535, _1170537] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170535), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22589 ^ _779571 : [(22598 ^ _779571) ^ [] : [-(c_Nitpick_Onorm__frac(_1170537, _1170535) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1170537), _1170535)), 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), _1170537))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1170535)))), -(_1170537 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1170535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22590 ^ _779571) ^ [] : [22591 ^ _779571 : [(22594 ^ _779571) ^ [] : [_1170535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22592 ^ _779571) ^ [] : [_1170537 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1170537, _1170535) = 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)))]]], (18593 ^ _779571) ^ [_1098481, _1098483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098481), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098481)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098483)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098483))], (6273 ^ _779571) ^ [_881276, _881278, _881280, _881282, _881284, _881286, _881288, _881290, _881292, _881294, _881296, _881298] : [-(c_Com_Ocom_Ocom__rec(_881276, _881278, _881280, _881282, _881284, _881286, _881288, _881290, _881292, c_Com_Ocom_OCall(_881294, _881296, _881298)) = hAPP(hAPP(hAPP(_881292, _881294), _881296), _881298))], (3764 ^ _779571) ^ [_837589, _837591, _837593, _837595, _837597, _837599, _837601, _837603] : [-(c_New__Random__Sequence_Oneg__bind(_837603, _837599, _837595, _837591) = c_New__Random__Sequence_Oneg__bind(_837601, _837597, _837593, _837589)), _837603 = _837601, _837599 = _837597, _837595 = _837593, _837591 = _837589], (50252 ^ _779571) ^ [_1789299] : [class_Orderings_Olinorder(_1789299), -(c_List_Olinorder__class_Osorted(_1789299, c_List_Olist_ONil(_1789299)))], (36610 ^ _779571) ^ [_1459622, _1459624, _1459626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459622, tc_HOL_Obool)), _1459624), _1459626)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459622, tc_HOL_Obool)), _1459624), _1459626) = _1459624)], (51105 ^ _779571) ^ [_1808451, _1808453] : [class_Lattices_Odistrib__lattice(_1808451), -(class_Lattices_Odistrib__lattice(tc_fun(_1808453, _1808451)))], (31003 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (40941 ^ _779571) ^ [_1558690] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1558690), c_Int_OInteg)), -(_1558690 = hAPP(c_Int_ORep__Integ, 40944 ^ [_1558690]))], (5246 ^ _779571) ^ [_860650, _860652] : [_860652 = _860650, -(c_List_Otranspose__rel(_860652) = c_List_Otranspose__rel(_860650))], (50568 ^ _779571) ^ [_1795783, _1795785, _1795787] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1795783), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1795783))), _1795785))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795787), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1795783))), _1795785))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1795783), _1795783), hAPP(hAPP(c_COMBC(tc_List_Olist(_1795783), tc_Nat_Onat, _1795783), c_List_Onth(_1795783)), _1795787)), hAPP(c_List_Ofilter(tc_List_Olist(_1795783), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1795783)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795787)), c_Nat_Osize__class_Osize(tc_List_Olist(_1795783)))), c_List_Otranspose(_1795783, _1795785))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1795783)), _1795785), _1795787))], (31053 ^ _779571) ^ [_1338711, _1338713, _1338715, _1338717] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338711), _1338713)), 31056 ^ _779571 : [(31057 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338711, tc_fun(_1338715, tc_HOL_Obool)), _1338713), _1338717))), 31060 ^ _779571 : [(31061 ^ _779571) ^ [_1338895] : [hBOOL(hAPP(hAPP(c_member(_1338711), _1338895), _1338713)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338715), hAPP(_1338717, _1338895))))]]], (31067 ^ _779571) ^ [] : [31069 ^ _779571 : [(31072 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338715), hAPP(_1338717, 31068 ^ [_1338711, _1338713, _1338715, _1338717])))], (31070 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338711), 31068 ^ [_1338711, _1338713, _1338715, _1338717]), _1338713)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338711, tc_fun(_1338715, tc_HOL_Obool)), _1338713), _1338717))))]]], (11018 ^ _779571) ^ [_962440, _962442, _962444] : [class_Orderings_Olinorder(_962440), 11021 ^ _779571 : [(11028 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962440), _962444), _962442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962440), _962442), _962444))], (11022 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962440), _962442), _962444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962440), _962444), _962442)))]]], (37261 ^ _779571) ^ [_1475346, _1475348, _1475350, _1475352, _1475354] : [class_Groups_Ocomm__monoid__mult(_1475346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475348), _1475350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475348), _1475352)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475348, tc_HOL_Obool)), _1475350), _1475352) = c_Orderings_Obot__class_Obot(tc_fun(_1475348, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1475348, _1475346), _1475354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475348, tc_HOL_Obool)), _1475350), _1475352)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1475346), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1475348, _1475346), _1475354), _1475350)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1475348, _1475346), _1475354), _1475352)))], (19489 ^ _779571) ^ [_1113892, _1113894] : [class_Int_Onumber__ring(_1113892), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113892), c_Groups_Oone__class_Oone(_1113892)), c_Groups_Oone__class_Oone(_1113892))), hAPP(c_Int_Onumber__class_Onumber__of(_1113892), _1113894)) = hAPP(c_Int_Onumber__class_Onumber__of(_1113892), c_Int_OBit0(_1113894)))], (11034 ^ _779571) ^ [_962649, _962651, _962653] : [class_Orderings_Olinorder(_962649), 11037 ^ _779571 : [(11044 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962649), _962653), _962651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962649), _962651), _962653))], (11038 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962649), _962651), _962653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962649), _962653), _962651)))]]], (19799 ^ _779571) ^ [_1119274, _1119276, _1119278] : [class_Rings_Olinordered__idom(_1119274), 19802 ^ _779571 : [(19803 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119274), c_Groups_Ozero__class_Ozero(_1119274)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119274), hAPP(hAPP(c_Power_Opower__class_Opower(_1119274), _1119276), 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(_1119274), _1119278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1119276 = c_Groups_Ozero__class_Ozero(_1119274), _1119278 = c_Groups_Ozero__class_Ozero(_1119274)], (19813 ^ _779571) ^ [] : [19814 ^ _779571 : [(19817 ^ _779571) ^ [] : [-(_1119278 = c_Groups_Ozero__class_Ozero(_1119274))], (19815 ^ _779571) ^ [] : [-(_1119276 = c_Groups_Ozero__class_Ozero(_1119274))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119274), c_Groups_Ozero__class_Ozero(_1119274)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119274), hAPP(hAPP(c_Power_Opower__class_Opower(_1119274), _1119276), 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(_1119274), _1119278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (35209 ^ _779571) ^ [_1427728, _1427730] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1427728, tc_HOL_Obool)), _1427730), hAPP(c_Set_OPow(_1427728), _1427730))))], (33659 ^ _779571) ^ [_1394099, _1394101, _1394103, _1394105, _1394107, _1394109, _1394111] : [hBOOL(hAPP(_1394099, _1394101)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1394103, _1394103)), hAPP(hAPP(c_Product__Type_OPair(_1394103, _1394103), _1394105), _1394107)), hAPP(_1394109, _1394101))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1394111, _1394103), tc_prod(_1394111, _1394103))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1394111, _1394103), tc_prod(_1394111, _1394103)), hAPP(hAPP(c_Product__Type_OPair(_1394111, _1394103), _1394101), _1394105)), hAPP(hAPP(c_Product__Type_OPair(_1394111, _1394103), _1394101), _1394107))), c_Recdef_Osame__fst(_1394111, _1394103, _1394099, _1394109))))], (30162 ^ _779571) ^ [_1320234, _1320236] : [-(hBOOL(hAPP(hAPP(c_member(_1320234), 30163 ^ [_1320234, _1320236]), _1320236))), -(_1320236 = c_Orderings_Obot__class_Obot(tc_fun(_1320234, tc_HOL_Obool)))], (45189 ^ _779571) ^ [_1668533, _1668535, _1668537] : [class_Complete__Lattice_Ocomplete__lattice(_1668533), -(c_Complete__Lattice_OSup__class_OSup(_1668533, hAPP(hAPP(c_Set_Oinsert(_1668533), _1668535), _1668537)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1668533), _1668535), c_Complete__Lattice_OSup__class_OSup(_1668533, _1668537)))], (15644 ^ _779571) ^ [_1045033, _1045035, _1045037] : [class_Groups_Oab__group__add(_1045033), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045033), _1045035), _1045037) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045033), _1045035), hAPP(c_Groups_Ouminus__class_Ouminus(_1045033), _1045037)))], (35207 ^ _779571) ^ [_1427690, _1427692] : [hAPP(c_Set_OPow(_1427690), _1427692) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427690, tc_HOL_Obool), tc_HOL_Obool))], (16803 ^ _779571) ^ [_1067459, _1067461, _1067463, _1067465] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067459), _1067461), _1067463)), hAPP(c_Int_Onumber__class_Onumber__of(_1067459), _1067465)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067459), _1067461), hAPP(c_Int_Onumber__class_Onumber__of(_1067459), _1067465))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067459), _1067463), hAPP(c_Int_Onumber__class_Onumber__of(_1067459), _1067465)))), class_Int_Onumber(_1067459), class_Rings_Oring(_1067459)], (4840 ^ _779571) ^ [_854351, _854353] : [_854353 = _854351, -(c_Option_Othe(_854353) = c_Option_Othe(_854351))], (17551 ^ _779571) ^ [_1081576, _1081578, _1081580, _1081582] : [class_Rings_Olinordered__semidom(_1081576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081576), hAPP(hAPP(c_Power_Opower__class_Opower(_1081576), _1081578), hAPP(c_Nat_OSuc, _1081580))), hAPP(hAPP(c_Power_Opower__class_Opower(_1081576), _1081582), hAPP(c_Nat_OSuc, _1081580)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081576), c_Groups_Ozero__class_Ozero(_1081576)), _1081582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081576), _1081578), _1081582)))], (41878 ^ _779571) ^ [_1588992, _1588994, _1588996] : [c_Wellfounded_Owf(_1588992, _1588994), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588992, _1588992)), hAPP(hAPP(c_Product__Type_OPair(_1588992, _1588992), _1588996), _1588996)), _1588994))], (45882 ^ _779571) ^ [_1684404, _1684406, _1684408, _1684410, _1684412, _1684414, _1684416] : [hAPP(_1684404, _1684406) = hAPP(c_Option_Ooption_OSome(_1684408), _1684410), -(c_Map_Omap__comp(_1684408, _1684412, _1684414, _1684416, _1684404, _1684406) = hAPP(_1684416, _1684410))], (48632 ^ _779571) ^ [_1753789, _1753791, _1753793, _1753795, _1753797, _1753799, _1753801, _1753803] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1753789, _1753789)), hAPP(hAPP(c_Product__Type_OPair(_1753789, _1753789), _1753791), _1753793)), _1753795)), _1753797 = hAPP(hAPP(c_List_Oappend(_1753789), _1753799), hAPP(hAPP(c_List_Olist_OCons(_1753789), _1753791), _1753801)), _1753803 = hAPP(hAPP(c_List_Oappend(_1753789), _1753799), hAPP(hAPP(c_List_Olist_OCons(_1753789), _1753793), _1753801)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753789), tc_List_Olist(_1753789))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753789), tc_List_Olist(_1753789)), _1753797), _1753803)), c_List_Olistrel1(_1753789, _1753795))))], (33389 ^ _779571) ^ [_1388316, _1388318, _1388320] : [class_Orderings_Olinorder(_1388316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388316), _1388318)), -(hBOOL(hAPP(hAPP(c_member(_1388316), _1388320), _1388318))), -(_1388318 = c_Orderings_Obot__class_Obot(tc_fun(_1388316, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1388316, hAPP(hAPP(c_Set_Oinsert(_1388316), _1388320), _1388318)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388316), _1388320), c_Big__Operators_Olinorder__class_OMin(_1388316, _1388318)))], (9352 ^ _779571) ^ [_934402, _934404, _934406, _934408, _934410] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_934402), 9355 ^ _779571 : [(9356 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934404), _934408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934406), _934410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934404), _934410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934406), _934408)), -(_934404 = _934406), -(_934408 = _934410)], (9366 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934404), _934408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934406), _934410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934404), _934410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934402), _934406), _934408))), 9369 ^ _779571 : [(9372 ^ _779571) ^ [] : [_934408 = _934410], (9370 ^ _779571) ^ [] : [_934404 = _934406]]]]], (46813 ^ _779571) ^ [_1708959, _1708961, _1708963, _1708965, _1708967, _1708969] : [-(c_List_Ofoldr(_1708959, _1708961, _1708963, hAPP(hAPP(c_List_Olist_OCons(_1708959), _1708965), _1708967), _1708969) = hAPP(hAPP(_1708963, _1708965), c_List_Ofoldr(_1708959, _1708961, _1708963, _1708967, _1708969)))], (17255 ^ _779571) ^ [_1076264, _1076266, _1076268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1076264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076264), _1076266)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076264), _1076268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076266), _1076268)))], (18081 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (49271 ^ _779571) ^ [_1768619, _1768621, _1768623] : [-(c_List_Olist_Olist__size(_1768619, _1768621, _1768623) = 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(_1768619, tc_Nat_Onat), _1768621), _1768623))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768619)), _1768623)))], (13801 ^ _779571) ^ [_1011453, _1011455] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011453, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011455)) = 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), _1011453), _1011455)))], (32959 ^ _779571) ^ [_1380802, _1380804, _1380806] : [class_Orderings_Olinorder(_1380802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380802), _1380804)), hBOOL(hAPP(hAPP(c_member(_1380802), _1380806), _1380804)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1380802), _1380806), c_Big__Operators_Olinorder__class_OMax(_1380802, _1380804)) = c_Big__Operators_Olinorder__class_OMax(_1380802, _1380804))], (1262 ^ _779571) ^ [_798114, _798116] : [-(class_Lattices_Obounded__lattice__bot(_798114)), _798116 = _798114, class_Lattices_Obounded__lattice__bot(_798116)], (41646 ^ _779571) ^ [_1581595, _1581597, _1581599, _1581601] : [-(c_Product__Type_Oapfst(_1581595, _1581597, _1581599, _1581601) = c_Product__Type_Omap__pair(_1581595, _1581597, _1581599, _1581599, _1581601, c_Fun_Oid(_1581599)))], (29329 ^ _779571) ^ [_1303882, _1303884, _1303886, _1303888] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303882, tc_fun(_1303884, tc_HOL_Obool)), _1303886), _1303888) = c_Orderings_Obot__class_Obot(tc_fun(_1303884, tc_HOL_Obool)), 29332 ^ _779571 : [(29333 ^ _779571) ^ [_1303998] : [hBOOL(hAPP(hAPP(c_member(_1303882), _1303998), _1303886)), -(hAPP(_1303888, _1303998) = c_Orderings_Obot__class_Obot(tc_fun(_1303884, tc_HOL_Obool)))]]], (17139 ^ _779571) ^ [_1074177, _1074179, _1074181, _1074183] : [class_Rings_Olinordered__semidom(_1074177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074177), c_Groups_Oone__class_Oone(_1074177)), _1074179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074177), hAPP(hAPP(c_Power_Opower__class_Opower(_1074177), _1074179), _1074181)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074177), _1074179), _1074183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074181), _1074183)))], (1592 ^ _779571) ^ [_802239, _802241] : [-(class_Rings_Ocomm__semiring(_802239)), _802241 = _802239, class_Rings_Ocomm__semiring(_802241)], (11214 ^ _779571) ^ [_965730] : [_965730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965730), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19213 ^ _779571) ^ [_1109062] : [c_Int_OMin = c_Int_OBit0(_1109062)], (8468 ^ _779571) ^ [_919845, _919847, _919849, _919851] : [class_Orderings_Oorder(_919845), _919847 = _919849, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919845), _919851), _919849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919845), _919851), _919847)))], (46622 ^ _779571) ^ [_1702422, _1702424] : [-(c_List_Olenlex(_1702422, _1702424) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1702422)), tc_List_Olist(_1702422)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1702422), c_Wellfounded_Oless__than, c_List_Olex(_1702422, _1702424))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1702422), tc_List_Olist(_1702422), tc_prod(tc_Nat_Onat, tc_List_Olist(_1702422))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1702422), tc_prod(tc_Nat_Onat, tc_List_Olist(_1702422))), tc_List_Olist(_1702422)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1702422))), c_Nat_Osize__class_Osize(tc_List_Olist(_1702422)))), c_COMBI(tc_List_Olist(_1702422)))))], (32604 ^ _779571) ^ [_1374305, _1374307, _1374309, _1374311, _1374313] : [class_Groups_Ocomm__monoid__add(_1374305), class_Groups_Oordered__ab__semigroup__add(_1374305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374307), _1374309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374307, tc_HOL_Obool)), _1374311), _1374309)), 32622 ^ _779571 : [(32625 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374305), c_Groups_Ozero__class_Ozero(_1374305)), hAPP(_1374313, 32621 ^ [_1374305, _1374307, _1374309, _1374311, _1374313])))], (32623 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374307), 32621 ^ [_1374305, _1374307, _1374309, _1374311, _1374313]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374307, tc_HOL_Obool)), _1374309), _1374311))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374307, _1374305), _1374313), _1374311)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374307, _1374305), _1374313), _1374309))))], (35565 ^ _779571) ^ [] : [-(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))))))], (29888 ^ _779571) ^ [] : [-(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))], (15772 ^ _779571) ^ [_1047359, _1047361, _1047363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047359), _1047361)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047361), _1047363)), _1047359) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047361), _1047359)), _1047363))], (10147 ^ _779571) ^ [_948615, _948617] : [class_Rings_Olinordered__idom(_948615), 10150 ^ _779571 : [(10157 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948615), _948617), c_Groups_Ozero__class_Ozero(_948615))), -(c_Groups_Osgn__class_Osgn(_948615, _948617) = hAPP(c_Groups_Ouminus__class_Ouminus(_948615), c_Groups_Oone__class_Oone(_948615)))], (10151 ^ _779571) ^ [] : [c_Groups_Osgn__class_Osgn(_948615, _948617) = hAPP(c_Groups_Ouminus__class_Ouminus(_948615), c_Groups_Oone__class_Oone(_948615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948615), _948617), c_Groups_Ozero__class_Ozero(_948615))))]]], (24833 ^ _779571) ^ [_1213606, _1213608, _1213610, _1213612, _1213614, _1213616] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1213606, _1213608, _1213610), _1213612), hAPP(hAPP(c_Product__Type_OPair(_1213606, _1213608), _1213614), _1213616)) = hAPP(hAPP(_1213612, _1213614), _1213616))], (28559 ^ _779571) ^ [_1286682] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1286682) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286682))], (36030 ^ _779571) ^ [_1447563, _1447565, _1447567, _1447569, _1447571, _1447573, _1447575, _1447577, _1447579, _1447581] : [c_Equiv__Relations_Oequiv(_1447563, _1447565, _1447567), c_Equiv__Relations_Oequiv(_1447569, _1447571, _1447573), c_Equiv__Relations_Ocongruent2(_1447563, _1447569, tc_fun(_1447575, tc_HOL_Obool), _1447567, _1447573, _1447577), hBOOL(hAPP(hAPP(c_member(_1447563), _1447579), _1447565)), hBOOL(hAPP(hAPP(c_member(_1447569), _1447581), _1447571)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447563, tc_fun(_1447575, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447563, _1447563, _1447567), hAPP(hAPP(c_Set_Oinsert(_1447563), _1447579), c_Orderings_Obot__class_Obot(tc_fun(_1447563, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1447569, tc_fun(_1447575, tc_HOL_Obool)), tc_fun(_1447575, tc_HOL_Obool), _1447563), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447569, tc_fun(_1447575, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447569, _1447569, _1447573), hAPP(hAPP(c_Set_Oinsert(_1447569), _1447581), c_Orderings_Obot__class_Obot(tc_fun(_1447569, tc_HOL_Obool)))))), _1447577)) = hAPP(hAPP(_1447577, _1447579), _1447581))], (12938 ^ _779571) ^ [_996301, _996303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996301), _996303))))], (19515 ^ _779571) ^ [_1114404] : [class_Int_Onumber__ring(_1114404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114404), c_Groups_Oone__class_Oone(_1114404)), c_Groups_Oone__class_Oone(_1114404)) = hAPP(c_Int_Onumber__class_Onumber__of(_1114404), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (48287 ^ _779571) ^ [_1744555, _1744557, _1744559, _1744561, _1744563, _1744565] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744555)), _1744557) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744559)), _1744561), -(c_Map_Omap__upds(_1744555, _1744559, _1744563, hAPP(hAPP(c_List_Oappend(_1744555), _1744557), _1744565), _1744561) = c_Map_Omap__upds(_1744555, _1744559, _1744563, _1744557, _1744561))], (46138 ^ _779571) ^ [_1690563, _1690565, _1690567, _1690569, _1690571] : [hAPP(c_Map_Omap__of(_1690563, _1690565, _1690567), _1690569) = hAPP(c_Option_Ooption_OSome(_1690565), _1690571), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1690563, _1690565)), hAPP(hAPP(c_Product__Type_OPair(_1690563, _1690565), _1690569), _1690571)), hAPP(c_List_Oset(tc_prod(_1690563, _1690565)), _1690567))))], (30648 ^ _779571) ^ [_1330150, _1330152, _1330154, _1330156, _1330158] : [hBOOL(hAPP(hAPP(c_member(_1330150), _1330152), c_SetInterval_Oord_OgreaterThanLessThan(_1330150, _1330154, _1330156, _1330158))), 30651 ^ _779571 : [(30654 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1330154, _1330152), _1330158)))], (30652 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1330154, _1330156), _1330152)))]]], (49997 ^ _779571) ^ [_1784921, _1784923] : [49998 ^ _779571 : [(50001 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784923), _1784921))], (49999 ^ _779571) ^ [] : [_1784923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1784921, _1784923) = c_List_Olist_ONil(tc_Nat_Onat))], (47197 ^ _779571) ^ [_1718914] : [47199 ^ _779571 : [(47202 ^ _779571) ^ [] : [47198 ^ [_1718914] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47200 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47198 ^ [_1718914]), hAPP(c_List_Oset(tc_Nat_Onat), _1718914))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1718914) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24127 ^ _779571) ^ [_1199807, _1199809, _1199811] : [_1199809 = _1199811, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199807, tc_HOL_Obool)), _1199809) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199807, tc_HOL_Obool)), _1199811))], (20075 ^ _779571) ^ [_1124815, _1124817, _1124819] : [class_Rings_Odivision__ring(_1124815), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1124815), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124815), _1124817), _1124819)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124815), hAPP(c_Groups_Ouminus__class_Ouminus(_1124815), _1124817)), _1124819))], (4618 ^ _779571) ^ [_851020, _851022, _851024, _851026] : [-(c_Big__Operators_Olattice__class_OSup__fin(_851026, _851022) = c_Big__Operators_Olattice__class_OSup__fin(_851024, _851020)), _851026 = _851024, _851022 = _851020], (18979 ^ _779571) ^ [_1104851, _1104853] : [class_Int_Onumber__ring(_1104851), class_Rings_Olinordered__idom(_1104851), 18986 ^ _779571 : [(18993 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1104853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104851), c_Groups_Oone__class_Oone(_1104851)), hAPP(c_Int_Onumber__class_Onumber__of(_1104851), _1104853))))], (18987 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104851), c_Groups_Oone__class_Oone(_1104851)), hAPP(c_Int_Onumber__class_Onumber__of(_1104851), _1104853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1104853)))]]], (38369 ^ _779571) ^ [_1500331, _1500333, _1500335, _1500337, _1500339, _1500341] : [c_Fun_Oinj__on(_1500331, _1500333, _1500335, _1500337), c_Fun_Oinj__on(_1500333, _1500339, _1500341, hAPP(c_Set_Oimage(_1500331, _1500333, _1500335), _1500337)), -(c_Fun_Oinj__on(_1500331, _1500339, hAPP(c_Fun_Ocomp(_1500333, _1500339, _1500331, _1500341), _1500335), _1500337))], (18235 ^ _779571) ^ [_1093037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093037), 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), _1093037)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1093037)))], (282 ^ _779571) ^ [_783696, _783698, _783700, _783702, _783704, _783706, _783708, _783710, _783712, _783714, _783716, _783718] : [-(c_Equiv__Relations_Ocongruent2(_783716, _783712, _783708, _783704, _783700, _783696)), c_Equiv__Relations_Ocongruent2(_783718, _783714, _783710, _783706, _783702, _783698), _783718 = _783716, _783714 = _783712, _783710 = _783708, _783706 = _783704, _783702 = _783700, _783698 = _783696], (43302 ^ _779571) ^ [_1622653, _1622655, _1622657] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1622653, _1622653), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1622653, _1622653), _1622655)), c_Transitive__Closure_Ortrancl(_1622653, _1622655)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1622653, _1622653), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1622653, _1622653)), hAPP(hAPP(c_Product__Type_OPair(_1622653, _1622653), _1622657), _1622657)), c_Transitive__Closure_Otrancl(_1622653, _1622655)))], (45990 ^ _779571) ^ [_1686811, _1686813, _1686815, _1686817, _1686819, _1686821] : [-(c_Map_Omap__comp(_1686811, _1686813, _1686815, _1686817, _1686819, _1686821) = c_Option_Ooption_ONone(_1686813)), 45991 ^ _779571 : [(45994 ^ _779571) ^ [_1686923] : [hAPP(_1686819, _1686821) = hAPP(c_Option_Ooption_OSome(_1686811), _1686923), hAPP(_1686817, _1686923) = c_Option_Ooption_ONone(_1686813)], (45992 ^ _779571) ^ [] : [hAPP(_1686819, _1686821) = c_Option_Ooption_ONone(_1686811)]]], (47977 ^ _779571) ^ [_1737155, _1737157, _1737159, _1737161] : [-(hAPP(hAPP(c_List_Oappend(_1737155), hAPP(hAPP(c_List_Olist_OCons(_1737155), _1737157), _1737159)), _1737161) = hAPP(hAPP(c_List_Olist_OCons(_1737155), _1737157), hAPP(hAPP(c_List_Oappend(_1737155), _1737159), _1737161)))], (28158 ^ _779571) ^ [_1279041, _1279043, _1279045, _1279047] : [hBOOL(hAPP(_1279041, _1279043)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279045, tc_HOL_Obool)), _1279047), _1279041), _1279043)))], (15858 ^ _779571) ^ [_1049062, _1049064, _1049066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049062), _1049064)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049064), _1049062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1049066), _1049062)), _1049064))], (38257 ^ _779571) ^ [] : [-(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))], (6803 ^ _779571) ^ [_891640, _891642] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_891640, _891642)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49002 ^ _779571) ^ [_1762625, _1762627, _1762629] : [-(hAPP(c_List_Orotate(_1762625, _1762627), _1762629) = hAPP(c_List_Orotate(_1762625, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1762627, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762625)), _1762629))), _1762629))], (44454 ^ _779571) ^ [_1649392, _1649394, _1649396, _1649398] : [-(hAPP(c_Set_OCollect(_1649392), hAPP(hAPP(c_COMBB(tc_fun(_1649394, tc_HOL_Obool), tc_HOL_Obool, _1649392), c_HOL_OAll(_1649394)), hAPP(hAPP(c_COMBB(tc_fun(_1649394, tc_HOL_Obool), tc_fun(_1649394, tc_HOL_Obool), _1649392), hAPP(c_COMBS(_1649394, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1649394), c_fimplies), hAPP(hAPP(c_COMBC(_1649394, tc_fun(_1649394, tc_HOL_Obool), tc_HOL_Obool), c_member(_1649394)), _1649396)))), _1649398))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649394, tc_fun(_1649392, tc_HOL_Obool)), _1649396), hAPP(hAPP(c_COMBB(tc_fun(_1649392, tc_HOL_Obool), tc_fun(_1649392, tc_HOL_Obool), _1649394), c_Set_OCollect(_1649392)), hAPP(c_COMBC(_1649392, _1649394, tc_HOL_Obool), _1649398))))], (5414 ^ _779571) ^ [_863290, _863292, _863294, _863296] : [-(c_List_Ozip(_863296, _863292) = c_List_Ozip(_863294, _863290)), _863296 = _863294, _863292 = _863290], (19077 ^ _779571) ^ [_1106574, _1106576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106574), 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)))), _1106576)), 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)))), _1106574)) = 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), _1106576), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1106574))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40425 ^ _779571) ^ [_1547104, _1547106, _1547108] : [class_Lattices_Osemilattice__inf(_1547104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547104), _1547106)), hBOOL(hAPP(hAPP(c_member(_1547104), _1547108), _1547106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1547104), hAPP(c_Finite__Set_Ofold1(_1547104, c_Lattices_Osemilattice__inf__class_Oinf(_1547104)), _1547106)), _1547108)))], (6774 ^ _779571) ^ [_891016, _891018, _891020, _891022, _891024] : [c_Com_Ocom_OCall(_891016, _891018, _891020) = c_Com_Ocom_OAss(_891022, _891024)], (32115 ^ _779571) ^ [_1363883, _1363885, _1363887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363883)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1363885), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1363887)), 32122 ^ _779571 : [(32123 ^ _779571) ^ [_1364091] : [32125 ^ _779571 : [(32131 ^ _779571) ^ [] : [-(_1364091 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32127 ^ [_1363883, _1363885, _1363887, _1364091]), 32124 ^ [_1363883, _1363885, _1363887, _1364091]))], (32129 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32127 ^ [_1363883, _1363885, _1363887, _1364091]), _1363887)))], (32126 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32124 ^ [_1363883, _1363885, _1363887, _1364091]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1363883))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363885), _1364091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363885), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1364091), _1363883))))]]], (45177 ^ _779571) ^ [_1668333] : [class_Complete__Lattice_Ocomplete__lattice(_1668333), -(c_Complete__Lattice_OSup__class_OSup(_1668333, c_Orderings_Obot__class_Obot(tc_fun(_1668333, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1668333))], (35727 ^ _779571) ^ [_1440465, _1440467, _1440469, _1440471, _1440473, _1440475] : [c_Finite__Set_Ofolding(_1440465, _1440467, _1440469, _1440471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440465), _1440473)), -(hAPP(c_Fun_Ocomp(_1440467, _1440467, _1440467, hAPP(_1440469, _1440475)), hAPP(_1440471, _1440473)) = hAPP(c_Fun_Ocomp(_1440467, _1440467, _1440467, hAPP(_1440471, _1440473)), hAPP(_1440469, _1440475)))], (16937 ^ _779571) ^ [_1070236, _1070238] : [class_Int_Onumber__ring(_1070236), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1070236), hAPP(c_Int_Onumber__class_Onumber__of(_1070236), _1070238)) = hAPP(c_Int_Onumber__class_Onumber__of(_1070236), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1070238)))], (47879 ^ _779571) ^ [_1734874, _1734876, _1734878, _1734880, _1734882] : [-(hAPP(hAPP(c_List_Olist__update(_1734874, hAPP(hAPP(c_List_Oappend(_1734874), _1734876), hAPP(hAPP(c_List_Olist_OCons(_1734874), _1734878), _1734880))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734874)), _1734876)), _1734882) = hAPP(hAPP(c_List_Oappend(_1734874), _1734876), hAPP(hAPP(c_List_Olist_OCons(_1734874), _1734882), _1734880)))], (47238 ^ _779571) ^ [_1719667, _1719669] : [-(c_List_Olistrelp(_1719667, _1719669, c_List_Olist_ONil(_1719667), c_List_Olist_ONil(_1719667)))], (44101 ^ _779571) ^ [_1642096, _1642098, _1642100] : [class_Orderings_Olinorder(_1642096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642096), _1642098)), -(c_Big__Operators_Olattice_OSup__fin(_1642096, c_Orderings_Oord__class_Omax(_1642096), hAPP(hAPP(c_Set_Oinsert(_1642096), _1642100), _1642098)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642096, _1642096, c_Orderings_Oord__class_Omax(_1642096)), _1642100), _1642098))], (35460 ^ _779571) ^ [_1433325, _1433327, _1433329, _1433331, _1433333, _1433335, _1433337, _1433339] : [hAPP(c_Fun_Ocomp(_1433325, _1433327, _1433329, _1433331), _1433333) = hAPP(c_Fun_Ocomp(_1433335, _1433327, _1433329, _1433337), _1433339), 35463 ^ _779571 : [(35464 ^ _779571) ^ [_1433440] : [-(hAPP(_1433331, hAPP(_1433333, _1433440)) = hAPP(_1433337, hAPP(_1433339, _1433440)))]]], (43905 ^ _779571) ^ [_1638140, _1638142, _1638144, _1638146] : [class_Lattices_Osemilattice__sup(_1638140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638140), _1638142)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1638140, _1638140, c_Lattices_Osemilattice__sup__class_Osup(_1638140)), _1638144), hAPP(hAPP(c_Set_Oinsert(_1638140), _1638146), _1638142)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1638140), _1638146), hAPP(hAPP(c_Finite__Set_Ofold(_1638140, _1638140, c_Lattices_Osemilattice__sup__class_Osup(_1638140)), _1638144), _1638142)))], (15846 ^ _779571) ^ [_1048818, _1048820, _1048822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048818), _1048820)), _1048822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048822), _1048820))))], (34156 ^ _779571) ^ [_1404155, _1404157, _1404159, _1404161, _1404163, _1404165, _1404167] : [-(_1404155 = _1404157), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404159, _1404161), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404159, _1404161), _1404163), _1404155), _1404165)), _1404157), _1404167) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404159, _1404161), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404159, _1404161), _1404163), _1404157), _1404167)), _1404155), _1404165))], (19991 ^ _779571) ^ [_1122982, _1122984, _1122986, _1122988] : [19993 ^ _779571 : [(19998 ^ _779571) ^ [] : [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(_1122986, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19992 ^ [_1122982, _1122984, _1122986, _1122988]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1122986, 19992 ^ [_1122982, _1122984, _1122986, _1122988])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19996 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19992 ^ [_1122982, _1122984, _1122986, _1122988]), _1122984)))], (19994 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122982), 19992 ^ [_1122982, _1122984, _1122986, _1122988])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122982), _1122984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1122986, _1122982)), _1122988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122988), hAPP(_1122986, _1122984))), 20012 ^ _779571 : [(20017 ^ _779571) ^ [] : [-(hAPP(_1122986, 20011 ^ [_1122982, _1122984, _1122986, _1122988]) = _1122988)], (20015 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20011 ^ [_1122982, _1122984, _1122986, _1122988]), _1122984)))], (20013 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122982), 20011 ^ [_1122982, _1122984, _1122986, _1122988])))]]], (8007 ^ _779571) ^ [_912383, _912385] : [_912383 = c_Option_Ooption_ONone(_912385), 8010 ^ _779571 : [(8011 ^ _779571) ^ [_912455] : [_912383 = hAPP(c_Option_Ooption_OSome(_912385), _912455)]]], (17171 ^ _779571) ^ [_1074781, _1074783, _1074785, _1074787] : [class_Rings_Olinordered__semidom(_1074781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074783), _1074785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074781), c_Groups_Ozero__class_Ozero(_1074781)), _1074787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074781), _1074787), c_Groups_Oone__class_Oone(_1074781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074781), hAPP(hAPP(c_Power_Opower__class_Opower(_1074781), _1074787), _1074785)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074781), _1074787), _1074783))))], (51607 ^ _779571) ^ [_1813612, _1813614] : [hBOOL(_1813612), hBOOL(_1813614), -(hBOOL(hAPP(hAPP(c_fconj, _1813612), _1813614)))], (13526 ^ _779571) ^ [_1006126, _1006128, _1006130] : [class_Lattices_Oboolean__algebra(_1006126), 13529 ^ _779571 : [(13536 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006126), _1006130), _1006128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006126), hAPP(c_Groups_Ouminus__class_Ouminus(_1006126), _1006128)), hAPP(c_Groups_Ouminus__class_Ouminus(_1006126), _1006130))))], (13530 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006126), hAPP(c_Groups_Ouminus__class_Ouminus(_1006126), _1006128)), hAPP(c_Groups_Ouminus__class_Ouminus(_1006126), _1006130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006126), _1006130), _1006128)))]]], (36268 ^ _779571) ^ [_1452992, _1452994] : [class_Lattices_Obounded__lattice__bot(_1452992), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452992), _1452994), c_Orderings_Obot__class_Obot(_1452992)) = c_Orderings_Obot__class_Obot(_1452992))], (1910 ^ _779571) ^ [_807280, _807282, _807284, _807286, _807288, _807290, _807292, _807294, _807296, _807298, _807300, _807302, _807304, _807306, _807308, _807310, _807312, _807314, _807316, _807318] : [-(c_Com_Ocom_Ocom__case(_807318, _807314, _807310, _807306, _807302, _807298, _807294, _807290, _807286, _807282) = c_Com_Ocom_Ocom__case(_807316, _807312, _807308, _807304, _807300, _807296, _807292, _807288, _807284, _807280)), _807318 = _807316, _807314 = _807312, _807310 = _807308, _807306 = _807304, _807302 = _807300, _807298 = _807296, _807294 = _807292, _807290 = _807288, _807286 = _807284, _807282 = _807280], (16499 ^ _779571) ^ [_1061864, _1061866, _1061868] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1061864), _1061866)), _1061868) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1061864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061866), _1061868)))], (7216 ^ _779571) ^ [_898817, _898819, _898821, _898823] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_898817, _898819)), _898821), _898823)), 7221 ^ _779571 : [(7224 ^ _779571) ^ [] : [hBOOL(hAPP(_898817, _898821))], (7222 ^ _779571) ^ [] : [-(_898823 = _898821)]], 7225 ^ _779571 : [(7231 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_898817, _898819)), 7227 ^ [_898817, _898819, _898821, _898823]), _898823)))], (7229 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898819), _898821), 7227 ^ [_898817, _898819, _898821, _898823])))], (7226 ^ _779571) ^ [] : [-(hBOOL(hAPP(_898817, _898821)))]]], (47372 ^ _779571) ^ [_1722097, _1722099] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1722097)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1722099)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1722097), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1722099)) = c_List_Olist_ONil(tc_Int_Oint))], (32737 ^ _779571) ^ [_1376783, _1376785] : [32738 ^ _779571 : [(32741 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376785), _1376783))], (32739 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376783), _1376785)))]], -(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)))), _1376783, _1376785) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (11138 ^ _779571) ^ [_964549] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964549), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28150 ^ _779571) ^ [_1278823, _1278825, _1278827, _1278829] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278823, tc_HOL_Obool)), _1278825), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278823, tc_HOL_Obool)), _1278827), _1278829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278823, tc_HOL_Obool)), _1278827), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278823, tc_HOL_Obool)), _1278825), _1278829)))], (36770 ^ _779571) ^ [_1463797, _1463799, _1463801, _1463803] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463797, tc_HOL_Obool)), _1463799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463797, tc_HOL_Obool)), _1463801), _1463803)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463797, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463797, tc_HOL_Obool)), _1463799), _1463801)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463797, tc_HOL_Obool)), _1463799), _1463803)))], (31524 ^ _779571) ^ [_1351226, _1351228] : [c_Nat__Transfer_Onat__set(_1351226), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1351228), _1351226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351228)))], (12411 ^ _779571) ^ [_986794] : [12412 ^ _779571 : [(12413 ^ _779571) ^ [_986851] : [hBOOL(hAPP(_986794, _986851))]], 12415 ^ _779571 : [(12418 ^ _779571) ^ [] : [-(hBOOL(hAPP(_986794, hAPP(c_Int_Onat, 12414 ^ [_986794]))))], (12416 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12414 ^ [_986794])))]]], (47242 ^ _779571) ^ [_1719729, _1719731, _1719733, _1719735, _1719737] : [class_Orderings_Olinorder(_1719729), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1719731, _1719729, _1719733), _1719735), _1719737) = c_List_Olist_ONil(_1719731)], (49207 ^ _779571) ^ [_1766935, _1766937, _1766939] : [class_Orderings_Olinorder(_1766935), -(c_Big__Operators_Olinorder__class_OMin(_1766935, hAPP(c_List_Oset(_1766935), hAPP(hAPP(c_List_Olist_OCons(_1766935), _1766937), _1766939))) = hAPP(c_List_Ofoldl(_1766935, _1766935, c_Orderings_Oord__class_Omin(_1766935), _1766937), _1766939))], (29882 ^ _779571) ^ [_1314079, _1314081] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314079, _1314081, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314079), tc_HOL_Obool))))], (36848 ^ _779571) ^ [_1465547, _1465549, _1465551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465547, tc_HOL_Obool)), _1465549), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1465547, tc_HOL_Obool)), _1465551))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465547, tc_HOL_Obool)), _1465549), _1465551) = c_Orderings_Obot__class_Obot(tc_fun(_1465547, tc_HOL_Obool)))], (43899 ^ _779571) ^ [_1638001, _1638003, _1638005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1638001), _1638003)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1638001, tc_HOL_Obool)), _1638003), _1638005) = hAPP(hAPP(c_Finite__Set_Ofold(_1638001, tc_fun(_1638001, tc_HOL_Obool), c_Set_Oinsert(_1638001)), _1638005), _1638003))], (6134 ^ _779571) ^ [_878514, _878516, _878518, _878520, _878522] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_878514, _878516), _878518, _878520, _878522), 6139 ^ _779571 : [(6142 ^ _779571) ^ [] : [hBOOL(hAPP(_878514, _878518))], (6140 ^ _779571) ^ [] : [-(_878522 = _878518)]], 6143 ^ _779571 : [(6149 ^ _779571) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_878514, _878516), 6145 ^ [_878514, _878516, _878518, _878520, _878522], _878520, _878522))], (6147 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_878516, _878518, _878520, 6145 ^ [_878514, _878516, _878518, _878520, _878522]))], (6144 ^ _779571) ^ [] : [-(hBOOL(hAPP(_878514, _878518)))]]], (9016 ^ _779571) ^ [_928977, _928979] : [class_Rings_Ocomm__semiring__1(_928977), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928977), c_Groups_Oone__class_Oone(_928977)), _928979) = _928979)], (41332 ^ _779571) ^ [_1568935, _1568937, _1568939, _1568941, _1568943, _1568945] : [hBOOL(hAPP(hAPP(c_member(_1568935), _1568937), _1568939)), -(hAPP(c_Fun_Ooverride__on(_1568935, _1568941, _1568943, _1568945, _1568939), _1568937) = hAPP(_1568945, _1568937))], (45596 ^ _779571) ^ [_1677767, _1677769, _1677771, _1677773, _1677775, _1677777, _1677779, _1677781] : [c_Finite__Set_Ofolding__image__simple__idem(_1677767, _1677769, _1677771, _1677773, _1677775, _1677777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677769), _1677779)), -(hAPP(_1677777, hAPP(hAPP(c_Set_Oinsert(_1677769), _1677781), _1677779)) = hAPP(hAPP(_1677771, hAPP(_1677775, _1677781)), hAPP(_1677777, _1677779)))], (42914 ^ _779571) ^ [_1612618, _1612620, _1612622, _1612624, _1612626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612618, _1612618)), hAPP(hAPP(c_Product__Type_OPair(_1612618, _1612618), _1612620), _1612622)), _1612624)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1612618, _1612618)), hAPP(hAPP(c_Product__Type_OPair(_1612618, _1612618), _1612622), _1612626)), _1612624)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612618, _1612618)), hAPP(hAPP(c_Product__Type_OPair(_1612618, _1612618), _1612620), _1612626)), c_Transitive__Closure_Otrancl(_1612618, _1612624))))], (22208 ^ _779571) ^ [_1162845, _1162847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162845), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162847)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162845)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162847))], (40857 ^ _779571) ^ [_1556402, _1556404, _1556406, _1556408, _1556410, _1556412, _1556414, _1556416, _1556418, _1556420] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1556402, _1556404), tc_prod(_1556406, _1556408), tc_prod(_1556410, _1556412), c_Product__Type_Omap__pair(_1556402, _1556406, _1556404, _1556408, _1556414, _1556416)), c_Product__Type_Omap__pair(_1556410, _1556402, _1556412, _1556404, _1556418, _1556420)) = c_Product__Type_Omap__pair(_1556410, _1556406, _1556412, _1556408, hAPP(c_Fun_Ocomp(_1556402, _1556406, _1556410, _1556414), _1556418), hAPP(c_Fun_Ocomp(_1556404, _1556408, _1556412, _1556416), _1556420)))], (42421 ^ _779571) ^ [_1601668, _1601670, _1601672] : [-(hAPP(c_New__DSequence_Oneg__single(_1601668, _1601670), _1601672) = c_Lazy__Sequence_Ohb__single(_1601668, _1601670))], (34507 ^ _779571) ^ [_1411086, _1411088, _1411090, _1411092, _1411094] : [class_Fields_Ofield(_1411086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411088), _1411090)), -(hAPP(_1411092, _1411094) = c_Groups_Ozero__class_Ozero(_1411086)), 34518 ^ _779571 : [(34525 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411088), _1411094), _1411090))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411088, _1411086), _1411092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411088, tc_HOL_Obool)), _1411090), hAPP(hAPP(c_Set_Oinsert(_1411088), _1411094), c_Orderings_Obot__class_Obot(tc_fun(_1411088, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411088, _1411086), _1411092), _1411090))], (34519 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1411088), _1411094), _1411090)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411088, _1411086), _1411092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411088, tc_HOL_Obool)), _1411090), hAPP(hAPP(c_Set_Oinsert(_1411088), _1411094), c_Orderings_Obot__class_Obot(tc_fun(_1411088, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1411086), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411088, _1411086), _1411092), _1411090)), hAPP(_1411092, _1411094)))]]], (28993 ^ _779571) ^ [_1296564, _1296566, _1296568, _1296570] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1296564), _1296566), _1296568), _1296570)), -(_1296566 = _1296570), -(hBOOL(hAPP(_1296568, _1296570)))], (27555 ^ _779571) ^ [_1266704, _1266706, _1266708, _1266710, _1266712, _1266714, _1266716, _1266718] : [class_Groups_Ocomm__monoid__add(_1266704), class_Orderings_Oord(_1266706), _1266708 = _1266710, _1266712 = _1266714, 27573 ^ _779571 : [(27578 ^ _779571) ^ [] : [hAPP(_1266716, 27572 ^ [_1266704, _1266706, _1266708, _1266710, _1266712, _1266714, _1266716, _1266718]) = hAPP(_1266718, 27572 ^ [_1266704, _1266706, _1266708, _1266710, _1266712, _1266714, _1266716, _1266718])], (27576 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266706), 27572 ^ [_1266704, _1266706, _1266708, _1266710, _1266712, _1266714, _1266716, _1266718]), _1266714)))], (27574 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266706), _1266710), 27572 ^ [_1266704, _1266706, _1266708, _1266710, _1266712, _1266714, _1266716, _1266718])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1266706, _1266704), _1266716), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1266706, _1266708), _1266712)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1266706, _1266704), _1266718), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1266706, _1266710), _1266714)))], (43647 ^ _779571) ^ [_1631667, _1631669, _1631671, _1631673, _1631675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631667, _1631667)), hAPP(hAPP(c_Product__Type_OPair(_1631667, _1631667), _1631669), _1631671)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631667, _1631667), tc_HOL_Obool), _1631673), _1631675))), 43652 ^ _779571 : [(43655 ^ _779571) ^ [] : [-(_1631669 = _1631671)], (43653 ^ _779571) ^ [] : [-(_1631673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43658 ^ _779571 : [(43663 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631667, _1631667)), hAPP(hAPP(c_Product__Type_OPair(_1631667, _1631667), 43656 ^ [_1631667, _1631669, _1631671, _1631673, _1631675]), _1631671)), _1631675)))], (43661 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631667, _1631667)), hAPP(hAPP(c_Product__Type_OPair(_1631667, _1631667), _1631669), 43656 ^ [_1631667, _1631669, _1631671, _1631673, _1631675])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631667, _1631667), tc_HOL_Obool), 43657 ^ [_1631667, _1631669, _1631671, _1631673, _1631675]), _1631675))))], (43659 ^ _779571) ^ [] : [-(_1631673 = hAPP(c_Nat_OSuc, 43657 ^ [_1631667, _1631669, _1631671, _1631673, _1631675]))]]], (31718 ^ _779571) ^ [_1355190, _1355192, _1355194, _1355196, _1355198] : [class_Groups_Ocomm__monoid__add(_1355190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355192), _1355194)), -(hBOOL(hAPP(hAPP(c_member(_1355192), _1355196), _1355194))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355192, _1355190), _1355198), hAPP(hAPP(c_Set_Oinsert(_1355192), _1355196), _1355194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355190), hAPP(_1355198, _1355196)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355192, _1355190), _1355198), _1355194)))], (24721 ^ _779571) ^ [_1211276, _1211278] : [class_Orderings_Olinorder(_1211276), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211276), _1211278), _1211278) = _1211278)], (37724 ^ _779571) ^ [_1486584, _1486586, _1486588, _1486590, _1486592, _1486594] : [hBOOL(hAPP(hAPP(_1486584, _1486586), _1486588)), hBOOL(hAPP(hAPP(_1486590, _1486586), _1486588)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486592, tc_fun(_1486594, tc_HOL_Obool))), _1486584), _1486590), _1486586), _1486588)))], (27369 ^ _779571) ^ [_1262697, _1262699, _1262701, _1262703] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262697), _1262699)), 27372 ^ _779571 : [(27373 ^ _779571) ^ [_1262851] : [27375 ^ _779571 : [(27381 ^ _779571) ^ [] : [-(_1262851 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27377 ^ [_1262697, _1262699, _1262701, _1262703, _1262851]), 27374 ^ [_1262697, _1262699, _1262701, _1262703, _1262851]))], (27379 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27377 ^ [_1262697, _1262699, _1262701, _1262703, _1262851]), _1262701)))], (27376 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27374 ^ [_1262697, _1262699, _1262701, _1262703, _1262851]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1262699))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262851), _1262703))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262851), _1262699)), _1262703))))]]], (34003 ^ _779571) ^ [_1400602, _1400604] : [class_Orderings_Olinorder(_1400602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400602), _1400604)), -(_1400604 = c_Orderings_Obot__class_Obot(tc_fun(_1400602, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1400602), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400602), 34016 ^ [_1400602, _1400604]), 34017 ^ [_1400602, _1400604])), hAPP(hAPP(c_Set_Oinsert(_1400602), 34016 ^ [_1400602, _1400604]), hAPP(hAPP(c_Set_Oinsert(_1400602), 34017 ^ [_1400602, _1400604]), c_Orderings_Obot__class_Obot(tc_fun(_1400602, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1400602), c_Big__Operators_Olattice_OInf__fin(_1400602, c_Orderings_Oord__class_Omin(_1400602), _1400604)), _1400604)))], (24549 ^ _779571) ^ [_1207832, _1207834, _1207836] : [class_Orderings_Olinorder(_1207832), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207832), _1207834), _1207836) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207832), _1207836), _1207834))], (27536 ^ _779571) ^ [_1266363, _1266365] : [c_Nat__Transfer_Ois__nat(_1266363), c_Nat__Transfer_Ois__nat(_1266365), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1266363, _1266365) = 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, _1266363), hAPP(c_Int_Onat, _1266365))))], (35882 ^ _779571) ^ [_1444319, _1444321, _1444323, _1444325, _1444327, _1444329, _1444331] : [c_Equiv__Relations_Oequiv(_1444319, _1444321, _1444323), hBOOL(hAPP(hAPP(c_member(tc_fun(_1444319, tc_HOL_Obool)), _1444325), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1444319), _1444321), _1444323))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1444319, tc_HOL_Obool)), _1444327), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1444319), _1444321), _1444323))), hBOOL(hAPP(hAPP(c_member(_1444319), _1444329), _1444325)), hBOOL(hAPP(hAPP(c_member(_1444319), _1444331), _1444327)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1444319, _1444319)), hAPP(hAPP(c_Product__Type_OPair(_1444319, _1444319), _1444329), _1444331)), _1444323)), -(_1444325 = _1444327)], (35813 ^ _779571) ^ [_1442698, _1442700, _1442702, _1442704, _1442706] : [c_Equiv__Relations_Oequiv(_1442698, _1442700, _1442702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442698, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442698, _1442698, _1442702), hAPP(hAPP(c_Set_Oinsert(_1442698), _1442704), c_Orderings_Obot__class_Obot(tc_fun(_1442698, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1442698, _1442698, _1442702), hAPP(hAPP(c_Set_Oinsert(_1442698), _1442706), c_Orderings_Obot__class_Obot(tc_fun(_1442698, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1442698), _1442704), _1442700)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442698, _1442698)), hAPP(hAPP(c_Product__Type_OPair(_1442698, _1442698), _1442706), _1442704)), _1442702)))], (3520 ^ _779571) ^ [_833689, _833691] : [_833691 = _833689, -(c_Rings_Oinverse__class_Odivide(_833691) = c_Rings_Oinverse__class_Odivide(_833689))], (18913 ^ _779571) ^ [_1103928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1103928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103928)))], (10291 ^ _779571) ^ [_951056, _951058] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951056), _951058) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _951056 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _951058 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (18581 ^ _779571) ^ [_1098296] : [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), _1098296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1098296)))], (24341 ^ _779571) ^ [_1203980, _1203982, _1203984, _1203986] : [class_Orderings_Olinorder(_1203980), 24344 ^ _779571 : [(24345 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203980), _1203984), _1203986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), _1203984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), _1203986)))], (24355 ^ _779571) ^ [] : [24356 ^ _779571 : [(24359 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), _1203986))], (24357 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), _1203984))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203980), _1203982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203980), _1203984), _1203986))))]]], (34654 ^ _779571) ^ [_1414398, _1414400] : [-(c_Map_Oran(_1414398, _1414400, hAPP(c_COMBK(tc_Option_Ooption(_1414400), _1414398), c_Option_Ooption_ONone(_1414400))) = c_Orderings_Obot__class_Obot(tc_fun(_1414400, tc_HOL_Obool)))], (6153 ^ _779571) ^ [_878855, _878857, _878859, _878861, _878863, _878865, _878867, _878869, _878871, _878873, _878875] : [-(c_Com_Ocom_Ocom__case(_878855, _878857, _878859, _878861, _878863, _878865, _878867, _878869, _878871, c_Com_Ocom_OSemi(_878873, _878875)) = hAPP(hAPP(_878863, _878873), _878875))], (15962 ^ _779571) ^ [_1051626, _1051628, _1051630] : [hBOOL(hAPP(_1051626, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051628), _1051630))), 15965 ^ _779571 : [(15972 ^ _779571) ^ [_1051811] : [_1051628 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051630), _1051811), -(hBOOL(hAPP(_1051626, _1051811)))], (15966 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051628), _1051630)), -(hBOOL(hAPP(_1051626, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (29236 ^ _779571) ^ [_1302037, _1302039, _1302041, _1302043] : [_1302043 = c_Orderings_Obot__class_Obot(tc_fun(_1302037, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1302037, _1302039, _1302041), _1302043) = c_Orderings_Obot__class_Obot(tc_fun(_1302039, tc_HOL_Obool)))], (11350 ^ _779571) ^ [_968035, _968037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968035), _968037)), 11353 ^ _779571 : [(11356 ^ _779571) ^ [] : [_968035 = _968037], (11354 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968035), _968037)))]]], (51473 ^ _779571) ^ [_1812151, _1812153] : [-(class_Smallcheck_Osmall(tc_prod(_1812151, _1812153))), class_Smallcheck_Osmall(_1812151), class_Smallcheck_Osmall(_1812153)], (27518 ^ _779571) ^ [_1266005, _1266007, _1266009] : [class_Groups_Oordered__ab__group__add(_1266005), -(hAPP(c_Set_Oimage(_1266005, _1266005, c_Groups_Ouminus__class_Ouminus(_1266005)), c_SetInterval_Oord__class_OatLeastAtMost(_1266005, _1266007, _1266009)) = c_SetInterval_Oord__class_OatLeastAtMost(_1266005, hAPP(c_Groups_Ouminus__class_Ouminus(_1266005), _1266009), hAPP(c_Groups_Ouminus__class_Ouminus(_1266005), _1266007)))], (18859 ^ _779571) ^ [_1103029, _1103031] : [c_Int_Oiszero(_1103029, hAPP(c_Int_Onumber__class_Onumber__of(_1103029), c_Int_OBit1(_1103031))), class_Int_Onumber__ring(_1103029), class_Int_Oring__char__0(_1103029)], (1742 ^ _779571) ^ [_804114, _804116] : [-(class_Groups_Ozero(_804114)), _804116 = _804114, class_Groups_Ozero(_804116)], (23071 ^ _779571) ^ [_1179661, _1179663, _1179665] : [hBOOL(hAPP(_1179661, hAPP(hAPP(c_Product__Type_OPair(_1179663, _1179665), 23072 ^ [_1179661, _1179663, _1179665]), 23073 ^ [_1179661, _1179663, _1179665]))), 23076 ^ _779571 : [(23077 ^ _779571) ^ [_1179808] : [-(hBOOL(hAPP(_1179661, _1179808)))]]], (7716 ^ _779571) ^ [_907359, _907361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907359), hAPP(c_Nat_OSuc, _907361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907359), _907361))), -(_907359 = _907361)], (16427 ^ _779571) ^ [_1060447, _1060449] : [class_Groups_Oordered__ab__group__add__abs(_1060447), 16430 ^ _779571 : [(16437 ^ _779571) ^ [] : [_1060449 = c_Groups_Ozero__class_Ozero(_1060447), -(hAPP(c_Groups_Oabs__class_Oabs(_1060447), _1060449) = c_Groups_Ozero__class_Ozero(_1060447))], (16431 ^ _779571) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1060447), _1060449) = c_Groups_Ozero__class_Ozero(_1060447), -(_1060449 = c_Groups_Ozero__class_Ozero(_1060447))]]], (16252 ^ _779571) ^ [_1057424, _1057426] : [-(_1057424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057424), _1057426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1057426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057424), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1057426)))], (35434 ^ _779571) ^ [_1432620, _1432622, _1432624, _1432626, _1432628] : [-(hAPP(c_Relation_OImage(_1432620, _1432622, _1432624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432620, tc_HOL_Obool)), _1432626), _1432628)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432622, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1432620, _1432622, _1432624), _1432626)), hAPP(c_Relation_OImage(_1432620, _1432622, _1432624), _1432628)))], (34445 ^ _779571) ^ [_1409793, _1409795, _1409797, _1409799] : [class_Groups_Ocomm__monoid__mult(_1409793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409795), _1409797)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409795, _1409793), hAPP(c_COMBK(_1409793, _1409795), _1409799)), _1409797) = hAPP(hAPP(c_Power_Opower__class_Opower(_1409793), _1409799), hAPP(c_Finite__Set_Ocard(_1409795), _1409797)))], (13256 ^ _779571) ^ [_1001446, _1001448, _1001450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001446)), _1001446 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001448), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001446), _1001450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001450), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43252 ^ _779571) ^ [_1621510, _1621512, _1621514, _1621516] : [c_Wellfounded_Oacyclic(_1621510, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1621510, _1621510)), hAPP(hAPP(c_Product__Type_OPair(_1621510, _1621510), _1621512), _1621514)), _1621516)), 43255 ^ _779571 : [(43258 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621510, _1621510)), hAPP(hAPP(c_Product__Type_OPair(_1621510, _1621510), _1621514), _1621512)), c_Transitive__Closure_Ortrancl(_1621510, _1621516)))], (43256 ^ _779571) ^ [] : [-(c_Wellfounded_Oacyclic(_1621510, _1621516))]]], (26432 ^ _779571) ^ [_1243862] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243862), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1243862) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (41171 ^ _779571) ^ [_1563625, _1563627, _1563629] : [-(hBOOL(hAPP(_1563625, _1563627))), -(hAPP(c_Set_OCollect(_1563629), hAPP(hAPP(c_COMBS(_1563629, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563629), c_fconj), hAPP(c_fequal, _1563627))), _1563625)) = c_Orderings_Obot__class_Obot(tc_fun(_1563629, tc_HOL_Obool)))], (36566 ^ _779571) ^ [_1458842, _1458844, _1458846] : [class_Lattices_Osemilattice__inf(_1458842), 36569 ^ _779571 : [(36576 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458842), _1458844), _1458846) = _1458844, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458842), _1458844), _1458846)))], (36570 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458842), _1458844), _1458846)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458842), _1458844), _1458846) = _1458844)]]], (11050 ^ _779571) ^ [_962858, _962860, _962862, _962864] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_962858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962858), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962858), _962860), _962862)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962858), _962860), _962864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962858), _962862), _962864)))], (7788 ^ _779571) ^ [_908654, _908656, _908658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908656), _908658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908654), _908656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908654), _908658))))], (18815 ^ _779571) ^ [_1102293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102293), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1102293)), c_Int_OMin)))], (48265 ^ _779571) ^ [_1743812, _1743814, _1743816, _1743818] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743812), tc_List_Olist(_1743812))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743812), tc_List_Olist(_1743812)), _1743814), _1743816)), c_List_Olexord(_1743812, _1743818)))), 48266 ^ _779571 : [(48273 ^ _779571) ^ [_1744119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744119), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743812)), _1743814)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743812)), _1743816)))), hAPP(hAPP(c_List_Otake(_1743812), _1744119), _1743814) = hAPP(hAPP(c_List_Otake(_1743812), _1744119), _1743816), hBOOL(hAPP(hAPP(c_member(tc_prod(_1743812, _1743812)), hAPP(hAPP(c_Product__Type_OPair(_1743812, _1743812), hAPP(hAPP(c_List_Onth(_1743812), _1743814), _1744119)), hAPP(hAPP(c_List_Onth(_1743812), _1743816), _1744119))), _1743818))], (48267 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743812)), _1743814)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743812)), _1743816))), hAPP(hAPP(c_List_Otake(_1743812), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743812)), _1743814)), _1743816) = _1743814]]], (51529 ^ _779571) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (17519 ^ _779571) ^ [_1080918, _1080920] : [class_Power_Opower(_1080918), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1080918), _1080920), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1080918))], (24617 ^ _779571) ^ [_1209377, _1209379, _1209381] : [class_Groups_Olinordered__ab__group__add(_1209377), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1209377), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209377), _1209379), _1209381)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209377), hAPP(c_Groups_Ouminus__class_Ouminus(_1209377), _1209379)), hAPP(c_Groups_Ouminus__class_Ouminus(_1209377), _1209381)))], (6301 ^ _779571) ^ [_881809, _881811, _881813] : [hBOOL(hAPP(c_Com_OWT, _881809)), hBOOL(hAPP(c_Com_OWT, _881811)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_881813, _881809, _881811))))], (31448 ^ _779571) ^ [_1347941, _1347943, _1347945, _1347947, _1347949, _1347951] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1347941, tc_fun(_1347943, tc_fun(_1347945, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1347941, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_fun(_1347943, tc_fun(_1347945, tc_HOL_Obool)), _1347941), hAPP(c_COMBC(_1347943, tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_fun(_1347945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347945, tc_fun(tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_fun(_1347945, tc_HOL_Obool)), _1347943), c_COMBC(_1347945, tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347945, tc_prod(_1347943, _1347945)), tc_fun(_1347945, tc_fun(tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_HOL_Obool)), _1347943), hAPP(c_COMBB(tc_prod(_1347943, _1347945), tc_fun(tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool), tc_HOL_Obool), _1347945), c_member(tc_prod(_1347943, _1347945)))), c_Product__Type_OPair(_1347943, _1347945))))), _1347947)), _1347949), _1347951)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1347943, _1347945)), hAPP(hAPP(c_Product__Type_OPair(_1347943, _1347945), _1347949), _1347951)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1347941, tc_fun(tc_prod(_1347943, _1347945), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1347941, tc_HOL_Obool))), _1347947))))], (44856 ^ _779571) ^ [_1660768, _1660770] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1660768), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1660768, tc_HOL_Obool), _1660770)))), 44857 ^ _779571 : [(44858 ^ _779571) ^ [_1660832] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1660768, tc_HOL_Obool)), _1660832), _1660770)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660768), _1660832))]]], (18377 ^ _779571) ^ [_1095087, _1095089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1095087)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1095089)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095087)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1095087))))], (8742 ^ _779571) ^ [_923942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923942), 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)), _923942)), _923942)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32371 ^ _779571) ^ [_1368755, _1368757, _1368759, _1368761] : [hBOOL(hAPP(hAPP(c_member(_1368755), _1368757), c_SetInterval_Oord_OatLeast(_1368755, _1368759, _1368761))), -(hBOOL(hAPP(hAPP(_1368759, _1368761), _1368757)))], (15730 ^ _779571) ^ [_1046643, _1046645] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046643), _1046645))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046643), _1046645)) = _1046643)], (9648 ^ _779571) ^ [_939861, _939863, _939865] : [class_Rings_Olinordered__semiring__strict(_939861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939861), c_Groups_Ozero__class_Ozero(_939861)), _939863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939861), c_Groups_Ozero__class_Ozero(_939861)), _939865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939861), c_Groups_Ozero__class_Ozero(_939861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939861), _939863), _939865))))], (39623 ^ _779571) ^ [_1527093, _1527095, _1527097, _1527099, _1527101] : [hBOOL(hAPP(hAPP(c_member(_1527093), _1527095), hAPP(c_Relation_OImage(_1527097, _1527093, _1527099), _1527101))), 39627 ^ _779571 : [(39630 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527097), 39626 ^ [_1527093, _1527095, _1527097, _1527099, _1527101]), _1527101)))], (39628 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527097, _1527093)), hAPP(hAPP(c_Product__Type_OPair(_1527097, _1527093), 39626 ^ [_1527093, _1527095, _1527097, _1527099, _1527101]), _1527095)), _1527099)))]]], (38901 ^ _779571) ^ [_1510911, _1510913, _1510915, _1510917, _1510919] : [c_Fun_Oinj__on(_1510911, _1510913, _1510915, hAPP(hAPP(c_Set_Oinsert(_1510911), _1510917), _1510919)), 38904 ^ _779571 : [(38907 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1510913), hAPP(_1510915, _1510917)), hAPP(c_Set_Oimage(_1510911, _1510913, _1510915), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510911, tc_HOL_Obool)), _1510919), hAPP(hAPP(c_Set_Oinsert(_1510911), _1510917), c_Orderings_Obot__class_Obot(tc_fun(_1510911, tc_HOL_Obool)))))))], (38905 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1510911, _1510913, _1510915, _1510919))]]], (17825 ^ _779571) ^ [_1086435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086435), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086435)))], (37056 ^ _779571) ^ [_1470361, _1470363, _1470365] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470361), _1470363)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470361), _1470365)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470361), _1470363)), hAPP(c_Finite__Set_Ocard(_1470361), _1470365)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470361, tc_HOL_Obool)), _1470363), _1470365))), hAPP(c_Finite__Set_Ocard(_1470361), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470361, tc_HOL_Obool)), _1470363), _1470365))))], (50890 ^ _779571) ^ [_1803973, _1803975] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803973), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1803973))), _1803975))), 50893 ^ _779571 : [(50900 ^ _779571) ^ [] : [-(_1803975 = c_List_Olist_ONil(tc_List_Olist(_1803973))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1803973))), c_List_Otranspose(_1803973, _1803975)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803973)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1803973)), _1803975), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50894 ^ _779571) ^ [] : [_1803975 = c_List_Olist_ONil(tc_List_Olist(_1803973)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1803973))), c_List_Otranspose(_1803973, _1803975)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (30202 ^ _779571) ^ [_1320867, _1320869, _1320871, _1320873] : [hBOOL(hAPP(hAPP(c_member(_1320867), _1320869), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320867, tc_HOL_Obool)), _1320871), _1320873))), -(hBOOL(hAPP(hAPP(c_member(_1320867), _1320869), _1320871)))], (48774 ^ _779571) ^ [_1757568, _1757570, _1757572, _1757574] : [-(hAPP(hAPP(c_List_Odrop(_1757568), _1757570), hAPP(hAPP(c_List_Odrop(_1757568), _1757572), _1757574)) = hAPP(hAPP(c_List_Odrop(_1757568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757570), _1757572)), _1757574))], (7664 ^ _779571) ^ [_906582, _906584] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906582), _906584))), 7667 ^ _779571 : [(7674 ^ _779571) ^ [] : [_906582 = _906584, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906582), hAPP(c_Nat_OSuc, _906584))))], (7668 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906582), hAPP(c_Nat_OSuc, _906584))), -(_906582 = _906584)]]], (16943 ^ _779571) ^ [_1070347, _1070349] : [class_Rings_Olinordered__idom(_1070347), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070347), c_Groups_Osgn__class_Osgn(_1070347, _1070349)), hAPP(c_Groups_Oabs__class_Oabs(_1070347), _1070349)) = _1070349)], (1032 ^ _779571) ^ [_795239, _795241] : [-(class_Rings_Oring__no__zero__divisors(_795239)), _795241 = _795239, class_Rings_Oring__no__zero__divisors(_795241)], (23637 ^ _779571) ^ [_1190009, _1190011, _1190013, _1190015] : [class_Orderings_Olinorder(_1190009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190009), _1190011), _1190013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190009), _1190011), _1190015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190009), _1190011), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190009), _1190013), _1190015))))], (6730 ^ _779571) ^ [_889943, _889945, _889947] : [hAPP(c_Com_Ocom_OBODY, _889943) = c_Com_Ocom_OWhile(_889945, _889947)], (35555 ^ _779571) ^ [_1436000] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1436000)) = _1436000)], (24305 ^ _779571) ^ [_1203134, _1203136, _1203138] : [class_Orderings_Olinorder(_1203134), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203134), _1203136), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203134), _1203136), _1203138)) = _1203136)], (19359 ^ _779571) ^ [_1111633] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111633)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111633))))], (4092 ^ _779571) ^ [_842645, _842647, _842649, _842651, _842653, _842655] : [-(c_Smallcheck_Oorelse(_842655, _842651, _842647) = c_Smallcheck_Oorelse(_842653, _842649, _842645)), _842655 = _842653, _842651 = _842649, _842647 = _842645], (47081 ^ _779571) ^ [_1716282, _1716284, _1716286, _1716288] : [class_Groups_Oab__group__add(_1716282), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1716282), hAPP(c_List_Omonoid__add__class_Olistsum(_1716282), hAPP(hAPP(c_List_Omap(_1716284, _1716282), _1716286), _1716288))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1716282), hAPP(hAPP(c_List_Omap(_1716284, _1716282), hAPP(c_Fun_Ocomp(_1716282, _1716282, _1716284, c_Groups_Ouminus__class_Ouminus(_1716282)), _1716286)), _1716288)))], (26538 ^ _779571) ^ [_1246080, _1246082, _1246084, _1246086] : [class_Rings_Ocomm__ring(_1246080), class_Rings_Odvd(_1246080), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246080), _1246082), _1246084)), 26549 ^ _779571 : [(26556 ^ _779571) ^ [_1246506, _1246508] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246080), _1246082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1246080), _1246508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246080), _1246506), _1246084))), _1246086))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246080), _1246082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246080), _1246508), _1246086))))], (26550 ^ _779571) ^ [_1246333, _1246335] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246080), _1246082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246080), _1246335), _1246086))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246080), _1246082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1246080), _1246335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246080), _1246333), _1246084))), _1246086))))]]], (18345 ^ _779571) ^ [_1094633] : [class_Int_Onumber__ring(_1094633), -(c_Groups_Ozero__class_Ozero(_1094633) = hAPP(c_Int_Onumber__class_Onumber__of(_1094633), c_Int_OPls))], (51401 ^ _779571) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (50758 ^ _779571) ^ [_1800060, _1800062, _1800064, _1800066, _1800068] : [-(c_List_Ofoldr(_1800060, _1800062, _1800064, _1800066, _1800068) = hAPP(c_List_Ofoldl(_1800062, _1800060, hAPP(c_COMBC(_1800060, _1800062, _1800062), _1800064), _1800068), hAPP(c_List_Orev(_1800060), _1800066)))], (34144 ^ _779571) ^ [_1403988, _1403990, _1403992, _1403994, _1403996] : [hAPP(_1403988, _1403990) = _1403992, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1403994, _1403996), _1403988), _1403990), _1403992) = _1403988)], (45237 ^ _779571) ^ [_1669727, _1669729, _1669731] : [class_Complete__Lattice_Ocomplete__lattice(_1669727), -(c_Complete__Lattice_OSup__class_OSup(_1669727, hAPP(hAPP(c_Set_Oinsert(_1669727), _1669729), hAPP(hAPP(c_Set_Oinsert(_1669727), _1669731), c_Orderings_Obot__class_Obot(tc_fun(_1669727, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1669727), _1669729), _1669731))], (25848 ^ _779571) ^ [_1232289, _1232291, _1232293, _1232295] : [class_Rings_Osemiring__1(_1232289), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1232289), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232291, tc_Nat_Onat), _1232293), _1232295)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232291, _1232289), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1232289, _1232291), c_Nat_Osemiring__1__class_Oof__nat(_1232289)), _1232293)), _1232295))], (48960 ^ _779571) ^ [_1762117, _1762119, _1762121] : [-(_1762117 = c_List_Olist_ONil(_1762119)), -(hAPP(c_List_Ohd(_1762119), hAPP(hAPP(c_List_Oappend(_1762119), _1762117), _1762121)) = hAPP(c_List_Ohd(_1762119), _1762117))], (9060 ^ _779571) ^ [_929739, _929741, _929743] : [class_Rings_Osemiring__1(_929739), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _929741), _929743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929739), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929739), _929741)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929739), _929743)))], (41716 ^ _779571) ^ [_1583796, _1583798, _1583800, _1583802, _1583804, _1583806] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583796, _1583798, _1583800), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583796, _1583798), tc_HOL_Obool)), _1583802), _1583804)), _1583806) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583796, _1583800), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583796, _1583798, _1583800), _1583802), _1583806)), hAPP(hAPP(c_Relation_Orel__comp(_1583796, _1583798, _1583800), _1583804), _1583806)))], (29996 ^ _779571) ^ [_1317055, _1317057, _1317059, _1317061] : [hBOOL(hAPP(hAPP(c_member(_1317055), _1317057), hAPP(hAPP(c_Set_Oinsert(_1317055), _1317059), _1317061))), -(_1317057 = _1317059), -(hBOOL(hAPP(hAPP(c_member(_1317055), _1317057), _1317061)))], (43028 ^ _779571) ^ [_1616253, _1616255] : [-(c_Transitive__Closure_Ortrancl(_1616253, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1616253, _1616253), tc_HOL_Obool)), _1616255), c_Relation_OId(_1616253))) = c_Transitive__Closure_Ortrancl(_1616253, _1616255))], (51379 ^ _779571) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (100 ^ _779571) ^ [_780945, _780947] : [-(class_Rings_Oinverse(_780945)), _780947 = _780945, class_Rings_Oinverse(_780947)], (39292 ^ _779571) ^ [_1519214, _1519216, _1519218, _1519220] : [class_Groups_Ocomm__monoid__mult(_1519214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519216), _1519218)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1519216, _1519214), _1519220), _1519218) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519214, _1519216, c_Groups_Otimes__class_Otimes(_1519214)), _1519220), c_Groups_Oone__class_Oone(_1519214)), _1519218))], (12471 ^ _779571) ^ [_987764, _987766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987766)), 12478 ^ _779571 : [(12485 ^ _779571) ^ [] : [_987764 = _987766, -(hAPP(c_Int_Onat, _987764) = hAPP(c_Int_Onat, _987766))], (12479 ^ _779571) ^ [] : [hAPP(c_Int_Onat, _987764) = hAPP(c_Int_Onat, _987766), -(_987764 = _987766)]]], (12380 ^ _779571) ^ [_986255] : [12381 ^ _779571 : [(12382 ^ _779571) ^ [_986312] : [hBOOL(hAPP(_986255, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _986312)))]], 12384 ^ _779571 : [(12387 ^ _779571) ^ [] : [-(hBOOL(hAPP(_986255, 12383 ^ [_986255])))], (12385 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12383 ^ [_986255])))]]], (39531 ^ _779571) ^ [_1524901, _1524903, _1524905, _1524907] : [c_Fun_Oinj__on(_1524901, _1524903, _1524905, c_Orderings_Otop__class_Otop(tc_fun(_1524901, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1524901, _1524903, _1524905), hAPP(c_Set_Oimage(_1524901, _1524903, _1524905), _1524907)) = _1524907)], (30363 ^ _779571) ^ [_1324180, _1324182, _1324184] : [_1324182 = _1324184, -(hBOOL(hAPP(hAPP(c_member(_1324180), _1324182), hAPP(c_fequal, _1324184))))], (28930 ^ _779571) ^ [_1294864, _1294866, _1294868, _1294870, _1294872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294864, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294866, tc_fun(_1294864, tc_HOL_Obool)), _1294868), _1294870)), _1294872)), 28933 ^ _779571 : [(28934 ^ _779571) ^ [_1294997] : [hBOOL(hAPP(hAPP(c_member(_1294866), _1294997), _1294868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294864, tc_HOL_Obool)), hAPP(_1294870, _1294997)), _1294872)))]]], (43224 ^ _779571) ^ [_1620826, _1620828, _1620830, _1620832] : [hBOOL(hAPP(hAPP(c_member(_1620826), _1620828), c_Wellfounded_Oacc(_1620826, _1620830))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620826, _1620826)), hAPP(hAPP(c_Product__Type_OPair(_1620826, _1620826), _1620832), _1620828)), c_Transitive__Closure_Ortrancl(_1620826, _1620830))), -(hBOOL(hAPP(hAPP(c_member(_1620826), _1620832), c_Wellfounded_Oacc(_1620826, _1620830))))], (28983 ^ _779571) ^ [_1296376] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1296376)) = 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), _1296376))))], (29061 ^ _779571) ^ [] : [-(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)))], (38485 ^ _779571) ^ [_1502654, _1502656] : [-(c_Equiv__Relations_Oequivp(_1502654, _1502656)), 38490 ^ _779571 : [(38493 ^ _779571) ^ [] : [hAPP(_1502656, 38486 ^ [_1502654, _1502656]) = hAPP(_1502656, 38487 ^ [_1502654, _1502656])], (38491 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1502656, 38486 ^ [_1502654, _1502656]), 38487 ^ [_1502654, _1502656])))]], 38494 ^ _779571 : [(38497 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1502656, 38486 ^ [_1502654, _1502656]), 38487 ^ [_1502654, _1502656]))], (38495 ^ _779571) ^ [] : [-(hAPP(_1502656, 38486 ^ [_1502654, _1502656]) = hAPP(_1502656, 38487 ^ [_1502654, _1502656]))]]], (26254 ^ _779571) ^ [_1240707, _1240709, _1240711, _1240713] : [class_Divides_Osemiring__div(_1240707), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240707), _1240709), _1240711)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240707), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240707), _1240711), _1240709)), _1240713) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240707), hAPP(hAPP(c_Power_Opower__class_Opower(_1240707), _1240711), _1240713)), hAPP(hAPP(c_Power_Opower__class_Opower(_1240707), _1240709), _1240713)))], (7288 ^ _779571) ^ [_900230, _900232, _900234] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900230))), _900232), _900234)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _900230)), _900232), _900234)))], (4908 ^ _779571) ^ [_855421, _855423] : [_855423 = _855421, -(c_Option_Ooption_OSome(_855423) = c_Option_Ooption_OSome(_855421))], (42081 ^ _779571) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (41005 ^ _779571) ^ [_1560135, _1560137, _1560139, _1560141] : [-(hAPP(c_Set_OCollect(tc_prod(_1560135, _1560137)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560135, _1560137, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1560135, tc_fun(_1560137, tc_HOL_Obool), tc_fun(_1560137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1560137, tc_HOL_Obool), tc_fun(_1560137, tc_HOL_Obool)), _1560135), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560137)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560135), c_fconj), _1560139))), _1560141))) = hAPP(hAPP(c_Product__Type_OSigma(_1560135, _1560137), hAPP(c_Set_OCollect(_1560135), _1560139)), hAPP(hAPP(c_COMBB(tc_fun(_1560137, tc_HOL_Obool), tc_fun(_1560137, tc_HOL_Obool), _1560135), c_Set_OCollect(_1560137)), _1560141)))], (6112 ^ _779571) ^ [_878164, _878166] : [hAPP(c_Nat_OSuc, _878164) = hAPP(c_Nat_OSuc, _878166), -(_878164 = _878166)], (35438 ^ _779571) ^ [_1432778, _1432780, _1432782, _1432784, _1432786, _1432788] : [-(hAPP(c_Set_Oimage(_1432778, _1432780, hAPP(c_Fun_Ocomp(_1432782, _1432780, _1432778, _1432784), _1432786)), _1432788) = hAPP(c_Set_Oimage(_1432782, _1432780, _1432784), hAPP(c_Set_Oimage(_1432778, _1432782, _1432786), _1432788)))], (18297 ^ _779571) ^ [_1093977, _1093979, _1093981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093977), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093977)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093979)), _1093981)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30036 ^ _779571) ^ [_1317775, _1317777, _1317779, _1317781] : [30037 ^ _779571 : [(30040 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1317775), _1317777), _1317781))], (30038 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1317775), _1317777), _1317779))]], -(hBOOL(hAPP(hAPP(c_member(_1317775), _1317777), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317775, tc_HOL_Obool)), _1317781), _1317779))))], (49604 ^ _779571) ^ [_1775800, _1775802, _1775804] : [hBOOL(hAPP(hAPP(c_member(_1775800), _1775802), hAPP(c_List_Oset(_1775800), c_List_Obutlast(_1775800, _1775804)))), -(hBOOL(hAPP(hAPP(c_member(_1775800), _1775802), hAPP(c_List_Oset(_1775800), _1775804))))], (23987 ^ _779571) ^ [_1197091, _1197093] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197091, tc_HOL_Obool)), _1197093), _1197093)))], (19897 ^ _779571) ^ [_1121346, _1121348, _1121350] : [class_Rings_Olinordered__idom(_1121346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121346), _1121348), c_Groups_Ozero__class_Ozero(_1121346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121346), hAPP(hAPP(c_Power_Opower__class_Opower(_1121346), _1121348), 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)))), _1121350)))), c_Groups_Ozero__class_Ozero(_1121346))))], (50250 ^ _779571) ^ [_1789262, _1789264] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1789262), _1789264)) = c_List_Oupt(_1789262, _1789264))], (47414 ^ _779571) ^ [_1723034, _1723036, _1723038, _1723040, _1723042] : [-(hAPP(hAPP(c_List_Ozip(_1723034, _1723036), hAPP(hAPP(c_List_Olist_OCons(_1723034), _1723038), _1723040)), _1723042) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1723034, _1723036)), _1723036, c_List_Olist_ONil(tc_prod(_1723034, _1723036)), hAPP(hAPP(c_COMBC(_1723036, tc_fun(tc_List_Olist(_1723036), tc_List_Olist(tc_prod(_1723034, _1723036))), tc_fun(tc_List_Olist(_1723036), tc_List_Olist(tc_prod(_1723034, _1723036)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1723034, _1723036)), tc_List_Olist(tc_prod(_1723034, _1723036))), tc_fun(tc_fun(tc_List_Olist(_1723036), tc_List_Olist(tc_prod(_1723034, _1723036))), tc_fun(tc_List_Olist(_1723036), tc_List_Olist(tc_prod(_1723034, _1723036)))), _1723036), c_COMBB(tc_List_Olist(tc_prod(_1723034, _1723036)), tc_List_Olist(tc_prod(_1723034, _1723036)), tc_List_Olist(_1723036))), hAPP(hAPP(c_COMBB(tc_prod(_1723034, _1723036), tc_fun(tc_List_Olist(tc_prod(_1723034, _1723036)), tc_List_Olist(tc_prod(_1723034, _1723036))), _1723036), c_List_Olist_OCons(tc_prod(_1723034, _1723036))), hAPP(c_Product__Type_OPair(_1723034, _1723036), _1723038)))), hAPP(c_List_Ozip(_1723034, _1723036), _1723040))), _1723042))], (12878 ^ _779571) ^ [_995289, _995291, _995293] : [class_Rings_Olinordered__idom(_995289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995289), c_Groups_Ozero__class_Ozero(_995289)), _995291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995289), c_Groups_Ozero__class_Ozero(_995289)), _995293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995289), _995293), c_Groups_Oone__class_Oone(_995289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995289), _995291), _995293)), _995291)))], (42819 ^ _779571) ^ [_1610563, _1610565] : [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), _1610563), _1610565)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610563), _1610565)))], (51237 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (47159 ^ _779571) ^ [_1718186, _1718188] : [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), _1718186), _1718188))), 47162 ^ _779571 : [(47169 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1718186), _1718188))), -(c_List_Oupto(_1718186, _1718188) = c_List_Olist_ONil(tc_Int_Oint))], (47163 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1718186), _1718188)), -(c_List_Oupto(_1718186, _1718188) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1718186), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1718186), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1718188)))]]], (44979 ^ _779571) ^ [_1663950, _1663952, _1663954] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1663950, tc_HOL_Obool)), _1663952), _1663954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663950, tc_HOL_Obool)), _1663952), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663950, tc_HOL_Obool), _1663954))))], (50539 ^ _779571) ^ [_1794782, _1794784, _1794786, _1794788] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1794782, tc_Nat_Onat), _1794782), c_Product__Type_Ofst(_1794782, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1794782, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1794782, 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(_1794782, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1794782, tc_Nat_Onat))), _1794784)), hAPP(hAPP(c_List_Ozip(_1794782, tc_Nat_Onat), _1794786), c_List_Oupt(_1794788, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794782)), _1794786)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1794782, tc_Nat_Onat), _1794782), c_Product__Type_Ofst(_1794782, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1794782, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1794782, 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(_1794782, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1794782, 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(_1794782, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1794782, tc_Nat_Onat))), _1794788))), _1794784)), hAPP(hAPP(c_List_Ozip(_1794782, tc_Nat_Onat), _1794786), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794782)), _1794786))))))], (32695 ^ _779571) ^ [_1376055, _1376057, _1376059] : [class_Rings_Osemiring__1(_1376055), hBOOL(hAPP(hAPP(c_member(_1376055), _1376057), c_Nat_Osemiring__1__class_ONats(_1376055))), hBOOL(hAPP(hAPP(c_member(_1376055), _1376059), c_Nat_Osemiring__1__class_ONats(_1376055))), -(hBOOL(hAPP(hAPP(c_member(_1376055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1376055), _1376057), _1376059)), c_Nat_Osemiring__1__class_ONats(_1376055))))], (21145 ^ _779571) ^ [_1143506, _1143508, _1143510, _1143512] : [class_Fields_Ofield__inverse__zero(_1143506), class_Int_Onumber(_1143506), 21152 ^ _779571 : [(21153 ^ _779571) ^ [] : [_1143508 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143506), _1143510), hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512)), 21156 ^ _779571 : [(21163 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512) = c_Groups_Ozero__class_Ozero(_1143506), -(_1143508 = c_Groups_Ozero__class_Ozero(_1143506))], (21157 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512) = c_Groups_Ozero__class_Ozero(_1143506)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143506), _1143508), hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512)) = _1143510)]]], (21169 ^ _779571) ^ [] : [-(_1143508 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143506), _1143510), hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512))), 21172 ^ _779571 : [(21175 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143506), _1143508), hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512)) = _1143510], (21173 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512) = c_Groups_Ozero__class_Ozero(_1143506)]], 21176 ^ _779571 : [(21179 ^ _779571) ^ [] : [_1143508 = c_Groups_Ozero__class_Ozero(_1143506)], (21177 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1143506), _1143512) = c_Groups_Ozero__class_Ozero(_1143506))]]]]], (47380 ^ _779571) ^ [_1722232, _1722234] : [-(c_List_Oset__Cons(_1722232, _1722234, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1722232)), c_List_Olist_ONil(_1722232)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1722232), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1722232, tc_List_Olist(_1722232), hAPP(hAPP(c_COMBC(_1722232, tc_List_Olist(_1722232), tc_List_Olist(_1722232)), c_List_Olist_OCons(_1722232)), c_List_Olist_ONil(_1722232))), _1722234))], (39537 ^ _779571) ^ [_1525039, _1525041, _1525043, _1525045] : [hBOOL(hAPP(hAPP(c_member(_1525039), _1525041), _1525043)), -(hAPP(c_Set_Ovimage(_1525045, _1525039, hAPP(c_COMBK(_1525039, _1525045), _1525041)), _1525043) = c_Orderings_Otop__class_Otop(tc_fun(_1525045, tc_HOL_Obool)))], (49299 ^ _779571) ^ [_1769321, _1769323, _1769325, _1769327] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769321)), hAPP(hAPP(c_List_Oappend(_1769321), _1769323), _1769325)), c_List_Olists(_1769321, _1769327))), 49302 ^ _779571 : [(49305 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769321)), _1769325), c_List_Olists(_1769321, _1769327))))], (49303 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769321)), _1769323), c_List_Olists(_1769321, _1769327))))]]], (15522 ^ _779571) ^ [_1042523, _1042525, _1042527] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042525), _1042527)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042523), _1042525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042523), _1042527)))], (48385 ^ _779571) ^ [_1746773, _1746775, _1746777] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746773)), hAPP(hAPP(c_List_Otake(_1746773), _1746775), _1746777)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746773)), _1746777)), _1746775))], (19563 ^ _779571) ^ [_1115149] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115149), 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, _1115149)))], (9088 ^ _779571) ^ [_930223] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930223))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18117 ^ _779571) ^ [_1091253] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1091253) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1091253))], (31341 ^ _779571) ^ [_1346218, _1346220] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346218), _1346220))), -(hAPP(c_Finite__Set_Ocard(_1346218), _1346220) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16124 ^ _779571) ^ [_1055242, _1055244] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055242, _1055244) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055242, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1055244)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22472 ^ _779571) ^ [_1168111, _1168113] : [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(_1168111))), 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)), _1168113)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168111)), hAPP(c_Nat_OSuc, _1168113))))], (31393 ^ _779571) ^ [_1347031, _1347033, _1347035] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1347031), _1347033)), 31396 ^ _779571 : [(31397 ^ _779571) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1347031, tc_Nat_Onat), _1347035), _1347033) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 31400 ^ _779571 : [(31401 ^ _779571) ^ [_1347193] : [hBOOL(hAPP(hAPP(c_member(_1347031), _1347193), _1347033)), -(hAPP(_1347035, _1347193) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31407 ^ _779571) ^ [] : [31409 ^ _779571 : [(31412 ^ _779571) ^ [] : [hAPP(_1347035, 31408 ^ [_1347031, _1347033, _1347035]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31410 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347031), 31408 ^ [_1347031, _1347033, _1347035]), _1347033)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1347031, tc_Nat_Onat), _1347035), _1347033) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13904 ^ _779571) ^ [_1013220, _1013222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013220), 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, _1013222, _1013220)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30969 ^ _779571) ^ [_1337134, _1337136] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1337134, _1337136))))], (16699 ^ _779571) ^ [_1065449, _1065451, _1065453] : [class_Groups_Oordered__ab__group__add__abs(_1065449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065449), _1065451), _1065453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065449), hAPP(c_Groups_Ouminus__class_Ouminus(_1065449), _1065451)), _1065453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065449), hAPP(c_Groups_Oabs__class_Oabs(_1065449), _1065451)), _1065453)))], (24727 ^ _779571) ^ [_1211367, _1211369] : [class_Orderings_Olinorder(_1211367), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211367), _1211369), _1211369) = _1211369)], (24689 ^ _779571) ^ [_1210687] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1210687)) = _1210687)], (35531 ^ _779571) ^ [_1435275, _1435277, _1435279, _1435281, _1435283] : [hBOOL(hAPP(hAPP(c_member(_1435275), _1435277), hAPP(c_Relation_OImage(_1435279, _1435275, _1435281), hAPP(hAPP(c_Set_Oinsert(_1435279), _1435283), c_Orderings_Obot__class_Obot(tc_fun(_1435279, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1435279, _1435275)), hAPP(hAPP(c_Product__Type_OPair(_1435279, _1435275), _1435283), _1435277)), _1435281)))], (40719 ^ _779571) ^ [_1552834, _1552836, _1552838, _1552840, _1552842, _1552844] : [class_Groups_Ocomm__monoid__add(_1552834), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552836), _1552838)), 40729 ^ _779571 : [(40732 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552840), hAPP(_1552842, 40728 ^ [_1552834, _1552836, _1552838, _1552840, _1552842, _1552844])))], (40730 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552836), 40728 ^ [_1552834, _1552836, _1552838, _1552840, _1552842, _1552844]), _1552838)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552836, _1552834), hAPP(hAPP(c_COMBS(_1552836, tc_fun(_1552840, tc_HOL_Obool), _1552834), hAPP(hAPP(c_COMBB(tc_fun(_1552840, _1552834), tc_fun(tc_fun(_1552840, tc_HOL_Obool), _1552834), _1552836), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552840, _1552834)), _1552844)), _1552842)), _1552838) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1552836, _1552840), _1552834), hAPP(c_Product__Type_Oprod_Oprod__case(_1552836, _1552840, _1552834), _1552844)), hAPP(hAPP(c_Product__Type_OSigma(_1552836, _1552840), _1552838), _1552842)))], (39499 ^ _779571) ^ [_1524210, _1524212, _1524214, _1524216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524210), hAPP(c_Set_Ovimage(_1524210, _1524212, _1524214), _1524216))), hAPP(c_Set_Oimage(_1524210, _1524212, _1524214), c_Orderings_Otop__class_Otop(tc_fun(_1524210, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1524212, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524212), _1524216)))], (29792 ^ _779571) ^ [_1312294, _1312296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312294), _1312296)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1312294), hAPP(c_Nat_OSuc, _1312296)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1312296), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1312294), _1312296)))], (31029 ^ _779571) ^ [_1338246, _1338248, _1338250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338246), _1338250)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338246), hAPP(hAPP(c_Set_Oinsert(_1338246), _1338248), _1338250))))], (23351 ^ _779571) ^ [_1184826, _1184828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184828)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184826, _1184828), c_Divides_OposDivAlg(_1184826, _1184828))))], (11104 ^ _779571) ^ [_963909, _963911, _963913, _963915] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_963909), 11107 ^ _779571 : [(11114 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963909), _963913), _963915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963909), _963911), _963913)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963909), _963911), _963915))))], (11108 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963909), _963911), _963913)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963909), _963911), _963915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963909), _963913), _963915)))]]], (18197 ^ _779571) ^ [_1092415] : [class_Int_Onumber__ring(_1092415), -(hAPP(c_Int_Oring__1__class_Oof__int(_1092415), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1092415), c_Int_OMin))], (37754 ^ _779571) ^ [_1487226] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1487226)), c_Int_OInteg)))], (27173 ^ _779571) ^ [_1258634, _1258636, _1258638] : [class_Groups_Ocomm__monoid__add(_1258634), hAPP(_1258636, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1258634), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258634), _1258636), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1258638)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258634), _1258636), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258638)))], (22105 ^ _779571) ^ [] : [-(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))], (49317 ^ _779571) ^ [_1769739, _1769741, _1769743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769739, tc_HOL_Obool)), _1769741), _1769743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1769739), tc_HOL_Obool)), c_List_Olists(_1769739, _1769741)), c_List_Olists(_1769739, _1769743))))], (47278 ^ _779571) ^ [_1720348] : [class_Orderings_Olinorder(_1720348), -(c_List_Olinorder__class_Osorted__list__of__set(_1720348, c_Orderings_Obot__class_Obot(tc_fun(_1720348, tc_HOL_Obool))) = c_List_Olist_ONil(_1720348))], (47248 ^ _779571) ^ [_1719835] : [-(hBOOL(hAPP(c_List_Odistinct(_1719835), c_List_Olist_ONil(_1719835))))], (28949 ^ _779571) ^ [_1295385, _1295387, _1295389, _1295391, _1295393, _1295395] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295385, tc_fun(_1295387, tc_HOL_Obool)), _1295389), hAPP(hAPP(c_COMBB(_1295391, tc_fun(_1295387, tc_HOL_Obool), _1295385), _1295393), _1295395)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295391, tc_fun(_1295387, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1295385, _1295391, _1295395), _1295389)), _1295393))], (14337 ^ _779571) ^ [_1021357, _1021359] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1021357)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1021359)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021357), _1021359)))], (13400 ^ _779571) ^ [_1004084, _1004086, _1004088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004084)), 13403 ^ _779571 : [(13410 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004086), _1004088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004084), _1004086)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004084), _1004088))))], (13404 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004084), _1004086)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004084), _1004088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004086), _1004088)))]]], (35872 ^ _779571) ^ [_1444058, _1444060, _1444062, _1444064, _1444066] : [c_Equiv__Relations_Oequiv(_1444058, _1444060, _1444062), hBOOL(hAPP(hAPP(c_member(tc_prod(_1444058, _1444058)), hAPP(hAPP(c_Product__Type_OPair(_1444058, _1444058), _1444064), _1444066)), _1444062)), -(hAPP(c_Relation_OImage(_1444058, _1444058, _1444062), hAPP(hAPP(c_Set_Oinsert(_1444058), _1444064), c_Orderings_Obot__class_Obot(tc_fun(_1444058, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1444058, _1444058, _1444062), hAPP(hAPP(c_Set_Oinsert(_1444058), _1444066), c_Orderings_Obot__class_Obot(tc_fun(_1444058, tc_HOL_Obool)))))], (26774 ^ _779571) ^ [_1250685, _1250687] : [hAPP(_1250685, 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), _1250685), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1250687)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1250685), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1250687)))], (41662 ^ _779571) ^ [_1581917, _1581919, _1581921, _1581923] : [class_Groups_Ocomm__monoid__mult(_1581917), c_Fun_Oinj__on(_1581919, _1581917, _1581921, _1581923), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581919, _1581917), _1581921), _1581923) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581917, _1581917), c_Fun_Oid(_1581917)), hAPP(c_Set_Oimage(_1581919, _1581917, _1581921), _1581923)))], (48299 ^ _779571) ^ [_1744861, _1744863] : [-(hAPP(hAPP(c_List_Otake(_1744861), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1744863) = c_List_Olist_ONil(_1744861))], (5252 ^ _779571) ^ [_860735, _860737] : [_860737 = _860735, -(c_Groups_Ozero__class_Ozero(_860737) = c_Groups_Ozero__class_Ozero(_860735))], (23123 ^ _779571) ^ [_1180731, _1180733, _1180735, _1180737] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1180731, _1180733, _1180735), hAPP(hAPP(c_COMBB(tc_fun(_1180733, tc_prod(_1180731, _1180733)), tc_fun(_1180733, _1180735), _1180731), hAPP(c_COMBB(tc_prod(_1180731, _1180733), _1180735, _1180733), _1180737)), c_Product__Type_OPair(_1180731, _1180733))) = _1180737)], (15306 ^ _779571) ^ [_1038511, _1038513, _1038515, _1038517, _1038519] : [class_Groups_Oordered__ab__group__add(_1038511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038511), _1038513), _1038515) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038511), _1038517), _1038519), 15313 ^ _779571 : [(15320 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038511), _1038517), _1038519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038511), _1038513), _1038515)))], (15314 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038511), _1038513), _1038515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038511), _1038517), _1038519)))]]], (3268 ^ _779571) ^ [_829723, _829725, _829727, _829729, _829731, _829733] : [-(c_Partial__Function_Oflat__lub(_829733, _829729, _829725) = c_Partial__Function_Oflat__lub(_829731, _829727, _829723)), _829733 = _829731, _829729 = _829727, _829725 = _829723], (24065 ^ _779571) ^ [_1198546, _1198548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198548)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198546), _1198548) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1198546, _1198548)))], (19751 ^ _779571) ^ [_1118328, _1118330, _1118332] : [class_Rings_Olinordered__semidom(_1118328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118328), hAPP(hAPP(c_Power_Opower__class_Opower(_1118328), _1118330), 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(_1118328), _1118332), 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(_1118328), c_Groups_Ozero__class_Ozero(_1118328)), _1118332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118328), _1118330), _1118332)))], (48992 ^ _779571) ^ [_1762459, _1762461, _1762463] : [-(hAPP(hAPP(c_List_Odrop(_1762459), _1762461), hAPP(c_List_Otl(_1762459), _1762463)) = hAPP(c_List_Otl(_1762459), hAPP(hAPP(c_List_Odrop(_1762459), _1762461), _1762463)))], (35185 ^ _779571) ^ [_1426943, _1426945, _1426947, _1426949, _1426951] : [35188 ^ _779571 : [(35191 ^ _779571) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1426945, _1426947, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1426945)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1426945), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1426945), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 35187 ^ [_1426943, _1426945, _1426947, _1426949, _1426951]))), _1426949), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1426945), hAPP(_1426951, 35186 ^ [_1426943, _1426945, _1426947, _1426949, _1426951])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1426945), tc_HOL_Obool))))], (35189 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1426943, 35186 ^ [_1426943, _1426945, _1426947, _1426949, _1426951]), 35187 ^ [_1426943, _1426945, _1426947, _1426949, _1426951])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1426945, _1426947, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1426945)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1426945), _1426943), _1426949), _1426951)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1426945), tc_HOL_Obool)))))], (45147 ^ _779571) ^ [_1667735] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667735, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1667735, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1667735, tc_HOL_Obool)))], (30760 ^ _779571) ^ [_1332624, _1332626, _1332628] : [-(hBOOL(hAPP(hAPP(c_member(_1332624), _1332626), _1332628))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332624, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1332624), _1332626), _1332628)), hAPP(hAPP(c_Set_Oinsert(_1332624), _1332626), c_Orderings_Obot__class_Obot(tc_fun(_1332624, tc_HOL_Obool)))) = _1332628)], (6790 ^ _779571) ^ [_891403, _891405, _891407, _891409] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_891403, _891405)), _891407), _891409)), 6794 ^ _779571 : [(6797 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891405), 6793 ^ [_891403, _891405, _891407, _891409]), _891409)))], (6795 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891403), _891407), 6793 ^ [_891403, _891405, _891407, _891409])))]]], (38517 ^ _779571) ^ [_1503229, _1503231, _1503233, _1503235, _1503237] : [c_Equiv__Relations_Oequivp(_1503229, _1503231), hBOOL(hAPP(hAPP(_1503231, _1503233), _1503235)), hBOOL(hAPP(hAPP(_1503231, _1503235), _1503237)), -(hBOOL(hAPP(hAPP(_1503231, _1503233), _1503237)))], (51543 ^ _779571) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (41451 ^ _779571) ^ [_1573497, _1573499] : [-(hAPP(c_Set_OPow(_1573497), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1573497, tc_HOL_Obool)), _1573499)) = hAPP(c_Set_OCollect(tc_fun(_1573497, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1573497, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1573497, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1573497, tc_HOL_Obool), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1573497, tc_HOL_Obool)), c_COMBS(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1573497, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1573497, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1573497, tc_HOL_Obool), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_fun(_1573497, tc_HOL_Obool)), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_fun(_1573497, tc_HOL_Obool)), tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1573497, tc_HOL_Obool)), c_COMBB(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1573497, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1573497, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573497, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1573497, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1573497, tc_HOL_Obool)), _1573499)), c_Set_OPow(_1573497))))))], (10454 ^ _779571) ^ [_953618, _953620, _953622] : [class_Orderings_Oorder(_953618), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953618), _953620), _953622)), 10461 ^ _779571 : [(10468 ^ _779571) ^ [] : [_953622 = _953620, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953618), _953622), _953620)))], (10462 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953618), _953622), _953620)), -(_953622 = _953620)]]], (28070 ^ _779571) ^ [_1277041, _1277043, _1277045, _1277047] : [28072 ^ _779571 : [(28075 ^ _779571) ^ [] : [hBOOL(hAPP(_1277047, 28071 ^ [_1277041, _1277043, _1277045, _1277047]))], (28073 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277041), 28071 ^ [_1277041, _1277043, _1277045, _1277047]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277041, tc_HOL_Obool)), _1277043), _1277045))))]], 28076 ^ _779571 : [(28083 ^ _779571) ^ [_1277358] : [hBOOL(hAPP(hAPP(c_member(_1277041), _1277358), _1277045)), -(hBOOL(hAPP(_1277047, _1277358)))], (28077 ^ _779571) ^ [_1277261] : [hBOOL(hAPP(hAPP(c_member(_1277041), _1277261), _1277043)), -(hBOOL(hAPP(_1277047, _1277261)))]]], (41941 ^ _779571) ^ [_1590103, _1590105, _1590107] : [c_Wellfounded_Owf(_1590103, _1590105), -(c_Wellfounded_Owf(_1590103, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1590103, _1590103), tc_HOL_Obool)), _1590105), _1590107)))], (45888 ^ _779571) ^ [_1684557, _1684559, _1684561, _1684563, _1684565, _1684567, _1684569] : [c_Map_Omap__comp(_1684557, _1684559, _1684561, _1684563, _1684565, _1684567) = hAPP(c_Option_Ooption_OSome(_1684559), _1684569), 45892 ^ _779571 : [(45895 ^ _779571) ^ [] : [-(hAPP(_1684563, 45891 ^ [_1684557, _1684559, _1684561, _1684563, _1684565, _1684567, _1684569]) = hAPP(c_Option_Ooption_OSome(_1684559), _1684569))], (45893 ^ _779571) ^ [] : [-(hAPP(_1684565, _1684567) = hAPP(c_Option_Ooption_OSome(_1684557), 45891 ^ [_1684557, _1684559, _1684561, _1684563, _1684565, _1684567, _1684569]))]]], (48353 ^ _779571) ^ [_1745905, _1745907, _1745909, _1745911] : [hBOOL(hAPP(hAPP(c_member(_1745905), _1745907), hAPP(c_List_Oset(_1745905), hAPP(hAPP(c_List_Otake(_1745905), _1745909), _1745911)))), -(hBOOL(hAPP(hAPP(c_member(_1745905), _1745907), hAPP(c_List_Oset(_1745905), _1745911))))], (34835 ^ _779571) ^ [] : [-(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)))))], (4180 ^ _779571) ^ [_844099, _844101, _844103, _844105, _844107, _844109, _844111, _844113, _844115, _844117] : [-(c_Sum__Type_Osum_Osum__case(_844117, _844113, _844109, _844105, _844101) = c_Sum__Type_Osum_Osum__case(_844115, _844111, _844107, _844103, _844099)), _844117 = _844115, _844113 = _844111, _844109 = _844107, _844105 = _844103, _844101 = _844099], (15294 ^ _779571) ^ [_1038321, _1038323] : [class_Groups_Ogroup__add(_1038321), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038321), _1038323), _1038323) = c_Groups_Ozero__class_Ozero(_1038321))], (19579 ^ _779571) ^ [_1115433] : [-(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)))), _1115433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115433), _1115433))], (20533 ^ _779571) ^ [_1132601, _1132603, _1132605, _1132607] : [class_Rings_Odivision__ring(_1132601), -(_1132603 = c_Groups_Ozero__class_Ozero(_1132601)), 20540 ^ _779571 : [(20547 ^ _779571) ^ [] : [_1132605 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132601), _1132607), _1132603), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132601), _1132605), _1132603) = _1132607)], (20541 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132601), _1132605), _1132603) = _1132607, -(_1132605 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132601), _1132607), _1132603))]]], (51039 ^ _779571) ^ [_1807368, _1807370] : [-(_1807368 = c_List_Olist_ONil(_1807370)), hBOOL(hAPP(c_List_Odistinct(_1807370), _1807368)), -(c_List_OtakeWhile(_1807370, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1807370), c_fNot), hAPP(hAPP(c_COMBC(_1807370, _1807370, tc_HOL_Obool), c_fequal), c_List_Olast(_1807370, _1807368))), _1807368) = c_List_Obutlast(_1807370, _1807368))], (14367 ^ _779571) ^ [_1021993, _1021995, _1021997] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021993, _1021995)), _1021997) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021993), _1021997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021995), _1021997)))], (13649 ^ _779571) ^ [_1008338, _1008340] : [class_Divides_Osemiring__div(_1008338), -(c_Divides_Odiv__class_Omod(_1008338, c_Groups_Ozero__class_Ozero(_1008338), _1008340) = c_Groups_Ozero__class_Ozero(_1008338))], (10032 ^ _779571) ^ [_946640, _946642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946640)), 10035 ^ _779571 : [(10042 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946642), _946640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946642)), hAPP(c_Int_Onat, _946640))))], (10036 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946642)), hAPP(c_Int_Onat, _946640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946642), _946640)))]]], (43339 ^ _779571) ^ [_1623779, _1623781, _1623783, _1623785, _1623787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623779, _1623781)), hAPP(hAPP(c_Product__Type_OPair(_1623779, _1623781), _1623783), _1623785)), hAPP(c_Relation_Oconverse(_1623781, _1623779), _1623787))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623781, _1623779)), hAPP(hAPP(c_Product__Type_OPair(_1623781, _1623779), _1623785), _1623783)), _1623787)))], (45125 ^ _779571) ^ [_1666936, _1666938, _1666940, _1666942] : [-(hAPP(c_Set_Oimage(_1666936, _1666938, _1666940), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666936, tc_HOL_Obool), _1666942)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1666936, tc_HOL_Obool), tc_fun(_1666938, tc_HOL_Obool)), _1666942), c_Set_Oimage(_1666936, _1666938, _1666940)))], (43052 ^ _779571) ^ [_1616795, _1616797] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616795, _1616795), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616795, _1616797)), c_Relation_OId(_1616795)) = c_Transitive__Closure_Ortrancl(_1616795, _1616797))], (42559 ^ _779571) ^ [_1604706, _1604708] : [42560 ^ _779571 : [(42561 ^ _779571) ^ [_1604752] : [hBOOL(hAPP(_1604706, _1604752))]], -(hBOOL(hAPP(_1604706, c_Hilbert__Choice_OEps(_1604708, _1604706))))], (49364 ^ _779571) ^ [_1770874] : [-(c_List_Olists(_1770874, c_Orderings_Obot__class_Obot(tc_fun(_1770874, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1770874)), c_List_Olist_ONil(_1770874)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1770874), tc_HOL_Obool))))], (47260 ^ _779571) ^ [_1720027, _1720029, _1720031] : [-(hAPP(hAPP(c_List_Ozip(_1720027, _1720029), _1720031), c_List_Olist_ONil(_1720029)) = c_List_Olist_ONil(tc_prod(_1720027, _1720029)))], (40873 ^ _779571) ^ [_1556995, _1556997, _1556999, _1557001, _1557003, _1557005, _1557007] : [-(hAPP(c_Product__Type_Ofst(_1556995, _1556997), hAPP(c_Product__Type_Omap__pair(_1556999, _1556995, _1557001, _1556997, _1557003, _1557005), _1557007)) = hAPP(_1557003, hAPP(c_Product__Type_Ofst(_1556999, _1557001), _1557007)))], (41045 ^ _779571) ^ [_1561182, _1561184, _1561186, _1561188, _1561190] : [c_Finite__Set_Ofun__left__comm__idem(_1561182, _1561184, _1561186), -(hAPP(hAPP(_1561186, _1561188), hAPP(hAPP(_1561186, _1561188), _1561190)) = hAPP(hAPP(_1561186, _1561188), _1561190))], (28953 ^ _779571) ^ [_1295546, _1295548, _1295550, _1295552, _1295554, _1295556] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295546, tc_fun(_1295548, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1295550, _1295546, _1295552), _1295554)), _1295556) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295550, tc_fun(_1295548, tc_HOL_Obool)), _1295554), hAPP(hAPP(c_COMBB(_1295546, tc_fun(_1295548, tc_HOL_Obool), _1295550), _1295556), _1295552)))], (39224 ^ _779571) ^ [_1517782, _1517784, _1517786, _1517788, _1517790] : [class_Groups_Ocomm__monoid__mult(_1517782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517784), _1517786)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517782, _1517784, c_Groups_Otimes__class_Otimes(_1517782)), hAPP(hAPP(c_COMBS(_1517784, _1517782, _1517782), hAPP(hAPP(c_COMBB(_1517782, tc_fun(_1517782, _1517782), _1517784), c_Groups_Otimes__class_Otimes(_1517782)), _1517788)), _1517790)), c_Groups_Oone__class_Oone(_1517782)), _1517786) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1517782), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517782, _1517784, c_Groups_Otimes__class_Otimes(_1517782)), _1517788), c_Groups_Oone__class_Oone(_1517782)), _1517786)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517782, _1517784, c_Groups_Otimes__class_Otimes(_1517782)), _1517790), c_Groups_Oone__class_Oone(_1517782)), _1517786)))], (35237 ^ _779571) ^ [_1428380] : [-(hAPP(c_Set_OPow(_1428380), c_Orderings_Otop__class_Otop(tc_fun(_1428380, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1428380, tc_HOL_Obool), tc_HOL_Obool)))], (35273 ^ _779571) ^ [_1429286, _1429288, _1429290, _1429292, _1429294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429286, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1429288, _1429286, _1429290), _1429292)), _1429294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1429286, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1429288, tc_HOL_Obool), tc_fun(_1429286, tc_HOL_Obool), c_Set_Oimage(_1429288, _1429286, _1429290)), hAPP(c_Set_OPow(_1429288), _1429292))), hAPP(c_Set_OPow(_1429286), _1429294))))], (34212 ^ _779571) ^ [_1405191, _1405193, _1405195, _1405197] : [class_Rings_Ocomm__semiring__1(_1405191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405193), _1405195)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405193, _1405191), _1405197), _1405195) = c_Groups_Ozero__class_Ozero(_1405191)), 34221 ^ _779571 : [(34222 ^ _779571) ^ [_1405372] : [hBOOL(hAPP(hAPP(c_member(_1405193), _1405372), _1405195)), hAPP(_1405197, _1405372) = c_Groups_Ozero__class_Ozero(_1405191)]]], (50582 ^ _779571) ^ [_1796286, _1796288, _1796290] : [-(hAPP(c_List_Ofilter(_1796286, _1796288), c_List_Oconcat(_1796286, _1796290)) = c_List_Oconcat(_1796286, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796286), tc_List_Olist(_1796286)), c_List_Ofilter(_1796286, _1796288)), _1796290)))], (3746 ^ _779571) ^ [_837288, _837290, _837292, _837294, _837296, _837298, _837300, _837302] : [-(c_New__Random__Sequence_Oneg__map(_837302, _837298, _837294, _837290) = c_New__Random__Sequence_Oneg__map(_837300, _837296, _837292, _837288)), _837302 = _837300, _837298 = _837296, _837294 = _837292, _837290 = _837288], (36128 ^ _779571) ^ [_1449629, _1449631] : [class_Lattices_Obounded__lattice__top(_1449629), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449629), _1449631), c_Orderings_Otop__class_Otop(_1449629)) = _1449631)], (10385 ^ _779571) ^ [_952497, _952499, _952501, _952503] : [class_Orderings_Oord(_952497), 10388 ^ _779571 : [(10395 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952497), hAPP(_952501, 10396 ^ [_952497, _952499, _952501, _952503])), hAPP(_952503, 10396 ^ [_952497, _952499, _952501, _952503]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952499, _952497)), _952501), _952503)))], (10389 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952499, _952497)), _952501), _952503)), 10392 ^ _779571 : [(10393 ^ _779571) ^ [_952654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952497), hAPP(_952501, _952654)), hAPP(_952503, _952654))))]]]]], (34985 ^ _779571) ^ [_1422530, _1422532] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1422530, _1422530)), hAPP(hAPP(c_Product__Type_OPair(_1422530, _1422530), 34986 ^ [_1422530, _1422532]), 34986 ^ [_1422530, _1422532])), _1422532))), -(c_Relation_Oirrefl(_1422530, _1422532))], (16136 ^ _779571) ^ [_1055403, _1055405] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055403, _1055405) = 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), _1055403), _1055405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12564 ^ _779571) ^ [_989343, _989345, _989347, _989349] : [class_Groups_Oordered__comm__monoid__add(_989343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989343), c_Groups_Ozero__class_Ozero(_989343)), _989345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989343), _989347), _989349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989343), _989347), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989343), _989345), _989349))))], (29782 ^ _779571) ^ [_1312077] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1312077)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1312077)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1312077)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (5158 ^ _779571) ^ [_859266, _859268, _859270, _859272, _859274, _859276] : [-(c_Divides_Odiv__class_Omod(_859276, _859272, _859268) = c_Divides_Odiv__class_Omod(_859274, _859270, _859266)), _859276 = _859274, _859272 = _859270, _859268 = _859266], (45664 ^ _779571) ^ [_1679308, _1679310, _1679312] : [-(c_Map_Omap__add(_1679308, _1679310, _1679312, hAPP(c_COMBK(tc_Option_Ooption(_1679310), _1679308), c_Option_Ooption_ONone(_1679310))) = _1679312)], (46410 ^ _779571) ^ [_1696887, _1696889, _1696891, _1696893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696887, _1696887)), hAPP(hAPP(c_Product__Type_OPair(_1696887, _1696887), _1696889), _1696891)), hAPP(c_List_Oset(tc_prod(_1696887, _1696887)), hAPP(hAPP(c_List_Ozip(_1696887, _1696887), _1696893), _1696893)))), 46413 ^ _779571 : [(46416 ^ _779571) ^ [] : [-(_1696889 = _1696891)], (46414 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696887), _1696889), hAPP(c_List_Oset(_1696887), _1696893))))]]], (4718 ^ _779571) ^ [_852526, _852528, _852530, _852532] : [-(c_Product__Type_OSigma(_852532, _852528) = c_Product__Type_OSigma(_852530, _852526)), _852532 = _852530, _852528 = _852526], (42852 ^ _779571) ^ [_1611097, _1611099, _1611101, _1611103] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611097, _1611097)), hAPP(hAPP(c_Product__Type_OPair(_1611097, _1611097), _1611099), _1611101)), _1611103)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611097, _1611097)), hAPP(hAPP(c_Product__Type_OPair(_1611097, _1611097), _1611099), _1611101)), c_Transitive__Closure_Otrancl(_1611097, _1611103))))], (41330 ^ _779571) ^ [_1568886] : [-(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)))), _1568886))))], (26096 ^ _779571) ^ [_1237646, _1237648, _1237650] : [class_Divides_Osemiring__div(_1237646), 26099 ^ _779571 : [(26106 ^ _779571) ^ [] : [c_Divides_Odiv__class_Omod(_1237646, _1237650, _1237648) = c_Groups_Ozero__class_Ozero(_1237646), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237646), _1237648), _1237650)))], (26100 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237646), _1237648), _1237650)), -(c_Divides_Odiv__class_Omod(_1237646, _1237650, _1237648) = c_Groups_Ozero__class_Ozero(_1237646))]]], (29640 ^ _779571) ^ [_1309299, _1309301, _1309303, _1309305, _1309307] : [-(_1309299 = c_Orderings_Obot__class_Obot(tc_fun(_1309301, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309301, tc_fun(_1309303, tc_HOL_Obool)), _1309299), hAPP(hAPP(c_COMBB(tc_fun(_1309303, tc_HOL_Obool), tc_fun(_1309303, tc_HOL_Obool), _1309301), hAPP(c_Set_Oinsert(_1309303), _1309305)), _1309307)) = hAPP(hAPP(c_Set_Oinsert(_1309303), _1309305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309301, tc_fun(_1309303, tc_HOL_Obool)), _1309299), _1309307)))], (5076 ^ _779571) ^ [_858021, _858023, _858025, _858027, _858029, _858031] : [-(c_List_Oremove1(_858031, _858027, _858023) = c_List_Oremove1(_858029, _858025, _858021)), _858031 = _858029, _858027 = _858025, _858023 = _858021], (46418 ^ _779571) ^ [_1697086, _1697088, _1697090, _1697092] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697086, _1697086)), hAPP(hAPP(c_Product__Type_OPair(_1697086, _1697086), _1697088), _1697090)), hAPP(c_List_Oset(tc_prod(_1697086, _1697086)), hAPP(hAPP(c_List_Ozip(_1697086, _1697086), _1697092), _1697092))))), hBOOL(hAPP(hAPP(c_member(_1697086), _1697088), hAPP(c_List_Oset(_1697086), _1697092))), _1697088 = _1697090], (37337 ^ _779571) ^ [_1476865, _1476867, _1476869] : [class_Orderings_Olinorder(_1476865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476865), _1476867)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476865), _1476869)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476865, tc_HOL_Obool)), _1476867), _1476869) = c_Orderings_Obot__class_Obot(tc_fun(_1476865, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1476865), c_Big__Operators_Olinorder__class_OMin(_1476865, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476865, tc_HOL_Obool)), _1476867), _1476869))), c_Big__Operators_Olinorder__class_OMin(_1476865, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476865, tc_HOL_Obool)), _1476867), _1476869))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1476865), c_Big__Operators_Olinorder__class_OMin(_1476865, _1476867)), c_Big__Operators_Olinorder__class_OMin(_1476865, _1476869)))], (43272 ^ _779571) ^ [_1621978] : [-(c_Relation_OId(_1621978) = hAPP(c_Set_OCollect(tc_prod(_1621978, _1621978)), hAPP(hAPP(c_COMBB(tc_fun(_1621978, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1621978, _1621978)), c_HOL_OEx(_1621978)), hAPP(hAPP(c_COMBC(tc_prod(_1621978, _1621978), tc_fun(_1621978, tc_prod(_1621978, _1621978)), tc_fun(_1621978, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1621978, _1621978), tc_HOL_Obool), tc_fun(tc_fun(_1621978, tc_prod(_1621978, _1621978)), tc_fun(_1621978, tc_HOL_Obool)), tc_prod(_1621978, _1621978)), c_COMBB(tc_prod(_1621978, _1621978), tc_HOL_Obool, _1621978)), c_fequal)), hAPP(hAPP(c_COMBS(_1621978, _1621978, tc_prod(_1621978, _1621978)), c_Product__Type_OPair(_1621978, _1621978)), c_COMBI(_1621978))))))], (1702 ^ _779571) ^ [_803614, _803616] : [-(class_Rings_Osemiring(_803614)), _803616 = _803614, class_Rings_Osemiring(_803616)], (27666 ^ _779571) ^ [_1269399, _1269401, _1269403] : [class_Groups_Ocomm__monoid__add(_1269399), class_Groups_Ocomm__monoid__mult(_1269399), c_Nat__Transfer_Onat__set(_1269401), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1269399), _1269403), _1269401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269399), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1269399, tc_Nat_Onat), _1269403), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1269401)))], (29065 ^ _779571) ^ [] : [-(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)))], (1382 ^ _779571) ^ [_799614, _799616] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_799614)), _799616 = _799614, class_Groups_Oordered__ab__semigroup__add__imp__le(_799616)], (8211 ^ _779571) ^ [_915711, _915713, _915715] : [class_Rings_Olinordered__semidom(_915711), 8214 ^ _779571 : [(8221 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915713), _915715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915711), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915711), _915713)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915711), _915715))))], (8215 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915711), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915711), _915713)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915711), _915715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915713), _915715)))]]], (38821 ^ _779571) ^ [_1509260, _1509262, _1509264, _1509266, _1509268, _1509270, _1509272, _1509274] : [class_Groups_Ocomm__monoid__mult(_1509260), c_Fun_Oinj__on(_1509262, _1509264, _1509266, _1509268), _1509270 = hAPP(c_Set_Oimage(_1509262, _1509264, _1509266), _1509268), _1509272 = hAPP(c_Fun_Ocomp(_1509264, _1509260, _1509262, _1509274), _1509266), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1509264, _1509260), _1509274), _1509270) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1509262, _1509260), _1509272), _1509268))], (41233 ^ _779571) ^ [_1565468, _1565470, _1565472, _1565474, _1565476, _1565478] : [-(hAPP(c_Set_Oimage(_1565468, _1565470, hAPP(hAPP(c_COMBS(_1565468, _1565470, _1565470), hAPP(hAPP(c_COMBS(_1565468, _1565470, tc_fun(_1565470, _1565470)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565470, tc_fun(_1565470, _1565470)), _1565468), c_If(_1565470)), _1565472)), _1565474)), _1565476)), _1565478) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565470, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1565468, _1565470, _1565474), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565468, tc_HOL_Obool)), _1565478), hAPP(c_Set_OCollect(_1565468), _1565472)))), hAPP(c_Set_Oimage(_1565468, _1565470, _1565476), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565468, tc_HOL_Obool)), _1565478), hAPP(c_Set_OCollect(_1565468), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565468), c_fNot), _1565472))))))], (42058 ^ _779571) ^ [_1592665, _1592667] : [c_Wellfounded_Owf(_1592665, _1592667), -(c_Wellfounded_Owf(tc_List_Olist(_1592665), c_List_Olenlex(_1592665, _1592667)))], (14176 ^ _779571) ^ [_1018246, _1018248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1018246, _1018248))))], (5040 ^ _779571) ^ [_857481, _857483] : [_857483 = _857481, -(c_Finite__Set_Ofinite(_857483) = c_Finite__Set_Ofinite(_857481))], (41356 ^ _779571) ^ [_1569774] : [-(c_Int_Oint__ge__less__than(_1569774) = 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), _1569774)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (10764 ^ _779571) ^ [_958795, _958797, _958799, _958801] : [class_Orderings_Oorder(_958795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958795), _958797), _958799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958795), _958801), _958797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958795), _958801), _958799)))], (44141 ^ _779571) ^ [_1642991, _1642993, _1642995] : [class_Groups_Oab__semigroup__mult(_1642991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642991), _1642993)), -(hBOOL(hAPP(hAPP(c_member(_1642991), _1642995), _1642993))), -(hAPP(c_Finite__Set_Ofold1(_1642991, c_Groups_Otimes__class_Otimes(_1642991)), hAPP(hAPP(c_Set_Oinsert(_1642991), _1642995), _1642993)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642991, _1642991, c_Groups_Otimes__class_Otimes(_1642991)), _1642995), _1642993))], (11743 ^ _779571) ^ [_974791, _974793, _974795] : [class_Groups_Oordered__comm__monoid__add(_974791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974791), _974793), c_Groups_Ozero__class_Ozero(_974791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974791), _974795), c_Groups_Ozero__class_Ozero(_974791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974791), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974791), _974793), _974795)), c_Groups_Ozero__class_Ozero(_974791))))], (12389 ^ _779571) ^ [_986416] : [12391 ^ _779571 : [(12394 ^ _779571) ^ [] : [hBOOL(hAPP(_986416, 12390 ^ [_986416]))], (12392 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12390 ^ [_986416])))]], 12395 ^ _779571 : [(12396 ^ _779571) ^ [_986543] : [-(hBOOL(hAPP(_986416, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _986543))))]]], (23040 ^ _779571) ^ [_1178996, _1178998] : [_1178996 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1178996, _1178998) = 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)))], (16403 ^ _779571) ^ [_1060052, _1060054] : [-(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), _1060052)), _1060054))))], (7258 ^ _779571) ^ [_899657, _899659, _899661, _899663] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _899657)), _899659, _899661, _899663), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _899657), _899659, hAPP(c_Nat_OSuc, _899661), _899663))], (35643 ^ _779571) ^ [_1438498, _1438500, _1438502, _1438504, _1438506, _1438508] : [c_Finite__Set_Ofolding(_1438498, _1438500, _1438502, _1438504), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438498), _1438506)), hBOOL(hAPP(hAPP(c_member(_1438498), _1438508), _1438506)), -(hAPP(_1438504, _1438506) = hAPP(c_Fun_Ocomp(_1438500, _1438500, _1438500, hAPP(_1438504, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1438498, tc_HOL_Obool)), _1438506), hAPP(hAPP(c_Set_Oinsert(_1438498), _1438508), c_Orderings_Obot__class_Obot(tc_fun(_1438498, tc_HOL_Obool)))))), hAPP(_1438502, _1438508)))], (35034 ^ _779571) ^ [_1423688, _1423690, _1423692, _1423694] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1423688, _1423688)), hAPP(hAPP(c_Product__Type_OPair(_1423688, _1423688), _1423690), _1423692)), c_Relation_OId__on(_1423688, _1423694)))), _1423690 = _1423692, hBOOL(hAPP(hAPP(c_member(_1423688), _1423690), _1423694))], (51303 ^ _779571) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (15392 ^ _779571) ^ [_1040136, _1040138, _1040140] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1040136)), _1040138)), hAPP(c_Nat_OSuc, _1040140)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040136), _1040138)), _1040140))], (20471 ^ _779571) ^ [_1131530, _1131532, _1131534, _1131536] : [class_Fields_Ofield__inverse__zero(_1131530), -(_1131532 = c_Groups_Ozero__class_Ozero(_1131530)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131530), _1131532), _1131534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131530), _1131532), _1131536)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131530), _1131534), _1131536))], (30991 ^ _779571) ^ [_1337512, _1337514, _1337516] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337512), _1337514)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337512, tc_HOL_Obool)), _1337514), _1337516))))], (9836 ^ _779571) ^ [_943372] : [class_Rings_Olinordered__semidom(_943372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943372), c_Groups_Oone__class_Oone(_943372)), c_Groups_Ozero__class_Ozero(_943372)))], (4738 ^ _779571) ^ [_852824, _852826] : [_852826 = _852824, -(c_Orderings_Otop__class_Otop(_852826) = c_Orderings_Otop__class_Otop(_852824))], (43357 ^ _779571) ^ [_1624256, _1624258, _1624260] : [-(hAPP(c_Relation_Oconverse(_1624256, _1624258), hAPP(c_Relation_Oconverse(_1624258, _1624256), _1624260)) = _1624260)], (12550 ^ _779571) ^ [_989088, _989090, _989092] : [class_Groups_Oordered__comm__monoid__add(_989088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989088), c_Groups_Ozero__class_Ozero(_989088)), _989090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989088), c_Groups_Ozero__class_Ozero(_989088)), _989092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989088), c_Groups_Ozero__class_Ozero(_989088)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989088), _989090), _989092))))], (6772 ^ _779571) ^ [_890957, _890959, _890961, _890963, _890965] : [c_Com_Ocom_OLocal(_890957, _890959, _890961) = c_Com_Ocom_OAss(_890963, _890965)], (27620 ^ _779571) ^ [_1268065, _1268067, _1268069] : [class_Orderings_Olinorder(_1268065), 27623 ^ _779571 : [(27630 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268065), _1268069), _1268067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268065, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1268065), _1268067)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1268065), _1268069))))], (27624 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268065, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1268065), _1268067)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1268065), _1268069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268065), _1268069), _1268067)))]]], (18839 ^ _779571) ^ [_1102685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102685), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1102685)), c_Int_OMin)))], (13629 ^ _779571) ^ [_1007972, _1007974, _1007976, _1007978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007974), _1007976)), -(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), _1007976), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007978, _1007972))), _1007974)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007976), _1007972))))], (3028 ^ _779571) ^ [_825903, _825905, _825907, _825909, _825911, _825913, _825915, _825917] : [-(c_Lazy__Sequence_Obind(_825917, _825913, _825909, _825905) = c_Lazy__Sequence_Obind(_825915, _825911, _825907, _825903)), _825917 = _825915, _825913 = _825911, _825909 = _825907, _825905 = _825903], (48978 ^ _779571) ^ [_1762269, _1762271] : [-(_1762269 = c_List_Olist_ONil(_1762271)), -(hAPP(c_List_Orotate1(_1762271), _1762269) = hAPP(hAPP(c_List_Oappend(_1762271), hAPP(c_List_Otl(_1762271), _1762269)), hAPP(hAPP(c_List_Olist_OCons(_1762271), hAPP(c_List_Ohd(_1762271), _1762269)), c_List_Olist_ONil(_1762271))))], (8854 ^ _779571) ^ [_926052, _926054, _926056, _926058, _926060] : [class_Rings_Ocomm__semiring__1(_926052), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), _926054), _926056)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), _926058), _926060)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), _926058), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926052), _926054), _926056)), _926060)))], (43014 ^ _779571) ^ [_1615918, _1615920, _1615922, _1615924, _1615926] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615918, _1615918)), hAPP(hAPP(c_Product__Type_OPair(_1615918, _1615918), _1615920), _1615922)), _1615924)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615918, _1615918)), hAPP(hAPP(c_Product__Type_OPair(_1615918, _1615918), _1615922), _1615926)), c_Transitive__Closure_Ortrancl(_1615918, _1615924))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615918, _1615918)), hAPP(hAPP(c_Product__Type_OPair(_1615918, _1615918), _1615920), _1615926)), c_Transitive__Closure_Ortrancl(_1615918, _1615924))))], (11841 ^ _779571) ^ [_976644, _976646, _976648, _976650] : [class_Rings_Oordered__ring(_976644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976644), _976646), _976648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976644), _976650), c_Groups_Ozero__class_Ozero(_976644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976644), _976650), _976648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976644), _976650), _976646))))], (19765 ^ _779571) ^ [_1118591, _1118593, _1118595] : [class_Rings_Olinordered__idom(_1118591), 19768 ^ _779571 : [(19777 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118591), hAPP(hAPP(c_Power_Opower__class_Opower(_1118591), _1118593), 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(_1118591), _1118595), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1118591)))), _1118593 = c_Groups_Ozero__class_Ozero(_1118591), _1118595 = c_Groups_Ozero__class_Ozero(_1118591)], (19769 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118591), hAPP(hAPP(c_Power_Opower__class_Opower(_1118591), _1118593), 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(_1118591), _1118595), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1118591))), 19772 ^ _779571 : [(19775 ^ _779571) ^ [] : [-(_1118595 = c_Groups_Ozero__class_Ozero(_1118591))], (19773 ^ _779571) ^ [] : [-(_1118593 = c_Groups_Ozero__class_Ozero(_1118591))]]]]], (19281 ^ _779571) ^ [_1110240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110240), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1110240)), c_Int_OPls)))], (5436 ^ _779571) ^ [_863609, _863611, _863613, _863615] : [-(c_List_Olast(_863615, _863611) = c_List_Olast(_863613, _863609)), _863615 = _863613, _863611 = _863609], (45724 ^ _779571) ^ [_1680416, _1680418, _1680420, _1680422, _1680424, _1680426] : [-(hAPP(c_Map_Omap__add(_1680416, _1680418, _1680420, _1680422), _1680424) = hAPP(c_Option_Ooption_OSome(_1680418), _1680426)), 45725 ^ _779571 : [(45728 ^ _779571) ^ [] : [hAPP(_1680422, _1680424) = c_Option_Ooption_ONone(_1680418), hAPP(_1680420, _1680424) = hAPP(c_Option_Ooption_OSome(_1680418), _1680426)], (45726 ^ _779571) ^ [] : [hAPP(_1680422, _1680424) = hAPP(c_Option_Ooption_OSome(_1680418), _1680426)]]], (22172 ^ _779571) ^ [_1162240, _1162242] : [c_Code__Numeral_OSuc__code__numeral(_1162240) = c_Code__Numeral_OSuc__code__numeral(_1162242), -(_1162240 = _1162242)], (23127 ^ _779571) ^ [_1180905, _1180907] : [-(c_Divides_Opdivmod(_1180905, _1180907) = 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), _1180905)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1180907))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1180905), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1180907))))], (41620 ^ _779571) ^ [_1581091, _1581093] : [-(c_Product__Type_Oapfst(_1581091, _1581091, _1581093, c_Fun_Oid(_1581091)) = c_Fun_Oid(tc_prod(_1581091, _1581093)))], (26196 ^ _779571) ^ [_1239588, _1239590, _1239592] : [class_Divides_Oring__div(_1239588), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239588), _1239590), _1239592)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239588), _1239592), hAPP(c_Groups_Ouminus__class_Ouminus(_1239588), _1239590)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239588), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239588), _1239592), _1239590)))], (43024 ^ _779571) ^ [_1616185, _1616187] : [-(c_Transitive__Closure_Ortrancl(_1616185, c_Transitive__Closure_Ortrancl(_1616185, _1616187)) = c_Transitive__Closure_Ortrancl(_1616185, _1616187))], (33057 ^ _779571) ^ [_1382384, _1382386, _1382388] : [class_Lattices_Olattice(_1382384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382384), _1382386)), -(_1382386 = c_Orderings_Obot__class_Obot(tc_fun(_1382384, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382384), _1382388)), -(_1382388 = c_Orderings_Obot__class_Obot(tc_fun(_1382384, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1382384, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1382384, tc_HOL_Obool)), _1382386), _1382388)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1382384), c_Big__Operators_Olattice__class_OSup__fin(_1382384, _1382386)), c_Big__Operators_Olattice__class_OSup__fin(_1382384, _1382388)))], (35136 ^ _779571) ^ [_1425840, _1425842, _1425844, _1425846, _1425848] : [class_Groups_Ocomm__monoid__add(_1425840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425842), _1425844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1425842, tc_HOL_Obool)), _1425846), _1425844)), 35150 ^ _779571 : [(35153 ^ _779571) ^ [] : [hAPP(_1425848, 35149 ^ [_1425840, _1425842, _1425844, _1425846, _1425848]) = c_Groups_Ozero__class_Ozero(_1425840)], (35151 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425842), 35149 ^ [_1425840, _1425842, _1425844, _1425846, _1425848]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425842, tc_HOL_Obool)), _1425844), _1425846))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425842, _1425840), _1425848), _1425846) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425842, _1425840), _1425848), _1425844))], (41103 ^ _779571) ^ [_1562194, _1562196, _1562198] : [hBOOL(hAPP(hAPP(c_member(_1562194), _1562196), hAPP(c_Set_OCollect(_1562194), _1562198))), -(hBOOL(hAPP(_1562198, _1562196)))], (32163 ^ _779571) ^ [_1364829, _1364831, _1364833, _1364835] : [hBOOL(hAPP(hAPP(_1364833, _1364831), _1364835)), -(hBOOL(hAPP(hAPP(c_member(_1364829), _1364831), c_SetInterval_Oord_OlessThan(_1364829, _1364833, _1364835))))], (8108 ^ _779571) ^ [_913954, _913956, _913958] : [class_Nat_Osemiring__char__0(_913954), 8111 ^ _779571 : [(8118 ^ _779571) ^ [] : [_913956 = _913958, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913954), _913956) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913954), _913958))], (8112 ^ _779571) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913954), _913956) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913954), _913958), -(_913956 = _913958)]]], (51547 ^ _779571) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (44810 ^ _779571) ^ [_1659865, _1659867, _1659869, _1659871, _1659873] : [-(_1659865 = c_Orderings_Obot__class_Obot(tc_fun(_1659867, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659867, tc_fun(_1659869, tc_HOL_Obool)), _1659865), hAPP(hAPP(c_COMBB(tc_fun(_1659869, tc_HOL_Obool), tc_fun(_1659869, tc_HOL_Obool), _1659867), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659869, tc_HOL_Obool)), _1659871)), _1659873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659869, tc_HOL_Obool)), _1659871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659867, tc_fun(_1659869, tc_HOL_Obool)), _1659865), _1659873)))], (11278 ^ _779571) ^ [_966845, _966847, _966849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966847), _966849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966845), _966847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966845), _966849)))], (51629 ^ _779571) ^ [_1813925, _1813927] : [hBOOL(_1813925), -(hBOOL(hAPP(hAPP(c_fdisj, _1813925), _1813927)))], (50792 ^ _779571) ^ [_1800958, _1800960, _1800962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800958), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800960)), _1800962))), -(hAPP(hAPP(c_List_Onth(_1800960), hAPP(c_List_Orev(_1800960), _1800962)), _1800958) = hAPP(hAPP(c_List_Onth(_1800960), _1800962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800960)), _1800962)), hAPP(c_Nat_OSuc, _1800958))))], (50985 ^ _779571) ^ [_1806391, _1806393] : [-(c_List_OtakeWhile(_1806391, _1806393, c_List_Olist_ONil(_1806391)) = c_List_Olist_ONil(_1806391))], (33515 ^ _779571) ^ [_1390925, _1390927, _1390929, _1390931, _1390933, _1390935, _1390937, _1390939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1390925, _1390927), tc_prod(_1390925, _1390927))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1390925, _1390927), tc_prod(_1390925, _1390927)), hAPP(hAPP(c_Product__Type_OPair(_1390925, _1390927), _1390929), _1390931)), hAPP(hAPP(c_Product__Type_OPair(_1390925, _1390927), _1390933), _1390935))), c_Wellfounded_Olex__prod(_1390925, _1390927, _1390937, _1390939))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1390925, _1390925)), hAPP(hAPP(c_Product__Type_OPair(_1390925, _1390925), _1390929), _1390933)), _1390937))), 33522 ^ _779571 : [(33525 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1390927, _1390927)), hAPP(hAPP(c_Product__Type_OPair(_1390927, _1390927), _1390931), _1390935)), _1390939)))], (33523 ^ _779571) ^ [] : [-(_1390929 = _1390933)]]], (4226 ^ _779571) ^ [_844858, _844860, _844862, _844864] : [-(c_List_Olenlex(_844864, _844860) = c_List_Olenlex(_844862, _844858)), _844864 = _844862, _844860 = _844858], (19331 ^ _779571) ^ [_1111133, _1111135] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1111133)), c_Int_OBit0(_1111135)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1111133), _1111135)))], (12089 ^ _779571) ^ [_981190] : [class_Rings_Olinordered__semidom(_981190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981190), c_Groups_Oone__class_Oone(_981190)), c_Groups_Ozero__class_Ozero(_981190)))], (18943 ^ _779571) ^ [] : [-(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)))))], (51493 ^ _779571) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (23000 ^ _779571) ^ [_1178283, _1178285, _1178287] : [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), _1178283), _1178285))), -(hBOOL(hAPP(hAPP(_1178287, _1178283), _1178285))), 23007 ^ _779571 : [(23010 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1178287, 23005 ^ [_1178283, _1178285, _1178287]), 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)))), 23006 ^ [_1178283, _1178285, _1178287])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23005 ^ [_1178283, _1178285, _1178287]), 23006 ^ [_1178283, _1178285, _1178287]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23006 ^ [_1178283, _1178285, _1178287]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23020 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1178287, 23005 ^ [_1178283, _1178285, _1178287]), 23006 ^ [_1178283, _1178285, _1178287]))], (23008 ^ _779571) ^ [] : [-(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), 23005 ^ [_1178283, _1178285, _1178287]), 23006 ^ [_1178283, _1178285, _1178287]))))]]], (39022 ^ _779571) ^ [_1513831] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1513831))], (42260 ^ _779571) ^ [_1597500, _1597502, _1597504] : [hAPP(c_Relation_ODomain(_1597500, _1597502), _1597504) = c_Orderings_Obot__class_Obot(tc_fun(_1597500, tc_HOL_Obool)), -(_1597504 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1597500, _1597502), tc_HOL_Obool)))], (23761 ^ _779571) ^ [_1192247, _1192249, _1192251, _1192253] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1192247), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192247), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192247), _1192249), _1192251)), _1192253) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192247), _1192249), _1192253)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192247), _1192251), _1192253)))], (18621 ^ _779571) ^ [_1098995, _1098997] : [class_Int_Onumber__ring(_1098995), 18624 ^ _779571 : [(18631 ^ _779571) ^ [] : [c_Int_Oiszero(_1098995, hAPP(c_Int_Onumber__class_Onumber__of(_1098995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098997), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098995), _1098997) = c_Groups_Oone__class_Oone(_1098995))], (18625 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1098995), _1098997) = c_Groups_Oone__class_Oone(_1098995), -(c_Int_Oiszero(_1098995, hAPP(c_Int_Onumber__class_Onumber__of(_1098995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098997), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (40088 ^ _779571) ^ [_1538289, _1538291, _1538293, _1538295, _1538297, _1538299] : [hBOOL(hAPP(hAPP(c_member(_1538289), _1538291), _1538293)), hBOOL(hAPP(hAPP(c_member(_1538295), _1538297), hAPP(_1538299, _1538291))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538289, _1538295)), hAPP(hAPP(c_Product__Type_OPair(_1538289, _1538295), _1538291), _1538297)), hAPP(hAPP(c_Product__Type_OSigma(_1538289, _1538295), _1538293), _1538299))))], (41672 ^ _779571) ^ [_1582125, _1582127] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1582125), _1582127)), -(_1582127 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1582125, 41676 ^ [_1582125, _1582127]), 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)), 41675 ^ [_1582125, _1582127]))))], (48371 ^ _779571) ^ [_1746453, _1746455, _1746457, _1746459, _1746461, _1746463, _1746465] : [-(hBOOL(hAPP(hAPP(c_member(_1746453), _1746455), hAPP(c_List_Oset(_1746453), hAPP(hAPP(c_List_Otake(_1746453), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746457)), _1746459)), _1746461))))), -(c_Map_Omap__upds(_1746453, _1746457, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1746453, tc_Option_Ooption(_1746457)), _1746463), _1746455), hAPP(c_Option_Ooption_OSome(_1746457), _1746465)), _1746461, _1746459) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1746453, tc_Option_Ooption(_1746457)), c_Map_Omap__upds(_1746453, _1746457, _1746463, _1746461, _1746459)), _1746455), hAPP(c_Option_Ooption_OSome(_1746457), _1746465)))], (41043 ^ _779571) ^ [_1561152, _1561154] : [-(hAPP(c_Set_OCollect(_1561152), _1561154) = _1561154)], (23397 ^ _779571) ^ [_1185790, _1185792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185792), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1185790, _1185792) = 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), _1185790), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185792)))))], (35418 ^ _779571) ^ [_1432215, _1432217, _1432219, _1432221, _1432223, _1432225] : [class_Groups_Ocomm__monoid__add(_1432215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432217), _1432219)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432221), _1432223)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(_1432217, _1432221), _1432215), _1432225), c_Sum__Type_OPlus(_1432217, _1432221, _1432219, _1432223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432215), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1432217, _1432215), hAPP(c_Fun_Ocomp(tc_sum(_1432217, _1432221), _1432215, _1432217, _1432225), c_Sum__Type_OInl(_1432217, _1432221))), _1432219)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1432221, _1432215), hAPP(c_Fun_Ocomp(tc_sum(_1432217, _1432221), _1432215, _1432221, _1432225), c_Sum__Type_OInr(_1432221, _1432217))), _1432223)))], (35717 ^ _779571) ^ [_1440212, _1440214, _1440216, _1440218, _1440220, _1440222, _1440224, _1440226] : [c_Finite__Set_Ofolding(_1440212, _1440214, _1440216, _1440218), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440212), _1440220)), -(hAPP(c_Fun_Ocomp(_1440214, _1440214, _1440222, hAPP(_1440216, _1440224)), hAPP(c_Fun_Ocomp(_1440214, _1440214, _1440222, hAPP(_1440218, _1440220)), _1440226)) = hAPP(c_Fun_Ocomp(_1440214, _1440214, _1440222, hAPP(_1440218, _1440220)), hAPP(c_Fun_Ocomp(_1440214, _1440214, _1440222, hAPP(_1440216, _1440224)), _1440226)))], (34100 ^ _779571) ^ [_1402957, _1402959, _1402961, _1402963] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1402957, _1402959), _1402961), _1402963), hAPP(_1402961, _1402963)) = _1402961)], (23575 ^ _779571) ^ [_1188949, _1188951, _1188953, _1188955] : [class_Orderings_Olinorder(_1188949), 23578 ^ _779571 : [(23587 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188949), _1188953), _1188955)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), _1188953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), _1188955))], (23579 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188949), _1188953), _1188955))), 23582 ^ _779571 : [(23585 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), _1188955)))], (23583 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188949), _1188951), _1188953)))]]]]], (42020 ^ _779571) ^ [_1591752, _1591754] : [-(c_FunDef_Oreduction__pair(_1591752, _1591754)), c_Wellfounded_Owf(_1591752, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool), tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool)), _1591754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1591752, _1591752, _1591752), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool), tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool)), _1591754)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool), tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool)), _1591754))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool), tc_fun(tc_prod(_1591752, _1591752), tc_HOL_Obool)), _1591754)))], (47420 ^ _779571) ^ [_1723517, _1723519, _1723521, _1723523] : [-(hAPP(c_List_Olist_Olist__case(_1723517, _1723519, _1723521, _1723523), c_List_Olist_ONil(_1723519)) = _1723521)], (41426 ^ _779571) ^ [_1572755, _1572757, _1572759, _1572761] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572755), hAPP(c_Set_OCollect(_1572755), _1572757))), 41429 ^ _779571 : [(41430 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572759), hAPP(c_Set_OCollect(_1572759), hAPP(hAPP(c_COMBB(tc_fun(_1572755, tc_HOL_Obool), tc_HOL_Obool, _1572759), c_HOL_OEx(_1572755)), hAPP(hAPP(c_COMBB(tc_fun(_1572755, tc_HOL_Obool), tc_fun(_1572755, tc_HOL_Obool), _1572759), hAPP(c_COMBS(_1572755, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572755), c_fconj), _1572757))), _1572761))))), 41433 ^ _779571 : [(41434 ^ _779571) ^ [_1573038] : [hBOOL(hAPP(_1572757, _1573038)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572759), hAPP(c_Set_OCollect(_1572759), hAPP(hAPP(c_COMBC(_1572759, _1572755, tc_HOL_Obool), _1572761), _1573038)))))]]], (41440 ^ _779571) ^ [] : [41442 ^ _779571 : [(41445 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572759), hAPP(c_Set_OCollect(_1572759), hAPP(hAPP(c_COMBC(_1572759, _1572755, tc_HOL_Obool), _1572761), 41441 ^ [_1572755, _1572757, _1572759, _1572761]))))], (41443 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1572757, 41441 ^ [_1572755, _1572757, _1572759, _1572761])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572759), hAPP(c_Set_OCollect(_1572759), hAPP(hAPP(c_COMBB(tc_fun(_1572755, tc_HOL_Obool), tc_HOL_Obool, _1572759), c_HOL_OEx(_1572755)), hAPP(hAPP(c_COMBB(tc_fun(_1572755, tc_HOL_Obool), tc_fun(_1572755, tc_HOL_Obool), _1572759), hAPP(c_COMBS(_1572755, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572755), c_fconj), _1572757))), _1572761))))))]]], (39840 ^ _779571) ^ [_1531702, _1531704, _1531706] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1531702, hAPP(hAPP(c_COMBC(_1531702, tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_fun(_1531702, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531702, tc_fun(tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_fun(_1531702, tc_HOL_Obool)), _1531702), c_COMBC(_1531702, tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531702, tc_prod(_1531702, _1531702)), tc_fun(_1531702, tc_fun(tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_HOL_Obool)), _1531702), hAPP(c_COMBB(tc_prod(_1531702, _1531702), tc_fun(tc_fun(tc_prod(_1531702, _1531702), tc_HOL_Obool), tc_HOL_Obool), _1531702), c_member(tc_prod(_1531702, _1531702)))), c_Product__Type_OPair(_1531702, _1531702)))), _1531704)), _1531706)), -(hBOOL(hAPP(hAPP(c_member(_1531702), _1531706), c_Wellfounded_Oacc(_1531702, _1531704))))], (41953 ^ _779571) ^ [_1590327, _1590329] : [hBOOL(hAPP(hAPP(c_member(_1590327), 41954 ^ [_1590327, _1590329]), c_Wellfounded_Oacc(_1590327, _1590329))), -(c_Wellfounded_Owf(_1590327, _1590329))], (29190 ^ _779571) ^ [_1301084, _1301086, _1301088] : [c_Orderings_Obot__class_Obot(tc_fun(_1301084, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1301084), _1301086), _1301088)], (23859 ^ _779571) ^ [_1194295, _1194297, _1194299, _1194301, _1194303] : [-(hAPP(c_Product__Type_Ofst(_1194295, _1194297), hAPP(c_Product__Type_Oapsnd(_1194299, _1194297, _1194295, _1194301), _1194303)) = hAPP(c_Product__Type_Ofst(_1194295, _1194299), _1194303))], (42894 ^ _779571) ^ [_1612084, _1612086, _1612088, _1612090, _1612092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612084, _1612084)), hAPP(hAPP(c_Product__Type_OPair(_1612084, _1612084), _1612086), _1612088)), c_Transitive__Closure_Otrancl(_1612084, _1612090))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1612084, _1612084)), hAPP(hAPP(c_Product__Type_OPair(_1612084, _1612084), _1612088), _1612092)), _1612090)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612084, _1612084)), hAPP(hAPP(c_Product__Type_OPair(_1612084, _1612084), _1612086), _1612092)), c_Transitive__Closure_Otrancl(_1612084, _1612090))))], (36860 ^ _779571) ^ [_1465827, _1465829, _1465831, _1465833, _1465835] : [class_Orderings_Olinorder(_1465827), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465827, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1465827, _1465829, _1465831)), c_SetInterval_Oord__class_OatLeastAtMost(_1465827, _1465833, _1465835)) = c_SetInterval_Oord__class_OatLeastAtMost(_1465827, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465827), _1465829), _1465833), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1465827), _1465831), _1465835)))], (8026 ^ _779571) ^ [_912651, _912653] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_912651)), hAPP(c_Option_Ooption_OSome(_912651), _912653)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47011 ^ _779571) ^ [_1714381, _1714383, _1714385] : [hBOOL(hAPP(c_List_Odistinct(_1714381), _1714383)), -(hBOOL(hAPP(c_List_Odistinct(_1714381), c_List_Osublist(_1714381, _1714383, _1714385))))], (45404 ^ _779571) ^ [_1673469, _1673471, _1673473, _1673475, _1673477, _1673479] : [-(_1673469 = c_Orderings_Obot__class_Obot(tc_fun(_1673471, tc_HOL_Obool))), 45410 ^ _779571 : [(45413 ^ _779571) ^ [] : [c_Fun_Oinj__on(_1673473, _1673475, _1673477, hAPP(_1673479, 45409 ^ [_1673469, _1673471, _1673473, _1673475, _1673477, _1673479]))], (45411 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673471), 45409 ^ [_1673469, _1673471, _1673473, _1673475, _1673477, _1673479]), _1673469)))]], -(c_Fun_Oinj__on(_1673473, _1673475, _1673477, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1673471, tc_fun(_1673473, tc_HOL_Obool)), _1673469), _1673479)))], (23207 ^ _779571) ^ [_1182581, _1182583, _1182585, _1182587, _1182589, _1182591, _1182593] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1182581, _1182583, tc_fun(_1182585, tc_HOL_Obool)), _1182587), hAPP(hAPP(c_Product__Type_OPair(_1182581, _1182583), _1182589), _1182591)), _1182593)), -(hBOOL(hAPP(hAPP(hAPP(_1182587, _1182589), _1182591), _1182593)))], (34857 ^ _779571) ^ [_1418694, _1418696, _1418698, _1418700] : [c_Wellfounded_Omax__extp(_1418694, hAPP(hAPP(c_COMBC(_1418694, tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_fun(_1418694, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418694, tc_fun(tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_fun(_1418694, tc_HOL_Obool)), _1418694), c_COMBC(_1418694, tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418694, tc_prod(_1418694, _1418694)), tc_fun(_1418694, tc_fun(tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_HOL_Obool)), _1418694), hAPP(c_COMBB(tc_prod(_1418694, _1418694), tc_fun(tc_fun(tc_prod(_1418694, _1418694), tc_HOL_Obool), tc_HOL_Obool), _1418694), c_member(tc_prod(_1418694, _1418694)))), c_Product__Type_OPair(_1418694, _1418694)))), _1418696), _1418698, _1418700), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418694, tc_HOL_Obool), tc_fun(_1418694, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418694, tc_HOL_Obool), tc_fun(_1418694, tc_HOL_Obool)), _1418698), _1418700)), c_Wellfounded_Omax__ext(_1418694, _1418696))))], (41968 ^ _779571) ^ [_1590599, _1590601] : [c_Wellfounded_Owf(_1590599, _1590601), 41972 ^ _779571 : [(41973 ^ _779571) ^ [_1590735] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590599, _1590599)), hAPP(hAPP(c_Product__Type_OPair(_1590599, _1590599), hAPP(_1590735, hAPP(c_Nat_OSuc, 41971 ^ [_1590599, _1590601, _1590735]))), hAPP(_1590735, 41971 ^ [_1590599, _1590601, _1590735]))), _1590601))]]], (6259 ^ _779571) ^ [_881053, _881055, _881057, _881059, _881061, _881063] : [-(c_Com_Ocom_OLocal(_881053, _881055, _881057) = c_Com_Ocom_OLocal(_881059, _881061, _881063)), _881053 = _881059, _881055 = _881061, _881057 = _881063], (12143 ^ _779571) ^ [_982102, _982104] : [class_Groups_Olinordered__ab__group__add(_982102), 12146 ^ _779571 : [(12153 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982102), c_Groups_Ozero__class_Ozero(_982102)), _982104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982102), hAPP(c_Groups_Ouminus__class_Ouminus(_982102), _982104)), _982104)))], (12147 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982102), hAPP(c_Groups_Ouminus__class_Ouminus(_982102), _982104)), _982104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982102), c_Groups_Ozero__class_Ozero(_982102)), _982104)))]]], (26318 ^ _779571) ^ [_1241783, _1241785, _1241787] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1241785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241783), _1241787)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241783), _1241785)))], (48832 ^ _779571) ^ [_1758911, _1758913, _1758915, _1758917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758911), _1758913)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758915)), _1758917))), -(hAPP(hAPP(c_List_Onth(_1758915), hAPP(hAPP(c_List_Odrop(_1758915), _1758911), _1758917)), _1758913) = hAPP(hAPP(c_List_Onth(_1758915), _1758917), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758911), _1758913)))], (51347 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (10305 ^ _779571) ^ [_951280, _951282] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951280), _951282), 10308 ^ _779571 : [(10311 ^ _779571) ^ [] : [-(_951282 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10309 ^ _779571) ^ [] : [-(_951280 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (40030 ^ _779571) ^ [_1536866, _1536868, _1536870, _1536872, _1536874] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1536866, _1536868, hAPP(hAPP(c_Set_Oinsert(_1536866), _1536870), _1536872)), _1536874)), 40035 ^ _779571 : [(40040 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1536866), 40033 ^ [_1536866, _1536868, _1536870, _1536872, _1536874]), 40034 ^ [_1536866, _1536868, _1536870, _1536872, _1536874]))], (40038 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1536866, _1536866, _1536868, 40033 ^ [_1536866, _1536868, _1536870, _1536872, _1536874], 40034 ^ [_1536866, _1536868, _1536870, _1536872, _1536874]), _1536874)))], (40036 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1536866), _1536870), _1536872) = hAPP(hAPP(c_Set_Oinsert(_1536866), 40033 ^ [_1536866, _1536868, _1536870, _1536872, _1536874]), 40034 ^ [_1536866, _1536868, _1536870, _1536872, _1536874]))]]], (48996 ^ _779571) ^ [_1762559, _1762561, _1762563] : [-(_1762559 = c_List_Olist_ONil(_1762561)), -(hAPP(c_List_Otl(_1762561), hAPP(hAPP(c_List_Oappend(_1762561), _1762559), _1762563)) = hAPP(hAPP(c_List_Oappend(_1762561), hAPP(c_List_Otl(_1762561), _1762559)), _1762563))], (11433 ^ _779571) ^ [_969341, _969343, _969345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969341), _969343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969341), _969345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969343), _969345)))], (49128 ^ _779571) ^ [_1765344, _1765346, _1765348, _1765350, _1765352, _1765354] : [-(hAPP(c_List_Ofoldl(_1765344, _1765346, _1765348, _1765350), hAPP(hAPP(c_List_Olist_OCons(_1765346), _1765352), _1765354)) = hAPP(c_List_Ofoldl(_1765344, _1765346, _1765348, hAPP(hAPP(_1765348, _1765350), _1765352)), _1765354))], (45229 ^ _779571) ^ [_1669364, _1669366, _1669368, _1669370, _1669372] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669364, tc_fun(_1669366, tc_HOL_Obool)), _1669368), hAPP(hAPP(c_COMBS(_1669364, tc_fun(_1669366, tc_HOL_Obool), tc_fun(_1669366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1669366, tc_HOL_Obool), tc_fun(tc_fun(_1669366, tc_HOL_Obool), tc_fun(_1669366, tc_HOL_Obool)), _1669364), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669366, tc_HOL_Obool))), _1669370)), _1669372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669366, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669366, tc_HOL_Obool), hAPP(c_Set_Oimage(_1669364, tc_fun(_1669366, tc_HOL_Obool), _1669370), _1669368))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669366, tc_HOL_Obool), hAPP(c_Set_Oimage(_1669364, tc_fun(_1669366, tc_HOL_Obool), _1669372), _1669368))))], (4446 ^ _779571) ^ [_848372, _848374] : [_848374 = _848372, -(c_HOL_OEx(_848374) = c_HOL_OEx(_848372))], (12279 ^ _779571) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50724 ^ _779571) ^ [_1799435, _1799437] : [class_Groups_Ocomm__monoid__add(_1799435), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1799435), hAPP(c_List_Orev(_1799435), _1799437)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1799435), _1799437))], (3692 ^ _779571) ^ [_836447, _836449, _836451, _836453] : [-(c_Wellfounded_Omin__ext(_836453, _836449) = c_Wellfounded_Omin__ext(_836451, _836447)), _836453 = _836451, _836449 = _836447], (23129 ^ _779571) ^ [_1180970, _1180972] : [_1180970 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1180972, _1180970) = 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), _1180972)))], (44944 ^ _779571) ^ [_1662930, _1662932] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1662930, tc_HOL_Obool), _1662932) = hAPP(c_Set_OCollect(_1662930), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1662930, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1662930), c_HOL_OAll(tc_fun(_1662930, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1662930, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1662930, tc_HOL_Obool), tc_HOL_Obool), _1662930), hAPP(c_COMBS(tc_fun(_1662930, 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(_1662930, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1662930, tc_HOL_Obool), tc_fun(tc_fun(_1662930, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1662930, tc_HOL_Obool))), _1662932)))), c_member(_1662930)))))], (26929 ^ _779571) ^ [_1253800, _1253802] : [26931 ^ _779571 : [(26934 ^ _779571) ^ [] : [hBOOL(hAPP(_1253802, 26930 ^ [_1253800, _1253802]))], (26932 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26930 ^ [_1253800, _1253802]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1253800))))]], 26935 ^ _779571 : [(26936 ^ _779571) ^ [_1253955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253955), _1253800)), -(hBOOL(hAPP(_1253802, _1253955)))]]], (46114 ^ _779571) ^ [_1689986, _1689988, _1689990, _1689992, _1689994, _1689996] : [-(hBOOL(hAPP(hAPP(c_member(_1689986), _1689988), hAPP(c_List_Oset(_1689986), _1689990)))), -(hAPP(hAPP(c_List_Omap(_1689986, _1689992), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1689986, _1689992), _1689994), _1689988), _1689996)), _1689990) = hAPP(hAPP(c_List_Omap(_1689986, _1689992), _1689994), _1689990))], (4328 ^ _779571) ^ [_846495, _846497, _846499, _846501] : [-(c_Hilbert__Choice_OEps(_846501, _846497) = c_Hilbert__Choice_OEps(_846499, _846495)), _846501 = _846499, _846497 = _846495], (29620 ^ _779571) ^ [_1308803, _1308805, _1308807, _1308809, _1308811] : [_1308803 = c_Orderings_Obot__class_Obot(tc_fun(_1308805, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1308807), _1308809), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308805, tc_fun(_1308807, tc_HOL_Obool)), _1308803), _1308811)) = hAPP(hAPP(c_Set_Oinsert(_1308807), _1308809), c_Orderings_Obot__class_Obot(tc_fun(_1308807, tc_HOL_Obool))))], (48948 ^ _779571) ^ [_1761948, _1761950, _1761952] : [_1761948 = c_List_Olist_ONil(_1761950), -(hAPP(c_List_Ohd(_1761950), hAPP(hAPP(c_List_Oappend(_1761950), _1761948), _1761952)) = hAPP(c_List_Ohd(_1761950), _1761952))], (22220 ^ _779571) ^ [_1163029, _1163031, _1163033, _1163035] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1163029, _1163031, _1163033, c_Code__Numeral_OSuc__code__numeral(_1163035)) = hAPP(hAPP(_1163033, _1163035), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1163029, _1163031, _1163033, _1163035)))], (37898 ^ _779571) ^ [_1491050, _1491052] : [class_Lattices_Olattice(_1491050), -(c_Big__Operators_Olattice__class_OInf__fin(_1491050, hAPP(hAPP(c_Set_Oinsert(_1491050), _1491052), c_Orderings_Obot__class_Obot(tc_fun(_1491050, tc_HOL_Obool)))) = _1491052)], (50938 ^ _779571) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (36890 ^ _779571) ^ [_1466542, _1466544, _1466546, _1466548] : [class_Orderings_Oorder(_1466542), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466542, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1466542, _1466544, _1466546)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1466542, _1466546, _1466548)) = c_Orderings_Obot__class_Obot(tc_fun(_1466542, tc_HOL_Obool)))], (33835 ^ _779571) ^ [_1397474, _1397476, _1397478] : [class_Orderings_Olinorder(_1397474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397474), _1397476)), hBOOL(hAPP(hAPP(c_member(_1397474), _1397478), _1397476)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1397474), _1397478), c_Big__Operators_Olattice_OInf__fin(_1397474, c_Orderings_Oord__class_Omin(_1397474), _1397476)) = _1397478)], (19357 ^ _779571) ^ [_1111568, _1111570] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111568))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111570))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111568)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111570)))], (48518 ^ _779571) ^ [_1750197, _1750199, _1750201, _1750203, _1750205] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750197), tc_List_Olist(_1750197))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750197), tc_List_Olist(_1750197)), _1750199), _1750201)), c_List_Olistrel1(_1750197, _1750203))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750197), tc_List_Olist(_1750197))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750197), tc_List_Olist(_1750197)), hAPP(hAPP(c_List_Olist_OCons(_1750197), _1750205), _1750199)), hAPP(hAPP(c_List_Olist_OCons(_1750197), _1750205), _1750201))), c_List_Olistrel1(_1750197, _1750203))))], (48034 ^ _779571) ^ [_1738560, _1738562, _1738564, _1738566] : [hAPP(hAPP(c_List_Oappend(_1738560), _1738562), _1738564) = hAPP(hAPP(c_List_Oappend(_1738560), _1738566), _1738564), -(_1738562 = _1738566)], (44530 ^ _779571) ^ [_1652049, _1652051, _1652053, _1652055] : [c_Orderings_Otop__class_Otop(tc_fun(_1652049, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652051, tc_fun(_1652049, tc_HOL_Obool)), _1652053), _1652055), 44533 ^ _779571 : [(44534 ^ _779571) ^ [_1652165] : [hBOOL(hAPP(hAPP(c_member(_1652051), _1652165), _1652053)), -(hAPP(_1652055, _1652165) = c_Orderings_Otop__class_Otop(tc_fun(_1652049, tc_HOL_Obool)))]]], (9216 ^ _779571) ^ [_932147, _932149, _932151] : [class_Groups_Oordered__ab__group__add(_932147), 9219 ^ _779571 : [(9226 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932147), _932151), hAPP(c_Groups_Ouminus__class_Ouminus(_932147), _932149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932147), _932149), hAPP(c_Groups_Ouminus__class_Ouminus(_932147), _932151))))], (9220 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932147), _932149), hAPP(c_Groups_Ouminus__class_Ouminus(_932147), _932151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932147), _932151), hAPP(c_Groups_Ouminus__class_Ouminus(_932147), _932149))))]]], (41074 ^ _779571) ^ [_1561735, _1561737] : [c_Orderings_Obot__class_Obot(tc_fun(_1561735, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561735), _1561737), 41077 ^ _779571 : [(41078 ^ _779571) ^ [_1561820] : [hBOOL(hAPP(_1561737, _1561820))]]], (28046 ^ _779571) ^ [_1276620, _1276622, _1276624] : [class_Lattices_Olattice(_1276620), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276620), _1276622), _1276624) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276620), _1276624), _1276622))], (29194 ^ _779571) ^ [_1301184, _1301186, _1301188] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301184, tc_HOL_Obool)), _1301186), _1301188) = c_Orderings_Obot__class_Obot(tc_fun(_1301184, tc_HOL_Obool)), 29197 ^ _779571 : [(29200 ^ _779571) ^ [] : [-(_1301188 = c_Orderings_Obot__class_Obot(tc_fun(_1301184, tc_HOL_Obool)))], (29198 ^ _779571) ^ [] : [-(_1301186 = c_Orderings_Obot__class_Obot(tc_fun(_1301184, tc_HOL_Obool)))]]], (2484 ^ _779571) ^ [_817169, _817171] : [_817171 = _817169, -(c_Hoare__Mirabelle_OMGT(_817171) = c_Hoare__Mirabelle_OMGT(_817169))], (20139 ^ _779571) ^ [_1125839, _1125841] : [c_Nat__Transfer_Ois__nat(_1125839), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1125839), _1125841)))], (7690 ^ _779571) ^ [_906963, _906965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906963), _906965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906963), hAPP(c_Nat_OSuc, _906965))))], (35599 ^ _779571) ^ [_1437285, _1437287, _1437289, _1437291, _1437293] : [c_Hoare__Mirabelle_Ohoare__valids(_1437285, _1437287, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1437285)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1437285), c_Hoare__Mirabelle_Opeek__and(_1437285, _1437289, _1437291)), _1437293), _1437289)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1437285), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1437285, _1437287, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1437285)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1437285), _1437289), c_Com_Ocom_OWhile(_1437291, _1437293)), c_Hoare__Mirabelle_Opeek__and(_1437285, _1437289, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1437291)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1437285), tc_HOL_Obool)))))], (48361 ^ _779571) ^ [_1746115, _1746117, _1746119, _1746121] : [-(hAPP(hAPP(c_List_Otake(_1746115), hAPP(c_Nat_OSuc, _1746117)), hAPP(hAPP(c_List_Olist_OCons(_1746115), _1746119), _1746121)) = hAPP(hAPP(c_List_Olist_OCons(_1746115), _1746119), hAPP(hAPP(c_List_Otake(_1746115), _1746117), _1746121)))], (24991 ^ _779571) ^ [_1217674, _1217676, _1217678] : [-(c_Random__Sequence_Oempty(_1217674, _1217676, _1217678) = 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(_1217674)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1217674)))], (25228 ^ _779571) ^ [_1221849, _1221851] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221849), _1221851)), 25233 ^ _779571 : [(25236 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221851), _1221849))], (25234 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221849), _1221851)))]], -(_1221849 = _1221851)], (47005 ^ _779571) ^ [_1714293, _1714295, _1714297, _1714299] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1714293), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1714295), _1714297)))), -(hAPP(c_Random_Opick(_1714295, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714295)), _1714297), _1714299)), _1714293) = hAPP(c_Random_Opick(_1714295, _1714299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1714293), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1714295), _1714297))))], (50720 ^ _779571) ^ [_1799335, _1799337] : [-(hAPP(c_List_Oset(_1799335), c_List_Oconcat(_1799335, _1799337)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1799335), tc_fun(_1799335, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1799335)), _1799337)), c_List_Oset(_1799335)))], (7369 ^ _779571) ^ [_901900, _901902, _901904] : [-(c_Sum__Type_OProjl(_901900, _901902, hAPP(c_Sum__Type_OInl(_901900, _901902), _901904)) = _901904)], (43935 ^ _779571) ^ [_1638809, _1638811, _1638813, _1638815] : [class_Orderings_Olinorder(_1638809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638809), _1638811)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1638809, _1638809, c_Orderings_Oord__class_Omax(_1638809)), _1638813), hAPP(hAPP(c_Set_Oinsert(_1638809), _1638815), _1638811)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1638809), _1638815), hAPP(hAPP(c_Finite__Set_Ofold(_1638809, _1638809, c_Orderings_Oord__class_Omax(_1638809)), _1638813), _1638811)))], (16289 ^ _779571) ^ [_1058083, _1058085, _1058087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058087), 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), _1058087), _1058085))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1058083)))))], (48740 ^ _779571) ^ [_1756857, _1756859, _1756861] : [-(hAPP(hAPP(c_List_Odrop(_1756857), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1756857), _1756859), _1756861)) = _1756861)], (24375 ^ _779571) ^ [_1204543, _1204545, _1204547] : [class_Orderings_Olinorder(_1204543), 24378 ^ _779571 : [(24385 ^ _779571) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204543), _1204545), _1204547) = _1204547, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204543), _1204545), _1204547)))], (24379 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204543), _1204545), _1204547)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204543), _1204545), _1204547) = _1204547)]]], (7622 ^ _779571) ^ [_905931, _905933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905931), _905933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905933), hAPP(c_Nat_OSuc, _905931))))], (3490 ^ _779571) ^ [_833218, _833220, _833222, _833224, _833226, _833228, _833230, _833232] : [-(c_Random__Sequence_Obind(_833232, _833228, _833224, _833220) = c_Random__Sequence_Obind(_833230, _833226, _833222, _833218)), _833232 = _833230, _833228 = _833226, _833224 = _833222, _833220 = _833218], (29608 ^ _779571) ^ [_1308591, _1308593, _1308595, _1308597] : [_1308591 = c_Orderings_Obot__class_Obot(tc_fun(_1308593, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1308593, _1308595, hAPP(c_COMBK(_1308595, _1308593), _1308597)), _1308591) = c_Orderings_Obot__class_Obot(tc_fun(_1308595, tc_HOL_Obool)))], (45243 ^ _779571) ^ [_1669868, _1669870, _1669872] : [class_Complete__Lattice_Ocomplete__lattice(_1669868), -(c_Complete__Lattice_OInf__class_OInf(_1669868, hAPP(hAPP(c_Set_Oinsert(_1669868), _1669870), hAPP(hAPP(c_Set_Oinsert(_1669868), _1669872), c_Orderings_Obot__class_Obot(tc_fun(_1669868, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1669868), _1669870), _1669872))], (29880 ^ _779571) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (49848 ^ _779571) ^ [_1781488, _1781490] : [-(c_List_Ofoldr(tc_List_Olist(_1781488), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1781488)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1781488))), c_List_Otranspose(_1781488, _1781490), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1781488))), hAPP(c_List_Ofilter(tc_List_Olist(_1781488), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1781488)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1781488), tc_List_Olist(_1781488), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1781488)))), _1781490)))], (42354 ^ _779571) ^ [_1600552, _1600554, _1600556, _1600558] : [hBOOL(hAPP(c_Predicate_ODomainP(_1600552, _1600554, _1600556), _1600558)), -(hBOOL(hAPP(hAPP(_1600556, _1600558), 42357 ^ [_1600552, _1600554, _1600556, _1600558])))], (37565 ^ _779571) ^ [_1481451, _1481453, _1481455, _1481457, _1481459, _1481461, _1481463, _1481465, _1481467] : [c_Equiv__Relations_Oequiv(_1481451, _1481453, _1481455), c_Equiv__Relations_Oequiv(_1481457, _1481459, _1481461), c_Equiv__Relations_Ocongruent2(_1481451, _1481457, tc_fun(_1481463, tc_HOL_Obool), _1481455, _1481461, _1481465), hBOOL(hAPP(hAPP(c_member(_1481457), _1481467), _1481459)), -(c_Equiv__Relations_Ocongruent(_1481451, tc_fun(_1481463, tc_HOL_Obool), _1481455, hAPP(hAPP(c_COMBB(tc_fun(_1481457, tc_fun(_1481463, tc_HOL_Obool)), tc_fun(_1481463, tc_HOL_Obool), _1481451), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481457, tc_fun(_1481463, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1481457, _1481457, _1481461), hAPP(hAPP(c_Set_Oinsert(_1481457), _1481467), c_Orderings_Obot__class_Obot(tc_fun(_1481457, tc_HOL_Obool)))))), _1481465)))], (34739 ^ _779571) ^ [_1416428, _1416430, _1416432, _1416434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1416428), _1416430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1416432), _1416434)), -(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), _1416428), _1416432)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1416430), _1416434))), c_FunDef_Opair__leq)))], (38407 ^ _779571) ^ [_1501042, _1501044] : [-(c_Fun_Oinj__on(_1501042, _1501042, c_COMBI(_1501042), _1501044))], (4810 ^ _779571) ^ [_853896, _853898, _853900, _853902] : [-(c_Product__Type_OPair(_853902, _853898) = c_Product__Type_OPair(_853900, _853896)), _853902 = _853900, _853898 = _853896], (38052 ^ _779571) ^ [_1493690, _1493692, _1493694] : [class_Lattices_Olattice(_1493690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493690), _1493692)), -(hBOOL(hAPP(hAPP(c_member(_1493690), _1493694), _1493692))), -(_1493692 = c_Orderings_Obot__class_Obot(tc_fun(_1493690, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1493690, hAPP(hAPP(c_Set_Oinsert(_1493690), _1493694), _1493692)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493690), _1493694), c_Big__Operators_Olattice__class_OInf__fin(_1493690, _1493692)))], (27974 ^ _779571) ^ [_1275004, _1275006, _1275008, _1275010, _1275012] : [class_Lattices_Olattice(_1275004), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275006, _1275004)), _1275008), _1275010), _1275012) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275004), hAPP(_1275008, _1275012)), hAPP(_1275010, _1275012)))], (45736 ^ _779571) ^ [_1680667, _1680669, _1680671, _1680673, _1680675, _1680677] : [hAPP(c_Map_Omap__add(_1680667, _1680669, _1680671, _1680673), _1680675) = hAPP(c_Option_Ooption_OSome(_1680669), _1680677), -(hAPP(_1680673, _1680675) = hAPP(c_Option_Ooption_OSome(_1680669), _1680677)), 45743 ^ _779571 : [(45746 ^ _779571) ^ [] : [-(hAPP(_1680671, _1680675) = hAPP(c_Option_Ooption_OSome(_1680669), _1680677))], (45744 ^ _779571) ^ [] : [-(hAPP(_1680673, _1680675) = c_Option_Ooption_ONone(_1680669))]]], (36914 ^ _779571) ^ [_1467086, _1467088, _1467090, _1467092, _1467094] : [class_Orderings_Olinorder(_1467086), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467086, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1467086, _1467088, _1467090)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1467086, _1467092, _1467094)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1467086, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1467086), _1467088), _1467092), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1467086), _1467090), _1467094)))], (37513 ^ _779571) ^ [_1480249, _1480251, _1480253, _1480255, _1480257, _1480259, _1480261, _1480263, _1480265, _1480267] : [c_Equiv__Relations_Ocongruent2(_1480249, _1480251, _1480253, _1480255, _1480257, _1480259), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480249, _1480249)), hAPP(hAPP(c_Product__Type_OPair(_1480249, _1480249), _1480261), _1480263)), _1480255)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480251, _1480251)), hAPP(hAPP(c_Product__Type_OPair(_1480251, _1480251), _1480265), _1480267)), _1480257)), -(hAPP(hAPP(_1480259, _1480261), _1480265) = hAPP(hAPP(_1480259, _1480263), _1480267))], (1952 ^ _779571) ^ [_808229, _808231, _808233, _808235, _808237, _808239, _808241, _808243, _808245, _808247, _808249, _808251, _808253, _808255, _808257, _808259, _808261, _808263, _808265, _808267] : [-(c_Com_Ocom_Ocom__rec(_808267, _808263, _808259, _808255, _808251, _808247, _808243, _808239, _808235, _808231) = c_Com_Ocom_Ocom__rec(_808265, _808261, _808257, _808253, _808249, _808245, _808241, _808237, _808233, _808229)), _808267 = _808265, _808263 = _808261, _808259 = _808257, _808255 = _808253, _808251 = _808249, _808247 = _808245, _808243 = _808241, _808239 = _808237, _808235 = _808233, _808231 = _808229], (24495 ^ _779571) ^ [_1206628, _1206630, _1206632, _1206634] : [class_Orderings_Olinorder(_1206628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206628), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206628), _1206630), _1206632)), _1206634)), 24502 ^ _779571 : [(24505 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206628), _1206632), _1206634)))], (24503 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206628), _1206630), _1206634)))]]], (29454 ^ _779571) ^ [_1306143, _1306145, _1306147] : [class_Orderings_Oorder(_1306143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306143), _1306145), _1306147)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306143, _1306147), _1306145) = c_Orderings_Obot__class_Obot(tc_fun(_1306143, tc_HOL_Obool)))], (23325 ^ _779571) ^ [_1184451, _1184453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184451), 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)), _1184453)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184451, _1184453), c_Divides_OnegDivAlg(_1184451, _1184453))))], (20629 ^ _779571) ^ [_1134043, _1134045, _1134047] : [class_Rings_Odivision__ring(_1134043), -(_1134045 = c_Groups_Ozero__class_Ozero(_1134043)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1134043), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134043), _1134047), _1134045)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134043), _1134047), hAPP(c_Groups_Ouminus__class_Ouminus(_1134043), _1134045)))], (22140 ^ _779571) ^ [_1161795, _1161797, _1161799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1161795), _1161797)), -(c_Random_Ominus__shift(_1161799, _1161795, _1161797) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1161799), _1161795)), _1161797))], (19907 ^ _779571) ^ [_1121541, _1121543] : [class_Rings_Oring__1(_1121541), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121541), hAPP(c_Groups_Ouminus__class_Ouminus(_1121541), c_Groups_Oone__class_Oone(_1121541))), 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)))), _1121543))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1121541), c_Groups_Oone__class_Oone(_1121541)))], (30872 ^ _779571) ^ [_1335221, _1335223] : [c_Option_Oset(_1335221, _1335223) = c_Orderings_Obot__class_Obot(tc_fun(_1335221, tc_HOL_Obool)), -(_1335223 = c_Option_Ooption_ONone(_1335221))], (49864 ^ _779571) ^ [_1781976] : [-(c_List_Otranspose(_1781976, c_List_Olist_ONil(tc_List_Olist(_1781976))) = c_List_Olist_ONil(tc_List_Olist(_1781976)))], (4996 ^ _779571) ^ [_856805, _856807] : [_856807 = _856805, -(c_SetInterval_Oord__class_OlessThan(_856807) = c_SetInterval_Oord__class_OlessThan(_856805))], (44402 ^ _779571) ^ [_1647943, _1647945, _1647947, _1647949, _1647951, _1647953] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647943, tc_fun(_1647945, tc_HOL_Obool)), _1647947), _1647949), _1647951)), -(hBOOL(hAPP(hAPP(_1647949, _1647953), _1647951))), hBOOL(hAPP(hAPP(c_member(_1647943), _1647953), _1647947))], (45297 ^ _779571) ^ [_1670723, _1670725, _1670727, _1670729, _1670731, _1670733, _1670735, _1670737] : [c_Fun_Oinj__on(_1670723, _1670725, _1670727, _1670729), 45303 ^ _779571 : [(45306 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1670723, tc_HOL_Obool)), hAPP(_1670735, 45302 ^ [_1670723, _1670725, _1670727, _1670729, _1670731, _1670733, _1670735, _1670737])), _1670729))], (45304 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670731), 45302 ^ [_1670723, _1670725, _1670727, _1670729, _1670731, _1670733, _1670735, _1670737]), _1670733)))]], hBOOL(hAPP(hAPP(c_member(_1670731), _1670737), _1670733)), -(hAPP(c_Set_Oimage(_1670723, _1670725, _1670727), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670731, tc_fun(_1670723, tc_HOL_Obool)), _1670733), _1670735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670731, tc_fun(_1670725, tc_HOL_Obool)), _1670733), hAPP(hAPP(c_COMBB(tc_fun(_1670723, tc_HOL_Obool), tc_fun(_1670725, tc_HOL_Obool), _1670731), c_Set_Oimage(_1670723, _1670725, _1670727)), _1670735)))], (6379 ^ _779571) ^ [_883296, _883298, _883300, _883302, _883304] : [c_Com_Ocom_OCall(_883296, _883298, _883300) = c_Com_Ocom_OSemi(_883302, _883304)], (23803 ^ _779571) ^ [_1193228, _1193230, _1193232] : [class_Orderings_Olinorder(_1193228), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193228), _1193230), _1193232) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193228), _1193232), _1193230))], (34998 ^ _779571) ^ [_1422910] : [-(c_Relation_OId__on(_1422910, c_Orderings_Obot__class_Obot(tc_fun(_1422910, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1422910, _1422910), tc_HOL_Obool)))], (39872 ^ _779571) ^ [_1532820, _1532822, _1532824, _1532826] : [_1532824 = _1532826, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1532820, _1532822, hAPP(hAPP(c_Set_Oinsert(_1532820), _1532824), c_Orderings_Obot__class_Obot(tc_fun(_1532820, tc_HOL_Obool)))), _1532826)))], (40859 ^ _779571) ^ [_1556497, _1556499, _1556501, _1556503, _1556505, _1556507, _1556509, _1556511, _1556513, _1556515] : [-(c_Product__Type_Omap__pair(_1556497, _1556499, _1556501, _1556503, hAPP(c_Fun_Ocomp(_1556505, _1556499, _1556497, _1556507), _1556509), hAPP(c_Fun_Ocomp(_1556511, _1556503, _1556501, _1556513), _1556515)) = hAPP(c_Fun_Ocomp(tc_prod(_1556505, _1556511), tc_prod(_1556499, _1556503), tc_prod(_1556497, _1556501), c_Product__Type_Omap__pair(_1556505, _1556499, _1556511, _1556503, _1556507, _1556513)), c_Product__Type_Omap__pair(_1556497, _1556505, _1556501, _1556511, _1556509, _1556515)))], (49818 ^ _779571) ^ [_1780302, _1780304, _1780306, _1780308, _1780310] : [c_List_Opartition(_1780302, _1780304, _1780306) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780302), tc_List_Olist(_1780302)), _1780308), _1780310), 49821 ^ _779571 : [(49828 ^ _779571) ^ [_1780564] : [hBOOL(hAPP(hAPP(c_member(_1780302), _1780564), hAPP(c_List_Oset(_1780302), _1780310))), hBOOL(hAPP(_1780304, _1780564))], (49822 ^ _779571) ^ [_1780455] : [hBOOL(hAPP(hAPP(c_member(_1780302), _1780455), hAPP(c_List_Oset(_1780302), _1780308))), -(hBOOL(hAPP(_1780304, _1780455)))]]], (1622 ^ _779571) ^ [_802614, _802616] : [-(class_Orderings_Opreorder(_802614)), _802616 = _802614, class_Orderings_Opreorder(_802616)], (128 ^ _779571) ^ [_781339, _781341, _781343, _781345, _781347, _781349] : [-(c_Nitpick_Oless__eq__frac(_781347, _781343, _781339)), c_Nitpick_Oless__eq__frac(_781349, _781345, _781341), _781349 = _781347, _781345 = _781343, _781341 = _781339], (19311 ^ _779571) ^ [_1110763, _1110765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110763)), c_Int_OBit0(_1110765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110763), _1110765)))], (32895 ^ _779571) ^ [_1379771, _1379773] : [class_Rings_Oring__1(_1379771), -(hBOOL(hAPP(hAPP(c_member(_1379771), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1379771), _1379773)), c_Int_Oring__1__class_OInts(_1379771))))], (49076 ^ _779571) ^ [_1764200, _1764202, _1764204] : [-(hAPP(c_List_Otl(_1764200), hAPP(hAPP(c_List_Otake(_1764200), _1764202), _1764204)) = hAPP(hAPP(c_List_Otake(_1764200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1764202), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1764200), _1764204)))], (19345 ^ _779571) ^ [_1111396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1111396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1111396)))], (35605 ^ _779571) ^ [_1437512] : [-(c_Nitpick_Odenom(_1437512) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1437512, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1437512)))], (4834 ^ _779571) ^ [_854266, _854268] : [_854268 = _854266, -(c_Set_OCollect(_854268) = c_Set_OCollect(_854266))], (608 ^ _779571) ^ [_789075, _789077, _789079, _789081] : [-(c_Nitpick_Owf_H(_789079, _789075)), c_Nitpick_Owf_H(_789081, _789077), _789081 = _789079, _789077 = _789075], (12367 ^ _779571) ^ [_986045] : [-(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), _986045))))], (31416 ^ _779571) ^ [_1347451, _1347453] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347451), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347453), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 31423 ^ _779571 : [(31430 ^ _779571) ^ [] : [_1347451 = _1347453, -(hAPP(c_Code__Numeral_Oof__nat, _1347451) = hAPP(c_Code__Numeral_Oof__nat, _1347453))], (31424 ^ _779571) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1347451) = hAPP(c_Code__Numeral_Oof__nat, _1347453), -(_1347451 = _1347453)]]], (46010 ^ _779571) ^ [_1687406, _1687408] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1687406), hAPP(c_List_Oset(_1687406), _1687408))))], (50386 ^ _779571) ^ [_1791752, _1791754, _1791756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1791752), _1791754)), _1791756)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1791752, _1791756)), _1791754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1791752), _1791754))], (19059 ^ _779571) ^ [_1106191, _1106193] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106191))), _1106193) = 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)))), _1106191), _1106193))], (19469 ^ _779571) ^ [_1113540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1113540)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113540), c_Int_OMin)))], (34923 ^ _779571) ^ [_1420636, _1420638] : [-(c_FunDef_Orp__inv__image(_1420636, _1420638) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))))), tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))), tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)), tc_fun(tc_fun(_1420638, _1420636), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool)), c_COMBS(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)), tc_fun(tc_fun(_1420638, _1420636), tc_fun(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), tc_fun(tc_prod(_1420636, _1420636), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool))), tc_fun(_1420638, _1420636)), c_Product__Type_OPair(tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool), tc_fun(tc_prod(_1420638, _1420638), tc_HOL_Obool)))), c_Relation_Oinv__image(_1420636, _1420638))))), c_Relation_Oinv__image(_1420636, _1420638))))], (29013 ^ _779571) ^ [_1296884, _1296886, _1296888] : [-(hAPP(hAPP(c_Set_Oinsert(_1296884), _1296886), hAPP(hAPP(c_Set_Oinsert(_1296884), _1296886), _1296888)) = hAPP(hAPP(c_Set_Oinsert(_1296884), _1296886), _1296888))], (7942 ^ _779571) ^ [_911315, _911317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911315), _911317)), -(_911317 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911315), 7945 ^ [_911315, _911317])))], (10922 ^ _779571) ^ [_961091, _961093, _961095] : [class_Orderings_Olinorder(_961091), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961091), _961093), _961095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961091), _961095), _961093)))], (11499 ^ _779571) ^ [_970605, _970607, _970609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970605), _970607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970607), _970609))))], (51431 ^ _779571) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (45135 ^ _779571) ^ [_1667328, _1667330, _1667332] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667328, tc_HOL_Obool)), _1667330), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667328, tc_HOL_Obool), _1667332)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1667328, tc_HOL_Obool), tc_fun(_1667328, tc_HOL_Obool)), _1667332), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667328, tc_HOL_Obool)), _1667330)))], (19061 ^ _779571) ^ [_1106236, _1106238] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106236))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106238)) = 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)))), _1106236), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106238)))], (13968 ^ _779571) ^ [_1014254, _1014256, _1014258, _1014260] : [class_Groups_Ouminus(_1014254), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014256, _1014254)), _1014258), _1014260) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014254), hAPP(_1014258, _1014260)))], (24391 ^ _779571) ^ [_1204799, _1204801, _1204803, _1204805] : [class_Orderings_Olinorder(_1204799), 24394 ^ _779571 : [(24403 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204799), _1204801), _1204803)), _1204805))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), _1204801), _1204805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), _1204803), _1204805))], (24395 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204799), _1204801), _1204803)), _1204805)), 24398 ^ _779571 : [(24401 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), _1204803), _1204805)))], (24399 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204799), _1204801), _1204805)))]]]]], (27708 ^ _779571) ^ [_1270102, _1270104, _1270106, _1270108] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270102, tc_HOL_Obool)), _1270104), _1270106), _1270108)), -(hBOOL(hAPP(_1270104, _1270108))), -(hBOOL(hAPP(_1270106, _1270108)))], (34622 ^ _779571) ^ [_1413776, _1413778, _1413780, _1413782] : [-(hAPP(c_Map_Orestrict__map(_1413776, _1413778, hAPP(c_COMBK(tc_Option_Ooption(_1413778), _1413776), c_Option_Ooption_ONone(_1413778)), _1413780), _1413782) = c_Option_Ooption_ONone(_1413778))], (24257 ^ _779571) ^ [_1202287, _1202289, _1202291, _1202293] : [class_Orderings_Olinorder(_1202287), 24260 ^ _779571 : [(24269 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202287), _1202289), _1202291)), _1202293))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), _1202289), _1202293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), _1202291), _1202293))], (24261 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202287), _1202289), _1202291)), _1202293)), 24264 ^ _779571 : [(24267 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), _1202291), _1202293)))], (24265 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202287), _1202289), _1202293)))]]]]], (17333 ^ _779571) ^ [_1077538, _1077540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077538)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077538), _1077540)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1077538)), _1077540))], (2758 ^ _779571) ^ [_821400, _821402, _821404, _821406] : [-(c_Nitpick_Oint__lcm(_821406, _821402) = c_Nitpick_Oint__lcm(_821404, _821400)), _821406 = _821404, _821402 = _821400], (22962 ^ _779571) ^ [_1177487, _1177489, _1177491] : [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), _1177487), _1177489))), -(hBOOL(hAPP(hAPP(_1177491, _1177487), _1177489))), 22969 ^ _779571 : [(22972 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1177491, 22967 ^ [_1177487, _1177489, _1177491]), 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)))), 22968 ^ [_1177487, _1177489, _1177491])))), -(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), 22967 ^ [_1177487, _1177489, _1177491]), 22968 ^ [_1177487, _1177489, _1177491])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22968 ^ [_1177487, _1177489, _1177491]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22982 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1177491, 22967 ^ [_1177487, _1177489, _1177491]), 22968 ^ [_1177487, _1177489, _1177491]))], (22970 ^ _779571) ^ [] : [-(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), 22967 ^ [_1177487, _1177489, _1177491]), 22968 ^ [_1177487, _1177489, _1177491]))))]]], (4056 ^ _779571) ^ [_842035, _842037, _842039, _842041, _842043, _842045, _842047, _842049, _842051, _842053] : [-(c_Finite__Set_Ofold__graph(_842053, _842049, _842045, _842041, _842037) = c_Finite__Set_Ofold__graph(_842051, _842047, _842043, _842039, _842035)), _842053 = _842051, _842049 = _842047, _842045 = _842043, _842041 = _842039, _842037 = _842035], (49967 ^ _779571) ^ [_1784475, _1784477] : [class_Orderings_Olinorder(_1784475), -(_1784477 = c_List_Olist_ONil(_1784475)), c_List_Olinorder__class_Osorted(_1784475, _1784477), -(c_List_Olinorder__class_Osorted(_1784475, c_List_Obutlast(_1784475, _1784477)))], (9280 ^ _779571) ^ [_933342, _933344, _933346] : [class_Rings_Oring__no__zero__divisors(_933342), 9283 ^ _779571 : [(9284 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933342), _933344), _933346) = c_Groups_Ozero__class_Ozero(_933342), -(_933344 = c_Groups_Ozero__class_Ozero(_933342)), -(_933346 = c_Groups_Ozero__class_Ozero(_933342))], (9294 ^ _779571) ^ [] : [9295 ^ _779571 : [(9298 ^ _779571) ^ [] : [_933346 = c_Groups_Ozero__class_Ozero(_933342)], (9296 ^ _779571) ^ [] : [_933344 = c_Groups_Ozero__class_Ozero(_933342)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933342), _933344), _933346) = c_Groups_Ozero__class_Ozero(_933342))]]], (25820 ^ _779571) ^ [_1231778, _1231780] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231778)), _1231780)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231778), _1231780)))], (49499 ^ _779571) ^ [_1773359, _1773361, _1773363, _1773365] : [49502 ^ _779571 : [(49507 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773359, _1773359)), hAPP(hAPP(c_Product__Type_OPair(_1773359, _1773359), 49501 ^ [_1773359, _1773361, _1773363, _1773365]), 49500 ^ [_1773359, _1773361, _1773363, _1773365])), _1773361))], (49505 ^ _779571) ^ [] : [49500 ^ [_1773359, _1773361, _1773363, _1773365] = 49501 ^ [_1773359, _1773361, _1773363, _1773365]], (49503 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773359, _1773359)), hAPP(hAPP(c_Product__Type_OPair(_1773359, _1773359), 49500 ^ [_1773359, _1773361, _1773363, _1773365]), 49501 ^ [_1773359, _1773361, _1773363, _1773365])), _1773361))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773359), tc_List_Olist(_1773359))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773359), tc_List_Olist(_1773359)), _1773363), _1773365)), c_List_Olexord(_1773359, _1773361)))), -(_1773363 = _1773365), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773359), tc_List_Olist(_1773359))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773359), tc_List_Olist(_1773359)), _1773365), _1773363)), c_List_Olexord(_1773359, _1773361))))], (28154 ^ _779571) ^ [_1278956, _1278958, _1278960] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278956, tc_HOL_Obool)), _1278958), _1278960) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278956, tc_HOL_Obool)), _1278960), _1278958))], (17805 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24793 ^ _779571) ^ [_1212735, _1212737, _1212739, _1212741, _1212743, _1212745, _1212747] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1212735, _1212737, _1212739, _1212741), _1212743), _1212745), _1212747) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1212737, _1212739, _1212741), _1212745), hAPP(_1212743, _1212747)))], (30523 ^ _779571) ^ [_1327358, _1327360, _1327362, _1327364] : [hBOOL(hAPP(hAPP(c_member(_1327358), _1327364), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327358, tc_HOL_Obool)), _1327360), _1327362))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327358, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1327358, tc_fun(_1327358, tc_HOL_Obool), tc_HOL_Obool), c_member(_1327358)), _1327360)), hAPP(hAPP(c_COMBC(_1327358, tc_fun(_1327358, tc_HOL_Obool), tc_HOL_Obool), c_member(_1327358)), _1327362)), _1327364)))], (36180 ^ _779571) ^ [_1450848, _1450850, _1450852, _1450854] : [hBOOL(hAPP(hAPP(c_member(_1450848), _1450850), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450848, tc_HOL_Obool)), _1450852), _1450854))), -(hBOOL(hAPP(hAPP(c_member(_1450848), _1450850), _1450854)))], (49862 ^ _779571) ^ [_1781893, _1781895, _1781897, _1781899, _1781901] : [-(c_List_Omap__filter(_1781893, _1781895, _1781897, hAPP(hAPP(c_List_Olist_OCons(_1781893), _1781899), _1781901)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1781895), _1781895, c_List_Omap__filter(_1781893, _1781895, _1781897, _1781901), hAPP(hAPP(c_COMBC(_1781895, tc_List_Olist(_1781895), tc_List_Olist(_1781895)), c_List_Olist_OCons(_1781895)), c_List_Omap__filter(_1781893, _1781895, _1781897, _1781901))), hAPP(_1781897, _1781899)))], (6871 ^ _779571) ^ [_892949, _892951, _892953] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892949), _892951)), _892953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892951), _892953)))], (19117 ^ _779571) ^ [_1107413, _1107415] : [_1107413 = _1107415, -(c_Int_OBit0(_1107413) = c_Int_OBit0(_1107415))], (24999 ^ _779571) ^ [_1217871, _1217873, _1217875] : [hBOOL(hAPP(c_Predicate_OPowp(_1217871, _1217873), _1217875)), 25002 ^ _779571 : [(25003 ^ _779571) ^ [_1217955] : [hBOOL(hAPP(hAPP(c_member(_1217871), _1217955), _1217875)), -(hBOOL(hAPP(_1217873, _1217955)))]]], (7371 ^ _779571) ^ [_901937, _901939, _901941] : [-(c_Sum__Type_OProjr(_901937, _901939, hAPP(c_Sum__Type_OInr(_901939, _901937), _901941)) = _901941)], (10502 ^ _779571) ^ [_954356, _954358, _954360, _954362] : [class_Orderings_Oord(_954356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954356), _954358), _954360)), _954360 = _954362, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954356), _954358), _954362)))], (48395 ^ _779571) ^ [_1747049, _1747051, _1747053, _1747055] : [-(hAPP(hAPP(c_List_Otake(_1747049), _1747051), hAPP(hAPP(c_List_Olist_OCons(_1747049), _1747053), _1747055)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1747049), c_List_Olist_ONil(_1747049), hAPP(hAPP(c_COMBB(tc_List_Olist(_1747049), tc_List_Olist(_1747049), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1747049), _1747053)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1747049), tc_List_Olist(_1747049)), c_List_Otake(_1747049)), _1747055)), _1747051))], (42161 ^ _779571) ^ [_1595367, _1595369, _1595371, _1595373] : [hBOOL(hAPP(hAPP(c_member(_1595369), _1595373), hAPP(c_Relation_ORange(_1595367, _1595369), _1595371))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1595367, _1595369, hAPP(hAPP(c_COMBC(_1595367, tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_fun(_1595369, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595369, tc_fun(tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_fun(_1595369, tc_HOL_Obool)), _1595367), c_COMBC(_1595369, tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595369, tc_prod(_1595367, _1595369)), tc_fun(_1595369, tc_fun(tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_HOL_Obool)), _1595367), hAPP(c_COMBB(tc_prod(_1595367, _1595369), tc_fun(tc_fun(tc_prod(_1595367, _1595369), tc_HOL_Obool), tc_HOL_Obool), _1595369), c_member(tc_prod(_1595367, _1595369)))), c_Product__Type_OPair(_1595367, _1595369)))), _1595371)), _1595373)))], (48896 ^ _779571) ^ [_1760631, _1760633, _1760635, _1760637] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1760631) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1760633), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1760631)), hAPP(hAPP(c_List_Olist_OCons(_1760633), _1760635), _1760637)) = hAPP(hAPP(c_List_Odrop(_1760633), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1760631)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1760637))], (6399 ^ _779571) ^ [_883737, _883739, _883741, _883743, _883745] : [hAPP(_883737, 6400 ^ [_883737, _883739, _883741, _883743, _883745]) = hAPP(c_Nat_Onat_Onat__rec(_883739, _883741, _883743), 6400 ^ [_883737, _883739, _883741, _883743, _883745]), -(hAPP(_883737, hAPP(c_Nat_OSuc, _883745)) = hAPP(hAPP(_883743, _883745), hAPP(_883737, _883745)))], (25614 ^ _779571) ^ [_1228073, _1228075, _1228077, _1228079] : [class_Divides_Osemiring__div(_1228073), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228073), _1228075), _1228077)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228073), _1228075), _1228079)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228073), _1228075), c_Divides_Odiv__class_Omod(_1228073, _1228077, _1228079))))], (24809 ^ _779571) ^ [_1213236, _1213238, _1213240, _1213242, _1213244] : [_1213236 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1213238, _1213240, _1213242, _1213244), _1213236) = c_Lazy__Sequence_Oempty(_1213240))], (8802 ^ _779571) ^ [_925052, _925054] : [class_Rings_Oring__1__no__zero__divisors(_925052), 8805 ^ _779571 : [(8806 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925052), _925054), _925054) = c_Groups_Oone__class_Oone(_925052), -(_925054 = c_Groups_Oone__class_Oone(_925052)), -(_925054 = hAPP(c_Groups_Ouminus__class_Ouminus(_925052), c_Groups_Oone__class_Oone(_925052)))], (8816 ^ _779571) ^ [] : [8817 ^ _779571 : [(8820 ^ _779571) ^ [] : [_925054 = hAPP(c_Groups_Ouminus__class_Ouminus(_925052), c_Groups_Oone__class_Oone(_925052))], (8818 ^ _779571) ^ [] : [_925054 = c_Groups_Oone__class_Oone(_925052)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925052), _925054), _925054) = c_Groups_Oone__class_Oone(_925052))]]], (29077 ^ _779571) ^ [_1298310] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298310)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1298310), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1298310)))], (20297 ^ _779571) ^ [_1128690, _1128692, _1128694] : [class_Fields_Olinordered__field(_1128690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128690), c_Groups_Ozero__class_Ozero(_1128690)), _1128692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128690), _1128694), c_Groups_Ozero__class_Ozero(_1128690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128690), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128690), _1128692), _1128694)), c_Groups_Ozero__class_Ozero(_1128690))))], (30441 ^ _779571) ^ [_1325512, _1325514] : [_1325512 = _1325514, -(hAPP(c_Int_ORep__Integ, _1325512) = hAPP(c_Int_ORep__Integ, _1325514))], (45149 ^ _779571) ^ [_1667777, _1667779, _1667781, _1667783] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667777, tc_fun(_1667779, tc_HOL_Obool)), _1667781), _1667783) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667779, tc_HOL_Obool), hAPP(c_Set_Oimage(_1667777, tc_fun(_1667779, tc_HOL_Obool), _1667783), _1667781)))], (23179 ^ _779571) ^ [_1181858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181858)), 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), _1181858)) = 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), _1181858))))))], (3992 ^ _779571) ^ [_841091, _841093] : [_841093 = _841091, -(c_SetInterval_Oord__class_OgreaterThan(_841093) = c_SetInterval_Oord__class_OgreaterThan(_841091))], (15812 ^ _779571) ^ [_1048140, _1048142, _1048144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048140), _1048142)), 15815 ^ _779571 : [(15822 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048144), _1048140)), _1048142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048142), _1048140))))], (15816 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048142), _1048140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048144), _1048140)), _1048142)))]]], (48126 ^ _779571) ^ [_1740413, _1740415, _1740417] : [_1740413 = hAPP(hAPP(c_List_Oappend(_1740415), _1740413), _1740417), -(_1740417 = c_List_Olist_ONil(_1740415))], (29422 ^ _779571) ^ [_1305528, _1305530, _1305532] : [class_Orderings_Oorder(_1305528), 29425 ^ _779571 : [(29432 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305528), _1305530), _1305532))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1305528, _1305530, _1305532) = c_Orderings_Obot__class_Obot(tc_fun(_1305528, tc_HOL_Obool)))], (29426 ^ _779571) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1305528, _1305530, _1305532) = c_Orderings_Obot__class_Obot(tc_fun(_1305528, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305528), _1305530), _1305532))]]], (6955 ^ _779571) ^ [_894254, _894256] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _894254), _894256)), 6956 ^ _779571 : [(6963 ^ _779571) ^ [] : [_894254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _894256 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6957 ^ _779571) ^ [] : [_894254 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _894256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50423 ^ _779571) ^ [_1792450, _1792452] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1792450, _1792452) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1792450), _1792452)))], (49014 ^ _779571) ^ [_1762923, _1762925] : [hBOOL(hAPP(c_List_Odistinct(_1762923), _1762925)), -(hBOOL(hAPP(c_List_Odistinct(_1762923), hAPP(c_List_Otl(_1762923), _1762925))))], (14964 ^ _779571) ^ [_1032245, _1032247, _1032249] : [-(hBOOL(hAPP(_1032245, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032247), _1032249)))), 14967 ^ _779571 : [(14970 ^ _779571) ^ [] : [hBOOL(hAPP(_1032245, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14968 ^ _779571) ^ [] : [-(_1032249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14971 ^ _779571 : [(14976 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14974 ^ [_1032245, _1032247, _1032249]), _1032249)))], (14978 ^ _779571) ^ [] : [-(_1032247 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032249), 14973 ^ [_1032245, _1032247, _1032249])), 14974 ^ [_1032245, _1032247, _1032249]))], (14980 ^ _779571) ^ [] : [hBOOL(hAPP(_1032245, 14973 ^ [_1032245, _1032247, _1032249]))], (14972 ^ _779571) ^ [] : [_1032249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (39907 ^ _779571) ^ [_1533688, _1533690, _1533692, _1533694] : [c_Wellfounded_Omax__extp(_1533688, _1533690, _1533692, _1533694), 39910 ^ _779571 : [(39913 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533688), _1533694)))], (39915 ^ _779571) ^ [] : [_1533694 = c_Orderings_Obot__class_Obot(tc_fun(_1533688, tc_HOL_Obool))], (39917 ^ _779571) ^ [_1533904] : [hBOOL(hAPP(hAPP(c_member(_1533688), _1533904), _1533692)), 39921 ^ _779571 : [(39924 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1533690, _1533904), 39920 ^ [_1533688, _1533690, _1533692, _1533694, _1533904])))], (39922 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533688), 39920 ^ [_1533688, _1533690, _1533692, _1533694, _1533904]), _1533694)))]]], (39911 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533688), _1533692)))]]], (25464 ^ _779571) ^ [_1225618, _1225620] : [_1225618 = _1225620, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225618), _1225620)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225620), _1225618)))], (21527 ^ _779571) ^ [_1150120, _1150122, _1150124, _1150126] : [class_Fields_Olinordered__field(_1150120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150120), c_Groups_Ozero__class_Ozero(_1150120)), _1150122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150120), _1150124), _1150122)), _1150126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150120), _1150124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150120), _1150126), _1150122))))], (26834 ^ _779571) ^ [_1251908, _1251910, _1251912, _1251914, _1251916] : [class_Orderings_Oorder(_1251908), 26837 ^ _779571 : [(26858 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1251908, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1251908, _1251910, _1251912)), c_SetInterval_Oord__class_OatLeastAtMost(_1251908, _1251914, _1251916)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251914), _1251916)), 26861 ^ _779571 : [(26864 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251914), _1251910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251912), _1251916)), 26871 ^ _779571 : [(26874 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251908), _1251912), _1251916))], (26872 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251908), _1251914), _1251910))]]], (26862 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251910), _1251912)))]]], (26838 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1251908, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1251908, _1251910, _1251912)), c_SetInterval_Oord__class_OatLeastAtMost(_1251908, _1251914, _1251916))), 26841 ^ _779571 : [(26842 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251910), _1251912)), 26845 ^ _779571 : [(26850 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251908), _1251914), _1251910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251908), _1251912), _1251916)))], (26848 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251912), _1251916)))], (26846 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251914), _1251910)))]]], (26856 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251908), _1251914), _1251916)))]]]]], (30245 ^ _779571) ^ [_1321826, _1321828, _1321830, _1321832, _1321834] : [hBOOL(hAPP(hAPP(c_member(_1321826), _1321828), _1321830)), -(hBOOL(hAPP(hAPP(c_member(_1321832), hAPP(_1321834, _1321828)), hAPP(c_Set_Oimage(_1321826, _1321832, _1321834), _1321830))))], (46084 ^ _779571) ^ [_1689266, _1689268, _1689270, _1689272, _1689274] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1689266), tc_Option_Ooption(_1689268), _1689270, hAPP(c_Option_Omap(_1689266, _1689268), _1689272)), hAPP(c_COMBK(tc_Option_Ooption(_1689266), _1689270), c_Option_Ooption_ONone(_1689266))), _1689274) = c_Option_Ooption_ONone(_1689268))], (50541 ^ _779571) ^ [_1794987, _1794989, _1794991] : [50542 ^ _779571 : [(50545 ^ _779571) ^ [] : [_1794991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50543 ^ _779571) ^ [] : [-(_1794987 = c_List_Olist_ONil(tc_List_Olist(_1794989)))]], 50549 ^ _779571 : [(50552 ^ _779571) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794989)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1794989)), _1794987), 50548 ^ [_1794987, _1794989, _1794991])) = _1794991], (50550 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50548 ^ [_1794987, _1794989, _1794991]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1794989))), _1794987))))]], -(c_List_Otranspose(_1794989, _1794987) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1794989)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1794989)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1794989), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1794989)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1794989)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1794989), hAPP(hAPP(c_COMBB(tc_List_Olist(_1794989), tc_fun(tc_Nat_Onat, _1794989), tc_Nat_Onat), c_List_Onth(_1794989)), hAPP(c_List_Onth(tc_List_Olist(_1794989)), _1794987))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1794989))), _1794987)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1794991)))], (48530 ^ _779571) ^ [_1750687, _1750689, _1750691, _1750693] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750687), tc_List_Olist(_1750687))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750687), tc_List_Olist(_1750687)), _1750689), _1750691)), c_List_Olistrel1(_1750687, _1750693))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750687)), _1750689) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750687)), _1750691))], (5172 ^ _779571) ^ [_859487, _859489, _859491, _859493, _859495, _859497] : [-(c_Product__Type_Oprod_Oprod__case(_859497, _859493, _859489) = c_Product__Type_Oprod_Oprod__case(_859495, _859491, _859487)), _859497 = _859495, _859493 = _859491, _859489 = _859487], (48028 ^ _779571) ^ [_1738424, _1738426, _1738428, _1738430] : [_1738428 = _1738430, -(hAPP(hAPP(c_List_Oappend(_1738424), _1738426), _1738428) = hAPP(hAPP(c_List_Oappend(_1738424), _1738426), _1738430))], (48040 ^ _779571) ^ [_1738669, _1738671, _1738673, _1738675] : [_1738671 = _1738675, -(hAPP(hAPP(c_List_Oappend(_1738669), _1738671), _1738673) = hAPP(hAPP(c_List_Oappend(_1738669), _1738675), _1738673))], (6391 ^ _779571) ^ [_883605, _883607, _883609] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_883605, _883607, _883609)], (29536 ^ _779571) ^ [_1307439, _1307441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307439, tc_HOL_Obool)), _1307441), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307439, tc_HOL_Obool)), _1307441))), -(_1307441 = c_Orderings_Obot__class_Obot(tc_fun(_1307439, tc_HOL_Obool)))], (46120 ^ _779571) ^ [_1690072, _1690074, _1690076, _1690078] : [c_Fun_Oinj__on(_1690072, _1690074, _1690076, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1690072, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1690072), tc_fun(_1690072, tc_HOL_Obool), c_List_Oset(_1690072)), _1690078))), -(c_Fun_Oinj__on(tc_List_Olist(_1690072), tc_List_Olist(_1690074), hAPP(c_List_Omap(_1690072, _1690074), _1690076), _1690078))], (11282 ^ _779571) ^ [_966959, _966961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966959)), _966961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966959), _966961)))], (17037 ^ _779571) ^ [_1072226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1072226)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1072226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22296 ^ _779571) ^ [_1164268, _1164270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164268), _1164270)), -(c_Divides_Odivmod__nat(_1164268, _1164270) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164268))], (51555 ^ _779571) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (48880 ^ _779571) ^ [_1760213, _1760215, _1760217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1760213), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760215)), _1760217))), -(hAPP(hAPP(c_List_Olist_OCons(_1760215), hAPP(hAPP(c_List_Onth(_1760215), _1760217), _1760213)), hAPP(hAPP(c_List_Odrop(_1760215), hAPP(c_Nat_OSuc, _1760213)), _1760217)) = hAPP(hAPP(c_List_Odrop(_1760215), _1760213), _1760217))], (15510 ^ _779571) ^ [_1042237, _1042239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042237), _1042239)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1042239, _1042237) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042239), _1042237), _1042237))], (42571 ^ _779571) ^ [_1604916, _1604918] : [42572 ^ _779571 : [(42573 ^ _779571) ^ [_1604962] : [hBOOL(hAPP(_1604916, _1604962))]], -(hBOOL(hAPP(_1604916, c_Hilbert__Choice_OEps(_1604918, _1604916))))], (24531 ^ _779571) ^ [_1207439, _1207441, _1207443, _1207445] : [class_Orderings_Olinorder(_1207439), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207439), _1207441), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207439), _1207443), _1207445)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207439), _1207443), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207439), _1207441), _1207445)))], (36896 ^ _779571) ^ [_1466669, _1466671, _1466673, _1466675] : [class_Orderings_Oorder(_1466669), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466669, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1466669, _1466671, _1466673)), c_SetInterval_Oord__class_OatLeastAtMost(_1466669, _1466673, _1466675)) = c_Orderings_Obot__class_Obot(tc_fun(_1466669, tc_HOL_Obool)))], (15840 ^ _779571) ^ [_1048677, _1048679, _1048681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048677), _1048679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048679), _1048681)), _1048677))))], (14680 ^ _779571) ^ [_1027116, _1027118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027116)), 14683 ^ _779571 : [(14690 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027118)), -(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), _1027118), _1027116))))], (14684 ^ _779571) ^ [] : [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), _1027118), _1027116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027118)))]]], (26386 ^ _779571) ^ [_1243011, _1243013] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243011), _1243013)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1243011), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243013), _1243011)) = _1243013)], (47691 ^ _779571) ^ [_1730369, _1730371, _1730373] : [-(hAPP(hAPP(c_List_Olist__update(_1730369, c_List_Olist_ONil(_1730369)), _1730371), _1730373) = c_List_Olist_ONil(_1730369))], (42075 ^ _779571) ^ [_1593163, _1593165] : [c_Wellfounded_Owf(_1593163, _1593165), -(c_Wellfounded_Owf(tc_List_Olist(_1593163), c_List_Olex(_1593163, _1593165)))], (7600 ^ _779571) ^ [_905640, _905642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905640), _905642)), _905642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13030 ^ _779571) ^ [_997682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997682)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _997682)) = _997682)], (49175 ^ _779571) ^ [_1766271, _1766273] : [-(c_List_Olist_Olist__size(_1766271, _1766273, c_List_Olist_ONil(_1766271)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24225 ^ _779571) ^ [_1201635, _1201637] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1201635)), hAPP(c_Nat_OSuc, _1201637)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1201635))), 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, _1201637))), 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)), _1201637)))))], (15762 ^ _779571) ^ [_1047172, _1047174, _1047176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047172), _1047174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047176), _1047172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047172), _1047176)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047174), _1047176))))], (41354 ^ _779571) ^ [_1569728] : [-(c_Int_Oint__ge__less__than2(_1569728) = 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), _1569728)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (32512 ^ _779571) ^ [_1372173, _1372175, _1372177, _1372179, _1372181] : [class_Groups_Oordered__comm__monoid__add(_1372173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372175), _1372177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372175, tc_HOL_Obool)), _1372179), _1372177)), 32526 ^ _779571 : [(32529 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372173), c_Groups_Ozero__class_Ozero(_1372173)), hAPP(_1372181, 32525 ^ [_1372173, _1372175, _1372177, _1372179, _1372181])))], (32527 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372175), 32525 ^ [_1372173, _1372175, _1372177, _1372179, _1372181]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372175, tc_HOL_Obool)), _1372177), _1372179))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372173), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372175, _1372173), _1372181), _1372179)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372175, _1372173), _1372181), _1372177))))], (15902 ^ _779571) ^ [_1050085, _1050087, _1050089, _1050091, _1050093, _1050095] : [class_Rings_Oordered__ring(_1050085), 15905 ^ _779571 : [(15912 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050085), _1050091), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050085), _1050093), _1050087)), _1050089)), _1050095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), _1050087), _1050089)), _1050091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), _1050093), _1050089)), _1050095))))], (15906 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), _1050087), _1050089)), _1050091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), _1050093), _1050089)), _1050095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050085), _1050091), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050085), _1050093), _1050087)), _1050089)), _1050095))))]]], (36274 ^ _779571) ^ [_1453091, _1453093, _1453095, _1453097] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453091, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1453091), _1453093), _1453095)), hAPP(hAPP(c_Set_Oinsert(_1453091), _1453093), _1453097)) = hAPP(hAPP(c_Set_Oinsert(_1453091), _1453093), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453091, tc_HOL_Obool)), _1453095), _1453097)))], (8942 ^ _779571) ^ [_927795, _927797, _927799, _927801] : [class_Rings_Ocomm__semiring__1(_927795), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927795), _927797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927795), _927799), _927801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927795), _927799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927795), _927797), _927801)))], (6367 ^ _779571) ^ [_882918, _882920, _882922, _882924, _882926] : [c_Com_Ocom_OWhile(_882918, _882920) = c_Com_Ocom_OCall(_882922, _882924, _882926)], (42451 ^ _779571) ^ [_1602099, _1602101, _1602103, _1602105] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1602099), _1602101))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602103), hAPP(c_Set_Oimage(_1602099, _1602103, _1602105), _1602101))), 42459 ^ _779571 : [(42462 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1602099), hAPP(c_Set_OCollect(_1602099), hAPP(hAPP(c_COMBS(_1602099, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1602099), c_fconj), hAPP(hAPP(c_COMBC(_1602099, tc_fun(_1602099, tc_HOL_Obool), tc_HOL_Obool), c_member(_1602099)), _1602101))), hAPP(hAPP(c_COMBC(_1602099, _1602103, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1602103, tc_fun(_1602103, tc_HOL_Obool), _1602099), c_fequal), _1602105)), hAPP(_1602105, 42458 ^ [_1602099, _1602101, _1602103, _1602105]))))))], (42460 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602099), 42458 ^ [_1602099, _1602101, _1602103, _1602105]), _1602101)))]]], (41624 ^ _779571) ^ [_1581165, _1581167] : [-(hAPP(c_Set_Ovimage(_1581165, _1581165, c_Fun_Oid(_1581165)), _1581167) = _1581167)], (21067 ^ _779571) ^ [_1142122, _1142124, _1142126, _1142128] : [class_Fields_Ofield(_1142122), -(_1142124 = c_Groups_Ozero__class_Ozero(_1142122)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142122), _1142126), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142122), _1142128), _1142124)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142122), _1142124), _1142126)), _1142128)), _1142124))], (51703 ^ _779571) ^ [] : [-(c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H))], (33983 ^ _779571) ^ [_1400152, _1400154] : [class_Orderings_Olinorder(_1400152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400152), _1400154)), -(_1400154 = c_Orderings_Obot__class_Obot(tc_fun(_1400152, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1400152), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1400152), 33996 ^ [_1400152, _1400154]), 33997 ^ [_1400152, _1400154])), hAPP(hAPP(c_Set_Oinsert(_1400152), 33996 ^ [_1400152, _1400154]), hAPP(hAPP(c_Set_Oinsert(_1400152), 33997 ^ [_1400152, _1400154]), c_Orderings_Obot__class_Obot(tc_fun(_1400152, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1400152), c_Big__Operators_Olattice_OSup__fin(_1400152, c_Orderings_Oord__class_Omax(_1400152), _1400154)), _1400154)))], (21979 ^ _779571) ^ [_1158901, _1158903, _1158905, _1158907] : [class_Fields_Olinordered__field__inverse__zero(_1158901), class_Int_Onumber(_1158901), 21986 ^ _779571 : [(21987 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158901), _1158903), _1158905)), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907))), 21990 ^ _779571 : [(21997 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158905))), 22000 ^ _779571 : [(22007 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), c_Groups_Ozero__class_Ozero(_1158901)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907))))], (22001 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), c_Groups_Ozero__class_Ozero(_1158901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)), _1158905)), _1158903)))]]], (21991 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), _1158903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)), _1158905))))]]], (22013 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158901), _1158903), _1158905)), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)))), 22016 ^ _779571 : [(22019 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), _1158903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)), _1158905)))], (22017 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158905)))]], 22020 ^ _779571 : [(22023 ^ _779571) ^ [] : [22024 ^ _779571 : [(22027 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)), _1158905)), _1158903))], (22025 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), c_Groups_Ozero__class_Ozero(_1158901))))]], 22028 ^ _779571 : [(22031 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), hAPP(c_Int_Onumber__class_Onumber__of(_1158901), _1158907)))], (22029 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), c_Groups_Ozero__class_Ozero(_1158901)))]]], (22021 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158905))]]]]], (50655 ^ _779571) ^ [_1798014, _1798016] : [50657 ^ _779571 : [(50660 ^ _779571) ^ [] : [50656 ^ [_1798014, _1798016] = c_List_Olist_ONil(_1798014)], (50658 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1798014)), 50656 ^ [_1798014, _1798016]), hAPP(c_List_Oset(tc_List_Olist(_1798014)), _1798016))))]], -(c_List_Oconcat(_1798014, _1798016) = c_List_Olist_ONil(_1798014))], (30620 ^ _779571) ^ [_1329616, _1329618, _1329620, _1329622] : [-(hBOOL(hAPP(hAPP(c_member(_1329616), _1329618), _1329620))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329616, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1329616), _1329618), _1329622)), _1329620) = hAPP(hAPP(c_Set_Oinsert(_1329616), _1329618), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329616, tc_HOL_Obool)), _1329622), _1329620)))], (50844 ^ _779571) ^ [_1802702, _1802704, _1802706, _1802708] : [-(c_List_Oconcat(_1802702, hAPP(hAPP(c_List_Omap(_1802704, tc_List_Olist(_1802702)), hAPP(hAPP(c_COMBC(_1802704, tc_List_Olist(_1802702), tc_List_Olist(_1802702)), hAPP(hAPP(c_COMBB(_1802702, tc_fun(tc_List_Olist(_1802702), tc_List_Olist(_1802702)), _1802704), c_List_Olist_OCons(_1802702)), _1802706)), c_List_Olist_ONil(_1802702))), _1802708)) = hAPP(hAPP(c_List_Omap(_1802704, _1802702), _1802706), _1802708))], (47115 ^ _779571) ^ [_1717050, _1717052, _1717054, _1717056] : [class_Groups_Ocomm__monoid__add(_1717050), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717050), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1717050), _1717052), c_List_Oupto(_1717054, _1717056))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1717050), _1717052), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1717054, _1717056))))], (23141 ^ _779571) ^ [_1181118, _1181120] : [_1181118 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1181118, _1181120) = 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)))], (40983 ^ _779571) ^ [_1559575, _1559577, _1559579] : [40984 ^ _779571 : [(40987 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559575), hAPP(c_Set_OCollect(_1559575), _1559579)))], (40985 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559575), hAPP(c_Set_OCollect(_1559575), _1559577)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559575), hAPP(c_Set_OCollect(_1559575), hAPP(hAPP(c_COMBS(_1559575, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559575), c_fconj), _1559577)), _1559579)))))], (1272 ^ _779571) ^ [_798239, _798241] : [-(class_Lattices_Osemilattice__sup(_798239)), _798241 = _798239, class_Lattices_Osemilattice__sup(_798241)], (22352 ^ _779571) ^ [_1165404, _1165406] : [class_Rings_Osemiring__1(_1165404), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165404), _1165406) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1165404, hAPP(hAPP(c_COMBC(_1165404, _1165404, _1165404), c_Groups_Oplus__class_Oplus(_1165404)), c_Groups_Oone__class_Oone(_1165404)), _1165406, c_Groups_Ozero__class_Ozero(_1165404)))], (44197 ^ _779571) ^ [_1643857, _1643859, _1643861] : [class_Orderings_Olinorder(_1643857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643857), _1643859)), -(hBOOL(hAPP(hAPP(c_member(_1643857), _1643861), _1643859))), -(c_Big__Operators_Olinorder__class_OMax(_1643857, hAPP(hAPP(c_Set_Oinsert(_1643857), _1643861), _1643859)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643857, _1643857, c_Orderings_Oord__class_Omax(_1643857)), _1643861), _1643859))], (43405 ^ _779571) ^ [_1625255, _1625257, _1625259] : [-(hAPP(c_Relation_ORange(_1625255, _1625257), _1625259) = hAPP(c_Relation_ODomain(_1625257, _1625255), hAPP(c_Relation_Oconverse(_1625255, _1625257), _1625259)))], (37443 ^ _779571) ^ [_1478887, _1478889, _1478891] : [class_Orderings_Olinorder(_1478887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478887), _1478889)), -(_1478889 = c_Orderings_Obot__class_Obot(tc_fun(_1478887, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478887), _1478891)), -(_1478891 = c_Orderings_Obot__class_Obot(tc_fun(_1478887, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478887, tc_HOL_Obool)), _1478889), _1478891) = c_Orderings_Obot__class_Obot(tc_fun(_1478887, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1478887, c_Orderings_Oord__class_Omin(_1478887), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478887, tc_HOL_Obool)), _1478889), _1478891)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1478887), c_Big__Operators_Olattice_OInf__fin(_1478887, c_Orderings_Oord__class_Omin(_1478887), _1478889)), c_Big__Operators_Olattice_OInf__fin(_1478887, c_Orderings_Oord__class_Omin(_1478887), _1478891)))], (9522 ^ _779571) ^ [_937656, _937658] : [class_Groups_Ogroup__add(_937656), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937656), hAPP(c_Groups_Ouminus__class_Ouminus(_937656), _937658)), _937658) = c_Groups_Ozero__class_Ozero(_937656))], (29202 ^ _779571) ^ [_1301337, _1301339, _1301341] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301337, tc_HOL_Obool)), _1301339), _1301341) = c_Orderings_Obot__class_Obot(tc_fun(_1301337, tc_HOL_Obool))), _1301339 = c_Orderings_Obot__class_Obot(tc_fun(_1301337, tc_HOL_Obool)), _1301341 = c_Orderings_Obot__class_Obot(tc_fun(_1301337, tc_HOL_Obool))], (51409 ^ _779571) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (46722 ^ _779571) ^ [_1705146, _1705148] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1705146), _1705148))), -(c_Nitpick_Ocard_H(_1705146, _1705148) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25218 ^ _779571) ^ [_1221683, _1221685] : [-(_1221683 = _1221685), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221683), _1221685)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221685), _1221683))], (41243 ^ _779571) ^ [_1565886, _1565888, _1565890, _1565892, _1565894] : [class_Groups_Ocomm__monoid__add(_1565886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565888), _1565890)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565888, _1565886), _1565892), hAPP(c_Set_OCollect(_1565888), hAPP(hAPP(c_COMBS(_1565888, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565888), c_fconj), hAPP(hAPP(c_COMBC(_1565888, tc_fun(_1565888, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565888)), _1565890))), hAPP(hAPP(c_COMBC(_1565888, tc_fun(_1565888, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565888)), _1565894)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565888, _1565886), hAPP(hAPP(c_COMBC(_1565888, _1565886, _1565886), hAPP(hAPP(c_COMBS(_1565888, _1565886, tc_fun(_1565886, _1565886)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565886, tc_fun(_1565886, _1565886)), _1565888), c_If(_1565886)), hAPP(hAPP(c_COMBC(_1565888, tc_fun(_1565888, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565888)), _1565894))), _1565892)), c_Groups_Ozero__class_Ozero(_1565886))), _1565890))], (46002 ^ _779571) ^ [_1687076, _1687078, _1687080, _1687082, _1687084] : [-(c_Map_Omap__of(_1687076, _1687078, hAPP(hAPP(c_List_Omap(tc_prod(_1687076, _1687080), tc_prod(_1687076, _1687078)), hAPP(c_Product__Type_Oprod_Oprod__case(_1687076, _1687080, tc_prod(_1687076, _1687078)), hAPP(hAPP(c_COMBC(_1687076, tc_fun(_1687080, _1687078), tc_fun(_1687080, tc_prod(_1687076, _1687078))), hAPP(hAPP(c_COMBB(tc_fun(_1687078, tc_prod(_1687076, _1687078)), tc_fun(tc_fun(_1687080, _1687078), tc_fun(_1687080, tc_prod(_1687076, _1687078))), _1687076), c_COMBB(_1687078, tc_prod(_1687076, _1687078), _1687080)), c_Product__Type_OPair(_1687076, _1687078))), _1687082))), _1687084)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1687080), tc_Option_Ooption(_1687078), _1687076, hAPP(c_Option_Omap(_1687080, _1687078), _1687082)), c_Map_Omap__of(_1687076, _1687080, _1687084)))], (21855 ^ _779571) ^ [_1156519, _1156521] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156519), hAPP(c_Int_Onumber__class_Onumber__of(_1156519), c_Int_OMin)), _1156521) = hAPP(c_Groups_Ouminus__class_Ouminus(_1156519), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156519), c_Groups_Oone__class_Oone(_1156519)), _1156521))), class_Fields_Ofield__inverse__zero(_1156519), class_Int_Onumber__ring(_1156519)], (25106 ^ _779571) ^ [_1219821, _1219823] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219821), _1219823)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219823), _1219821)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1219821) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1219823))], (14910 ^ _779571) ^ [_1031057, _1031059, _1031061, _1031063] : [class_Divides_Osemiring__div(_1031057), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031057), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031057), _1031059), _1031061)), _1031061)), c_Divides_Odiv__class_Omod(_1031057, _1031059, _1031061))), _1031063) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031057), _1031059), _1031063))], (32709 ^ _779571) ^ [_1376310] : [class_Rings_Osemiring__1(_1376310), -(hBOOL(hAPP(hAPP(c_member(_1376310), c_Groups_Oone__class_Oone(_1376310)), c_Nat_Osemiring__1__class_ONats(_1376310))))], (10191 ^ _779571) ^ [_949254, _949256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _949254)), 10194 ^ _779571 : [(10201 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949254), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _949256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _949254)), _949256)))], (10195 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _949254)), _949256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949254), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _949256))))]]], (23115 ^ _779571) ^ [_1180544, _1180546, _1180548, _1180550, _1180552, _1180554] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180544, _1180546, _1180548), _1180550), hAPP(hAPP(c_Product__Type_OPair(_1180544, _1180546), _1180552), _1180554)) = hAPP(hAPP(_1180550, _1180552), _1180554))], (16102 ^ _779571) ^ [_1054671, _1054673, _1054675, _1054677, _1054679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054671), _1054673)), -(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), _1054671), _1054675)), _1054677)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054673), _1054675)), _1054679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054677), 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), _1054673), _1054671)), _1054675)), _1054679)))], (51087 ^ _779571) ^ [_1808214, _1808216] : [class_Lattices_Obounded__lattice(_1808214), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1808216, _1808214)))], (27498 ^ _779571) ^ [_1265619, _1265621] : [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)), _1265619)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1265619), _1265621)))], (34624 ^ _779571) ^ [_1413821, _1413823, _1413825, _1413827, _1413829] : [-(hBOOL(hAPP(hAPP(c_member(_1413821), _1413823), _1413825))), -(hAPP(c_Map_Orestrict__map(_1413821, _1413827, _1413829, _1413825), _1413823) = c_Option_Ooption_ONone(_1413827))], (3064 ^ _779571) ^ [_826505, _826507, _826509, _826511, _826513, _826515, _826517, _826519] : [-(c_Random__Sequence_ORandom(_826519, _826515, _826511, _826507) = c_Random__Sequence_ORandom(_826517, _826513, _826509, _826505)), _826519 = _826517, _826515 = _826513, _826511 = _826509, _826507 = _826505], (8934 ^ _779571) ^ [_927609, _927611] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _927609)), _927611) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _927609), _927611)))], (40152 ^ _779571) ^ [_1540076, _1540078, _1540080] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1540076, _1540078), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1540076, _1540078), _1540080), hAPP(c_COMBK(tc_fun(_1540078, tc_HOL_Obool), _1540076), c_Orderings_Otop__class_Otop(tc_fun(_1540078, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1540076, _1540078), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1540076, tc_HOL_Obool)), _1540080)), hAPP(c_COMBK(tc_fun(_1540078, tc_HOL_Obool), _1540076), c_Orderings_Otop__class_Otop(tc_fun(_1540078, tc_HOL_Obool)))))], (28835 ^ _779571) ^ [_1292381, _1292383, _1292385, _1292387, _1292389] : [28837 ^ _779571 : [(28840 ^ _779571) ^ [] : [hBOOL(hAPP(_1292389, 28836 ^ [_1292381, _1292383, _1292385, _1292387, _1292389]))], (28838 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292381), 28836 ^ [_1292381, _1292383, _1292385, _1292387, _1292389]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292383, tc_fun(_1292381, tc_HOL_Obool)), _1292385), _1292387))))]], 28841 ^ _779571 : [(28842 ^ _779571) ^ [_1292603] : [hBOOL(hAPP(hAPP(c_member(_1292383), _1292603), _1292385)), 28845 ^ _779571 : [(28846 ^ _779571) ^ [_1292700] : [hBOOL(hAPP(hAPP(c_member(_1292381), _1292700), hAPP(_1292387, _1292603))), -(hBOOL(hAPP(_1292389, _1292700)))]]]]], (50170 ^ _779571) ^ [_1788059, _1788061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1788059), _1788061)), -(c_List_Oupt(_1788059, _1788061) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1788059), c_List_Oupt(hAPP(c_Nat_OSuc, _1788059), _1788061)))], (18187 ^ _779571) ^ [_1092313, _1092315] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1092313), _1092315) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1092313 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1092313 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (8138 ^ _779571) ^ [_914400, _914402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _914400), _914402)), -(_914402 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914400), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8141 ^ [_914400, _914402]))))], (24093 ^ _779571) ^ [_1199064, _1199066, _1199068, _1199070, _1199072] : [-(c_Product__Type_Oprod_Oprod__size(_1199064, _1199066, _1199068, _1199070, _1199072) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1199068, hAPP(c_Product__Type_Ofst(_1199064, _1199066), _1199072))), hAPP(_1199070, hAPP(c_Product__Type_Osnd(_1199064, _1199066), _1199072)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45965 ^ _779571) ^ [_1686184, _1686186, _1686188, _1686190, _1686192] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1686184), tc_List_Olist(_1686186), tc_List_Olist(_1686188), hAPP(c_List_Omap(_1686184, _1686186), _1686190)), hAPP(c_List_Omap(_1686188, _1686184), _1686192)) = hAPP(c_List_Omap(_1686188, _1686186), hAPP(c_Fun_Ocomp(_1686184, _1686186, _1686188, _1686190), _1686192)))], (49628 ^ _779571) ^ [_1776229, _1776231, _1776233] : [-(_1776229 = c_List_Olist_ONil(_1776231)), -(c_List_Obutlast(_1776231, hAPP(hAPP(c_List_Oappend(_1776231), _1776233), _1776229)) = hAPP(hAPP(c_List_Oappend(_1776231), _1776233), c_List_Obutlast(_1776231, _1776229)))], (51689 ^ _779571) ^ [_1814698, _1814700] : [v_Q(_1814700, _1814698), 51692 ^ _779571 : [(51693 ^ _779571) ^ [_1814763] : [c_Natural_Oevaln(v_d, _1814698, v_n, _1814763), -(v_R(_1814700, _1814763))]]], (50188 ^ _779571) ^ [_1788333, _1788335] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1788333, _1788335)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1788333), _1788335))], (50270 ^ _779571) ^ [_1789549, _1789551] : [class_Orderings_Olinorder(_1789549), c_List_Olinorder__class_Osorted(_1789549, _1789551), -(c_List_Olinorder__class_Osorted(_1789549, hAPP(c_List_Otl(_1789549), _1789551)))], (48656 ^ _779571) ^ [_1754550, _1754552, _1754554, _1754556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754550), tc_List_Olist(_1754550))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754550), tc_List_Olist(_1754550)), _1754552), _1754554)), c_List_Olistrel1(_1754550, _1754556))), 48661 ^ _779571 : [(48666 ^ _779571) ^ [] : [-(_1754554 = hAPP(hAPP(c_List_Olist__update(_1754550, _1754552), 48660 ^ [_1754550, _1754552, _1754554, _1754556]), 48659 ^ [_1754550, _1754552, _1754554, _1754556]))], (48664 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48660 ^ [_1754550, _1754552, _1754554, _1754556]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754550)), _1754552))))], (48662 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1754550, _1754550)), hAPP(hAPP(c_Product__Type_OPair(_1754550, _1754550), hAPP(hAPP(c_List_Onth(_1754550), _1754552), 48660 ^ [_1754550, _1754552, _1754554, _1754556])), 48659 ^ [_1754550, _1754552, _1754554, _1754556])), _1754556)))]]], (20283 ^ _779571) ^ [_1128435, _1128437, _1128439] : [class_Fields_Olinordered__field(_1128435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128435), _1128437), c_Groups_Ozero__class_Ozero(_1128435))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128435), c_Groups_Ozero__class_Ozero(_1128435)), _1128439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128435), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128435), _1128437), _1128439)), c_Groups_Ozero__class_Ozero(_1128435))))], (23377 ^ _779571) ^ [_1185253, _1185255, _1185257, _1185259, _1185261, _1185263, _1185265] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185253, _1185255), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185257), _1185259))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185261, _1185255), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185263), _1185265))), -(_1185255 = 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), _1185253), _1185261), _1185255), 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), _1185257), _1185263)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1185259), _1185265)), _1185255))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1185259), _1185265), _1185255)))))], (23233 ^ _779571) ^ [_1183220, _1183222, _1183224, _1183226, _1183228] : [-(hAPP(c_Product__Type_Osnd(_1183220, _1183222), hAPP(c_Product__Type_Oapsnd(_1183224, _1183222, _1183220, _1183226), _1183228)) = hAPP(_1183226, hAPP(c_Product__Type_Osnd(_1183220, _1183224), _1183228)))], (27447 ^ _779571) ^ [_1264445, _1264447, _1264449] : [class_Groups_Oordered__ab__group__add(_1264445), -(hAPP(c_Set_Oimage(_1264445, _1264445, c_Groups_Ouminus__class_Ouminus(_1264445)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1264445, _1264447, _1264449)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1264445, hAPP(c_Groups_Ouminus__class_Ouminus(_1264445), _1264449)), hAPP(c_Groups_Ouminus__class_Ouminus(_1264445), _1264447)))], (16931 ^ _779571) ^ [_1070125, _1070127] : [class_Int_Onumber__ring(_1070125), -(hAPP(c_Int_Onumber__class_Onumber__of(_1070125), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1070127)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070125), hAPP(c_Int_Onumber__class_Onumber__of(_1070125), _1070127)))], (46146 ^ _779571) ^ [_1690801, _1690803, _1690805, _1690807] : [hAPP(c_Map_Omap__of(_1690801, _1690803, _1690805), _1690807) = c_Option_Ooption_ONone(_1690803), hBOOL(hAPP(hAPP(c_member(_1690801), _1690807), hAPP(c_Set_Oimage(tc_prod(_1690801, _1690803), _1690801, c_Product__Type_Ofst(_1690801, _1690803)), hAPP(c_List_Oset(tc_prod(_1690801, _1690803)), _1690805))))], (25758 ^ _779571) ^ [_1230656, _1230658, _1230660, _1230662] : [class_Divides_Osemiring__div(_1230656), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), _1230658), _1230660)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), _1230658), _1230662)), 25769 ^ _779571 : [(25776 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), _1230660), _1230662)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230656), _1230660), _1230658)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230656), _1230662), _1230658))))], (25770 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230656), _1230660), _1230658)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230656), _1230662), _1230658))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230656), _1230660), _1230662)))]]], (8167 ^ _779571) ^ [_914994] : [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), _914994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _914994)))], (13952 ^ _779571) ^ [_1014013, _1014015, _1014017] : [class_Lattices_Oboolean__algebra(_1014013), 13955 ^ _779571 : [(13962 ^ _779571) ^ [] : [_1014015 = _1014017, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1014013), _1014015) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014013), _1014017))], (13956 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1014013), _1014015) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014013), _1014017), -(_1014015 = _1014017)]]], (35432 ^ _779571) ^ [_1432576, _1432578, _1432580] : [-(hAPP(c_Relation_OImage(_1432576, _1432578, _1432580), c_Orderings_Obot__class_Obot(tc_fun(_1432576, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1432578, tc_HOL_Obool)))], (36544 ^ _779571) ^ [_1458462, _1458464, _1458466, _1458468] : [class_Lattices_Osemilattice__inf(_1458462), 36547 ^ _779571 : [(36556 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458462), _1458466), _1458468)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), _1458466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), _1458468))], (36548 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458462), _1458466), _1458468))), 36551 ^ _779571 : [(36554 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), _1458468)))], (36552 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458462), _1458464), _1458466)))]]]]], (21347 ^ _779571) ^ [_1146853, _1146855] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146853), _1146855), hAPP(c_Int_Onumber__class_Onumber__of(_1146853), c_Int_OBit1(c_Int_OPls))) = _1146855), class_Fields_Ofield(_1146853), class_Int_Onumber__ring(_1146853)], (45494 ^ _779571) ^ [_1675395, _1675397, _1675399, _1675401] : [class_Lattices_Osemilattice__sup(_1675395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1675395), _1675397)), 45504 ^ _779571 : [(45507 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675395), 45503 ^ [_1675395, _1675397, _1675399, _1675401]), _1675399))], (45505 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675395), 45503 ^ [_1675395, _1675397, _1675399, _1675401]), _1675397)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675395), hAPP(hAPP(c_Finite__Set_Ofold(_1675395, _1675395, c_Lattices_Osemilattice__sup__class_Osup(_1675395)), _1675401), _1675397)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1675395), _1675399), _1675401))))], (10434 ^ _779571) ^ [_953288, _953290, _953292] : [class_Orderings_Opreorder(_953288), _953290 = _953292, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953288), _953290), _953292)))], (9072 ^ _779571) ^ [_929961, _929963] : [class_Rings_Oring__1(_929961), 9075 ^ _779571 : [(9082 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _929963), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_929961), _929963) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929961), hAPP(c_Int_Onat, _929963)))], (9076 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _929963), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_929961), _929963) = hAPP(c_Groups_Ouminus__class_Ouminus(_929961), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929961), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929963)))))]]], (50580 ^ _779571) ^ [_1796253, _1796255] : [-(c_Fun_Oinj__on(tc_List_Olist(_1796253), tc_List_Olist(_1796253), c_List_Orev(_1796253), _1796255))], (7351 ^ _779571) ^ [_901587, _901589, _901591, _901593] : [hAPP(c_Sum__Type_OInr(_901587, _901589), _901591) = hAPP(c_Sum__Type_OInr(_901587, _901589), _901593), -(_901591 = _901593)], (45151 ^ _779571) ^ [_1667834, _1667836, _1667838, _1667840] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667834, tc_HOL_Obool), hAPP(c_Set_Oimage(_1667836, tc_fun(_1667834, tc_HOL_Obool), _1667838), _1667840)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667836, tc_fun(_1667834, tc_HOL_Obool)), _1667840), _1667838))], (40194 ^ _779571) ^ [_1541416, _1541418, _1541420, _1541422, _1541424] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1541416, _1541418), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541416, tc_HOL_Obool)), _1541420), _1541422)), hAPP(c_COMBK(tc_fun(_1541418, tc_HOL_Obool), _1541416), _1541424)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1541416, _1541418), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1541416, _1541418), _1541420), hAPP(c_COMBK(tc_fun(_1541418, tc_HOL_Obool), _1541416), _1541424))), hAPP(hAPP(c_Product__Type_OSigma(_1541416, _1541418), _1541422), hAPP(c_COMBK(tc_fun(_1541418, tc_HOL_Obool), _1541416), _1541424))))], (6770 ^ _779571) ^ [_890901, _890903, _890905, _890907] : [c_Com_Ocom_OSemi(_890901, _890903) = c_Com_Ocom_OAss(_890905, _890907)], (20179 ^ _779571) ^ [_1126514, _1126516, _1126518] : [class_Fields_Olinordered__field__inverse__zero(_1126514), 20182 ^ _779571 : [(20197 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126514), _1126516), _1126518)), c_Groups_Ozero__class_Ozero(_1126514)))), 20198 ^ _779571 : [(20205 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), _1126516), c_Groups_Ozero__class_Ozero(_1126514))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), c_Groups_Ozero__class_Ozero(_1126514)), _1126518))], (20199 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), c_Groups_Ozero__class_Ozero(_1126514)), _1126516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), _1126518), c_Groups_Ozero__class_Ozero(_1126514)))]]], (20183 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126514), _1126516), _1126518)), c_Groups_Ozero__class_Ozero(_1126514))), 20188 ^ _779571 : [(20191 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), _1126518), c_Groups_Ozero__class_Ozero(_1126514))))], (20189 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), c_Groups_Ozero__class_Ozero(_1126514)), _1126516)))]], 20192 ^ _779571 : [(20195 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), c_Groups_Ozero__class_Ozero(_1126514)), _1126518)))], (20193 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126514), _1126516), c_Groups_Ozero__class_Ozero(_1126514))))]]]]], (40685 ^ _779571) ^ [_1551870, _1551872, _1551874, _1551876] : [-(c_Fun_Oinj__on(_1551870, tc_prod(_1551872, _1551870), 40683 ^ [_1551870, _1551872, _1551874, _1551876], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551872, tc_fun(_1551870, tc_HOL_Obool)), _1551874), _1551876)))], (47799 ^ _779571) ^ [_1732747, _1732749, _1732751] : [class_Orderings_Olinorder(_1732747), -(hAPP(c_List_Oset(_1732747), c_List_Olinorder__class_Oinsort__insert__key(_1732747, _1732747, c_COMBI(_1732747), _1732749, _1732751)) = hAPP(hAPP(c_Set_Oinsert(_1732747), _1732749), hAPP(c_List_Oset(_1732747), _1732751)))], (6629 ^ _779571) ^ [_887952, _887954, _887956, _887958] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887952, _887954)), _887956), _887958))), 6630 ^ _779571 : [(6637 ^ _779571) ^ [] : [hBOOL(hAPP(_887952, _887956)), 6640 ^ _779571 : [(6641 ^ _779571) ^ [_888171] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887954), _887956), _888171)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887952, _887954)), _888171), _887958))]]], (6631 ^ _779571) ^ [] : [_887958 = _887956, -(hBOOL(hAPP(_887952, _887956)))]]], (19619 ^ _779571) ^ [_1116161, _1116163, _1116165] : [class_Rings_Olinordered__semidom(_1116161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116161), hAPP(hAPP(c_Power_Opower__class_Opower(_1116161), _1116163), 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(_1116161), _1116165), 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(_1116161), c_Groups_Ozero__class_Ozero(_1116161)), _1116165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116161), _1116163), _1116165)))], (7458 ^ _779571) ^ [_903330, _903332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903330), _903332)), _903332 = _903330], (40312 ^ _779571) ^ [_1544334, _1544336, _1544338, _1544340] : [-(_1544334 = c_Orderings_Obot__class_Obot(tc_fun(_1544336, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1544336, _1544338), _1544338, c_Product__Type_Osnd(_1544336, _1544338)), hAPP(hAPP(c_Product__Type_OSigma(_1544336, _1544338), _1544334), hAPP(c_COMBK(tc_fun(_1544338, tc_HOL_Obool), _1544336), _1544340))) = _1544340)], (36330 ^ _779571) ^ [_1454378, _1454380, _1454382] : [class_Lattices_Osemilattice__inf(_1454378), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454378), _1454380), _1454382) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454378), _1454382), _1454380))], (36644 ^ _779571) ^ [_1460395, _1460397, _1460399, _1460401, _1460403] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460395, tc_fun(_1460397, tc_HOL_Obool)), _1460399), hAPP(hAPP(c_COMBB(tc_fun(_1460397, tc_HOL_Obool), tc_fun(_1460397, tc_HOL_Obool), _1460395), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460397, tc_HOL_Obool)), _1460401)), _1460403)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460397, tc_HOL_Obool)), _1460401), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460395, tc_fun(_1460397, tc_HOL_Obool)), _1460399), _1460403)))], (46342 ^ _779571) ^ [_1694995, _1694997, _1694999] : [hBOOL(hAPP(c_List_Odistinct(_1694995), _1694997)), -(hBOOL(hAPP(c_List_Odistinct(_1694995), c_List_Oremove1(_1694995, _1694999, _1694997))))], (49408 ^ _779571) ^ [_1771937, _1771939, _1771941, _1771943, _1771945] : [class_Groups_Omonoid__add(_1771937), class_Groups_Oordered__ab__semigroup__add(_1771937), 49418 ^ _779571 : [(49421 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1771937), hAPP(_1771943, 49417 ^ [_1771937, _1771939, _1771941, _1771943, _1771945])), hAPP(_1771945, 49417 ^ [_1771937, _1771939, _1771941, _1771943, _1771945])))], (49419 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771939), 49417 ^ [_1771937, _1771939, _1771941, _1771943, _1771945]), hAPP(c_List_Oset(_1771939), _1771941))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1771937), hAPP(c_List_Omonoid__add__class_Olistsum(_1771937), hAPP(hAPP(c_List_Omap(_1771939, _1771937), _1771943), _1771941))), hAPP(c_List_Omonoid__add__class_Olistsum(_1771937), hAPP(hAPP(c_List_Omap(_1771939, _1771937), _1771945), _1771941)))))], (42565 ^ _779571) ^ [_1604812, _1604814] : [42566 ^ _779571 : [(42567 ^ _779571) ^ [_1604858] : [hBOOL(hAPP(_1604812, _1604858))]], -(hBOOL(hAPP(_1604812, c_Hilbert__Choice_OEps(_1604814, _1604812))))], (31564 ^ _779571) ^ [_1351936, _1351938, _1351940] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351936), _1351938)), 31567 ^ _779571 : [(31587 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351936, tc_Nat_Onat), _1351940), _1351938) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 31588 ^ _779571 : [(31589 ^ _779571) ^ [_1352417] : [hBOOL(hAPP(hAPP(c_member(_1351936), _1352417), _1351938)), hAPP(_1351940, _1352417) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31597 ^ _779571 : [(31602 ^ _779571) ^ [] : [hAPP(_1351940, 31596 ^ [_1351936, _1351938, _1351940, _1352417]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31600 ^ _779571) ^ [] : [_1352417 = 31596 ^ [_1351936, _1351938, _1351940, _1352417]], (31598 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351936), 31596 ^ [_1351936, _1351938, _1351940, _1352417]), _1351938)))]]]]], (31568 ^ _779571) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351936, tc_Nat_Onat), _1351940), _1351938) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31572 ^ _779571 : [(31577 ^ _779571) ^ [_1352256] : [hBOOL(hAPP(hAPP(c_member(_1351936), _1352256), _1351938)), -(31571 ^ [_1351936, _1351938, _1351940] = _1352256), -(hAPP(_1351940, _1352256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31575 ^ _779571) ^ [] : [-(hAPP(_1351940, 31571 ^ [_1351936, _1351938, _1351940]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31573 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351936), 31571 ^ [_1351936, _1351938, _1351940]), _1351938)))]]]]], (45582 ^ _779571) ^ [_1677490, _1677492, _1677494, _1677496, _1677498, _1677500, _1677502, _1677504] : [c_Finite__Set_Ofolding__image__simple__idem(_1677490, _1677492, _1677494, _1677496, _1677498, _1677500), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677492), _1677502)), hBOOL(hAPP(hAPP(c_member(_1677492), _1677504), _1677502)), -(hAPP(hAPP(_1677494, hAPP(_1677498, _1677504)), hAPP(_1677500, _1677502)) = hAPP(_1677500, _1677502))], (26142 ^ _779571) ^ [_1238487, _1238489, _1238491] : [class_Divides_Osemiring__div(_1238487), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238487), _1238489), _1238491)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238487), _1238489), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238487), _1238491), _1238489)) = _1238491)], (4798 ^ _779571) ^ [_853726, _853728] : [_853728 = _853726, -(c_Set_Oinsert(_853728) = c_Set_Oinsert(_853726))], (43883 ^ _779571) ^ [_1637665, _1637667, _1637669, _1637671, _1637673, _1637675] : [c_Finite__Set_Ofolding(_1637665, _1637667, _1637669, _1637671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1637665), _1637673)), -(hAPP(hAPP(_1637671, _1637673), _1637675) = hAPP(hAPP(c_Finite__Set_Ofold(_1637665, _1637667, _1637669), _1637675), _1637673))], (44450 ^ _779571) ^ [_1649228, _1649230, _1649232, _1649234] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1649228, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649230, tc_fun(_1649228, tc_HOL_Obool)), _1649232), _1649234)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649230, tc_fun(_1649228, tc_HOL_Obool)), _1649232), hAPP(hAPP(c_COMBB(tc_fun(_1649228, tc_HOL_Obool), tc_fun(_1649228, tc_HOL_Obool), _1649230), c_Groups_Ouminus__class_Ouminus(tc_fun(_1649228, tc_HOL_Obool))), _1649234)))], (3004 ^ _779571) ^ [_825517, _825519] : [_825519 = _825517, -(c_New__DSequence_Opos__empty(_825519) = c_New__DSequence_Opos__empty(_825517))], (8440 ^ _779571) ^ [_919407, _919409, _919411, _919413] : [class_Orderings_Oorder(_919407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919407), _919409), _919411)), _919409 = _919413, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919407), _919413), _919411)))], (6377 ^ _779571) ^ [_883237, _883239, _883241, _883243, _883245] : [c_Com_Ocom_OLocal(_883237, _883239, _883241) = c_Com_Ocom_OSemi(_883243, _883245)], (46728 ^ _779571) ^ [_1705212, _1705214, _1705216, _1705218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705212), tc_List_Olist(_1705212))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705212), tc_List_Olist(_1705212)), _1705214), _1705216)), c_List_Olistrel(_1705212, _1705218))), 46731 ^ _779571 : [(46734 ^ _779571) ^ [_1705548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1705212, _1705212)), _1705548), hAPP(c_List_Oset(tc_prod(_1705212, _1705212)), hAPP(hAPP(c_List_Ozip(_1705212, _1705212), _1705214), _1705216)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1705212, _1705212, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1705212, tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_fun(_1705212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1705212, tc_fun(tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_fun(_1705212, tc_HOL_Obool)), _1705212), c_COMBC(_1705212, tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1705212, tc_prod(_1705212, _1705212)), tc_fun(_1705212, tc_fun(tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_HOL_Obool)), _1705212), hAPP(c_COMBB(tc_prod(_1705212, _1705212), tc_fun(tc_fun(tc_prod(_1705212, _1705212), tc_HOL_Obool), tc_HOL_Obool), _1705212), c_member(tc_prod(_1705212, _1705212)))), c_Product__Type_OPair(_1705212, _1705212)))), _1705218)), _1705548)))], (46732 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705212)), _1705214) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705212)), _1705216))]]], (27980 ^ _779571) ^ [_1275141, _1275143, _1275145, _1275147, _1275149] : [class_Lattices_Olattice(_1275141), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275143, _1275141)), _1275145), _1275147), _1275149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275141), hAPP(_1275145, _1275149)), hAPP(_1275147, _1275149)))], (25934 ^ _779571) ^ [_1234088, _1234090, _1234092, _1234094, _1234096] : [class_Groups_Ocomm__monoid__add(_1234088), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234090, _1234088), hAPP(hAPP(c_COMBS(_1234090, _1234088, _1234088), hAPP(hAPP(c_COMBB(_1234088, tc_fun(_1234088, _1234088), _1234090), c_Groups_Oplus__class_Oplus(_1234088)), _1234092)), _1234094)), _1234096) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234090, _1234088), _1234092), _1234096)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234090, _1234088), _1234094), _1234096)))], (38185 ^ _779571) ^ [_1496312, _1496314, _1496316, _1496318, _1496320, _1496322, _1496324] : [c_Finite__Set_Ofolding__idem(_1496312, _1496314, _1496316, _1496318), -(hAPP(c_Fun_Ocomp(_1496314, _1496314, _1496320, hAPP(_1496316, _1496322)), hAPP(c_Fun_Ocomp(_1496314, _1496314, _1496320, hAPP(_1496316, _1496322)), _1496324)) = hAPP(c_Fun_Ocomp(_1496314, _1496314, _1496320, hAPP(_1496316, _1496322)), _1496324))], (6823 ^ _779571) ^ [_891989, _891991, _891993] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_891989, _891991, _891993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891991)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891993))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25550 ^ _779571) ^ [_1227039, _1227041] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227039), _1227041)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227041), _1227039))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227041), _1227039)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227039), _1227041)))], (50509 ^ _779571) ^ [_1794199, _1794201, _1794203, _1794205, _1794207] : [class_Orderings_Olinorder(_1794199), c_Fun_Oinj__on(_1794201, _1794199, _1794203, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1794201, tc_HOL_Obool)), hAPP(c_List_Oset(_1794201), _1794205)), hAPP(c_List_Oset(_1794201), _1794207))), c_List_Olinorder__class_Osorted(_1794199, hAPP(hAPP(c_List_Omap(_1794201, _1794199), _1794203), _1794205)), hBOOL(hAPP(c_List_Odistinct(_1794199), hAPP(hAPP(c_List_Omap(_1794201, _1794199), _1794203), _1794205))), c_List_Olinorder__class_Osorted(_1794199, hAPP(hAPP(c_List_Omap(_1794201, _1794199), _1794203), _1794207)), hBOOL(hAPP(c_List_Odistinct(_1794199), hAPP(hAPP(c_List_Omap(_1794201, _1794199), _1794203), _1794207))), hAPP(c_List_Oset(_1794201), _1794205) = hAPP(c_List_Oset(_1794201), _1794207), -(_1794205 = _1794207)], (11439 ^ _779571) ^ [_969460, _969462, _969464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969462), _969464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969460), _969462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969460), _969464))))], (480 ^ _779571) ^ [_786953, _786955, _786957, _786959, _786961, _786963] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_786961, _786957, _786953)), c_Hoare__Mirabelle_Ohoare__derivs(_786963, _786959, _786955), _786963 = _786961, _786959 = _786957, _786955 = _786953], (16595 ^ _779571) ^ [_1063452, _1063454] : [class_Groups_Oordered__ab__group__add__abs(_1063452), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063452), c_Groups_Ozero__class_Ozero(_1063452)), hAPP(c_Groups_Oabs__class_Oabs(_1063452), _1063454))))], (12365 ^ _779571) ^ [_986017] : [-(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), _986017))))], (45477 ^ _779571) ^ [_1675031, _1675033, _1675035, _1675037] : [class_Lattices_Osemilattice__inf(_1675031), hBOOL(hAPP(c_Finite__Set_Ofinite(_1675031), _1675033)), 45487 ^ _779571 : [(45490 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675031), _1675035), 45486 ^ [_1675031, _1675033, _1675035, _1675037]))], (45488 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675031), 45486 ^ [_1675031, _1675033, _1675035, _1675037]), _1675033)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675031), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1675031), _1675035), _1675037)), hAPP(hAPP(c_Finite__Set_Ofold(_1675031, _1675031, c_Lattices_Osemilattice__inf__class_Oinf(_1675031)), _1675037), _1675033))))], (39172 ^ _779571) ^ [_1516792, _1516794, _1516796, _1516798, _1516800, _1516802, _1516804] : [c_Finite__Set_Ofolding__image(_1516792, _1516794, _1516796, _1516798, _1516800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516794), _1516802)), -(hAPP(hAPP(_1516800, _1516804), _1516802) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516792, _1516794, _1516796), _1516804), _1516798), _1516802))], (44730 ^ _779571) ^ [_1657736, _1657738, _1657740, _1657742] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657736, tc_fun(_1657738, tc_HOL_Obool)), _1657740), _1657742) = hAPP(c_Set_OCollect(_1657738), hAPP(hAPP(c_COMBB(tc_fun(_1657736, tc_HOL_Obool), tc_HOL_Obool, _1657738), c_HOL_OAll(_1657736)), hAPP(hAPP(c_COMBB(tc_fun(_1657736, tc_HOL_Obool), tc_fun(_1657736, tc_HOL_Obool), _1657738), hAPP(c_COMBS(_1657736, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1657736), c_fimplies), hAPP(hAPP(c_COMBC(_1657736, tc_fun(_1657736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1657736)), _1657740)))), hAPP(hAPP(c_COMBC(_1657738, tc_fun(_1657736, tc_fun(_1657738, tc_HOL_Obool)), tc_fun(_1657736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1657738, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1657736, tc_fun(_1657738, tc_HOL_Obool)), tc_fun(_1657736, tc_HOL_Obool)), _1657738), c_COMBB(tc_fun(_1657738, tc_HOL_Obool), tc_HOL_Obool, _1657736)), c_member(_1657738))), _1657742)))))], (37293 ^ _779571) ^ [_1476040, _1476042, _1476044] : [class_Lattices_Olattice(_1476040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476040), _1476042)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476040), _1476044)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476040, tc_HOL_Obool)), _1476042), _1476044) = c_Orderings_Obot__class_Obot(tc_fun(_1476040, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1476040), c_Big__Operators_Olattice__class_OSup__fin(_1476040, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476040, tc_HOL_Obool)), _1476042), _1476044))), c_Big__Operators_Olattice__class_OSup__fin(_1476040, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476040, tc_HOL_Obool)), _1476042), _1476044))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1476040), c_Big__Operators_Olattice__class_OSup__fin(_1476040, _1476042)), c_Big__Operators_Olattice__class_OSup__fin(_1476040, _1476044)))], (45045 ^ _779571) ^ [_1665292, _1665294] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665292, tc_HOL_Obool), hAPP(c_Set_OPow(_1665292), _1665294)) = _1665294)], (29280 ^ _779571) ^ [_1302876, _1302878] : [class_Orderings_Obot(_1302876), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302876), c_Orderings_Obot__class_Obot(_1302876)), _1302878)))], (14748 ^ _779571) ^ [_1028174, _1028176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028176), 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), _1028174), _1028176)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19065 ^ _779571) ^ [_1106345, _1106347] : [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), _1106345))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1106347)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106345))) = 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), _1106347), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106345)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1152 ^ _779571) ^ [_796739, _796741] : [-(class_Int_Oring__char__0(_796739)), _796741 = _796739, class_Int_Oring__char__0(_796741)], (11883 ^ _779571) ^ [_977451, _977453, _977455, _977457] : [class_Rings_Oordered__semiring(_977451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977451), _977453), _977455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977451), c_Groups_Ozero__class_Ozero(_977451)), _977457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977451), _977457), _977453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977451), _977457), _977455))))], (32169 ^ _779571) ^ [_1364959, _1364961] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1364959), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1364961))), 32172 ^ _779571 : [(32175 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364959), _1364961))], (32173 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364961), _1364959)))]]], (43869 ^ _779571) ^ [_1637445, _1637447, _1637449] : [class_Orderings_Olinorder(_1637445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1637445), _1637447)), -(hBOOL(hAPP(hAPP(c_member(_1637445), _1637449), _1637447))), -(c_Big__Operators_Olattice_OSup__fin(_1637445, c_Orderings_Oord__class_Omax(_1637445), hAPP(hAPP(c_Set_Oinsert(_1637445), _1637449), _1637447)) = hAPP(hAPP(c_Finite__Set_Ofold(_1637445, _1637445, c_Orderings_Oord__class_Omax(_1637445)), _1637449), _1637447))], (31852 ^ _779571) ^ [_1357998, _1358000, _1358002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1357998), _1358000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1357998), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357998, tc_HOL_Obool)), _1358000), hAPP(hAPP(c_Set_Oinsert(_1357998), _1358002), c_Orderings_Obot__class_Obot(tc_fun(_1357998, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1357998), _1358000))))], (25714 ^ _779571) ^ [_1229862, _1229864, _1229866, _1229868, _1229870] : [class_Rings_Ocomm__semiring__1(_1229862), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229862), _1229864), _1229866)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229862), _1229868), _1229870)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229862), _1229864), _1229868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229862), _1229866), _1229870))))], (42143 ^ _779571) ^ [_1594600, _1594602, _1594604, _1594606] : [42144 ^ _779571 : [(42145 ^ _779571) ^ [_1594675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594604, _1594600)), hAPP(hAPP(c_Product__Type_OPair(_1594604, _1594600), _1594675), _1594602)), _1594606))]], -(hBOOL(hAPP(hAPP(c_member(_1594600), _1594602), hAPP(c_Relation_ORange(_1594604, _1594600), _1594606))))], (2336 ^ _779571) ^ [_814837, _814839, _814841, _814843, _814845, _814847] : [-(c_Power_Opower_Opower(_814847, _814843, _814839) = c_Power_Opower_Opower(_814845, _814841, _814837)), _814847 = _814845, _814843 = _814841, _814839 = _814837], (39577 ^ _779571) ^ [_1526057, _1526059, _1526061, _1526063, _1526065, _1526067] : [-(hBOOL(hAPP(hAPP(c_member(_1526057), _1526059), _1526061))), 39580 ^ _779571 : [(39587 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526057), _1526063), _1526061))), -(hAPP(c_Set_Ovimage(_1526065, _1526057, hAPP(hAPP(c_COMBC(_1526065, _1526057, _1526057), hAPP(hAPP(c_COMBC(_1526065, _1526057, tc_fun(_1526057, _1526057)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1526057, tc_fun(_1526057, _1526057)), _1526065), c_If(_1526057)), hAPP(hAPP(c_COMBC(_1526065, tc_fun(_1526065, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526065)), _1526067))), _1526059)), _1526063)), _1526061) = c_Orderings_Obot__class_Obot(tc_fun(_1526065, tc_HOL_Obool)))], (39581 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1526057), _1526063), _1526061)), -(hAPP(c_Set_Ovimage(_1526065, _1526057, hAPP(hAPP(c_COMBC(_1526065, _1526057, _1526057), hAPP(hAPP(c_COMBC(_1526065, _1526057, tc_fun(_1526057, _1526057)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1526057, tc_fun(_1526057, _1526057)), _1526065), c_If(_1526057)), hAPP(hAPP(c_COMBC(_1526065, tc_fun(_1526065, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526065)), _1526067))), _1526059)), _1526063)), _1526061) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1526065, tc_HOL_Obool)), _1526067))]]], (29854 ^ _779571) ^ [_1313559, _1313561] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1313559), _1313561)), -(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)))), _1313561, _1313559) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (13440 ^ _779571) ^ [_1004687, _1004689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004687), _1004689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004689), _1004687)), -(_1004687 = _1004689)], (5136 ^ _779571) ^ [_858947, _858949] : [_858949 = _858947, -(c_List_Ohd(_858949) = c_List_Ohd(_858947))], (44594 ^ _779571) ^ [_1653985, _1653987, _1653989, _1653991, _1653993, _1653995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653985, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1653987, _1653985, _1653989), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653991, tc_fun(_1653987, tc_HOL_Obool)), _1653993), _1653995))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653991, tc_fun(_1653985, tc_HOL_Obool)), _1653993), hAPP(hAPP(c_COMBB(tc_fun(_1653987, tc_HOL_Obool), tc_fun(_1653985, tc_HOL_Obool), _1653991), c_Relation_OImage(_1653987, _1653985, _1653989)), _1653995)))))], (50005 ^ _779571) ^ [_1785054, _1785056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1785054), _1785056)), -(c_List_Oupt(_1785056, _1785054) = c_List_Olist_ONil(tc_Nat_Onat))], (45378 ^ _779571) ^ [_1672947, _1672949, _1672951, _1672953] : [-(_1672947 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1672949, tc_HOL_Obool), tc_HOL_Obool))), 45384 ^ _779571 : [(45387 ^ _779571) ^ [] : [c_Fun_Oinj__on(_1672949, _1672951, _1672953, 45383 ^ [_1672947, _1672949, _1672951, _1672953])], (45385 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1672949, tc_HOL_Obool)), 45383 ^ [_1672947, _1672949, _1672951, _1672953]), _1672947)))]], -(c_Fun_Oinj__on(_1672949, _1672951, _1672953, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1672949, tc_HOL_Obool), _1672947)))], (3324 ^ _779571) ^ [_830607, _830609, _830611, _830613, _830615, _830617] : [-(c_SetInterval_Oord_OatLeast(_830617, _830613, _830609) = c_SetInterval_Oord_OatLeast(_830615, _830611, _830607)), _830617 = _830615, _830613 = _830611, _830609 = _830607], (35476 ^ _779571) ^ [_1433776, _1433778, _1433780, _1433782, _1433784, _1433786, _1433788] : [-(hAPP(c_Fun_Ocomp(_1433776, _1433778, _1433780, _1433782), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1433780, _1433776), _1433784), _1433786), _1433788)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1433780, _1433778), hAPP(c_Fun_Ocomp(_1433776, _1433778, _1433780, _1433782), _1433784)), _1433786), hAPP(_1433782, _1433788)))], (6805 ^ _779571) ^ [_891670] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _891670)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9346 ^ _779571) ^ [_934243, _934245, _934247, _934249] : [class_Rings_Ocomm__semiring__1(_934243), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934243), _934245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934243), _934247), _934249)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934243), _934245), _934247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934243), _934245), _934249)))], (23481 ^ _779571) ^ [_1187220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187220)), 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), _1187220)) = 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), _1187220))))))], (6311 ^ _779571) ^ [_881980, _881982, _881984] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_881980, _881982, _881984))), 6314 ^ _779571 : [(6317 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _881984)))], (6315 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _881982)))]]], (6544 ^ _779571) ^ [_886359, _886361, _886363, _886365] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886359), _886361), _886363)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886359), _886361), _886365)), -(_886365 = _886363)], (50946 ^ _779571) ^ [_1805545, _1805547, _1805549, _1805551, _1805553] : [-(hAPP(hAPP(c_List_Ozip(_1805545, _1805547), c_List_OtakeWhile(_1805545, _1805549, _1805551)), _1805553) = c_List_OtakeWhile(tc_prod(_1805545, _1805547), hAPP(c_Fun_Ocomp(_1805545, tc_HOL_Obool, tc_prod(_1805545, _1805547), _1805549), c_Product__Type_Ofst(_1805545, _1805547)), hAPP(hAPP(c_List_Ozip(_1805545, _1805547), _1805551), _1805553)))], (22406 ^ _779571) ^ [_1166706, _1166708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1166706)), hAPP(c_Code__Numeral_Oof__nat, _1166708))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1166706), _1166708)))], (10275 ^ _779571) ^ [_950756, _950758, _950760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950756), _950758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950756), _950760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950758), _950760))))], (23487 ^ _779571) ^ [_1187353, _1187355, _1187357] : [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), _1187353), _1187355))), -(hBOOL(hAPP(hAPP(_1187357, _1187353), _1187355))), 23494 ^ _779571 : [(23497 ^ _779571) ^ [] : [-(23493 ^ [_1187353, _1187355, _1187357] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1187357, 23493 ^ [_1187353, _1187355, _1187357]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23492 ^ [_1187353, _1187355, _1187357], 23493 ^ [_1187353, _1187355, _1187357]))))], (23503 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1187357, 23492 ^ [_1187353, _1187355, _1187357]), 23493 ^ [_1187353, _1187355, _1187357]))], (23495 ^ _779571) ^ [] : [-(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), 23492 ^ [_1187353, _1187355, _1187357]), 23493 ^ [_1187353, _1187355, _1187357]))))]]], (43102 ^ _779571) ^ [_1618062, _1618064, _1618066] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618062, _1618062)), hAPP(hAPP(c_Product__Type_OPair(_1618062, _1618062), _1618064), _1618066)), c_Relation_OId(_1618062))), -(_1618064 = _1618066)], (42597 ^ _779571) ^ [_1605457, _1605459] : [42599 ^ _779571 : [(42602 ^ _779571) ^ [] : [42598 ^ [_1605457, _1605459] = c_Orderings_Obot__class_Obot(tc_fun(_1605457, tc_HOL_Obool))], (42600 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605457, tc_HOL_Obool)), 42598 ^ [_1605457, _1605459]), hAPP(c_Relation_OImage(_1605457, _1605457, _1605459), 42598 ^ [_1605457, _1605459]))))]], -(c_Wellfounded_Owf(_1605457, _1605459))], (6786 ^ _779571) ^ [_891310, _891312, _891314, _891316, _891318] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_891310, _891312, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_891310), _891314), _891316), _891318)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51563 ^ _779571) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (29067 ^ _779571) ^ [_1298017, _1298019, _1298021, _1298023] : [hAPP(c_Set_Oimage(_1298017, _1298019, _1298021), c_Orderings_Otop__class_Otop(tc_fun(_1298017, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1298019, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298019, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298019, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1298017, _1298019, _1298021), _1298023))), hAPP(c_Set_Oimage(_1298017, _1298019, _1298021), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298017, tc_HOL_Obool)), _1298023)))))], (1532 ^ _779571) ^ [_801489, _801491] : [-(class_Rings_Oordered__semiring(_801489)), _801491 = _801489, class_Rings_Oordered__semiring(_801491)], (18705 ^ _779571) ^ [_1100515, _1100517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100515)), c_Int_OBit1(_1100517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100515), _1100517)))], (15934 ^ _779571) ^ [_1050963, _1050965, _1050967, _1050969, _1050971, _1050973] : [class_Rings_Oordered__ring(_1050963), 15937 ^ _779571 : [(15944 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050963), _1050969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050963), _1050971), _1050965)), _1050967)), _1050973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), _1050965), _1050967)), _1050969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), _1050971), _1050967)), _1050973))))], (15938 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), _1050965), _1050967)), _1050969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), _1050971), _1050967)), _1050973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050963), _1050969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050963), _1050971), _1050965)), _1050967)), _1050973))))]]], (31035 ^ _779571) ^ [_1338359, _1338361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1338359, _1338361)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1338359, _1338361), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338361), c_Orderings_Otop__class_Otop(tc_fun(_1338361, tc_HOL_Obool)))))], (33441 ^ _779571) ^ [_1389223, _1389225] : [class_Groups_Olinordered__ab__group__add(_1389223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389223), _1389225)), -(_1389225 = c_Orderings_Obot__class_Obot(tc_fun(_1389223, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1389223), c_Big__Operators_Olinorder__class_OMin(_1389223, _1389225)) = c_Big__Operators_Olinorder__class_OMax(_1389223, hAPP(c_Set_Oimage(_1389223, _1389223, c_Groups_Ouminus__class_Ouminus(_1389223)), _1389225)))], (47069 ^ _779571) ^ [_1716016, _1716018, _1716020] : [class_Groups_Omonoid__add(_1716016), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716016), hAPP(hAPP(c_List_Omap(_1716018, _1716016), hAPP(c_COMBK(_1716016, _1716018), c_Groups_Ozero__class_Ozero(_1716016))), _1716020)) = c_Groups_Ozero__class_Ozero(_1716016))], (6171 ^ _779571) ^ [_879303, _879305, _879307, _879309, _879311, _879313, _879315, _879317, _879319, _879321, _879323] : [-(c_Com_Ocom_Ocom__rec(_879303, _879305, _879307, _879309, _879311, _879313, _879315, _879317, _879319, c_Com_Ocom_OSemi(_879321, _879323)) = hAPP(hAPP(hAPP(hAPP(_879311, _879321), _879323), c_Com_Ocom_Ocom__rec(_879303, _879305, _879307, _879309, _879311, _879313, _879315, _879317, _879319, _879321)), c_Com_Ocom_Ocom__rec(_879303, _879305, _879307, _879309, _879311, _879313, _879315, _879317, _879319, _879323)))], (16130 ^ _779571) ^ [_1055335, _1055337] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055335, _1055337) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055335, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1055337)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055335, _1055337)), _1055337))], (10628 ^ _779571) ^ [_956388, _956390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956388), _956390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956388)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956390))))], (49937 ^ _779571) ^ [_1783862, _1783864, _1783866] : [class_Orderings_Olinorder(_1783862), -(c_List_Olinorder__class_Osorted(_1783862, hAPP(c_List_Ofilter(_1783862, hAPP(hAPP(c_COMBC(_1783862, _1783862, tc_HOL_Obool), c_fequal), hAPP(_1783864, _1783866))), _1783866)))], (9904 ^ _779571) ^ [_944549, _944551] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944549)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944551)), _944549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _944551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27962 ^ _779571) ^ [_1274709, _1274711] : [class_Lattices_Olattice(_1274709), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274709), _1274711), _1274711) = _1274711)], (7874 ^ _779571) ^ [_910249, _910251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910249), hAPP(c_Nat_OSuc, _910251))), -(_910249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7882 ^ _779571 : [(7885 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 7881 ^ [_910249, _910251]), _910251)))], (7883 ^ _779571) ^ [] : [-(_910249 = hAPP(c_Nat_OSuc, 7881 ^ [_910249, _910251]))]]], (20109 ^ _779571) ^ [_1125438, _1125440] : [c_Nat__Transfer_Ois__nat(_1125438), c_Nat__Transfer_Ois__nat(_1125440), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125438), _1125440)))], (26660 ^ _779571) ^ [_1248452, _1248454] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248452), _1248454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1248452), _1248454)))], (20063 ^ _779571) ^ [_1124557, _1124559, _1124561] : [class_Fields_Ofield__inverse__zero(_1124557), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124557), hAPP(c_Groups_Ouminus__class_Ouminus(_1124557), _1124559)), hAPP(c_Groups_Ouminus__class_Ouminus(_1124557), _1124561)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124557), _1124559), _1124561))], (48327 ^ _779571) ^ [_1745322, _1745324, _1745326, _1745328, _1745330] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1745322, _1745324)), _1745326), hAPP(hAPP(c_List_Ozip(_1745322, _1745324), _1745328), _1745330)) = hAPP(hAPP(c_List_Ozip(_1745322, _1745324), hAPP(hAPP(c_List_Otake(_1745322), _1745326), _1745328)), hAPP(hAPP(c_List_Otake(_1745324), _1745326), _1745330)))], (43451 ^ _779571) ^ [_1626610, _1626612, _1626614] : [c_Relation_Orefl__on(_1626610, _1626612, _1626614), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626610, _1626610), tc_HOL_Obool)), _1626614), hAPP(hAPP(c_Relation_Orel__comp(_1626610, _1626610, _1626610), hAPP(c_Relation_Oconverse(_1626610, _1626610), _1626614)), _1626614))))], (51525 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (17153 ^ _779571) ^ [_1074442, _1074444, _1074446, _1074448] : [class_Rings_Olinordered__semidom(_1074442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074444), _1074446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074442), c_Groups_Ozero__class_Ozero(_1074442)), _1074448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074442), _1074448), c_Groups_Oone__class_Oone(_1074442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074442), hAPP(hAPP(c_Power_Opower__class_Opower(_1074442), _1074448), _1074446)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074442), _1074448), _1074444))))], (14526 ^ _779571) ^ [_1024575, _1024577, _1024579] : [-(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), _1024575), _1024577)), _1024579), _1024577) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024579, _1024577))], (43520 ^ _779571) ^ [_1628284, _1628286, _1628288, _1628290] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628284, _1628284), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1628286), _1628288)), _1628290) = hAPP(hAPP(c_Relation_Orel__comp(_1628284, _1628284, _1628284), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628284, _1628284), tc_HOL_Obool), _1628286), _1628290)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628284, _1628284), tc_HOL_Obool), _1628288), _1628290)))], (18789 ^ _779571) ^ [_1101867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101867), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1101867)), c_Int_OPls)))], (23889 ^ _779571) ^ [_1194939, _1194941] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1194939), _1194941) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1194939, _1194941)))], (22864 ^ _779571) ^ [_1176047, _1176049] : [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), _1176047), _1176049))), 22867 ^ _779571 : [(22876 ^ _779571) ^ [] : [-(c_Divides_OposDivAlg(_1176047, _1176049) = hAPP(c_Divides_Oadjust(_1176049), c_Divides_OposDivAlg(_1176047, 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)))), _1176049)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176047), _1176049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176049), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22868 ^ _779571) ^ [] : [22869 ^ _779571 : [(22872 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176049), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22870 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176047), _1176049))]], -(c_Divides_OposDivAlg(_1176047, _1176049) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176047))]]], (21307 ^ _779571) ^ [_1146131, _1146133, _1146135] : [class_Fields_Olinordered__field(_1146131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146131), _1146133), _1146135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146131), _1146133), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146131), _1146133), _1146135)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146131), c_Groups_Oone__class_Oone(_1146131)), c_Groups_Oone__class_Oone(_1146131))))))], (51219 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (43192 ^ _779571) ^ [_1620225] : [-(hAPP(c_Relation_ORange(_1620225, _1620225), c_Relation_OId(_1620225)) = c_Orderings_Otop__class_Otop(tc_fun(_1620225, tc_HOL_Obool)))], (40930 ^ _779571) ^ [_1558508, _1558510] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1558508), c_Int_OInteg)), hBOOL(hAPP(_1558510, hAPP(c_Int_ORep__Integ, 40935 ^ [_1558508, _1558510]))), -(hBOOL(hAPP(_1558510, _1558508)))], (44169 ^ _779571) ^ [_1643429, _1643431, _1643433] : [class_Lattices_Olattice(_1643429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643429), _1643431)), -(hBOOL(hAPP(hAPP(c_member(_1643429), _1643433), _1643431))), -(c_Big__Operators_Olattice__class_OInf__fin(_1643429, hAPP(hAPP(c_Set_Oinsert(_1643429), _1643433), _1643431)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643429, _1643429, c_Lattices_Osemilattice__inf__class_Oinf(_1643429)), _1643433), _1643431))], (50354 ^ _779571) ^ [_1791058, _1791060, _1791062, _1791064, _1791066, _1791068] : [class_Orderings_Olinorder(_1791058), c_List_Olinorder__class_Osorted(_1791058, hAPP(hAPP(c_List_Omap(_1791060, _1791058), _1791062), _1791064)), hBOOL(hAPP(_1791066, _1791068)), -(hAPP(c_List_Ofilter(_1791060, _1791066), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1791060, _1791058, _1791062), _1791068), _1791064)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1791060, _1791058, _1791062), _1791068), hAPP(c_List_Ofilter(_1791060, _1791066), _1791064)))], (2816 ^ _779571) ^ [_822297, _822299, _822301, _822303] : [-(c_Nitpick_Oinverse__frac(_822303, _822299) = c_Nitpick_Oinverse__frac(_822301, _822297)), _822303 = _822301, _822299 = _822297], (46286 ^ _779571) ^ [_1693985, _1693987] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1693985, _1693987))))], (45137 ^ _779571) ^ [_1667395, _1667397, _1667399] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667395, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667395, tc_HOL_Obool), _1667397)), _1667399) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1667395, tc_HOL_Obool), tc_fun(_1667395, tc_HOL_Obool)), _1667397), hAPP(hAPP(c_COMBC(tc_fun(_1667395, tc_HOL_Obool), tc_fun(_1667395, tc_HOL_Obool), tc_fun(_1667395, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667395, tc_HOL_Obool))), _1667399)))], (6679 ^ _779571) ^ [_888932, _888934, _888936, _888938, _888940] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_888932, _888934, _888936)), _888938), _888940)), 6684 ^ _779571 : [(6687 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888934), _888938), _888940)))], (6685 ^ _779571) ^ [] : [-(hBOOL(hAPP(_888932, _888938)))]], 6688 ^ _779571 : [(6691 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888936), _888938), _888940)))], (6689 ^ _779571) ^ [] : [hBOOL(hAPP(_888932, _888938))]]], (6907 ^ _779571) ^ [_893544, _893546] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _893544)), _893546) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893544), _893546)))], (4672 ^ _779571) ^ [_851837, _851839] : [_851839 = _851837, -(c_Orderings_Oord__class_Omin(_851839) = c_Orderings_Oord__class_Omin(_851837))], (51357 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (48339 ^ _779571) ^ [_1745623, _1745625, _1745627] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745623, tc_HOL_Obool)), hAPP(c_List_Oset(_1745623), hAPP(hAPP(c_List_Otake(_1745623), _1745625), _1745627))), hAPP(c_List_Oset(_1745623), _1745627))))], (51363 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (24771 ^ _779571) ^ [_1212195, _1212197, _1212199, _1212201, _1212203] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1212195, _1212197, _1212199, hAPP(c_COMBK(_1212197, _1212195), _1212201), hAPP(c_COMBK(_1212197, _1212199), _1212201)), _1212203) = _1212201)], (11194 ^ _779571) ^ [_965384, _965386, _965388] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965384)), _965386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965384)), _965388), -(_965386 = _965388)], (25688 ^ _779571) ^ [_1229397, _1229399, _1229401] : [class_Rings_Ocomm__semiring__1(_1229397), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229397), _1229399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229397), _1229401), _1229399))))], (13789 ^ _779571) ^ [_1011212] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1011212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7508 ^ _779571) ^ [_903943, _903945, _903947, _903949] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_903943), 7511 ^ _779571 : [(7518 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903943), _903945), _903949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903943), _903945), _903947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903943), _903949), _903947))))], (7512 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903943), _903945), _903947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903943), _903949), _903947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903943), _903945), _903949)))]]], (15382 ^ _779571) ^ [_1039983, _1039985] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039983), _1039985) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039985), _1039983) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1039983 = _1039985)], (7918 ^ _779571) ^ [_910934] : [7919 ^ _779571 : [(7920 ^ _779571) ^ [_910976] : [_910934 = hAPP(c_Nat_OSuc, _910976)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _910934)))], (39751 ^ _779571) ^ [_1529785, _1529787, _1529789, _1529791] : [-(c_Map_Odom(_1529785, _1529787, c_Map_Orestrict__map(_1529785, _1529787, _1529789, _1529791)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529785, tc_HOL_Obool)), c_Map_Odom(_1529785, _1529787, _1529789)), _1529791))], (23717 ^ _779571) ^ [_1191518, _1191520, _1191522, _1191524] : [class_Orderings_Olinorder(_1191518), 23720 ^ _779571 : [(23721 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191518), _1191520), _1191522)), _1191524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), _1191520), _1191524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), _1191522), _1191524)))], (23731 ^ _779571) ^ [] : [23732 ^ _779571 : [(23735 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), _1191522), _1191524))], (23733 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), _1191520), _1191524))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191518), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191518), _1191520), _1191522)), _1191524)))]]], (24661 ^ _779571) ^ [_1210262, _1210264] : [hAPP(c_Code__Numeral_Onat__of, _1210262) = hAPP(c_Code__Numeral_Onat__of, _1210264), -(_1210262 = _1210264)], (3372 ^ _779571) ^ [_831387, _831389, _831391, _831393] : [-(c_FunDef_Orp__inv__image(_831393, _831389) = c_FunDef_Orp__inv__image(_831391, _831387)), _831393 = _831391, _831389 = _831387], (47075 ^ _779571) ^ [_1716141, _1716143] : [class_Groups_Oordered__ab__group__add__abs(_1716141), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716141), hAPP(c_Groups_Oabs__class_Oabs(_1716141), hAPP(c_List_Omonoid__add__class_Olistsum(_1716141), _1716143))), hAPP(c_List_Omonoid__add__class_Olistsum(_1716141), hAPP(hAPP(c_List_Omap(_1716141, _1716141), c_Groups_Oabs__class_Oabs(_1716141)), _1716143)))))], (25400 ^ _779571) ^ [_1224569, _1224571, _1224573] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224569), _1224571)), 25411 ^ _779571 : [(25414 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224573), _1224569))], (25412 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224569), _1224573)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224571), _1224573)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224573), _1224571)))], (44155 ^ _779571) ^ [_1643215, _1643217, _1643219] : [class_Lattices_Olattice(_1643215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643215), _1643217)), -(hBOOL(hAPP(hAPP(c_member(_1643215), _1643219), _1643217))), -(c_Big__Operators_Olattice__class_OSup__fin(_1643215, hAPP(hAPP(c_Set_Oinsert(_1643215), _1643219), _1643217)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643215, _1643215, c_Lattices_Osemilattice__sup__class_Osup(_1643215)), _1643219), _1643217))], (41003 ^ _779571) ^ [_1560050, _1560052, _1560054] : [-(hAPP(hAPP(c_Set_Oinsert(_1560050), _1560052), _1560054) = hAPP(c_Set_OCollect(_1560050), hAPP(hAPP(c_COMBS(_1560050, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560050), c_fdisj), hAPP(hAPP(c_COMBC(_1560050, _1560050, tc_HOL_Obool), c_fequal), _1560052))), hAPP(hAPP(c_COMBC(_1560050, tc_fun(_1560050, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560050)), _1560054))))], (7321 ^ _779571) ^ [_900932, _900934, _900936, _900938] : [hAPP(c_Sum__Type_OInl(_900932, _900934), _900936) = hAPP(c_Sum__Type_OInr(_900934, _900932), _900938)], (28533 ^ _779571) ^ [_1286191, _1286193] : [class_Groups_Oordered__ab__group__add(_1286191), -(hAPP(c_Set_Oimage(_1286191, _1286191, c_Groups_Ouminus__class_Ouminus(_1286191)), hAPP(c_SetInterval_Oord__class_OatMost(_1286191), _1286193)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1286191), hAPP(c_Groups_Ouminus__class_Ouminus(_1286191), _1286193)))], (5874 ^ _779571) ^ [_873816, _873818, _873820, _873822, _873824] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_873816, _873818), _873820, _873822, _873824), 5879 ^ _779571 : [(5882 ^ _779571) ^ [] : [hBOOL(hAPP(_873816, _873820))], (5880 ^ _779571) ^ [] : [-(_873824 = _873820)]], 5883 ^ _779571 : [(5889 ^ _779571) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_873816, _873818), 5885 ^ [_873816, _873818, _873820, _873822, _873824], _873822, _873824))], (5887 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_873818, _873820, _873822, 5885 ^ [_873816, _873818, _873820, _873822, _873824]))], (5884 ^ _779571) ^ [] : [-(hBOOL(hAPP(_873816, _873820)))]]], (49443 ^ _779571) ^ [_1772639, _1772641, _1772643] : [-(_1772639 = c_List_Olist_ONil(_1772641)), -(c_List_Olast(_1772641, hAPP(hAPP(c_List_Oappend(_1772641), _1772643), _1772639)) = c_List_Olast(_1772641, _1772639))], (31299 ^ _779571) ^ [_1345450, _1345452, _1345454, _1345456] : [class_Groups_Ocomm__monoid__add(_1345450), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345452), _1345454))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345452, _1345450), _1345456), _1345454) = c_Groups_Ozero__class_Ozero(_1345450))], (43407 ^ _779571) ^ [_1625300, _1625302] : [c_Wellfounded_Owf(_1625300, hAPP(c_Relation_Oconverse(_1625300, _1625300), _1625302)), -(c_Wellfounded_Owf(_1625300, hAPP(c_Relation_Oconverse(_1625300, _1625300), c_Transitive__Closure_Otrancl(_1625300, _1625302))))], (39250 ^ _779571) ^ [_1518475, _1518477, _1518479, _1518481] : [class_Groups_Ocomm__monoid__add(_1518475), 39253 ^ _779571 : [(39260 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518477), _1518479))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1518477, _1518475), _1518481), _1518479) = c_Groups_Ozero__class_Ozero(_1518475))], (39254 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518477), _1518479)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1518477, _1518475), _1518481), _1518479) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518475, _1518477, c_Groups_Oplus__class_Oplus(_1518475)), _1518481), c_Groups_Ozero__class_Ozero(_1518475)), _1518479))]]], (32681 ^ _779571) ^ [_1375800, _1375802, _1375804] : [class_Rings_Osemiring__1(_1375800), hBOOL(hAPP(hAPP(c_member(_1375800), _1375802), c_Nat_Osemiring__1__class_ONats(_1375800))), hBOOL(hAPP(hAPP(c_member(_1375800), _1375804), c_Nat_Osemiring__1__class_ONats(_1375800))), -(hBOOL(hAPP(hAPP(c_member(_1375800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1375800), _1375802), _1375804)), c_Nat_Osemiring__1__class_ONats(_1375800))))], (43389 ^ _779571) ^ [_1624989, _1624991] : [c_Wellfounded_Oacyclic(_1624989, hAPP(c_Relation_Oconverse(_1624989, _1624989), _1624991)), -(c_Wellfounded_Oacyclic(_1624989, _1624991))], (6833 ^ _779571) ^ [_892217, _892219, _892221, _892223] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_892217, _892219)), _892221), _892223)), -(_892223 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _892221), _892217), hAPP(_892219, _892221)))], (44261 ^ _779571) ^ [_1645105, _1645107, _1645109, _1645111, _1645113] : [c_Finite__Set_Ofun__left__comm(_1645105, _1645107, _1645109), -(c_Finite__Set_Ofun__left__comm(_1645111, _1645107, hAPP(hAPP(c_COMBB(_1645105, tc_fun(_1645107, _1645107), _1645111), _1645109), _1645113)))], (30160 ^ _779571) ^ [_1320183, _1320185, _1320187] : [-(hBOOL(hAPP(hAPP(c_member(_1320183), _1320185), hAPP(hAPP(c_Set_Oinsert(_1320183), _1320185), _1320187))))], (24467 ^ _779571) ^ [_1206108, _1206110, _1206112, _1206114] : [class_Orderings_Olinorder(_1206108), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206108), _1206110), _1206112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206108), _1206114), _1206112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206108), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206108), _1206110), _1206114)), _1206112)))], (41700 ^ _779571) ^ [_1583231, _1583233, _1583235, _1583237, _1583239, _1583241, _1583243] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583231, _1583233, _1583235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583237, tc_fun(tc_prod(_1583231, _1583233), tc_HOL_Obool)), _1583239), _1583241)), _1583243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583237, tc_fun(tc_prod(_1583231, _1583235), tc_HOL_Obool)), _1583239), hAPP(hAPP(c_COMBC(_1583237, tc_fun(tc_prod(_1583233, _1583235), tc_HOL_Obool), tc_fun(tc_prod(_1583231, _1583235), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1583231, _1583233), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1583233, _1583235), tc_HOL_Obool), tc_fun(tc_prod(_1583231, _1583235), tc_HOL_Obool)), _1583237), c_Relation_Orel__comp(_1583231, _1583233, _1583235)), _1583241)), _1583243)))], (41057 ^ _779571) ^ [_1561416, _1561418, _1561420] : [-(hAPP(hAPP(c_Set_Oinsert(_1561416), _1561418), hAPP(c_Set_OCollect(_1561416), _1561420)) = hAPP(c_Set_OCollect(_1561416), hAPP(hAPP(c_COMBS(_1561416, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561416), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1561416), c_fNot), hAPP(hAPP(c_COMBC(_1561416, _1561416, tc_HOL_Obool), c_fequal), _1561418)))), _1561420)))], (26706 ^ _779571) ^ [_1249227, _1249229, _1249231] : [class_Rings_Ocomm__semiring__1(_1249227), 26711 ^ _779571 : [(26714 ^ _779571) ^ [] : [_1249231 = c_Groups_Oone__class_Oone(_1249227)], (26712 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1249229))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249227), _1249231), hAPP(hAPP(c_Power_Opower__class_Opower(_1249227), _1249231), _1249229))))], (47422 ^ _779571) ^ [_1723556, _1723558] : [-(c_Random_Oselect(_1723556, _1723558) = 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(_1723556, 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(_1723556)), _1723558)))), hAPP(hAPP(c_COMBB(_1723556, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1723556, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1723556, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1723556, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1723556), _1723558)), c_Code__Numeral_Onat__of))))], (23679 ^ _779571) ^ [_1190778, _1190780, _1190782, _1190784] : [class_Orderings_Olinorder(_1190778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190778), _1190780), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190778), _1190782), _1190784))), 23686 ^ _779571 : [(23689 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190778), _1190780), _1190784)))], (23687 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190778), _1190780), _1190782)))]]], (46388 ^ _779571) ^ [_1696126, _1696128, _1696130, _1696132, _1696134, _1696136, _1696138, _1696140] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1696126, _1696128), _1696130), _1696132), hAPP(hAPP(c_List_Ozip(_1696126, _1696128), hAPP(hAPP(c_List_Omap(_1696134, _1696126), _1696136), _1696138)), _1696140)) = hAPP(hAPP(c_List_Omap(tc_prod(_1696134, _1696128), _1696130), hAPP(c_Product__Type_Oprod_Oprod__case(_1696134, _1696128, _1696130), hAPP(hAPP(c_COMBB(tc_fun(_1696128, tc_prod(_1696126, _1696128)), tc_fun(_1696128, _1696130), _1696134), hAPP(c_COMBB(tc_prod(_1696126, _1696128), _1696130, _1696128), _1696132)), hAPP(hAPP(c_COMBB(_1696126, tc_fun(_1696128, tc_prod(_1696126, _1696128)), _1696134), c_Product__Type_OPair(_1696126, _1696128)), _1696136)))), hAPP(hAPP(c_List_Ozip(_1696134, _1696128), _1696138), _1696140)))], (41622 ^ _779571) ^ [_1581128, _1581130] : [-(c_Product__Type_Oapsnd(_1581128, _1581128, _1581130, c_Fun_Oid(_1581128)) = c_Fun_Oid(tc_prod(_1581130, _1581128)))], (11316 ^ _779571) ^ [_967535, _967537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967535), hAPP(c_Nat_OSuc, _967537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967535), _967537))), -(_967535 = hAPP(c_Nat_OSuc, _967537))], (48437 ^ _779571) ^ [_1747914, _1747916, _1747918, _1747920, _1747922, _1747924] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747914)), _1747916) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747918)), _1747920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747914, tc_HOL_Obool)), hAPP(c_List_Oset(_1747914), _1747916)), _1747922)), -(c_Map_Orestrict__map(_1747914, _1747918, c_Map_Omap__upds(_1747914, _1747918, _1747924, _1747916, _1747920), _1747922) = c_Map_Omap__upds(_1747914, _1747918, c_Map_Orestrict__map(_1747914, _1747918, _1747924, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1747914, tc_HOL_Obool)), _1747922), hAPP(c_List_Oset(_1747914), _1747916))), _1747916, _1747920))], (8356 ^ _779571) ^ [_918189, _918191] : [_918189 = _918191, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918189) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918191))], (30838 ^ _779571) ^ [_1334370, _1334372, _1334374, _1334376] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1334370, tc_HOL_Obool)), _1334372), hAPP(hAPP(c_Set_Oinsert(_1334370), _1334374), _1334376)))), 30841 ^ _779571 : [(30844 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1334370, tc_HOL_Obool)), _1334372), _1334376))], (30842 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1334370), _1334374), _1334376)))]], 30845 ^ _779571 : [(30848 ^ _779571) ^ [] : [30849 ^ _779571 : [(30852 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1334370, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334370, tc_HOL_Obool)), _1334372), hAPP(hAPP(c_Set_Oinsert(_1334370), _1334374), c_Orderings_Obot__class_Obot(tc_fun(_1334370, tc_HOL_Obool))))), _1334376))], (30850 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1334370), _1334374), _1334372)))]], 30853 ^ _779571 : [(30856 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334370, tc_HOL_Obool)), _1334372), _1334376))], (30854 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1334370), _1334374), _1334372))]]], (30846 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1334370), _1334374), _1334376))]]], (45233 ^ _779571) ^ [_1669573, _1669575, _1669577] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669573, tc_HOL_Obool)), _1669575), _1669577) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669573, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1669573, tc_HOL_Obool)), _1669575), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1669573, tc_HOL_Obool)), _1669577), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1669573, tc_HOL_Obool), tc_HOL_Obool))))))], (34897 ^ _779571) ^ [_1420122, _1420124, _1420126, _1420128] : [c_FunDef_Oreduction__pair(_1420122, _1420124), -(c_FunDef_Oreduction__pair(_1420126, hAPP(hAPP(c_FunDef_Orp__inv__image(_1420122, _1420126), _1420124), _1420128)))], (47679 ^ _779571) ^ [_1730157, _1730159, _1730161, _1730163] : [hAPP(hAPP(c_List_Olist__update(_1730157, _1730159), _1730161), _1730163) = c_List_Olist_ONil(_1730157), -(_1730159 = c_List_Olist_ONil(_1730157))], (4528 ^ _779571) ^ [_849647, _849649, _849651, _849653, _849655, _849657, _849659, _849661] : [-(c_Nat_Onat_Onat__case(_849661, _849657, _849653, _849649) = c_Nat_Onat_Onat__case(_849659, _849655, _849651, _849647)), _849661 = _849659, _849657 = _849655, _849653 = _849651, _849649 = _849647], (13773 ^ _779571) ^ [_1010904, _1010906, _1010908] : [class_Divides_Oring__div(_1010904), -(c_Divides_Odiv__class_Omod(_1010904, hAPP(c_Groups_Ouminus__class_Ouminus(_1010904), _1010906), _1010908) = c_Divides_Odiv__class_Omod(_1010904, hAPP(c_Groups_Ouminus__class_Ouminus(_1010904), c_Divides_Odiv__class_Omod(_1010904, _1010906, _1010908)), _1010908))], (33731 ^ _779571) ^ [_1395650, _1395652, _1395654] : [class_Orderings_Olinorder(_1395650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395650), _1395652)), hBOOL(hAPP(hAPP(c_member(_1395650), _1395654), _1395652)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1395650), _1395654), c_Big__Operators_Olattice_OInf__fin(_1395650, c_Orderings_Oord__class_Omin(_1395650), _1395652)) = c_Big__Operators_Olattice_OInf__fin(_1395650, c_Orderings_Oord__class_Omin(_1395650), _1395652))], (27926 ^ _779571) ^ [_1274086, _1274088, _1274090, _1274092, _1274094] : [class_Lattices_Osemilattice__sup(_1274086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274086), _1274088), _1274090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274086), _1274092), _1274094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274086), _1274088), _1274092)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274086), _1274090), _1274094))))], (43242 ^ _779571) ^ [_1621263, _1621265, _1621267, _1621269] : [-(c_Wellfounded_Owf(_1621263, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1621263, _1621263)), hAPP(hAPP(c_Product__Type_OPair(_1621263, _1621263), _1621265), _1621267)), _1621269))), c_Wellfounded_Owf(_1621263, _1621269), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621263, _1621263)), hAPP(hAPP(c_Product__Type_OPair(_1621263, _1621263), _1621267), _1621265)), c_Transitive__Closure_Ortrancl(_1621263, _1621269))))], (43327 ^ _779571) ^ [_1623413, _1623415, _1623417, _1623419, _1623421] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623413, _1623415)), hAPP(hAPP(c_Product__Type_OPair(_1623413, _1623415), _1623417), _1623419)), hAPP(c_Relation_Oconverse(_1623415, _1623413), _1623421))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623415, _1623413)), hAPP(hAPP(c_Product__Type_OPair(_1623415, _1623413), _1623419), _1623417)), _1623421)))], (34 ^ _779571) ^ [_780024, _780026, _780028, _780030] : [-(c_Int_Oiszero(_780028, _780024)), c_Int_Oiszero(_780030, _780026), _780030 = _780028, _780026 = _780024], (47731 ^ _779571) ^ [_1731333, _1731335, _1731337, _1731339, _1731341] : [-(hAPP(hAPP(c_List_Olist__update(_1731333, hAPP(hAPP(c_List_Olist_OCons(_1731333), _1731335), _1731337)), hAPP(c_Nat_OSuc, _1731339)), _1731341) = hAPP(hAPP(c_List_Olist_OCons(_1731333), _1731335), hAPP(hAPP(c_List_Olist__update(_1731333, _1731337), _1731339), _1731341)))], (50738 ^ _779571) ^ [_1799688, _1799690, _1799692] : [_1799690 = hAPP(c_List_Orev(_1799688), _1799692), -(hAPP(c_List_Orev(_1799688), _1799690) = _1799692)], (6736 ^ _779571) ^ [_890096, _890098, _890100, _890102] : [c_Com_Ocom_OCond(_890096, _890098, _890100) = hAPP(c_Com_Ocom_OBODY, _890102)], (25970 ^ _779571) ^ [_1235324, _1235326, _1235328, _1235330, _1235332] : [class_Fields_Ofield(_1235324), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235324), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235326, _1235324), _1235328), _1235330)), _1235332) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235326, _1235324), hAPP(hAPP(c_COMBC(_1235326, _1235324, _1235324), hAPP(hAPP(c_COMBB(_1235324, tc_fun(_1235324, _1235324), _1235326), c_Rings_Oinverse__class_Odivide(_1235324)), _1235328)), _1235332)), _1235330))], (35683 ^ _779571) ^ [_1439425, _1439427, _1439429, _1439431, _1439433, _1439435, _1439437, _1439439] : [c_Finite__Set_Ofolding(_1439425, _1439427, _1439429, _1439431), -(hAPP(c_Fun_Ocomp(_1439427, _1439427, _1439433, hAPP(_1439429, _1439435)), hAPP(c_Fun_Ocomp(_1439427, _1439427, _1439433, hAPP(_1439429, _1439437)), _1439439)) = hAPP(c_Fun_Ocomp(_1439427, _1439427, _1439433, hAPP(_1439429, _1439437)), hAPP(c_Fun_Ocomp(_1439427, _1439427, _1439433, hAPP(_1439429, _1439435)), _1439439)))], (44331 ^ _779571) ^ [_1646445, _1646447, _1646449, _1646451, _1646453, _1646455] : [c_Finite__Set_Ofun__left__comm(_1646445, _1646447, _1646449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646445), _1646451)), -(hBOOL(hAPP(hAPP(c_member(_1646445), _1646453), _1646451))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1646445, _1646447, _1646449), _1646455), hAPP(hAPP(c_Set_Oinsert(_1646445), _1646453), _1646451)) = hAPP(hAPP(c_Finite__Set_Ofold(_1646445, _1646447, _1646449), hAPP(hAPP(_1646449, _1646453), _1646455)), _1646451))], (51497 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (26736 ^ _779571) ^ [_1249734, _1249736, _1249738] : [-(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), _1249734)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1249736))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1249738))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1249734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1249734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249738), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1249736)))))], (2654 ^ _779571) ^ [_819798, _819800, _819802, _819804, _819806, _819808, _819810, _819812] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_819812, _819808, _819804, _819800) = c_New__Random__Sequence_Opos__not__random__dseq(_819810, _819806, _819802, _819798)), _819812 = _819810, _819808 = _819806, _819804 = _819802, _819800 = _819798], (4846 ^ _779571) ^ [_854436, _854438, _854440, _854442, _854444, _854446, _854448, _854450] : [-(c_Option_Ooption_Ooption__case(_854450, _854446, _854442, _854438) = c_Option_Ooption_Ooption__case(_854448, _854444, _854440, _854436)), _854450 = _854448, _854446 = _854444, _854442 = _854440, _854438 = _854436], (16467 ^ _779571) ^ [_1061233] : [class_Rings_Olinordered__idom(_1061233), -(hAPP(c_Groups_Oabs__class_Oabs(_1061233), c_Groups_Oone__class_Oone(_1061233)) = c_Groups_Oone__class_Oone(_1061233))], (42128 ^ _779571) ^ [_1594263, _1594265, _1594267] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1594263, _1594265)), _1594267)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1594265), hAPP(c_Relation_ORange(_1594263, _1594265), _1594267))))], (6612 ^ _779571) ^ [_887645, _887647, _887649, _887651] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887645, _887647)), _887649), _887651)), 6617 ^ _779571 : [(6620 ^ _779571) ^ [] : [hBOOL(hAPP(_887645, _887649))], (6618 ^ _779571) ^ [] : [-(_887651 = _887649)]], 6621 ^ _779571 : [(6627 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887645, _887647)), 6623 ^ [_887645, _887647, _887649, _887651]), _887651)))], (6625 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887647), _887649), 6623 ^ [_887645, _887647, _887649, _887651])))], (6622 ^ _779571) ^ [] : [-(hBOOL(hAPP(_887645, _887649)))]]], (13132 ^ _779571) ^ [_999523, _999525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _999523)), 13135 ^ _779571 : [(13142 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _999523), _999525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _999523)), hAPP(c_Int_Onat, _999525))))], (13136 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _999523)), hAPP(c_Int_Onat, _999525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _999523), _999525)))]]], (47945 ^ _779571) ^ [_1736350, _1736352, _1736354, _1736356, _1736358] : [-(hAPP(hAPP(c_List_Oappend(_1736350), _1736352), _1736354) = hAPP(hAPP(c_List_Olist_OCons(_1736350), _1736356), _1736358)), 47946 ^ _779571 : [(47953 ^ _779571) ^ [_1736533] : [_1736352 = hAPP(hAPP(c_List_Olist_OCons(_1736350), _1736356), _1736533), hAPP(hAPP(c_List_Oappend(_1736350), _1736533), _1736354) = _1736358], (47947 ^ _779571) ^ [] : [_1736352 = c_List_Olist_ONil(_1736350), _1736354 = hAPP(hAPP(c_List_Olist_OCons(_1736350), _1736356), _1736358)]]], (24513 ^ _779571) ^ [_1207010, _1207012, _1207014, _1207016] : [class_Orderings_Olinorder(_1207010), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207010), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207010), _1207012), _1207014)), _1207016) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207010), _1207012), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207010), _1207014), _1207016)))], (43196 ^ _779571) ^ [] : [-(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))))], (4236 ^ _779571) ^ [_845007, _845009, _845011, _845013] : [-(c_Relation_Oinv__image(_845013, _845009) = c_Relation_Oinv__image(_845011, _845007)), _845013 = _845011, _845009 = _845007], (6289 ^ _779571) ^ [_881629, _881631] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_881629, _881631))), -(hBOOL(hAPP(c_Com_OWT, _881631)))], (40132 ^ _779571) ^ [_1539629, _1539631, _1539633, _1539635] : [hAPP(hAPP(c_Product__Type_OSigma(_1539629, _1539631), _1539633), hAPP(c_COMBK(tc_fun(_1539631, tc_HOL_Obool), _1539629), _1539635)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1539629, _1539631), tc_HOL_Obool)), -(_1539633 = c_Orderings_Obot__class_Obot(tc_fun(_1539629, tc_HOL_Obool))), -(_1539635 = c_Orderings_Obot__class_Obot(tc_fun(_1539631, tc_HOL_Obool)))], (47624 ^ _779571) ^ [_1728562, _1728564, _1728566, _1728568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728562), tc_List_Olist(_1728562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1728562), tc_List_Olist(_1728562)), _1728564), _1728566)), c_List_Olistrel(_1728562, _1728568))), 47627 ^ _779571 : [(47630 ^ _779571) ^ [_1728791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728791), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728562)), _1728564))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1728562, _1728562)), hAPP(hAPP(c_Product__Type_OPair(_1728562, _1728562), hAPP(hAPP(c_List_Onth(_1728562), _1728564), _1728791)), hAPP(hAPP(c_List_Onth(_1728562), _1728566), _1728791))), _1728568)))], (47628 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728562)), _1728564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728562)), _1728566))]]], (17297 ^ _779571) ^ [_1076936, _1076938] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076936), _1076938)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076936)), _1076938))], (50372 ^ _779571) ^ [_1791434] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1791434) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1791434)))], (48838 ^ _779571) ^ [_1759112, _1759114, _1759116, _1759118, _1759120] : [hAPP(hAPP(c_List_Oappend(_1759112), _1759114), _1759116) = hAPP(hAPP(c_List_Oappend(_1759112), _1759118), _1759120), 48841 ^ _779571 : [(48850 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759114)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759118)))), 48853 ^ _779571 : [(48856 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1759112), hAPP(hAPP(c_List_Odrop(_1759112), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759118)), _1759114)), _1759116) = _1759120)], (48854 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1759112), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759118)), _1759114) = _1759118)]]], (48842 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759114)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759118))), 48845 ^ _779571 : [(48848 ^ _779571) ^ [] : [-(_1759116 = hAPP(hAPP(c_List_Oappend(_1759112), hAPP(hAPP(c_List_Odrop(_1759112), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759114)), _1759118)), _1759120))], (48846 ^ _779571) ^ [] : [-(_1759114 = hAPP(hAPP(c_List_Otake(_1759112), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759112)), _1759114)), _1759118))]]]]], (42401 ^ _779571) ^ [_1601336, _1601338] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601336, _1601336)), _1601338)), 42404 ^ _779571 : [(42411 ^ _779571) ^ [] : [c_Wellfounded_Oacyclic(_1601336, _1601338), -(c_Wellfounded_Owf(_1601336, _1601338))], (42405 ^ _779571) ^ [] : [c_Wellfounded_Owf(_1601336, _1601338), -(c_Wellfounded_Oacyclic(_1601336, _1601338))]]], (17803 ^ _779571) ^ [_1086160] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086160)))], (38108 ^ _779571) ^ [_1494745, _1494747, _1494749] : [class_Lattices_Olattice(_1494745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494745), _1494747)), -(_1494747 = c_Orderings_Obot__class_Obot(tc_fun(_1494745, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494745), _1494749)), -(_1494749 = c_Orderings_Obot__class_Obot(tc_fun(_1494745, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494745, tc_HOL_Obool)), _1494747), _1494749) = c_Orderings_Obot__class_Obot(tc_fun(_1494745, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1494745, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494745, tc_HOL_Obool)), _1494747), _1494749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1494745), c_Big__Operators_Olattice__class_OInf__fin(_1494745, _1494747)), c_Big__Operators_Olattice__class_OInf__fin(_1494745, _1494749)))], (43433 ^ _779571) ^ [_1626005, _1626007, _1626009, _1626011] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626005, _1626005)), hAPP(hAPP(c_Product__Type_OPair(_1626005, _1626005), _1626007), _1626009)), c_Transitive__Closure_Otrancl(_1626005, hAPP(c_Relation_Oconverse(_1626005, _1626005), _1626011)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626005, _1626005)), hAPP(hAPP(c_Product__Type_OPair(_1626005, _1626005), _1626007), _1626009)), hAPP(c_Relation_Oconverse(_1626005, _1626005), c_Transitive__Closure_Otrancl(_1626005, _1626011)))))], (44582 ^ _779571) ^ [_1653522, _1653524, _1653526, _1653528] : [hBOOL(hAPP(hAPP(c_member(_1653524), _1653528), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653522, tc_fun(_1653524, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1653522, tc_HOL_Obool))), _1653526))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653522, tc_fun(_1653524, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1653522, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1653524, tc_HOL_Obool), tc_fun(_1653524, tc_HOL_Obool), _1653522), hAPP(c_COMBC(_1653524, tc_fun(_1653524, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653524))), _1653526)), _1653528)))], (9842 ^ _779571) ^ [_943468] : [class_Rings_Olinordered__semidom(_943468), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943468), c_Groups_Ozero__class_Ozero(_943468)), c_Groups_Oone__class_Oone(_943468))))], (16461 ^ _779571) ^ [_1061104, _1061106, _1061108] : [class_Groups_Oordered__ab__group__add__abs(_1061104), -(hAPP(c_Groups_Oabs__class_Oabs(_1061104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061104), _1061106), _1061108)) = hAPP(c_Groups_Oabs__class_Oabs(_1061104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061104), _1061108), _1061106)))], (5841 ^ _779571) ^ [_873160, _873162, _873164, _873166, _873168, _873170, _873172] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873160), _873162), _873164), _873166) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873160), _873168), _873170), _873172)), _873162 = _873168, _873164 = _873170, _873166 = _873172], (20269 ^ _779571) ^ [_1128180, _1128182, _1128184] : [class_Fields_Olinordered__field(_1128180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128180), _1128182), c_Groups_Ozero__class_Ozero(_1128180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128180), _1128184), c_Groups_Ozero__class_Ozero(_1128180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128180), c_Groups_Ozero__class_Ozero(_1128180)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128180), _1128182), _1128184))))], (10137 ^ _779571) ^ [_948450, _948452] : [class_Rings_Olinordered__idom(_948450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948450), _948452), c_Groups_Ozero__class_Ozero(_948450))), -(c_Groups_Osgn__class_Osgn(_948450, _948452) = hAPP(c_Groups_Ouminus__class_Ouminus(_948450), c_Groups_Oone__class_Oone(_948450)))], (44489 ^ _779571) ^ [_1650554, _1650556, _1650558, _1650560, _1650562, _1650564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650556, _1650558)), hAPP(hAPP(c_Product__Type_OPair(_1650556, _1650558), _1650562), _1650564)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650554, tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1650554, tc_HOL_Obool))), _1650560))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650554, tc_fun(_1650556, tc_fun(_1650558, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1650554, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_fun(_1650556, tc_fun(_1650558, tc_HOL_Obool)), _1650554), hAPP(c_COMBC(_1650556, tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_fun(_1650558, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650558, tc_fun(tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_fun(_1650558, tc_HOL_Obool)), _1650556), c_COMBC(_1650558, tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650558, tc_prod(_1650556, _1650558)), tc_fun(_1650558, tc_fun(tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_HOL_Obool)), _1650556), hAPP(c_COMBB(tc_prod(_1650556, _1650558), tc_fun(tc_fun(tc_prod(_1650556, _1650558), tc_HOL_Obool), tc_HOL_Obool), _1650558), c_member(tc_prod(_1650556, _1650558)))), c_Product__Type_OPair(_1650556, _1650558))))), _1650560)), _1650562), _1650564)))], (25009 ^ _779571) ^ [_1218054, _1218056, _1218058] : [25011 ^ _779571 : [(25014 ^ _779571) ^ [] : [hBOOL(hAPP(_1218056, 25010 ^ [_1218054, _1218056, _1218058]))], (25012 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1218054), 25010 ^ [_1218054, _1218056, _1218058]), _1218058)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1218054, _1218056), _1218058)))], (36310 ^ _779571) ^ [_1453941, _1453943, _1453945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453941, tc_HOL_Obool)), _1453943), _1453945) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453941, tc_HOL_Obool)), _1453945), _1453943))], (51317 ^ _779571) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (42427 ^ _779571) ^ [_1601803, _1601805] : [c_Nitpick_Owf_H(_1601803, _1601805), 42430 ^ _779571 : [(42433 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601803, _1601803)), _1601805))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (42431 ^ _779571) ^ [] : [-(c_Wellfounded_Oacyclic(_1601803, _1601805))]]], (50602 ^ _779571) ^ [_1796851, _1796853, _1796855] : [hAPP(hAPP(c_List_Olist_OCons(_1796851), _1796853), c_List_Olist_ONil(_1796851)) = hAPP(c_List_Orev(_1796851), _1796855), -(_1796855 = hAPP(hAPP(c_List_Olist_OCons(_1796851), _1796853), c_List_Olist_ONil(_1796851)))], (39926 ^ _779571) ^ [_1534088, _1534090, _1534092, _1534094] : [-(c_Wellfounded_Omax__extp(_1534088, _1534090, _1534092, _1534094)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534088), _1534092)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534088), _1534094)), -(_1534094 = c_Orderings_Obot__class_Obot(tc_fun(_1534088, tc_HOL_Obool))), 39940 ^ _779571 : [(39943 ^ _779571) ^ [_1534433] : [hBOOL(hAPP(hAPP(c_member(_1534088), _1534433), _1534094)), hBOOL(hAPP(hAPP(_1534090, 39939 ^ [_1534088, _1534090, _1534092, _1534094]), _1534433))], (39941 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534088), 39939 ^ [_1534088, _1534090, _1534092, _1534094]), _1534092)))]]], (18907 ^ _779571) ^ [_1103815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103815), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1103815)), c_Int_OPls)))], (15192 ^ _779571) ^ [_1036520, _1036522, _1036524] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036520), _1036522)), _1036524) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036520), _1036524)), _1036522))], (25474 ^ _779571) ^ [_1225771, _1225773] : [_1225773 = _1225771, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225771), _1225773)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225773), _1225771)))], (7323 ^ _779571) ^ [_900991, _900993, _900995, _900997] : [hAPP(c_Sum__Type_OInl(_900991, _900993), _900995) = hAPP(c_Sum__Type_OInr(_900993, _900991), _900997)], (46181 ^ _779571) ^ [_1691406, _1691408, _1691410] : [hBOOL(hAPP(c_List_Odistinct(_1691406), hAPP(hAPP(c_List_Omap(tc_prod(_1691406, _1691408), _1691406), c_Product__Type_Ofst(_1691406, _1691408)), _1691410))), -(c_Map_Oran(_1691406, _1691408, c_Map_Omap__of(_1691406, _1691408, _1691410)) = hAPP(c_Set_Oimage(tc_prod(_1691406, _1691408), _1691408, c_Product__Type_Osnd(_1691406, _1691408)), hAPP(c_List_Oset(tc_prod(_1691406, _1691408)), _1691410)))], (6025 ^ _779571) ^ [_876573, _876575, _876577, _876579, _876581] : [c_Com_Ocom_OCond(_876573, _876575, _876577) = c_Com_Ocom_OSemi(_876579, _876581)], (47310 ^ _779571) ^ [_1720921, _1720923, _1720925] : [hAPP(hAPP(c_List_Olist_OCons(_1720921), _1720923), _1720925) = c_List_Olist_ONil(_1720921)], (24137 ^ _779571) ^ [_1200021, _1200023, _1200025, _1200027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1200021, tc_HOL_Obool)), _1200023), _1200025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1200021, tc_HOL_Obool)), _1200025), _1200027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1200021, tc_HOL_Obool)), _1200023), _1200027)))], (36866 ^ _779571) ^ [_1465986, _1465988, _1465990, _1465992, _1465994] : [class_Orderings_Olinorder(_1465986), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465986, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1465986, _1465988), _1465990)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1465986, _1465992), _1465994)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1465986, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465986), _1465988), _1465992)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1465986), _1465990), _1465994)))], (14359 ^ _779571) ^ [_1021864, _1021866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021864), _1021866)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021864, _1021866) = _1021864)], (19545 ^ _779571) ^ [] : [-(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))))], (28371 ^ _779571) ^ [_1283109, _1283111, _1283113] : [class_Orderings_Olinorder(_1283109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283109), _1283111), _1283113)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283109, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1283109, _1283111, _1283113)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1283109), _1283113)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1283109), _1283111))], (49084 ^ _779571) ^ [_1764332, _1764334, _1764336] : [-(hAPP(c_List_Orotate(_1764332, _1764334), _1764336) = hAPP(hAPP(c_List_Oappend(_1764332), hAPP(hAPP(c_List_Odrop(_1764332), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1764334, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764332)), _1764336))), _1764336)), hAPP(hAPP(c_List_Otake(_1764332), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1764334, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764332)), _1764336))), _1764336)))], (16965 ^ _779571) ^ [_1070762, _1070764, _1070766] : [class_Rings_Oordered__ring__abs(_1070762), -(hAPP(c_Groups_Oabs__class_Oabs(_1070762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070762), _1070764), _1070766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070762), hAPP(c_Groups_Oabs__class_Oabs(_1070762), _1070764)), hAPP(c_Groups_Oabs__class_Oabs(_1070762), _1070766))), 16972 ^ _779571 : [(16975 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070762), _1070764), c_Groups_Ozero__class_Ozero(_1070762)))], (16973 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070762), c_Groups_Ozero__class_Ozero(_1070762)), _1070764))]], 16976 ^ _779571 : [(16979 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070762), _1070766), c_Groups_Ozero__class_Ozero(_1070762)))], (16977 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070762), c_Groups_Ozero__class_Ozero(_1070762)), _1070766))]]], (17323 ^ _779571) ^ [_1077373, _1077375] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1077373) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077375)), _1077373 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077375)), 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), _1077375)))], (6177 ^ _779571) ^ [_879568, _879570] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_879568, _879570))), 6180 ^ _779571 : [(6183 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879570)))], (6181 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879568)))]]], (6809 ^ _779571) ^ [_891716, _891718, _891720] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_891716, _891718, _891720)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18409 ^ _779571) ^ [_1095559, _1095561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1095559)), _1095561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095559), _1095561)))], (6187 ^ _779571) ^ [_879762, _879764, _879766, _879768, _879770, _879772, _879774, _879776, _879778, _879780, _879782, _879784] : [-(c_Com_Ocom_Ocom__case(_879762, _879764, _879766, _879768, _879770, _879772, _879774, _879776, _879778, c_Com_Ocom_OCall(_879780, _879782, _879784)) = hAPP(hAPP(hAPP(_879778, _879780), _879782), _879784))], (146 ^ _779571) ^ [_781608, _781610, _781612, _781614, _781616, _781618, _781620, _781622] : [-(c_Orderings_Oorder_Ostrict__mono(_781620, _781616, _781612, _781608)), c_Orderings_Oorder_Ostrict__mono(_781622, _781618, _781614, _781610), _781622 = _781620, _781618 = _781616, _781614 = _781612, _781610 = _781608], (7644 ^ _779571) ^ [_906209, _906211] : [7645 ^ _779571 : [(7648 ^ _779571) ^ [] : [_906209 = _906211], (7646 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906209), _906211))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906209), hAPP(c_Nat_OSuc, _906211))))], (6387 ^ _779571) ^ [_883513, _883515, _883517] : [c_Com_Ocom_OCall(_883513, _883515, _883517) = c_Com_Ocom_OSKIP], (49622 ^ _779571) ^ [_1776124, _1776126, _1776128] : [_1776124 = c_List_Olist_ONil(_1776126), -(c_List_Obutlast(_1776126, hAPP(hAPP(c_List_Oappend(_1776126), _1776128), _1776124)) = c_List_Obutlast(_1776126, _1776128))], (6564 ^ _779571) ^ [_886708] : [hAPP(c_Nat_OSuc, _886708) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47833 ^ _779571) ^ [_1733502, _1733504, _1733506, _1733508, _1733510, _1733512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733502), tc_List_Olist(_1733502))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733502), tc_List_Olist(_1733502)), hAPP(hAPP(c_List_Olist_OCons(_1733502), _1733504), _1733506)), hAPP(hAPP(c_List_Olist_OCons(_1733502), _1733508), _1733510))), c_List_Olexord(_1733502, _1733512))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733502, _1733502)), hAPP(hAPP(c_Product__Type_OPair(_1733502, _1733502), _1733504), _1733508)), _1733512))), 47840 ^ _779571 : [(47843 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733502), tc_List_Olist(_1733502))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733502), tc_List_Olist(_1733502)), _1733506), _1733510)), c_List_Olexord(_1733502, _1733512))))], (47841 ^ _779571) ^ [] : [-(_1733504 = _1733508)]]], (22848 ^ _779571) ^ [_1175642, _1175644] : [-(c_Divides_Odivmod__int(_1175642, _1175644) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1175642), _1175644)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175642, _1175644)))], (36072 ^ _779571) ^ [_1448618, _1448620, _1448622, _1448624] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448618, tc_HOL_Obool)), _1448620), _1448622), _1448624)), 36075 ^ _779571 : [(36078 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1448622, _1448624)))], (36076 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1448620, _1448624)))]]], (31213 ^ _779571) ^ [_1341808, _1341810] : [class_Finite__Set_Ofinite(_1341808), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341808), _1341810)))], (45748 ^ _779571) ^ [_1680876, _1680878, _1680880, _1680882, _1680884, _1680886] : [-(c_Map_Omap__add(_1680876, _1680878, _1680880, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1680876, tc_Option_Ooption(_1680878)), _1680882), _1680884), hAPP(c_Option_Ooption_OSome(_1680878), _1680886))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1680876, tc_Option_Ooption(_1680878)), c_Map_Omap__add(_1680876, _1680878, _1680880, _1680882)), _1680884), hAPP(c_Option_Ooption_OSome(_1680878), _1680886)))], (47685 ^ _779571) ^ [_1730260, _1730262, _1730264, _1730266] : [_1730262 = c_List_Olist_ONil(_1730260), -(hAPP(hAPP(c_List_Olist__update(_1730260, _1730262), _1730264), _1730266) = c_List_Olist_ONil(_1730260))], (8306 ^ _779571) ^ [] : [-(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)))], (2022 ^ _779571) ^ [_809620, _809622, _809624, _809626, _809628, _809630] : [-(c_Com_Ocom_OLocal(_809630, _809626, _809622) = c_Com_Ocom_OLocal(_809628, _809624, _809620)), _809630 = _809628, _809626 = _809624, _809622 = _809620], (2710 ^ _779571) ^ [_820652, _820654, _820656, _820658] : [-(c_Nitpick_Onumber__of__frac(_820658, _820654) = c_Nitpick_Onumber__of__frac(_820656, _820652)), _820658 = _820656, _820654 = _820652], (19209 ^ _779571) ^ [_1108986] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1108986)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1108986)))], (50071 ^ _779571) ^ [_1786239, _1786241, _1786243] : [class_Orderings_Olinorder(_1786239), 50074 ^ _779571 : [(50087 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1786239, hAPP(hAPP(c_List_Olist_OCons(_1786239), _1786241), _1786243))), c_List_Olinorder__class_Osorted(_1786239, _1786243), 50093 ^ _779571 : [(50096 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1786239), _1786241), 50092 ^ [_1786239, _1786241, _1786243]))], (50094 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786239), 50092 ^ [_1786239, _1786241, _1786243]), hAPP(c_List_Oset(_1786239), _1786243))))]]], (50075 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1786239, hAPP(hAPP(c_List_Olist_OCons(_1786239), _1786241), _1786243)), 50078 ^ _779571 : [(50081 ^ _779571) ^ [_1786425] : [hBOOL(hAPP(hAPP(c_member(_1786239), _1786425), hAPP(c_List_Oset(_1786239), _1786243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1786239), _1786241), _1786425)))], (50079 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1786239, _1786243))]]]]], (1412 ^ _779571) ^ [_799989, _799991] : [-(class_Rings_Olinordered__semiring__strict(_799989)), _799991 = _799989, class_Rings_Olinordered__semiring__strict(_799991)], (19705 ^ _779571) ^ [_1117627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1117627), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1117627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1117627 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23553 ^ _779571) ^ [_1188586, _1188588, _1188590] : [class_Orderings_Olinorder(_1188586), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188586), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188586), _1188588), _1188590)), _1188590)))], (6987 ^ _779571) ^ [_894765, _894767] : [class_Groups_Ocomm__monoid__add(_894765), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894765), c_Groups_Ozero__class_Ozero(_894765)), _894767) = _894767)], (51169 ^ _779571) ^ [_1809291, _1809293] : [class_Groups_Ominus(_1809291), -(class_Groups_Ominus(tc_fun(_1809293, _1809291)))], (3904 ^ _779571) ^ [_839785, _839787, _839789, _839791] : [-(c_Wellfounded_Omax__ext(_839791, _839787) = c_Wellfounded_Omax__ext(_839789, _839785)), _839791 = _839789, _839787 = _839785], (6412 ^ _779571) ^ [_884044, _884046, _884048] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _884046))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_884044, _884046, _884048))))], (44915 ^ _779571) ^ [_1662062, _1662064, _1662066, _1662068, _1662070, _1662072, _1662074] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662062, tc_fun(_1662064, tc_fun(_1662066, tc_HOL_Obool))), _1662068), _1662070), _1662072), _1662074)), 44918 ^ _779571 : [(44919 ^ _779571) ^ [_1662190] : [hBOOL(hAPP(hAPP(c_member(_1662062), _1662190), _1662068)), -(hBOOL(hAPP(hAPP(hAPP(_1662070, _1662190), _1662072), _1662074)))]]], (20311 ^ _779571) ^ [_1128945, _1128947, _1128949] : [class_Fields_Olinordered__field(_1128945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128945), c_Groups_Ozero__class_Ozero(_1128945)), _1128947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128945), c_Groups_Ozero__class_Ozero(_1128945)), _1128949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128945), c_Groups_Ozero__class_Ozero(_1128945)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128945), _1128947), _1128949))))], (51245 ^ _779571) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (5400 ^ _779571) ^ [_863069, _863071, _863073, _863075, _863077, _863079] : [-(c_Map_Omap__of(_863079, _863075, _863071) = c_Map_Omap__of(_863077, _863073, _863069)), _863079 = _863077, _863075 = _863073, _863071 = _863069], (42248 ^ _779571) ^ [_1597279, _1597281, _1597283] : [c_Wellfounded_OwfP(_1597279, _1597281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597279, tc_fun(_1597279, tc_HOL_Obool))), _1597283), _1597281)), -(c_Wellfounded_OwfP(_1597279, _1597283))], (36908 ^ _779571) ^ [_1466955, _1466957, _1466959, _1466961] : [class_Orderings_Oorder(_1466955), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466955, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1466955, _1466957, _1466959)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1466955, _1466959), _1466961)) = c_Orderings_Obot__class_Obot(tc_fun(_1466955, tc_HOL_Obool)))], (8736 ^ _779571) ^ [_923833] : [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)), _923833)), _923833)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923833), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34903 ^ _779571) ^ [_1420221, _1420223, _1420225] : [class_Orderings_Olinorder(_1420221), hAPP(_1420223, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1420221), 34908 ^ [_1420221, _1420223, _1420225]), 34909 ^ [_1420221, _1420223, _1420225])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1420221), hAPP(_1420223, 34908 ^ [_1420221, _1420223, _1420225])), hAPP(_1420223, 34909 ^ [_1420221, _1420223, _1420225])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420221), _1420225)), -(_1420225 = c_Orderings_Obot__class_Obot(tc_fun(_1420221, tc_HOL_Obool))), -(hAPP(_1420223, c_Big__Operators_Olattice_OInf__fin(_1420221, c_Orderings_Oord__class_Omin(_1420221), _1420225)) = c_Big__Operators_Olattice_OInf__fin(_1420221, c_Orderings_Oord__class_Omin(_1420221), hAPP(c_Set_Oimage(_1420221, _1420221, _1420223), _1420225)))], (43351 ^ _779571) ^ [_1624119, _1624121, _1624123, _1624125] : [-(hAPP(c_Relation_Oconverse(_1624119, _1624119), hAPP(hAPP(c_Relation_Oinv__image(_1624121, _1624119), _1624123), _1624125)) = hAPP(hAPP(c_Relation_Oinv__image(_1624121, _1624119), hAPP(c_Relation_Oconverse(_1624121, _1624121), _1624123)), _1624125))], (32383 ^ _779571) ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368979), _1368981)), 32389 ^ _779571 : [(32392 ^ _779571) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1368983, _1368985, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1368983)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1368983), hAPP(_1368993, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995])), hAPP(_1368989, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995])), hAPP(_1368995, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1368983), tc_HOL_Obool))))], (32390 ^ _779571) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1368983, _1368985, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1368983)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1368983), hAPP(_1368987, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995])), hAPP(_1368989, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995])), hAPP(_1368991, 32388 ^ [_1368979, _1368981, _1368983, _1368985, _1368987, _1368989, _1368991, _1368993, _1368995]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1368983), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1368983, _1368985, hAPP(c_Set_Oimage(_1368979, tc_Hoare__Mirabelle_Otriple(_1368983), hAPP(hAPP(c_COMBS(_1368979, tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983)), hAPP(hAPP(c_COMBS(_1368979, tc_Com_Ocom, tc_fun(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983))), hAPP(hAPP(c_COMBB(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983))), _1368979), c_Hoare__Mirabelle_Otriple_Otriple(_1368983)), _1368987)), _1368989)), _1368991)), _1368981)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1368983, _1368985, hAPP(c_Set_Oimage(_1368979, tc_Hoare__Mirabelle_Otriple(_1368983), hAPP(hAPP(c_COMBS(_1368979, tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983)), hAPP(hAPP(c_COMBS(_1368979, tc_Com_Ocom, tc_fun(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983))), hAPP(hAPP(c_COMBB(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1368983, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1368983))), _1368979), c_Hoare__Mirabelle_Otriple_Otriple(_1368983)), _1368993)), _1368989)), _1368995)), _1368981)))], (34841 ^ _779571) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (49834 ^ _779571) ^ [_1780684, _1780686] : [-(c_List_Opartition(_1780684, _1780686, c_List_Olist_ONil(_1780684)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780684), tc_List_Olist(_1780684)), c_List_Olist_ONil(_1780684)), c_List_Olist_ONil(_1780684)))], (48754 ^ _779571) ^ [_1757205, _1757207, _1757209] : [hBOOL(hAPP(c_List_Odistinct(_1757205), _1757207)), -(hBOOL(hAPP(c_List_Odistinct(_1757205), hAPP(hAPP(c_List_Odrop(_1757205), _1757209), _1757207))))], (5424 ^ _779571) ^ [_863439, _863441] : [_863441 = _863439, -(c_List_Olist_ONil(_863441) = c_List_Olist_ONil(_863439))], (110 ^ _779571) ^ [_781070, _781072, _781074, _781076, _781078, _781080] : [-(c_Nitpick_Oless__frac(_781078, _781074, _781070)), c_Nitpick_Oless__frac(_781080, _781076, _781072), _781080 = _781078, _781076 = _781074, _781072 = _781070], (21867 ^ _779571) ^ [_1156718, _1156720, _1156722, _1156724] : [class_Fields_Olinordered__field__inverse__zero(_1156718), class_Int_Onumber(_1156718), 21874 ^ _779571 : [(21875 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156720), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156718), _1156722), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)))), 21878 ^ _779571 : [(21885 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), c_Groups_Ozero__class_Ozero(_1156718)), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)))), 21888 ^ _779571 : [(21895 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)), c_Groups_Ozero__class_Ozero(_1156718)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156720), c_Groups_Ozero__class_Ozero(_1156718))))], (21889 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)), c_Groups_Ozero__class_Ozero(_1156718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156718), _1156720), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)))))]]], (21879 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), c_Groups_Ozero__class_Ozero(_1156718)), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156718), _1156720), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))), _1156722)))]]], (21901 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156720), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156718), _1156722), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))))), 21904 ^ _779571 : [(21907 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156718), _1156720), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))), _1156722))], (21905 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), c_Groups_Ozero__class_Ozero(_1156718)), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))))]], 21908 ^ _779571 : [(21911 ^ _779571) ^ [] : [21912 ^ _779571 : [(21915 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156718), _1156720), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724))))], (21913 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)), c_Groups_Ozero__class_Ozero(_1156718))))]], 21916 ^ _779571 : [(21919 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156718), _1156720), c_Groups_Ozero__class_Ozero(_1156718)))], (21917 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)), c_Groups_Ozero__class_Ozero(_1156718)))]]], (21909 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156718), c_Groups_Ozero__class_Ozero(_1156718)), hAPP(c_Int_Onumber__class_Onumber__of(_1156718), _1156724)))]]]]], (36902 ^ _779571) ^ [_1466796, _1466798, _1466800, _1466802, _1466804] : [class_Orderings_Olinorder(_1466796), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466796, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1466796, _1466798, _1466800)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1466796, _1466802, _1466804)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1466796, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1466796), _1466798), _1466802), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1466796), _1466800), _1466804)))], (29750 ^ _779571) ^ [_1311546] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1311546), hAPP(c_Nat_OSuc, _1311546)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1311546), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (36016 ^ _779571) ^ [_1447262, _1447264, _1447266, _1447268, _1447270, _1447272] : [c_Equiv__Relations_Oequiv(_1447262, _1447264, _1447266), c_Equiv__Relations_Ocongruent(_1447262, tc_fun(_1447268, tc_HOL_Obool), _1447266, _1447270), hBOOL(hAPP(hAPP(c_member(_1447262), _1447272), _1447264)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447262, tc_fun(_1447268, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447262, _1447262, _1447266), hAPP(hAPP(c_Set_Oinsert(_1447262), _1447272), c_Orderings_Obot__class_Obot(tc_fun(_1447262, tc_HOL_Obool))))), _1447270) = hAPP(_1447270, _1447272))], (18285 ^ _779571) ^ [_1093777] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1093777)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093777) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19603 ^ _779571) ^ [] : [-(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))))], (22127 ^ _779571) ^ [_1161505, _1161507, _1161509] : [class_Fields_Olinordered__field(_1161505), 22133 ^ _779571 : [(22136 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161505), _1161507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161505), _1161509), 22132 ^ [_1161505, _1161507, _1161509])))], (22134 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161505), c_Groups_Ozero__class_Ozero(_1161505)), 22132 ^ [_1161505, _1161507, _1161509])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161505), _1161507), _1161509)))], (50286 ^ _779571) ^ [_1789848, _1789850] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789848)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789850)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789848), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789850)) = c_List_Olist_ONil(tc_Nat_Onat))], (19547 ^ _779571) ^ [_1114885, _1114887] : [class_Rings_Ocomm__semiring__1(_1114885), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114885), _1114887), _1114887) = hAPP(hAPP(c_Power_Opower__class_Opower(_1114885), _1114887), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22506 ^ _779571) ^ [_1169084, _1169086] : [-(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), _1169084)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1169086), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1169084))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (51195 ^ _779571) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (48365 ^ _779571) ^ [_1746256, _1746258, _1746260, _1746262, _1746264, _1746266, _1746268] : [hBOOL(hAPP(hAPP(c_member(_1746256), _1746258), hAPP(c_List_Oset(_1746256), hAPP(hAPP(c_List_Otake(_1746256), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746260)), _1746262)), _1746264)))), -(c_Map_Omap__upds(_1746256, _1746260, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1746256, tc_Option_Ooption(_1746260)), _1746266), _1746258), hAPP(c_Option_Ooption_OSome(_1746260), _1746268)), _1746264, _1746262) = c_Map_Omap__upds(_1746256, _1746260, _1746266, _1746264, _1746262))], (44732 ^ _779571) ^ [_1657919, _1657921, _1657923, _1657925, _1657927] : [_1657919 = c_Orderings_Obot__class_Obot(tc_fun(_1657921, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657921, tc_fun(_1657923, tc_HOL_Obool)), _1657919), hAPP(hAPP(c_COMBB(tc_fun(_1657923, tc_HOL_Obool), tc_fun(_1657923, tc_HOL_Obool), _1657921), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657923, tc_HOL_Obool)), _1657925)), _1657927)) = c_Orderings_Otop__class_Otop(tc_fun(_1657923, tc_HOL_Obool)))], (48341 ^ _779571) ^ [_1745678, _1745680, _1745682, _1745684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1745678), _1745680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745682, tc_HOL_Obool)), hAPP(c_List_Oset(_1745682), hAPP(hAPP(c_List_Otake(_1745682), _1745678), _1745684))), hAPP(c_List_Oset(_1745682), hAPP(hAPP(c_List_Otake(_1745682), _1745680), _1745684)))))], (49287 ^ _779571) ^ [_1769102, _1769104, _1769106] : [c_Equiv__Relations_Oequiv(_1769102, _1769104, _1769106), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1769102), c_List_Olists(_1769102, _1769104), c_List_Olistrel(_1769102, _1769106)))], (28951 ^ _779571) ^ [_1295462, _1295464, _1295466, _1295468, _1295470, _1295472] : [-(hAPP(c_Set_Oimage(_1295462, _1295464, _1295466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295468, tc_fun(_1295462, tc_HOL_Obool)), _1295470), _1295472)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295468, tc_fun(_1295464, tc_HOL_Obool)), _1295470), hAPP(hAPP(c_COMBB(tc_fun(_1295462, tc_HOL_Obool), tc_fun(_1295464, tc_HOL_Obool), _1295468), c_Set_Oimage(_1295462, _1295464, _1295466)), _1295472)))], (49816 ^ _779571) ^ [_1780215, _1780217, _1780219] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1780215, tc_HOL_Obool)), hAPP(c_List_Oset(_1780215), _1780217)), hAPP(hAPP(c_Set_Oinsert(_1780215), _1780219), c_Orderings_Obot__class_Obot(tc_fun(_1780215, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1780215), hAPP(c_List_Ofilter(_1780215, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1780215), c_fNot), hAPP(hAPP(c_COMBC(_1780215, _1780215, tc_HOL_Obool), c_fequal), _1780219))), _1780217)))], (49054 ^ _779571) ^ [_1763701, _1763703, _1763705] : [-(hAPP(c_List_Orotate1(_1763701), hAPP(c_List_Orotate(_1763701, _1763703), _1763705)) = hAPP(c_List_Orotate(_1763701, _1763703), hAPP(c_List_Orotate1(_1763701), _1763705)))], (48514 ^ _779571) ^ [_1750105, _1750107] : [-(c_List_Olistrel(_1750105, c_Transitive__Closure_Ortrancl(_1750105, _1750107)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750105), c_List_Olistrel1(_1750105, _1750107)))], (39846 ^ _779571) ^ [_1532043, _1532045, _1532047] : [hBOOL(hAPP(hAPP(c_member(_1532043), _1532047), c_Wellfounded_Oacc(_1532043, _1532045))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1532043, hAPP(hAPP(c_COMBC(_1532043, tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_fun(_1532043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532043, tc_fun(tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_fun(_1532043, tc_HOL_Obool)), _1532043), c_COMBC(_1532043, tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532043, tc_prod(_1532043, _1532043)), tc_fun(_1532043, tc_fun(tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_HOL_Obool)), _1532043), hAPP(c_COMBB(tc_prod(_1532043, _1532043), tc_fun(tc_fun(tc_prod(_1532043, _1532043), tc_HOL_Obool), tc_HOL_Obool), _1532043), c_member(tc_prod(_1532043, _1532043)))), c_Product__Type_OPair(_1532043, _1532043)))), _1532045)), _1532047)))], (2452 ^ _779571) ^ [_816647, _816649, _816651, _816653, _816655, _816657] : [-(c_Nat_Onat_Onat__rec(_816657, _816653, _816649) = c_Nat_Onat_Onat__rec(_816655, _816651, _816647)), _816657 = _816655, _816653 = _816651, _816649 = _816647], (25676 ^ _779571) ^ [_1229179, _1229181] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229179), _1229181)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229179)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229181))))], (27680 ^ _779571) ^ [_1269644, _1269646] : [c_Nat__Transfer_Onat__set(_1269644), c_Nat__Transfer_Onat__set(_1269646), 27687 ^ _779571 : [(27694 ^ _779571) ^ [] : [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), _1269644)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1269646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1269644), _1269646)))], (27688 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1269644), _1269646)), -(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), _1269644)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1269646))))]]], (34273 ^ _779571) ^ [_1406272, _1406274, _1406276, _1406278] : [class_Groups_Ocomm__monoid__mult(_1406272), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1406274), _1406276))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406274, _1406272), _1406278), _1406276) = c_Groups_Oone__class_Oone(_1406272))], (38801 ^ _779571) ^ [_1508887, _1508889, _1508891, _1508893, _1508895, _1508897] : [c_Fun_Oinj__on(_1508887, _1508889, _1508891, _1508893), -(hBOOL(hAPP(hAPP(c_member(_1508889), _1508895), hAPP(c_Set_Oimage(_1508887, _1508889, _1508891), _1508893)))), -(c_Fun_Oinj__on(_1508887, _1508889, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1508887, _1508889), _1508891), _1508897), _1508895), _1508893))], (44452 ^ _779571) ^ [_1649310, _1649312, _1649314, _1649316] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1649310, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649312, tc_fun(_1649310, tc_HOL_Obool)), _1649314), _1649316)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649312, tc_fun(_1649310, tc_HOL_Obool)), _1649314), hAPP(hAPP(c_COMBB(tc_fun(_1649310, tc_HOL_Obool), tc_fun(_1649310, tc_HOL_Obool), _1649312), c_Groups_Ouminus__class_Ouminus(tc_fun(_1649310, tc_HOL_Obool))), _1649316)))], (19481 ^ _779571) ^ [_1113736] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113736)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1113736)))], (25084 ^ _779571) ^ [_1219373] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219373), _1219373)))], (29055 ^ _779571) ^ [_1297864, _1297866] : [class_Lattices_Obounded__lattice__top(_1297864), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1297864), c_Orderings_Otop__class_Otop(_1297864)), _1297866) = c_Orderings_Otop__class_Otop(_1297864))], (41326 ^ _779571) ^ [_1568726, _1568728, _1568730, _1568732] : [-(c_Fun_Ooverride__on(_1568726, _1568728, _1568730, _1568732, c_Orderings_Obot__class_Obot(tc_fun(_1568726, tc_HOL_Obool))) = _1568730)], (30985 ^ _779571) ^ [_1337401, _1337403, _1337405, _1337407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337401), _1337403)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337405), hAPP(c_Set_Oimage(_1337401, _1337405, _1337407), _1337403))))], (36646 ^ _779571) ^ [_1460485, _1460487, _1460489, _1460491, _1460493] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460485, tc_fun(_1460487, tc_HOL_Obool)), _1460489), hAPP(hAPP(c_COMBC(_1460485, tc_fun(_1460487, tc_HOL_Obool), tc_fun(_1460487, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460487, tc_HOL_Obool), tc_fun(tc_fun(_1460487, tc_HOL_Obool), tc_fun(_1460487, tc_HOL_Obool)), _1460485), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460487, tc_HOL_Obool))), _1460491)), _1460493)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460487, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460485, tc_fun(_1460487, tc_HOL_Obool)), _1460489), _1460491)), _1460493))], (5142 ^ _779571) ^ [_859032, _859034] : [_859034 = _859032, -(c_List_Odrop(_859034) = c_List_Odrop(_859032))], (41352 ^ _779571) ^ [_1569600, _1569602, _1569604, _1569606] : [-(c_Nitpick_Oprod(_1569600, _1569602, _1569604, _1569606) = hAPP(c_Set_OCollect(tc_prod(_1569600, _1569602)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569600, _1569602, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1569600, tc_fun(_1569602, tc_HOL_Obool), tc_fun(_1569602, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1569602, tc_HOL_Obool), tc_fun(_1569602, tc_HOL_Obool)), _1569600), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569602)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569600), c_fconj), hAPP(hAPP(c_COMBC(_1569600, tc_fun(_1569600, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569600)), _1569604)))), hAPP(hAPP(c_COMBC(_1569602, tc_fun(_1569602, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569602)), _1569606)))))], (27868 ^ _779571) ^ [_1273087, _1273089, _1273091, _1273093] : [class_Lattices_Osemilattice__sup(_1273087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273087), _1273089), _1273091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273087), _1273089), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273087), _1273093), _1273091))))], (14453 ^ _779571) ^ [_1023440, _1023442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023442, _1023440)), _1023440)))], (42606 ^ _779571) ^ [_1605654, _1605656, _1605658, _1605660, _1605662, _1605664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605654, tc_HOL_Obool)), _1605656), _1605658)), 42612 ^ _779571 : [(42615 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605660, tc_HOL_Obool)), hAPP(_1605662, 42611 ^ [_1605654, _1605656, _1605658, _1605660, _1605662, _1605664])), hAPP(_1605664, 42611 ^ [_1605654, _1605656, _1605658, _1605660, _1605662, _1605664])))], (42613 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605654), 42611 ^ [_1605654, _1605656, _1605658, _1605660, _1605662, _1605664]), _1605656)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605654, _1605660), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1605654, _1605660), _1605656), _1605662)), hAPP(hAPP(c_Product__Type_OSigma(_1605654, _1605660), _1605658), _1605664))))], (38984 ^ _779571) ^ [_1512814, _1512816, _1512818, _1512820] : [c_Fun_Oinj__on(_1512814, tc_fun(tc_fun(_1512814, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1512814, tc_fun(tc_prod(_1512814, _1512814), tc_HOL_Obool), tc_fun(tc_fun(_1512814, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512814, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1512814, _1512814), tc_HOL_Obool), tc_fun(tc_fun(_1512814, tc_HOL_Obool), tc_HOL_Obool)), _1512814), c_Equiv__Relations_Oquotient(_1512814)), hAPP(hAPP(c_COMBC(_1512814, tc_fun(_1512814, tc_HOL_Obool), tc_fun(_1512814, tc_HOL_Obool)), c_Set_Oinsert(_1512814)), c_Orderings_Obot__class_Obot(tc_fun(_1512814, tc_HOL_Obool))))), _1512816), _1512818), hBOOL(hAPP(hAPP(c_member(_1512814), _1512820), _1512818)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512814, tc_HOL_Obool)), _1512818), hAPP(hAPP(c_Set_Oinsert(_1512814), _1512820), c_Orderings_Obot__class_Obot(tc_fun(_1512814, tc_HOL_Obool))))), _1512816) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1512814, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512814), _1512818), _1512816)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512814), hAPP(hAPP(c_Set_Oinsert(_1512814), _1512820), c_Orderings_Obot__class_Obot(tc_fun(_1512814, tc_HOL_Obool)))), _1512816)))], (49602 ^ _779571) ^ [_1775770] : [-(c_List_Obutlast(_1775770, c_List_Olist_ONil(_1775770)) = c_List_Olist_ONil(_1775770))], (16142 ^ _779571) ^ [_1055496, _1055498] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055496, _1055498) = 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), _1055496), _1055498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055498), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055496, _1055498)))], (30413 ^ _779571) ^ [_1325013, _1325015, _1325017, _1325019] : [_1325013 = _1325015, hBOOL(hAPP(hAPP(c_member(_1325017), _1325015), _1325019)), -(hBOOL(hAPP(hAPP(c_member(_1325017), _1325013), _1325019)))], (42134 ^ _779571) ^ [_1594376, _1594378, _1594380] : [-(hAPP(c_Set_Oimage(tc_prod(_1594376, _1594378), _1594378, c_Product__Type_Osnd(_1594376, _1594378)), _1594380) = hAPP(c_Relation_ORange(_1594376, _1594378), _1594380))], (36424 ^ _779571) ^ [_1456341, _1456343] : [class_Lattices_Olattice(_1456341), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456341), _1456343), _1456343) = _1456343)], (50692 ^ _779571) ^ [_1798675, _1798677, _1798679, _1798681] : [-(hAPP(hAPP(c_List_Omap(_1798675, _1798677), _1798679), c_List_Oconcat(_1798675, _1798681)) = c_List_Oconcat(_1798677, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798675), tc_List_Olist(_1798677)), hAPP(c_List_Omap(_1798675, _1798677), _1798679)), _1798681)))], (15086 ^ _779571) ^ [_1034574, _1034576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034574)), -(c_SMT_Oz3div(_1034576, _1034574) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034576), _1034574))], (43538 ^ _779571) ^ [_1628787, _1628789] : [-(c_Relation_Ototal__on(_1628787, c_Orderings_Obot__class_Obot(tc_fun(_1628787, tc_HOL_Obool)), _1628789))], (11326 ^ _779571) ^ [_967653, _967655] : [11327 ^ _779571 : [(11330 ^ _779571) ^ [] : [_967653 = hAPP(c_Nat_OSuc, _967655)], (11328 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967653), _967655))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967653), hAPP(c_Nat_OSuc, _967655))))], (28441 ^ _779571) ^ [_1284751, _1284753, _1284755] : [class_Orderings_Olinorder(_1284751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284751), _1284753), _1284755)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284751, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1284751), _1284753)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1284751, _1284753, _1284755)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1284751), _1284755))], (51435 ^ _779571) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (20039 ^ _779571) ^ [_1123983, _1123985, _1123987, _1123989, _1123991] : [class_Fields_Ofield__inverse__zero(_1123983), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123983), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123983), _1123985), _1123987)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123983), _1123989), _1123991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123983), _1123985), _1123989)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123983), _1123987), _1123991)))], (47252 ^ _779571) ^ [_1719897, _1719899, _1719901, _1719903] : [-(c_List_Ofoldr(_1719897, _1719899, _1719901, c_List_Olist_ONil(_1719897), _1719903) = _1719903)], (6510 ^ _779571) ^ [_885806, _885808, _885810, _885812] : [c_Com_Ocom_OAss(_885806, _885808) = c_Com_Ocom_OAss(_885810, _885812), 6513 ^ _779571 : [(6516 ^ _779571) ^ [] : [-(_885808 = _885812)], (6514 ^ _779571) ^ [] : [-(_885806 = _885810)]]], (10558 ^ _779571) ^ [_955240, _955242, _955244] : [class_Orderings_Oorder(_955240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955240), _955242), _955244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955240), _955244), _955242)), -(_955244 = _955242)], (28317 ^ _779571) ^ [_1282098, _1282100, _1282102] : [class_Groups_Oordered__ab__group__add(_1282098), -(hAPP(c_Set_Oimage(_1282098, _1282098, c_Groups_Ouminus__class_Ouminus(_1282098)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1282098, _1282100, _1282102)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1282098, hAPP(c_Groups_Ouminus__class_Ouminus(_1282098), _1282102), hAPP(c_Groups_Ouminus__class_Ouminus(_1282098), _1282100)))], (36920 ^ _779571) ^ [_1467245, _1467247, _1467249, _1467251] : [class_Orderings_Olinorder(_1467245), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467245, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1467245, _1467247, _1467249)), hAPP(c_SetInterval_Oord__class_OatMost(_1467245), _1467251)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467245, _1467247, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1467245), _1467249), _1467251)))], (8042 ^ _779571) ^ [_912841, _912843, _912845] : [hAPP(c_Option_Ooption_OSome(_912841), _912843) = hAPP(c_Option_Ooption_OSome(_912841), _912845), -(_912843 = _912845)], (2316 ^ _779571) ^ [_814539, _814541, _814543, _814545] : [-(c_SMT_Oz3div(_814545, _814541) = c_SMT_Oz3div(_814543, _814539)), _814545 = _814543, _814541 = _814539], (26064 ^ _779571) ^ [_1237131, _1237133, _1237135, _1237137] : [class_Rings_Oidom(_1237131), 26067 ^ _779571 : [(26068 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237131), _1237133), _1237135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237131), _1237137), _1237135))), -(_1237135 = c_Groups_Ozero__class_Ozero(_1237131)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237131), _1237133), _1237137)))], (26078 ^ _779571) ^ [] : [26079 ^ _779571 : [(26082 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237131), _1237133), _1237137))], (26080 ^ _779571) ^ [] : [_1237135 = c_Groups_Ozero__class_Ozero(_1237131)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237131), _1237133), _1237135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237131), _1237137), _1237135))))]]], (49779 ^ _779571) ^ [_1779496, _1779498, _1779500] : [hAPP(c_List_Ofilter(_1779496, _1779498), _1779500) = c_List_Olist_ONil(_1779496), 49782 ^ _779571 : [(49783 ^ _779571) ^ [_1779593] : [hBOOL(hAPP(hAPP(c_member(_1779496), _1779593), hAPP(c_List_Oset(_1779496), _1779500))), hBOOL(hAPP(_1779498, _1779593))]]], (31930 ^ _779571) ^ [_1359766, _1359768, _1359770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359766), _1359768)), hBOOL(hAPP(hAPP(c_member(_1359766), _1359770), _1359768)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1359766), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359766, tc_HOL_Obool)), _1359768), hAPP(hAPP(c_Set_Oinsert(_1359766), _1359770), c_Orderings_Obot__class_Obot(tc_fun(_1359766, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1359766), _1359768))], (6418 ^ _779571) ^ [_884147, _884149, _884151] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _884147))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_884149, _884147, _884151))))], (44576 ^ _779571) ^ [_1653303, _1653305, _1653307, _1653309] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653303, tc_fun(_1653305, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1653303, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1653305, tc_HOL_Obool), tc_fun(_1653305, tc_HOL_Obool), _1653303), hAPP(c_COMBC(_1653305, tc_fun(_1653305, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653305))), _1653307)), _1653309)), -(hBOOL(hAPP(hAPP(c_member(_1653305), _1653309), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653303, tc_fun(_1653305, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1653303, tc_HOL_Obool))), _1653307))))], (41636 ^ _779571) ^ [_1581414] : [-(hAPP(c_Set_Oimage(_1581414, _1581414, c_Fun_Oid(_1581414)), c_Orderings_Otop__class_Otop(tc_fun(_1581414, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1581414, tc_HOL_Obool)))], (6444 ^ _779571) ^ [_884640] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _884640), _884640)))], (11451 ^ _779571) ^ [_969696, _969698, _969700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969696), _969698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969700), _969698))))], (6811 ^ _779571) ^ [_891750, _891752] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_891750, _891752)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23947 ^ _779571) ^ [_1196362, _1196364, _1196366, _1196368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196362, tc_HOL_Obool)), _1196364), _1196366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196362, tc_HOL_Obool)), _1196366), _1196368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196362, tc_HOL_Obool)), _1196364), _1196368)))], (31812 ^ _779571) ^ [_1357034, _1357036, _1357038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1357034), _1357036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357034, tc_HOL_Obool)), _1357038), _1357036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1357034), _1357038)), hAPP(c_Finite__Set_Ocard(_1357034), _1357036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1357034, tc_HOL_Obool)), _1357038), _1357036)))], (40044 ^ _779571) ^ [_1537456, _1537458, _1537460] : [class_Groups_Oab__semigroup__mult(_1537456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537456), _1537458)), -(_1537458 = c_Orderings_Obot__class_Obot(tc_fun(_1537456, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537456), _1537460)), -(_1537460 = c_Orderings_Obot__class_Obot(tc_fun(_1537456, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537456, tc_HOL_Obool)), _1537458), _1537460) = c_Orderings_Obot__class_Obot(tc_fun(_1537456, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1537456, c_Groups_Otimes__class_Otimes(_1537456)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537456, tc_HOL_Obool)), _1537458), _1537460)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1537456), hAPP(c_Finite__Set_Ofold1(_1537456, c_Groups_Otimes__class_Otimes(_1537456)), _1537458)), hAPP(c_Finite__Set_Ofold1(_1537456, c_Groups_Otimes__class_Otimes(_1537456)), _1537460)))], (45468 ^ _779571) ^ [_1674815, _1674817, _1674819] : [45470 ^ _779571 : [(45473 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1674815), _1674819), 45469 ^ [_1674815, _1674817, _1674819]))], (45471 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674815, tc_HOL_Obool)), 45469 ^ [_1674815, _1674817, _1674819]), _1674817)))]], -(hBOOL(hAPP(hAPP(c_member(_1674815), _1674819), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1674815, tc_HOL_Obool), _1674817))))], (18385 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (45249 ^ _779571) ^ [_1670009, _1670011, _1670013] : [class_Complete__Lattice_Ocomplete__lattice(_1670009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670009), _1670011)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1670009), _1670013), c_Complete__Lattice_OSup__class_OSup(_1670009, _1670011)) = hAPP(hAPP(c_Finite__Set_Ofold(_1670009, _1670009, c_Lattices_Osemilattice__sup__class_Osup(_1670009)), _1670013), _1670011))], (5831 ^ _779571) ^ [_872983, _872985, _872987, _872989, _872991, _872993, _872995] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872983), _872985), _872987), _872989) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872983), _872991), _872993), _872995), 5834 ^ _779571 : [(5839 ^ _779571) ^ [] : [-(_872989 = _872995)], (5837 ^ _779571) ^ [] : [-(_872987 = _872993)], (5835 ^ _779571) ^ [] : [-(_872985 = _872991)]]], (38090 ^ _779571) ^ [_1494397, _1494399, _1494401] : [class_Lattices_Olattice(_1494397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494397), _1494399)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494397), _1494401)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494397, tc_HOL_Obool)), _1494399), _1494401) = c_Orderings_Obot__class_Obot(tc_fun(_1494397, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1494397), c_Big__Operators_Olattice__class_OInf__fin(_1494397, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494397, tc_HOL_Obool)), _1494399), _1494401))), c_Big__Operators_Olattice__class_OInf__fin(_1494397, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494397, tc_HOL_Obool)), _1494399), _1494401))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1494397), c_Big__Operators_Olattice__class_OInf__fin(_1494397, _1494399)), c_Big__Operators_Olattice__class_OInf__fin(_1494397, _1494401)))], (34049 ^ _779571) ^ [_1401768, _1401770, _1401772, _1401774, _1401776, _1401778] : [-(hBOOL(hAPP(hAPP(c_member(_1401768), _1401770), _1401772))), -(hAPP(c_Set_Oimage(_1401768, _1401774, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1401768, _1401774), _1401776), _1401770), _1401778)), _1401772) = hAPP(c_Set_Oimage(_1401768, _1401774, _1401776), _1401772))], (14315 ^ _779571) ^ [_1020876, _1020878, _1020880] : [-(hBOOL(hAPP(_1020876, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020878), _1020880)))), 14316 ^ _779571 : [(14323 ^ _779571) ^ [_1021044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020880), _1021044)), _1020878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020880), hAPP(c_Nat_OSuc, _1021044)))), hBOOL(hAPP(_1020876, _1021044))], (14317 ^ _779571) ^ [] : [_1020880 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1020876, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (17989 ^ _779571) ^ [_1089102] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089102))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089102)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (168 ^ _779571) ^ [_781961, _781963, _781965, _781967, _781969, _781971, _781973, _781975] : [-(c_Orderings_Oorder_Omono(_781973, _781969, _781965, _781961)), c_Orderings_Oorder_Omono(_781975, _781971, _781967, _781963), _781975 = _781973, _781971 = _781969, _781967 = _781965, _781963 = _781961], (9954 ^ _779571) ^ [_945358, _945360] : [class_Int_Oring__char__0(_945358), 9957 ^ _779571 : [(9964 ^ _779571) ^ [] : [_945360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_945358) = hAPP(c_Int_Oring__1__class_Oof__int(_945358), _945360))], (9958 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_945358) = hAPP(c_Int_Oring__1__class_Oof__int(_945358), _945360), -(_945360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (190 ^ _779571) ^ [_782314, _782316, _782318, _782320] : [-(c_Nitpick_Orefl_H(_782318, _782314)), c_Nitpick_Orefl_H(_782320, 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964838), _964842), -(_964840 = _964842), -(_964838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47284 ^ _779571) ^ [_1720441] : [-(hAPP(c_List_Oset(_1720441), c_List_Olist_ONil(_1720441)) = c_Orderings_Obot__class_Obot(tc_fun(_1720441, tc_HOL_Obool)))], (41219 ^ _779571) ^ [_1564775, _1564777, _1564779, _1564781, _1564783, _1564785, _1564787] : [class_Groups_Ocomm__monoid__add(_1564775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564777), _1564779)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564781), _1564783)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1564777, _1564775), hAPP(hAPP(c_COMBS(_1564777, tc_fun(_1564781, tc_HOL_Obool), _1564775), hAPP(hAPP(c_COMBB(tc_fun(_1564781, _1564775), tc_fun(tc_fun(_1564781, tc_HOL_Obool), _1564775), _1564777), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1564781, _1564775)), _1564785)), hAPP(hAPP(c_COMBB(tc_fun(_1564781, tc_HOL_Obool), tc_fun(_1564781, tc_HOL_Obool), _1564777), 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hAPP(c_COMBS(_1564777, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564777), c_fconj), hAPP(hAPP(c_COMBC(_1564777, tc_fun(_1564777, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564777)), _1564779)))), hAPP(c_COMBC(_1564777, _1564781, tc_HOL_Obool), _1564787))))), _1564783))], (46811 ^ _779571) ^ [_1708906, _1708908, _1708910] : [-(hAPP(c_List_Oset(_1708906), hAPP(hAPP(c_List_Olist_OCons(_1708906), _1708908), _1708910)) = hAPP(hAPP(c_Set_Oinsert(_1708906), _1708908), hAPP(c_List_Oset(_1708906), _1708910)))], (19509 ^ _779571) ^ [_1114287, _1114289] : [class_Int_Onumber__ring(_1114287), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114287), _1114289), hAPP(c_Int_Onumber__class_Onumber__of(_1114287), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114287), _1114289), _1114289))], (15528 ^ _779571) ^ [_1042682, _1042684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042682), _1042684)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042684), _1042682)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1042684)), hAPP(c_Int_Onat, _1042682)))], (19543 ^ _779571) ^ [] : [-(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))))], (22306 ^ _779571) ^ [_1164444] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1164444)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1164444)), 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))))], (4702 ^ _779571) ^ [_852292, _852294] : [_852294 = _852292, -(c_Lattices_Osemilattice__inf__class_Oinf(_852294) = c_Lattices_Osemilattice__inf__class_Oinf(_852292))], (8636 ^ _779571) ^ [_922140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922140)), 8640 ^ _779571 : [(8643 ^ _779571) ^ [] : [-(_922140 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8639 ^ [_922140]))], (8641 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8639 ^ [_922140])))]]], (39380 ^ _779571) ^ [_1521163, _1521165, _1521167, _1521169, _1521171] : [class_Groups_Ocomm__monoid__mult(_1521163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521165), _1521167)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521165), _1521169)), 39394 ^ _779571 : [(39397 ^ _779571) ^ [] : [hAPP(_1521171, 39393 ^ [_1521163, _1521165, _1521167, _1521169, _1521171]) = c_Groups_Oone__class_Oone(_1521163)], (39395 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521165), 39393 ^ [_1521163, _1521165, _1521167, _1521169, _1521171]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521165, tc_HOL_Obool)), _1521167), _1521169))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1521163, _1521165, c_Groups_Otimes__class_Otimes(_1521163)), _1521171), c_Groups_Oone__class_Oone(_1521163)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521165, tc_HOL_Obool)), _1521167), _1521169)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1521163), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1521163, _1521165, c_Groups_Otimes__class_Otimes(_1521163)), _1521171), c_Groups_Oone__class_Oone(_1521163)), _1521167)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1521163, _1521165, c_Groups_Otimes__class_Otimes(_1521163)), _1521171), c_Groups_Oone__class_Oone(_1521163)), _1521169)))], (18341 ^ _779571) ^ [] : [c_Int_OMin = c_Int_OPls], (18427 ^ _779571) ^ [_1095855] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095855), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095855)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1095855)))], (12928 ^ _779571) ^ [_996148, _996150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _996150)), -(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), _996150), _996148))))], (16343 ^ _779571) ^ [_1059137, _1059139] : [-(_1059137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1059139, _1059137) = c_Nitpick_Onat__gcd(_1059137, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1059139, _1059137)))], (31882 ^ _779571) ^ [_1358646, _1358648, _1358650, _1358652, _1358654] : [class_Groups_Ocomm__monoid__add(_1358646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358648), _1358650)), hBOOL(hAPP(hAPP(c_member(_1358648), _1358652), _1358650)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358648, _1358646), _1358654), _1358650) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1358646), hAPP(_1358654, _1358652)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358648, _1358646), _1358654), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358648, tc_HOL_Obool)), _1358650), hAPP(hAPP(c_Set_Oinsert(_1358648), _1358652), c_Orderings_Obot__class_Obot(tc_fun(_1358648, tc_HOL_Obool)))))))], (20093 ^ _779571) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (51359 ^ _779571) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (1282 ^ _779571) ^ [_798364, _798366] : [-(class_Lattices_Osemilattice__inf(_798364)), _798366 = _798364, class_Lattices_Osemilattice__inf(_798366)], (36280 ^ _779571) ^ [_1453307, _1453309, _1453311, _1453313] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453307, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453307, tc_HOL_Obool)), _1453309), _1453311)), _1453313) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453307, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453307, tc_HOL_Obool)), _1453309), _1453313)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453307, tc_HOL_Obool)), _1453311), _1453313)))], (3570 ^ _779571) ^ [_834458, _834460, _834462, _834464, _834466, _834468] : [-(c_Finite__Set_Ofold1Set(_834468, _834464, _834460) = c_Finite__Set_Ofold1Set(_834466, _834462, _834458)), _834468 = _834466, _834464 = _834462, _834460 = _834458], (2774 ^ _779571) ^ [_821634, _821636, _821638, _821640, _821642, _821644] : [-(c_Product__Type_Ointernal__split(_821644, _821640, _821636) = c_Product__Type_Ointernal__split(_821642, _821638, _821634)), _821644 = _821642, _821640 = _821638, _821636 = _821634], (18681 ^ _779571) ^ [_1100069, _1100071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1100069)), c_Int_OBit1(_1100071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100069), _1100071)))], (46937 ^ _779571) ^ [_1711673, _1711675, _1711677, _1711679] : [-(c_Map_Omap__of(_1711673, _1711675, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1711673, _1711675)), _1711677), _1711679)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1711673, tc_Option_Ooption(_1711675)), c_Map_Omap__of(_1711673, _1711675, _1711679)), hAPP(c_Product__Type_Ofst(_1711673, _1711675), _1711677)), hAPP(c_Option_Ooption_OSome(_1711675), hAPP(c_Product__Type_Osnd(_1711673, _1711675), _1711677))))], (2986 ^ _779571) ^ [_825216, _825218, _825220, _825222, _825224, _825226, _825228, _825230] : [-(c_New__Random__Sequence_Opos__empty(_825230, _825226, _825222, _825218) = c_New__Random__Sequence_Opos__empty(_825228, _825224, _825220, _825216)), _825230 = _825228, _825226 = _825224, _825222 = _825220, _825218 = _825216], (24979 ^ _779571) ^ [_1217318, _1217320, _1217322, _1217324, _1217326, _1217328] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1217318, _1217320, _1217322, _1217324), _1217326), _1217328) = hAPP(_1217324, hAPP(hAPP(c_Product__Type_OPair(_1217318, _1217320), _1217326), _1217328)))], (18501 ^ _779571) ^ [_1097046, _1097048] : [class_Int_Onumber__ring(_1097046), class_Rings_Olinordered__idom(_1097046), 18508 ^ _779571 : [(18515 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097048), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097046), hAPP(c_Int_Onumber__class_Onumber__of(_1097046), _1097048)), c_Groups_Ozero__class_Ozero(_1097046))))], (18509 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097046), hAPP(c_Int_Onumber__class_Onumber__of(_1097046), _1097048)), c_Groups_Ozero__class_Ozero(_1097046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097048), c_Int_OPls)))]]], (19581 ^ _779571) ^ [_1115465, _1115467, _1115469] : [class_Groups_Omonoid__mult(_1115465), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1115465), _1115467), 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)))), _1115469)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1115465), hAPP(hAPP(c_Power_Opower__class_Opower(_1115465), _1115467), _1115469)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (18925 ^ _779571) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (11340 ^ _779571) ^ [_967856, _967858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967858)), _967856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967856), _967858))], (27758 ^ _779571) ^ [_1271029, _1271031, _1271033, _1271035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271029, tc_HOL_Obool)), _1271031), _1271033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271029, tc_HOL_Obool)), _1271035), _1271033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271029, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271029, tc_HOL_Obool)), _1271031), _1271035)), _1271033)))], (39463 ^ _779571) ^ [_1523286, _1523288, _1523290, _1523292, _1523294] : [hBOOL(hAPP(hAPP(c_member(_1523286), _1523288), hAPP(c_Set_Ovimage(_1523286, _1523290, _1523292), _1523294))), -(hBOOL(hAPP(hAPP(c_member(_1523290), hAPP(_1523292, _1523288)), _1523294)))], (1792 ^ _779571) ^ [_804739, _804741, _804743, _804745, _804747, _804749] : [-(c_Hoare__Mirabelle_Otriple__valid(_804747, _804743, _804739)), c_Hoare__Mirabelle_Otriple__valid(_804749, _804745, _804741), _804749 = _804747, _804745 = _804743, _804741 = _804739], (2572 ^ _779571) ^ [_818467, _818469, _818471, _818473] : [-(c_Divides_OnegDivAlg(_818473, _818469) = c_Divides_OnegDivAlg(_818471, _818467)), _818473 = _818471, _818469 = _818467], (24081 ^ _779571) ^ [_1198822, _1198824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198824), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198822), _1198824) = 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), _1198822), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198824)))))], (34703 ^ _779571) ^ [_1415673, _1415675, _1415677, _1415679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1415673), _1415675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1415677), _1415679)), -(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), _1415673), _1415677)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1415675), _1415679))), c_FunDef_Opair__less)))], (18439 ^ _779571) ^ [_1096009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096009), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096009))], (24745 ^ _779571) ^ [_1211685, _1211687] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1211685), _1211687) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211685)), hAPP(c_Code__Numeral_Onat__of, _1211687))))], (36654 ^ _779571) ^ [_1460883, _1460885, _1460887, _1460889, _1460891, _1460893, _1460895] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460883, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460885, tc_fun(_1460883, tc_HOL_Obool)), _1460887), _1460889)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460891, tc_fun(_1460883, tc_HOL_Obool)), _1460893), _1460895)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460885, tc_fun(_1460883, tc_HOL_Obool)), _1460887), hAPP(hAPP(c_COMBB(tc_fun(_1460891, tc_fun(_1460883, tc_HOL_Obool)), tc_fun(_1460883, tc_HOL_Obool), _1460885), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460891, tc_fun(_1460883, tc_HOL_Obool)), _1460893)), hAPP(hAPP(c_COMBC(_1460885, tc_fun(_1460891, tc_fun(_1460883, tc_HOL_Obool)), tc_fun(_1460891, tc_fun(_1460883, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1460883, tc_HOL_Obool), tc_fun(_1460883, tc_HOL_Obool)), tc_fun(tc_fun(_1460891, tc_fun(_1460883, tc_HOL_Obool)), tc_fun(_1460891, tc_fun(_1460883, tc_HOL_Obool))), _1460885), c_COMBB(tc_fun(_1460883, tc_HOL_Obool), tc_fun(_1460883, tc_HOL_Obool), _1460891)), hAPP(hAPP(c_COMBB(tc_fun(_1460883, tc_HOL_Obool), tc_fun(tc_fun(_1460883, tc_HOL_Obool), tc_fun(_1460883, tc_HOL_Obool)), _1460885), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460883, tc_HOL_Obool))), _1460889))), _1460895))))], (23087 ^ _779571) ^ [_1180009, _1180011, _1180013, _1180015, _1180017, _1180019] : [-(hAPP(hAPP(c_Product__Type_OPair(_1180009, _1180011), _1180013), _1180015) = hAPP(hAPP(c_Product__Type_OPair(_1180009, _1180011), _1180017), _1180019)), _1180013 = _1180017, _1180015 = _1180019], (1202 ^ _779571) ^ [_797364, _797366] : [-(class_Rings_Oring(_797364)), _797366 = _797364, class_Rings_Oring(_797366)], (42960 ^ _779571) ^ [_1614318, _1614320, _1614322, _1614324] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614318, _1614318)), hAPP(hAPP(c_Product__Type_OPair(_1614318, _1614318), _1614322), _1614324)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool)), _1614320), c_Relation_OId(_1614318)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1614318, tc_fun(_1614318, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1614318, tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_fun(_1614318, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614318, tc_fun(tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_fun(_1614318, tc_HOL_Obool)), _1614318), c_COMBC(_1614318, tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614318, tc_prod(_1614318, _1614318)), tc_fun(_1614318, tc_fun(tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_HOL_Obool)), _1614318), hAPP(c_COMBB(tc_prod(_1614318, _1614318), tc_fun(tc_fun(tc_prod(_1614318, _1614318), tc_HOL_Obool), tc_HOL_Obool), _1614318), c_member(tc_prod(_1614318, _1614318)))), c_Product__Type_OPair(_1614318, _1614318)))), _1614320)), c_fequal), _1614322), _1614324)))], (32071 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (2296 ^ _779571) ^ [_814241, _814243, _814245, _814247] : [-(c_Int_Onat__aux(_814247, _814243) = c_Int_Onat__aux(_814245, _814241)), _814247 = _814245, _814243 = _814241], (50065 ^ _779571) ^ [_1786110, _1786112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1786110), _1786112)), -(c_List_Oupt(_1786110, hAPP(c_Nat_OSuc, _1786112)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1786110, _1786112)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1786112), c_List_Olist_ONil(tc_Nat_Onat))))], (49189 ^ _779571) ^ [_1766562, _1766564] : [class_Complete__Lattice_Ocomplete__lattice(_1766562), -(c_Complete__Lattice_OInf__class_OInf(_1766562, hAPP(c_List_Oset(_1766562), _1766564)) = hAPP(c_List_Ofoldl(_1766562, _1766562, c_Lattices_Osemilattice__inf__class_Oinf(_1766562), c_Orderings_Otop__class_Otop(_1766562)), _1766564))], (51361 ^ _779571) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (6746 ^ _779571) ^ [_890354, _890356, _890358, _890360] : [hAPP(c_Com_Ocom_OBODY, _890354) = c_Com_Ocom_OLocal(_890356, _890358, _890360)], (46384 ^ _779571) ^ [_1695879, _1695881, _1695883] : [-(hAPP(hAPP(c_List_Ozip(_1695879, _1695881), hAPP(hAPP(c_List_Omap(tc_prod(_1695879, _1695881), _1695879), c_Product__Type_Ofst(_1695879, _1695881)), _1695883)), hAPP(hAPP(c_List_Omap(tc_prod(_1695879, _1695881), _1695881), c_Product__Type_Osnd(_1695879, _1695881)), _1695883)) = _1695883)], (32901 ^ _779571) ^ [_1379874, _1379876, _1379878] : [class_Rings_Oring__1(_1379874), hBOOL(hAPP(hAPP(c_member(_1379874), _1379876), c_Int_Oring__1__class_OInts(_1379874))), -(hBOOL(hAPP(hAPP(c_member(_1379874), hAPP(hAPP(c_Power_Opower__class_Opower(_1379874), _1379876), _1379878)), c_Int_Oring__1__class_OInts(_1379874))))], (50884 ^ _779571) ^ [_1803440, _1803442, _1803444, _1803446] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1803440)), c_List_Otranspose__rel(_1803440)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803440)), hAPP(hAPP(c_List_Olist_OCons(_1803440), _1803442), _1803444)), _1803446))), -(c_List_Otranspose(_1803440, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803440)), hAPP(hAPP(c_List_Olist_OCons(_1803440), _1803442), _1803444)), _1803446)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803440)), hAPP(hAPP(c_List_Olist_OCons(_1803440), _1803442), c_List_Oconcat(_1803440, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803440), tc_List_Olist(_1803440)), c_List_Olist_Olist__case(tc_List_Olist(_1803440), _1803440, c_List_Olist_ONil(_1803440), hAPP(hAPP(c_COMBB(tc_List_Olist(_1803440), tc_fun(tc_List_Olist(_1803440), tc_List_Olist(_1803440)), _1803440), c_COMBK(tc_List_Olist(_1803440), tc_List_Olist(_1803440))), hAPP(hAPP(c_COMBC(_1803440, tc_List_Olist(_1803440), tc_List_Olist(_1803440)), c_List_Olist_OCons(_1803440)), c_List_Olist_ONil(_1803440))))), _1803446)))), c_List_Otranspose(_1803440, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803440)), _1803444), c_List_Oconcat(tc_List_Olist(_1803440), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803440), tc_List_Olist(tc_List_Olist(_1803440))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1803440)), _1803440, c_List_Olist_ONil(tc_List_Olist(_1803440)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1803440), tc_List_Olist(tc_List_Olist(_1803440))), _1803440), hAPP(hAPP(c_COMBC(tc_List_Olist(_1803440), tc_List_Olist(tc_List_Olist(_1803440)), tc_List_Olist(tc_List_Olist(_1803440))), c_List_Olist_OCons(tc_List_Olist(_1803440))), c_List_Olist_ONil(tc_List_Olist(_1803440)))))), _1803446))))))], (30216 ^ _779571) ^ [_1321194, _1321196, _1321198, _1321200] : [-(hBOOL(hAPP(hAPP(c_member(_1321194), _1321196), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321194, tc_HOL_Obool)), _1321198), _1321200)))), hBOOL(hAPP(hAPP(c_member(_1321194), _1321196), _1321198)), -(hBOOL(hAPP(hAPP(c_member(_1321194), _1321196), _1321200)))], (47468 ^ _779571) ^ [_1724782, _1724784, _1724786, _1724788] : [hBOOL(hAPP(c_List_Odistinct(_1724782), _1724784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724786), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724782)), _1724784))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724782)), _1724784))), 47479 ^ _779571 : [(47486 ^ _779571) ^ [] : [_1724786 = _1724788, -(hAPP(hAPP(c_List_Onth(_1724782), _1724784), _1724786) = hAPP(hAPP(c_List_Onth(_1724782), _1724784), _1724788))], (47480 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Onth(_1724782), _1724784), _1724786) = hAPP(hAPP(c_List_Onth(_1724782), _1724784), _1724788), -(_1724786 = _1724788)]]], (22714 ^ _779571) ^ [_1173045] : [-(c_Hoare__Mirabelle_OMGT(_1173045) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1173045), c_Natural_Oevalc(_1173045)))], (51111 ^ _779571) ^ [_1808530, _1808532] : [class_Lattices_Oboolean__algebra(_1808530), -(class_Lattices_Oboolean__algebra(tc_fun(_1808532, _1808530)))], (12329 ^ _779571) ^ [_985459, _985461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985459), _985461)), 12332 ^ _779571 : [(12339 ^ _779571) ^ [] : [_985461 = _985459, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985461), hAPP(c_Nat_OSuc, _985459))))], (12333 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985461), hAPP(c_Nat_OSuc, _985459))), -(_985461 = _985459)]]], (13601 ^ _779571) ^ [_1007442, _1007444, _1007446, _1007448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007444), _1007446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1007446), 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), _1007444), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007448, _1007442))), _1007446)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19989 ^ _779571) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22146 ^ _779571) ^ [_1161910, _1161912, _1161914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1161910), _1161912))), -(c_Random_Ominus__shift(_1161914, _1161910, _1161912) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1161910), _1161912))], (17073 ^ _779571) ^ [_1072861, _1072863] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072861), _1072863))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1072861))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1072863))))], (6562 ^ _779571) ^ [_886673] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _886673)], (43076 ^ _779571) ^ [_1617448, _1617450] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1617448, _1617448, _1617448), c_Transitive__Closure_Ortrancl(_1617448, _1617450)), c_Transitive__Closure_Ortrancl(_1617448, _1617450)) = c_Transitive__Closure_Ortrancl(_1617448, _1617450))], (24765 ^ _779571) ^ [_1212115, _1212117, _1212119, _1212121, _1212123] : [-(_1212115 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1212117, _1212119, _1212115, _1212121), _1212123) = hAPP(hAPP(c_Product__Type_Oscomp(_1212119, _1212117, _1212119, tc_prod(_1212117, _1212119)), hAPP(_1212121, _1212123)), c_Random_Oiterate(_1212117, _1212119, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1212115), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1212121)))], (51323 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (30291 ^ _779571) ^ [_1322772, _1322774, _1322776, _1322778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322772, tc_HOL_Obool)), _1322774), _1322776)), hBOOL(hAPP(hAPP(c_member(_1322772), _1322778), _1322774)), -(hBOOL(hAPP(hAPP(c_member(_1322772), _1322778), _1322776)))], (28791 ^ _779571) ^ [_1291326, _1291328, _1291330, _1291332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291326, _1291328)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291330, _1291332))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291326), _1291328)), 28798 ^ _779571 : [(28801 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291328), _1291332)))], (28799 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291330), _1291326)))]]], (22480 ^ _779571) ^ [_1168290, _1168292, _1168294, _1168296, _1168298] : [-(c_Nat_Onat_Onat__case(_1168290, _1168292, _1168294, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168296)), _1168298)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1168290), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1168296))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1168290, _1168290), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1168290, tc_fun(_1168290, _1168290)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1168290, tc_fun(_1168290, _1168290)), tc_Int_Oint), c_If(_1168290)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1168290, _1168292, _1168294, _1168298))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1168290, tc_Int_Oint), _1168294), 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)), _1168298)))))], (16949 ^ _779571) ^ [_1070454, _1070456] : [class_Rings_Olinordered__idom(_1070454), -(hAPP(c_Groups_Oabs__class_Oabs(_1070454), _1070456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070454), _1070456), c_Groups_Osgn__class_Osgn(_1070454, _1070456)))], (4246 ^ _779571) ^ [_845156, _845158, _845160, _845162] : [-(c_Nitpick_Ocard_H(_845162, _845158) = c_Nitpick_Ocard_H(_845160, _845156)), _845162 = _845160, _845158 = _845156], (11563 ^ _779571) ^ [_971718, _971720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971720)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _971718)), hAPP(c_Int_Onat, _971720)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _971718), _971720)))], (19257 ^ _779571) ^ [_1109803, _1109805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109803), _1109805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1109803)), c_Int_OBit1(_1109805))))], (35567 ^ _779571) ^ [_1436224] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1436224) = 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), _1436224), 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))))))], (43696 ^ _779571) ^ [_1632802, _1632804, _1632806, _1632808, _1632810] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632802, _1632802)), hAPP(hAPP(c_Product__Type_OPair(_1632802, _1632802), _1632804), _1632806)), c_Transitive__Closure_Ortrancl(_1632802, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1632802, _1632802), tc_HOL_Obool)), _1632808), _1632810)))), 43702 ^ _779571 : [(43708 ^ _779571) ^ [] : [43704 ^ [_1632802, _1632804, _1632806, _1632808, _1632810] = 43701 ^ [_1632802, _1632804, _1632806, _1632808, _1632810]], (43706 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632802, _1632802)), hAPP(hAPP(c_Product__Type_OPair(_1632802, _1632802), 43704 ^ [_1632802, _1632804, _1632806, _1632808, _1632810]), 43701 ^ [_1632802, _1632804, _1632806, _1632808, _1632810])), _1632810)))], (43703 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632802, _1632802)), hAPP(hAPP(c_Product__Type_OPair(_1632802, _1632802), 43701 ^ [_1632802, _1632804, _1632806, _1632808, _1632810]), _1632806)), c_Transitive__Closure_Ortrancl(_1632802, _1632808))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632802, _1632802)), hAPP(hAPP(c_Product__Type_OPair(_1632802, _1632802), _1632804), _1632806)), c_Transitive__Closure_Ortrancl(_1632802, _1632808))))], (13571 ^ _779571) ^ [_1006977, _1006979, _1006981, _1006983] : [_1006977 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006979), _1006981)), _1006983), -(_1006979 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006977, _1006979) = _1006983), 13578 ^ _779571 : [(13581 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006983), _1006979))], (13579 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006979)))]], 13586 ^ _779571 : [(13589 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006979), _1006983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006983), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13587 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006979))]]], (43690 ^ _779571) ^ [_1632619, _1632621, _1632623, _1632625, _1632627] : [c_Relation_Osingle__valued(_1632619, _1632621, hAPP(c_Relation_Oconverse(_1632621, _1632619), _1632623)), -(hAPP(c_Relation_OImage(_1632621, _1632619, _1632623), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632621, tc_HOL_Obool)), _1632625), _1632627)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632619, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1632621, _1632619, _1632623), _1632625)), hAPP(c_Relation_OImage(_1632621, _1632619, _1632623), _1632627)))], (51349 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (25154 ^ _779571) ^ [_1220595, _1220597, _1220599] : [class_Rings_Olinordered__idom(_1220595), 25157 ^ _779571 : [(25164 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220595), _1220597), _1220599)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220595), _1220597), hAPP(c_Groups_Oabs__class_Oabs(_1220595), _1220599))))], (25158 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220595), _1220597), hAPP(c_Groups_Oabs__class_Oabs(_1220595), _1220599))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220595), _1220597), _1220599)))]]], (8412 ^ _779571) ^ [_918941, _918943, _918945, _918947] : [class_Orderings_Oorder(_918941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918941), _918943), _918945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918941), _918947), _918943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918941), _918947), _918945)))], (7373 ^ _779571) ^ [_901974, _901976, _901978, _901980, _901982, _901984] : [-(c_Sum__Type_Osum_Osum__rec(_901974, _901976, _901978, _901980, _901982, hAPP(c_Sum__Type_OInl(_901974, _901978), _901984)) = hAPP(_901980, _901984))], (9928 ^ _779571) ^ [_944957] : [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)), _944957)), _944957) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36968 ^ _779571) ^ [_1468329, _1468331, _1468333] : [class_Orderings_Oorder(_1468329), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468329, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1468329), _1468331)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1468329, _1468331, _1468333)) = c_Orderings_Obot__class_Obot(tc_fun(_1468329, tc_HOL_Obool)))], (24537 ^ _779571) ^ [_1207582, _1207584, _1207586] : [class_Orderings_Olinorder(_1207582), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207582), _1207584), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207582), _1207584), _1207586)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207582), _1207584), _1207586))], (51439 ^ _779571) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (27287 ^ _779571) ^ [_1260896, _1260898, _1260900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260896)), 27290 ^ _779571 : [(27291 ^ _779571) ^ [_1261030] : [27293 ^ _779571 : [(27299 ^ _779571) ^ [] : [-(_1261030 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27295 ^ [_1260896, _1260898, _1260900, _1261030]), 27292 ^ [_1260896, _1260898, _1260900, _1261030]))], (27297 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27295 ^ [_1260896, _1260898, _1260900, _1261030]), _1260898)))], (27294 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27292 ^ [_1260896, _1260898, _1260900, _1261030]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1260896))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260900), _1261030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261030), _1260896))))]]], (46275 ^ _779571) ^ [_1693736, _1693738, _1693740, _1693742, _1693744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693736, _1693738)), hAPP(hAPP(c_Product__Type_OPair(_1693736, _1693738), _1693740), _1693742)), hAPP(c_List_Oset(tc_prod(_1693736, _1693738)), _1693744))), -(hAPP(c_Map_Omap__of(_1693736, _1693738, _1693744), _1693740) = hAPP(c_Option_Ooption_OSome(_1693738), 46278 ^ [_1693736, _1693738, _1693740, _1693742, _1693744]))], (20021 ^ _779571) ^ [_1123626, _1123628] : [class_Rings_Odivision__ring__inverse__zero(_1123626), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123626), _1123628), c_Groups_Ozero__class_Ozero(_1123626)) = c_Groups_Ozero__class_Ozero(_1123626))], (6275 ^ _779571) ^ [_881345, _881347, _881349, _881351, _881353, _881355, _881357, _881359, _881361, _881363, _881365, _881367] : [-(c_Com_Ocom_Ocom__rec(_881345, _881347, _881349, _881351, _881353, _881355, _881357, _881359, _881361, c_Com_Ocom_OLocal(_881363, _881365, _881367)) = hAPP(hAPP(hAPP(hAPP(_881351, _881363), _881365), _881367), c_Com_Ocom_Ocom__rec(_881345, _881347, _881349, _881351, _881353, _881355, _881357, _881359, _881361, _881367)))], (40166 ^ _779571) ^ [_1540721, _1540723, _1540725, _1540727] : [-(hAPP(c_Set_Oimage(tc_prod(_1540721, _1540723), tc_prod(_1540723, _1540721), hAPP(c_Product__Type_Oprod_Oprod__case(_1540721, _1540723, tc_prod(_1540723, _1540721)), hAPP(c_COMBC(_1540723, _1540721, tc_prod(_1540723, _1540721)), c_Product__Type_OPair(_1540723, _1540721)))), hAPP(hAPP(c_Product__Type_OSigma(_1540721, _1540723), _1540725), hAPP(c_COMBK(tc_fun(_1540723, tc_HOL_Obool), _1540721), _1540727))) = hAPP(hAPP(c_Product__Type_OSigma(_1540723, _1540721), _1540727), hAPP(c_COMBK(tc_fun(_1540721, tc_HOL_Obool), _1540723), _1540725)))], (1012 ^ _779571) ^ [_794989, _794991] : [-(class_Rings_Oring__1__no__zero__divisors(_794989)), _794991 = _794989, class_Rings_Oring__1__no__zero__divisors(_794991)], (49078 ^ _779571) ^ [_1764255, _1764257, _1764259] : [-(_1764255 = c_List_Olist_ONil(_1764257)), -(hAPP(hAPP(c_List_Otake(_1764257), hAPP(c_Nat_OSuc, _1764259)), _1764255) = hAPP(hAPP(c_List_Olist_OCons(_1764257), hAPP(c_List_Ohd(_1764257), _1764255)), hAPP(hAPP(c_List_Otake(_1764257), _1764259), hAPP(c_List_Otl(_1764257), _1764255))))], (48908 ^ _779571) ^ [_1760921, _1760923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760921)), _1760923)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1760921), _1760923) = _1760923)], (19159 ^ _779571) ^ [_1108184, _1108186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1108184)), c_Int_OBit0(_1108186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108184), _1108186)))], (34126 ^ _779571) ^ [_1403526, _1403528, _1403530, _1403532] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1403526), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403528, tc_Nat_Onat), _1403530), _1403532)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403528, _1403526), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1403526, _1403528), c_Nat_Osemiring__1__class_Oof__nat(_1403526)), _1403530)), _1403532)), class_Groups_Ocomm__monoid__mult(_1403526), class_Rings_Osemiring__1(_1403526)], (41011 ^ _779571) ^ [_1560437, _1560439] : [-(hAPP(c_Set_OCollect(_1560437), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560437), c_fNot), _1560439)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1560437, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1560437), _1560439)))], (20833 ^ 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_1195173, _1195175), _1195177), _1195179) = hAPP(hAPP(_1195177, hAPP(c_Product__Type_Ofst(_1195171, _1195173), _1195179)), hAPP(c_Product__Type_Osnd(_1195171, _1195173), _1195179)))], (13270 ^ _779571) ^ [_1001675, _1001677, _1001679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001675)), _1001675 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001675), _1001679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001677), _1001675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1001679)))], (8886 ^ _779571) ^ [_926886, _926888, _926890] : [class_Groups_Ogroup__add(_926886), 8889 ^ _779571 : [(8896 ^ _779571) ^ [] : [_926888 = _926890, -(hAPP(c_Groups_Ouminus__class_Ouminus(_926886), _926888) = hAPP(c_Groups_Ouminus__class_Ouminus(_926886), _926890))], (8890 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_926886), _926888) = hAPP(c_Groups_Ouminus__class_Ouminus(_926886), _926890), -(_926888 = _926890)]]], (14880 ^ _779571) ^ [_1030551, _1030553, _1030555, _1030557] : [class_Divides_Osemiring__div(_1030551), -(_1030553 = c_Groups_Ozero__class_Ozero(_1030551)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030551), _1030555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030551), _1030553), _1030557))), _1030553) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030551), _1030557), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030551), _1030555), _1030553)))], (35468 ^ _779571) ^ [_1433546, _1433548, _1433550, _1433552, _1433554, _1433556, _1433558] : [-(hAPP(c_Product__Type_Oapsnd(_1433546, _1433548, _1433550, _1433552), hAPP(c_Product__Type_Oapsnd(_1433554, _1433546, _1433550, _1433556), _1433558)) = hAPP(c_Product__Type_Oapsnd(_1433554, _1433548, _1433550, hAPP(c_Fun_Ocomp(_1433546, _1433548, _1433554, _1433552), _1433556)), _1433558))], (8974 ^ _779571) ^ [_928354, _928356] : [class_Groups_Ocomm__monoid__mult(_928354), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928354), _928356), c_Groups_Oone__class_Oone(_928354)) = _928356)], (9544 ^ _779571) ^ [_938017, _938019] : [class_Groups_Ogroup__add(_938017), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938017), _938019), hAPP(c_Groups_Ouminus__class_Ouminus(_938017), _938019)) = c_Groups_Ozero__class_Ozero(_938017))], (19089 ^ _779571) ^ [_1106848, _1106850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106848), 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)))), _1106850))), 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)))), _1106848)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106850), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1106848))], (18929 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28561 ^ _779571) ^ [_1286712, _1286714] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1286712, _1286714)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286714), hAPP(c_Nat_OSuc, _1286712)))], (29952 ^ _779571) ^ [_1316211, _1316213] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1316211, _1316213), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1316211), _1316213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1316213), _1316211)))], (51511 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (31076 ^ _779571) ^ [_1339201, _1339203] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1339201), _1339203)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1339201)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1339203))))], (36140 ^ _779571) ^ [_1449819, _1449821] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449819, tc_HOL_Obool)), _1449821), c_Orderings_Otop__class_Otop(tc_fun(_1449819, tc_HOL_Obool))) = _1449821)], (51177 ^ _779571) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (15434 ^ _779571) ^ [_1040814, _1040816, _1040818] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040814), _1040816)), _1040818) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040816), _1040818)))], (25180 ^ _779571) ^ [_1221058, _1221060] : [class_Rings_Ocomm__semiring__1(_1221058), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221058), c_Groups_Oone__class_Oone(_1221058)), _1221060)))], (16823 ^ _779571) ^ [_1067945, _1067947, _1067949] : [class_Int_Onumber__ring(_1067945), class_Rings_Olinordered__idom(_1067945), 16830 ^ _779571 : [(16837 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067947), _1067949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067945), hAPP(c_Int_Onumber__class_Onumber__of(_1067945), _1067947)), hAPP(c_Int_Onumber__class_Onumber__of(_1067945), _1067949))))], (16831 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067945), hAPP(c_Int_Onumber__class_Onumber__of(_1067945), _1067947)), hAPP(c_Int_Onumber__class_Onumber__of(_1067945), _1067949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067947), _1067949)))]]], (45203 ^ _779571) ^ [_1668890] : [class_Complete__Lattice_Ocomplete__lattice(_1668890), -(c_Complete__Lattice_OSup__class_OSup(_1668890, c_Orderings_Otop__class_Otop(tc_fun(_1668890, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1668890))], (14365 ^ _779571) ^ [_1021959, _1021961] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021959, _1021961)), _1021959)))], (17061 ^ _779571) ^ [_1072672] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072672), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1072672) = _1072672)], (17291 ^ _779571) ^ [_1076829] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076829)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076829))], (13861 ^ _779571) ^ [_1012517, _1012519] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012517, _1012519) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1012517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012519), 13864 ^ [_1012517, _1012519]))], (1562 ^ _779571) ^ [_801864, _801866] : [-(class_Rings_Ocomm__semiring__1(_801864)), _801866 = _801864, class_Rings_Ocomm__semiring__1(_801866)], (17205 ^ _779571) ^ [_1075422, _1075424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075422)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075422), _1075424)))], (8201 ^ _779571) ^ [_915536, _915538, _915540] : [class_Rings_Olinordered__semidom(_915536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915538), _915540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915536), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915536), _915538)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915536), _915540))))], (10820 ^ 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1056390), _1056392)), _1056396))))], (16196 ^ _779571) ^ [] : [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), _1056388), _1056392)), _1056394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1056390), _1056392)), _1056396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056394), 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), _1056390), _1056388)), _1056392)), _1056396))))]]], (29033 ^ _779571) ^ [_1297374, _1297376] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297374, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1297374, tc_HOL_Obool))), _1297376) = c_Orderings_Otop__class_Otop(tc_fun(_1297374, tc_HOL_Obool)))], (8766 ^ _779571) ^ [_924478, _924480, _924482] : [class_Rings_Olinordered__semidom(_924478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924478), c_Groups_Oone__class_Oone(_924478)), _924480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924478), c_Groups_Oone__class_Oone(_924478)), _924482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924478), c_Groups_Oone__class_Oone(_924478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924478), _924480), _924482))))], (8506 ^ _779571) ^ [_920443, _920445, _920447] : [class_Orderings_Opreorder(_920443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920443), _920445), _920447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920443), _920447), _920445))], (34168 ^ _779571) ^ [_1404379, _1404381, _1404383, _1404385, _1404387, _1404389] : [-(_1404379 = _1404381), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404383, _1404385), _1404387), _1404381), _1404389), _1404379) = hAPP(_1404387, _1404379))], (41095 ^ _779571) ^ [_1562052] : [class_Lattices_Oab__semigroup__idem__mult(_1562052), -(c_Finite__Set_Ofun__left__comm__idem(_1562052, _1562052, c_Groups_Otimes__class_Otimes(_1562052)))], (51369 ^ _779571) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (8830 ^ _779571) ^ [_925488, _925490, _925492] : [class_Rings_Oring(_925488), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925488), hAPP(c_Groups_Ouminus__class_Ouminus(_925488), _925490)), _925492) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925488), _925490), hAPP(c_Groups_Ouminus__class_Ouminus(_925488), _925492)))], (45165 ^ _779571) ^ [_1668098, _1668100, _1668102] : [class_Complete__Lattice_Ocomplete__lattice(_1668098), hBOOL(hAPP(hAPP(c_member(_1668098), _1668100), _1668102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1668098), c_Complete__Lattice_OInf__class_OInf(_1668098, _1668102)), _1668100)))], (20069 ^ _779571) ^ [_1124686, _1124688, _1124690] : [class_Fields_Ofield__inverse__zero(_1124686), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1124686), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124686), _1124688), _1124690)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124686), _1124688), hAPP(c_Groups_Ouminus__class_Ouminus(_1124686), _1124690)))], (51247 ^ _779571) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (2980 ^ _779571) ^ [_825131, _825133] : [_825133 = _825131, -(c_Lazy__Sequence_Oempty(_825133) = c_Lazy__Sequence_Oempty(_825131))], (34543 ^ _779571) ^ [_1411933, _1411935, _1411937, _1411939, _1411941] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1411933, tc_Option_Ooption(_1411935)), _1411937), _1411939), hAPP(c_Option_Ooption_OSome(_1411935), _1411941)) = hAPP(c_COMBK(tc_Option_Ooption(_1411935), _1411933), c_Option_Ooption_ONone(_1411935))], (16421 ^ _779571) ^ [_1060356] : [class_Groups_Oordered__ab__group__add__abs(_1060356), -(hAPP(c_Groups_Oabs__class_Oabs(_1060356), c_Groups_Ozero__class_Ozero(_1060356)) = c_Groups_Ozero__class_Ozero(_1060356))], (48403 ^ _779571) ^ [_1747264, _1747266, _1747268, _1747270] : [-(_1747264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1747266), _1747264), hAPP(hAPP(c_List_Olist_OCons(_1747266), _1747268), _1747270)) = hAPP(hAPP(c_List_Olist_OCons(_1747266), _1747268), hAPP(hAPP(c_List_Otake(_1747266), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1747264), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1747270)))], (20619 ^ _779571) ^ [_1133895, _1133897, _1133899] : [class_Rings_Odivision__ring(_1133895), -(_1133897 = c_Groups_Ozero__class_Ozero(_1133895)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133895), hAPP(c_Groups_Ouminus__class_Ouminus(_1133895), _1133899)), hAPP(c_Groups_Ouminus__class_Ouminus(_1133895), _1133897)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133895), _1133899), _1133897))], (28170 ^ _779571) ^ [_1279263, _1279265] : [c_Nat__Transfer_Onat__set(_1279263), c_Nat__Transfer_Onat__set(_1279265), 28177 ^ _779571 : [(28184 ^ _779571) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279263) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279265), -(_1279263 = _1279265)], (28178 ^ _779571) ^ [] : [_1279263 = _1279265, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279263) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279265))]]], (29214 ^ _779571) ^ [_1301565, _1301567] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301565, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1301565, tc_HOL_Obool))), _1301567) = _1301567)], (17847 ^ _779571) ^ [_1086748] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086748))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086748) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14232 ^ _779571) ^ [_1019371, _1019373, _1019375] : [-(hBOOL(hAPP(_1019371, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019373), _1019375)))), 14235 ^ _779571 : [(14238 ^ _779571) ^ [] : [hBOOL(hAPP(_1019371, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14236 ^ _779571) ^ [] : [-(_1019375 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14241 ^ _779571 : [(14242 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019375)))], (14248 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14244 ^ [_1019371, _1019373, _1019375]), _1019375)))], (14252 ^ _779571) ^ [] : [hBOOL(hAPP(_1019371, 14243 ^ [_1019371, _1019373, _1019375]))], (14250 ^ _779571) ^ [] : [-(_1019373 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019375), 14243 ^ [_1019371, _1019373, _1019375])), 14244 ^ [_1019371, _1019373, _1019375]))], (14246 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14244 ^ [_1019371, _1019373, _1019375])))]], 14253 ^ _779571 : [(14254 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019375), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14260 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14256 ^ [_1019371, _1019373, _1019375]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14264 ^ _779571) ^ [] : [hBOOL(hAPP(_1019371, 14255 ^ [_1019371, _1019373, _1019375]))], (14262 ^ _779571) ^ [] : [-(_1019373 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019375), 14255 ^ [_1019371, _1019373, _1019375])), 14256 ^ [_1019371, _1019373, _1019375]))], (14258 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019375), 14256 ^ [_1019371, _1019373, _1019375])))]]], (34652 ^ _779571) ^ [_1414303, _1414305, _1414307, _1414309, _1414311, _1414313] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414303, tc_Option_Ooption(_1414305)), c_Map_Orestrict__map(_1414303, _1414305, _1414307, _1414309)), _1414311), _1414313) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414303, tc_Option_Ooption(_1414305)), c_Map_Orestrict__map(_1414303, _1414305, _1414307, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414303, tc_HOL_Obool)), _1414309), hAPP(hAPP(c_Set_Oinsert(_1414303), _1414311), c_Orderings_Obot__class_Obot(tc_fun(_1414303, tc_HOL_Obool)))))), _1414311), _1414313))], (46504 ^ _779571) ^ [_1699408, _1699410, _1699412, _1699414, _1699416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699408), tc_List_Olist(_1699408))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1699408), tc_List_Olist(_1699408)), _1699410), _1699412)), hAPP(c_List_Olexn(_1699408, _1699414), _1699416))), 46507 ^ _779571 : [(46510 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699408)), _1699412) = _1699416)], (46508 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699408)), _1699410) = _1699416)]]], (51487 ^ _779571) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (3648 ^ _779571) ^ [_835755, _835757, _835759, _835761, _835763, _835765, _835767, _835769] : [-(c_Product__Type_Oapsnd(_835769, _835765, _835761, _835757) = c_Product__Type_Oapsnd(_835767, _835763, _835759, _835755)), _835769 = _835767, _835765 = _835763, _835761 = _835759, _835757 = _835755], (9794 ^ _779571) ^ [_942565, _942567, _942569, _942571] : [class_Rings_Olinordered__comm__semiring__strict(_942565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942565), _942567), _942569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942565), c_Groups_Ozero__class_Ozero(_942565)), _942571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942565), _942571), _942567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942565), _942571), _942569))))], (22442 ^ _779571) ^ [_1167398, _1167400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167398)), hAPP(c_Nat_OSuc, _1167400))), -(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(_1167398))), 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)), _1167400)))))], (23117 ^ _779571) ^ [_1180602, _1180604, _1180606, _1180608, _1180610] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180602, _1180604, tc_HOL_Obool), _1180606), hAPP(hAPP(c_Product__Type_OPair(_1180602, _1180604), _1180608), _1180610))), -(hBOOL(hAPP(hAPP(_1180606, _1180608), _1180610)))], (22302 ^ _779571) ^ [_1164367] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164367) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164367)))], (22350 ^ _779571) ^ [_1165369] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1165369) = 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), _1165369), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43526 ^ _779571) ^ [_1628500, _1628502, _1628504, _1628506] : [-(hAPP(_1628500, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1628502, _1628502), _1628504), _1628500), _1628506)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1628502, _1628502), _1628504), _1628500), hAPP(_1628500, _1628506)))], (4148 ^ _779571) ^ [_843529, _843531] : [_843531 = _843529, -(c_Smallcheck_Osmall__class_Osmall(_843531) = c_Smallcheck_Osmall__class_Osmall(_843529))], (25946 ^ _779571) ^ [_1234452, _1234454, _1234456, _1234458, _1234460] : [class_Rings_Osemiring__0(_1234452), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234452), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234454, _1234452), _1234456), _1234458)), _1234460) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234454, _1234452), hAPP(hAPP(c_COMBC(_1234454, _1234452, _1234452), hAPP(hAPP(c_COMBB(_1234452, tc_fun(_1234452, _1234452), _1234454), c_Groups_Otimes__class_Otimes(_1234452)), _1234456)), _1234460)), _1234458))], (31107 ^ _779571) ^ [_1339930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1339930)), 31111 ^ _779571 : [(31112 ^ _779571) ^ [_1340010] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1340010), _1339930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1340010), 31110 ^ [_1339930])))]]], (31606 ^ _779571) ^ [_1352770, _1352772, _1352774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1352770), _1352772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1352770, tc_HOL_Obool)), _1352774), _1352772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1352770), _1352774)), hAPP(c_Finite__Set_Ocard(_1352770), _1352772))))], (19611 ^ _779571) ^ [_1116017] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116017), _1116017)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1116017)], (46179 ^ _779571) ^ [_1691323, _1691325, _1691327, _1691329] : [-(c_Map_Omap__of(_1691323, _1691325, hAPP(hAPP(c_List_Omap(_1691323, tc_prod(_1691323, _1691325)), hAPP(hAPP(c_COMBS(_1691323, _1691325, tc_prod(_1691323, _1691325)), c_Product__Type_OPair(_1691323, _1691325)), _1691327)), _1691329)) = c_Map_Orestrict__map(_1691323, _1691325, hAPP(c_Fun_Ocomp(_1691325, tc_Option_Ooption(_1691325), _1691323, c_Option_Ooption_OSome(_1691325)), _1691327), hAPP(c_List_Oset(_1691323), _1691329)))], (42986 ^ _779571) ^ [_1615216, _1615218] : [-(c_Transitive__Closure_Otrancl(_1615216, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1615216, _1615216), tc_HOL_Obool)), _1615218), c_Relation_OId(_1615216))) = c_Transitive__Closure_Ortrancl(_1615216, _1615218))], (43491 ^ _779571) ^ [_1627505, _1627507, _1627509] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627505, _1627505)), _1627507), c_Transitive__Closure_Ortrancl(_1627505, _1627509))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627505, _1627505)), _1627507), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1627505, _1627505), 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(_1627505, _1627505), tc_HOL_Obool), tc_fun(tc_prod(_1627505, _1627505), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1627505, _1627505), tc_HOL_Obool)), _1627509)))))], (38895 ^ _779571) ^ [_1510712, _1510714, _1510716, _1510718] : [c_Fun_Oinj__on(_1510712, _1510714, _1510716, c_Orderings_Otop__class_Otop(tc_fun(_1510712, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510714, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510712, _1510714, _1510716), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510712, tc_HOL_Obool)), _1510718))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510714, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510712, _1510714, _1510716), _1510718)))))], (47250 ^ _779571) ^ [_1719864, _1719866] : [-(c_List_Oremove1(_1719864, _1719866, c_List_Olist_ONil(_1719864)) = c_List_Olist_ONil(_1719864))], (6558 ^ _779571) ^ [_886603] : [hAPP(c_Nat_OSuc, _886603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34937 ^ _779571) ^ [_1421556, _1421558, _1421560] : [class_Orderings_Olinorder(_1421556), hAPP(_1421558, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1421556), 34942 ^ [_1421556, _1421558, _1421560]), 34943 ^ [_1421556, _1421558, _1421560])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1421556), hAPP(_1421558, 34942 ^ [_1421556, _1421558, _1421560])), hAPP(_1421558, 34943 ^ [_1421556, _1421558, _1421560])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421556), _1421560)), -(_1421560 = c_Orderings_Obot__class_Obot(tc_fun(_1421556, tc_HOL_Obool))), -(hAPP(_1421558, c_Big__Operators_Olinorder__class_OMax(_1421556, _1421560)) = c_Big__Operators_Olinorder__class_OMax(_1421556, hAPP(c_Set_Oimage(_1421556, _1421556, _1421558), _1421560)))], (29860 ^ _779571) ^ [_1313656, _1313658] : [-(c_Set_Othe__elem(_1313656, hAPP(hAPP(c_Set_Oinsert(_1313656), _1313658), c_Orderings_Obot__class_Obot(tc_fun(_1313656, tc_HOL_Obool)))) = _1313658)], (10474 ^ _779571) ^ [_953918, _953920, _953922, _953924] : [class_Orderings_Oord(_953918), _953920 = _953922, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953918), _953922), _953924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953918), _953920), _953924)))], (22642 ^ _779571) ^ [_1171312] : [-(c_Divides_Oadjust(_1171312) = 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)), _1171312))))), 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)), _1171312))))), 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))))))))], (11557 ^ _779571) ^ [_971595, _971597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971595)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _971595), _971597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _971595)), hAPP(c_Int_Onat, _971597)))], (51279 ^ _779571) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (1392 ^ _779571) ^ [_799739, _799741] : [-(class_Rings_Olinordered__comm__semiring__strict(_799739)), _799741 = _799739, class_Rings_Olinordered__comm__semiring__strict(_799741)], (8902 ^ _779571) ^ [_927127, _927129, _927131] : [class_Int_Oring__char__0(_927127), 8905 ^ _779571 : [(8912 ^ _779571) ^ [] : [_927129 = _927131, -(hAPP(c_Int_Oring__1__class_Oof__int(_927127), _927129) = hAPP(c_Int_Oring__1__class_Oof__int(_927127), _927131))], (8906 ^ _779571) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_927127), _927129) = hAPP(c_Int_Oring__1__class_Oof__int(_927127), _927131), -(_927129 = _927131)]]], (48319 ^ _779571) ^ [_1745169, _1745171] : [-(hAPP(hAPP(c_List_Otake(_1745169), _1745171), c_List_Olist_ONil(_1745169)) = c_List_Olist_ONil(_1745169))], (8836 ^ _779571) ^ [_925617, _925619, _925621] : [class_Rings_Oring(_925617), -(hAPP(c_Groups_Ouminus__class_Ouminus(_925617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925617), _925619), _925621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925617), hAPP(c_Groups_Ouminus__class_Ouminus(_925617), _925619)), _925621))], (12748 ^ _779571) ^ [_992819, _992821, _992823, _992825, _992827] : [class_Rings_Olinordered__semiring__strict(_992819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992819), _992821), _992823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992819), _992825), _992827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992819), c_Groups_Ozero__class_Ozero(_992819)), _992821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992819), c_Groups_Ozero__class_Ozero(_992819)), _992825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992819), _992821), _992825)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992819), _992823), _992827))))], (37092 ^ _779571) ^ [_1471391, _1471393, _1471395, _1471397, _1471399, _1471401] : [c_Finite__Set_Ofolding(_1471391, _1471393, _1471395, _1471397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471391), _1471399)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471391), _1471401)), -(hAPP(c_Fun_Ocomp(_1471393, _1471393, _1471393, hAPP(_1471397, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471391, tc_HOL_Obool)), _1471399), _1471401))), hAPP(_1471397, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471391, tc_HOL_Obool)), _1471399), _1471401))) = hAPP(c_Fun_Ocomp(_1471393, _1471393, _1471393, hAPP(_1471397, _1471399)), hAPP(_1471397, _1471401)))], (36534 ^ _779571) ^ [_1458283, _1458285, _1458287, _1458289] : [class_Lattices_Osemilattice__inf(_1458283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458283), _1458285), _1458287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458283), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458283), _1458285), _1458289)), _1458287)))], (49891 ^ _779571) ^ [_1782652, _1782654] : [-(c_Random_Oselect__weight(_1782652, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1782652), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1782652, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1782652, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1782652)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1782654)) = c_Random_Oselect__weight(_1782652, _1782654))], (10402 ^ _779571) ^ [_952843, _952845, _952847] : [class_Orderings_Olinorder(_952843), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952843), _952845), _952847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952843), _952847), _952845)))], (6859 ^ _779571) ^ [_892745, _892747, _892749] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892745), _892747) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892745), _892749), -(_892747 = _892749)], (43178 ^ _779571) ^ [_1619923, _1619925, _1619927, _1619929] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619923, _1619923)), hAPP(hAPP(c_Product__Type_OPair(_1619923, _1619923), _1619925), _1619927)), c_Transitive__Closure_Ortrancl(_1619923, _1619929)))), 43179 ^ _779571 : [(43182 ^ _779571) ^ [] : [-(_1619925 = _1619927), hBOOL(hAPP(hAPP(c_member(tc_prod(_1619923, _1619923)), hAPP(hAPP(c_Product__Type_OPair(_1619923, _1619923), _1619925), _1619927)), c_Transitive__Closure_Otrancl(_1619923, _1619929)))], (43180 ^ _779571) ^ [] : [_1619925 = _1619927]]], (6566 ^ _779571) ^ [_886734, _886736, _886738, _886740] : [c_Natural_Oevaln(_886734, _886736, _886738, _886740), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886734), _886736), _886740)))], (1102 ^ _779571) ^ [_796114, _796116] : [-(class_Rings_Oordered__ring(_796114)), _796116 = _796114, class_Rings_Oordered__ring(_796116)], (9232 ^ _779571) ^ [_932430, _932432, _932434] : [class_Groups_Oab__group__add(_932430), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932430), _932432), _932434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932430), hAPP(c_Groups_Ouminus__class_Ouminus(_932430), _932432)), hAPP(c_Groups_Ouminus__class_Ouminus(_932430), _932434)))], (39030 ^ _779571) ^ [_1513952] : [class_Nat_Osemiring__char__0(_1513952), -(c_Fun_Oinj__on(tc_Nat_Onat, _1513952, c_Nat_Osemiring__1__class_Oof__nat(_1513952), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (44756 ^ _779571) ^ [_1658566, _1658568, _1658570, _1658572, _1658574] : [_1658566 = c_Orderings_Obot__class_Obot(tc_fun(_1658568, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658568, tc_fun(_1658570, tc_HOL_Obool)), _1658566), hAPP(hAPP(c_COMBC(_1658568, tc_fun(_1658570, tc_HOL_Obool), tc_fun(_1658570, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1658570, tc_HOL_Obool), tc_fun(tc_fun(_1658570, tc_HOL_Obool), tc_fun(_1658570, tc_HOL_Obool)), _1658568), c_Groups_Ominus__class_Ominus(tc_fun(_1658570, tc_HOL_Obool))), _1658572)), _1658574)) = c_Orderings_Otop__class_Otop(tc_fun(_1658570, tc_HOL_Obool)))], (3046 ^ _779571) ^ [_826204, _826206, _826208, _826210, _826212, _826214, _826216, _826218] : [-(c_New__DSequence_Opos__bind(_826218, _826214, _826210, _826206) = c_New__DSequence_Opos__bind(_826216, _826212, _826208, _826204)), _826218 = _826216, _826214 = _826212, _826210 = _826208, _826206 = _826204], (13940 ^ _779571) ^ [_1013831, _1013833] : [class_Lattices_Oab__semigroup__idem__mult(_1013831), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013831), _1013833), _1013833) = _1013833)], (27441 ^ _779571) ^ [_1264310, _1264312, _1264314] : [class_Groups_Oordered__ab__group__add(_1264310), -(hAPP(c_Set_Oimage(_1264310, _1264310, c_Groups_Ouminus__class_Ouminus(_1264310)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1264310, _1264312), _1264314)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1264310, hAPP(c_Groups_Ouminus__class_Ouminus(_1264310), _1264314), hAPP(c_Groups_Ouminus__class_Ouminus(_1264310), _1264312)))], (45793 ^ _779571) ^ [_1682283, _1682285, _1682287] : [-(c_Smallcheck_Oorelse(_1682283, _1682285, _1682287) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1682283), _1682283, _1682287, c_Option_Ooption_OSome(_1682283)), _1682285))], (47143 ^ _779571) ^ [_1717798, _1717800, _1717802, _1717804] : [class_Groups_Ocomm__monoid__add(_1717798), 47146 ^ _779571 : [(47153 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1717800), _1717802))), -(c_Nitpick_Osetsum_H(_1717800, _1717798, _1717804, _1717802) = c_Groups_Ozero__class_Ozero(_1717798))], (47147 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1717800), _1717802)), -(c_Nitpick_Osetsum_H(_1717800, _1717798, _1717804, _1717802) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717798), hAPP(hAPP(c_List_Omap(_1717800, _1717798), _1717804), c_Hilbert__Choice_OEps(tc_List_Olist(_1717800), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717800), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1717800)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717800), tc_fun(_1717800, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1717800, tc_HOL_Obool), tc_fun(tc_fun(_1717800, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1717800)), c_fequal), c_List_Oset(_1717800))), _1717802))), c_List_Odistinct(_1717800))))))]]], (27307 ^ _779571) ^ [_1261304, _1261306] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1261304), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261306), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1261304, _1261306))], (35689 ^ _779571) ^ [_1439606, _1439608, _1439610, _1439612, _1439614, _1439616, _1439618, _1439620] : [c_Finite__Set_Ofolding(_1439606, _1439608, _1439610, _1439612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439606), _1439614)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439606), _1439616)), -(hAPP(c_Fun_Ocomp(_1439608, _1439608, _1439618, hAPP(_1439612, _1439616)), hAPP(c_Fun_Ocomp(_1439608, _1439608, _1439618, hAPP(_1439612, _1439614)), _1439620)) = hAPP(c_Fun_Ocomp(_1439608, _1439608, _1439618, hAPP(_1439612, _1439614)), hAPP(c_Fun_Ocomp(_1439608, _1439608, _1439618, hAPP(_1439612, _1439616)), _1439620)))], (19495 ^ _779571) ^ [_1114031] : [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), _1114031))), 19498 ^ _779571 : [(19501 ^ _779571) ^ [] : [-(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(_1114031)))))], (19499 ^ _779571) ^ [] : [-(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(_1114031)))))]]], (41275 ^ _779571) ^ [_1567192, _1567194] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1567192)), -(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)), _1567192))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1567194))))) = 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)), _1567192))), 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, _1567194))))))], (23597 ^ _779571) ^ [_1189329, _1189331, _1189333, _1189335] : [class_Orderings_Olinorder(_1189329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189329), _1189331), _1189333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189329), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189329), _1189331), _1189335)), _1189333)))], (39763 ^ _779571) ^ [_1530069, _1530071, _1530073] : [c_Map_Odom(_1530069, _1530071, _1530073) = c_Orderings_Obot__class_Obot(tc_fun(_1530069, tc_HOL_Obool)), -(_1530073 = hAPP(c_COMBK(tc_Option_Ooption(_1530071), _1530069), c_Option_Ooption_ONone(_1530071)))], (38379 ^ _779571) ^ [_1500518, _1500520, _1500522, _1500524, _1500526, _1500528] : [c_Fun_Oinj__on(_1500518, _1500520, _1500522, _1500524), 38382 ^ _779571 : [(38389 ^ _779571) ^ [] : [c_Fun_Oinj__on(_1500518, _1500526, hAPP(c_Fun_Ocomp(_1500520, _1500526, _1500518, _1500528), _1500522), _1500524), -(c_Fun_Oinj__on(_1500520, _1500526, _1500528, hAPP(c_Set_Oimage(_1500518, _1500520, _1500522), _1500524)))], (38383 ^ _779571) ^ [] : [c_Fun_Oinj__on(_1500520, _1500526, _1500528, hAPP(c_Set_Oimage(_1500518, _1500520, _1500522), _1500524)), -(c_Fun_Oinj__on(_1500518, _1500526, hAPP(c_Fun_Ocomp(_1500520, _1500526, _1500518, _1500528), _1500522), _1500524))]]], (35115 ^ _779571) ^ [_1425389, _1425391, _1425393, _1425395, _1425397] : [class_Groups_Ocomm__monoid__add(_1425389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425391), _1425393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1425391, tc_HOL_Obool)), _1425395), _1425393)), 35129 ^ _779571 : [(35132 ^ _779571) ^ [] : [hAPP(_1425397, 35128 ^ [_1425389, _1425391, _1425393, _1425395, _1425397]) = c_Groups_Ozero__class_Ozero(_1425389)], (35130 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425391), 35128 ^ [_1425389, _1425391, _1425393, _1425395, _1425397]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425391, tc_HOL_Obool)), _1425393), _1425395))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425391, _1425389), _1425397), _1425393) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425391, _1425389), _1425397), _1425395))], (44698 ^ _779571) ^ [_1656587, _1656589, _1656591, _1656593] : [-(_1656587 = c_Orderings_Obot__class_Obot(tc_fun(_1656589, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656589, tc_fun(_1656591, tc_HOL_Obool)), _1656587), hAPP(c_COMBK(tc_fun(_1656591, tc_HOL_Obool), _1656589), _1656593)) = _1656593)], (41830 ^ _779571) ^ [_1587868, _1587870] : [hAPP(hAPP(c_Relation_Orel__comp(_1587868, _1587868, _1587868), _1587870), _1587870) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587868, _1587868), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1587868, _1587870))], (44768 ^ _779571) ^ [_1658918, _1658920, _1658922, _1658924, _1658926] : [_1658918 = c_Orderings_Obot__class_Obot(tc_fun(_1658920, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658922, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658920, tc_fun(_1658922, tc_HOL_Obool)), _1658918), _1658924)), _1658926) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658922, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1658922, tc_HOL_Obool))), _1658926))], (7934 ^ _779571) ^ [_911159, _911161] : [7935 ^ _779571 : [(7938 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _911161))], (7936 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _911159))]], -(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), _911159), _911161))))], (17229 ^ _779571) ^ [_1075869, _1075871] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075869)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075871)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1075869), _1075871)))], (46528 ^ _779571) ^ [_1699970, _1699972] : [hBOOL(hAPP(c_List_Odistinct(_1699970), _1699972)), -(hAPP(c_Finite__Set_Ocard(_1699970), hAPP(c_List_Oset(_1699970), _1699972)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699970)), _1699972))], (32533 ^ _779571) ^ [_1372659, _1372661, _1372663, _1372665, _1372667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1372659, _1372661)), hAPP(_1372659, _1372663))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1372665, _1372665)), hAPP(hAPP(c_Product__Type_OPair(_1372665, _1372665), _1372661), _1372663)), _1372667)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1372665, _1372665)), hAPP(hAPP(c_Product__Type_OPair(_1372665, _1372665), _1372661), _1372663)), c_Wellfounded_Omlex__prod(_1372665, _1372659, _1372667))))], (17909 ^ _779571) ^ [_1087824, _1087826, _1087828] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087824)))), 17912 ^ _779571 : [(17919 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087826)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087826)), _1087828)) = 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), _1087824), _1087826))), _1087828))], (17913 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087826))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087826)), _1087828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087824)), _1087828))]]], (7171 ^ _779571) ^ [_897858, _897860, _897862, _897864] : [class_Rings_Ocomm__semiring__1(_897858), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897858), _897860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897858), _897862), _897864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897858), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897858), _897860), _897862)), _897864))], (234 ^ _779571) ^ [_783052, _783054] : [-(class_Fields_Olinordered__field(_783052)), _783054 = _783052, class_Fields_Olinordered__field(_783054)], (20887 ^ _779571) ^ [_1138843, _1138845, _1138847, _1138849] : [class_Fields_Olinordered__field(_1138843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138843), c_Groups_Ozero__class_Ozero(_1138843)), _1138845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138843), _1138847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138843), _1138849), _1138845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138843), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138843), _1138847), _1138845)), _1138849)))], (29323 ^ _779571) ^ [_1303793, _1303795, _1303797, _1303799] : [-(_1303793 = c_Orderings_Obot__class_Obot(tc_fun(_1303795, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303795, tc_fun(_1303797, tc_HOL_Obool)), _1303793), hAPP(c_COMBK(tc_fun(_1303797, tc_HOL_Obool), _1303795), _1303799)) = _1303799)], (32715 ^ _779571) ^ [_1376405, _1376407] : [class_Rings_Osemiring__1(_1376405), -(hBOOL(hAPP(hAPP(c_member(_1376405), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376405), _1376407)), c_Nat_Osemiring__1__class_ONats(_1376405))))], (18783 ^ _779571) ^ [_1101772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1101772)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101772), c_Int_OPls)))], (30190 ^ _779571) ^ [_1320631, _1320633, _1320635] : [_1320631 = c_Orderings_Obot__class_Obot(tc_fun(_1320633, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1320633), _1320635), _1320631))], (41591 ^ _779571) ^ [_1580192, _1580194, _1580196, _1580198, _1580200, _1580202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1580192), _1580194)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580196), _1580198)), 41601 ^ _779571 : [(41604 ^ _779571) ^ [] : [hAPP(c_Finite__Set_Ocard(_1580192), hAPP(c_Set_OCollect(_1580192), hAPP(hAPP(c_COMBS(_1580192, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580192), c_fconj), hAPP(hAPP(c_COMBC(_1580192, tc_fun(_1580192, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580192)), _1580194))), hAPP(hAPP(c_COMBC(_1580192, _1580196, tc_HOL_Obool), _1580200), 41600 ^ [_1580192, _1580194, _1580196, _1580198, _1580200, _1580202])))) = hAPP(_1580202, 41600 ^ [_1580192, _1580194, _1580196, _1580198, _1580200, _1580202])], (41602 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580196), 41600 ^ [_1580192, _1580194, _1580196, _1580198, _1580200, _1580202]), _1580198)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580192, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1580196, tc_HOL_Obool), tc_Nat_Onat, _1580192), c_Finite__Set_Ocard(_1580196)), hAPP(hAPP(c_COMBB(tc_fun(_1580196, tc_HOL_Obool), tc_fun(_1580196, tc_HOL_Obool), _1580192), c_Set_OCollect(_1580196)), hAPP(hAPP(c_COMBB(tc_fun(_1580196, tc_HOL_Obool), tc_fun(_1580196, tc_HOL_Obool), _1580192), hAPP(c_COMBS(_1580196, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580196), c_fconj), hAPP(hAPP(c_COMBC(_1580196, tc_fun(_1580196, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580196)), _1580198)))), _1580200)))), _1580194) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580196, tc_Nat_Onat), _1580202), _1580198))], (47276 ^ _779571) ^ [_1720316] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720316)), c_List_Olist_ONil(_1720316)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17765 ^ _779571) ^ [_1085522, _1085524] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085522))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085522)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085524)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14784 ^ _779571) ^ [_1028750, _1028752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028750), 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)), _1028752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028750), _1028752)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13048 ^ _779571) ^ [_998002, _998004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998002), _998004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _998002), c_Groups_Oone__class_Oone(tc_Int_Oint))), _998004)))], (35633 ^ _779571) ^ [_1438145, _1438147, _1438149, _1438151, _1438153, _1438155, _1438157] : [c_Hoare__Mirabelle_Ohoare__derivs(_1438145, _1438147, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1438145)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1438145), c_Hoare__Mirabelle_Opeek__and(_1438145, _1438149, _1438151)), _1438153), _1438155)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1438145), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1438145, _1438147, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1438145)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1438145), c_Hoare__Mirabelle_Opeek__and(_1438145, _1438149, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1438151))), _1438157), _1438155)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1438145), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1438145, _1438147, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1438145)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1438145), _1438149), c_Com_Ocom_OCond(_1438151, _1438153, _1438157)), _1438155)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1438145), tc_HOL_Obool)))))], (18419 ^ _779571) ^ [_1095724] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1095724) = c_Int_Opred(_1095724))], (25516 ^ _779571) ^ [_1226466, _1226468] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226466), _1226468)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226468), _1226466))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226468), _1226466)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226466), _1226468)))], (21221 ^ _779571) ^ [_1144711, _1144713, _1144715, _1144717] : [class_Fields_Ofield__inverse__zero(_1144711), class_Int_Onumber(_1144711), 21228 ^ _779571 : [(21229 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144711), _1144713), _1144715) = hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717), 21232 ^ _779571 : [(21239 ^ _779571) ^ [] : [_1144715 = c_Groups_Ozero__class_Ozero(_1144711), -(hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717) = c_Groups_Ozero__class_Ozero(_1144711))], (21233 ^ _779571) ^ [] : [-(_1144715 = c_Groups_Ozero__class_Ozero(_1144711)), -(_1144713 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144711), hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717)), _1144715))]]], (21245 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144711), _1144713), _1144715) = hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717)), 21248 ^ _779571 : [(21251 ^ _779571) ^ [] : [_1144713 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144711), hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717)), _1144715)], (21249 ^ _779571) ^ [] : [_1144715 = c_Groups_Ozero__class_Ozero(_1144711)]], 21252 ^ _779571 : [(21255 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1144711), _1144717) = c_Groups_Ozero__class_Ozero(_1144711)], (21253 ^ _779571) ^ [] : [-(_1144715 = c_Groups_Ozero__class_Ozero(_1144711))]]]]], (33275 ^ _779571) ^ [_1386497, _1386499, _1386501] : [class_Orderings_Olinorder(_1386497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386497), _1386499)), hBOOL(hAPP(hAPP(c_member(_1386497), _1386501), _1386499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386497), c_Big__Operators_Olinorder__class_OMin(_1386497, _1386499)), _1386501)))], (2704 ^ _779571) ^ [_820567, _820569] : [_820569 = _820567, -(c_Nitpick_Oone__frac(_820569) = c_Nitpick_Oone__frac(_820567))], (49806 ^ _779571) ^ [_1780041, _1780043, _1780045, _1780047] : [hBOOL(hAPP(hAPP(c_member(_1780041), _1780043), hAPP(c_List_Oset(_1780041), _1780045))), -(hBOOL(hAPP(_1780047, _1780043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780041)), hAPP(c_List_Ofilter(_1780041, _1780047), _1780045))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780041)), _1780045))))], (41265 ^ _779571) ^ [_1566809, _1566811, _1566813, _1566815, _1566817, _1566819] : [class_Groups_Ocomm__monoid__add(_1566809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566811), _1566813)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566811, _1566809), hAPP(hAPP(c_COMBS(_1566811, _1566809, _1566809), hAPP(hAPP(c_COMBS(_1566811, _1566809, tc_fun(_1566809, _1566809)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1566809, tc_fun(_1566809, _1566809)), _1566811), c_If(_1566809)), _1566815)), _1566817)), _1566819)), _1566813) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1566809), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566811, _1566809), _1566817), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566811, tc_HOL_Obool)), _1566813), hAPP(c_Set_OCollect(_1566811), _1566815)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566811, _1566809), _1566819), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566811, tc_HOL_Obool)), _1566813), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1566811, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1566811), _1566815))))))], (890 ^ _779571) ^ [_793280, _793282, _793284, _793286, _793288, _793290] : [-(c_Equiv__Relations_Oequiv(_793288, _793284, _793280)), c_Equiv__Relations_Oequiv(_793290, _793286, _793282), _793290 = _793288, _793286 = _793284, _793282 = _793280], (22678 ^ _779571) ^ [_1171957, _1171959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171959)), -(c_Divides_OposDivAlg(_1171957, _1171959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171957), _1171959)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171957, _1171959)))], (37734 ^ _779571) ^ [_1486787, _1486789, _1486791, _1486793, _1486795, _1486797] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486787, tc_fun(_1486789, tc_HOL_Obool))), _1486791), _1486793), _1486795), _1486797)), 37737 ^ _779571 : [(37740 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1486793, _1486795), _1486797)))], (37738 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1486791, _1486795), _1486797)))]]], (18391 ^ _779571) ^ [] : [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)], (30802 ^ _779571) ^ [_1333567, _1333569, _1333571, _1333573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333567, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333567, tc_HOL_Obool)), _1333569), hAPP(hAPP(c_Set_Oinsert(_1333567), _1333571), c_Orderings_Obot__class_Obot(tc_fun(_1333567, tc_HOL_Obool))))), _1333573)), hBOOL(hAPP(hAPP(c_member(_1333567), _1333571), _1333569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333567, tc_HOL_Obool)), _1333569), hAPP(hAPP(c_Set_Oinsert(_1333567), _1333571), _1333573))))], (21841 ^ _779571) ^ [_1156235, _1156237, _1156239, _1156241] : [class_Fields_Ofield(_1156235), -(_1156237 = c_Groups_Ozero__class_Ozero(_1156235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1156239), _1156241)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156235), _1156237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1156241), _1156239)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156235), hAPP(hAPP(c_Power_Opower__class_Opower(_1156235), _1156237), _1156241)), hAPP(hAPP(c_Power_Opower__class_Opower(_1156235), _1156237), _1156239)))], (24147 ^ _779571) ^ [_1200218, _1200220] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1200218), _1200220) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1200218, _1200220)))], (45119 ^ _779571) ^ [_1666825, _1666827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1666825), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666825, tc_HOL_Obool), _1666827))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1666825, tc_HOL_Obool)), _1666827)))], (24981 ^ _779571) ^ [_1217374, _1217376, _1217378, _1217380] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1217374, _1217376, _1217378), c_Product__Type_Ocurry(_1217374, _1217376, _1217378, _1217380)) = _1217380)], (11505 ^ _779571) ^ [_970731, _970733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _970731), _970733)), 11508 ^ _779571 : [(11511 ^ _779571) ^ [] : [_970731 = _970733], (11509 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _970731), _970733)))]]], (29222 ^ _779571) ^ [_1301734, _1301736] : [_1301736 = c_Orderings_Obot__class_Obot(tc_fun(_1301734, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301734, tc_HOL_Obool)), _1301736), c_Orderings_Obot__class_Obot(tc_fun(_1301734, tc_HOL_Obool)))))], (23519 ^ _779571) ^ [_1188029] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188029) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13330 ^ _779571) ^ [_1002725, _1002727, _1002729, _1002731, _1002733, _1002735] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002725), _1002727)), _1002729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002731), _1002733)), _1002735), 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), _1002731), _1002733)), _1002735))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002735), _1002731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002731), _1002725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002727), _1002733)))], (8388 ^ _779571) ^ [_918646, _918648, _918650] : [class_Orderings_Olinorder(_918646), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918646), _918648), _918650))), -(_918648 = _918650), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918646), _918650), _918648)))], (6975 ^ _779571) ^ [_894575, _894577] : [class_Groups_Omonoid__add(_894575), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894575), c_Groups_Ozero__class_Ozero(_894575)), _894577) = _894577)], (34749 ^ _779571) ^ [_1416631, _1416633, _1416635, _1416637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1416631), _1416633)), 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)), _1416631), _1416635)), 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)), _1416633), _1416637)), 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)), _1416633), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1416635), _1416637))), c_FunDef_Omin__strict)))], (16875 ^ _779571) ^ [_1068857, _1068859, _1068861] : [class_Int_Onumber__ring(_1068857), -(hAPP(c_Int_Onumber__class_Onumber__of(_1068857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068859), _1068861)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068857), hAPP(c_Int_Onumber__class_Onumber__of(_1068857), _1068859)), hAPP(c_Int_Onumber__class_Onumber__of(_1068857), _1068861)))], (8866 ^ _779571) ^ [_926406, _926408, _926410, _926412] : [class_Rings_Ocomm__semiring__1(_926406), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926406), _926408), _926410)), _926412) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926406), _926408), _926412)), _926410))], (50916 ^ _779571) ^ [_1804592, _1804594] : [-(c_List_Oconcat(tc_List_Olist(_1804592), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1804592), tc_List_Olist(tc_List_Olist(_1804592))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1804592)), _1804592, c_List_Olist_ONil(tc_List_Olist(_1804592)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1804592), tc_List_Olist(tc_List_Olist(_1804592))), _1804592), hAPP(hAPP(c_COMBC(tc_List_Olist(_1804592), tc_List_Olist(tc_List_Olist(_1804592)), tc_List_Olist(tc_List_Olist(_1804592))), c_List_Olist_OCons(tc_List_Olist(_1804592))), c_List_Olist_ONil(tc_List_Olist(_1804592)))))), _1804594)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1804592), tc_List_Olist(_1804592)), c_List_Otl(_1804592)), hAPP(c_List_Ofilter(tc_List_Olist(_1804592), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1804592)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1804592), tc_List_Olist(_1804592), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1804592)))), _1804594)))], (9374 ^ _779571) ^ [_934820, _934822, _934824, _934826] : [class_Rings_Ocomm__semiring__1(_934820), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934820), _934822), _934824)), _934826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934820), _934822), _934826)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934820), _934824), _934826)))], (36336 ^ _779571) ^ [_1454487, _1454489, _1454491] : [class_Lattices_Olattice(_1454487), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454487), _1454489), _1454491) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454487), _1454491), _1454489))], (41398 ^ _779571) ^ [_1571277, _1571279, _1571281] : [class_Orderings_Olinorder(_1571277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571277), _1571279)), -(_1571279 = c_Orderings_Obot__class_Obot(tc_fun(_1571277, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571277), _1571281)), -(_1571281 = c_Orderings_Obot__class_Obot(tc_fun(_1571277, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1571277), c_Big__Operators_Olattice_OInf__fin(_1571277, c_Orderings_Oord__class_Omin(_1571277), _1571279)), c_Big__Operators_Olattice_OInf__fin(_1571277, c_Orderings_Oord__class_Omin(_1571277), _1571281)) = c_Big__Operators_Olattice_OInf__fin(_1571277, c_Orderings_Oord__class_Omin(_1571277), hAPP(c_Set_OCollect(_1571277), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_HOL_Obool), tc_HOL_Obool, _1571277), c_HOL_OEx(_1571277)), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool)), tc_fun(_1571277, tc_HOL_Obool), _1571277), hAPP(c_COMBB(tc_fun(_1571277, tc_HOL_Obool), tc_HOL_Obool, _1571277), c_HOL_OEx(_1571277))), hAPP(hAPP(c_COMBC(_1571277, tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool)), tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_fun(tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool))), tc_fun(tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool)), tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool))), _1571277), c_COMBS(_1571277, tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_fun(_1571277, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1571277, tc_fun(tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool))), _1571277), hAPP(c_COMBB(tc_fun(_1571277, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool)), _1571277), c_COMBS(_1571277, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool)), tc_fun(_1571277, tc_fun(_1571277, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1571277), hAPP(c_COMBB(tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1571277), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571277), c_fconj))), hAPP(hAPP(c_COMBC(_1571277, tc_fun(_1571277, tc_fun(_1571277, _1571277)), tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1571277, _1571277), tc_fun(_1571277, tc_HOL_Obool)), tc_fun(tc_fun(_1571277, tc_fun(_1571277, _1571277)), tc_fun(_1571277, tc_fun(_1571277, tc_HOL_Obool))), _1571277), c_COMBB(tc_fun(_1571277, _1571277), tc_fun(_1571277, tc_HOL_Obool), _1571277)), hAPP(hAPP(c_COMBB(tc_fun(_1571277, tc_HOL_Obool), tc_fun(tc_fun(_1571277, _1571277), tc_fun(_1571277, tc_HOL_Obool)), _1571277), c_COMBB(_1571277, tc_HOL_Obool, _1571277)), c_fequal))), c_Orderings_Oord__class_Omax(_1571277)))))), hAPP(hAPP(c_COMBC(_1571277, tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571277, tc_HOL_Obool), tc_fun(_1571277, tc_HOL_Obool)), _1571277), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571277)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571277), c_fconj), hAPP(hAPP(c_COMBC(_1571277, tc_fun(_1571277, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571277)), _1571279)))), hAPP(hAPP(c_COMBC(_1571277, tc_fun(_1571277, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571277)), _1571281))))))))], (7887 ^ _779571) ^ [_910429, _910431] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910429), hAPP(c_Nat_OSuc, _910431)))), 7888 ^ _779571 : [(7891 ^ _779571) ^ [_910517] : [_910429 = hAPP(c_Nat_OSuc, _910517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910517), _910431))], (7889 ^ _779571) ^ [] : [_910429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (14501 ^ _779571) ^ [_1024215] : [-(_1024215 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024215), _1024215) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (13791 ^ _779571) ^ [_1011239] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011239, _1011239) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6587 ^ _779571) ^ [_887132, _887134, _887136] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887132, _887134)), _887136), _887136)), hBOOL(hAPP(_887132, _887136)), 6595 ^ _779571 : [(6598 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887132, _887134)), 6594 ^ [_887132, _887134, _887136]), _887136)))], (6596 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887134), _887136), 6594 ^ [_887132, _887134, _887136])))]]], (40160 ^ _779571) ^ [_1540413, _1540415, _1540417, _1540419, _1540421] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1540413, _1540415), _1540417), hAPP(hAPP(c_COMBS(_1540413, tc_fun(_1540415, tc_HOL_Obool), tc_fun(_1540415, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540415, tc_HOL_Obool), tc_fun(tc_fun(_1540415, tc_HOL_Obool), tc_fun(_1540415, tc_HOL_Obool)), _1540413), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540415, tc_HOL_Obool))), _1540419)), _1540421)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540413, _1540415), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1540413, _1540415), _1540417), _1540419)), hAPP(hAPP(c_Product__Type_OSigma(_1540413, _1540415), _1540417), _1540421)))], (31005 ^ _779571) ^ [_1337759, _1337761] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1337759, _1337761)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1337759, _1337761), tc_HOL_Obool)))), 31008 ^ _779571 : [(31011 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337761), c_Orderings_Otop__class_Otop(tc_fun(_1337761, tc_HOL_Obool)))))], (31009 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337759), c_Orderings_Otop__class_Otop(tc_fun(_1337759, tc_HOL_Obool)))))]]], (17055 ^ _779571) ^ [_1072581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072581), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1072581) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1072581))], (19955 ^ _779571) ^ [_1122373, _1122375] : [class_Fields_Olinordered__field__inverse__zero(_1122373), class_Int_Onumber__ring(_1122373), 19962 ^ _779571 : [(19969 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122373), c_Groups_Ozero__class_Ozero(_1122373)), _1122375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122373), c_Groups_Ozero__class_Ozero(_1122373)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122373), _1122375), hAPP(c_Int_Onumber__class_Onumber__of(_1122373), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19963 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122373), c_Groups_Ozero__class_Ozero(_1122373)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122373), _1122375), hAPP(c_Int_Onumber__class_Onumber__of(_1122373), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122373), c_Groups_Ozero__class_Ozero(_1122373)), _1122375)))]]], (51579 ^ _779571) ^ [_1813281, _1813283] : [hBOOL(hAPP(hAPP(c_fequal, _1813281), _1813283)), -(_1813281 = _1813283)], (20505 ^ _779571) ^ [_1132141, _1132143, _1132145, _1132147] : [class_Rings_Odivision__ring(_1132141), -(_1132143 = c_Groups_Ozero__class_Ozero(_1132141)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132141), _1132145), _1132143) = _1132147, -(_1132145 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132141), _1132147), _1132143))], (16301 ^ _779571) ^ [_1058377, _1058379, _1058381] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058377, _1058379) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058381, _1058379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058381), _1058377)), -(_1058377 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058379), 16308 ^ [_1058377, _1058379, _1058381])))], (27646 ^ _779571) ^ [_1268577, _1268579] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1268577, _1268579) = 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), _1268577), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1268579))))], (19503 ^ _779571) ^ [_1114170, _1114172] : [class_Int_Onumber__ring(_1114170), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114170), hAPP(c_Int_Onumber__class_Onumber__of(_1114170), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1114172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114170), _1114172), _1114172))], (38970 ^ _779571) ^ [_1512539, _1512541, _1512543, _1512545, _1512547] : [c_Fun_Oinj__on(_1512539, _1512541, _1512543, _1512545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512541, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512539, _1512541, _1512543), _1512545)), _1512547)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512541), _1512547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1512539), _1512545)), hAPP(c_Finite__Set_Ocard(_1512541), _1512547))))], (41253 ^ _779571) ^ [_1566295, _1566297, _1566299, _1566301, _1566303, _1566305] : [class_Groups_Ocomm__monoid__add(_1566295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566297), _1566299)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566297, _1566295), _1566301), _1566299) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566303, _1566295), hAPP(hAPP(c_COMBB(tc_fun(_1566297, tc_HOL_Obool), _1566295, _1566303), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566297, _1566295), _1566301)), hAPP(hAPP(c_COMBB(tc_fun(_1566297, tc_HOL_Obool), tc_fun(_1566297, tc_HOL_Obool), _1566303), c_Set_OCollect(_1566297)), hAPP(hAPP(c_COMBB(tc_fun(_1566297, tc_HOL_Obool), tc_fun(_1566297, tc_HOL_Obool), _1566303), hAPP(c_COMBS(_1566297, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566297), c_fconj), hAPP(hAPP(c_COMBC(_1566297, tc_fun(_1566297, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566297)), _1566299)))), hAPP(c_COMBC(_1566297, _1566303, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1566303, tc_fun(_1566303, tc_HOL_Obool), _1566297), c_fequal), _1566305)))))), hAPP(c_Set_Oimage(_1566297, _1566303, _1566305), _1566299)))], (24453 ^ _779571) ^ [_1205859, _1205861, _1205863, _1205865] : [class_Orderings_Olinorder(_1205859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205859), _1205861), _1205863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205859), _1205865), _1205863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205859), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205859), _1205861), _1205865)), _1205863)))], (20087 ^ _779571) ^ [_1125103, _1125105, _1125107] : [class_Fields_Olinordered__field__inverse__zero(_1125103), -(hAPP(c_Groups_Oabs__class_Oabs(_1125103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125103), _1125105), _1125107)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125103), hAPP(c_Groups_Oabs__class_Oabs(_1125103), _1125105)), hAPP(c_Groups_Oabs__class_Oabs(_1125103), _1125107)))], (3190 ^ _779571) ^ [_828434, _828436, _828438, _828440] : [-(c_Set_Othe__elem(_828440, _828436) = c_Set_Othe__elem(_828438, _828434)), _828440 = _828438, _828436 = _828434], (6941 ^ _779571) ^ [_894070, _894072] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _894070), _894072), 6946 ^ _779571 : [(6949 ^ _779571) ^ [] : [-(_894072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6947 ^ _779571) ^ [] : [-(_894070 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6950 ^ _779571 : [(6953 ^ _779571) ^ [] : [-(_894072 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6951 ^ _779571) ^ [] : [-(_894070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42583 ^ _779571) ^ [_1605113, _1605115, _1605117] : [42584 ^ _779571 : [(42585 ^ _779571) ^ [_1605167] : [hBOOL(hAPP(_1605113, _1605167))]], _1605115 = c_Hilbert__Choice_OEps(_1605117, _1605113), -(hBOOL(hAPP(_1605113, _1605115)))], (44706 ^ _779571) ^ [_1656858, _1656860, _1656862, _1656864, _1656866] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656858, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656860, tc_fun(_1656858, tc_HOL_Obool)), _1656862), _1656864)), _1656866) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656860, tc_fun(_1656858, tc_HOL_Obool)), _1656862), hAPP(hAPP(c_COMBC(_1656860, tc_fun(_1656858, tc_HOL_Obool), tc_fun(_1656858, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1656858, tc_HOL_Obool), tc_fun(tc_fun(_1656858, tc_HOL_Obool), tc_fun(_1656858, tc_HOL_Obool)), _1656860), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656858, tc_HOL_Obool))), _1656864)), _1656866)))], (51405 ^ _779571) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (27073 ^ _779571) ^ [_1256590, _1256592, _1256594, _1256596, _1256598] : [class_Orderings_Olinorder(_1256590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256590), _1256592), _1256594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256590), _1256596), _1256598)), 27084 ^ _779571 : [(27093 ^ _779571) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256590, _1256592), _1256594) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256590, _1256596), _1256598)), _1256592 = _1256596, _1256594 = _1256598], (27085 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256590, _1256592), _1256594) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256590, _1256596), _1256598), 27088 ^ _779571 : [(27091 ^ _779571) ^ [] : [-(_1256594 = _1256598)], (27089 ^ _779571) ^ [] : [-(_1256592 = _1256596)]]]]], (43413 ^ _779571) ^ [_1625407, _1625409] : [-(c_Transitive__Closure_Otrancl(_1625407, hAPP(c_Relation_Oconverse(_1625407, _1625407), _1625409)) = hAPP(c_Relation_Oconverse(_1625407, _1625407), c_Transitive__Closure_Otrancl(_1625407, _1625409)))], (51423 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (5336 ^ _779571) ^ [_862039, _862041] : [_862041 = _862039, -(c_List_Otake(_862041) = c_List_Otake(_862039))], (31088 ^ _779571) ^ [_1339447, _1339449, _1339451, _1339453, _1339455, _1339457, _1339459] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339447, tc_fun(_1339449, tc_fun(_1339451, tc_HOL_Obool))), _1339453), _1339455), _1339457), _1339459)), 31092 ^ _779571 : [(31095 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1339455, 31091 ^ [_1339447, _1339449, _1339451, _1339453, _1339455, _1339457, _1339459]), _1339457), _1339459)))], (31093 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339447), 31091 ^ [_1339447, _1339449, _1339451, _1339453, _1339455, _1339457, _1339459]), _1339453)))]]], (49050 ^ _779571) ^ [_1763611, _1763613] : [-(c_List_Orotate(_1763611, _1763613) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1763611), tc_List_Olist(_1763611)), _1763613), c_List_Orotate1(_1763611)))], (51335 ^ _779571) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (2008 ^ _779571) ^ [_809399, _809401, _809403, _809405, _809407, _809409] : [-(c_Com_Ocom_OCall(_809409, _809405, _809401) = c_Com_Ocom_OCall(_809407, _809403, _809399)), _809409 = _809407, _809405 = _809403, _809401 = _809399], (51489 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (36080 ^ _779571) ^ [_1448763, _1448765, _1448767, _1448769] : [hBOOL(hAPP(hAPP(c_member(_1448763), _1448765), _1448767)), hBOOL(hAPP(hAPP(c_member(_1448763), _1448765), _1448769)), -(hBOOL(hAPP(hAPP(c_member(_1448763), _1448765), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448763, tc_HOL_Obool)), _1448767), _1448769))))], (8566 ^ _779571) ^ [_921361, _921363, _921365] : [class_Orderings_Olinorder(_921361), -(_921363 = _921365), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921361), _921363), _921365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921361), _921365), _921363)))], (30529 ^ _779571) ^ [_1327587, _1327589, _1327591, _1327593, _1327595] : [hBOOL(hAPP(hAPP(c_member(_1327587), _1327589), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327591, tc_fun(_1327587, tc_HOL_Obool)), _1327593), _1327595))), 30533 ^ _779571 : [(30536 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327587), _1327589), hAPP(_1327595, 30532 ^ [_1327587, _1327589, _1327591, _1327593, _1327595]))))], (30534 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327591), 30532 ^ [_1327587, _1327589, _1327591, _1327593, _1327595]), _1327593)))]]], (16633 ^ _779571) ^ [_1064029, _1064031, _1064033] : [class_Groups_Oordered__ab__group__add__abs(_1064029), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064029), hAPP(c_Groups_Oabs__class_Oabs(_1064029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064029), _1064031), _1064033))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064029), hAPP(c_Groups_Oabs__class_Oabs(_1064029), _1064031)), hAPP(c_Groups_Oabs__class_Oabs(_1064029), _1064033)))))], (8964 ^ _779571) ^ [_928179, _928181] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928179), _928181) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928181), _928179))], (51235 ^ _779571) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (28985 ^ _779571) ^ [_1296414, _1296416] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1296414, tc_HOL_Obool)), _1296416)))], (50248 ^ _779571) ^ [_1789234, _1789236] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1789234, _1789236)))], (26638 ^ _779571) ^ [_1248048, _1248050] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1248048), _1248050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248048), _1248050)))], (43353 ^ _779571) ^ [_1624178, _1624180] : [-(hAPP(c_Relation_Oconverse(_1624178, _1624178), c_Relation_OId__on(_1624178, _1624180)) = c_Relation_OId__on(_1624178, _1624180))], (10412 ^ _779571) ^ [_952961, _952963, _952965] : [class_Orderings_Oorder(_952961), 10415 ^ _779571 : [(10424 ^ _779571) ^ [] : [-(_952963 = _952965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952961), _952963), _952965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952961), _952965), _952963))], (10416 ^ _779571) ^ [] : [_952963 = _952965, 10419 ^ _779571 : [(10422 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952961), _952965), _952963)))], (10420 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952961), _952963), _952965)))]]]]], (17525 ^ _779571) ^ [_1081013, _1081015, _1081017, _1081019] : [class_Groups_Omonoid__mult(_1081013), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081013), _1081015), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1081017), _1081019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081013), hAPP(hAPP(c_Power_Opower__class_Opower(_1081013), _1081015), _1081017)), hAPP(hAPP(c_Power_Opower__class_Opower(_1081013), _1081015), _1081019)))], (26418 ^ _779571) ^ [_1243611, _1243613, _1243615] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243613), _1243615))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243611), _1243615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243615), _1243613)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243611), _1243613)))], (24797 ^ _779571) ^ [_1212848, _1212850, _1212852, _1212854, _1212856, _1212858] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1212848, _1212850, _1212852, _1212854, _1212856), hAPP(c_Sum__Type_OInl(_1212848, _1212852), _1212858)) = hAPP(_1212854, _1212858))], (51133 ^ _779571) ^ [_1808817, _1808819] : [class_Lattices_Olattice(_1808817), -(class_Lattices_Olattice(tc_fun(_1808819, _1808817)))], (46879 ^ _779571) ^ [_1710278, _1710280, _1710282, _1710284, _1710286, _1710288] : [class_Orderings_Olinorder(_1710278), 46882 ^ _779571 : [(46889 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710278), hAPP(_1710280, _1710282)), hAPP(_1710280, _1710284)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710286, _1710278, _1710280), _1710282), hAPP(hAPP(c_List_Olist_OCons(_1710286), _1710284), _1710288)) = hAPP(hAPP(c_List_Olist_OCons(_1710286), _1710284), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710286, _1710278, _1710280), _1710282), _1710288)))], (46883 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710278), hAPP(_1710280, _1710282)), hAPP(_1710280, _1710284))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710286, _1710278, _1710280), _1710282), hAPP(hAPP(c_List_Olist_OCons(_1710286), _1710284), _1710288)) = hAPP(hAPP(c_List_Olist_OCons(_1710286), _1710282), hAPP(hAPP(c_List_Olist_OCons(_1710286), _1710284), _1710288)))]]], (51553 ^ _779571) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (42536 ^ _779571) ^ [_1604173, _1604175, _1604177, _1604179, _1604181, _1604183] : [hBOOL(hAPP(hAPP(c_member(_1604173), _1604175), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1604177, _1604179, tc_fun(_1604173, tc_HOL_Obool)), _1604181), _1604183))), 42541 ^ _779571 : [(42544 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604173), _1604175), hAPP(hAPP(_1604181, 42539 ^ [_1604173, _1604175, _1604177, _1604179, _1604181, _1604183]), 42540 ^ [_1604173, _1604175, _1604177, _1604179, _1604181, _1604183]))))], (42542 ^ _779571) ^ [] : [-(_1604183 = hAPP(hAPP(c_Product__Type_OPair(_1604177, _1604179), 42539 ^ [_1604173, _1604175, _1604177, _1604179, _1604181, _1604183]), 42540 ^ [_1604173, _1604175, _1604177, _1604179, _1604181, _1604183]))]]], (51429 ^ _779571) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (51069 ^ _779571) ^ [_1807977, _1807979] : [class_Lattices_Obounded__lattice(_1807977), -(class_Lattices_Obounded__lattice(tc_fun(_1807979, _1807977)))], (48084 ^ _779571) ^ [_1739675, _1739677, _1739679] : [hAPP(hAPP(c_List_Oappend(_1739675), _1739677), _1739679) = _1739677, -(_1739679 = c_List_Olist_ONil(_1739675))], (7905 ^ _779571) ^ [_910744] : [_910744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910744), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (41632 ^ _779571) ^ [_1581340, _1581342, _1581344] : [-(hAPP(c_Fun_Ocomp(_1581340, _1581340, _1581342, c_Fun_Oid(_1581340)), _1581344) = _1581344)], (23841 ^ _779571) ^ [_1193957, _1193959, _1193961, _1193963] : [_1193957 = _1193959, 23844 ^ _779571 : [(23847 ^ _779571) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1193961, _1193963), _1193957) = hAPP(c_Product__Type_Osnd(_1193961, _1193963), _1193959))], (23845 ^ _779571) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1193961, _1193963), _1193957) = hAPP(c_Product__Type_Ofst(_1193961, _1193963), _1193959))]]], (47699 ^ _779571) ^ [_1730634, _1730636, _1730638, _1730640] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730634)), hAPP(hAPP(c_List_Olist__update(_1730634, _1730636), _1730638), _1730640)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730634)), _1730636))], (31235 ^ _779571) ^ [_1342190, _1342192, _1342194, _1342196] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1342190, tc_fun(_1342192, tc_HOL_Obool))), _1342194), _1342196)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1342190, _1342192)), hAPP(hAPP(c_Product__Type_OPair(_1342190, _1342192), _1342194), _1342196)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1342190, _1342192), tc_HOL_Obool)))))], (9256 ^ _779571) ^ [_932946, _932948] : [class_Rings_Ocomm__semiring__1(_932946), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932946), c_Groups_Ozero__class_Ozero(_932946)), _932948) = c_Groups_Ozero__class_Ozero(_932946))], (16246 ^ _779571) ^ [_1057341, _1057343] : [_1057341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057341), _1057343) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41161 ^ _779571) ^ [_1563355, _1563357] : [-(hAPP(c_Set_OCollect(_1563355), hAPP(c_fequal, _1563357)) = hAPP(hAPP(c_Set_Oinsert(_1563355), _1563357), c_Orderings_Obot__class_Obot(tc_fun(_1563355, tc_HOL_Obool))))], (4902 ^ _779571) ^ [_855336, _855338] : [_855338 = _855336, -(c_If(_855338) = c_If(_855336))], (41370 ^ _779571) ^ [_1570071, _1570073, _1570075] : [c_Predicate_Oreflp(_1570071, _1570073), -(hBOOL(hAPP(hAPP(_1570073, _1570075), _1570075)))], (50154 ^ _779571) ^ [_1787804, _1787806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787804), _1787806)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1787804, _1787806)) = _1787804)], (7363 ^ _779571) ^ [_901795, _901797, _901799, _901801] : [hAPP(c_Sum__Type_OInl(_901795, _901797), _901799) = hAPP(c_Sum__Type_OInl(_901795, _901797), _901801), -(_901799 = _901801)], (17845 ^ _779571) ^ [_1086688, _1086690, _1086692, _1086694, _1086696] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1086688, _1086690, _1086692), _1086694), hAPP(c_Nat_OSuc, _1086696)) = hAPP(hAPP(_1086692, _1086694), hAPP(hAPP(c_Power_Opower_Opower(_1086688, _1086690, _1086692), _1086694), _1086696)))], (34364 ^ _779571) ^ [_1407976, _1407978, _1407980] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1407976), _1407978)), 34367 ^ _779571 : [(34368 ^ _779571) ^ [] : [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(_1407976, tc_Nat_Onat), _1407980), _1407978))), 34371 ^ _779571 : [(34372 ^ _779571) ^ [_1408144] : [hBOOL(hAPP(hAPP(c_member(_1407976), _1408144), _1407978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1407980, _1408144))))]]], (34378 ^ _779571) ^ [] : [34380 ^ _779571 : [(34383 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1407980, 34379 ^ [_1407976, _1407978, _1407980])))], (34381 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407976), 34379 ^ [_1407976, _1407978, _1407980]), _1407978)))]], -(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(_1407976, tc_Nat_Onat), _1407980), _1407978))))]]], (47254 ^ _779571) ^ [_1719934, _1719936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1719934), _1719936)), -(c_List_Oupto(_1719936, _1719934) = c_List_Olist_ONil(tc_Int_Oint))], (14564 ^ _779571) ^ [_1025241, _1025243, _1025245] : [class_Divides_Osemiring__div(_1025241), -(_1025243 = c_Groups_Ozero__class_Ozero(_1025241)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025241), _1025245), _1025243)), _1025243) = _1025245)], (47967 ^ _779571) ^ [_1736946, _1736948, _1736950, _1736952, _1736954, _1736956] : [hAPP(hAPP(c_List_Olist_OCons(_1736946), _1736948), _1736950) = _1736952, _1736954 = hAPP(hAPP(c_List_Oappend(_1736946), _1736950), _1736956), -(hAPP(hAPP(c_List_Olist_OCons(_1736946), _1736948), _1736954) = hAPP(hAPP(c_List_Oappend(_1736946), _1736952), _1736956))], (46716 ^ _779571) ^ [_1704909, _1704911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1704909), _1704911)), -(c_Nitpick_Ocard_H(_1704909, _1704911) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704909)), c_Hilbert__Choice_OEps(tc_List_Olist(_1704909), hAPP(hAPP(c_COMBS(tc_List_Olist(_1704909), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1704909)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704909), tc_fun(_1704909, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1704909, tc_HOL_Obool), tc_fun(tc_fun(_1704909, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1704909)), c_fequal), c_List_Oset(_1704909))), _1704911))), c_List_Odistinct(_1704909)))))], (42193 ^ _779571) ^ [_1596248, _1596250, _1596252] : [c_Wellfounded_Owf(_1596248, _1596250), c_Wellfounded_Owf(_1596248, _1596252), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1596248, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1596248, _1596248), _1596250)), hAPP(c_Relation_ORange(_1596248, _1596248), _1596252)) = c_Orderings_Obot__class_Obot(tc_fun(_1596248, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1596248, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1596248, _1596248), tc_HOL_Obool)), _1596250), _1596252)))], (25664 ^ _779571) ^ [_1228948, _1228950] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228948)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228950))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228948), _1228950)))], (46642 ^ _779571) ^ [_1703162, _1703164, _1703166] : [-(_1703162 = _1703164), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703166)), _1703162) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703166)), _1703164), 46648 ^ _779571 : [(46651 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1703166, _1703166, tc_HOL_Obool), c_fequal), 46647 ^ [_1703162, _1703164, _1703166]))], (46649 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1703166, _1703166)), 46647 ^ [_1703162, _1703164, _1703166]), hAPP(c_List_Oset(tc_prod(_1703166, _1703166)), hAPP(hAPP(c_List_Ozip(_1703166, _1703166), _1703162), _1703164)))))]]], (5604 ^ _779571) ^ [_866085, _866087] : [_866087 = _866085, -(c_COMBI(_866087) = c_COMBI(_866085))], (5588 ^ _779571) ^ [_865851, _865853] : [_865853 = _865851, -(tc_Option_Ooption(_865853) = tc_Option_Ooption(_865851))], (15432 ^ _779571) ^ [_1040777, _1040779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040777), _1040779)), _1040777) = _1040779)], (8687 ^ _779571) ^ [_922978] : [-(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, _922978)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29039 ^ _779571) ^ [_1297533, _1297535, _1297537, _1297539] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297533, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1297533), _1297535), _1297537)), _1297539) = hAPP(hAPP(c_Set_Oinsert(_1297533), _1297535), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297533, tc_HOL_Obool)), _1297537), _1297539)))], (51419 ^ _779571) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (11420 ^ _779571) ^ [_969102, _969104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969102), _969104)), -(_969104 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969102), 11423 ^ [_969102, _969104]))], (32745 ^ _779571) ^ [_1376931, _1376933] : [class_Rings_Olinordered__idom(_1376931), hBOOL(hAPP(hAPP(c_member(_1376931), _1376933), c_Int_Oring__1__class_OInts(_1376931))), 32752 ^ _779571 : [(32759 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376931), _1376933), c_Groups_Ozero__class_Ozero(_1376931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376931), c_Groups_Oone__class_Oone(_1376931)), _1376933)), _1376933)), c_Groups_Ozero__class_Ozero(_1376931))))], (32753 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376931), c_Groups_Oone__class_Oone(_1376931)), _1376933)), _1376933)), c_Groups_Ozero__class_Ozero(_1376931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376931), _1376933), c_Groups_Ozero__class_Ozero(_1376931))))]]], (4708 ^ _779571) ^ [_852377, _852379, _852381, _852383] : [-(c_Fun_Ofun__upd(_852383, _852379) = c_Fun_Ofun__upd(_852381, _852377)), _852383 = _852381, _852379 = _852377], (25240 ^ _779571) ^ [_1222039, _1222041] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222039), _1222041))), 25241 ^ _779571 : [(25242 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222039), _1222041)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222041), _1222039)))], (25248 ^ _779571) ^ [] : [_1222039 = _1222041]]], (49802 ^ _779571) ^ [_1779917, _1779919, _1779921] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1779917), tc_List_Olist(_1779917)), c_List_Opartition(_1779917, _1779919, _1779921)) = hAPP(c_List_Ofilter(_1779917, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1779917, c_fNot), _1779919)), _1779921))], (4658 ^ _779571) ^ [_851616, _851618, _851620, _851622, _851624, _851626] : [-(c_Big__Operators_Olattice_OInf__fin(_851626, _851622, _851618) = c_Big__Operators_Olattice_OInf__fin(_851624, _851620, _851616)), _851626 = _851624, _851622 = _851620, _851618 = _851616], (29027 ^ _779571) ^ [_1297221, _1297223, _1297225, _1297227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297221, tc_HOL_Obool)), _1297223), _1297225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297221, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1297221), _1297227), _1297223)), hAPP(hAPP(c_Set_Oinsert(_1297221), _1297227), _1297225))))], (44131 ^ _779571) ^ [_1642776, _1642778, _1642780, _1642782] : [class_Complete__Lattice_Ocomplete__lattice(_1642776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642778), _1642780)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1642778, _1642776), _1642780), _1642782) = hAPP(hAPP(c_Finite__Set_Ofold(_1642778, _1642776, hAPP(hAPP(c_COMBB(_1642776, tc_fun(_1642776, _1642776), _1642778), c_Lattices_Osemilattice__sup__class_Osup(_1642776)), _1642782)), c_Orderings_Obot__class_Obot(_1642776)), _1642780))], (28347 ^ _779571) ^ [_1282645, _1282647, _1282649] : [class_Orderings_Olinorder(_1282645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282645), _1282647), _1282649)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282645, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1282645), _1282647)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1282645, _1282647), _1282649)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1282645), _1282649))], (32813 ^ _779571) ^ [_1378326, _1378328] : [class_Orderings_Olinorder(_1378326), -(c_Big__Operators_Olinorder__class_OMax(_1378326, hAPP(hAPP(c_Set_Oinsert(_1378326), _1378328), c_Orderings_Obot__class_Obot(tc_fun(_1378326, tc_HOL_Obool)))) = _1378328)], (5342 ^ _779571) ^ [_862124, _862126] : [_862126 = _862124, -(c_List_Olist_OCons(_862126) = c_List_Olist_OCons(_862124))], (2678 ^ _779571) ^ [_820184, _820186, _820188, _820190] : [-(c_Code__Numeral_Onat__of__aux(_820190, _820186) = c_Code__Numeral_Onat__of__aux(_820188, _820184)), _820190 = _820188, _820186 = _820184], (28539 ^ _779571) ^ [_1286314, _1286316] : [class_Groups_Oordered__ab__group__add(_1286314), -(hAPP(c_Set_Oimage(_1286314, _1286314, c_Groups_Ouminus__class_Ouminus(_1286314)), hAPP(c_SetInterval_Oord__class_OatLeast(_1286314), _1286316)) = hAPP(c_SetInterval_Oord__class_OatMost(_1286314), hAPP(c_Groups_Ouminus__class_Ouminus(_1286314), _1286316)))], (10345 ^ _779571) ^ [_951885, _951887, _951889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951887), _951889)), -(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, _951885)), _951887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _951885)), _951889))))], (19553 ^ _779571) ^ [_1114992, _1114994] : [class_Groups_Omonoid__mult(_1114992), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114992), _1114994), 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(_1114992), _1114994), _1114994))], (9028 ^ _779571) ^ [_929167, _929169, _929171] : [class_Rings_Oring__1(_929167), -(hAPP(c_Int_Oring__1__class_Oof__int(_929167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _929169), _929171)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929167), hAPP(c_Int_Oring__1__class_Oof__int(_929167), _929169)), hAPP(c_Int_Oring__1__class_Oof__int(_929167), _929171)))], (16258 ^ _779571) ^ [_1057486, _1057488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057488)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1057488), _1057486)), _1057488) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1057488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057486), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (11539 ^ _779571) ^ [_971294, _971296] : [11540 ^ _779571 : [(11543 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971296))], (11541 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971294))]], 11544 ^ _779571 : [(11551 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _971294), _971296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _971294)), hAPP(c_Int_Onat, _971296))))], (11545 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _971294)), hAPP(c_Int_Onat, _971296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _971294), _971296)))]]], (12704 ^ _779571) ^ [_991973, _991975, _991977, _991979, _991981] : [class_Rings_Olinordered__semiring__strict(_991973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991973), _991975), _991977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991973), _991979), _991981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991973), c_Groups_Ozero__class_Ozero(_991973)), _991975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991973), c_Groups_Ozero__class_Ozero(_991973)), _991979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991973), _991975), _991979)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991973), _991977), _991981))))], (25264 ^ _779571) ^ [_1222441, _1222443] : [25271 ^ _779571 : [(25274 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222443), _1222441))], (25272 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222441), _1222443)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222441), _1222443)), -(_1222441 = _1222443)], (48329 ^ _779571) ^ [_1745398, _1745400, _1745402, _1745404] : [-(hAPP(hAPP(c_List_Otake(_1745398), _1745400), hAPP(hAPP(c_List_Otake(_1745398), _1745402), _1745404)) = hAPP(hAPP(c_List_Otake(_1745398), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1745400), _1745402)), _1745404))], (11136 ^ _779571) ^ [_964523] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _964523) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36656 ^ _779571) ^ [_1461086, _1461088, _1461090, _1461092] : [class_Lattices_Olattice(_1461086), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1461086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461086), _1461088), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461086), _1461090), _1461092))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461086), _1461088), _1461090)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461086), _1461088), _1461092)))))], (42825 ^ _779571) ^ [_1610668, _1610670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610668), _1610670)), -(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), _1610668), _1610670)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (42990 ^ _779571) ^ [_1615310, _1615312] : [-(c_Transitive__Closure_Otrancl(_1615310, c_Transitive__Closure_Ortrancl(_1615310, _1615312)) = c_Transitive__Closure_Ortrancl(_1615310, _1615312))], (50192 ^ _779571) ^ [_1788407, _1788409, _1788411] : [class_Orderings_Olinorder(_1788407), c_List_Olinorder__class_Osorted(_1788407, _1788409), hBOOL(hAPP(c_List_Odistinct(_1788407), _1788409)), c_List_Olinorder__class_Osorted(_1788407, _1788411), hBOOL(hAPP(c_List_Odistinct(_1788407), _1788411)), hAPP(c_List_Oset(_1788407), _1788409) = hAPP(c_List_Oset(_1788407), _1788411), -(_1788409 = _1788411)], (50760 ^ _779571) ^ [_1800117, _1800119] : [-(hAPP(c_List_Oset(_1800117), hAPP(c_List_Orev(_1800117), _1800119)) = hAPP(c_List_Oset(_1800117), _1800119))], (38221 ^ _779571) ^ [_1497062, _1497064, _1497066, _1497068, _1497070, _1497072] : [c_Finite__Set_Ofolding__idem(_1497062, _1497064, _1497066, _1497068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497062), _1497070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497062, tc_HOL_Obool)), _1497072), _1497070)), -(hAPP(c_Fun_Ocomp(_1497064, _1497064, _1497064, hAPP(_1497068, _1497070)), hAPP(_1497068, _1497072)) = hAPP(_1497068, _1497070))], (32311 ^ _779571) ^ [_1367571, _1367573, _1367575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367571)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1367573), _1367575)), 32318 ^ _779571 : [(32319 ^ _779571) ^ [_1367767] : [32321 ^ _779571 : [(32327 ^ _779571) ^ [] : [-(_1367767 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32323 ^ [_1367571, _1367573, _1367575, _1367767]), 32320 ^ [_1367571, _1367573, _1367575, _1367767]))], (32325 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32323 ^ [_1367571, _1367573, _1367575, _1367767]), _1367575)))], (32322 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32320 ^ [_1367571, _1367573, _1367575, _1367767]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1367571))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367573), _1367767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367573), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1367767), _1367571))))]]], (42167 ^ _779571) ^ [_1595724, _1595726, _1595728, _1595730] : [hBOOL(hAPP(hAPP(c_member(_1595724), _1595726), hAPP(c_Relation_ORange(_1595728, _1595724), _1595730))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595728, _1595724)), hAPP(hAPP(c_Product__Type_OPair(_1595728, _1595724), 42170 ^ [_1595724, _1595726, _1595728, _1595730]), _1595726)), _1595730)))], (3876 ^ _779571) ^ [_839343, _839345, _839347, _839349, _839351, _839353] : [-(c_Predicate_ODomainP(_839353, _839349, _839345) = c_Predicate_ODomainP(_839351, _839347, _839343)), _839353 = _839351, _839349 = _839347, _839345 = _839343], (14409 ^ _779571) ^ [_1022780] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1022780), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1022780)], (49253 ^ _779571) ^ [_1768004, _1768006, _1768008, _1768010, _1768012] : [hBOOL(hAPP(hAPP(c_member(_1768004), _1768006), hAPP(c_List_Oset(_1768004), _1768008))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768010), hAPP(_1768012, _1768006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768010), c_List_Olist_Olist__size(_1768004, _1768012, _1768008))))], (7195 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34977 ^ _779571) ^ [_1422362] : [-(c_Wellfounded_Omeasure(_1422362) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1422362), c_Wellfounded_Oless__than))], (51189 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (31438 ^ _779571) ^ [_1347779, _1347781] : [c_Nat__Transfer_Onat__set(_1347779), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1347781), _1347779)), -(c_Nat__Transfer_Ois__nat(_1347781))], (39074 ^ _779571) ^ [_1514752, _1514754, _1514756, _1514758, _1514760, _1514762, _1514764] : [c_Typedef_Otype__definition(_1514752, _1514754, _1514756, _1514758, _1514760), hBOOL(hAPP(hAPP(c_member(_1514754), _1514762), _1514760)), hBOOL(hAPP(hAPP(c_member(_1514754), _1514764), _1514760)), 39085 ^ _779571 : [(39092 ^ _779571) ^ [] : [_1514762 = _1514764, -(hAPP(_1514758, _1514762) = hAPP(_1514758, _1514764))], (39086 ^ _779571) ^ [] : [hAPP(_1514758, _1514762) = hAPP(_1514758, _1514764), -(_1514762 = _1514764)]]], (42373 ^ _779571) ^ [_1600892, _1600894, _1600896, _1600898] : [-(c_New__Random__Sequence_Oneg__map(_1600892, _1600894, _1600896, _1600898) = c_New__Random__Sequence_Oneg__bind(_1600892, _1600894, _1600898, hAPP(c_Fun_Ocomp(_1600894, 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(_1600894)))))), _1600892, c_New__Random__Sequence_Oneg__single(_1600894)), _1600896)))], (30772 ^ _779571) ^ [_1332871, _1332873, _1332875, _1332877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332871, tc_HOL_Obool)), _1332873), hAPP(hAPP(c_Set_Oinsert(_1332871), _1332875), _1332877))), 30775 ^ _779571 : [(30782 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332871), _1332875), _1332873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332871, tc_HOL_Obool)), _1332873), _1332877)))], (30776 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332871), _1332875), _1332873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332871, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332871, tc_HOL_Obool)), _1332873), hAPP(hAPP(c_Set_Oinsert(_1332871), _1332875), c_Orderings_Obot__class_Obot(tc_fun(_1332871, tc_HOL_Obool))))), _1332877)))]]], (22340 ^ _779571) ^ [_1165188, _1165190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165188), 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)), _1165190)), -(c_Divides_OnegDivAlg(_1165188, _1165190) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1165188), _1165190)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165188, _1165190)))], (43421 ^ _779571) ^ [_1625631, _1625633, _1625635, _1625637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625631, _1625631)), hAPP(hAPP(c_Product__Type_OPair(_1625631, _1625631), _1625633), _1625635)), c_Transitive__Closure_Ortrancl(_1625631, hAPP(c_Relation_Oconverse(_1625631, _1625631), _1625637)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625631, _1625631)), hAPP(hAPP(c_Product__Type_OPair(_1625631, _1625631), _1625635), _1625633)), c_Transitive__Closure_Ortrancl(_1625631, _1625637))))], (50059 ^ _779571) ^ [_1786061, _1786063] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1786061), _1786063))), -(c_List_Oupt(_1786061, hAPP(c_Nat_OSuc, _1786063)) = c_List_Olist_ONil(tc_Nat_Onat))], (47989 ^ _779571) ^ [_1737490, _1737492, _1737494, _1737496] : [-(hAPP(hAPP(c_List_Oappend(_1737490), hAPP(hAPP(c_List_Oappend(_1737490), _1737492), _1737494)), _1737496) = hAPP(hAPP(c_List_Oappend(_1737490), _1737492), hAPP(hAPP(c_List_Oappend(_1737490), _1737494), _1737496)))], (7402 ^ _779571) ^ [_902457] : [-(_902457 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_902457 = hAPP(c_Nat_OSuc, 7405 ^ [_902457]))], (28505 ^ _779571) ^ [_1285724, _1285726, _1285728, _1285730] : [c_Hoare__Mirabelle_Ohoare__derivs(_1285724, _1285726, _1285728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1285724), tc_HOL_Obool)), _1285726), _1285730)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1285724, _1285730, _1285728))], (39721 ^ _779571) ^ [_1529237, _1529239, _1529241, _1529243, _1529245, _1529247] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529237, _1529239, _1529241, _1529243, _1529245), _1529247)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529237), _1529245)))], (37042 ^ _779571) ^ [_1470000, _1470002, _1470004, _1470006, _1470008] : [class_Groups_Ocomm__monoid__mult(_1470000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470002), _1470004)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470002), _1470006)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470000), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1470002, _1470000), _1470008), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470002, tc_HOL_Obool)), _1470004), _1470006))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1470002, _1470000), _1470008), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470002, tc_HOL_Obool)), _1470004), _1470006))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470000), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1470002, _1470000), _1470008), _1470004)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1470002, _1470000), _1470008), _1470006)))], (5684 ^ _779571) ^ [_870063, _870065] : [hAPP(_870063, 5685 ^ [_870063, _870065]) = hAPP(_870065, 5685 ^ [_870063, _870065]), -(_870063 = _870065)], (35251 ^ _779571) ^ [_1428652, _1428654, _1428656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428652, tc_HOL_Obool)), _1428654), _1428656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1428652, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1428652), _1428654)), hAPP(c_Set_OPow(_1428652), _1428656))))], (24775 ^ _779571) ^ [_1212374, _1212376, _1212378, _1212380, _1212382, _1212384, _1212386] : [c_Sum__Type_Osum_Osum__case(_1212374, _1212376, _1212378, _1212380, _1212382) = c_Sum__Type_Osum_Osum__case(_1212374, _1212376, _1212378, _1212384, _1212386), 24778 ^ _779571 : [(24781 ^ _779571) ^ [] : [-(_1212382 = _1212386)], (24779 ^ _779571) ^ [] : [-(_1212380 = _1212384)]]], (7971 ^ _779571) ^ [_911810, _911812, _911814, _911816] : [class_Rings_Olinordered__semidom(_911810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911810), c_Groups_Ozero__class_Ozero(_911810)), _911812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911810), _911814), _911816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911810), _911814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911810), _911812), _911816))))], (22318 ^ _779571) ^ [_1164742, _1164744] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1164742), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1164744))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1164742), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1164744))), 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))))], (38811 ^ _779571) ^ [_1509047, _1509049, _1509051, _1509053, _1509055, _1509057] : [class_Groups_Ocomm__monoid__mult(_1509047), c_Fun_Oinj__on(_1509049, _1509051, _1509053, _1509055), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1509051, _1509047), _1509057), hAPP(c_Set_Oimage(_1509049, _1509051, _1509053), _1509055)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1509049, _1509047), hAPP(c_Fun_Ocomp(_1509051, _1509047, _1509049, _1509057), _1509053)), _1509055))], (51517 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (25964 ^ _779571) ^ [_1235175, _1235177, _1235179, _1235181] : [class_Groups_Oab__group__add(_1235175), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235177, _1235175), hAPP(hAPP(c_COMBB(_1235175, _1235175, _1235177), c_Groups_Ouminus__class_Ouminus(_1235175)), _1235179)), _1235181) = hAPP(c_Groups_Ouminus__class_Ouminus(_1235175), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235177, _1235175), _1235179), _1235181)))], (2424 ^ _779571) ^ [_816197, _816199, _816201, _816203] : [-(c_Quickcheck_Obeyond(_816203, _816199) = c_Quickcheck_Obeyond(_816201, _816197)), _816203 = _816201, _816199 = _816197], (43190 ^ _779571) ^ [_1620189] : [-(hAPP(c_Relation_ODomain(_1620189, _1620189), c_Relation_OId(_1620189)) = c_Orderings_Otop__class_Otop(tc_fun(_1620189, tc_HOL_Obool)))], (37211 ^ _779571) ^ [_1474195, _1474197, _1474199, _1474201, _1474203] : [class_Groups_Ocomm__monoid__add(_1474195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474197), _1474199)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474197), _1474201)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474197, tc_HOL_Obool)), _1474199), _1474201) = c_Orderings_Obot__class_Obot(tc_fun(_1474197, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474197, _1474195), _1474203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474197, tc_HOL_Obool)), _1474199), _1474201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1474195), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474197, _1474195), _1474203), _1474199)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474197, _1474195), _1474203), _1474201)))], (26008 ^ _779571) ^ [_1236121, _1236123] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236121), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1236123)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236121)), _1236123)))], (22834 ^ _779571) ^ [_1175370, _1175372, _1175374, _1175376] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175370, _1175372), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175374), _1175376))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1175370, _1175372) = _1175376)], (5062 ^ _779571) ^ [_857800, _857802, _857804, _857806, _857808, _857810] : [-(c_List_Olinorder__class_Oinsort__key(_857810, _857806, _857802) = c_List_Olinorder__class_Oinsort__key(_857808, _857804, _857800)), _857810 = _857808, _857806 = _857804, _857802 = _857800], (18821 ^ _779571) ^ [_1102406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1102406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1102406)))], (45635 ^ _779571) ^ [_1678665, _1678667, _1678669] : [hBOOL(hAPP(hAPP(c_member(_1678665), _1678667), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1678665, tc_HOL_Obool), _1678669))), 45639 ^ _779571 : [(45642 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1678665, tc_HOL_Obool)), 45638 ^ [_1678665, _1678667, _1678669]), _1678669)))], (45640 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678665), _1678667), 45638 ^ [_1678665, _1678667, _1678669])))]]], (19045 ^ _779571) ^ [_1105896, _1105898] : [class_Int_Onumber__ring(_1105896), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105896), hAPP(c_Int_Onumber__class_Onumber__of(_1105896), _1105898)), c_Groups_Oone__class_Oone(_1105896)) = hAPP(c_Int_Onumber__class_Onumber__of(_1105896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105898), c_Int_OBit1(c_Int_OPls))))], (28955 ^ _779571) ^ [_1295623, _1295625, _1295627, _1295629, _1295631] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295623, tc_fun(_1295625, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295623, tc_HOL_Obool)), _1295627), _1295629)), _1295631) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295625, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295623, tc_fun(_1295625, tc_HOL_Obool)), _1295627), _1295631)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295623, tc_fun(_1295625, tc_HOL_Obool)), _1295629), _1295631)))], (43361 ^ _779571) ^ [_1624388, _1624390, _1624392] : [c_Relation_Orefl__on(_1624388, _1624390, hAPP(c_Relation_Oconverse(_1624388, _1624388), _1624392)), -(c_Relation_Orefl__on(_1624388, _1624390, _1624392))], (41567 ^ _779571) ^ [_1578417, _1578419, _1578421] : [class_Orderings_Olinorder(_1578417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578417), _1578419)), -(_1578419 = c_Orderings_Obot__class_Obot(tc_fun(_1578417, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1578417), _1578421), c_Big__Operators_Olattice_OSup__fin(_1578417, c_Orderings_Oord__class_Omax(_1578417), _1578419)) = c_Big__Operators_Olattice_OSup__fin(_1578417, c_Orderings_Oord__class_Omax(_1578417), hAPP(c_Set_OCollect(_1578417), hAPP(hAPP(c_COMBB(tc_fun(_1578417, tc_HOL_Obool), tc_HOL_Obool, _1578417), c_HOL_OEx(_1578417)), hAPP(hAPP(c_COMBC(_1578417, tc_fun(_1578417, tc_HOL_Obool), tc_fun(_1578417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578417, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1578417, tc_HOL_Obool), tc_fun(_1578417, tc_HOL_Obool)), _1578417), c_COMBS(_1578417, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578417, tc_HOL_Obool), tc_fun(_1578417, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1578417), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578417), c_fconj)), hAPP(hAPP(c_COMBC(_1578417, tc_fun(_1578417, _1578417), tc_fun(_1578417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578417, tc_HOL_Obool), tc_fun(tc_fun(_1578417, _1578417), tc_fun(_1578417, tc_HOL_Obool)), _1578417), c_COMBB(_1578417, tc_HOL_Obool, _1578417)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1578417), _1578421))))), hAPP(hAPP(c_COMBC(_1578417, tc_fun(_1578417, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578417)), _1578419))))))], (11513 ^ _779571) ^ [_970858, _970860] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _970858), _970860))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _970858), _970860)), -(_970858 = _970860)], (44958 ^ _779571) ^ [_1663359] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663359, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1663359, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1663359, tc_HOL_Obool)))], (32873 ^ _779571) ^ [_1379400, _1379402] : [class_Int_Onumber__ring(_1379400), -(hBOOL(hAPP(hAPP(c_member(_1379400), hAPP(c_Int_Onumber__class_Onumber__of(_1379400), _1379402)), c_Int_Oring__1__class_OInts(_1379400))))], (36792 ^ _779571) ^ [_1464450, _1464452, _1464454] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464450, tc_HOL_Obool)), _1464452), _1464454) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464450, tc_HOL_Obool)), _1464452), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464450, tc_HOL_Obool)), _1464454)))], (50948 ^ _779571) ^ [_1805619, _1805621, _1805623, _1805625] : [hBOOL(hAPP(hAPP(c_member(_1805619), _1805621), hAPP(c_List_Oset(_1805619), c_List_OtakeWhile(_1805619, _1805623, _1805625)))), 50951 ^ _779571 : [(50954 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1805623, _1805621)))], (50952 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805619), _1805621), hAPP(c_List_Oset(_1805619), _1805625))))]]], (7782 ^ _779571) ^ [_908535, _908537, _908539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908535), _908537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908535), _908539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908537), _908539)))], (12197 ^ _779571) ^ [_982983, _982985] : [-(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), _982983), _982985)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982985))], (47324 ^ _779571) ^ [_1721212, _1721214] : [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(_1721212)), _1721214))), _1721214 = c_List_Olist_ONil(_1721212)], (14387 ^ _779571) ^ [_1022383, _1022385] : [class_Divides_Osemiring__div(_1022383), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1022383), _1022385), c_Groups_Oone__class_Oone(_1022383)) = _1022385)], (49004 ^ _779571) ^ [_1762675, _1762677, _1762679] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762675)), hAPP(c_List_Orotate(_1762675, _1762677), _1762679)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762675)), _1762679))], (46630 ^ _779571) ^ [_1702851, _1702853, _1702855] : [_1702851 = _1702853, 46633 ^ _779571 : [(46636 ^ _779571) ^ [_1703007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1702855, _1702855)), _1703007), hAPP(c_List_Oset(tc_prod(_1702855, _1702855)), hAPP(hAPP(c_List_Ozip(_1702855, _1702855), _1702851), _1702853)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1702855, _1702855, tc_HOL_Obool), c_fequal), _1703007)))], (46634 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702855)), _1702851) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702855)), _1702853))]]], (22644 ^ _779571) ^ [_1171373, _1171375] : [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), _1171373))), 22647 ^ _779571 : [(22654 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171375)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171373)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171375), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171373)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171373)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171375), 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), _1171373)))))], (22648 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171375)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171373))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171375), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171373)) = 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), _1171375)))]]], (47719 ^ _779571) ^ [_1730987, _1730989, _1730991, _1730993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730987)), _1730989)), _1730991)), -(hAPP(hAPP(c_List_Olist__update(_1730987, _1730989), _1730991), _1730993) = _1730989)], (1002 ^ _779571) ^ [_794864, _794866] : [-(class_Groups_Olinordered__ab__group__add(_794864)), _794866 = _794864, class_Groups_Olinordered__ab__group__add(_794866)], (14268 ^ _779571) ^ [_1020085, _1020087, _1020089, _1020091] : [_1020085 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1020087), _1020089)), _1020091), -(_1020087 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1020085), _1020087) = _1020089), 14275 ^ _779571 : [(14278 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020091), _1020087))], (14276 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020087)))]], 14283 ^ _779571 : [(14286 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020087), _1020091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020091), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14284 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020087))]]], (30511 ^ _779571) ^ [_1326957, _1326959, _1326961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326957, tc_HOL_Obool)), _1326959), _1326961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326957, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326957, tc_fun(_1326957, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326957)), _1326959)), hAPP(hAPP(c_COMBC(_1326957, tc_fun(_1326957, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326957)), _1326961))))], (31678 ^ _779571) ^ [_1354305, _1354307, _1354309, _1354311, _1354313] : [class_Groups_Ocomm__monoid__add(_1354305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354307), _1354309)), 31685 ^ _779571 : [(31692 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1354307), _1354311), _1354309))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354307, _1354305), hAPP(hAPP(c_COMBC(_1354307, _1354305, _1354305), hAPP(hAPP(c_COMBS(_1354307, _1354305, tc_fun(_1354305, _1354305)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1354305, tc_fun(_1354305, _1354305)), _1354307), c_If(_1354305)), hAPP(hAPP(c_COMBC(_1354307, _1354307, tc_HOL_Obool), c_fequal), _1354311))), _1354313)), c_Groups_Ozero__class_Ozero(_1354305))), _1354309) = c_Groups_Ozero__class_Ozero(_1354305))], (31686 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1354307), _1354311), _1354309)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354307, _1354305), hAPP(hAPP(c_COMBC(_1354307, _1354305, _1354305), hAPP(hAPP(c_COMBS(_1354307, _1354305, tc_fun(_1354305, _1354305)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1354305, tc_fun(_1354305, _1354305)), _1354307), c_If(_1354305)), hAPP(hAPP(c_COMBC(_1354307, _1354307, tc_HOL_Obool), c_fequal), _1354311))), _1354313)), c_Groups_Ozero__class_Ozero(_1354305))), _1354309) = hAPP(_1354313, _1354311))]]], (23371 ^ _779571) ^ [_1185136] : [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), _1185136))), -(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), _1185136)) = 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), _1185136))))], (16214 ^ _779571) ^ [_1056871, _1056873] : [-(_1056871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1056871), _1056873) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056871), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1056873)))], (39447 ^ _779571) ^ [_1522884, _1522886, _1522888] : [-(hAPP(c_Set_Ovimage(_1522884, _1522886, _1522888), c_Orderings_Obot__class_Obot(tc_fun(_1522886, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1522884, tc_HOL_Obool)))], (39006 ^ _779571) ^ [_1513507, _1513509, _1513511, _1513513, _1513515, _1513517, _1513519, _1513521] : [c_Finite__Set_Ofolding__image(_1513507, _1513509, _1513511, _1513513, _1513515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513509), _1513517)), c_Fun_Oinj__on(_1513509, _1513509, _1513519, _1513517), -(hAPP(hAPP(_1513515, _1513521), hAPP(c_Set_Oimage(_1513509, _1513509, _1513519), _1513517)) = hAPP(hAPP(_1513515, hAPP(c_Fun_Ocomp(_1513509, _1513507, _1513509, _1513521), _1513519)), _1513517))], (9386 ^ _779571) ^ [_935138, _935140, _935142, _935144, _935146] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_935138), 9389 ^ _779571 : [(9390 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935140), _935142)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935144), _935146)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935140), _935146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935144), _935142)), -(_935140 = _935144), -(_935142 = _935146)], (9400 ^ _779571) ^ [] : [9401 ^ _779571 : [(9404 ^ _779571) ^ [] : [_935142 = _935146], (9402 ^ _779571) ^ [] : [_935140 = _935144]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935140), _935142)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935144), _935146)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935140), _935146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935138), _935144), _935142)))]]], (22424 ^ _779571) ^ [_1167017] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1167017)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1167017)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167017)), 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)))))], (44708 ^ _779571) ^ [_1656967, _1656969, _1656971, _1656973, _1656975] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656967, tc_HOL_Obool)), _1656969), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656971, tc_fun(_1656967, tc_HOL_Obool)), _1656973), _1656975)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656971, tc_fun(_1656967, tc_HOL_Obool)), _1656973), hAPP(hAPP(c_COMBB(tc_fun(_1656967, tc_HOL_Obool), tc_fun(_1656967, tc_HOL_Obool), _1656971), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656967, tc_HOL_Obool)), _1656969)), _1656975)))], (8645 ^ _779571) ^ [_922270, _922272] : [class_Rings_Olinordered__idom(_922270), 8648 ^ _779571 : [(8655 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922272), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922270), hAPP(c_Int_Oring__1__class_Oof__int(_922270), _922272)), c_Groups_Ozero__class_Ozero(_922270))))], (8649 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922270), hAPP(c_Int_Oring__1__class_Oof__int(_922270), _922272)), c_Groups_Ozero__class_Ozero(_922270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922272), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (42976 ^ _779571) ^ [_1614965, _1614967, _1614969, _1614971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614965, _1614965)), hAPP(hAPP(c_Product__Type_OPair(_1614965, _1614965), _1614967), _1614969)), c_Transitive__Closure_Otrancl(_1614965, _1614971))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614965, _1614965)), hAPP(hAPP(c_Product__Type_OPair(_1614965, _1614965), _1614967), _1614969)), c_Transitive__Closure_Ortrancl(_1614965, _1614971))))], (40910 ^ _779571) ^ [_1558073, _1558075, _1558077, _1558079, _1558081] : [c_Finite__Set_Ofolding__one__idem(_1558073, _1558075, _1558077), hAPP(_1558079, hAPP(hAPP(_1558075, 40915 ^ [_1558073, _1558075, _1558077, _1558079, _1558081]), 40916 ^ [_1558073, _1558075, _1558077, _1558079, _1558081])) = hAPP(hAPP(_1558075, hAPP(_1558079, 40915 ^ [_1558073, _1558075, _1558077, _1558079, _1558081])), hAPP(_1558079, 40916 ^ [_1558073, _1558075, _1558077, _1558079, _1558081])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558073), _1558081)), -(_1558081 = c_Orderings_Obot__class_Obot(tc_fun(_1558073, tc_HOL_Obool))), -(hAPP(_1558079, hAPP(_1558077, _1558081)) = hAPP(_1558077, hAPP(c_Set_Oimage(_1558073, _1558073, _1558079), _1558081)))], (51327 ^ _779571) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (39212 ^ _779571) ^ [_1517546, _1517548, _1517550, _1517552] : [c_Fun_Oinj__on(_1517546, _1517548, _1517550, _1517552), -(c_Fun_Oinj__on(_1517548, _1517546, c_Fun_Othe__inv__into(_1517546, _1517548, _1517552, _1517550), hAPP(c_Set_Oimage(_1517546, _1517548, _1517550), _1517552)))], (32247 ^ _779571) ^ [_1366421, _1366423, _1366425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366421)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1366423), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1366425)), 32257 ^ _779571 : [(32263 ^ _779571) ^ [] : [-(_1366423 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32259 ^ [_1366421, _1366423, _1366425]), 32256 ^ [_1366421, _1366423, _1366425]))], (32261 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32259 ^ [_1366421, _1366423, _1366425]), _1366425)))], (32258 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32256 ^ [_1366421, _1366423, _1366425]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1366421))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1366423), _1366421) = _1366423)], (3428 ^ _779571) ^ [_832241, _832243] : [_832243 = _832241, -(c_Nitpick_ORep__Frac(_832243) = c_Nitpick_ORep__Frac(_832241))], (40340 ^ _779571) ^ [_1544766, _1544768] : [class_Orderings_Olinorder(_1544766), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544766), _1544768)), -(c_Big__Operators_Olinorder__class_OMin(_1544766, _1544768) = hAPP(c_Finite__Set_Ofold1(_1544766, c_Orderings_Oord__class_Omin(_1544766)), _1544768))], (24629 ^ _779571) ^ [_1209655, _1209657] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209655), _1209657)), _1209657) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1209655), _1209657))], (27103 ^ _779571) ^ [_1257071, _1257073] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257071), hAPP(c_Nat_OSuc, _1257073)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1257071, _1257073))], (30381 ^ _779571) ^ [_1324491, _1324493, _1324495, _1324497] : [_1324491 = _1324493, 30384 ^ _779571 : [(30391 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324495), _1324497), _1324493)), -(hBOOL(hAPP(hAPP(c_member(_1324495), _1324497), _1324491)))], (30385 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324495), _1324497), _1324491)), -(hBOOL(hAPP(hAPP(c_member(_1324495), _1324497), _1324493)))]]], (29906 ^ _779571) ^ [] : [-(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))))], (4934 ^ _779571) ^ [_855812, _855814, _855816, _855818] : [-(c_List_Oupto(_855818, _855814) = c_List_Oupto(_855816, _855812)), _855818 = _855816, _855814 = _855812], (29908 ^ _779571) ^ [_1314658, _1314660, _1314662, _1314664, _1314666] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314658, _1314660, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314658)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314658), hAPP(hAPP(c_COMBC(_1314658, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1314658), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1314658), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1314662))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1314664))), c_Com_Ocom_OWhile(_1314664, _1314666)), _1314662)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314658), tc_HOL_Obool)))))], (38659 ^ _779571) ^ [_1505884, _1505886, _1505888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505884), _1505886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505884, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1505884, _1505884, _1505888), _1505886)), _1505886)), c_Fun_Oinj__on(_1505884, _1505884, _1505888, _1505886), -(hAPP(c_Set_Oimage(_1505884, _1505884, _1505888), _1505886) = _1505886)], (25658 ^ _779571) ^ [_1228843, _1228845] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228843), _1228845)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228843)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228845))))], (11070 ^ _779571) ^ [_963248, _963250, _963252, _963254, _963256] : [class_Groups_Oordered__ab__semigroup__add(_963248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963248), _963250), _963252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963248), _963254), _963256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963248), _963250), _963254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963248), _963252), _963256))))], (39485 ^ _779571) ^ [_1523842, _1523844, _1523846, _1523848, _1523850] : [hBOOL(hAPP(hAPP(c_member(_1523842), _1523844), hAPP(c_Set_Ovimage(_1523842, _1523846, _1523848), hAPP(hAPP(c_Set_Oinsert(_1523846), _1523850), c_Orderings_Obot__class_Obot(tc_fun(_1523846, tc_HOL_Obool)))))), -(hAPP(_1523848, _1523844) = _1523850)], (16455 ^ _779571) ^ [_1060965, _1060967, _1060969] : [class_Rings_Olinordered__idom(_1060965), -(hAPP(c_Groups_Oabs__class_Oabs(_1060965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060965), _1060967), _1060969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060965), hAPP(c_Groups_Oabs__class_Oabs(_1060965), _1060967)), hAPP(c_Groups_Oabs__class_Oabs(_1060965), _1060969)))], (46152 ^ _779571) ^ [_1690951, _1690953, _1690955, _1690957] : [-(hBOOL(hAPP(hAPP(c_member(_1690951), _1690957), hAPP(c_Set_Oimage(tc_prod(_1690951, _1690953), _1690951, c_Product__Type_Ofst(_1690951, _1690953)), hAPP(c_List_Oset(tc_prod(_1690951, _1690953)), _1690955))))), -(hAPP(c_Map_Omap__of(_1690951, _1690953, _1690955), _1690957) = c_Option_Ooption_ONone(_1690953))], (15632 ^ _779571) ^ [_1044809, _1044811] : [class_Groups_Ogroup__add(_1044809), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044809), c_Groups_Ozero__class_Ozero(_1044809)), _1044811) = hAPP(c_Groups_Ouminus__class_Ouminus(_1044809), _1044811))], (41314 ^ _779571) ^ [_1568540, _1568542, _1568544, _1568546, _1568548, _1568550] : [-(hBOOL(hAPP(hAPP(c_member(_1568540), _1568542), _1568544))), -(hAPP(c_Fun_Ooverride__on(_1568540, _1568546, _1568548, _1568550, _1568544), _1568542) = hAPP(_1568548, _1568542))], (5726 ^ _779571) ^ [_871028, _871030, _871032] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _871028, _871030, _871032), -(_871032 = _871028)], (44602 ^ _779571) ^ [_1654226, _1654228, _1654230, _1654232, _1654234] : [class_Complete__Lattice_Ocomplete__lattice(_1654226), 44605 ^ _779571 : [(44606 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654226), _1654228), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654230, _1654226), _1654232), _1654234))), 44609 ^ _779571 : [(44610 ^ _779571) ^ [_1654407] : [hBOOL(hAPP(hAPP(c_member(_1654230), _1654407), _1654232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654226), _1654228), hAPP(_1654234, _1654407))))]]], (44616 ^ _779571) ^ [] : [44618 ^ _779571 : [(44621 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654226), _1654228), hAPP(_1654234, 44617 ^ [_1654226, _1654228, _1654230, _1654232, _1654234])))], (44619 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1654230), 44617 ^ [_1654226, _1654228, _1654230, _1654232, _1654234]), _1654232)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1654226), _1654228), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654230, _1654226), _1654232), _1654234))))]]], (44225 ^ _779571) ^ [_1644291, _1644293, _1644295, _1644297, _1644299, _1644301] : [c_Finite__Set_Ofun__left__comm(_1644291, _1644293, _1644295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644291), _1644297)), hBOOL(hAPP(hAPP(c_member(_1644291), _1644299), _1644297)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1644291, _1644293, _1644295), _1644301), _1644297) = hAPP(hAPP(_1644295, _1644299), hAPP(hAPP(c_Finite__Set_Ofold(_1644291, _1644293, _1644295), _1644301), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1644291, tc_HOL_Obool)), _1644297), hAPP(hAPP(c_Set_Oinsert(_1644291), _1644299), c_Orderings_Obot__class_Obot(tc_fun(_1644291, tc_HOL_Obool)))))))], (37000 ^ _779571) ^ [_1469043, _1469045, _1469047] : [class_Lattices_Oboolean__algebra(_1469043), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1469043), _1469045), _1469047) = c_Orderings_Obot__class_Obot(_1469043), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1469043), _1469045), _1469047) = c_Orderings_Otop__class_Otop(_1469043), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1469043), _1469045) = _1469047)], (18753 ^ _779571) ^ [_1101287] : [_1101287 = c_Int_OMin, -(c_Int_OBit1(_1101287) = c_Int_OMin)], (9274 ^ _779571) ^ [_933243, _933245] : [class_Rings_Omult__zero(_933243), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933243), _933245), c_Groups_Ozero__class_Ozero(_933243)) = c_Groups_Ozero__class_Ozero(_933243))], (24983 ^ _779571) ^ [_1217415, _1217417, _1217419, _1217421] : [-(c_Product__Type_Ocurry(_1217415, _1217417, _1217419, hAPP(c_Product__Type_Oprod_Oprod__case(_1217415, _1217417, _1217419), _1217421)) = _1217421)], (49493 ^ _779571) ^ [_1773297, _1773299] : [-(_1773297 = c_List_Olist_ONil(_1773299)), -(c_List_Olast(_1773299, _1773297) = hAPP(hAPP(c_List_Onth(_1773299), _1773297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773299)), _1773297)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (29317 ^ _779571) ^ [_1303656, _1303658, _1303660, _1303662] : [_1303656 = c_Orderings_Obot__class_Obot(tc_fun(_1303658, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303658, tc_fun(_1303660, tc_HOL_Obool)), _1303656), hAPP(c_COMBK(tc_fun(_1303660, tc_HOL_Obool), _1303658), _1303662)) = c_Orderings_Obot__class_Obot(tc_fun(_1303660, tc_HOL_Obool)))], (49392 ^ _779571) ^ [_1771647, _1771649, _1771651, _1771653] : [-(_1771647 = c_List_Olist_ONil(_1771649)), 49395 ^ _779571 : [(49402 ^ _779571) ^ [] : [-(_1771651 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771649)), _1771647)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1771649, hAPP(hAPP(c_List_Olist__update(_1771649, _1771647), _1771651), _1771653)) = c_List_Olast(_1771649, _1771647))], (49396 ^ _779571) ^ [] : [_1771651 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771649)), _1771647)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1771649, hAPP(hAPP(c_List_Olist__update(_1771649, _1771647), _1771651), _1771653)) = _1771653)]]], (16337 ^ _779571) ^ [_1059060, _1059062] : [_1059060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1059062, _1059060) = _1059062)], (17309 ^ _779571) ^ [_1077163, _1077165] : [-(_1077163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1077165), _1077163) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077165), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1077165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1077163), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (46358 ^ _779571) ^ [_1695323, _1695325, _1695327, _1695329, _1695331] : [hBOOL(hAPP(hAPP(c_member(_1695323), _1695325), hAPP(c_List_Oset(_1695323), _1695327))), -(hAPP(c_Map_Omap__of(_1695323, _1695329, hAPP(hAPP(c_List_Ozip(_1695323, _1695329), _1695327), hAPP(hAPP(c_List_Omap(_1695323, _1695329), _1695331), _1695327))), _1695325) = hAPP(c_Option_Ooption_OSome(_1695329), hAPP(_1695331, _1695325)))], (31548 ^ _779571) ^ [_1351612, _1351614, _1351616] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351612), _1351614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351612, tc_HOL_Obool)), _1351616), _1351614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1351612), _1351616)), hAPP(c_Finite__Set_Ocard(_1351612), _1351614))))], (1782 ^ _779571) ^ [_804614, _804616] : [-(hBOOL(_804614)), _804616 = _804614, hBOOL(_804616)], (34283 ^ _779571) ^ [_1406396, _1406398, _1406400, _1406402] : [class_Groups_Ocomm__monoid__mult(_1406396), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1406398), _1406400))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406398, _1406396), _1406402), _1406400) = c_Groups_Oone__class_Oone(_1406396))], (18687 ^ _779571) ^ [_1100170, _1100172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100170), _1100172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1100170)), c_Int_OBit1(_1100172))))], (6973 ^ _779571) ^ [_894526, _894528, _894530] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_894526, _894528)), _894530), hAPP(hAPP(hAPP(c_Natural_Oupdate, _894530), _894526), hAPP(_894528, _894530)))))], (20461 ^ _779571) ^ [_1131368, _1131370, _1131372, _1131374] : [class_Fields_Ofield__inverse__zero(_1131368), -(_1131370 = c_Groups_Ozero__class_Ozero(_1131368)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131368), _1131372), _1131370)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131368), _1131374), _1131370)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131368), _1131372), _1131374))], (26654 ^ _779571) ^ [_1248331, _1248333] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248333), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248331)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248333))))], (13074 ^ _779571) ^ [_998486, _998488] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998486)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998488))))), _998486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _998488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20359 ^ _779571) ^ [_1129790, _1129792, _1129794] : [class_Fields_Olinordered__field__inverse__zero(_1129790), 20362 ^ _779571 : [(20377 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129790), _1129792), _1129794)))), 20378 ^ _779571 : [(20385 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), _1129792), c_Groups_Ozero__class_Ozero(_1129790))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), _1129794), c_Groups_Ozero__class_Ozero(_1129790)))], (20379 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), _1129792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), _1129794))]]], (20363 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129790), _1129792), _1129794))), 20368 ^ _779571 : [(20371 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), _1129794)))], (20369 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), c_Groups_Ozero__class_Ozero(_1129790)), _1129792)))]], 20372 ^ _779571 : [(20375 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), _1129794), c_Groups_Ozero__class_Ozero(_1129790))))], (20373 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129790), _1129792), c_Groups_Ozero__class_Ozero(_1129790))))]]]]], (37066 ^ _779571) ^ [_1470618, _1470620, _1470622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470618), _1470620)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470618), _1470622)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470618), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470618, tc_HOL_Obool)), _1470620), _1470622))), hAPP(c_Finite__Set_Ocard(_1470618), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470618, tc_HOL_Obool)), _1470620), _1470622))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470618), _1470620)), hAPP(c_Finite__Set_Ocard(_1470618), _1470622)))], (3164 ^ _779571) ^ [_828051, _828053] : [_828053 = _828051, -(c_Int_OBit1(_828053) = c_Int_OBit1(_828051))], (48222 ^ _779571) ^ [_1742362, _1742364, _1742366, _1742368] : [-(c_List_Osublist(_1742362, hAPP(hAPP(c_List_Oappend(_1742362), _1742364), _1742366), _1742368) = hAPP(hAPP(c_List_Oappend(_1742362), c_List_Osublist(_1742362, _1742364, _1742368)), c_List_Osublist(_1742362, _1742366, 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(_1742362)), _1742364)))), _1742368)))))], (25252 ^ _779571) ^ [_1222249, _1222251] : [25259 ^ _779571 : [(25262 ^ _779571) ^ [] : [_1222249 = _1222251], (25260 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222249), _1222251)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222249), _1222251)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222251), _1222249)))], (37381 ^ _779571) ^ [_1477690, _1477692, _1477694] : [class_Orderings_Olinorder(_1477690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477690), _1477692)), -(_1477692 = c_Orderings_Obot__class_Obot(tc_fun(_1477690, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477690), _1477694)), -(_1477694 = c_Orderings_Obot__class_Obot(tc_fun(_1477690, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477690, tc_HOL_Obool)), _1477692), _1477694) = c_Orderings_Obot__class_Obot(tc_fun(_1477690, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1477690, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477690, tc_HOL_Obool)), _1477692), _1477694)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1477690), c_Big__Operators_Olinorder__class_OMax(_1477690, _1477692)), c_Big__Operators_Olinorder__class_OMax(_1477690, _1477694)))], (22308 ^ _779571) ^ [_1164481, _1164483] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1164481)), hAPP(c_Code__Numeral_Oof__nat, _1164483)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1164481), _1164483)))], (8151 ^ _779571) ^ [_914660, _914662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914660)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914660), _914662)))], (11485 ^ _779571) ^ [_970343, _970345, _970347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970343), _970345)), _970347)), 11488 ^ _779571 : [(11491 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970345), _970347)))], (11489 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970343), _970347)))]]], (15412 ^ _779571) ^ [_1040543, _1040545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040543), _1040545)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1040543, _1040545) = _1040543)], (2512 ^ _779571) ^ [_817573, _817575, _817577, _817579] : [-(c_Groups_Osgn__class_Osgn(_817579, _817575) = c_Groups_Osgn__class_Osgn(_817577, _817573)), _817579 = _817577, _817575 = _817573], (8124 ^ _779571) ^ [_914207] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_914207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51015 ^ _779571) ^ [_1806827, _1806829, _1806831, _1806833, _1806835] : [hBOOL(hAPP(hAPP(c_member(_1806827), _1806829), hAPP(c_List_Oset(_1806827), _1806831))), -(hBOOL(hAPP(_1806833, _1806829))), -(c_List_OtakeWhile(_1806827, _1806833, hAPP(hAPP(c_List_Oappend(_1806827), _1806831), _1806835)) = c_List_OtakeWhile(_1806827, _1806833, _1806831))], (29902 ^ _779571) ^ [_1314566, _1314568, _1314570] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314566, _1314568, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314566)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314566), _1314570), c_Com_Ocom_OSKIP), _1314570)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314566), tc_HOL_Obool)))))], (49519 ^ _779571) ^ [_1773905, _1773907, _1773909] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773905, _1773905)), hAPP(hAPP(c_Product__Type_OPair(_1773905, _1773905), 49520 ^ [_1773905, _1773907, _1773909]), 49520 ^ [_1773905, _1773907, _1773909])), _1773907))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773905), tc_List_Olist(_1773905))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773905), tc_List_Olist(_1773905)), _1773909), _1773909)), c_List_Olexord(_1773905, _1773907)))], (20639 ^ _779571) ^ [_1134191, _1134193, _1134195, _1134197] : [class_Fields_Ofield(_1134191), -(_1134193 = c_Groups_Ozero__class_Ozero(_1134191)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1134191), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134191), _1134195), _1134193)), _1134197) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134191), hAPP(hAPP(c_Power_Opower__class_Opower(_1134191), _1134195), _1134197)), hAPP(hAPP(c_Power_Opower__class_Opower(_1134191), _1134193), _1134197)))], (35557 ^ _779571) ^ [_1436029, _1436031, _1436033, _1436035, _1436037, _1436039, _1436041] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1436029, _1436031, _1436033), hAPP(c_Fun_Ocomp(_1436035, tc_fun(_1436031, _1436033), _1436029, _1436037), _1436039)), _1436041) = hAPP(hAPP(_1436037, hAPP(_1436039, hAPP(c_Product__Type_Ofst(_1436029, _1436031), _1436041))), hAPP(c_Product__Type_Osnd(_1436029, _1436031), _1436041)))], (49162 ^ _779571) ^ [_1766045, _1766047] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1766045), _1766047) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1766045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49168 ^ _779571 : [(49171 ^ _779571) ^ [] : [49167 ^ [_1766045, _1766047] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49169 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49167 ^ [_1766045, _1766047]), hAPP(c_List_Oset(tc_Nat_Onat), _1766047))))]]], (14644 ^ _779571) ^ [_1026590, _1026592] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026590), _1026592) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1026592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14653 ^ _779571 : [(14656 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026590), _1026592)))], (14654 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026590)))]], 14657 ^ _779571 : [(14660 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026592), _1026590)))], (14658 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1026590), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10185 ^ _779571) ^ [_949151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _949151)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _949151)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _949151)))], (49213 ^ _779571) ^ [_1767064, _1767066, _1767068] : [class_Orderings_Olinorder(_1767064), -(c_Big__Operators_Olinorder__class_OMax(_1767064, hAPP(c_List_Oset(_1767064), hAPP(hAPP(c_List_Olist_OCons(_1767064), _1767066), _1767068))) = hAPP(c_List_Ofoldl(_1767064, _1767064, c_Orderings_Oord__class_Omax(_1767064), _1767066), _1767068))], (7252 ^ _779571) ^ [_899532, _899534, _899536] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _899532)), _899534), _899536)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _899532))), _899534), _899536)))], (39543 ^ _779571) ^ [_1525164, _1525166, _1525168, _1525170] : [-(hBOOL(hAPP(hAPP(c_member(_1525164), _1525166), _1525168))), -(hAPP(c_Set_Ovimage(_1525170, _1525164, hAPP(c_COMBK(_1525164, _1525170), _1525166)), _1525168) = c_Orderings_Obot__class_Obot(tc_fun(_1525170, tc_HOL_Obool)))], (50370 ^ _779571) ^ [_1791396, _1791398] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1791396, _1791398) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1791396, hAPP(c_Nat_OSuc, _1791398))))], (14443 ^ _779571) ^ [_1023287, _1023289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023289)), -(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), _1023287), _1023289))))], (11655 ^ _779571) ^ [_973276, _973278] : [class_Groups_Olinordered__ab__group__add(_973276), 11658 ^ _779571 : [(11665 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), _973278), c_Groups_Ozero__class_Ozero(_973276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973276), _973278), _973278)), c_Groups_Ozero__class_Ozero(_973276))))], (11659 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973276), _973278), _973278)), c_Groups_Ozero__class_Ozero(_973276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), _973278), c_Groups_Ozero__class_Ozero(_973276))))]]], (51533 ^ _779571) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (45127 ^ _779571) ^ [_1666997, _1666999, _1667001, _1667003] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1666997, _1666999), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666997, tc_HOL_Obool), _1667001)), _1667003) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1666997, tc_HOL_Obool), tc_fun(tc_prod(_1666997, _1666999), tc_HOL_Obool)), _1667001), hAPP(hAPP(c_COMBC(tc_fun(_1666997, tc_HOL_Obool), tc_fun(_1666997, tc_fun(_1666999, tc_HOL_Obool)), tc_fun(tc_prod(_1666997, _1666999), tc_HOL_Obool)), c_Product__Type_OSigma(_1666997, _1666999)), _1667003)))], (14355 ^ _779571) ^ [_1021770, _1021772] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1021770), _1021772) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021770, _1021772)), _1021772))], (36250 ^ _779571) ^ [_1452732, _1452734, _1452736] : [36252 ^ _779571 : [(36258 ^ _779571) ^ [] : [-(36251 ^ [_1452732, _1452734, _1452736] = 36254 ^ [_1452732, _1452734, _1452736])], (36256 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452732), 36254 ^ [_1452732, _1452734, _1452736]), _1452736)))], (36253 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452732), 36251 ^ [_1452732, _1452734, _1452736]), _1452734)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452732, tc_HOL_Obool)), _1452734), _1452736) = c_Orderings_Obot__class_Obot(tc_fun(_1452732, tc_HOL_Obool)))], (25704 ^ _779571) ^ [_1229683, _1229685, _1229687, _1229689] : [class_Rings_Ocomm__semiring__1(_1229683), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229683), _1229685), _1229687)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229683), _1229685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229683), _1229689), _1229687))))], (7312 ^ _779571) ^ [_900744, _900746, _900748, _900750] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _900744), _900746, _900748, _900750), 7316 ^ _779571 : [(7319 ^ _779571) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900744)), _900746, 7315 ^ [_900744, _900746, _900748, _900750], _900750))], (7317 ^ _779571) ^ [] : [-(_900748 = hAPP(c_Nat_OSuc, 7315 ^ [_900744, _900746, _900748, _900750]))]]], (46033 ^ _779571) ^ [_1688020, _1688022, _1688024, _1688026, _1688028, _1688030, _1688032] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688020), tc_Option_Ooption(_1688022), tc_sum(_1688024, _1688026), hAPP(c_Option_Omap(_1688020, _1688022), _1688028)), c_Sum__Type_Osum_Osum__case(_1688024, tc_Option_Ooption(_1688020), _1688026, _1688030, _1688032)) = c_Sum__Type_Osum_Osum__case(_1688024, tc_Option_Ooption(_1688022), _1688026, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688020), tc_Option_Ooption(_1688022), _1688024, hAPP(c_Option_Omap(_1688020, _1688022), _1688028)), _1688030), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688020), tc_Option_Ooption(_1688022), _1688026, hAPP(c_Option_Omap(_1688020, _1688022), _1688028)), _1688032)))], (18777 ^ _779571) ^ [_1101671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1101671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1101671))))], (40250 ^ _779571) ^ [_1542908, _1542910, _1542912, _1542914] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1542908, _1542910)), hAPP(hAPP(c_Product__Type_OSigma(_1542908, _1542910), hAPP(hAPP(c_Set_Oinsert(_1542908), _1542912), c_Orderings_Obot__class_Obot(tc_fun(_1542908, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1542910, tc_HOL_Obool), _1542908), _1542914))) = hAPP(c_Finite__Set_Ocard(_1542910), _1542914))], (7282 ^ _779571) ^ [_900109, _900111, _900113] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _900109)), _900111), _900113)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900109))), _900111), _900113)))], (48766 ^ _779571) ^ [_1757430, _1757432] : [hBOOL(hAPP(c_List_Odistinct(_1757430), _1757432)), -(hBOOL(hAPP(c_List_Odistinct(_1757430), hAPP(c_List_Orotate1(_1757430), _1757432))))], (49040 ^ _779571) ^ [_1763422, _1763424, _1763426] : [_1763426 = c_List_Olist_ONil(_1763422), -(hAPP(c_List_Orotate(_1763422, _1763424), _1763426) = c_List_Olist_ONil(_1763422))], (32032 ^ _779571) ^ [_1362099, _1362101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362099, _1362099)), hAPP(hAPP(c_Product__Type_OPair(_1362099, _1362099), 32033 ^ [_1362099, _1362101]), 32033 ^ [_1362099, _1362101])), _1362101)), -(c_Nitpick_Orefl_H(_1362099, _1362101))], (28204 ^ _779571) ^ [_1279805, _1279807, _1279809, _1279811] : [class_Orderings_Olinorder(_1279805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279805), _1279807), _1279809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279805), _1279809), _1279811)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279805, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1279805, _1279807, _1279809)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1279805, _1279809, _1279811)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1279805, _1279807, _1279811))], (10640 ^ _779571) ^ [_956619, _956621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956619), _956621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956619)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956621))))], (26648 ^ _779571) ^ [_1248216, _1248218] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248216)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248218))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248218), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248216)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5282 ^ _779571) ^ [_861206, _861208, _861210, _861212] : [-(c_List_Otranspose(_861212, _861208) = c_List_Otranspose(_861210, _861206)), _861212 = _861210, _861208 = _861206], (28779 ^ _779571) ^ [_1290999, _1291001, _1291003, _1291005, _1291007] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290999, tc_fun(_1291001, tc_HOL_Obool)), _1291003), _1291005), _1291007))), 28780 ^ _779571 : [(28781 ^ _779571) ^ [_1291071] : [hBOOL(hAPP(hAPP(c_member(_1290999), _1291071), _1291003)), hBOOL(hAPP(hAPP(_1291005, _1291071), _1291007))]]], (41306 ^ _779571) ^ [_1568328, _1568330] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1568328), _1568330)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1568328, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1568328, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1568328, tc_HOL_Obool), tc_fun(_1568328, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1568328, tc_HOL_Obool))), _1568330)))))], (33885 ^ _779571) ^ [_1398311, _1398313, _1398315] : [class_Orderings_Olinorder(_1398311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398311), _1398313)), -(_1398313 = c_Orderings_Obot__class_Obot(tc_fun(_1398311, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398311), _1398315)), -(_1398315 = c_Orderings_Obot__class_Obot(tc_fun(_1398311, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1398311, c_Orderings_Oord__class_Omax(_1398311), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398311, tc_HOL_Obool)), _1398313), _1398315)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1398311), c_Big__Operators_Olattice_OSup__fin(_1398311, c_Orderings_Oord__class_Omax(_1398311), _1398313)), c_Big__Operators_Olattice_OSup__fin(_1398311, c_Orderings_Oord__class_Omax(_1398311), _1398315)))], (3126 ^ _779571) ^ [_827490, _827492, _827494, _827496, _827498, _827500] : [-(c_Random__Sequence_Oempty(_827500, _827496, _827492) = c_Random__Sequence_Oempty(_827498, _827494, _827490)), _827500 = _827498, _827496 = _827494, _827492 = _827490], (7432 ^ _779571) ^ [_902896, _902898, _902900] : [7433 ^ _779571 : [(7436 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_902900, _902898), _902896))], (7434 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902896), _902898)))]], 7439 ^ _779571 : [(7442 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_902900, _902898), _902896))], (7440 ^ _779571) ^ [] : [-(_902896 = _902898)]], 7445 ^ _779571 : [(7448 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_902900, _902898), _902896))], (7446 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902898), _902896)))]], -(hBOOL(hAPP(hAPP(_902900, _902898), _902896)))], (11304 ^ _779571) ^ [_967304, _967306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967304)), hAPP(c_Nat_OSuc, _967306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967304), _967306)))], (34610 ^ _779571) ^ [_1413580, _1413582, _1413584, _1413586, _1413588] : [-(hBOOL(hAPP(hAPP(c_member(_1413580), _1413582), _1413584))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1413580, tc_Option_Ooption(_1413586)), c_Map_Orestrict__map(_1413580, _1413586, _1413588, _1413584)), _1413582), c_Option_Ooption_ONone(_1413586)) = c_Map_Orestrict__map(_1413580, _1413586, _1413588, _1413584))], (42286 ^ _779571) ^ [_1598068, _1598070, _1598072] : [-(hAPP(c_Set_Oimage(tc_prod(_1598068, _1598070), _1598068, c_Product__Type_Ofst(_1598068, _1598070)), _1598072) = hAPP(c_Relation_ODomain(_1598068, _1598070), _1598072))], (36794 ^ _779571) ^ [_1464507, _1464509, _1464511] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464507, tc_HOL_Obool)), _1464509), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464507, tc_HOL_Obool)), _1464511)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464507, tc_HOL_Obool)), _1464509), _1464511))], (28298 ^ _779571) ^ [_1281793] : [c_Nat__Transfer_Onat__set(_1281793), 28301 ^ _779571 : [(28302 ^ _779571) ^ [_1281859] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1281859), _1281793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281859)))]]], (51067 ^ _779571) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (36284 ^ _779571) ^ [_1453464, _1453466, _1453468, _1453470] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453464, tc_HOL_Obool)), _1453466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453464, tc_HOL_Obool)), _1453468), _1453470)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453464, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453464, tc_HOL_Obool)), _1453466), _1453468)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453464, tc_HOL_Obool)), _1453466), _1453470)))], (46999 ^ _779571) ^ [_1714150, _1714152, _1714154, _1714156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1714150), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1714152), _1714154))), -(hAPP(c_Random_Opick(_1714152, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714152)), _1714154), _1714156)), _1714150) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1714152), _1714154))], (50704 ^ _779571) ^ [_1799019, _1799021] : [hBOOL(hAPP(c_List_Odistinct(_1799019), hAPP(c_List_Orev(_1799019), _1799021))), -(hBOOL(hAPP(c_List_Odistinct(_1799019), _1799021)))], (51297 ^ _779571) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (36372 ^ _779571) ^ [_1455223, _1455225, _1455227, _1455229] : [class_Lattices_Olattice(_1455223), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455223), _1455225), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455223), _1455227), _1455229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455223), _1455227), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455223), _1455225), _1455229)))], (36698 ^ _779571) ^ [_1462039, _1462041, _1462043, _1462045] : [hBOOL(hAPP(hAPP(c_member(_1462039), _1462041), _1462043)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462039, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1462039), _1462041), _1462045)), _1462043) = hAPP(hAPP(c_Set_Oinsert(_1462039), _1462041), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462039, tc_HOL_Obool)), _1462045), _1462043)))], (49961 ^ _779571) ^ [_1784364, _1784366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1784364), _1784366)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1784364, _1784366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1784366), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44592 ^ _779571) ^ [_1653908, _1653910, _1653912, _1653914, _1653916, _1653918] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653908, tc_fun(_1653910, tc_HOL_Obool)), _1653912), hAPP(hAPP(c_COMBB(_1653914, tc_fun(_1653910, tc_HOL_Obool), _1653908), _1653916), _1653918)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653914, tc_fun(_1653910, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1653908, _1653914, _1653918), _1653912)), _1653916))], (31826 ^ _779571) ^ [_1357299, _1357301, _1357303, _1357305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1357299), _1357301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357299, tc_HOL_Obool)), _1357301), _1357303)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357299, tc_Nat_Onat), _1357305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357299, tc_HOL_Obool)), _1357303), _1357301)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357299, tc_Nat_Onat), _1357305), _1357303)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357299, tc_Nat_Onat), _1357305), _1357301)))], (27912 ^ _779571) ^ [_1273837, _1273839, _1273841, _1273843] : [class_Lattices_Osemilattice__sup(_1273837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273837), _1273839), _1273841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273837), _1273843), _1273841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273837), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273837), _1273839), _1273843)), _1273841)))], (11236 ^ _779571) ^ [_966100, _966102, _966104] : [class_Groups_Oordered__ab__group__add(_966100), 11239 ^ _779571 : [(11246 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966100), hAPP(c_Groups_Ouminus__class_Ouminus(_966100), _966104)), _966102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966100), hAPP(c_Groups_Ouminus__class_Ouminus(_966100), _966102)), _966104)))], (11240 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966100), hAPP(c_Groups_Ouminus__class_Ouminus(_966100), _966102)), _966104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966100), hAPP(c_Groups_Ouminus__class_Ouminus(_966100), _966104)), _966102)))]]], (8454 ^ _779571) ^ [_919626, _919628, _919630, _919632] : [class_Orderings_Oord(_919626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919626), _919628), _919630)), _919630 = _919632, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919626), _919628), _919632)))], (49124 ^ _779571) ^ [_1765186, _1765188, _1765190, _1765192, _1765194, _1765196, _1765198] : [-(hAPP(c_List_Ofoldl(_1765186, _1765188, _1765190, _1765192), hAPP(hAPP(c_List_Omap(_1765194, _1765188), _1765196), _1765198)) = hAPP(c_List_Ofoldl(_1765186, _1765194, hAPP(hAPP(c_COMBC(_1765186, tc_fun(_1765194, _1765188), tc_fun(_1765194, _1765186)), hAPP(hAPP(c_COMBB(tc_fun(_1765188, _1765186), tc_fun(tc_fun(_1765194, _1765188), tc_fun(_1765194, _1765186)), _1765186), c_COMBB(_1765188, _1765186, _1765194)), _1765190)), _1765196), _1765192), _1765198))], (24369 ^ _779571) ^ [_1204436, _1204438, _1204440] : [class_Orderings_Olinorder(_1204436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204436), _1204438), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204436), _1204440), _1204438))))], (39276 ^ _779571) ^ [_1518942, _1518944, _1518946, _1518948] : [class_Groups_Ocomm__monoid__mult(_1518942), 39279 ^ _779571 : [(39286 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518944), _1518946))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1518944, _1518942), _1518948), _1518946) = c_Groups_Oone__class_Oone(_1518942))], (39280 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518944), _1518946)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1518944, _1518942), _1518948), _1518946) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518942, _1518944, c_Groups_Otimes__class_Otimes(_1518942)), _1518948), c_Groups_Oone__class_Oone(_1518942)), _1518946))]]], (19571 ^ _779571) ^ [_1115281, _1115283] : [class_Rings_Oring__1(_1115281), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1115281), hAPP(c_Groups_Ouminus__class_Ouminus(_1115281), _1115283)), 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(_1115281), _1115283), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (28531 ^ _779571) ^ [_1286159] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286159)) = hAPP(c_Nat_OSuc, _1286159))], (43524 ^ _779571) ^ [_1628429, _1628431, _1628433] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1628429, _1628429, _1628429), _1628431), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628429, _1628429), tc_HOL_Obool), _1628433), _1628431)) = hAPP(hAPP(c_Relation_Orel__comp(_1628429, _1628429, _1628429), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628429, _1628429), tc_HOL_Obool), _1628433), _1628431)), _1628431))], (15668 ^ _779571) ^ [_1045510, _1045512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1045510), _1045512)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045510), _1045512)))], (28089 ^ _779571) ^ [_1277463, _1277465, _1277467, _1277469] : [28093 ^ _779571 : [(28096 ^ _779571) ^ [] : [hBOOL(hAPP(_1277469, 28092 ^ [_1277463, _1277465, _1277467, _1277469]))], (28094 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277463), 28092 ^ [_1277463, _1277465, _1277467, _1277469]), _1277465)))]], 28098 ^ _779571 : [(28101 ^ _779571) ^ [] : [hBOOL(hAPP(_1277469, 28097 ^ [_1277463, _1277465, _1277467, _1277469]))], (28099 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277463), 28097 ^ [_1277463, _1277465, _1277467, _1277469]), _1277467)))]], 28102 ^ _779571 : [(28103 ^ _779571) ^ [_1277796] : [hBOOL(hAPP(hAPP(c_member(_1277463), _1277796), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277463, tc_HOL_Obool)), _1277465), _1277467))), -(hBOOL(hAPP(_1277469, _1277796)))]]], (8336 ^ _779571) ^ [_917867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917867)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18007 ^ _779571) ^ [_1089344, _1089346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1089344), _1089346)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1089344), _1089346) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (27940 ^ _779571) ^ [_1274357, _1274359, _1274361, _1274363] : [class_Lattices_Osemilattice__sup(_1274357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274357), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274357), _1274359), _1274361)), _1274363)), 27947 ^ _779571 : [(27950 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274357), _1274361), _1274363)))], (27948 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274357), _1274359), _1274363)))]]], (3434 ^ _779571) ^ [_832326, _832328, _832330, _832332] : [-(c_Com_Ocom_OWhile(_832332, _832328) = c_Com_Ocom_OWhile(_832330, _832326)), _832332 = _832330, _832328 = _832326], (49636 ^ _779571) ^ [_1776342, _1776344, _1776346] : [-(c_List_Obutlast(_1776342, hAPP(hAPP(c_List_Odrop(_1776342), _1776344), _1776346)) = hAPP(hAPP(c_List_Odrop(_1776342), _1776344), c_List_Obutlast(_1776342, _1776346)))], (16713 ^ _779571) ^ [_1065696, _1065698, _1065700] : [class_Groups_Oordered__ab__group__add__abs(_1065696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065696), hAPP(c_Groups_Oabs__class_Oabs(_1065696), _1065698)), _1065700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065696), hAPP(c_Groups_Ouminus__class_Ouminus(_1065696), _1065698)), _1065700)))], (19851 ^ _779571) ^ [_1120427, _1120429] : [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), _1120427))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1120429))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1120427))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120429)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120427)))], (24235 ^ _779571) ^ [_1201938, _1201940, _1201942, _1201944] : [class_Orderings_Olinorder(_1201938), 24238 ^ _779571 : [(24239 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201938), _1201942), _1201944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), _1201942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), _1201944)))], (24249 ^ _779571) ^ [] : [24250 ^ _779571 : [(24253 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), _1201944))], (24251 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), _1201942))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201938), _1201940), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201938), _1201942), _1201944))))]]], (41183 ^ _779571) ^ [_1563885, _1563887, _1563889] : [-(hBOOL(hAPP(_1563885, _1563887))), -(hAPP(c_Set_OCollect(_1563889), hAPP(hAPP(c_COMBS(_1563889, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563889), c_fconj), hAPP(hAPP(c_COMBC(_1563889, _1563889, tc_HOL_Obool), c_fequal), _1563887))), _1563885)) = c_Orderings_Obot__class_Obot(tc_fun(_1563889, tc_HOL_Obool)))], (21599 ^ _779571) ^ [_1151510, _1151512, _1151514, _1151516] : [class_Fields_Olinordered__field__inverse__zero(_1151510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151510), _1151512), _1151514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151510), _1151516), c_Groups_Ozero__class_Ozero(_1151510))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151510), c_Groups_Ozero__class_Ozero(_1151510)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151510), _1151512), _1151514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151510), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151510), _1151516), _1151512)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151510), _1151516), _1151514))))], (3962 ^ _779571) ^ [_840636, _840638, _840640, _840642, _840644, _840646] : [-(c_Finite__Set_Ofold__image(_840646, _840642, _840638) = c_Finite__Set_Ofold__image(_840644, _840640, _840636)), _840646 = _840644, _840642 = _840640, _840638 = _840636], (44483 ^ _779571) ^ [_1650071, _1650073, _1650075, _1650077, _1650079, _1650081] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650071, tc_fun(_1650073, tc_fun(_1650075, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1650071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_fun(_1650073, tc_fun(_1650075, tc_HOL_Obool)), _1650071), hAPP(c_COMBC(_1650073, tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_fun(_1650075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650075, tc_fun(tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_fun(_1650075, tc_HOL_Obool)), _1650073), c_COMBC(_1650075, tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650075, tc_prod(_1650073, _1650075)), tc_fun(_1650075, tc_fun(tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_HOL_Obool)), _1650073), hAPP(c_COMBB(tc_prod(_1650073, _1650075), tc_fun(tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool), tc_HOL_Obool), _1650075), c_member(tc_prod(_1650073, _1650075)))), c_Product__Type_OPair(_1650073, _1650075))))), _1650077)), _1650079), _1650081)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650073, _1650075)), hAPP(hAPP(c_Product__Type_OPair(_1650073, _1650075), _1650079), _1650081)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650071, tc_fun(tc_prod(_1650073, _1650075), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1650071, tc_HOL_Obool))), _1650077))))], (51031 ^ _779571) ^ [_1807138, _1807140, _1807142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807138)), c_List_OtakeWhile(_1807138, _1807140, _1807142))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807138)), _1807142))), hBOOL(hAPP(_1807140, hAPP(hAPP(c_List_Onth(_1807138), _1807142), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807138)), c_List_OtakeWhile(_1807138, _1807140, _1807142)))))], (13691 ^ _779571) ^ [_1009091, _1009093, _1009095, _1009097] : [class_Divides_Osemiring__div(_1009091), -(c_Divides_Odiv__class_Omod(_1009091, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009091), _1009093), _1009095), _1009097) = c_Divides_Odiv__class_Omod(_1009091, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009091), c_Divides_Odiv__class_Omod(_1009091, _1009093, _1009097)), c_Divides_Odiv__class_Omod(_1009091, _1009095, _1009097)), _1009097))], (4078 ^ _779571) ^ [_842424, _842426, _842428, _842430, _842432, _842434] : [-(c_Relation_Orel__comp(_842434, _842430, _842426) = c_Relation_Orel__comp(_842432, _842428, _842424)), _842434 = _842432, _842430 = _842428, _842426 = _842424], (35094 ^ _779571) ^ [_1424938, _1424940, _1424942, _1424944, _1424946] : [class_Groups_Ocomm__monoid__mult(_1424938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424940), _1424942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424940, tc_HOL_Obool)), _1424944), _1424942)), 35108 ^ _779571 : [(35111 ^ _779571) ^ [] : [hAPP(_1424946, 35107 ^ [_1424938, _1424940, _1424942, _1424944, _1424946]) = c_Groups_Oone__class_Oone(_1424938)], (35109 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1424940), 35107 ^ [_1424938, _1424940, _1424942, _1424944, _1424946]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1424940, tc_HOL_Obool)), _1424942), _1424944))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1424940, _1424938), _1424946), _1424942) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1424940, _1424938), _1424946), _1424944))], (28401 ^ _779571) ^ [_1283655, _1283657] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283655), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1283657) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1283655, _1283657))], (28190 ^ _779571) ^ [_1279536, _1279538, _1279540, _1279542] : [class_Orderings_Olinorder(_1279536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279536), _1279538), _1279540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279536), _1279540), _1279542)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279536, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1279536, _1279538, _1279540)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1279536, _1279540), _1279542)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1279536, _1279538, _1279542))], (15300 ^ _779571) ^ [_1038416, _1038418] : [class_Groups_Ogroup__add(_1038416), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038416), _1038418), c_Groups_Ozero__class_Ozero(_1038416)) = _1038418)], (45644 ^ _779571) ^ [_1678853, _1678855, _1678857, _1678859, _1678861, _1678863] : [-(hBOOL(hAPP(hAPP(c_member(_1678853), _1678855), c_Map_Odom(_1678853, _1678857, _1678859)))), -(c_Map_Omap__add(_1678853, _1678857, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1678853, tc_Option_Ooption(_1678857)), _1678861), _1678855), hAPP(c_Option_Ooption_OSome(_1678857), _1678863)), _1678859) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1678853, tc_Option_Ooption(_1678857)), c_Map_Omap__add(_1678853, _1678857, _1678861, _1678859)), _1678855), hAPP(c_Option_Ooption_OSome(_1678857), _1678863)))], (13795 ^ _779571) ^ [_1011317, _1011319, _1011321] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011317), _1011319), _1011321) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011317), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011319, _1011321)), _1011321))], (48058 ^ _779571) ^ [_1739050, _1739052, _1739054, _1739056, _1739058, _1739060] : [-(c_List_Ofoldr(_1739050, _1739052, _1739054, hAPP(hAPP(c_List_Oappend(_1739050), _1739056), _1739058), _1739060) = c_List_Ofoldr(_1739050, _1739052, _1739054, _1739056, c_List_Ofoldr(_1739050, _1739052, _1739054, _1739058, _1739060)))], (46592 ^ _779571) ^ [_1701297, _1701299, _1701301] : [hBOOL(hAPP(hAPP(c_member(_1701297), _1701299), hAPP(c_List_Oset(_1701297), _1701301))), -(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(_1701297)), _1701301))))], (3630 ^ _779571) ^ [_835454, _835456, _835458, _835460, _835462, _835464, _835466, _835468] : [-(c_Product__Type_Oapfst(_835468, _835464, _835460, _835456) = c_Product__Type_Oapfst(_835466, _835462, _835458, _835454)), _835468 = _835466, _835464 = _835462, _835460 = _835458, _835456 = _835454], (4106 ^ _779571) ^ [_842866, _842868, _842870, _842872, _842874, _842876] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_842876, _842872, _842868) = c_Smallcheck_Ofull__small__class_Ofull__small(_842874, _842870, _842866)), _842876 = _842874, _842872 = _842870, _842868 = _842866], (27888 ^ _779571) ^ [_1273427, _1273429, _1273431] : [class_Lattices_Osemilattice__sup(_1273427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273427), _1273429), _1273431)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273427), _1273431), _1273429) = _1273431)], (35353 ^ _779571) ^ [_1430938, _1430940, _1430942, _1430944, _1430946] : [c_Finite__Set_Ofolding__one__idem(_1430938, _1430940, _1430942), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430938), _1430944)), hBOOL(hAPP(hAPP(c_member(_1430938), _1430946), _1430944)), -(hAPP(hAPP(_1430940, _1430946), hAPP(_1430942, _1430944)) = hAPP(_1430942, _1430944))], (1482 ^ _779571) ^ [_800864, _800866] : [-(class_Rings_Olinordered__semiring(_800864)), _800866 = _800864, class_Rings_Olinordered__semiring(_800866)], (45417 ^ _779571) ^ [_1673761, _1673763, _1673765, _1673767, _1673769, _1673771, _1673773] : [c_Finite__Set_Ofun__left__comm(_1673761, _1673763, _1673765), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1673761, _1673763, _1673765, _1673767, hAPP(hAPP(c_Set_Oinsert(_1673761), _1673769), _1673771)), _1673773)), -(hBOOL(hAPP(hAPP(c_member(_1673761), _1673769), _1673771))), 45429 ^ _779571 : [(45432 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1673761, _1673763, _1673765, _1673767, _1673771), 45428 ^ [_1673761, _1673763, _1673765, _1673767, _1673769, _1673771, _1673773])))], (45430 ^ _779571) ^ [] : [-(_1673773 = hAPP(hAPP(_1673765, _1673769), 45428 ^ [_1673761, _1673763, _1673765, _1673767, _1673769, _1673771, _1673773]))]]], (31253 ^ _779571) ^ [_1343080, _1343082, _1343084, _1343086] : [_1343084 = _1343086, -(hAPP(hAPP(c_COMBC(_1343080, tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_fun(_1343082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343082, tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_fun(_1343082, tc_HOL_Obool)), _1343080), c_COMBC(_1343082, tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343082, tc_prod(_1343080, _1343082)), tc_fun(_1343082, tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), _1343080), hAPP(c_COMBB(tc_prod(_1343080, _1343082), tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool), _1343082), c_member(tc_prod(_1343080, _1343082)))), c_Product__Type_OPair(_1343080, _1343082)))), _1343084) = hAPP(hAPP(c_COMBC(_1343080, tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_fun(_1343082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343082, tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_fun(_1343082, tc_HOL_Obool)), _1343080), c_COMBC(_1343082, tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343082, tc_prod(_1343080, _1343082)), tc_fun(_1343082, tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool)), _1343080), hAPP(c_COMBB(tc_prod(_1343080, _1343082), tc_fun(tc_fun(tc_prod(_1343080, _1343082), tc_HOL_Obool), tc_HOL_Obool), _1343082), c_member(tc_prod(_1343080, _1343082)))), c_Product__Type_OPair(_1343080, _1343082)))), _1343086))], (24481 ^ _779571) ^ [_1206357, _1206359, _1206361, _1206363, _1206365] : [class_Orderings_Olinorder(_1206357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206357), _1206359), _1206361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206357), _1206363), _1206365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206357), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206357), _1206359), _1206363)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206357), _1206361), _1206365))))], (46231 ^ _779571) ^ [_1692672, _1692674, _1692676, _1692678, _1692680] : [hBOOL(hAPP(c_List_Odistinct(_1692672), hAPP(hAPP(c_List_Omap(tc_prod(_1692672, _1692674), _1692672), c_Product__Type_Ofst(_1692672, _1692674)), _1692676))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1692672, _1692674)), hAPP(hAPP(c_Product__Type_OPair(_1692672, _1692674), _1692678), _1692680)), hAPP(c_List_Oset(tc_prod(_1692672, _1692674)), _1692676))), -(hAPP(c_Map_Omap__of(_1692672, _1692674, _1692676), _1692678) = hAPP(c_Option_Ooption_OSome(_1692674), _1692680))], (7608 ^ _779571) ^ [_905771] : [-(_905771 = 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)), _905771)))], (31462 ^ _779571) ^ [_1348951, _1348953, _1348955, _1348957] : [-(c_Nitpick_Ofold__graph_H(_1348951, _1348953, _1348955, _1348957, c_Orderings_Obot__class_Obot(tc_fun(_1348951, tc_HOL_Obool)), _1348957))], (38241 ^ _779571) ^ [_1497669, _1497671] : [c_Equiv__Relations_Oequivp(_1497669, hAPP(hAPP(c_COMBC(_1497669, tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_fun(_1497669, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497669, tc_fun(tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_fun(_1497669, tc_HOL_Obool)), _1497669), c_COMBC(_1497669, tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497669, tc_prod(_1497669, _1497669)), tc_fun(_1497669, tc_fun(tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_HOL_Obool)), _1497669), hAPP(c_COMBB(tc_prod(_1497669, _1497669), tc_fun(tc_fun(tc_prod(_1497669, _1497669), tc_HOL_Obool), tc_HOL_Obool), _1497669), c_member(tc_prod(_1497669, _1497669)))), c_Product__Type_OPair(_1497669, _1497669)))), _1497671)), -(c_Equiv__Relations_Oequiv(_1497669, c_Orderings_Otop__class_Otop(tc_fun(_1497669, tc_HOL_Obool)), _1497671))], (21045 ^ _779571) ^ [_1141792] : [c_Nat__Transfer_Ois__nat(_1141792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141792)))], (12015 ^ _779571) ^ [_979854, _979856, _979858] : [class_Rings_Olinordered__ring__strict(_979854), 12018 ^ _779571 : [(12033 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979854), _979856), _979858)))), 12034 ^ _779571 : [(12041 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), _979856), c_Groups_Ozero__class_Ozero(_979854))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), _979858), c_Groups_Ozero__class_Ozero(_979854)))], (12035 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), _979856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), _979858))]]], (12019 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979854), _979856), _979858))), 12024 ^ _779571 : [(12027 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), _979858)))], (12025 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), c_Groups_Ozero__class_Ozero(_979854)), _979856)))]], 12028 ^ _779571 : [(12031 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), _979858), c_Groups_Ozero__class_Ozero(_979854))))], (12029 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979854), _979856), c_Groups_Ozero__class_Ozero(_979854))))]]]]], (12854 ^ _779571) ^ [_994823, _994825, _994827] : [class_Rings_Olinordered__ring(_994823), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994823), c_Groups_Ozero__class_Ozero(_994823)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_994823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994823), _994825), _994825)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994823), _994827), _994827)))))], (36222 ^ _779571) ^ [_1451833, _1451835, _1451837, _1451839] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451833, tc_HOL_Obool)), _1451835), _1451837)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451833, tc_HOL_Obool)), _1451837), _1451839))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451833, tc_HOL_Obool)), _1451839), _1451835)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451833, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451833, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_HOL_Obool)), _1451835), _1451837)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_HOL_Obool)), _1451837), _1451839))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_HOL_Obool)), _1451839), _1451835)))], (31247 ^ _779571) ^ [_1342531, _1342533, _1342535, _1342537] : [hAPP(hAPP(c_COMBC(_1342531, tc_fun(tc_prod(_1342531, _1342533), tc_HOL_Obool), tc_fun(_1342533, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342533, tc_fun(tc_fun(tc_prod(_1342531, _1342533), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1342531, _1342533), tc_HOL_Obool), tc_fun(_1342533, tc_HOL_Obool)), _1342531), c_COMBC(_1342533, tc_fun(tc_prod(_1342531, _1342533), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342533, tc_prod(_1342531, _1342533)), tc_fun(_1342533, tc_fun(tc_fun(tc_prod(_1342531, 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c_member(tc_prod(_1342531, _1342533)))), c_Product__Type_OPair(_1342531, _1342533)))), _1342537), -(_1342535 = _1342537)], (4774 ^ _779571) ^ [_853356, _853358, _853360, _853362] : [-(c_List_Olists(_853362, _853358) = c_List_Olists(_853360, _853356)), _853362 = _853360, _853358 = _853356], (34340 ^ _779571) ^ [_1407452, _1407454, _1407456, _1407458, _1407460] : [class_Fields_Ofield__inverse__zero(_1407452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407454), _1407456)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407454, _1407452), hAPP(hAPP(c_COMBS(_1407454, _1407452, _1407452), hAPP(hAPP(c_COMBB(_1407452, tc_fun(_1407452, _1407452), _1407454), c_Rings_Oinverse__class_Odivide(_1407452)), _1407458)), _1407460)), _1407456) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1407452), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407454, _1407452), _1407458), _1407456)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407454, _1407452), _1407460), _1407456)))], (20119 ^ _779571) ^ [_1125573, _1125575] : [c_Nat__Transfer_Ois__nat(_1125573), c_Nat__Transfer_Ois__nat(_1125575), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125573, _1125575)))], (29632 ^ _779571) ^ [_1309058, _1309060] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309058, tc_fun(_1309058, tc_HOL_Obool)), _1309060), hAPP(hAPP(c_COMBC(_1309058, tc_fun(_1309058, tc_HOL_Obool), tc_fun(_1309058, tc_HOL_Obool)), c_Set_Oinsert(_1309058)), c_Orderings_Obot__class_Obot(tc_fun(_1309058, tc_HOL_Obool)))) = _1309060)], (19233 ^ _779571) ^ [_1109402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109402), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1109402)), c_Int_OPls)))], (4212 ^ _779571) ^ [_844637, _844639, _844641, _844643, _844645, _844647] : [-(c_Map_Oran(_844647, _844643, _844639) = c_Map_Oran(_844645, _844641, _844637)), _844647 = _844645, _844643 = _844641, _844639 = _844637], (17467 ^ _779571) ^ [_1079979, _1079981, _1079983] : [class_Rings_Olinordered__semidom(_1079979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079979), c_Groups_Oone__class_Oone(_1079979)), _1079981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079979), c_Groups_Oone__class_Oone(_1079979)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079979), _1079981), _1079983))))], (51635 ^ _779571) ^ [_1814012, _1814014] : [hBOOL(_1814012), -(hBOOL(hAPP(hAPP(c_fdisj, _1814014), _1814012)))], (18833 ^ _779571) ^ [_1102590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1102590)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102590), c_Int_OMin)))], (21183 ^ _779571) ^ [_1144116, _1144118, _1144120, _1144122] : [class_Fields_Ofield__inverse__zero(_1144116), class_Int_Onumber(_1144116), 21190 ^ _779571 : [(21191 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144116), _1144120), _1144122), 21194 ^ _779571 : [(21201 ^ _779571) ^ [] : [_1144122 = c_Groups_Ozero__class_Ozero(_1144116), -(hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118) = c_Groups_Ozero__class_Ozero(_1144116))], (21195 ^ _779571) ^ [] : [-(_1144122 = c_Groups_Ozero__class_Ozero(_1144116)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144116), hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118)), _1144122) = _1144120)]]], (21207 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144116), _1144120), _1144122)), 21210 ^ _779571 : [(21213 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144116), hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118)), _1144122) = _1144120], (21211 ^ _779571) ^ [] : [_1144122 = c_Groups_Ozero__class_Ozero(_1144116)]], 21214 ^ _779571 : [(21217 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1144116), _1144118) = c_Groups_Ozero__class_Ozero(_1144116)], (21215 ^ _779571) ^ [] : [-(_1144122 = c_Groups_Ozero__class_Ozero(_1144116))]]]]], (35529 ^ _779571) ^ [_1435160, _1435162, _1435164, _1435166] : [-(hAPP(c_Relation_OImage(_1435160, _1435162, _1435164), _1435166) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435160, tc_fun(_1435162, tc_HOL_Obool)), _1435166), hAPP(hAPP(c_COMBB(tc_fun(_1435160, tc_HOL_Obool), tc_fun(_1435162, tc_HOL_Obool), _1435160), c_Relation_OImage(_1435160, _1435162, _1435164)), hAPP(hAPP(c_COMBC(_1435160, tc_fun(_1435160, tc_HOL_Obool), tc_fun(_1435160, tc_HOL_Obool)), c_Set_Oinsert(_1435160)), c_Orderings_Obot__class_Obot(tc_fun(_1435160, tc_HOL_Obool))))))], (35779 ^ _779571) ^ [_1441896, _1441898, _1441900] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1441896), _1441898), _1441900) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1441896, tc_HOL_Obool), tc_HOL_Obool)), -(_1441898 = c_Orderings_Obot__class_Obot(tc_fun(_1441896, tc_HOL_Obool)))], (37904 ^ _779571) ^ [_1491157] : [-(c_Relation_Orefl__on(_1491157, c_Orderings_Obot__class_Obot(tc_fun(_1491157, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1491157, _1491157), tc_HOL_Obool))))], (27453 ^ _779571) ^ [_1264604, _1264606, _1264608, _1264610, _1264612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264604, tc_HOL_Obool)), _1264606), hAPP(c_Set_Oimage(_1264608, _1264604, _1264610), _1264612))), 27457 ^ _779571 : [(27460 ^ _779571) ^ [] : [-(_1264606 = hAPP(c_Set_Oimage(_1264608, _1264604, _1264610), 27456 ^ [_1264604, _1264606, _1264608, _1264610, _1264612]))], (27458 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264608, tc_HOL_Obool)), 27456 ^ [_1264604, _1264606, _1264608, _1264610, _1264612]), _1264612)))]]], (18827 ^ _779571) ^ [_1102489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1102489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1102489))))], (33565 ^ _779571) ^ [_1392158, _1392160, _1392162] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1392158, tc_HOL_Obool), tc_fun(_1392158, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1392158, tc_HOL_Obool), tc_fun(_1392158, tc_HOL_Obool)), _1392160), _1392162)), c_Wellfounded_Ofinite__psubset(_1392158)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1392158, tc_HOL_Obool)), _1392160), _1392162)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392158), _1392162))], (40674 ^ _779571) ^ [_1551707, _1551709, _1551711, _1551713] : [c_Big__Operators_Osemilattice__big(_1551707, _1551709, _1551711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551707), _1551713)), -(hAPP(_1551711, _1551713) = hAPP(c_Finite__Set_Ofold1(_1551707, _1551709), _1551713))], (46755 ^ _779571) ^ [_1706739, _1706741, _1706743, _1706745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706739), tc_List_Olist(_1706739))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706739), tc_List_Olist(_1706739)), _1706741), _1706743)), c_List_Olistrel(_1706739, _1706745))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706739)), _1706741) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706739)), _1706743))], (2826 ^ _779571) ^ [_822446, _822448] : [_822448 = _822446, -(c_Nitpick_Ofrac(_822448) = c_Nitpick_Ofrac(_822446))], (49804 ^ _779571) ^ [_1779972, _1779974, _1779976, _1779978, _1779980] : [-(hAPP(c_List_Ofilter(_1779972, _1779974), hAPP(hAPP(c_List_Omap(_1779976, _1779972), _1779978), _1779980)) = hAPP(hAPP(c_List_Omap(_1779976, _1779972), _1779978), hAPP(c_List_Ofilter(_1779976, hAPP(c_Fun_Ocomp(_1779972, tc_HOL_Obool, _1779976, _1779974), _1779978)), _1779980)))], (27768 ^ _779571) ^ [_1271248, _1271250, _1271252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271248, tc_HOL_Obool)), _1271250), _1271252)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271248, tc_HOL_Obool)), _1271252), _1271250) = _1271252)], (15864 ^ _779571) ^ [_1049199, _1049201] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049199), _1049201) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049199), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1049201)))], (41364 ^ _779571) ^ [_1569950, _1569952] : [c_Relation_Orefl__on(_1569950, c_Orderings_Otop__class_Otop(tc_fun(_1569950, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569950, _1569950)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569950, _1569950, tc_HOL_Obool), _1569952))), -(c_Predicate_Oreflp(_1569950, _1569952))], (20027 ^ _779571) ^ [_1123725, _1123727] : [class_Rings_Odivision__ring(_1123725), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123725), c_Groups_Ozero__class_Ozero(_1123725)), _1123727) = c_Groups_Ozero__class_Ozero(_1123725))], (20703 ^ _779571) ^ [_1135315, _1135317, _1135319, _1135321, _1135323] : 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[-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893475) = _893475)], (36872 ^ _779571) ^ [_1466157, _1466159, _1466161] : [class_Orderings_Oorder(_1466157), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466157, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466157), _1466159)), c_SetInterval_Oord__class_OatLeastAtMost(_1466157, _1466159, _1466161)) = c_Orderings_Obot__class_Obot(tc_fun(_1466157, tc_HOL_Obool)))], (17315 ^ _779571) ^ [_1077240, _1077242] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1077240) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077242), 17318 ^ _779571 : [(17321 ^ _779571) ^ [] : [-(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), _1077242))))], (17319 ^ _779571) ^ [] : [-(_1077240 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077242)))]]], (8300 ^ _779571) ^ [_917385, _917387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917385), _917387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917385)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917387))))], (44896 ^ _779571) ^ [_1661591, _1661593, _1661595, _1661597, _1661599] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661591, tc_fun(_1661593, tc_HOL_Obool)), _1661595), _1661597), _1661599)), 44899 ^ _779571 : [(44900 ^ _779571) ^ [_1661700] : [hBOOL(hAPP(hAPP(c_member(_1661591), _1661700), _1661595)), -(hBOOL(hAPP(hAPP(_1661597, _1661700), _1661599)))]]], (17373 ^ _779571) ^ [_1078330, _1078332, _1078334] : [class_Rings_Osemiring__1(_1078330), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1078330), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1078332), _1078334)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1078330), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1078330), _1078332)), _1078334))], (28665 ^ _779571) ^ [_1288760, _1288762, _1288764] : [class_Orderings_Olinorder(_1288760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288760), _1288762), _1288764)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288760, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1288760, _1288762, _1288764)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288760), _1288764)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1288760), _1288762))], (36986 ^ _779571) ^ [_1468710, _1468712, _1468714, _1468716, _1468718, _1468720, _1468722, _1468724] : [c_Finite__Set_Ofolding__image__simple(_1468710, _1468712, _1468714, _1468716, _1468718, _1468720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468712), _1468722)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468712), _1468724)), -(hAPP(hAPP(_1468714, hAPP(_1468720, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468712, tc_HOL_Obool)), _1468722), _1468724))), hAPP(_1468720, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468712, tc_HOL_Obool)), _1468722), _1468724))) = hAPP(hAPP(_1468714, hAPP(_1468720, _1468722)), hAPP(_1468720, _1468724)))], (6452 ^ _779571) ^ [_884714, _884716, _884718, _884720, _884722] : [hBOOL(hAPP(_884714, _884716)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884718), _884716), _884720)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884714, _884718)), _884720), _884722)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884714, _884718)), _884716), _884722)))], (13729 ^ _779571) ^ [_1009922, _1009924, _1009926, _1009928] : [class_Divides_Osemiring__div(_1009922), -(c_Divides_Odiv__class_Omod(_1009922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009922), _1009924), _1009926), _1009928) = c_Divides_Odiv__class_Omod(_1009922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009922), c_Divides_Odiv__class_Omod(_1009922, _1009924, _1009928)), _1009926), _1009928))], (42180 ^ _779571) ^ [_1596015, _1596017, _1596019, _1596021] : [hBOOL(hAPP(c_Predicate_ORangeP(_1596015, _1596017, _1596019), _1596021)), -(hBOOL(hAPP(hAPP(_1596019, 42183 ^ [_1596015, _1596017, _1596019, _1596021]), _1596021)))], (23831 ^ _779571) ^ [_1193751, _1193753, _1193755, _1193757] : [hAPP(c_Product__Type_Ofst(_1193751, _1193753), _1193755) = hAPP(c_Product__Type_Ofst(_1193751, _1193753), _1193757), hAPP(c_Product__Type_Osnd(_1193751, _1193753), _1193755) = hAPP(c_Product__Type_Osnd(_1193751, _1193753), _1193757), -(_1193755 = _1193757)], (46160 ^ _779571) ^ [] : [c_Com_OWT__bodies, 46163 ^ _779571 : [(46164 ^ _779571) ^ [_1691132] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1691132), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1691132)))]]], (15650 ^ _779571) ^ [_1045152, _1045154, _1045156] : [class_Rings_Ocomm__ring__1(_1045152), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045152), _1045154), _1045156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045152), _1045154), hAPP(c_Groups_Ouminus__class_Ouminus(_1045152), _1045156)))], (7233 ^ _779571) ^ [_899130, _899132, _899134, _899136, _899138, _899140] : [-(c_Nitpick_Opair__box_Opair__box__size(_899130, _899132, _899134, _899136, c_Nitpick_Opair__box_OPairBox(_899130, _899132, _899138, _899140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_899134, _899138)), hAPP(_899136, _899140))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16775 ^ _779571) ^ [_1066823, _1066825, _1066827, _1066829] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066823), hAPP(c_Int_Onumber__class_Onumber__of(_1066823), _1066825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066823), _1066827), _1066829)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066823), hAPP(c_Int_Onumber__class_Onumber__of(_1066823), _1066825)), _1066827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066823), hAPP(c_Int_Onumber__class_Onumber__of(_1066823), _1066825)), _1066829))), class_Int_Onumber(_1066823), class_Rings_Osemiring(_1066823)], (40421 ^ _779571) ^ [_1546550, _1546552, _1546554, _1546556, _1546558, _1546560, _1546562, _1546564] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1546550, _1546552), tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1546550, _1546552), _1546558), hAPP(c_COMBK(tc_fun(_1546552, tc_HOL_Obool), _1546550), _1546560))), hAPP(c_Product__Type_Oprod_Oprod__case(_1546550, _1546552, tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1546550, tc_fun(_1546552, tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool))), tc_fun(_1546552, tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool)), tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool)), tc_fun(tc_fun(_1546552, tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool))), tc_fun(_1546552, tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool))), _1546550), c_COMBB(tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool)), tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool), _1546552)), hAPP(hAPP(c_COMBB(tc_fun(_1546554, tc_HOL_Obool), tc_fun(tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool)), tc_fun(tc_prod(_1546554, _1546556), tc_HOL_Obool)), _1546550), c_Product__Type_OSigma(_1546554, _1546556)), _1546562))), hAPP(hAPP(c_COMBB(tc_fun(_1546556, tc_HOL_Obool), tc_fun(_1546554, tc_fun(_1546556, tc_HOL_Obool)), _1546552), c_COMBK(tc_fun(_1546556, tc_HOL_Obool), _1546554)), _1546564)))) = hAPP(hAPP(c_Product__Type_OSigma(_1546554, _1546556), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1546550, tc_fun(_1546554, tc_HOL_Obool)), _1546558), _1546562)), hAPP(c_COMBK(tc_fun(_1546556, tc_HOL_Obool), _1546554), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1546552, tc_fun(_1546556, tc_HOL_Obool)), _1546560), _1546564))))], (29230 ^ _779571) ^ [_1301926, _1301928, _1301930, _1301932] : [hAPP(c_Set_Oimage(_1301926, _1301928, _1301930), _1301932) = c_Orderings_Obot__class_Obot(tc_fun(_1301928, tc_HOL_Obool)), -(_1301932 = c_Orderings_Obot__class_Obot(tc_fun(_1301926, tc_HOL_Obool)))], (14098 ^ _779571) ^ [_1016643, _1016645, _1016647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016643)), 14101 ^ _779571 : [(14102 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1016645, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016647), _1016643)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016647, _1016643))), 14105 ^ _779571 : [(14106 ^ _779571) ^ [_1016844, _1016846] : [-(hBOOL(hAPP(hAPP(_1016645, _1016846), _1016844))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016844), _1016643)), _1016647 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016643), _1016846)), _1016844)]]], (14120 ^ _779571) ^ [] : [14123 ^ _779571 : [(14126 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14122 ^ [_1016643, _1016645, _1016647]), _1016643)))], (14128 ^ _779571) ^ [] : [-(_1016647 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016643), 14121 ^ [_1016643, _1016645, _1016647])), 14122 ^ [_1016643, _1016645, _1016647]))], (14130 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1016645, 14121 ^ [_1016643, _1016645, _1016647]), 14122 ^ [_1016643, _1016645, _1016647]))], (14124 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14122 ^ [_1016643, _1016645, _1016647])))]], -(hBOOL(hAPP(hAPP(_1016645, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016647), _1016643)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016647, _1016643))))]]], (29075 ^ _779571) ^ [_1298261, _1298263] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298261, tc_HOL_Obool)), _1298263), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298261, tc_HOL_Obool)), _1298263)) = c_Orderings_Otop__class_Otop(tc_fun(_1298261, tc_HOL_Obool)))], (47492 ^ _779571) ^ [_1725232, _1725234] : [hBOOL(hAPP(c_List_Odistinct(_1725232), _1725234)), 47495 ^ _779571 : [(47496 ^ _779571) ^ [_1725364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725232)), _1725234))), 47499 ^ _779571 : [(47500 ^ _779571) ^ [_1725491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725491), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725232)), _1725234))), -(_1725364 = _1725491), hAPP(hAPP(c_List_Onth(_1725232), _1725234), _1725364) = hAPP(hAPP(c_List_Onth(_1725232), _1725234), _1725491)]]]]], (43276 ^ _779571) ^ [_1622163, _1622165] : [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), _1622163), _1622165)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622163), _1622165)))], (34893 ^ _779571) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (4134 ^ _779571) ^ [_843308, _843310, _843312, _843314, _843316, _843318] : [-(c_Smallcheck_Osmall_H(_843318, _843314, _843310) = c_Smallcheck_Osmall_H(_843316, _843312, _843308)), _843318 = _843316, _843314 = _843312, _843310 = _843308], (9550 ^ _779571) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43098 ^ _779571) ^ [_1617971, _1617973, _1617975] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1617971, _1617971, _1617973), c_Relation_OId(_1617971)), _1617975) = _1617975)], (5809 ^ _779571) ^ [_872646, _872648, _872650, _872652] : [-(hBOOL(hAPP(_872646, _872648))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_872646, _872650), _872648, _872652, _872648))], (18869 ^ _779571) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (33863 ^ _779571) ^ [_1397944, _1397946, _1397948] : [class_Orderings_Olinorder(_1397944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397944), _1397946)), -(_1397946 = c_Orderings_Obot__class_Obot(tc_fun(_1397944, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397944), _1397948)), -(_1397948 = c_Orderings_Obot__class_Obot(tc_fun(_1397944, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1397944, c_Orderings_Oord__class_Omin(_1397944), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397944, tc_HOL_Obool)), _1397946), _1397948)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1397944), c_Big__Operators_Olattice_OInf__fin(_1397944, c_Orderings_Oord__class_Omin(_1397944), _1397946)), c_Big__Operators_Olattice_OInf__fin(_1397944, c_Orderings_Oord__class_Omin(_1397944), _1397948)))], (1132 ^ _779571) ^ [_796489, _796491] : [-(class_Divides_Oring__div(_796489)), _796491 = _796489, class_Divides_Oring__div(_796491)], (8070 ^ _779571) ^ [_913338, _913340, _913342, _913344, _913346] : [-(c_Option_Ooption_Ooption__rec(_913338, _913340, _913342, _913344, hAPP(c_Option_Ooption_OSome(_913340), _913346)) = hAPP(_913344, _913346))], (51289 ^ _779571) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (47434 ^ _779571) ^ [_1723916, _1723918, _1723920, _1723922] : [-(hAPP(hAPP(c_List_Onth(_1723916), hAPP(hAPP(c_List_Olist_OCons(_1723916), _1723918), _1723920)), _1723922) = c_Nat_Onat_Onat__case(_1723916, _1723918, hAPP(c_List_Onth(_1723916), _1723920), _1723922))], (1512 ^ _779571) ^ [_801239, _801241] : [-(class_Groups_Ocomm__monoid__mult(_801239)), _801241 = _801239, class_Groups_Ocomm__monoid__mult(_801241)], (31910 ^ _779571) ^ [_1359296, _1359298, _1359300, _1359302, _1359304] : [class_Groups_Oab__group__add(_1359296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359298), _1359300)), 31917 ^ _779571 : [(31924 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359298), _1359302), _1359300))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359298, _1359296), _1359304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359298, tc_HOL_Obool)), _1359300), hAPP(hAPP(c_Set_Oinsert(_1359298), _1359302), c_Orderings_Obot__class_Obot(tc_fun(_1359298, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359298, _1359296), _1359304), _1359300))], (31918 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1359298), _1359302), _1359300)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359298, _1359296), _1359304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359298, tc_HOL_Obool)), _1359300), hAPP(hAPP(c_Set_Oinsert(_1359298), _1359302), c_Orderings_Obot__class_Obot(tc_fun(_1359298, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1359296), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359298, _1359296), _1359304), _1359300)), hAPP(_1359304, _1359302)))]]], (27972 ^ _779571) ^ [_1274944, _1274946, _1274948] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274944, tc_HOL_Obool)), _1274946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274944, tc_HOL_Obool)), _1274948), _1274946)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274944, tc_HOL_Obool)), _1274946), _1274948))], (5936 ^ _779571) ^ [_874932, _874934, _874936, _874938, _874940, _874942] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_874932, _874934, _874936), _874938, _874940, _874942), 5941 ^ _779571 : [(5944 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_874934, _874938, _874940, _874942))], (5942 ^ _779571) ^ [] : [-(hBOOL(hAPP(_874932, _874938)))]], 5945 ^ _779571 : [(5948 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_874936, _874938, _874940, _874942))], (5946 ^ _779571) ^ [] : [hBOOL(hAPP(_874932, _874938))]]], (22117 ^ _779571) ^ [_1161435, _1161437] : [-(c_Random_Olog(_1161435, _1161437) = 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(_1161435, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1161437), _1161435)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1161435), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1161437), _1161435)))], (19839 ^ _779571) ^ [_1120150, _1120152, _1120154] : [class_Groups_Omonoid__mult(_1120150), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1120150), _1120152), 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)))), _1120154))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120150), _1120152), hAPP(hAPP(c_Power_Opower__class_Opower(_1120150), hAPP(hAPP(c_Power_Opower__class_Opower(_1120150), _1120152), _1120154)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (26824 ^ _779571) ^ [_1251609, _1251611, _1251613, _1251615, _1251617] : [class_Groups_Ocomm__monoid__add(_1251609), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1251609), _1251611), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1251613), _1251615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1251617), _1251615))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1251609), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1251609, tc_Nat_Onat), _1251611), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1251615))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1251613, _1251617)))], (37684 ^ _779571) ^ [_1485726, _1485728, _1485730] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485726), _1485728)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485726), _1485730)), 37694 ^ _779571 : [(37697 ^ _779571) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37695 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485726), 37693 ^ [_1485726, _1485728, _1485730]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485726, tc_HOL_Obool)), _1485728), _1485730))))]], -(hAPP(c_Finite__Set_Ocard(_1485726), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485726, tc_HOL_Obool)), _1485728), _1485730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1485726), _1485728)), hAPP(c_Finite__Set_Ocard(_1485726), _1485730)))], (51233 ^ _779571) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (3158 ^ _779571) ^ [_827966, _827968] : [_827968 = _827966, -(c_Int_OBit0(_827968) = c_Int_OBit0(_827966))], (19937 ^ _779571) ^ [_1122095] : [-(_1122095 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 19940 ^ _779571 : [(19947 ^ _779571) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1122095, 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, _1122095) = 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), _1122095), 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)))], (19941 ^ _779571) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1122095, 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, _1122095) = 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), _1122095), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (23245 ^ _779571) ^ [_1183398, _1183400, _1183402] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183398, _1183398), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183400), _1183402))), -(_1183398 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1183402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47979 ^ _779571) ^ [_1737216, _1737218, _1737220] : [class_Groups_Omonoid__add(_1737216), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1737216), hAPP(hAPP(c_List_Oappend(_1737216), _1737218), _1737220)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1737216), hAPP(c_List_Omonoid__add__class_Olistsum(_1737216), _1737218)), hAPP(c_List_Omonoid__add__class_Olistsum(_1737216), _1737220)))], (48972 ^ _779571) ^ [_1762222, _1762224] : [-(_1762222 = c_List_Olist_ONil(_1762224)), -(hAPP(c_List_Ohd(_1762224), _1762222) = hAPP(hAPP(c_List_Onth(_1762224), _1762222), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45837 ^ _779571) ^ [_1683156, _1683158, _1683160, _1683162] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1683156), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1683158), _1683160)))), -(hBOOL(hAPP(hAPP(hAPP(_1683162, _1683156), _1683158), _1683160))), 45845 ^ _779571 : [(45848 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 45843 ^ [_1683156, _1683158, _1683160, _1683162]), 45844 ^ [_1683156, _1683158, _1683160, _1683162]))), hAPP(45842 ^ [_1683156, _1683158, _1683160, _1683162], 45844 ^ [_1683156, _1683158, _1683160, _1683162]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1683162, 45842 ^ [_1683156, _1683158, _1683160, _1683162]), 45843 ^ [_1683156, _1683158, _1683160, _1683162]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45844 ^ [_1683156, _1683158, _1683160, _1683162]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45858 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1683162, 45842 ^ [_1683156, _1683158, _1683160, _1683162]), 45843 ^ [_1683156, _1683158, _1683160, _1683162]), 45844 ^ [_1683156, _1683158, _1683160, _1683162]))], (45846 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 45842 ^ [_1683156, _1683158, _1683160, _1683162]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 45843 ^ [_1683156, _1683158, _1683160, _1683162]), 45844 ^ [_1683156, _1683158, _1683160, _1683162])))))]]], (31796 ^ _779571) ^ [_1356648, _1356650, _1356652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1356648), _1356650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356648, tc_HOL_Obool)), _1356650), _1356652)), -(hAPP(c_Finite__Set_Ocard(_1356648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356648, tc_HOL_Obool)), _1356652), _1356650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1356648), _1356652)), hAPP(c_Finite__Set_Ocard(_1356648), _1356650)))], (26562 ^ _779571) ^ [_1246693, _1246695, _1246697] : [class_Divides_Osemiring__div(_1246693), class_Int_Onumber(_1246693), 26569 ^ _779571 : [(26576 ^ _779571) ^ [] : [c_Divides_Odiv__class_Omod(_1246693, hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246697), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246695)) = c_Groups_Ozero__class_Ozero(_1246693), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246693), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246695)), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246697))))], (26570 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246693), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246695)), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246697))), -(c_Divides_Odiv__class_Omod(_1246693, hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246697), hAPP(c_Int_Onumber__class_Onumber__of(_1246693), _1246695)) = c_Groups_Ozero__class_Ozero(_1246693))]]], (32139 ^ _779571) ^ [_1364382, _1364384] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1364382), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1364384))), 32142 ^ _779571 : [(32145 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364384), _1364382))], (32143 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1364382), _1364384)))]]], (47671 ^ _779571) ^ [_1730029, _1730031, _1730033] : [-(hAPP(hAPP(c_List_Olist__update(_1730029, _1730031), _1730033), hAPP(hAPP(c_List_Onth(_1730029), _1730031), _1730033)) = _1730031)], (13006 ^ _779571) ^ [_997361] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997361))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _997361)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32051 ^ _779571) ^ [_1362587, _1362589, _1362591, _1362593, _1362595, _1362597] : [32052 ^ _779571 : [(32055 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1362593, _1362589), _1362591))], (32053 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1362587, _1362589), _1362591))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362595, tc_fun(_1362597, tc_HOL_Obool))), _1362593), _1362587), _1362589), _1362591)))], (16048 ^ _779571) ^ [_1053327, _1053329, _1053331, _1053333, _1053335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053327), _1053329)), 16051 ^ _779571 : [(16058 ^ _779571) ^ [] : [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), _1053329), _1053327)), _1053331)), _1053333)), _1053335)), -(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), _1053329), _1053331)), _1053333)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053327), _1053331)), _1053335))))], (16052 ^ _779571) ^ [] : [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), _1053329), _1053331)), _1053333)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053327), _1053331)), _1053335))), -(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), _1053329), _1053327)), _1053331)), _1053333)), _1053335)))]]], (30175 ^ _779571) ^ [_1320416, _1320418] : [30176 ^ _779571 : [(30177 ^ _779571) ^ [_1320469] : [hBOOL(hAPP(hAPP(c_member(_1320416), _1320469), _1320418))]], _1320418 = c_Orderings_Obot__class_Obot(tc_fun(_1320416, tc_HOL_Obool))], (40118 ^ _779571) ^ [_1539041, _1539043, _1539045, _1539047, _1539049] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1539041, _1539043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1539041, tc_HOL_Obool)), _1539045), _1539047)), hAPP(c_COMBK(tc_fun(_1539043, tc_HOL_Obool), _1539041), _1539049)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1539041, _1539043), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539041, _1539043), _1539045), hAPP(c_COMBK(tc_fun(_1539043, tc_HOL_Obool), _1539041), _1539049))), hAPP(hAPP(c_Product__Type_OSigma(_1539041, _1539043), _1539047), hAPP(c_COMBK(tc_fun(_1539043, tc_HOL_Obool), _1539041), _1539049))))], (29063 ^ _779571) ^ [] : [-(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)))], (7494 ^ _779571) ^ [_903709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903709), _903709))], (35053 ^ _779571) ^ [_1424084, _1424086, _1424088] : [class_Lattices_Olattice(_1424084), hAPP(_1424086, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1424084), 35058 ^ [_1424084, _1424086, _1424088]), 35059 ^ [_1424084, _1424086, _1424088])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1424084), hAPP(_1424086, 35058 ^ [_1424084, _1424086, _1424088])), hAPP(_1424086, 35059 ^ [_1424084, _1424086, _1424088])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424084), _1424088)), -(_1424088 = c_Orderings_Obot__class_Obot(tc_fun(_1424084, tc_HOL_Obool))), -(hAPP(_1424086, c_Big__Operators_Olattice__class_OSup__fin(_1424084, _1424088)) = c_Big__Operators_Olattice__class_OSup__fin(_1424084, hAPP(c_Set_Oimage(_1424084, _1424084, _1424086), _1424088)))], (34178 ^ _779571) ^ [_1404582, _1404584, _1404586, _1404588, _1404590] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404582, _1404584), _1404586), _1404588), _1404590) = _1404586, -(hAPP(_1404586, _1404588) = _1404590)], (10257 ^ _779571) ^ [_950403, _950405] : [-(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), _950403))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950405))))], (36440 ^ _779571) ^ [_1456611, _1456613, _1456615, _1456617] : [class_Lattices_Osemilattice__inf(_1456611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456611), _1456613), _1456615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456611), _1456613), _1456617)), _1456615)))], (31367 ^ _779571) ^ [_1346566, _1346568] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346566), c_Orderings_Otop__class_Otop(tc_fun(_1346566, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1346566), _1346568) = hAPP(c_Finite__Set_Ocard(_1346566), c_Orderings_Otop__class_Otop(tc_fun(_1346566, tc_HOL_Obool))), -(_1346568 = c_Orderings_Otop__class_Otop(tc_fun(_1346566, tc_HOL_Obool)))], (7339 ^ _779571) ^ [_901354, _901356, _901358, _901360] : [_901358 = _901360, -(hAPP(c_Sum__Type_OInl(_901354, _901356), _901358) = hAPP(c_Sum__Type_OInl(_901354, _901356), _901360))], (16791 ^ _779571) ^ [_1067197, _1067199, _1067201] : [class_Rings_Ocomm__semiring__1(_1067197), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067197), _1067199), hAPP(hAPP(c_Power_Opower__class_Opower(_1067197), _1067199), _1067201)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067197), _1067199), hAPP(c_Nat_OSuc, _1067201)))], (24801 ^ _779571) ^ [_1212961, _1212963, _1212965, _1212967, _1212969, _1212971, _1212973] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1212961, _1212963, _1212965, _1212967), _1212969), _1212971), _1212973) = hAPP(hAPP(_1212971, hAPP(c_Product__Type_Ofst(_1212963, _1212965), hAPP(_1212969, _1212973))), hAPP(c_Product__Type_Osnd(_1212963, _1212965), hAPP(_1212969, _1212973))))], (18951 ^ _779571) ^ [] : [-(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))))))], (41925 ^ _779571) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (6827 ^ _779571) ^ [_892090, _892092] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_892090, _892092)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _892092)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1172 ^ _779571) ^ [_796989, _796991] : [-(class_Groups_Osgn__if(_796989)), _796991 = _796989, class_Groups_Osgn__if(_796991)], (27309 ^ _779571) ^ [_1261345, _1261347, _1261349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261345)), 27312 ^ _779571 : [(27313 ^ _779571) ^ [_1261479] : [27315 ^ _779571 : [(27321 ^ _779571) ^ [] : [-(_1261479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27317 ^ [_1261345, _1261347, _1261349, _1261479]), 27314 ^ [_1261345, _1261347, _1261349, _1261479]))], (27319 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27317 ^ [_1261345, _1261347, _1261349, _1261479]), _1261347)))], (27316 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27314 ^ [_1261345, _1261347, _1261349, _1261479]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1261345))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261479), _1261349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1261479), _1261345)), _1261349)))]]], (42992 ^ _779571) ^ [_1615344, _1615346] : [-(c_Transitive__Closure_Ortrancl(_1615344, c_Transitive__Closure_Otrancl(_1615344, _1615346)) = c_Transitive__Closure_Ortrancl(_1615344, _1615346))], (29830 ^ _779571) ^ [_1313034, _1313036, _1313038] : [class_Orderings_Olinorder(_1313034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313034), _1313036), _1313038)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313034, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1313034), _1313036), c_Orderings_Obot__class_Obot(tc_fun(_1313034, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1313034, _1313036, _1313038)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1313034, _1313036), _1313038))], (10169 ^ _779571) ^ [_948959] : [-(_948959 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10172 ^ _779571 : [(10179 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948959))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _948959) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10173 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948959)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _948959) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (43518 ^ _779571) ^ [_1628247, _1628249] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628247, _1628247), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1628249) = _1628249)], (7183 ^ _779571) ^ [_898144, _898146, _898148] : [class_Rings_Ocomm__semiring__1(_898144), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898144), _898146), _898148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898144), _898148), _898146))], (35593 ^ _779571) ^ [_1437086, _1437088, _1437090, _1437092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1437086), _1437092)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1437090), _1437088))), -(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), _1437086), _1437088)), 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), _1437090), _1437092)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (19413 ^ _779571) ^ [_1112521, _1112523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112521), _1112523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112521)), c_Int_OBit1(_1112523))))], (7310 ^ _779571) ^ [_900694, _900696, _900698, _900700, _900702, _900704] : [-(c_Nitpick_Opair__box_Opair__box__case(_900694, _900696, _900698, _900700, c_Nitpick_Opair__box_OPairBox(_900694, _900696, _900702, _900704)) = hAPP(hAPP(_900700, _900702), _900704))], (49437 ^ _779571) ^ [_1772534, _1772536, _1772538] : [_1772534 = c_List_Olist_ONil(_1772536), -(c_List_Olast(_1772536, hAPP(hAPP(c_List_Oappend(_1772536), _1772538), _1772534)) = c_List_Olast(_1772536, _1772538))], (9594 ^ _779571) ^ [_938874, _938876, _938878, _938880] : [class_Rings_Olinordered__ring__strict(_938874), 9597 ^ _779571 : [(9612 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938874), _938876), _938878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938874), _938876), _938880)))), 9613 ^ _779571 : [(9620 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938876), c_Groups_Ozero__class_Ozero(_938874))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938880), _938878))], (9614 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), c_Groups_Ozero__class_Ozero(_938874)), _938876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938878), _938880))]]], (9598 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938874), _938876), _938878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938874), _938876), _938880))), 9603 ^ _779571 : [(9606 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938878), _938880)))], (9604 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), c_Groups_Ozero__class_Ozero(_938874)), _938876)))]], 9607 ^ _779571 : [(9610 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938880), _938878)))], (9608 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938874), _938876), c_Groups_Ozero__class_Ozero(_938874))))]]]]], (39593 ^ _779571) ^ [_1526562, _1526564, _1526566, _1526568, _1526570, _1526572, _1526574] : [c_Big__Operators_Ocomm__monoid__big(_1526562, _1526564, _1526566, _1526568, _1526570), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526564), _1526572))), -(hAPP(hAPP(_1526570, _1526574), _1526572) = _1526568)], (12770 ^ _779571) ^ [_993242, _993244, _993246, _993248, _993250] : [class_Rings_Olinordered__semiring__strict(_993242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993242), _993244), _993246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993242), _993248), _993250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993242), c_Groups_Ozero__class_Ozero(_993242)), _993246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993242), c_Groups_Ozero__class_Ozero(_993242)), _993248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993242), _993244), _993248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993242), _993246), _993250))))], (30251 ^ _779571) ^ [_1321957, _1321959, _1321961, _1321963, _1321965, _1321967] : [hBOOL(hAPP(hAPP(c_member(_1321957), _1321959), _1321961)), _1321963 = hAPP(_1321965, _1321959), -(hBOOL(hAPP(hAPP(c_member(_1321967), _1321963), hAPP(c_Set_Oimage(_1321957, _1321967, _1321965), _1321961))))], (6373 ^ _779571) ^ [_883110, _883112, _883114, _883116, _883118, _883120] : [c_Com_Ocom_OCond(_883110, _883112, _883114) = c_Com_Ocom_OCall(_883116, _883118, _883120)], (47017 ^ _779571) ^ [_1714484, _1714486, _1714488, _1714490] : [hBOOL(hAPP(hAPP(c_member(_1714484), _1714486), hAPP(c_List_Oset(_1714484), c_List_Osublist(_1714484, _1714488, _1714490)))), -(hBOOL(hAPP(hAPP(c_member(_1714484), _1714486), hAPP(c_List_Oset(_1714484), _1714488))))], (1162 ^ _779571) ^ [_796864, _796866] : [-(class_Int_Onumber__ring(_796864)), _796866 = _796864, class_Int_Onumber__ring(_796866)], (37130 ^ _779571) ^ [_1472177, _1472179, _1472181, _1472183, _1472185, _1472187, _1472189, _1472191] : [c_Finite__Set_Ofolding__image__simple(_1472177, _1472179, _1472181, _1472183, _1472185, _1472187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472179), _1472189)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472179), _1472191)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472179, tc_HOL_Obool)), _1472189), _1472191) = c_Orderings_Obot__class_Obot(tc_fun(_1472179, tc_HOL_Obool)), -(hAPP(_1472187, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472179, tc_HOL_Obool)), _1472189), _1472191)) = hAPP(hAPP(_1472181, hAPP(_1472187, _1472189)), hAPP(_1472187, _1472191)))], (50940 ^ _779571) ^ [_1805378, _1805380, _1805382, _1805384, _1805386] : [-(c_List_OtakeWhile(_1805378, _1805380, hAPP(hAPP(c_List_Omap(_1805382, _1805378), _1805384), _1805386)) = hAPP(hAPP(c_List_Omap(_1805382, _1805378), _1805384), c_List_OtakeWhile(_1805382, hAPP(c_Fun_Ocomp(_1805378, tc_HOL_Obool, _1805382, _1805380), _1805384), _1805386)))], (37742 ^ _779571) ^ [_1486960, _1486962, _1486964, _1486966, _1486968, _1486970] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486960, tc_fun(_1486962, tc_HOL_Obool))), _1486964), _1486966), _1486968), _1486970)), -(hBOOL(hAPP(hAPP(_1486964, _1486968), _1486970)))], (34875 ^ _779571) ^ [_1419590, _1419592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1419590), _1419592)), -(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), _1419590), _1419592)), c_Wellfounded_Oless__than)))], (35797 ^ _779571) ^ [_1442271, _1442273, _1442275] : [_1442273 = c_Orderings_Obot__class_Obot(tc_fun(_1442271, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1442271, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442271), _1442273), _1442275))], (20901 ^ _779571) ^ [_1139112, _1139114, _1139116, _1139118] : [class_Fields_Olinordered__field(_1139112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139112), c_Groups_Ozero__class_Ozero(_1139112)), _1139114)), 20908 ^ _779571 : [(20915 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139112), _1139116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139112), _1139118), _1139114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139112), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139112), _1139116), _1139114)), _1139118)))], (20909 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139112), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139112), _1139116), _1139114)), _1139118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139112), _1139116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139112), _1139118), _1139114))))]]], (23697 ^ _779571) ^ [_1191160, _1191162, _1191164, _1191166] : [class_Orderings_Olinorder(_1191160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191160), _1191162), _1191164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191160), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191160), _1191162), _1191166)), _1191164)))], (30971 ^ _779571) ^ [_1337165, _1337167] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1337165, _1337167))))], (49878 ^ _779571) ^ [_1782271, _1782273] : [49880 ^ _779571 : [(49883 ^ _779571) ^ [] : [49879 ^ [_1782271, _1782273] = c_List_Olist_ONil(_1782271)], (49881 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1782271)), 49879 ^ [_1782271, _1782273]), hAPP(c_List_Oset(tc_List_Olist(_1782271)), _1782273))))]], -(c_List_Otranspose(_1782271, _1782273) = c_List_Olist_ONil(tc_List_Olist(_1782271)))], (45789 ^ _779571) ^ [_1681967, _1681969, _1681971] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1681967)), hAPP(c_Set_Oimage(_1681969, tc_Option_Ooption(_1681967), c_Map_Omap__of(_1681969, _1681967, _1681971)), c_Orderings_Otop__class_Otop(tc_fun(_1681969, tc_HOL_Obool))))))], (49046 ^ _779571) ^ [_1763523] : [-(hAPP(c_List_Otl(_1763523), c_List_Olist_ONil(_1763523)) = c_List_Olist_ONil(_1763523))], (37672 ^ _779571) ^ [_1484406, _1484408, _1484410, _1484412, _1484414, _1484416] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484406, tc_fun(_1484408, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1484406, tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_fun(_1484408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484408, tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_fun(_1484408, tc_HOL_Obool)), _1484406), c_COMBC(_1484408, tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484408, tc_prod(_1484406, _1484408)), tc_fun(_1484408, tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), _1484406), hAPP(c_COMBB(tc_prod(_1484406, _1484408), tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool), _1484408), c_member(tc_prod(_1484406, _1484408)))), c_Product__Type_OPair(_1484406, _1484408)))), _1484410)), hAPP(hAPP(c_COMBC(_1484406, tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_fun(_1484408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484408, tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_fun(_1484408, tc_HOL_Obool)), _1484406), c_COMBC(_1484408, tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484408, tc_prod(_1484406, _1484408)), tc_fun(_1484408, tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool)), _1484406), hAPP(c_COMBB(tc_prod(_1484406, _1484408), tc_fun(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool), tc_HOL_Obool), _1484408), c_member(tc_prod(_1484406, _1484408)))), c_Product__Type_OPair(_1484406, _1484408)))), _1484412)), _1484414), _1484416)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484406, _1484408)), hAPP(hAPP(c_Product__Type_OPair(_1484406, _1484408), _1484414), _1484416)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1484406, _1484408), tc_HOL_Obool)), _1484410), _1484412))))], (10060 ^ _779571) ^ [_947130, _947132, _947134] : [class_Rings_Olinordered__ring(_947130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947130), _947132), _947132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947130), _947134), _947134))), c_Groups_Ozero__class_Ozero(_947130)))], (8277 ^ _779571) ^ [_916901, _916903, _916905, _916907] : [class_Orderings_Oorder(_916901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916901), hAPP(_916903, 8282 ^ [_916901, _916903, _916905, _916907])), hAPP(_916903, hAPP(c_Nat_OSuc, 8282 ^ [_916901, _916903, _916905, _916907])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916905), _916907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916901), hAPP(_916903, _916905)), hAPP(_916903, _916907))))], (27992 ^ _779571) ^ [_1275421, _1275423, _1275425, _1275427] : [class_Lattices_Olattice(_1275421), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275421), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275421), _1275423), _1275425)), _1275427) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275421), _1275423), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275421), _1275425), _1275427)))], (32377 ^ _779571) ^ [_1368864, _1368866, _1368868, _1368870] : [hBOOL(hAPP(hAPP(_1368868, _1368870), _1368866)), -(hBOOL(hAPP(hAPP(c_member(_1368864), _1368866), c_SetInterval_Oord_OatLeast(_1368864, _1368868, _1368870))))], (30301 ^ _779571) ^ [_1322957, _1322959, _1322961, _1322963] : [hBOOL(hAPP(hAPP(c_member(_1322957), _1322959), _1322961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322957, tc_HOL_Obool)), _1322961), _1322963)), -(hBOOL(hAPP(hAPP(c_member(_1322957), _1322959), _1322963)))], (48453 ^ _779571) ^ [_1748413, _1748415, _1748417, _1748419, _1748421, _1748423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748413), tc_List_Olist(_1748413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748413), tc_List_Olist(_1748413)), hAPP(hAPP(c_List_Oappend(_1748413), _1748415), hAPP(hAPP(c_List_Olist_OCons(_1748413), _1748417), c_List_Olist_ONil(_1748413)))), hAPP(hAPP(c_List_Oappend(_1748413), _1748419), hAPP(hAPP(c_List_Olist_OCons(_1748413), _1748421), c_List_Olist_ONil(_1748413))))), c_List_Olistrel1(_1748413, _1748423))), 48458 ^ _779571 : [(48461 ^ _779571) ^ [] : [-(_1748417 = _1748421)], (48459 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748413), tc_List_Olist(_1748413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748413), tc_List_Olist(_1748413)), _1748415), _1748419)), c_List_Olistrel1(_1748413, _1748423))))]], 48462 ^ _779571 : [(48465 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748413, _1748413)), hAPP(hAPP(c_Product__Type_OPair(_1748413, _1748413), _1748417), _1748421)), _1748423)))], (48463 ^ _779571) ^ [] : [-(_1748415 = _1748419)]]], (47859 ^ _779571) ^ [_1734262, _1734264, _1734266, _1734268] : [-(hAPP(hAPP(c_List_Onth(_1734262), hAPP(hAPP(c_List_Oappend(_1734262), _1734264), _1734266)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734262)), _1734264)), _1734268)) = hAPP(hAPP(c_List_Onth(_1734262), _1734266), _1734268))], (38409 ^ _779571) ^ [_1501092, _1501094, _1501096, _1501098] : [c_Fun_Oinj__on(_1501092, _1501094, _1501096, _1501098), 38412 ^ _779571 : [(38413 ^ _779571) ^ [_1501200] : [hBOOL(hAPP(hAPP(c_member(_1501092), _1501200), _1501098)), 38416 ^ _779571 : [(38417 ^ _779571) ^ [_1501302] : [hBOOL(hAPP(hAPP(c_member(_1501092), _1501302), _1501098)), hAPP(_1501096, _1501200) = hAPP(_1501096, _1501302), -(_1501200 = _1501302)]]]]], (49702 ^ _779571) ^ [_1777814, _1777816, _1777818, _1777820, _1777822] : [c_List_Opartition(_1777814, _1777816, _1777818) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1777814), tc_List_Olist(_1777814)), _1777820), _1777822), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1777814, tc_HOL_Obool)), hAPP(c_List_Oset(_1777814), _1777820)), hAPP(c_List_Oset(_1777814), _1777822)) = hAPP(c_List_Oset(_1777814), _1777818))], (7524 ^ _779571) ^ [_904250, _904252, _904254, _904256] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_904250), 7527 ^ _779571 : [(7534 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904250), _904254), _904256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904250), _904252), _904254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904250), _904252), _904256))))], (7528 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904250), _904252), _904254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904250), _904252), _904256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904250), _904254), _904256)))]]], (2748 ^ _779571) ^ [_821251, _821253, _821255, _821257] : [-(c_HOL_OLet(_821257, _821253) = c_HOL_OLet(_821255, _821251)), _821257 = _821255, _821253 = _821251], (49573 ^ _779571) ^ [_1775150, _1775152, _1775154, _1775156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1775150), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775152)), _1775154))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1775150), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775152)), _1775156))), 49583 ^ _779571 : [(49586 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Onth(_1775152), _1775154), 49582 ^ [_1775150, _1775152, _1775154, _1775156]) = hAPP(hAPP(c_List_Onth(_1775152), _1775156), 49582 ^ [_1775150, _1775152, _1775154, _1775156])], (49584 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49582 ^ [_1775150, _1775152, _1775154, _1775156]), _1775150)))]], -(hAPP(hAPP(c_List_Otake(_1775152), _1775150), _1775154) = hAPP(hAPP(c_List_Otake(_1775152), _1775150), _1775156))], (19375 ^ _779571) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (16009 ^ _779571) ^ [_1052505, _1052507, _1052509] : [-(hBOOL(hAPP(_1052505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052507), _1052509)))), 16012 ^ _779571 : [(16015 ^ _779571) ^ [] : [hBOOL(hAPP(_1052505, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16013 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052507), _1052509)))]], 16017 ^ _779571 : [(16020 ^ _779571) ^ [] : [hBOOL(hAPP(_1052505, 16016 ^ [_1052505, _1052507, _1052509]))], (16018 ^ _779571) ^ [] : [-(_1052507 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052509), 16016 ^ [_1052505, _1052507, _1052509]))]]], (33907 ^ _779571) ^ [_1398678, _1398680, _1398682] : [class_Orderings_Olinorder(_1398678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398678), _1398680)), -(hBOOL(hAPP(hAPP(c_member(_1398678), _1398682), _1398680))), -(_1398680 = c_Orderings_Obot__class_Obot(tc_fun(_1398678, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1398678, c_Orderings_Oord__class_Omin(_1398678), hAPP(hAPP(c_Set_Oinsert(_1398678), _1398682), _1398680)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1398678), _1398682), c_Big__Operators_Olattice_OInf__fin(_1398678, c_Orderings_Oord__class_Omin(_1398678), _1398680)))], (23823 ^ _779571) ^ [_1193594, _1193596, _1193598, _1193600, _1193602] : [hAPP(c_Product__Type_Ofst(_1193594, _1193596), hAPP(hAPP(c_Product__Type_OPair(_1193594, _1193596), _1193598), _1193600)) = _1193602, -(_1193598 = _1193602)], (3088 ^ _779571) ^ [_826891, _826893, _826895, _826897, _826899, _826901, _826903, _826905] : [-(c_Product__Type_Ocurry(_826905, _826901, _826897, _826893) = c_Product__Type_Ocurry(_826903, _826899, _826895, _826891)), _826905 = _826903, _826901 = _826899, _826897 = _826895, _826893 = _826891], (42120 ^ _779571) ^ [_1594072, _1594074, _1594076] : [_1594076 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594072, _1594074), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1594072, _1594074), _1594076) = c_Orderings_Obot__class_Obot(tc_fun(_1594074, tc_HOL_Obool)))], (34102 ^ _779571) ^ [_1403001, _1403003, _1403005, _1403007] : [class_Fields_Olinordered__field(_1403001), -(hAPP(c_Groups_Oabs__class_Oabs(_1403001), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403003, _1403001), _1403005), _1403007)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403003, _1403001), hAPP(hAPP(c_COMBB(_1403001, _1403001, _1403003), c_Groups_Oabs__class_Oabs(_1403001)), _1403005)), _1403007))], (37840 ^ _779571) ^ [_1489255, _1489257, _1489259] : [c_Relation_Orefl__on(_1489255, _1489257, _1489259), 37843 ^ _779571 : [(37850 ^ _779571) ^ [_1489739] : [hBOOL(hAPP(hAPP(c_member(_1489255), _1489739), _1489257)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1489255, _1489255)), hAPP(hAPP(c_Product__Type_OPair(_1489255, _1489255), _1489739), _1489739)), _1489259)))], (37844 ^ _779571) ^ [_1489466] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1489255, _1489255)), _1489466), _1489259)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1489255, _1489255, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1489255, tc_fun(_1489255, tc_HOL_Obool), tc_fun(_1489255, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1489255, tc_HOL_Obool), tc_fun(_1489255, tc_HOL_Obool)), _1489255), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1489255)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1489255), c_fconj), hAPP(hAPP(c_COMBC(_1489255, tc_fun(_1489255, tc_HOL_Obool), tc_HOL_Obool), c_member(_1489255)), _1489257)))), hAPP(hAPP(c_COMBC(_1489255, tc_fun(_1489255, tc_HOL_Obool), tc_HOL_Obool), c_member(_1489255)), _1489257))), _1489466)))]]], (25050 ^ _779571) ^ [_1218796, _1218798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218796)), 25053 ^ _779571 : [(25060 ^ _779571) ^ [] : [_1218798 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218796), _1218798)), _1218796)))], (25054 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218796), _1218798)), _1218796)), -(_1218798 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (7812 ^ _779571) ^ [_909130, _909132, _909134] : [class_Groups_Oordered__comm__monoid__add(_909130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909130), c_Groups_Ozero__class_Ozero(_909130)), _909132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909130), c_Groups_Ozero__class_Ozero(_909130)), _909134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909130), c_Groups_Ozero__class_Ozero(_909130)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909130), _909132), _909134))))], (51199 ^ _779571) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (42327 ^ _779571) ^ [_1599464, _1599466, _1599468] : [-(hAPP(c_Relation_ODomain(_1599464, _1599466), hAPP(c_Set_OCollect(tc_prod(_1599464, _1599466)), hAPP(c_Product__Type_Oprod_Oprod__case(_1599464, _1599466, tc_HOL_Obool), _1599468))) = hAPP(c_Set_OCollect(_1599464), hAPP(hAPP(c_COMBB(tc_fun(_1599466, tc_HOL_Obool), tc_HOL_Obool, _1599464), c_HOL_OEx(_1599466)), _1599468)))], (39024 ^ _779571) ^ [_1513856, _1513858] : [-(c_Fun_Oinj__on(_1513856, tc_Option_Ooption(_1513856), c_Option_Ooption_OSome(_1513856), _1513858))], (41517 ^ _779571) ^ [_1576334, _1576336, _1576338] : [class_Lattices_Odistrib__lattice(_1576334), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576334), _1576336)), -(_1576336 = c_Orderings_Obot__class_Obot(tc_fun(_1576334, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576334), _1576338), c_Big__Operators_Olattice__class_OSup__fin(_1576334, _1576336)) = c_Big__Operators_Olattice__class_OSup__fin(_1576334, hAPP(c_Set_OCollect(_1576334), hAPP(hAPP(c_COMBB(tc_fun(_1576334, tc_HOL_Obool), tc_HOL_Obool, _1576334), c_HOL_OEx(_1576334)), hAPP(hAPP(c_COMBC(_1576334, tc_fun(_1576334, tc_HOL_Obool), tc_fun(_1576334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576334, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1576334, tc_HOL_Obool), tc_fun(_1576334, tc_HOL_Obool)), _1576334), c_COMBS(_1576334, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576334, tc_HOL_Obool), tc_fun(_1576334, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1576334), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576334), c_fconj)), hAPP(hAPP(c_COMBC(_1576334, tc_fun(_1576334, _1576334), tc_fun(_1576334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576334, tc_HOL_Obool), tc_fun(tc_fun(_1576334, _1576334), tc_fun(_1576334, tc_HOL_Obool)), _1576334), c_COMBB(_1576334, tc_HOL_Obool, _1576334)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576334), _1576338))))), hAPP(hAPP(c_COMBC(_1576334, tc_fun(_1576334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576334)), _1576336))))))], (32879 ^ _779571) ^ [_1379503] : [class_Rings_Oring__1(_1379503), -(hBOOL(hAPP(hAPP(c_member(_1379503), c_Groups_Oone__class_Oone(_1379503)), c_Int_Oring__1__class_OInts(_1379503))))], (48888 ^ _779571) ^ [_1760419, _1760421, _1760423, _1760425] : [-(hAPP(c_List_Orotate1(_1760421), hAPP(hAPP(c_List_Olist_OCons(_1760421), _1760423), _1760425)) = hAPP(hAPP(c_List_Oappend(_1760421), _1760425), hAPP(hAPP(c_List_Olist_OCons(_1760421), _1760423), c_List_Olist_ONil(_1760421))))], (12233 ^ _779571) ^ [_983655, _983657, _983659] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983655), _983657)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983659), _983657)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983655), _983659))], (11358 ^ _779571) ^ [_968162, _968164] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968162), _968164))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968162), _968164)), -(_968162 = _968164)], (24967 ^ _779571) ^ [_1217068, _1217070, _1217072, _1217074, _1217076] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1217068, _1217070, tc_HOL_Obool, _1217072), _1217074), _1217076)), -(hBOOL(hAPP(_1217072, hAPP(hAPP(c_Product__Type_OPair(_1217068, _1217070), _1217074), _1217076))))], (6157 ^ _779571) ^ [_878987, _878989, _878991, _878993, _878995, _878997, _878999, _879001, _879003, _879005, _879007] : [-(c_Com_Ocom_Ocom__case(_878987, _878989, _878991, _878993, _878995, _878997, _878999, _879001, _879003, c_Com_Ocom_OWhile(_879005, _879007)) = hAPP(hAPP(_878999, _879005), _879007))], (16623 ^ _779571) ^ [_1063874, _1063876] : [class_Groups_Oordered__ab__group__add__abs(_1063874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063874), c_Groups_Ozero__class_Ozero(_1063874)), _1063876)), -(hAPP(c_Groups_Oabs__class_Oabs(_1063874), _1063876) = _1063876)], (43114 ^ _779571) ^ [_1618302, _1618304, _1618306, _1618308, _1618310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618302, _1618302)), hAPP(hAPP(c_Product__Type_OPair(_1618302, _1618302), _1618304), _1618306)), c_Transitive__Closure_Ortrancl(_1618302, _1618308))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618302, _1618302)), hAPP(hAPP(c_Product__Type_OPair(_1618302, _1618302), _1618306), _1618310)), c_Transitive__Closure_Otrancl(_1618302, _1618308))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618302, _1618302)), hAPP(hAPP(c_Product__Type_OPair(_1618302, _1618302), _1618304), _1618310)), c_Transitive__Closure_Otrancl(_1618302, _1618308))))], (28164 ^ _779571) ^ [_1279152, _1279154, _1279156, _1279158] : [hBOOL(hAPP(_1279152, _1279154)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279156, tc_HOL_Obool)), _1279152), _1279158), _1279154)))], (34598 ^ _779571) ^ [_1413208, _1413210, _1413212, _1413214, _1413216] : [hAPP(_1413208, _1413210) = c_Option_Ooption_ONone(_1413212), -(c_Map_Oran(_1413214, _1413212, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1413214, tc_Option_Ooption(_1413212)), _1413208), _1413210), hAPP(c_Option_Ooption_OSome(_1413212), _1413216))) = hAPP(hAPP(c_Set_Oinsert(_1413212), _1413216), c_Map_Oran(_1413214, _1413212, _1413208)))], (25086 ^ _779571) ^ [_1219401, _1219403] : [class_Rings_Ocomm__semiring__1(_1219401), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219401), _1219403), c_Groups_Ozero__class_Ozero(_1219401))))], (23559 ^ _779571) ^ [_1188693, _1188695, _1188697] : [class_Orderings_Olinorder(_1188693), 23562 ^ _779571 : [(23569 ^ _779571) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188693), _1188695), _1188697) = _1188695, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188693), _1188695), _1188697)))], (23563 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188693), _1188695), _1188697)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188693), _1188695), _1188697) = _1188695)]]], (1772 ^ _779571) ^ [_804489, _804491] : [-(class_Rings_Odvd(_804489)), _804491 = _804489, class_Rings_Odvd(_804491)], (26330 ^ _779571) ^ [_1242027, _1242029, _1242031, _1242033, _1242035] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242027), _1242029)), 26333 ^ _779571 : [(26340 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242035), _1242029))), _1242033))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242031), _1242033))))], (26334 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242031), _1242033))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242035), _1242029))), _1242033))))]]], (18107 ^ _779571) ^ [_1091139] : [class_Rings_Osemiring__1(_1091139), c_Int_Oiszero(_1091139, c_Groups_Oone__class_Oone(_1091139))], (28383 ^ _779571) ^ [_1283336, _1283338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1283336), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1283338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1283338), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1283336))))), -(_1283336 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1283338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1283338), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1283336))))], (46514 ^ _779571) ^ [_1699663, _1699665, _1699667, _1699669, _1699671, _1699673, _1699675] : [hAPP(hAPP(c_List_Omap(_1699663, _1699665), _1699667), _1699669) = hAPP(hAPP(c_List_Omap(_1699671, _1699665), _1699673), _1699675), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699663)), _1699669) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699671)), _1699675))], (28266 ^ _779571) ^ [_1281144, _1281146, _1281148] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1281144, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281144, tc_HOL_Obool)), _1281146), _1281148)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281144, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1281144, tc_HOL_Obool)), _1281146)), _1281148))], (15418 ^ _779571) ^ [_1040632, _1040634] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040632), _1040634))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1040632, _1040634) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040632), _1040634), _1040634))], (49062 ^ _779571) ^ [_1763922, _1763924, _1763926] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1763922, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763924)), _1763926)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1763924, _1763922), _1763926) = _1763926)], (17265 ^ _779571) ^ [_1076460, _1076462] : [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), _1076460), _1076462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1076460))), -(_1076462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28675 ^ _779571) ^ [_1288955, _1288957, _1288959, _1288961, _1288963] : [class_Groups_Ocomm__monoid__add(_1288955), class_Groups_Ocomm__monoid__mult(_1288955), _1288957 = _1288959, c_Nat__Transfer_Onat__set(_1288959), 28693 ^ _779571 : [(28696 ^ _779571) ^ [] : [hAPP(_1288961, 28692 ^ [_1288955, _1288957, _1288959, _1288961, _1288963]) = hAPP(_1288963, 28692 ^ [_1288955, _1288957, _1288959, _1288961, _1288963])], (28694 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28692 ^ [_1288955, _1288957, _1288959, _1288961, _1288963])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1288955), _1288961), _1288957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1288955), _1288963), _1288959))], (6033 ^ _779571) ^ [_876762, _876764, _876766, _876768] : [c_Com_Ocom_OWhile(_876762, _876764) = c_Com_Ocom_OSemi(_876766, _876768)], (34895 ^ _779571) ^ [_1420040, _1420042, _1420044] : [-(c_Wellfounded_Omlex__prod(_1420040, _1420042, _1420044) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1420040), _1420040), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1420040, c_Wellfounded_Oless__than, _1420044)), hAPP(hAPP(c_COMBS(_1420040, _1420040, tc_prod(tc_Nat_Onat, _1420040)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1420040, tc_prod(tc_Nat_Onat, _1420040)), _1420040), c_Product__Type_OPair(tc_Nat_Onat, _1420040)), _1420042)), c_COMBI(_1420040))))], (24933 ^ _779571) ^ [_1215980, _1215982, _1215984, _1215986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1215980), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1215982, _1215984, _1215980, _1215986) = 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(_1215982)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1215982)))], (13086 ^ _779571) ^ [_998679, _998681, _998683, _998685, _998687, _998689] : [class_Rings_Olinordered__semiring__1(_998679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998679), _998681), _998683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998679), _998685), _998683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998679), c_Groups_Ozero__class_Ozero(_998679)), _998687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998679), c_Groups_Ozero__class_Ozero(_998679)), _998689)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998679), _998687), _998689) = c_Groups_Oone__class_Oone(_998679), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998679), _998687), _998681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998679), _998689), _998685))), _998683)))], (47031 ^ _779571) ^ [_1714795, _1714797, _1714799] : [-(c_Random_Oselect__weight(_1714795, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714795)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1714795), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1714797)), _1714799)) = c_Random_Oselect__weight(_1714795, _1714799))], (49648 ^ _779571) ^ [_1776664, _1776666, _1776668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776664), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776666)), _1776668))), -(hAPP(hAPP(c_List_Otake(_1776666), _1776664), c_List_Obutlast(_1776666, _1776668)) = hAPP(hAPP(c_List_Otake(_1776666), _1776664), _1776668))], (29172 ^ _779571) ^ [_1300698, _1300700, _1300702, _1300704, _1300706] : [-(hAPP(hAPP(c_Set_Oinsert(_1300698), _1300700), hAPP(hAPP(c_Set_Oinsert(_1300698), _1300702), c_Orderings_Obot__class_Obot(tc_fun(_1300698, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1300698), _1300704), hAPP(hAPP(c_Set_Oinsert(_1300698), _1300706), c_Orderings_Obot__class_Obot(tc_fun(_1300698, tc_HOL_Obool))))), 29173 ^ _779571 : [(29180 ^ _779571) ^ [] : [_1300700 = _1300706, _1300702 = _1300704], (29174 ^ _779571) ^ [] : [_1300700 = _1300704, _1300702 = _1300706]]], (32845 ^ _779571) ^ [_1378890, _1378892, _1378894] : [class_Rings_Oring__1(_1378890), hBOOL(hAPP(hAPP(c_member(_1378890), _1378892), c_Int_Oring__1__class_OInts(_1378890))), hBOOL(hAPP(hAPP(c_member(_1378890), _1378894), c_Int_Oring__1__class_OInts(_1378890))), -(hBOOL(hAPP(hAPP(c_member(_1378890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378890), _1378892), _1378894)), c_Int_Oring__1__class_OInts(_1378890))))], (4300 ^ _779571) ^ [_846091, _846093, _846095, _846097] : [-(c_List_Olexn(_846097, _846093) = c_List_Olexn(_846095, _846091)), _846097 = _846095, _846093 = _846091], (27409 ^ _779571) ^ [_1263625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263625)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263625) = 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, _1263625))))], (47304 ^ _779571) ^ [_1720803, _1720805] : [_1720805 = c_List_Olist_ONil(_1720803), -(hAPP(c_List_Oset(_1720803), _1720805) = c_Orderings_Obot__class_Obot(tc_fun(_1720803, tc_HOL_Obool)))], (7306 ^ _779571) ^ [_900602, _900604, _900606, _900608] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_900602, _900604)), c_Nitpick_Opair__box_OPairBox(_900602, _900604, _900606, _900608)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19605 ^ _779571) ^ [_1115884] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1115884)), 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, _1115884, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17583 ^ _779571) ^ [_1082184, _1082186, _1082188] : [class_Rings_Olinordered__semidom(_1082184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082184), c_Groups_Oone__class_Oone(_1082184)), _1082186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082184), c_Groups_Oone__class_Oone(_1082184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082184), _1082186), hAPP(hAPP(c_Power_Opower__class_Opower(_1082184), _1082186), _1082188)))))], (44211 ^ _779571) ^ [_1644071, _1644073, _1644075] : [class_Orderings_Olinorder(_1644071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644071), _1644073)), -(hBOOL(hAPP(hAPP(c_member(_1644071), _1644075), _1644073))), -(c_Big__Operators_Olattice_OInf__fin(_1644071, c_Orderings_Oord__class_Omin(_1644071), hAPP(hAPP(c_Set_Oinsert(_1644071), _1644075), _1644073)) = hAPP(hAPP(c_Finite__Set_Ofold(_1644071, _1644071, c_Orderings_Oord__class_Omin(_1644071)), _1644075), _1644073))], (25600 ^ _779571) ^ [_1227832, _1227834, _1227836, _1227838] : [class_Divides_Osemiring__div(_1227832), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227832), _1227834), c_Divides_Odiv__class_Omod(_1227832, _1227836, _1227838))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227832), _1227834), _1227838)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227832), _1227834), _1227836)))], (7300 ^ _779571) ^ [_900487, _900489, _900491, _900493] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900487)), _900489, _900491, _900493), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _900487), _900489, hAPP(c_Nat_OSuc, _900491), _900493))], (29496 ^ _779571) ^ [_1306760, _1306762] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306760, tc_HOL_Obool)), _1306762), c_Orderings_Otop__class_Otop(tc_fun(_1306760, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1306760, tc_HOL_Obool)))], (51229 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (19633 ^ _779571) ^ [_1116424, _1116426, _1116428] : [class_Rings_Olinordered__semidom(_1116424), hAPP(hAPP(c_Power_Opower__class_Opower(_1116424), _1116426), 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(_1116424), _1116428), 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(_1116424), c_Groups_Ozero__class_Ozero(_1116424)), _1116426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116424), c_Groups_Ozero__class_Ozero(_1116424)), _1116428)), -(_1116426 = _1116428)], (39753 ^ _779571) ^ [_1529837, _1529839, _1529841, _1529843, _1529845, _1529847, _1529849] : [-(hBOOL(hAPP(hAPP(c_member(_1529837), _1529839), _1529841))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529837, _1529843, _1529845, _1529847, _1529841), _1529849)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529837, _1529843, _1529845, _1529847, hAPP(hAPP(c_Set_Oinsert(_1529837), _1529839), _1529841)), hAPP(hAPP(_1529845, _1529839), _1529849))))], (8350 ^ _779571) ^ [_918104, _918106] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918104) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918106), -(_918104 = _918106)], (36278 ^ _779571) ^ [_1453223, _1453225, _1453227, _1453229] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453223, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453223, tc_HOL_Obool)), _1453225), _1453227)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453223, tc_HOL_Obool)), _1453229), _1453227)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453223, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453223, tc_HOL_Obool)), _1453225), _1453227)), _1453229))], (10339 ^ _779571) ^ [_951754, _951756, _951758] : [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, _951754)), _951756)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _951754)), _951758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951756), _951758)))], (37425 ^ _779571) ^ [_1478515, _1478517, _1478519] : [class_Orderings_Olinorder(_1478515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478515), _1478517)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478515), _1478519)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478515, tc_HOL_Obool)), _1478517), _1478519) = c_Orderings_Obot__class_Obot(tc_fun(_1478515, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1478515), c_Big__Operators_Olattice_OInf__fin(_1478515, c_Orderings_Oord__class_Omin(_1478515), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478515, tc_HOL_Obool)), _1478517), _1478519))), c_Big__Operators_Olattice_OInf__fin(_1478515, c_Orderings_Oord__class_Omin(_1478515), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478515, tc_HOL_Obool)), _1478517), _1478519))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1478515), c_Big__Operators_Olattice_OInf__fin(_1478515, c_Orderings_Oord__class_Omin(_1478515), _1478517)), c_Big__Operators_Olattice_OInf__fin(_1478515, c_Orderings_Oord__class_Omin(_1478515), _1478519)))], (27616 ^ _779571) ^ [_1267991, _1267993] : [-(hAPP(c_Finite__Set_Ocard(_1267991), _1267993) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267991, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1267991), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1267993))], (51319 ^ _779571) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (45235 ^ _779571) ^ [_1669647, _1669649, _1669651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669647, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669647, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669647, tc_HOL_Obool), _1669649)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669647, tc_HOL_Obool), _1669651))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669647, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1669647, tc_HOL_Obool), tc_HOL_Obool)), _1669649), _1669651)))))], (1642 ^ _779571) ^ [_802864, _802866] : [-(class_Groups_Omonoid__mult(_802864)), _802866 = _802864, class_Groups_Omonoid__mult(_802866)], (41344 ^ _779571) ^ [_1569117] : [-(c_Wellfounded_Ofinite__psubset(_1569117) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1569117, tc_HOL_Obool), tc_fun(_1569117, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1569117, tc_HOL_Obool), tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1569117, tc_HOL_Obool), tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1569117, tc_HOL_Obool)), c_COMBS(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1569117, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1569117, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1569117, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1569117, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1569117)))))], (45215 ^ _779571) ^ [_1669076] : [class_Complete__Lattice_Ocomplete__lattice(_1669076), -(c_Complete__Lattice_OInf__class_OInf(_1669076, c_Orderings_Otop__class_Otop(tc_fun(_1669076, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1669076))], (27510 ^ _779571) ^ [_1265830, _1265832] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265830) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265832), -(_1265830 = _1265832)], (40405 ^ _779571) ^ [_1546090, _1546092, _1546094, _1546096, _1546098, _1546100] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546090, _1546092), hAPP(hAPP(c_Set_Oinsert(_1546090), _1546094), _1546096)), hAPP(c_COMBK(tc_fun(_1546092, tc_HOL_Obool), _1546090), hAPP(hAPP(c_Set_Oinsert(_1546092), _1546098), _1546100))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1546090, _1546092)), hAPP(hAPP(c_Product__Type_OPair(_1546090, _1546092), _1546094), _1546098)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546090, _1546092), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1546090, _1546092), _1546096), hAPP(c_COMBK(tc_fun(_1546092, tc_HOL_Obool), _1546090), hAPP(hAPP(c_Set_Oinsert(_1546092), _1546098), _1546100)))), hAPP(hAPP(c_Product__Type_OSigma(_1546090, _1546092), hAPP(hAPP(c_Set_Oinsert(_1546090), _1546094), _1546096)), hAPP(c_COMBK(tc_fun(_1546092, tc_HOL_Obool), _1546090), _1546100)))))], (27644 ^ _779571) ^ [_1268534, _1268536] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1268534), _1268536)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1268536), _1268534)))], (4546 ^ _779571) ^ [_849948, _849950, _849952, _849954] : [-(c_Nat_Ocompow(_849954, _849950) = c_Nat_Ocompow(_849952, _849948)), _849954 = _849952, _849950 = _849948], (36378 ^ _779571) ^ [_1455366, _1455368, _1455370, _1455372] : [class_Lattices_Osemilattice__inf(_1455366), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455366), _1455368), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455366), _1455370), _1455372)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455366), _1455370), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455366), _1455368), _1455372)))], (37896 ^ _779571) ^ [_1491021, _1491023] : [-(c_Relation_Orefl__on(_1491021, _1491023, c_Relation_OId__on(_1491021, _1491023)))], (15956 ^ _779571) ^ [_1051511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051511)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051511), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1051511)], (44183 ^ _779571) ^ [_1643643, _1643645, _1643647] : [class_Orderings_Olinorder(_1643643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643643), _1643645)), -(hBOOL(hAPP(hAPP(c_member(_1643643), _1643647), _1643645))), -(c_Big__Operators_Olinorder__class_OMin(_1643643, hAPP(hAPP(c_Set_Oinsert(_1643643), _1643647), _1643645)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643643, _1643643, c_Orderings_Oord__class_Omin(_1643643)), _1643647), _1643645))], (24919 ^ _779571) ^ [_1215602, _1215604, _1215606, _1215608] : [hBOOL(hAPP(_1215602, _1215604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215606, tc_HOL_Obool)), _1215602), _1215608)), -(hBOOL(hAPP(_1215608, _1215604)))], (24605 ^ _779571) ^ [_1209031, _1209033, _1209035, _1209037] : [class_Orderings_Olinorder(_1209031), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209031), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209031), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209031), _1209033), _1209035)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209031), _1209033), _1209037))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209031), _1209033), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209031), _1209035), _1209037)))))], (9552 ^ _779571) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (50966 ^ _779571) ^ [_1806000, _1806002, _1806004] : [50968 ^ _779571 : [(50971 ^ _779571) ^ [] : [hBOOL(hAPP(_1806002, 50967 ^ [_1806000, _1806002, _1806004]))], (50969 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806000), 50967 ^ [_1806000, _1806002, _1806004]), hAPP(c_List_Oset(_1806000), _1806004))))]], -(c_List_OtakeWhile(_1806000, _1806002, _1806004) = _1806004)], (30730 ^ _779571) ^ [_1331686, _1331688, _1331690, _1331692, _1331694] : [hBOOL(hAPP(hAPP(c_member(_1331686), _1331688), _1331690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331692, tc_HOL_Obool)), hAPP(_1331694, _1331688)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331686, tc_fun(_1331692, tc_HOL_Obool)), _1331690), _1331694))))], (31201 ^ _779571) ^ [_1341634] : [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)), _1341634))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1341634)))], (45913 ^ _779571) ^ [_1685114, _1685116, _1685118, _1685120, _1685122] : [hAPP(hAPP(c_List_Omap(_1685114, _1685116), _1685118), _1685120) = hAPP(hAPP(c_List_Omap(_1685114, _1685116), _1685118), _1685122), c_Fun_Oinj__on(_1685114, _1685116, _1685118, c_Orderings_Otop__class_Otop(tc_fun(_1685114, tc_HOL_Obool))), -(_1685120 = _1685122)], (49720 ^ _779571) ^ [_1778399, _1778401, _1778403, _1778405] : [hBOOL(hAPP(_1778399, _1778401)), -(hAPP(c_List_Ofilter(_1778403, _1778399), hAPP(hAPP(c_List_Olist_OCons(_1778403), _1778401), _1778405)) = hAPP(hAPP(c_List_Olist_OCons(_1778403), _1778401), hAPP(c_List_Ofilter(_1778403, _1778399), _1778405)))], (35412 ^ _779571) ^ [_1432078, _1432080] : [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)), _1432078), _1432080)), 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)), _1432078), 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)), _1432080), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (28058 ^ _779571) ^ [_1276838, _1276840] : [class_Lattices_Osemilattice__sup(_1276838), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276838), _1276840), _1276840) = _1276840)], (47442 ^ _779571) ^ [_1724152, _1724154, _1724156] : [47444 ^ _779571 : [(47447 ^ _779571) ^ [] : [hBOOL(hAPP(_1724156, 47443 ^ [_1724152, _1724154, _1724156]))], (47445 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724152), 47443 ^ [_1724152, _1724154, _1724156]), hAPP(c_List_Oset(_1724152), _1724154))))]], 47448 ^ _779571 : [(47449 ^ _779571) ^ [_1724336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724152)), _1724154))), -(hBOOL(hAPP(_1724156, hAPP(hAPP(c_List_Onth(_1724152), _1724154), _1724336))))]]], (9916 ^ _779571) ^ [_944749, _944751, _944753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _944749), _944751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _944753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _944753), _944749)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _944753), _944751))))], (26955 ^ _779571) ^ [_1254301, _1254303] : [26963 ^ _779571 : [(26966 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1254303, 26962 ^ [_1254301, _1254303])))], (26964 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26962 ^ [_1254301, _1254303]), _1254301)))]], 26956 ^ _779571 : [(26957 ^ _779571) ^ [_1254370] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1254370), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1254301))), hBOOL(hAPP(_1254303, _1254370))]]], (18403 ^ _779571) ^ [_1095462, _1095464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095462), _1095464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1095462)), _1095464)))], (36944 ^ _779571) ^ [_1467789, _1467791, _1467793, _1467795] : [class_Orderings_Olinorder(_1467789), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467789, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1467789, _1467791, _1467793)), hAPP(c_SetInterval_Oord__class_OatLeast(_1467789), _1467795)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467789, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1467789), _1467791), _1467795), _1467793))], (1722 ^ _779571) ^ [_803864, _803866] : [-(class_Groups_Ominus(_803864)), _803866 = _803864, class_Groups_Ominus(_803866)], (29085 ^ _779571) ^ [] : [-(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)))], (21421 ^ _779571) ^ [_1148136, _1148138, _1148140, _1148142] : [class_Fields_Olinordered__field__inverse__zero(_1148136), 21424 ^ _779571 : [(21425 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148136), _1148138), _1148140)), _1148142)), 21428 ^ _779571 : [(21435 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148140))), 21438 ^ _779571 : [(21445 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), _1148140), c_Groups_Ozero__class_Ozero(_1148136)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148142)))], (21439 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), _1148140), c_Groups_Ozero__class_Ozero(_1148136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148136), _1148142), _1148140)), _1148138)))]]], (21429 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), _1148138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148136), _1148142), _1148140))))]]], (21451 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148136), _1148138), _1148140)), _1148142))), 21454 ^ _779571 : [(21457 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), _1148138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148136), _1148142), _1148140)))], (21455 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148140)))]], 21458 ^ _779571 : [(21461 ^ _779571) ^ [] : [21462 ^ _779571 : [(21465 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148136), _1148142), _1148140)), _1148138))], (21463 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), _1148140), c_Groups_Ozero__class_Ozero(_1148136))))]], 21466 ^ _779571 : [(21469 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148142))], (21467 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), _1148140), c_Groups_Ozero__class_Ozero(_1148136)))]]], (21459 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148136), c_Groups_Ozero__class_Ozero(_1148136)), _1148140))]]]]], (39457 ^ _779571) ^ [_1523153, _1523155, _1523157, _1523159, _1523161] : [hBOOL(hAPP(hAPP(c_member(_1523157), hAPP(_1523159, _1523155)), _1523161)), -(hBOOL(hAPP(hAPP(c_member(_1523153), _1523155), hAPP(c_Set_Ovimage(_1523153, _1523157, _1523159), _1523161))))], (49893 ^ _779571) ^ [_1782715, _1782717] : [-(c_Random_Opick(_1782715, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1782715), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1782715, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1782715, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1782715)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1782717)) = c_Random_Opick(_1782715, _1782717))], (24687 ^ _779571) ^ [_1210658] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1210658)) = _1210658)], (25092 ^ _779571) ^ [_1219494] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1219494)))], (35703 ^ _779571) ^ [_1439931, _1439933, _1439935, _1439937, _1439939, _1439941] : [c_Finite__Set_Ofolding(_1439931, _1439933, _1439935, _1439937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439931), _1439939)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439931), _1439941)), -(hAPP(c_Fun_Ocomp(_1439933, _1439933, _1439933, hAPP(_1439937, _1439941)), hAPP(_1439937, _1439939)) = hAPP(c_Fun_Ocomp(_1439933, _1439933, _1439933, hAPP(_1439937, _1439939)), hAPP(_1439937, _1439941)))], (1142 ^ _779571) ^ [_796614, _796616] : [-(class_Rings_Ocomm__ring(_796614)), _796616 = _796614, class_Rings_Ocomm__ring(_796616)], (19485 ^ _779571) ^ [_1113802, _1113804] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1113802)), c_Int_OBit1(_1113804)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1113802)), _1113804)))], (29315 ^ _779571) ^ [_1303583, _1303585, _1303587] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303583, tc_fun(_1303585, tc_HOL_Obool)), _1303587), hAPP(c_COMBK(tc_fun(_1303585, tc_HOL_Obool), _1303583), c_Orderings_Obot__class_Obot(tc_fun(_1303585, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1303585, tc_HOL_Obool)))], (28789 ^ _779571) ^ [_1291223, _1291225, _1291227, _1291229] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1291223, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1291225)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1291223, tc_HOL_Obool), tc_Nat_Onat), _1291227), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1291229))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1291223, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1291229, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1291225), _1291229))), _1291227))], (39878 ^ _779571) ^ [_1532959, _1532961, _1532963] : [hBOOL(hAPP(hAPP(c_member(_1532959), _1532961), c_Wellfounded_Oacc(_1532959, _1532963))), 39881 ^ _779571 : [(39882 ^ _779571) ^ [_1533073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532959, _1532959)), hAPP(hAPP(c_Product__Type_OPair(_1532959, _1532959), _1533073), _1532961)), _1532963)), -(hBOOL(hAPP(hAPP(c_member(_1532959), _1533073), c_Wellfounded_Oacc(_1532959, _1532963))))]]], (38070 ^ _779571) ^ [_1493927, _1493929, _1493931] : [class_Lattices_Olattice(_1493927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493927), _1493929)), 38077 ^ _779571 : [(38084 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493927, tc_HOL_Obool)), _1493929), hAPP(hAPP(c_Set_Oinsert(_1493927), _1493931), c_Orderings_Obot__class_Obot(tc_fun(_1493927, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1493927, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1493927, hAPP(hAPP(c_Set_Oinsert(_1493927), _1493931), _1493929)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493927), _1493931), c_Big__Operators_Olattice__class_OInf__fin(_1493927, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493927, tc_HOL_Obool)), _1493929), hAPP(hAPP(c_Set_Oinsert(_1493927), _1493931), c_Orderings_Obot__class_Obot(tc_fun(_1493927, tc_HOL_Obool)))))))], (38078 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493927, tc_HOL_Obool)), _1493929), hAPP(hAPP(c_Set_Oinsert(_1493927), _1493931), c_Orderings_Obot__class_Obot(tc_fun(_1493927, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1493927, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1493927, hAPP(hAPP(c_Set_Oinsert(_1493927), _1493931), _1493929)) = _1493931)]]], (35940 ^ _779571) ^ [_1445500, _1445502, _1445504, _1445506, _1445508] : [c_Equiv__Relations_Oequiv(_1445500, _1445502, _1445504), 35943 ^ _779571 : [(35954 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445500, _1445500)), hAPP(hAPP(c_Product__Type_OPair(_1445500, _1445500), _1445506), _1445508)), _1445504))), hAPP(c_Relation_OImage(_1445500, _1445500, _1445504), hAPP(hAPP(c_Set_Oinsert(_1445500), _1445506), c_Orderings_Obot__class_Obot(tc_fun(_1445500, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1445500, _1445500, _1445504), hAPP(hAPP(c_Set_Oinsert(_1445500), _1445508), c_Orderings_Obot__class_Obot(tc_fun(_1445500, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1445500), _1445506), _1445502)), hBOOL(hAPP(hAPP(c_member(_1445500), _1445508), _1445502))], (35944 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1445500, _1445500)), hAPP(hAPP(c_Product__Type_OPair(_1445500, _1445500), _1445506), _1445508)), _1445504)), 35947 ^ _779571 : [(35952 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445500), _1445508), _1445502)))], (35950 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445500), _1445506), _1445502)))], (35948 ^ _779571) ^ [] : [-(hAPP(c_Relation_OImage(_1445500, _1445500, _1445504), hAPP(hAPP(c_Set_Oinsert(_1445500), _1445506), c_Orderings_Obot__class_Obot(tc_fun(_1445500, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1445500, _1445500, _1445504), hAPP(hAPP(c_Set_Oinsert(_1445500), _1445508), c_Orderings_Obot__class_Obot(tc_fun(_1445500, tc_HOL_Obool)))))]]]]], (25694 ^ _779571) ^ [_1229504, _1229506, _1229508, _1229510] : [class_Rings_Ocomm__semiring__1(_1229504), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229504), _1229506), _1229508)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229504), _1229506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229504), _1229508), _1229510))))], (16765 ^ _779571) ^ [_1066580, _1066582, _1066584, _1066586] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066580), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066580), _1066582), _1066584)), hAPP(c_Int_Onumber__class_Onumber__of(_1066580), _1066586)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066580), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066580), _1066582), hAPP(c_Int_Onumber__class_Onumber__of(_1066580), _1066586))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066580), _1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066580), _1066586)))), class_Int_Onumber(_1066580), class_Rings_Osemiring(_1066580)], (992 ^ _779571) ^ [_794739, _794741] : [-(class_Groups_Oordered__ab__group__add__abs(_794739)), _794741 = _794739, class_Groups_Oordered__ab__group__add__abs(_794741)], (47709 ^ _779571) ^ [_1730820, _1730822, _1730824, _1730826, _1730828] : [class_Orderings_Olinorder(_1730820), hBOOL(hAPP(c_List_Odistinct(_1730822), _1730824)), -(hBOOL(hAPP(c_List_Odistinct(_1730822), c_List_Olinorder__class_Oinsort__insert__key(_1730822, _1730820, _1730826, _1730828, _1730824))))], (7738 ^ _779571) ^ [_907689, _907691, _907693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _907689), _907691)), _907693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907689), _907693)))], (41608 ^ _779571) ^ [_1580902, _1580904] : [-(c_Fun_Oinj__on(_1580902, _1580902, c_Fun_Oid(_1580902), _1580904))], (30273 ^ _779571) ^ [_1322433, _1322435, _1322437, _1322439] : [hBOOL(hAPP(hAPP(c_member(_1322433), _1322435), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322433, tc_HOL_Obool)), _1322437), _1322439))), -(hBOOL(hAPP(hAPP(c_member(_1322433), _1322435), _1322437))), -(hBOOL(hAPP(hAPP(c_member(_1322433), _1322435), _1322439)))], (8338 ^ _779571) ^ [_917913, _917915] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917913) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917915), -(_917913 = _917915)], (37670 ^ _779571) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (49658 ^ _779571) ^ [_1776917, _1776919, _1776921, _1776923] : [_1776917 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776919)), _1776921)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1776919, hAPP(hAPP(c_List_Olist__update(_1776919, _1776921), _1776917), _1776923)) = c_List_Obutlast(_1776919, _1776921))], (15470 ^ _779571) ^ [_1041521, _1041523, _1041525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041521), _1041523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041521), _1041525)), 15477 ^ _779571 : [(15484 ^ _779571) ^ [] : [_1041523 = _1041525, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041523), _1041521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041525), _1041521))], (15478 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041523), _1041521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041525), _1041521), -(_1041523 = _1041525)]]], (51427 ^ _779571) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (1582 ^ _779571) ^ [_802114, _802116] : [-(class_Divides_Osemiring__div(_802114)), _802116 = _802114, class_Divides_Osemiring__div(_802116)], (45768 ^ _779571) ^ [_1681371, _1681373, _1681375, _1681377] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1681371)), hAPP(c_Set_Oimage(_1681373, tc_Option_Ooption(_1681371), _1681375), c_Orderings_Otop__class_Otop(tc_fun(_1681373, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1681371)), hAPP(c_Set_Oimage(_1681373, tc_Option_Ooption(_1681371), c_Map_Omap__add(_1681373, _1681371, _1681375, c_Map_Omap__of(_1681373, _1681371, _1681377))), c_Orderings_Otop__class_Otop(tc_fun(_1681373, tc_HOL_Obool))))))], (45008 ^ _779571) ^ [_1664515, _1664517, _1664519] : [class_Complete__Lattice_Ocomplete__lattice(_1664515), 45011 ^ _779571 : [(45012 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664515), c_Complete__Lattice_OSup__class_OSup(_1664515, _1664517)), _1664519)), 45015 ^ _779571 : [(45016 ^ _779571) ^ [_1664673] : [hBOOL(hAPP(hAPP(c_member(_1664515), _1664673), _1664517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664515), _1664673), _1664519)))]]], (45022 ^ _779571) ^ [] : [45024 ^ _779571 : [(45027 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664515), 45023 ^ [_1664515, _1664517, _1664519]), _1664519))], (45025 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664515), 45023 ^ [_1664515, _1664517, _1664519]), _1664517)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664515), c_Complete__Lattice_OSup__class_OSup(_1664515, _1664517)), _1664519)))]]], (29994 ^ _779571) ^ [_1317018, _1317020] : [hBOOL(hAPP(hAPP(c_member(_1317018), _1317020), c_Orderings_Obot__class_Obot(tc_fun(_1317018, tc_HOL_Obool))))], (7486 ^ _779571) ^ [_903562, _903564] : [7487 ^ _779571 : [(7490 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903564), _903562))], (7488 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903562), _903564))]], _903562 = _903564], (19201 ^ _779571) ^ [_1108828] : [-(c_Int_OBit0(_1108828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1108828), _1108828))], (15978 ^ _779571) ^ [_1051910, _1051912, _1051914] : [-(hBOOL(hAPP(_1051910, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051912), _1051914)))), 15981 ^ _779571 : [(15984 ^ _779571) ^ [] : [hBOOL(hAPP(_1051910, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15982 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051912), _1051914)))]], 15986 ^ _779571 : [(15989 ^ _779571) ^ [] : [hBOOL(hAPP(_1051910, 15985 ^ [_1051910, _1051912, _1051914]))], (15987 ^ _779571) ^ [] : [-(_1051912 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051914), 15985 ^ [_1051910, _1051912, _1051914]))]]], (36606 ^ _779571) ^ [_1459526, _1459528, _1459530] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459526, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459526, tc_HOL_Obool)), _1459528), _1459530)), _1459528)))], (22284 ^ _779571) ^ [_1164056, _1164058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164056)), _1164058)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164056), _1164058)))], (49868 ^ _779571) ^ [_1782061, _1782063] : [c_List_Otranspose(_1782061, _1782063) = c_List_Olist_ONil(tc_List_Olist(_1782061)), 49871 ^ _779571 : [(49872 ^ _779571) ^ [_1782156] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1782061)), _1782156), hAPP(c_List_Oset(tc_List_Olist(_1782061)), _1782063))), -(_1782156 = c_List_Olist_ONil(_1782061))]]], (7197 ^ _779571) ^ [_898349, _898351, _898353, _898355, _898357] : [c_Hoare__Mirabelle_Otriple__valid(_898349, _898351, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898349), _898353), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _898355))), _898357)), -(c_Hoare__Mirabelle_Otriple__valid(_898349, hAPP(c_Nat_OSuc, _898351), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898349), _898353), hAPP(c_Com_Ocom_OBODY, _898355)), _898357)))], (2872 ^ _779571) ^ [_823269, _823271, _823273, _823275, _823277, _823279, _823281, _823283] : [-(c_New__DSequence_Opos__decr__bind(_823283, _823279, _823275, _823271) = c_New__DSequence_Opos__decr__bind(_823281, _823277, _823273, _823269)), _823283 = _823281, _823279 = _823277, _823275 = _823273, _823271 = _823269], (4036 ^ _779571) ^ [_841737, _841739, _841741, _841743] : [-(c_Relation_ORange(_841743, _841739) = c_Relation_ORange(_841741, _841737)), _841743 = _841741, _841739 = _841737], (12055 ^ _779571) ^ [_980553, _980555, _980557, _980559, _980561] : [class_Groups_Oordered__cancel__ab__semigroup__add(_980553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980553), _980555), _980557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980553), _980559), _980561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980553), _980555), _980559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980553), _980557), _980561))))], (27024 ^ _779571) ^ [_1255722, _1255724] : [27026 ^ _779571 : [(27029 ^ _779571) ^ [] : [hBOOL(hAPP(_1255724, 27025 ^ [_1255722, _1255724]))], (27027 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27025 ^ [_1255722, _1255724]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1255722))))]], 27030 ^ _779571 : [(27031 ^ _779571) ^ [_1255875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255875), _1255722)), -(hBOOL(hAPP(_1255724, _1255875)))]]], (8062 ^ _779571) ^ [_913180, _913182, _913184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913180), _913182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913180), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913182), _913184))))], (13643 ^ _779571) ^ [_1008237, _1008239, _1008241] : [class_Divides_Osemiring__div(_1008237), -(c_Divides_Odiv__class_Omod(_1008237, c_Divides_Odiv__class_Omod(_1008237, _1008239, _1008241), _1008241) = c_Divides_Odiv__class_Omod(_1008237, _1008239, _1008241))], (24279 ^ _779571) ^ [_1202667, _1202669, _1202671, _1202673] : [class_Orderings_Olinorder(_1202667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202667), _1202669), _1202671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202667), _1202669), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202667), _1202673), _1202671))))], (34843 ^ _779571) ^ [_1418244, _1418246, _1418248, _1418250, _1418252, _1418254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool)), _1418246), _1418248)), c_Wellfounded_Omax__ext(_1418244, _1418250))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool)), _1418252), _1418254)), c_Wellfounded_Omax__ext(_1418244, _1418250))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1418244, tc_HOL_Obool), tc_fun(_1418244, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418244, tc_HOL_Obool)), _1418246), _1418252)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418244, tc_HOL_Obool)), _1418248), _1418254))), c_Wellfounded_Omax__ext(_1418244, _1418250))))], (19397 ^ _779571) ^ [_1112200] : [-(c_Int_Osucc(c_Int_OBit0(_1112200)) = c_Int_OBit1(_1112200))], (458 ^ _779571) ^ [_786600, _786602, _786604, _786606, _786608, _786610, _786612, _786614] : [-(c_Wellfounded_Omax__extp(_786612, _786608, _786604, _786600)), c_Wellfounded_Omax__extp(_786614, _786610, _786606, _786602), _786614 = _786612, _786610 = _786608, _786606 = _786604, _786602 = _786600], (33693 ^ _779571) ^ [_1394928, _1394930, _1394932] : [class_Orderings_Olinorder(_1394928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394928), _1394930)), hBOOL(hAPP(hAPP(c_member(_1394928), _1394932), _1394930)), 33704 ^ _779571 : [(33711 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394928, tc_HOL_Obool)), _1394930), hAPP(hAPP(c_Set_Oinsert(_1394928), _1394932), c_Orderings_Obot__class_Obot(tc_fun(_1394928, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1394928, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1394928, c_Orderings_Oord__class_Omin(_1394928), _1394930) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1394928), _1394932), c_Big__Operators_Olattice_OInf__fin(_1394928, c_Orderings_Oord__class_Omin(_1394928), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394928, tc_HOL_Obool)), _1394930), hAPP(hAPP(c_Set_Oinsert(_1394928), _1394932), c_Orderings_Obot__class_Obot(tc_fun(_1394928, tc_HOL_Obool)))))))], (33705 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394928, tc_HOL_Obool)), _1394930), hAPP(hAPP(c_Set_Oinsert(_1394928), _1394932), c_Orderings_Obot__class_Obot(tc_fun(_1394928, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1394928, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1394928, c_Orderings_Oord__class_Omin(_1394928), _1394930) = _1394932)]]], (41207 ^ _779571) ^ [_1564379, _1564381, _1564383] : [-(hAPP(hAPP(c_Set_Oinsert(_1564379), _1564381), _1564383) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564379, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1564379), hAPP(hAPP(c_COMBC(_1564379, _1564379, tc_HOL_Obool), c_fequal), _1564381))), _1564383))], (42104 ^ _779571) ^ [_1593716, _1593718, _1593720, _1593722, _1593724] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593716, _1593718)), hAPP(hAPP(c_Product__Type_OPair(_1593716, _1593718), _1593720), _1593722)), _1593724)), -(hBOOL(hAPP(hAPP(c_member(_1593718), _1593722), hAPP(c_Relation_ORange(_1593716, _1593718), _1593724))))], (27145 ^ _779571) ^ [_1257988, _1257990, _1257992, _1257994, _1257996] : [class_Groups_Ocomm__monoid__add(_1257988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1257990), _1257992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1257992), _1257994)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257988), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257988), _1257996), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257990), _1257992))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257988), _1257996), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257992), _1257994))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257988), _1257996), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257990), _1257994)))], (9022 ^ _779571) ^ [_929072, _929074] : [class_Groups_Omonoid__mult(_929072), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929072), c_Groups_Oone__class_Oone(_929072)), _929074) = _929074)], (7957 ^ _779571) ^ [_911587, _911589] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911587), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911587), _911589)))))], (9506 ^ _779571) ^ [_937390, _937392, _937394] : [class_Groups_Ogroup__add(_937390), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937390), _937392), _937394) = c_Groups_Ozero__class_Ozero(_937390), -(hAPP(c_Groups_Ouminus__class_Ouminus(_937390), _937392) = _937394)], (27820 ^ _779571) ^ [_1272272, _1272274, _1272276] : [class_Lattices_Osemilattice__sup(_1272272), 27823 ^ _779571 : [(27830 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272272), _1272274), _1272276) = _1272276, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272272), _1272274), _1272276)))], (27824 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272272), _1272274), _1272276)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272272), _1272274), _1272276) = _1272276)]]], (47725 ^ _779571) ^ [_1731110, _1731112, _1731114, _1731116, _1731118, _1731120] : [-(hAPP(hAPP(c_List_Omap(_1731110, _1731112), _1731114), hAPP(hAPP(c_List_Olist__update(_1731110, _1731116), _1731118), _1731120)) = hAPP(hAPP(c_List_Olist__update(_1731112, hAPP(hAPP(c_List_Omap(_1731110, _1731112), _1731114), _1731116)), _1731118), hAPP(_1731114, _1731120)))], (36802 ^ _779571) ^ [_1464691, _1464693, _1464695] : [-(hAPP(c_Relation_OImage(_1464691, _1464691, c_Relation_OId__on(_1464691, _1464693)), _1464695) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464691, tc_HOL_Obool)), _1464693), _1464695))], (51339 ^ _779571) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (15638 ^ _779571) ^ [_1044914, _1044916, _1044918] : [class_Groups_Ogroup__add(_1044914), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044914), _1044916), _1044918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044914), _1044916), hAPP(c_Groups_Ouminus__class_Ouminus(_1044914), _1044918)))], (42839 ^ _779571) ^ [_1610895, _1610897] : [c_Wellfounded_Oacyclic(_1610895, _1610897), 42842 ^ _779571 : [(42843 ^ _779571) ^ [_1610980] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610895, _1610895)), hAPP(hAPP(c_Product__Type_OPair(_1610895, _1610895), _1610980), _1610980)), c_Transitive__Closure_Otrancl(_1610895, _1610897)))]]], (23517 ^ _779571) ^ [_1187966, _1187968] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1187966)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1187968)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1187968))), 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), _1187966)), c_Int_Onat)))))], (29150 ^ _779571) ^ [_1300241, _1300243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300241, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1300241, tc_HOL_Obool))), _1300243)))], (25854 ^ _779571) ^ [_1232438, _1232440, _1232442] : [class_Rings_Ocomm__ring__1(_1232438), 25857 ^ _779571 : [(25864 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232438), _1232440), _1232442)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232438), _1232440), hAPP(c_Groups_Ouminus__class_Ouminus(_1232438), _1232442))))], (25858 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232438), _1232440), hAPP(c_Groups_Ouminus__class_Ouminus(_1232438), _1232442))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232438), _1232440), _1232442)))]]], (27129 ^ _779571) ^ [_1257590, _1257592, _1257594, _1257596, _1257598] : [class_Groups_Ocomm__monoid__add(_1257590), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257590), _1257592), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257594), _1257596)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257598), _1257596))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1257590), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1257590, tc_Nat_Onat), _1257592), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1257596))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257594), _1257598)))], (13542 ^ _779571) ^ [_1006409, _1006411, _1006413] : [class_Lattices_Oboolean__algebra(_1006409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006409), _1006411), _1006413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006409), hAPP(c_Groups_Ouminus__class_Ouminus(_1006409), _1006413)), hAPP(c_Groups_Ouminus__class_Ouminus(_1006409), _1006411))))], (51657 ^ _779571) ^ [_1814233, _1814235] : [hBOOL(_1814233), -(hBOOL(hAPP(hAPP(c_fimplies, _1814235), _1814233)))], (16108 ^ _779571) ^ [_1054872, _1054874, _1054876, _1054878, _1054880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054872), _1054874)), 16111 ^ _779571 : [(16118 ^ _779571) ^ [] : [_1054878 = 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), _1054874), _1054872)), _1054876)), _1054880), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054872), _1054876)), _1054878) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054874), _1054876)), _1054880))], (16112 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054872), _1054876)), _1054878) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054874), _1054876)), _1054880), -(_1054878 = 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), _1054874), _1054872)), _1054876)), _1054880))]]], (46777 ^ _779571) ^ [_1707419, _1707421, _1707423, _1707425] : [c_List_Olistrelp(_1707419, hAPP(hAPP(c_COMBC(_1707419, tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_fun(_1707419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707419, tc_fun(tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_fun(_1707419, tc_HOL_Obool)), _1707419), c_COMBC(_1707419, tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707419, tc_prod(_1707419, _1707419)), tc_fun(_1707419, tc_fun(tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_HOL_Obool)), _1707419), hAPP(c_COMBB(tc_prod(_1707419, _1707419), tc_fun(tc_fun(tc_prod(_1707419, _1707419), tc_HOL_Obool), tc_HOL_Obool), _1707419), c_member(tc_prod(_1707419, _1707419)))), c_Product__Type_OPair(_1707419, _1707419)))), _1707421), _1707423, _1707425), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707419), tc_List_Olist(_1707419))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707419), tc_List_Olist(_1707419)), _1707423), _1707425)), c_List_Olistrel(_1707419, _1707421))))], (9136 ^ _779571) ^ [_930897, _930899] : [class_Groups_Olinordered__ab__group__add(_930897), 9139 ^ _779571 : [(9146 ^ _779571) ^ [] : [_930899 = c_Groups_Ozero__class_Ozero(_930897), -(_930899 = hAPP(c_Groups_Ouminus__class_Ouminus(_930897), _930899))], (9140 ^ _779571) ^ [] : [_930899 = hAPP(c_Groups_Ouminus__class_Ouminus(_930897), _930899), -(_930899 = c_Groups_Ozero__class_Ozero(_930897))]]], (14534 ^ _779571) ^ [_1024789, _1024791, _1024793, _1024795] : [class_Divides_Osemiring__div(_1024789), -(_1024791 = c_Groups_Ozero__class_Ozero(_1024789)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024789), _1024791), _1024793)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024789), _1024791), _1024795)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024789), _1024793), _1024795))], (18241 ^ _779571) ^ [_1093095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093095), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093095)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17379 ^ _779571) ^ [_1078455, _1078457, _1078459, _1078461] : [class_Groups_Omonoid__mult(_1078455), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078455), _1078457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078459), _1078461)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1078455), hAPP(hAPP(c_Power_Opower__class_Opower(_1078455), _1078457), _1078459)), _1078461))], (44590 ^ _779571) ^ [_1653831, _1653833, _1653835, _1653837, _1653839, _1653841] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653831, tc_fun(_1653833, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1653835, _1653831, _1653837), _1653839)), _1653841) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653835, tc_fun(_1653833, tc_HOL_Obool)), _1653839), hAPP(hAPP(c_COMBB(_1653831, tc_fun(_1653833, tc_HOL_Obool), _1653835), _1653841), _1653837)))], (28726 ^ _779571) ^ [_1289973, _1289975, _1289977, _1289979] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289973, _1289975)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289977, _1289979)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289977), _1289979)), 28729 ^ _779571 : [(28732 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289977), _1289973)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289975), _1289979)), 28739 ^ _779571 : [(28746 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289975), _1289979)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289979), _1289975)))], (28740 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289977), _1289973)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289973), _1289977)))]]], (28730 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289973), _1289975)))]]], (47212 ^ _779571) ^ [_1719182, _1719184, _1719186, _1719188] : [c_List_Olist_ONil(_1719182) = hAPP(hAPP(c_List_Omap(_1719184, _1719182), _1719186), _1719188), -(_1719188 = c_List_Olist_ONil(_1719184))], (2366 ^ _779571) ^ [_815292, _815294, _815296, _815298] : [-(c_Random_Olog(_815298, _815294) = c_Random_Olog(_815296, _815292)), _815298 = _815296, _815294 = _815292], (35440 ^ _779571) ^ [_1432840, _1432842, _1432844, _1432846, _1432848, _1432850] : [-(hAPP(hAPP(c_Fun_Ocomp(_1432840, _1432842, _1432844, hAPP(c_COMBK(_1432842, _1432840), _1432846)), _1432848), _1432850) = _1432846)], (51591 ^ _779571) ^ [] : [hBOOL(c_fFalse)], (39000 ^ _779571) ^ [_1513394, _1513396, _1513398, _1513400, _1513402] : [c_Typedef_Otype__definition(_1513394, _1513396, _1513398, _1513400, _1513402), -(hAPP(c_Set_Oimage(_1513394, _1513396, _1513398), c_Orderings_Otop__class_Otop(tc_fun(_1513394, tc_HOL_Obool))) = _1513402)], (47811 ^ _779571) ^ [_1733037, _1733039, _1733041, _1733043, _1733045] : [class_Orderings_Olinorder(_1733037), hBOOL(hAPP(hAPP(c_member(_1733037), hAPP(_1733039, _1733041)), hAPP(c_Set_Oimage(_1733043, _1733037, _1733039), hAPP(c_List_Oset(_1733043), _1733045)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1733043, _1733037, _1733039, _1733041, _1733045) = _1733045)], (48794 ^ _779571) ^ [_1758025, _1758027, _1758029, _1758031] : [-(hAPP(hAPP(c_List_Otake(_1758025), _1758027), hAPP(hAPP(c_List_Odrop(_1758025), _1758029), _1758031)) = hAPP(hAPP(c_List_Odrop(_1758025), _1758029), hAPP(hAPP(c_List_Otake(_1758025), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758027), _1758029)), _1758031)))], (44720 ^ _779571) ^ [_1657527, _1657529, _1657531, _1657533, _1657535] : [class_Complete__Lattice_Ocomplete__lattice(_1657527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657529, tc_HOL_Obool)), _1657531), _1657533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657527), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657529, _1657527), _1657533), _1657535)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657529, _1657527), _1657531), _1657535))))], (32187 ^ _779571) ^ [_1365276, _1365278, _1365280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365276)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1365278), _1365280)), 32194 ^ _779571 : [(32195 ^ _779571) ^ [_1365466] : [32197 ^ _779571 : [(32203 ^ _779571) ^ [] : [-(_1365466 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32199 ^ [_1365276, _1365278, _1365280, _1365466]), 32196 ^ [_1365276, _1365278, _1365280, _1365466]))], (32201 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32199 ^ [_1365276, _1365278, _1365280, _1365466]), _1365280)))], (32198 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32196 ^ [_1365276, _1365278, _1365280, _1365466]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1365276))))]], -(_1365466 = _1365278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1365466), _1365276) = _1365278]]], (12305 ^ _779571) ^ [_985049, _985051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985049)), _985051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985049), _985051)))], (43552 ^ _779571) ^ [_1629024, _1629026, _1629028] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629024, _1629024)), hAPP(hAPP(c_Product__Type_OPair(_1629024, _1629024), _1629026), _1629026)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629024, _1629024), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629028))))], (45345 ^ _779571) ^ [_1672045, _1672047] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672045, tc_HOL_Obool), _1672047) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1672045, tc_HOL_Obool), tc_fun(_1672045, tc_HOL_Obool)), _1672047), c_COMBI(tc_fun(_1672045, tc_HOL_Obool))))], (1632 ^ _779571) ^ [_802739, _802741] : [-(class_Orderings_Olinorder(_802739)), _802741 = _802739, class_Orderings_Olinorder(_802741)], (5230 ^ _779571) ^ [_860416, _860418] : [_860418 = _860416, -(c_Orderings_Oord__class_Omax(_860418) = c_Orderings_Oord__class_Omax(_860416))], (30754 ^ _779571) ^ [_1332471, _1332473, _1332475] : [hBOOL(hAPP(hAPP(c_member(_1332471), _1332473), _1332475)), -(hAPP(hAPP(c_Set_Oinsert(_1332471), _1332473), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332471, tc_HOL_Obool)), _1332475), hAPP(hAPP(c_Set_Oinsert(_1332471), _1332473), c_Orderings_Obot__class_Obot(tc_fun(_1332471, tc_HOL_Obool))))) = _1332475)], (20603 ^ _779571) ^ [_1133673, _1133675] : [class_Rings_Odivision__ring__inverse__zero(_1133673), 20606 ^ _779571 : [(20613 ^ _779571) ^ [] : [-(_1133675 = c_Groups_Ozero__class_Ozero(_1133673)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133673), _1133675), _1133675) = c_Groups_Oone__class_Oone(_1133673))], (20607 ^ _779571) ^ [] : [_1133675 = c_Groups_Ozero__class_Ozero(_1133673), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133673), _1133675), _1133675) = c_Groups_Ozero__class_Ozero(_1133673))]]], (30357 ^ _779571) ^ [_1324085, _1324087, _1324089] : [hBOOL(hAPP(hAPP(c_member(_1324085), _1324087), hAPP(c_fequal, _1324089))), -(_1324087 = _1324089)], (12620 ^ _779571) ^ [_990359, _990361, _990363, _990365] : [class_Rings_Olinordered__semiring__strict(_990359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990359), _990361), _990363)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990359), _990361), _990365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990359), c_Groups_Ozero__class_Ozero(_990359)), _990361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990359), _990363), _990365)))], (51295 ^ _779571) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51575 ^ _779571) ^ [_1813174, _1813176, _1813178, _1813180, _1813182, _1813184] : [-(hAPP(hAPP(hAPP(c_COMBC(_1813174, _1813176, _1813178), _1813180), _1813182), _1813184) = hAPP(hAPP(_1813180, _1813184), _1813182))], (39445 ^ _779571) ^ [_1522850, _1522852] : [-(hAPP(c_Set_Ovimage(_1522850, _1522850, c_COMBI(_1522850)), _1522852) = _1522852)], (18851 ^ _779571) ^ [_1102893] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1102893))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1102893)))))], (982 ^ _779571) ^ [_794614, _794616] : [-(class_Rings_Olinordered__semiring__1__strict(_794614)), _794616 = _794614, class_Rings_Olinordered__semiring__1__strict(_794616)], (22782 ^ _779571) ^ [_1174372, _1174374, _1174376] : [22784 ^ _779571 : [(22787 ^ _779571) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1174372, _1174374), 22783 ^ [_1174372, _1174374, _1174376]))], (22785 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1174374, 22783 ^ [_1174372, _1174374, _1174376]), _1174376)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1174372, _1174374), _1174376)))], (41852 ^ _779571) ^ [_1588446, _1588448, _1588450] : [c_Wellfounded_Owf(_1588446, _1588448), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588446, _1588446)), hAPP(hAPP(c_Product__Type_OPair(_1588446, _1588446), _1588450), _1588450)), _1588448))], (38461 ^ _779571) ^ [_1502209, _1502211, _1502213, _1502215, _1502217, _1502219] : [c_Fun_Oinj__on(_1502209, _1502211, hAPP(c_Fun_Ocomp(_1502213, _1502211, _1502209, _1502215), _1502217), _1502219), -(c_Fun_Oinj__on(_1502209, _1502213, _1502217, _1502219))], (13723 ^ _779571) ^ [_1009787, _1009789, _1009791, _1009793] : [class_Divides_Osemiring__div(_1009787), -(c_Divides_Odiv__class_Omod(_1009787, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009787), _1009789), _1009791), _1009793) = c_Divides_Odiv__class_Omod(_1009787, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009787), _1009789), c_Divides_Odiv__class_Omod(_1009787, _1009791, _1009793)), _1009793))], (40449 ^ _779571) ^ [_1547574, _1547576, _1547578] : [class_Lattices_Osemilattice__inf(_1547574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547574), _1547576)), -(_1547576 = c_Orderings_Obot__class_Obot(tc_fun(_1547574, tc_HOL_Obool))), 40460 ^ _779571 : [(40461 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1547574), _1547578), hAPP(c_Finite__Set_Ofold1(_1547574, c_Lattices_Osemilattice__inf__class_Oinf(_1547574)), _1547576))), 40464 ^ _779571 : [(40465 ^ _779571) ^ [_1547867] : [hBOOL(hAPP(hAPP(c_member(_1547574), _1547867), _1547576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1547574), _1547578), _1547867)))]]], (40471 ^ _779571) ^ [] : [40473 ^ _779571 : [(40476 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1547574), _1547578), 40472 ^ [_1547574, _1547576, _1547578]))], (40474 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547574), 40472 ^ [_1547574, _1547576, _1547578]), _1547576)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1547574), _1547578), hAPP(c_Finite__Set_Ofold1(_1547574, c_Lattices_Osemilattice__inf__class_Oinf(_1547574)), _1547576))))]]], (38703 ^ _779571) ^ [_1506700, _1506702, _1506704, _1506706, _1506708] : [c_Fun_Oinj__on(_1506700, _1506702, _1506704, c_Orderings_Otop__class_Otop(tc_fun(_1506700, tc_HOL_Obool))), 38706 ^ _779571 : [(38713 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1506700, tc_HOL_Obool)), _1506706), _1506708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1506702, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1506700, _1506702, _1506704), _1506706)), hAPP(c_Set_Oimage(_1506700, _1506702, _1506704), _1506708))))], (38707 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1506702, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1506700, _1506702, _1506704), _1506706)), hAPP(c_Set_Oimage(_1506700, _1506702, _1506704), _1506708))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1506700, tc_HOL_Obool)), _1506706), _1506708)))]]], (42266 ^ _779571) ^ [_1597613, _1597615, _1597617] : [_1597617 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1597613, _1597615), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1597613, _1597615), _1597617) = c_Orderings_Obot__class_Obot(tc_fun(_1597613, tc_HOL_Obool)))], (24339 ^ _779571) ^ [_1203934, _1203936] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1203934)), hAPP(c_Nat_OSuc, _1203936)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1203934), _1203936)))], (50447 ^ _779571) ^ [_1792907, _1792909, _1792911] : [class_Orderings_Olinorder(_1792907), hBOOL(hAPP(hAPP(c_member(_1792907), _1792909), hAPP(c_List_Oset(_1792907), _1792911))), c_List_Olinorder__class_Osorted(_1792907, _1792911), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1792907, _1792907, c_COMBI(_1792907)), _1792909), c_List_Oremove1(_1792907, _1792909, _1792911)) = _1792911)], (7115 ^ _779571) ^ [_896722, _896724, _896726, _896728, _896730] : [class_Rings_Ocomm__semiring__1(_896722), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), _896724), _896726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), _896728), _896730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), _896724), _896728)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896722), _896726), _896730)))], (28218 ^ _779571) ^ [_1280070, _1280072, _1280074, _1280076] : [class_Orderings_Olinorder(_1280070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280070), _1280072), _1280074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280070), _1280074), _1280076)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280070, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1280070, _1280072), _1280074)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1280070, _1280074), _1280076)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1280070, _1280072), _1280076))], (51399 ^ _779571) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (4638 ^ _779571) ^ [_851318, _851320, _851322, _851324] : [-(c_Big__Operators_Olinorder__class_OMin(_851324, _851320) = c_Big__Operators_Olinorder__class_OMin(_851322, _851318)), _851324 = _851322, _851320 = _851318], (22832 ^ _779571) ^ [_1175337, _1175339] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175337, _1175339), c_Divides_Odivmod__nat(_1175337, _1175339))))], (1552 ^ _779571) ^ [_801739, _801741] : [-(class_Groups_Ocomm__monoid__add(_801739)), _801741 = _801739, class_Groups_Ocomm__monoid__add(_801741)], (49126 ^ _779571) ^ [_1765288, _1765290, _1765292, _1765294, _1765296] : [-(c_List_Olist_Olist__size(_1765288, _1765290, hAPP(hAPP(c_List_Omap(_1765292, _1765288), _1765294), _1765296)) = c_List_Olist_Olist__size(_1765292, hAPP(c_Fun_Ocomp(_1765288, tc_Nat_Onat, _1765292, _1765290), _1765294), _1765296))], (35617 ^ _779571) ^ [_1437743, _1437745, _1437747, _1437749, _1437751] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1437743, _1437745, _1437747), _1437749), _1437751))), hBOOL(hAPP(hAPP(_1437745, _1437749), _1437751)), hBOOL(hAPP(_1437747, _1437751))], (22170 ^ _779571) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (42315 ^ _779571) ^ [_1598840, _1598842] : [c_Wellfounded_OwfP(_1598840, hAPP(hAPP(c_COMBC(_1598840, tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_fun(_1598840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598840, tc_fun(tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_fun(_1598840, tc_HOL_Obool)), _1598840), c_COMBC(_1598840, tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598840, tc_prod(_1598840, _1598840)), tc_fun(_1598840, tc_fun(tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_HOL_Obool)), _1598840), hAPP(c_COMBB(tc_prod(_1598840, _1598840), tc_fun(tc_fun(tc_prod(_1598840, _1598840), tc_HOL_Obool), tc_HOL_Obool), _1598840), c_member(tc_prod(_1598840, _1598840)))), c_Product__Type_OPair(_1598840, _1598840)))), _1598842)), -(c_Wellfounded_Owf(_1598840, _1598842))], (6993 ^ _779571) ^ [_894860, _894862] : [class_Groups_Olinordered__ab__group__add(_894860), 6996 ^ _779571 : [(7003 ^ _779571) ^ [] : [_894862 = c_Groups_Ozero__class_Ozero(_894860), -(c_Groups_Ozero__class_Ozero(_894860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894860), _894862), _894862))], (6997 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_894860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894860), _894862), _894862), -(_894862 = c_Groups_Ozero__class_Ozero(_894860))]]], (19463 ^ _779571) ^ [_1113439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1113439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1113439))))], (50445 ^ _779571) ^ [_1792872] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1792872) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1792872))))], (43817 ^ _779571) ^ [_1635851, _1635853, _1635855, _1635857, _1635859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635851, _1635851)), hAPP(hAPP(c_Product__Type_OPair(_1635851, _1635851), _1635853), _1635855)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1635851, _1635851), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1635857)), _1635859))), 43821 ^ _779571 : [(43824 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635851, _1635851)), hAPP(hAPP(c_Product__Type_OPair(_1635851, _1635851), 43820 ^ [_1635851, _1635853, _1635855, _1635857, _1635859]), _1635855)), _1635859)))], (43822 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635851, _1635851)), hAPP(hAPP(c_Product__Type_OPair(_1635851, _1635851), _1635853), 43820 ^ [_1635851, _1635853, _1635855, _1635857, _1635859])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1635851, _1635851), tc_HOL_Obool), _1635857), _1635859))))]]], (5148 ^ _779571) ^ [_859117, _859119, _859121, _859123] : [-(c_List_Orotate(_859123, _859119) = c_List_Orotate(_859121, _859117)), _859123 = _859121, _859119 = _859117], (21317 ^ _779571) ^ [_1146346, _1146348] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146346), _1146348), hAPP(c_Int_Onumber__class_Onumber__of(_1146346), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1146346)), class_Fields_Ofield__inverse__zero(_1146346), class_Int_Onumber__ring(_1146346)], (48419 ^ _779571) ^ [_1747579, _1747581, _1747583, _1747585, _1747587, _1747589, _1747591] : [-(hBOOL(hAPP(hAPP(c_member(_1747579), _1747581), hAPP(c_List_Oset(_1747579), _1747583)))), -(c_Map_Omap__upds(_1747579, _1747585, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1747579, tc_Option_Ooption(_1747585)), _1747587), _1747581), hAPP(c_Option_Ooption_OSome(_1747585), _1747589)), _1747583, _1747591) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1747579, tc_Option_Ooption(_1747585)), c_Map_Omap__upds(_1747579, _1747585, _1747587, _1747583, _1747591)), _1747581), hAPP(c_Option_Ooption_OSome(_1747585), _1747589)))], (47536 ^ _779571) ^ [_1726429, _1726431, _1726433] : [-(_1726429 = _1726431), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726433)), _1726429) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726433)), _1726431), 47542 ^ _779571 : [(47545 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Onth(_1726433), _1726429), 47541 ^ [_1726429, _1726431, _1726433]) = hAPP(hAPP(c_List_Onth(_1726433), _1726431), 47541 ^ [_1726429, _1726431, _1726433])], (47543 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47541 ^ [_1726429, _1726431, _1726433]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726433)), _1726429))))]]], (18075 ^ _779571) ^ [_1090725] : [class_Int_Onumber__ring(_1090725), c_Int_Oiszero(_1090725, hAPP(c_Int_Onumber__class_Onumber__of(_1090725), c_Int_OMin))], (28655 ^ _779571) ^ [_1288565, _1288567, _1288569] : [class_Orderings_Olinorder(_1288565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288565), _1288567), _1288569)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288565, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1288565), _1288567)), c_SetInterval_Oord__class_OatLeastAtMost(_1288565, _1288567, _1288569)) = hAPP(c_SetInterval_Oord__class_OatMost(_1288565), _1288569))], (45897 ^ _779571) ^ [_1684761, _1684763, _1684765, _1684767, _1684769, _1684771, _1684773] : [-(c_Map_Omap__comp(_1684761, _1684763, _1684765, _1684767, _1684769, _1684771) = hAPP(c_Option_Ooption_OSome(_1684763), _1684773)), 45898 ^ _779571 : [(45899 ^ _779571) ^ [_1684839] : [hAPP(_1684769, _1684771) = hAPP(c_Option_Ooption_OSome(_1684761), _1684839), hAPP(_1684767, _1684839) = hAPP(c_Option_Ooption_OSome(_1684763), _1684773)]]], (22530 ^ _779571) ^ [_1169378, _1169380, _1169382] : [class_Int_Onumber__ring(_1169378), 22533 ^ _779571 : [(22540 ^ _779571) ^ [] : [-(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), _1169380)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1169378), hAPP(c_Int_Onumber__class_Onumber__of(_1169378), _1169382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1169380))) = c_Groups_Oone__class_Oone(_1169378))], (22534 ^ _779571) ^ [] : [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), _1169380))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1169378), hAPP(c_Int_Onumber__class_Onumber__of(_1169378), _1169382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1169380))) = hAPP(hAPP(c_HOL_OLet(_1169378, _1169378), hAPP(hAPP(c_Power_Opower__class_Opower(_1169378), hAPP(c_Int_Onumber__class_Onumber__of(_1169378), _1169382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169380))), hAPP(hAPP(c_COMBS(_1169378, _1169378, _1169378), hAPP(hAPP(c_COMBB(_1169378, tc_fun(_1169378, _1169378), _1169378), c_Groups_Otimes__class_Otimes(_1169378)), hAPP(c_Groups_Otimes__class_Otimes(_1169378), hAPP(c_Int_Onumber__class_Onumber__of(_1169378), _1169382)))), c_COMBI(_1169378))))]]], (8028 ^ _779571) ^ [_912688, _912690, _912692] : [class_Rings_Olinordered__idom(_912688), -(_912690 = _912692), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912688), _912690), _912692))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912688), _912692), _912690)))], (33943 ^ _779571) ^ [_1399176, _1399178, _1399180] : [class_Orderings_Olinorder(_1399176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399176), _1399178)), 33950 ^ _779571 : [(33957 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399176, tc_HOL_Obool)), _1399178), hAPP(hAPP(c_Set_Oinsert(_1399176), _1399180), c_Orderings_Obot__class_Obot(tc_fun(_1399176, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1399176, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1399176, c_Orderings_Oord__class_Omin(_1399176), hAPP(hAPP(c_Set_Oinsert(_1399176), _1399180), _1399178)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1399176), _1399180), c_Big__Operators_Olattice_OInf__fin(_1399176, c_Orderings_Oord__class_Omin(_1399176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399176, tc_HOL_Obool)), _1399178), hAPP(hAPP(c_Set_Oinsert(_1399176), _1399180), c_Orderings_Obot__class_Obot(tc_fun(_1399176, tc_HOL_Obool)))))))], (33951 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399176, tc_HOL_Obool)), _1399178), hAPP(hAPP(c_Set_Oinsert(_1399176), _1399180), c_Orderings_Obot__class_Obot(tc_fun(_1399176, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1399176, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1399176, c_Orderings_Oord__class_Omin(_1399176), hAPP(hAPP(c_Set_Oinsert(_1399176), _1399180), _1399178)) = _1399180)]]], (49048 ^ _779571) ^ [_1763555, _1763557, _1763559] : [-(hAPP(hAPP(c_List_Otake(_1763555), _1763557), hAPP(c_List_Otl(_1763555), _1763559)) = hAPP(c_List_Otl(_1763555), hAPP(hAPP(c_List_Otake(_1763555), hAPP(c_Nat_OSuc, _1763557)), _1763559)))], (13228 ^ _779571) ^ [_1001002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001002)), -(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)), _1001002))))], (20 ^ _779571) ^ [_779831, _779833, _779835, _779837] : [-(c_Option_Ois__none(_779835, _779831)), c_Option_Ois__none(_779837, _779833), _779837 = _779835, _779833 = _779831], (46284 ^ _779571) ^ [_1693950, _1693952] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1693950, _1693952) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1693950, _1693952)))], (21077 ^ _779571) ^ [_1142300, _1142302, _1142304, _1142306] : [class_Fields_Ofield__inverse__zero(_1142300), -(_1142302 = c_Groups_Ozero__class_Ozero(_1142300)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142300), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142300), _1142304), _1142302)), _1142306) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142300), _1142304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142300), _1142306), _1142302))), _1142302))], (46843 ^ _779571) ^ [_1709618, _1709620, _1709622, _1709624, _1709626] : [hAPP(hAPP(c_List_Olist_OCons(_1709618), _1709620), _1709622) = hAPP(hAPP(c_List_Olist_OCons(_1709618), _1709624), _1709626), 46846 ^ _779571 : [(46849 ^ _779571) ^ [] : [-(_1709622 = _1709626)], (46847 ^ _779571) ^ [] : [-(_1709620 = _1709624)]]], (41289 ^ _779571) ^ [_1567638, _1567640, _1567642, _1567644, _1567646, _1567648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567638), _1567640)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567642), _1567644)), 41299 ^ _779571 : [(41302 ^ _779571) ^ [] : [hAPP(c_Finite__Set_Ocard(_1567638), hAPP(c_Set_OCollect(_1567638), hAPP(hAPP(c_COMBS(_1567638, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567638), c_fconj), hAPP(hAPP(c_COMBC(_1567638, tc_fun(_1567638, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567638)), _1567640))), hAPP(hAPP(c_COMBC(_1567638, _1567642, tc_HOL_Obool), _1567646), 41298 ^ [_1567638, _1567640, _1567642, _1567644, _1567646, _1567648])))) = _1567648], (41300 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567642), 41298 ^ [_1567638, _1567640, _1567642, _1567644, _1567646, _1567648]), _1567644)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1567638, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1567642, tc_HOL_Obool), tc_Nat_Onat, _1567638), c_Finite__Set_Ocard(_1567642)), hAPP(hAPP(c_COMBB(tc_fun(_1567642, tc_HOL_Obool), tc_fun(_1567642, tc_HOL_Obool), _1567638), c_Set_OCollect(_1567642)), hAPP(hAPP(c_COMBB(tc_fun(_1567642, tc_HOL_Obool), tc_fun(_1567642, tc_HOL_Obool), _1567638), hAPP(c_COMBS(_1567642, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567642), c_fconj), hAPP(hAPP(c_COMBC(_1567642, tc_fun(_1567642, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567642)), _1567644)))), _1567646)))), _1567640) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1567648), hAPP(c_Finite__Set_Ocard(_1567642), _1567644)))], (29710 ^ _779571) ^ [_1310635, _1310637, _1310639, _1310641, _1310643] : [-(_1310635 = c_Orderings_Obot__class_Obot(tc_fun(_1310637, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310637, tc_fun(_1310639, tc_HOL_Obool)), _1310635), hAPP(hAPP(c_COMBC(_1310637, tc_fun(_1310639, tc_HOL_Obool), tc_fun(_1310639, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310639, tc_HOL_Obool), tc_fun(tc_fun(_1310639, tc_HOL_Obool), tc_fun(_1310639, tc_HOL_Obool)), _1310637), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310639, tc_HOL_Obool))), _1310641)), _1310643)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310639, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310637, tc_fun(_1310639, tc_HOL_Obool)), _1310635), _1310641)), _1310643))], (8580 ^ _779571) ^ [_921496, _921498, _921500] : [class_Orderings_Olinorder(_921496), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921496), _921498), _921500))), 8587 ^ _779571 : [(8594 ^ _779571) ^ [] : [_921500 = _921498, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921496), _921500), _921498))], (8588 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921496), _921500), _921498))), -(_921500 = _921498)]]], (24051 ^ _779571) ^ [_1198289, _1198291] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198289)), _1198291) = 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), _1198289)), _1198291))], (32885 ^ _779571) ^ [_1379598, _1379600] : [class_Rings_Oring__1(_1379598), hBOOL(hAPP(hAPP(c_member(_1379598), _1379600), c_Int_Oring__1__class_OInts(_1379598))), -(hBOOL(hAPP(hAPP(c_member(_1379598), hAPP(c_Groups_Ouminus__class_Ouminus(_1379598), _1379600)), c_Int_Oring__1__class_OInts(_1379598))))], (22178 ^ _779571) ^ [_1162321, _1162323] : [_1162321 = _1162323, -(c_Code__Numeral_OSuc__code__numeral(_1162321) = c_Code__Numeral_OSuc__code__numeral(_1162323))], (35217 ^ _779571) ^ [_1427911, _1427913, _1427915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427911, tc_HOL_Obool)), _1427913), _1427915)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1427911, tc_HOL_Obool)), _1427913), hAPP(c_Set_OPow(_1427911), _1427915))))], (3850 ^ _779571) ^ [_838960, _838962] : [_838962 = _838960, -(c_New__Random__Sequence_Opos__single(_838962) = c_New__Random__Sequence_Opos__single(_838960))], (8314 ^ _779571) ^ [_917604, _917606, _917608] : [class_Orderings_Olinorder(_917604), 8317 ^ _779571 : [(8318 ^ _779571) ^ [] : [-(_917606 = _917608), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917604), _917606), _917608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917604), _917608), _917606)))], (8328 ^ _779571) ^ [] : [8329 ^ _779571 : [(8332 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917604), _917608), _917606))], (8330 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917604), _917606), _917608))]], _917606 = _917608]]], (41191 ^ _779571) ^ [_1564070, _1564072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564070), hAPP(c_Set_OCollect(_1564070), _1564072))), 41194 ^ _779571 : [(41201 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564070), c_Orderings_Otop__class_Otop(tc_fun(_1564070, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564070), hAPP(c_Set_OCollect(_1564070), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564070), c_fNot), _1564072)))))], (41195 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564070), hAPP(c_Set_OCollect(_1564070), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564070), c_fNot), _1564072)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564070), c_Orderings_Otop__class_Otop(tc_fun(_1564070, tc_HOL_Obool)))))]]], (19327 ^ _779571) ^ [_1111057] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1111057)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1111057)))], (20427 ^ _779571) ^ [_1130874, _1130876, _1130878, _1130880] : [class_Fields_Ofield__inverse__zero(_1130874), 20430 ^ _779571 : [(20431 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130874), _1130876), _1130878) = _1130880, 20434 ^ _779571 : [(20441 ^ _779571) ^ [] : [_1130878 = c_Groups_Ozero__class_Ozero(_1130874), -(_1130880 = c_Groups_Ozero__class_Ozero(_1130874))], (20435 ^ _779571) ^ [] : [-(_1130878 = c_Groups_Ozero__class_Ozero(_1130874)), -(_1130876 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130874), _1130880), _1130878))]]], (20447 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130874), _1130876), _1130878) = _1130880), 20450 ^ _779571 : [(20453 ^ _779571) ^ [] : [_1130876 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130874), _1130880), _1130878)], (20451 ^ _779571) ^ [] : [_1130878 = c_Groups_Ozero__class_Ozero(_1130874)]], 20454 ^ _779571 : [(20457 ^ _779571) ^ [] : [_1130880 = c_Groups_Ozero__class_Ozero(_1130874)], (20455 ^ _779571) ^ [] : [-(_1130878 = c_Groups_Ozero__class_Ozero(_1130874))]]]]], (16312 ^ _779571) ^ [_1058574, _1058576, _1058578] : [16314 ^ _779571 : [(16319 ^ _779571) ^ [] : [hBOOL(hAPP(_1058576, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16313 ^ [_1058574, _1058576, _1058578]), _1058574)))], (16317 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1058576, 16313 ^ [_1058574, _1058576, _1058578])))], (16315 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16313 ^ [_1058574, _1058576, _1058578]), _1058574)))]], hBOOL(hAPP(_1058576, _1058578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058578), _1058574)), -(hBOOL(hAPP(_1058576, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43054 ^ _779571) ^ [_1616842, _1616844, _1616846] : [-(c_Transitive__Closure_Ortrancl(_1616842, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616842, _1616842), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616842, _1616844)), c_Transitive__Closure_Ortrancl(_1616842, _1616846))) = c_Transitive__Closure_Ortrancl(_1616842, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616842, _1616842), tc_HOL_Obool)), _1616844), _1616846)))], (10269 ^ _779571) ^ [_950633, _950635, _950637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950633), _950635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950637), _950633)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950637), _950635))))], (18269 ^ _779571) ^ [_1093506, _1093508] : [class_Int_Onumber__ring(_1093506), 18272 ^ _779571 : [(18279 ^ _779571) ^ [] : [c_Int_Oiszero(_1093506, hAPP(c_Int_Onumber__class_Onumber__of(_1093506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093508)))), -(c_Groups_Ozero__class_Ozero(_1093506) = hAPP(c_Int_Onumber__class_Onumber__of(_1093506), _1093508))], (18273 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_1093506) = hAPP(c_Int_Onumber__class_Onumber__of(_1093506), _1093508), -(c_Int_Oiszero(_1093506, hAPP(c_Int_Onumber__class_Onumber__of(_1093506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093508)))))]]], (44690 ^ _779571) ^ [_1656386, _1656388, _1656390] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656386, tc_fun(_1656388, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1656386, tc_HOL_Obool))), _1656390) = c_Orderings_Otop__class_Otop(tc_fun(_1656388, tc_HOL_Obool)))], (42048 ^ _779571) ^ [_1592474, _1592476, _1592478, _1592480] : [c_Wellfounded_Owf(_1592474, _1592476), c_Fun_Oinj__on(_1592474, _1592478, _1592480, c_Orderings_Otop__class_Otop(tc_fun(_1592474, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1592478, hAPP(c_Set_Oimage(tc_prod(_1592474, _1592474), tc_prod(_1592478, _1592478), c_Product__Type_Omap__pair(_1592474, _1592478, _1592474, _1592478, _1592480, _1592480)), _1592476)))], (7955 ^ _779571) ^ [_911548, _911550] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911548), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911550), _911548)))))], (45197 ^ _779571) ^ [_1668783, _1668785] : [class_Complete__Lattice_Ocomplete__lattice(_1668783), -(c_Complete__Lattice_OInf__class_OInf(_1668783, hAPP(hAPP(c_Set_Oinsert(_1668783), _1668785), c_Orderings_Obot__class_Obot(tc_fun(_1668783, tc_HOL_Obool)))) = _1668785)], (24611 ^ _779571) ^ [_1209204, _1209206, _1209208, _1209210] : [class_Orderings_Olinorder(_1209204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209204), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209204), _1209206), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209204), _1209208), _1209210))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209204), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209204), _1209206), _1209208)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209204), _1209206), _1209210)))))], (41720 ^ _779571) ^ [_1583942, _1583944, _1583946, _1583948] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583942, _1583944, _1583946), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583942, _1583944), tc_HOL_Obool))), _1583948) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583942, _1583946), tc_HOL_Obool)))], (9090 ^ _779571) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24135 ^ _779571) ^ [_1199961, _1199963, _1199965] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199961, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199961, tc_HOL_Obool)), _1199963), _1199965)), _1199965) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199961, tc_HOL_Obool)), _1199963), _1199965))], (29786 ^ _779571) ^ [_1312142, _1312144] : [class_Orderings_Olinorder(_1312142), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312142, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1312142), _1312144)), hAPP(hAPP(c_Set_Oinsert(_1312142), _1312144), c_Orderings_Obot__class_Obot(tc_fun(_1312142, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1312142), _1312144))], (51207 ^ _779571) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (13194 ^ _779571) ^ [_1000420, _1000422] : [-(hAPP(c_Int_Onat, _1000420) = _1000422), 13197 ^ _779571 : [(13200 ^ _779571) ^ [] : [_1000420 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1000422)], (13198 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000420)))]], 13201 ^ _779571 : [(13204 ^ _779571) ^ [] : [_1000422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13202 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000420))]]], (632 ^ _779571) ^ [_789393, _789395, _789397, _789399] : [-(c_Wellfounded_OwfP(_789397, _789393)), c_Wellfounded_OwfP(_789399, _789395), _789399 = _789397, _789395 = _789393], (45227 ^ _779571) ^ [_1669290, _1669292, _1669294] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669290, tc_HOL_Obool)), _1669292), _1669294) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669290, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1669290, tc_HOL_Obool)), _1669292), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1669290, tc_HOL_Obool)), _1669294), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1669290, tc_HOL_Obool), tc_HOL_Obool))))))], (45221 ^ _779571) ^ [_1669169, _1669171, _1669173] : [class_Complete__Lattice_Ocomplete__lattice(_1669169), -(c_Complete__Lattice_OInf__class_OInf(_1669169, hAPP(hAPP(c_Set_Oinsert(_1669169), _1669171), _1669173)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1669169), _1669171), c_Complete__Lattice_OInf__class_OInf(_1669169, _1669173)))], (51181 ^ _779571) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (27728 ^ _779571) ^ [_1270426, _1270428, _1270430, _1270432] : [class_Lattices_Osemilattice__sup(_1270426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270426), _1270428), _1270430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270426), _1270428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270426), _1270430), _1270432))))], (5785 ^ _779571) ^ [_872243, _872245, _872247, _872249, _872251, _872253] : [hBOOL(hAPP(_872243, _872245)), c_Natural_Oevaln(_872247, _872245, _872249, _872251), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_872243, _872247, _872253), _872245, _872249, _872251))], (14866 ^ _779571) ^ [_1030253, _1030255, _1030257] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030253), _1030255)), _1030257) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030253), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030255), _1030257))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030253), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030255, _1030257))), _1030257)))], (17593 ^ _779571) ^ [_1082383, _1082385, _1082387] : [class_Rings_Olinordered__semidom(_1082383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082383), c_Groups_Oone__class_Oone(_1082383)), _1082385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082383), hAPP(hAPP(c_Power_Opower__class_Opower(_1082383), _1082385), _1082387)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082383), _1082385), hAPP(hAPP(c_Power_Opower__class_Opower(_1082383), _1082385), _1082387)))))], (44432 ^ _779571) ^ [_1648582, _1648584, _1648586, _1648588] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1648586), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648582, tc_fun(_1648586, tc_HOL_Obool)), _1648584), _1648588)))), 44433 ^ _779571 : [(44434 ^ _779571) ^ [_1648656] : [hBOOL(hAPP(hAPP(c_member(_1648582), _1648656), _1648584)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648586), hAPP(_1648588, _1648656)))]]], (15698 ^ _779571) ^ [_1046038, _1046040] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046038), _1046040)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43315 ^ _779571) ^ [_1623132, _1623134] : [-(c_Transitive__Closure_Ortrancl(_1623132, hAPP(c_Relation_Oconverse(_1623132, _1623132), _1623134)) = hAPP(c_Relation_Oconverse(_1623132, _1623132), c_Transitive__Closure_Ortrancl(_1623132, _1623134)))], (31806 ^ _779571) ^ [_1356873, _1356875, _1356877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1356873), _1356875)), -(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(_1356873), _1356877)), hAPP(c_Finite__Set_Ocard(_1356873), _1356875))), hAPP(c_Finite__Set_Ocard(_1356873), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356873, tc_HOL_Obool)), _1356877), _1356875)))))], (49068 ^ _779571) ^ [_1764035, _1764037, _1764039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764035)), _1764037)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1764035, _1764039), _1764037) = _1764037)], (25024 ^ _779571) ^ [_1218371, _1218373, _1218375] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218371), _1218373)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218371), _1218375))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1218371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218373), _1218375)))], (33817 ^ _779571) ^ [_1397142, _1397144, _1397146] : [class_Orderings_Olinorder(_1397142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397142), _1397144)), -(_1397146 = c_Orderings_Obot__class_Obot(tc_fun(_1397142, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397142, tc_HOL_Obool)), _1397146), _1397144)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1397142), c_Big__Operators_Olattice_OSup__fin(_1397142, c_Orderings_Oord__class_Omax(_1397142), _1397146)), c_Big__Operators_Olattice_OSup__fin(_1397142, c_Orderings_Oord__class_Omax(_1397142), _1397144)) = c_Big__Operators_Olattice_OSup__fin(_1397142, c_Orderings_Oord__class_Omax(_1397142), _1397144))], (11445 ^ _779571) ^ [_969585, _969587, _969589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969585), _969587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969585), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969587), _969589))))], (42419 ^ _779571) ^ [_1601605, _1601607, _1601609, _1601611] : [-(c_New__Random__Sequence_Opos__map(_1601605, _1601607, _1601609, _1601611) = c_New__Random__Sequence_Opos__bind(_1601605, _1601607, _1601611, hAPP(c_Fun_Ocomp(_1601607, 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(_1601607))))), _1601605, c_New__Random__Sequence_Opos__single(_1601607)), _1601609)))], (6807 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48930 ^ _779571) ^ [_1761637, _1761639, _1761641] : [-(_1761637 = c_List_Olist_ONil(_1761639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761641), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761639)), _1761637))), -(hAPP(c_List_Ohd(_1761639), hAPP(hAPP(c_List_Odrop(_1761639), _1761641), _1761637)) = hAPP(hAPP(c_List_Onth(_1761639), _1761637), _1761641))], (22107 ^ _779571) ^ [_1161259, _1161261, _1161263] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1161259, _1161261, _1161263, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1161261)], (25628 ^ _779571) ^ [_1228314, _1228316, _1228318, _1228320] : [class_Divides_Osemiring__div(_1228314), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228314), _1228316), _1228318)), -(c_Divides_Odiv__class_Omod(_1228314, c_Divides_Odiv__class_Omod(_1228314, _1228320, _1228318), _1228316) = c_Divides_Odiv__class_Omod(_1228314, _1228320, _1228316))], (12491 ^ _779571) ^ [_988049, _988051, _988053, _988055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988049), _988051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988053), _988055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _988049), _988053)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _988051), _988055))))], (5208 ^ _779571) ^ [_860027, _860029, _860031, _860033, _860035, _860037, _860039, _860041, _860043, _860045] : [-(c_List_Ofoldr(_860045, _860041, _860037, _860033, _860029) = c_List_Ofoldr(_860043, _860039, _860035, _860031, _860027)), _860045 = _860043, _860041 = _860039, _860037 = _860035, _860033 = _860031, _860029 = _860027], (14399 ^ _779571) ^ [_1022601, _1022603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022603)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1022601)), hAPP(c_Int_Onat, _1022603)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022601), _1022603)))], (48826 ^ _779571) ^ [_1758839, _1758841, _1758843, _1758845] : [-(_1758839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1758841), _1758839), hAPP(hAPP(c_List_Olist_OCons(_1758841), _1758843), _1758845)) = hAPP(hAPP(c_List_Odrop(_1758841), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1758839), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1758845))], (46170 ^ _779571) ^ [] : [46172 ^ _779571 : [(46175 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 46171 ^ []))], (46173 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 46171 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (13874 ^ _779571) ^ [_1012733, _1012735] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012733, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1012735)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012733, _1012735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (406 ^ _779571) ^ [_785710, _785712, _785714, _785716, _785718, _785720, _785722, _785724, _785726, _785728] : [-(c_Finite__Set_Ofolding__image(_785726, _785722, _785718, _785714, _785710)), c_Finite__Set_Ofolding__image(_785728, _785724, _785720, _785716, _785712), _785728 = _785726, _785724 = _785722, _785720 = _785718, _785716 = _785714, _785712 = _785710], (44938 ^ _779571) ^ [_1662749, _1662751, _1662753, _1662755] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662749, tc_fun(_1662751, tc_HOL_Obool)), _1662753), _1662755) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1662751, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662749, tc_fun(_1662751, tc_HOL_Obool), _1662755), _1662753)))], (19333 ^ _779571) ^ [_1111188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111188)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111188), c_Int_OMin)))], (8872 ^ _779571) ^ [_926549, _926551, _926553] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926549), _926551)), _926553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926551), _926553)))], (30959 ^ _779571) ^ [_1336983, _1336985] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1336983, _1336985))))], (30714 ^ _779571) ^ [_1331290, _1331292, _1331294, _1331296, _1331298] : [class_Complete__Lattice_Ocomplete__lattice(_1331290), hBOOL(hAPP(hAPP(c_member(_1331292), _1331294), _1331296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331290), hAPP(_1331298, _1331294)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331292, _1331290), _1331296), _1331298))))], (42858 ^ _779571) ^ [_1611260, _1611262] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611260, _1611260), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1611260, _1611262)), hAPP(hAPP(c_Product__Type_OSigma(_1611260, _1611260), hAPP(c_Relation_OField(_1611260), _1611262)), hAPP(c_COMBK(tc_fun(_1611260, tc_HOL_Obool), _1611260), hAPP(c_Relation_OField(_1611260), _1611262))))))], (49714 ^ _779571) ^ [_1778162, _1778164, _1778166] : [-(hAPP(c_List_Oset(_1778162), hAPP(c_List_Ofilter(_1778162, _1778164), _1778166)) = hAPP(c_Set_OCollect(_1778162), hAPP(hAPP(c_COMBS(_1778162, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1778162), c_fconj), hAPP(hAPP(c_COMBC(_1778162, tc_fun(_1778162, tc_HOL_Obool), tc_HOL_Obool), c_member(_1778162)), hAPP(c_List_Oset(_1778162), _1778166)))), _1778164)))], (28611 ^ _779571) ^ [_1287679, _1287681] : [class_Orderings_Olinorder(_1287679), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1287679, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1287679), _1287681)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1287679), _1287681))], (17477 ^ _779571) ^ [_1080162, _1080164] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1080162), c_Groups_Ozero__class_Ozero(_1080162)), hAPP(c_Nat_OSuc, _1080164)) = c_Groups_Ozero__class_Ozero(_1080162)), class_Power_Opower(_1080162), class_Rings_Osemiring__0(_1080162)], (46903 ^ _779571) ^ [_1710845, _1710847, _1710849] : [-(hBOOL(hAPP(c_List_Odistinct(_1710845), hAPP(hAPP(c_List_Olist_OCons(_1710845), _1710847), _1710849)))), -(hBOOL(hAPP(hAPP(c_member(_1710845), _1710847), hAPP(c_List_Oset(_1710845), _1710849)))), hBOOL(hAPP(c_List_Odistinct(_1710845), _1710849))], (14768 ^ _779571) ^ [_1028494, _1028496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14771 ^ _779571 : [(14778 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028496), 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), _1028496), _1028494))))], (14772 ^ _779571) ^ [] : [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), _1028496), _1028494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4648 ^ _779571) ^ [_851467, _851469, _851471, _851473] : [-(c_Big__Operators_Olinorder__class_OMax(_851473, _851469) = c_Big__Operators_Olinorder__class_OMax(_851471, _851467)), _851473 = _851471, _851469 = _851467], (42085 ^ _779571) ^ [_1593318, _1593320, _1593322] : [c_Wellfounded_Owf(_1593318, _1593320), -(c_Wellfounded_Owf(tc_List_Olist(_1593318), hAPP(c_List_Olexn(_1593318, _1593320), _1593322)))], (9662 ^ _779571) ^ [_940116, _940118, _940120] : [class_Rings_Olinordered__semiring__strict(_940116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940116), c_Groups_Ozero__class_Ozero(_940116)), _940118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940116), _940120), c_Groups_Ozero__class_Ozero(_940116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940116), _940118), _940120)), c_Groups_Ozero__class_Ozero(_940116))))], (12511 ^ _779571) ^ [_988393, _988395] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988393)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988395)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988393), _988395)))], (43897 ^ _779571) ^ [_1637951, _1637953, _1637955, _1637957, _1637959] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1637951, _1637953, _1637955), _1637957), _1637959) = c_HOL_OThe(_1637953, c_Finite__Set_Ofold__graph(_1637951, _1637953, _1637955, _1637957, _1637959)))], (594 ^ _779571) ^ [_788882, _788884, _788886, _788888] : [-(c_FunDef_Oreduction__pair(_788886, _788882)), c_FunDef_Oreduction__pair(_788888, _788884), _788888 = _788886, _788884 = _788882], (29212 ^ _779571) ^ [_1301524, _1301526] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301524, tc_HOL_Obool)), _1301526), c_Orderings_Obot__class_Obot(tc_fun(_1301524, tc_HOL_Obool))) = _1301526)], (5530 ^ _779571) ^ [_865000, _865002, _865004, _865006] : [-(c_List_Oconcat(_865006, _865002) = c_List_Oconcat(_865004, _865000)), _865006 = _865004, _865002 = _865000], (10066 ^ _779571) ^ [_947274, _947276, _947278] : [class_Rings_Olinordered__ring__strict(_947274), 10069 ^ _779571 : [(10070 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947274), c_Groups_Ozero__class_Ozero(_947274)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947274), _947276), _947276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947274), _947278), _947278)))), _947276 = c_Groups_Ozero__class_Ozero(_947274), _947278 = c_Groups_Ozero__class_Ozero(_947274)], (10080 ^ _779571) ^ [] : [10081 ^ _779571 : [(10084 ^ _779571) ^ [] : [-(_947278 = c_Groups_Ozero__class_Ozero(_947274))], (10082 ^ _779571) ^ [] : [-(_947276 = c_Groups_Ozero__class_Ozero(_947274))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947274), c_Groups_Ozero__class_Ozero(_947274)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947274), _947276), _947276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947274), _947278), _947278)))))]]], (29498 ^ _779571) ^ [_1306806, _1306808, _1306810] : [class_Orderings_Oorder(_1306806), _1306808 = _1306810, -(c_SetInterval_Oord__class_OatLeastAtMost(_1306806, _1306808, _1306810) = hAPP(hAPP(c_Set_Oinsert(_1306806), _1306808), c_Orderings_Obot__class_Obot(tc_fun(_1306806, tc_HOL_Obool))))], (962 ^ _779571) ^ [_794364, _794366] : [-(c_List_Onat__list(_794364)), _794366 = _794364, c_List_Onat__list(_794366)], (8072 ^ _779571) ^ [_913383, _913385, _913387, _913389] : [-(hAPP(c_Option_Ooption_Ooption__case(_913383, _913385, _913387, _913389), c_Option_Ooption_ONone(_913385)) = _913387)], (50292 ^ _779571) ^ [_1789906, _1789908, _1789910, _1789912, _1789914] : [class_Orderings_Olinorder(_1789906), 50295 ^ _779571 : [(50302 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1789906, hAPP(hAPP(c_List_Omap(_1789908, _1789906), _1789910), _1789914)), -(c_List_Olinorder__class_Osorted(_1789906, hAPP(hAPP(c_List_Omap(_1789908, _1789906), _1789910), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1789908, _1789906, _1789910), _1789912), _1789914))))], (50296 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1789906, hAPP(hAPP(c_List_Omap(_1789908, _1789906), _1789910), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1789908, _1789906, _1789910), _1789912), _1789914))), -(c_List_Olinorder__class_Osorted(_1789906, hAPP(hAPP(c_List_Omap(_1789908, _1789906), _1789910), _1789914)))]]], (29354 ^ _779571) ^ [_1304436, _1304438] : [class_Lattices_Obounded__lattice__bot(_1304436), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1304436), _1304438), c_Orderings_Obot__class_Obot(_1304436)) = _1304438)], (6756 ^ _779571) ^ [_890544, _890546] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_890544, _890546))))], (43166 ^ _779571) ^ [_1619665, _1619667, _1619669, _1619671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619665, _1619665)), hAPP(hAPP(c_Product__Type_OPair(_1619665, _1619665), _1619667), _1619669)), c_Transitive__Closure_Ortrancl(_1619665, _1619671))), -(_1619667 = _1619669), 43173 ^ _779571 : [(43176 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619665, _1619665)), hAPP(hAPP(c_Product__Type_OPair(_1619665, _1619665), _1619667), _1619669)), c_Transitive__Closure_Otrancl(_1619665, _1619671))))], (43174 ^ _779571) ^ [] : [_1619667 = _1619669]]], (48224 ^ _779571) ^ [_1742462, _1742464, _1742466, _1742468] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742462), tc_List_Olist(_1742462))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742462), tc_List_Olist(_1742462)), _1742464), _1742466)), c_List_Olex(_1742462, _1742468))), 48227 ^ _779571 : [(48230 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742462)), _1742464) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742462)), _1742466))], (48228 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742462), tc_List_Olist(_1742462))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742462), tc_List_Olist(_1742462)), _1742464), _1742466)), c_List_Olexord(_1742462, _1742468))))]]], (13374 ^ _779571) ^ [_1003579, _1003581, _1003583, _1003585, _1003587, _1003589] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003579), _1003581)), _1003583) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003585), _1003587)), _1003589), 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), _1003585), _1003587)), _1003589)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003583), _1003579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1003585), _1003579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1003587), _1003581)))], (50374 ^ _779571) ^ [_1791466, _1791468, _1791470, _1791472] : [class_Groups_Ocomm__monoid__add(_1791466), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1791466), _1791468), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1791470, _1791472))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1791466), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1791466), _1791468), c_List_Oupt(_1791470, _1791472))))], (17777 ^ _779571) ^ [_1085706, _1085708] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085706))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085706), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085708)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36414 ^ _779571) ^ [_1456212] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1456212) = c_Orderings_Oord__class_Omin(_1456212)), class_Lattices_Osemilattice__inf(_1456212), class_Orderings_Olinorder(_1456212)], (26780 ^ _779571) ^ [_1250808, _1250810] : 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c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250810))], (26152 ^ _779571) ^ [_1238664, _1238666, _1238668, _1238670] : [class_Divides_Osemiring__div(_1238664), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238664), _1238666), _1238668)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238664), _1238670), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238664), _1238668), _1238666)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238664), _1238670), _1238668)), _1238666))], (33205 ^ _779571) ^ [_1384996, _1384998] : [class_Orderings_Olinorder(_1384996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384996), _1384998)), -(_1384998 = c_Orderings_Obot__class_Obot(tc_fun(_1384996, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1384996), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384996), 33218 ^ [_1384996, _1384998]), 33219 ^ [_1384996, _1384998])), hAPP(hAPP(c_Set_Oinsert(_1384996), 33218 ^ [_1384996, _1384998]), hAPP(hAPP(c_Set_Oinsert(_1384996), 33219 ^ [_1384996, _1384998]), c_Orderings_Obot__class_Obot(tc_fun(_1384996, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1384996), c_Big__Operators_Olinorder__class_OMax(_1384996, _1384998)), _1384998)))], (34604 ^ _779571) ^ [_1413389, _1413391, _1413393, _1413395, _1413397] : [hBOOL(hAPP(hAPP(c_member(_1413389), _1413391), _1413393)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1413389, tc_Option_Ooption(_1413395)), c_Map_Orestrict__map(_1413389, _1413395, _1413397, _1413393)), _1413391), c_Option_Ooption_ONone(_1413395)) = c_Map_Orestrict__map(_1413389, _1413395, _1413397, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413389, tc_HOL_Obool)), _1413393), hAPP(hAPP(c_Set_Oinsert(_1413389), _1413391), c_Orderings_Obot__class_Obot(tc_fun(_1413389, tc_HOL_Obool))))))], (30600 ^ _779571) ^ [_1329127, _1329129, _1329131, _1329133, _1329135] : [hBOOL(hAPP(hAPP(c_member(_1329127), _1329129), _1329131)), -(hAPP(hAPP(c_Set_Oinsert(_1329133), hAPP(_1329135, _1329129)), hAPP(c_Set_Oimage(_1329127, _1329133, _1329135), _1329131)) = hAPP(c_Set_Oimage(_1329127, _1329133, _1329135), _1329131))], (22726 ^ _779571) ^ [_1173347, _1173349, _1173351, _1173353, _1173355] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1173347, _1173349), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1173351), _1173353))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173355)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1173347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173349), _1173355)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1173351), _1173355)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173349), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1173351, _1173355))), _1173353)))))], (30975 ^ _779571) ^ [_1337227, _1337229] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1337227, _1337229))))], (28981 ^ _779571) ^ [_1296342, _1296344] : [-(hAPP(c_Set_Oimage(_1296342, _1296342, c_COMBI(_1296342)), _1296344) = _1296344)], (6891 ^ _779571) ^ [_893303, _893305] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893303), _893305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _893305 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15226 ^ _779571) ^ [_1037156, _1037158, _1037160] : [class_Rings_Oring__1(_1037156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037158), _1037160)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1037156), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037160), _1037158)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037156), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1037156), _1037160)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1037156), _1037158)))], (35573 ^ _779571) ^ [_1436421] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436421) = 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, _1436421)), 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))))))))], (42491 ^ _779571) ^ [_1603081, _1603083] : [42493 ^ _779571 : [(42496 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1603083), 42492 ^ [_1603081, _1603083]))], (42494 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42492 ^ [_1603081, _1603083]), _1603081)))]], -(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)), _1603083), _1603081))], (31436 ^ _779571) ^ [_1347748] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1347748)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (48504 ^ _779571) ^ [_1749851, _1749853, _1749855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1749851, _1749851), tc_HOL_Obool)), _1749853), _1749855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1749851), tc_List_Olist(_1749851)), tc_HOL_Obool)), c_List_Olistrel1(_1749851, _1749853)), c_List_Olistrel1(_1749851, _1749855))))], (17049 ^ _779571) ^ [_1072406, _1072408, _1072410, _1072412] : [class_Int_Onumber__ring(_1072406), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072406), hAPP(c_Int_Onumber__class_Onumber__of(_1072406), _1072408)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1072406), hAPP(c_Int_Onumber__class_Onumber__of(_1072406), _1072410)), _1072412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1072406), hAPP(c_Int_Onumber__class_Onumber__of(_1072406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072408), _1072410))), _1072412))], (23547 ^ _779571) ^ [_1188479, _1188481, _1188483] : [class_Orderings_Olinorder(_1188479), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188479), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188479), _1188481), _1188483)), _1188481)))], (22256 ^ _779571) ^ [_1163549] : [-(c_Divides_Odivmod__nat(_1163549, 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)), _1163549))], (9120 ^ _779571) ^ [_930665, _930667] : [class_Groups_Ogroup__add(_930665), 9123 ^ _779571 : [(9130 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_930665) = _930667, -(c_Groups_Ozero__class_Ozero(_930665) = hAPP(c_Groups_Ouminus__class_Ouminus(_930665), _930667))], (9124 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_930665) = hAPP(c_Groups_Ouminus__class_Ouminus(_930665), _930667), -(c_Groups_Ozero__class_Ozero(_930665) = _930667)]]], (8482 ^ _779571) ^ [_920064, _920066, _920068, _920070] : [class_Orderings_Oord(_920064), _920066 = _920068, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920064), _920068), _920070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920064), _920066), _920070)))], (29450 ^ _779571) ^ [_1305993, _1305995, _1305997, _1305999] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305993, tc_HOL_Obool)), _1305995), hAPP(hAPP(c_Set_Oinsert(_1305993), _1305997), _1305999)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305993, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305993, tc_HOL_Obool)), _1305995), hAPP(hAPP(c_Set_Oinsert(_1305993), _1305997), c_Orderings_Obot__class_Obot(tc_fun(_1305993, tc_HOL_Obool))))), _1305999))], (31858 ^ _779571) ^ [_1358163, _1358165, _1358167] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358163), _1358165)), -(hBOOL(hAPP(hAPP(c_member(_1358163), _1358167), _1358165))), -(hAPP(c_Finite__Set_Ocard(_1358163), hAPP(hAPP(c_Set_Oinsert(_1358163), _1358167), _1358165)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1358163), _1358165)))], (51227 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (6087 ^ _779571) ^ [_877676, _877678, _877680, _877682] : [-(c_Com_Ocom_OSemi(_877676, _877678) = c_Com_Ocom_OSemi(_877680, _877682)), _877676 = _877680, _877678 = _877682], (23165 ^ _779571) ^ [_1181552, _1181554, _1181556, _1181558, _1181560] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1181552, _1181554), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181556), _1181558))), -(_1181554 = 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)), _1181560)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1181552, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181554), _1181560)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181556), _1181560)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181554), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181556, _1181560))), _1181558)))))], (49761 ^ _779571) ^ [_1779154, _1779156, _1779158] : [hBOOL(hAPP(c_List_Odistinct(_1779154), _1779156)), -(hBOOL(hAPP(c_List_Odistinct(_1779154), hAPP(c_List_Ofilter(_1779154, _1779158), _1779156))))], (48510 ^ _779571) ^ [_1750002, _1750004] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1750002), tc_List_Olist(_1750002)), tc_HOL_Obool)), c_List_Olistrel1(_1750002, c_Transitive__Closure_Ortrancl(_1750002, _1750004))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750002), c_List_Olistrel1(_1750002, _1750004)))))], (40786 ^ _779571) ^ [_1554659, _1554661, _1554663, _1554665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554659), _1554661)), 40792 ^ _779571 : [(40795 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554663), hAPP(_1554665, 40791 ^ [_1554659, _1554661, _1554663, _1554665])))], (40793 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554659), 40791 ^ [_1554659, _1554661, _1554663, _1554665]), _1554661)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1554659, _1554663)), hAPP(hAPP(c_Product__Type_OSigma(_1554659, _1554663), _1554661), _1554665))))], (48311 ^ _779571) ^ [_1745026, _1745028, _1745030] : [48312 ^ _779571 : [(48315 ^ _779571) ^ [] : [_1745030 = c_List_Olist_ONil(_1745026)], (48313 ^ _779571) ^ [] : [_1745028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1745026), _1745028), _1745030) = c_List_Olist_ONil(_1745026))], (24181 ^ _779571) ^ [_1200809, _1200811, _1200813] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1200809, _1200811), _1200813))), _1200809 = 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), _1200813)), _1200811)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200813)), 24188 ^ _779571 : [(24191 ^ _779571) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1200813) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24189 ^ _779571) ^ [] : [-(_1200811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24192 ^ _779571 : [(24195 ^ _779571) ^ [] : [24196 ^ _779571 : [(24199 ^ _779571) ^ [] : [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), _1200813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200813)), _1200811))], (24197 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200811)))]], 24204 ^ _779571 : [(24207 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1200811), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200813)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24205 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200811))]]], (24193 ^ _779571) ^ [] : [_1200811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (30122 ^ _779571) ^ [_1319518, _1319520, _1319522, _1319524] : [-(hBOOL(hAPP(hAPP(c_member(_1319518), _1319520), _1319522))), -(hBOOL(hAPP(hAPP(c_member(_1319518), _1319520), _1319524))), 30129 ^ _779571 : [(30136 ^ _779571) ^ [] : [_1319522 = _1319524, -(hAPP(hAPP(c_Set_Oinsert(_1319518), _1319520), _1319522) = hAPP(hAPP(c_Set_Oinsert(_1319518), _1319520), _1319524))], (30130 ^ _779571) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1319518), _1319520), _1319522) = hAPP(hAPP(c_Set_Oinsert(_1319518), _1319520), _1319524), -(_1319522 = _1319524)]]], (12111 ^ _779571) ^ [_981560, _981562] : [class_Groups_Olinordered__ab__group__add(_981560), 12114 ^ _779571 : [(12121 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981560), _981562), c_Groups_Ozero__class_Ozero(_981560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981560), _981562), hAPP(c_Groups_Ouminus__class_Ouminus(_981560), _981562))))], (12115 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981560), _981562), hAPP(c_Groups_Ouminus__class_Ouminus(_981560), _981562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981560), _981562), c_Groups_Ozero__class_Ozero(_981560))))]]], (47412 ^ _779571) ^ [_1722986, _1722988, _1722990] : [-(c_List_Olistset(_1722986, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1722986, tc_HOL_Obool)), _1722988), _1722990)) = c_List_Oset__Cons(_1722986, _1722988, c_List_Olistset(_1722986, _1722990)))], (14900 ^ _779571) ^ [_1030893, _1030895, _1030897] : [class_Divides_Osemiring__div(_1030893), -(_1030895 = c_Groups_Ozero__class_Ozero(_1030893)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030893), _1030897), _1030895)), _1030895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030893), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030893), _1030897), _1030895)), c_Groups_Oone__class_Oone(_1030893)))], (2604 ^ _779571) ^ [_819005, _819007, _819009, _819011, _819013, _819015, _819017, _819019, _819021, _819023] : [-(c_Product__Type_Oprod_Oprod__rec(_819023, _819019, _819015, _819011, _819007) = c_Product__Type_Oprod_Oprod__rec(_819021, _819017, _819013, _819009, _819005)), _819023 = _819021, _819019 = _819017, _819015 = _819013, _819011 = _819009, _819007 = _819005], (39521 ^ _779571) ^ [_1524720, _1524722, _1524724, _1524726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524720), _1524722)), c_Fun_Oinj__on(_1524724, _1524720, _1524726, c_Orderings_Otop__class_Otop(tc_fun(_1524724, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524724), hAPP(c_Set_Ovimage(_1524724, _1524720, _1524726), _1524722))))], (39326 ^ _779571) ^ [_1520029, _1520031, _1520033, _1520035, _1520037, _1520039, _1520041] : [class_Groups_Oab__semigroup__mult(_1520029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520031), _1520033)), c_Fun_Oinj__on(_1520031, _1520035, _1520037, _1520033), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1520029, _1520035, c_Groups_Otimes__class_Otimes(_1520029)), _1520039), _1520041), hAPP(c_Set_Oimage(_1520031, _1520035, _1520037), _1520033)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1520029, _1520031, c_Groups_Otimes__class_Otimes(_1520029)), hAPP(c_Fun_Ocomp(_1520035, _1520029, _1520031, _1520039), _1520037)), _1520041), _1520033))], (20241 ^ _779571) ^ [_1127642, _1127644, _1127646, _1127648] : [class_Fields_Olinordered__field(_1127642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127642), _1127644), _1127646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127642), _1127648), c_Groups_Ozero__class_Ozero(_1127642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127642), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127642), _1127646), _1127648)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127642), _1127644), _1127648))))], (50614 ^ _779571) ^ [_1797125, _1797127, _1797129] : [hAPP(c_List_Orev(_1797125), _1797127) = hAPP(hAPP(c_List_Olist_OCons(_1797125), _1797129), c_List_Olist_ONil(_1797125)), -(_1797127 = hAPP(hAPP(c_List_Olist_OCons(_1797125), _1797129), c_List_Olist_ONil(_1797125)))], (5775 ^ _779571) ^ [_872082, _872084, _872086, _872088, _872090, _872092] : [-(hBOOL(hAPP(_872082, _872084))), c_Natural_Oevaln(_872086, _872084, _872088, _872090), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_872082, _872092, _872086), _872084, _872088, _872090))], (51651 ^ _779571) ^ [_1814193, _1814195] : [-(hBOOL(_1814193)), -(hBOOL(hAPP(hAPP(c_fimplies, _1814193), _1814195)))], (14994 ^ _779571) ^ [_1032890, _1032892, _1032894] : [hBOOL(hAPP(_1032890, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1032892, _1032894))), 14997 ^ _779571 : [(15004 ^ _779571) ^ [] : [-(_1032894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15007 ^ _779571 : [(15008 ^ _779571) ^ [_1033138, _1033140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033138), _1032894)), _1032892 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032894), _1033140)), _1033138), -(hBOOL(hAPP(_1032890, _1033138)))]]], (14998 ^ _779571) ^ [] : [_1032894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1032890, _1032892)))]]], (49987 ^ _779571) ^ [_1784819, _1784821] : [c_List_Oupt(_1784819, _1784821) = c_List_Olist_ONil(tc_Nat_Onat), -(_1784821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784821), _1784819)))], (42295 ^ _779571) ^ [_1598292, _1598294, _1598296, _1598298] : [42296 ^ _779571 : [(42297 ^ _779571) ^ [_1598367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598292, _1598296)), hAPP(hAPP(c_Product__Type_OPair(_1598292, _1598296), _1598294), _1598367)), _1598298))]], -(hBOOL(hAPP(hAPP(c_member(_1598292), _1598294), hAPP(c_Relation_ODomain(_1598292, _1598296), _1598298))))], (14934 ^ _779571) ^ [_1031657, _1031659, _1031661] : [class_Divides_Osemiring__div(_1031657), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031657), c_Divides_Odiv__class_Omod(_1031657, _1031659, _1031661)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031657), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031657), _1031659), _1031661)), _1031661)) = _1031659)], (15874 ^ _779571) ^ [_1049404, _1049406] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049404), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049406), _1049404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049406), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1049406, _1049404)))], (7209 ^ _779571) ^ [_898657, _898659, _898661, _898663] : [hAPP(_898657, 7210 ^ [_898657, _898659, _898661, _898663]) = hAPP(c_Nat_Onat_Onat__rec(_898659, _898661, _898663), 7210 ^ [_898657, _898659, _898661, _898663]), -(hAPP(_898657, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _898661)], (49195 ^ _779571) ^ [_1766677, _1766679, _1766681] : [class_Lattices_Olattice(_1766677), -(c_Big__Operators_Olattice__class_OSup__fin(_1766677, hAPP(c_List_Oset(_1766677), hAPP(hAPP(c_List_Olist_OCons(_1766677), _1766679), _1766681))) = hAPP(c_List_Ofoldl(_1766677, _1766677, c_Lattices_Osemilattice__sup__class_Osup(_1766677), _1766679), _1766681))], (41312 ^ _779571) ^ [_1568485, _1568487] : [-(hAPP(c_Set_OPow(_1568485), _1568487) = hAPP(c_Set_OCollect(tc_fun(_1568485, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1568485, tc_HOL_Obool), tc_fun(_1568485, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1568485, tc_HOL_Obool))), _1568487)))], (25276 ^ _779571) ^ [_1222638, _1222640] : [-(_1222638 = _1222640), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222638), _1222640)), 25283 ^ _779571 : [(25286 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222640), _1222638))], (25284 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222638), _1222640)))]]], (8000 ^ _779571) ^ [_912337, _912339] : [-(_912337 = hAPP(c_Option_Ooption_OSome(_912339), 8001 ^ [_912337, _912339])), -(_912337 = c_Option_Ooption_ONone(_912339))], (30961 ^ _779571) ^ [_1337014, _1337016] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1337014, _1337016))))], (11757 ^ _779571) ^ [_975046, _975048, _975050] : [class_Rings_Oordered__cancel__semiring(_975046), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975046), _975048), _975050)), c_Groups_Ozero__class_Ozero(_975046)))), 11762 ^ _779571 : [(11769 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975046), _975048), c_Groups_Ozero__class_Ozero(_975046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975046), c_Groups_Ozero__class_Ozero(_975046)), _975050))], (11763 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975046), c_Groups_Ozero__class_Ozero(_975046)), _975048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975046), _975050), c_Groups_Ozero__class_Ozero(_975046)))]]], (16677 ^ _779571) ^ [_1065071, _1065073, _1065075] : [class_Groups_Oordered__ab__group__add__abs(_1065071), 16680 ^ _779571 : [(16689 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), hAPP(c_Groups_Oabs__class_Oabs(_1065071), _1065073)), _1065075))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), _1065073), _1065075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), hAPP(c_Groups_Ouminus__class_Ouminus(_1065071), _1065073)), _1065075))], (16681 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), hAPP(c_Groups_Oabs__class_Oabs(_1065071), _1065073)), _1065075)), 16684 ^ _779571 : [(16687 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), hAPP(c_Groups_Ouminus__class_Ouminus(_1065071), _1065073)), _1065075)))], (16685 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065071), _1065073), _1065075)))]]]]], (19407 ^ _779571) ^ [_1112420, _1112422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112420)), c_Int_OBit1(_1112422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112420), _1112422)))], (39653 ^ _779571) ^ [_1527825, _1527827, _1527829, _1527831, _1527833] : [class_Groups_Ocomm__monoid__add(_1527825), class_Groups_Ocomm__monoid__mult(_1527825), _1527827 = _1527829, c_Nat__Transfer_Onat__set(_1527829), 39671 ^ _779571 : [(39674 ^ _779571) ^ [] : [hAPP(_1527831, 39670 ^ [_1527825, _1527827, _1527829, _1527831, _1527833]) = hAPP(_1527833, 39670 ^ [_1527825, _1527827, _1527829, _1527831, _1527833])], (39672 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 39670 ^ [_1527825, _1527827, _1527829, _1527831, _1527833])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1527825), _1527831), _1527827) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1527825), _1527833), _1527829))], (36704 ^ _779571) ^ [_1462210, _1462212, _1462214, _1462216] : [hBOOL(hAPP(hAPP(c_member(_1462210), _1462212), _1462214)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462210, tc_HOL_Obool)), _1462214), hAPP(hAPP(c_Set_Oinsert(_1462210), _1462212), _1462216)) = hAPP(hAPP(c_Set_Oinsert(_1462210), _1462212), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462210, tc_HOL_Obool)), _1462214), _1462216)))], (21327 ^ _779571) ^ [_1146501, _1146503, _1146505] : [class_Fields_Olinordered__field__inverse__zero(_1146501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146501), c_Groups_Ozero__class_Ozero(_1146501)), _1146503)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146501), hAPP(c_Groups_Oabs__class_Oabs(_1146501), _1146505)), _1146503) = hAPP(c_Groups_Oabs__class_Oabs(_1146501), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146501), _1146505), _1146503)))], (47661 ^ _779571) ^ [_1729811, _1729813, _1729815, _1729817] : [hBOOL(hAPP(c_List_Odistinct(_1729811), _1729813)), -(hBOOL(hAPP(hAPP(c_member(_1729811), _1729815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1729811, tc_HOL_Obool)), hAPP(c_List_Oset(_1729811), _1729813)), hAPP(hAPP(c_Set_Oinsert(_1729811), hAPP(hAPP(c_List_Onth(_1729811), _1729813), _1729817)), c_Orderings_Obot__class_Obot(tc_fun(_1729811, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1729811), hAPP(hAPP(c_List_Olist__update(_1729811, _1729813), _1729817), _1729815))))], (46014 ^ _779571) ^ [_1687519, _1687521, _1687523, _1687525, _1687527] : [hAPP(hAPP(c_List_Omap(_1687519, _1687521), _1687523), _1687525) = hAPP(hAPP(c_List_Omap(_1687519, _1687521), _1687527), _1687525), 46017 ^ _779571 : [(46018 ^ _779571) ^ [_1687642] : [hBOOL(hAPP(hAPP(c_member(_1687519), _1687642), hAPP(c_List_Oset(_1687519), _1687525))), -(hAPP(_1687523, _1687642) = hAPP(_1687527, _1687642))]]], (35201 ^ _779571) ^ [_1427494, _1427496, _1427498] : [-(hAPP(c_Set_OPow(_1427494), hAPP(hAPP(c_Set_Oinsert(_1427494), _1427496), _1427498)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1427494, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1427494), _1427498)), hAPP(c_Set_Oimage(tc_fun(_1427494, tc_HOL_Obool), tc_fun(_1427494, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1427494), _1427496)), hAPP(c_Set_OPow(_1427494), _1427498))))], (28525 ^ _779571) ^ [_1286054, _1286056, _1286058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1286054), tc_HOL_Obool)), _1286056), _1286058)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1286054, _1286058, _1286056))], (13552 ^ _779571) ^ [_1006587, _1006589] : [-(hBOOL(hAPP(_1006587, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1006587, _1006589)), 13560 ^ _779571 : [(13563 ^ _779571) ^ [_1006825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006825), 13559 ^ [_1006587, _1006589])), hBOOL(hAPP(_1006587, _1006825))], (13569 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1006587, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13559 ^ [_1006587, _1006589]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13561 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13559 ^ [_1006587, _1006589]), _1006589)))]]], (29890 ^ _779571) ^ [_1314181, _1314183, _1314185, _1314187, _1314189, _1314191, _1314193] : [c_Hoare__Mirabelle_Ohoare__derivs(_1314181, _1314183, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314181)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314181), _1314185), _1314187), _1314189)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314181), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1314181, _1314183, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314181)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314181), _1314189), _1314191), _1314193)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314181), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1314181, _1314183, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314181)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314181), _1314185), c_Com_Ocom_OSemi(_1314187, _1314191)), _1314193)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314181), tc_HOL_Obool)))))], (46540 ^ _779571) ^ [_1700208, _1700210, _1700212, _1700214, _1700216] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700208)), _1700210) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700212)), _1700214), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700208)), _1700216) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700212)), _1700214), hBOOL(hAPP(c_List_Odistinct(_1700212), _1700214)), c_Map_Omap__of(_1700212, _1700208, hAPP(hAPP(c_List_Ozip(_1700212, _1700208), _1700214), _1700210)) = c_Map_Omap__of(_1700212, _1700208, hAPP(hAPP(c_List_Ozip(_1700212, _1700208), _1700214), _1700216)), -(_1700210 = _1700216)], (42174 ^ _779571) ^ [_1595889, _1595891, _1595893, _1595895, _1595897] : [hBOOL(hAPP(hAPP(_1595889, _1595891), _1595893)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1595895, _1595897, _1595889), _1595893)))], (20659 ^ _779571) ^ [_1134527, _1134529, _1134531] : [class_Fields_Ofield__inverse__zero(_1134527), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134527), c_Groups_Oone__class_Oone(_1134527)), hAPP(hAPP(c_Power_Opower__class_Opower(_1134527), _1134529), _1134531)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1134527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134527), c_Groups_Oone__class_Oone(_1134527)), _1134529)), _1134531))], (48202 ^ _779571) ^ [_1741907, _1741909, _1741911, _1741913] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741909)), _1741911)))), -(hAPP(hAPP(c_List_Onth(_1741909), hAPP(hAPP(c_List_Oappend(_1741909), _1741911), _1741913)), _1741907) = hAPP(hAPP(c_List_Onth(_1741909), _1741913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1741907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741909)), _1741911))))], (14341 ^ _779571) ^ [_1021449, _1021451, _1021453] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021449, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021451), _1021453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021451), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021449), _1021451), _1021453))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021449, _1021451)))], (29904 ^ _779571) ^ [] : [-(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))))], (37076 ^ _779571) ^ [_1470875, _1470877, _1470879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470875), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470875, tc_HOL_Obool)), _1470877), _1470879))), -(hAPP(c_Finite__Set_Ocard(_1470875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470875, tc_HOL_Obool)), _1470877), _1470879)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470875), _1470877)), hAPP(c_Finite__Set_Ocard(_1470875), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470875, tc_HOL_Obool)), _1470877), _1470879))))], (25906 ^ _779571) ^ [_1233376, _1233378, _1233380, _1233382] : [class_Rings_Oring__1(_1233376), -(hAPP(c_Int_Oring__1__class_Oof__int(_1233376), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233378, tc_Int_Oint), _1233380), _1233382)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233378, _1233376), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1233376, _1233378), c_Int_Oring__1__class_Oof__int(_1233376)), _1233380)), _1233382))], (25082 ^ _779571) ^ [_1219286, _1219288, _1219290] : [-(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), _1219286)), 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))), _1219288))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1219290))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219290)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219286), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219286), 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), _1219290), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1219288)))))], (9528 ^ _779571) ^ [_937761, _937763, _937765] : [class_Groups_Ogroup__add(_937761), 9531 ^ _779571 : [(9538 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937761), _937763), _937765) = c_Groups_Ozero__class_Ozero(_937761), -(_937763 = hAPP(c_Groups_Ouminus__class_Ouminus(_937761), _937765))], (9532 ^ _779571) ^ [] : [_937763 = hAPP(c_Groups_Ouminus__class_Ouminus(_937761), _937765), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937761), _937763), _937765) = c_Groups_Ozero__class_Ozero(_937761))]]], (42934 ^ _779571) ^ [_1613094, _1613096] : [-(c_Transitive__Closure_Otrancl(_1613094, _1613096) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1613094, _1613094), tc_HOL_Obool)), _1613096), hAPP(hAPP(c_Relation_Orel__comp(_1613094, _1613094, _1613094), c_Transitive__Closure_Otrancl(_1613094, _1613096)), _1613096)))], (48742 ^ _779571) ^ [_1756900, _1756902, _1756904, _1756906, _1756908] : [-(hAPP(hAPP(c_List_Odrop(_1756900), _1756902), hAPP(hAPP(c_List_Omap(_1756904, _1756900), _1756906), _1756908)) = hAPP(hAPP(c_List_Omap(_1756904, _1756900), _1756906), hAPP(hAPP(c_List_Odrop(_1756904), _1756902), _1756908)))], (6005 ^ _779571) ^ [_876139, _876141, _876143, _876145, _876147] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_876139, _876141), _876143, _876145, _876147)), 6006 ^ _779571 : [(6007 ^ _779571) ^ [_876194] : [c_Natural_Oevaln(_876139, _876143, _876145, _876194), c_Natural_Oevaln(_876141, _876194, _876145, _876147)]]], (18795 ^ _779571) ^ [_1101968] : [-(c_Int_OBit1(_1101968) = 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)), _1101968)), _1101968))], (17409 ^ _779571) ^ [_1079035, _1079037, _1079039, _1079041] : [class_Rings_Olinordered__semidom(_1079035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079035), _1079037), _1079039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079035), c_Groups_Ozero__class_Ozero(_1079035)), _1079037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079035), hAPP(hAPP(c_Power_Opower__class_Opower(_1079035), _1079037), _1079041)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079035), _1079039), _1079041))))], (7842 ^ _779571) ^ [_909668, _909670] : [class_Rings_Olinordered__idom(_909668), 7845 ^ _779571 : [(7852 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909668), _909670), c_Groups_Ozero__class_Ozero(_909668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909668), _909670), _909670)), c_Groups_Ozero__class_Ozero(_909668))))], (7846 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909668), _909670), _909670)), c_Groups_Ozero__class_Ozero(_909668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909668), _909670), c_Groups_Ozero__class_Ozero(_909668))))]]], (29019 ^ _779571) ^ [_1297039, _1297041, _1297043] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297039, tc_HOL_Obool)), _1297041), hAPP(hAPP(c_Set_Oinsert(_1297039), _1297043), _1297041))))], (5496 ^ _779571) ^ [_864511, _864513] : [_864513 = _864511, -(c_Orderings_Oord__class_Oless(_864513) = c_Orderings_Oord__class_Oless(_864511))], (49323 ^ _779571) ^ [_1769874] : [-(c_List_Olists(_1769874, c_Orderings_Otop__class_Otop(tc_fun(_1769874, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1769874), tc_HOL_Obool)))], (25018 ^ _779571) ^ [_1218234, _1218236, _1218238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218234, tc_HOL_Obool)), _1218236), _1218238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1218234, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1218234, _1218236)), c_Predicate_OPowp(_1218234, _1218238))))], (43046 ^ _779571) ^ [_1616646, _1616648, _1616650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616646, _1616646), tc_HOL_Obool)), _1616648), c_Transitive__Closure_Ortrancl(_1616646, _1616650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616646, _1616646), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616646, _1616648)), c_Transitive__Closure_Ortrancl(_1616646, _1616650))))], (3930 ^ _779571) ^ [_840168, _840170] : [_840170 = _840168, -(c_Nat_Ofunpow(_840170) = c_Nat_Ofunpow(_840168))], (7325 ^ _779571) ^ [_901050, _901052, _901054, _901056] : [hAPP(c_Sum__Type_OInr(_901050, _901052), _901054) = hAPP(c_Sum__Type_OInl(_901052, _901050), _901056)], (40841 ^ _779571) ^ [_1555956, _1555958, _1555960, _1555962, _1555964, _1555966, _1555968, _1555970] : [c_Fun_Oinj__on(_1555956, _1555958, _1555960, _1555962), c_Fun_Oinj__on(_1555964, _1555966, _1555968, _1555970), -(c_Fun_Oinj__on(tc_prod(_1555956, _1555964), tc_prod(_1555958, _1555966), c_Product__Type_Omap__pair(_1555956, _1555958, _1555964, _1555966, _1555960, _1555968), hAPP(hAPP(c_Product__Type_OSigma(_1555956, _1555964), _1555962), hAPP(c_COMBK(tc_fun(_1555964, tc_HOL_Obool), _1555956), _1555970))))], (3788 ^ _779571) ^ [_837975, _837977, _837979, _837981, _837983, _837985, _837987, _837989] : [-(c_New__Random__Sequence_Opos__map(_837989, _837985, _837981, _837977) = c_New__Random__Sequence_Opos__map(_837987, _837983, _837979, _837975)), _837989 = _837987, _837985 = _837983, _837981 = _837979, _837977 = _837975], (7574 ^ _779571) ^ [_905218, _905220, _905222, _905224] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_905218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905218), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905218), _905220), _905222)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905218), _905224), _905222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905218), _905220), _905224)))], (13234 ^ _779571) ^ [_1001100] : [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, _1001100)))))], (42966 ^ _779571) ^ [_1614745, _1614747, _1614749] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614745, _1614745)), _1614747), _1614749)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614745, _1614745)), _1614747), c_Transitive__Closure_Ortrancl(_1614745, _1614749))))], (19227 ^ _779571) ^ [_1109307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1109307)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109307), c_Int_OPls)))], (1712 ^ _779571) ^ [_803739, _803741] : [-(class_Orderings_Oord(_803739)), _803741 = _803739, class_Orderings_Oord(_803741)], (35775 ^ _779571) ^ [_1441651, _1441653, _1441655, _1441657] : [-(c_Random__Sequence_Omap(_1441651, _1441653, _1441655, _1441657) = c_Random__Sequence_Obind(_1441651, _1441653, _1441657, hAPP(c_Fun_Ocomp(_1441653, 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(_1441653)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1441651, c_Random__Sequence_Osingle(_1441653)), _1441655)))], (29734 ^ _779571) ^ [_1311148] : [class_Lattices_Oboolean__algebra(_1311148), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1311148), c_Orderings_Obot__class_Obot(_1311148)) = c_Orderings_Otop__class_Otop(_1311148))], (3236 ^ _779571) ^ [_829185, _829187, _829189, _829191] : [-(c_Option_Oset(_829191, _829187) = c_Option_Oset(_829189, _829185)), _829191 = _829189, _829187 = _829185], (18139 ^ _779571) ^ [_1091619] : [class_Int_Onumber__ring(_1091619), -(hAPP(c_Int_Onumber__class_Onumber__of(_1091619), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1091619), c_Groups_Oone__class_Oone(_1091619)))], (50906 ^ _779571) ^ [_1804283, _1804285, _1804287] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1804283), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1804283))), _1804285))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1804287), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804283))), _1804285))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804283))), hAPP(c_List_Ofilter(tc_List_Olist(_1804283), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1804283)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1804287)), c_Nat_Osize__class_Osize(tc_List_Olist(_1804283)))), c_List_Otranspose(_1804283, _1804285))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1804283)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1804283)), _1804285), _1804287)))], (2306 ^ _779571) ^ [_814390, _814392, _814394, _814396] : [-(c_SMT_Oz3mod(_814396, _814392) = c_SMT_Oz3mod(_814394, _814390)), _814396 = _814394, _814392 = _814390], (17105 ^ _779571) ^ [_1073561, _1073563, _1073565] : [class_Rings_Olinordered__semidom(_1073561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073561), c_Groups_Oone__class_Oone(_1073561)), _1073563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073561), c_Groups_Oone__class_Oone(_1073561)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073561), _1073563), _1073565))))], (19199 ^ _779571) ^ [_1108799, _1108801] : [c_Int_OBit0(_1108799) = c_Int_OBit1(_1108801)], (2170 ^ _779571) ^ [_812102, _812104, _812106, _812108, _812110, _812112] : [-(c_Sum__Type_OProjl(_812112, _812108, _812104) = c_Sum__Type_OProjl(_812110, _812106, _812102)), _812112 = _812110, _812108 = _812106, _812104 = _812102], (8726 ^ _779571) ^ [_923653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _923653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _923653))))], (27814 ^ _779571) ^ [_1272165, _1272167, _1272169] : [class_Lattices_Osemilattice__sup(_1272165), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272165), _1272167), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272165), _1272169), _1272167))))], (49664 ^ _779571) ^ [_1777048, _1777050, _1777052, _1777054] : [-(_1777048 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777050)), _1777052)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1777050, hAPP(hAPP(c_List_Olist__update(_1777050, _1777052), _1777048), _1777054)) = hAPP(hAPP(c_List_Olist__update(_1777050, c_List_Obutlast(_1777050, _1777052)), _1777048), _1777054))], (30590 ^ _779571) ^ [_1328918, _1328920, _1328922, _1328924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328918, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328918), _1328920), _1328922)), _1328924))), hBOOL(hAPP(hAPP(c_member(_1328918), _1328920), _1328924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328918, tc_HOL_Obool)), _1328922), _1328924))], (5594 ^ _779571) ^ [_865936, _865938, _865940, _865942] : [-(tc_prod(_865942, _865938) = tc_prod(_865940, _865936)), _865942 = _865940, _865938 = _865936], (40423 ^ _779571) ^ [_1546824, _1546826, _1546828, _1546830] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546824, _1546826), _1546828), _1546830) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1546824, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), _1546828), hAPP(hAPP(c_COMBS(_1546824, tc_fun(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546826, tc_HOL_Obool), tc_fun(tc_fun(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), _1546824), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), _1546830)), hAPP(hAPP(c_COMBC(_1546824, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546826, tc_fun(tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), _1546824), c_COMBC(_1546826, tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546826, tc_prod(_1546824, _1546826)), tc_fun(_1546826, tc_fun(tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))), _1546824), hAPP(c_COMBB(tc_prod(_1546824, _1546826), tc_fun(tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool), tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool)), _1546826), c_Set_Oinsert(tc_prod(_1546824, _1546826)))), c_Product__Type_OPair(_1546824, _1546826)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1546824, _1546826), tc_HOL_Obool))))))], (6865 ^ _779571) ^ [_892844, _892846, _892848] : [_892846 = _892848, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892844), _892846) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892844), _892848))], (18171 ^ _779571) ^ [_1092087, _1092089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1092087), _1092089) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 18172 ^ _779571 : [(18179 ^ _779571) ^ [] : [_1092087 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1092089 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (18173 ^ _779571) ^ [] : [_1092087 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1092089 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (13697 ^ _779571) ^ [_1009234, _1009236, _1009238, _1009240] : [class_Divides_Osemiring__div(_1009234), -(c_Divides_Odiv__class_Omod(_1009234, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009234), _1009236), c_Divides_Odiv__class_Omod(_1009234, _1009238, _1009240)), _1009240) = c_Divides_Odiv__class_Omod(_1009234, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009234), _1009236), _1009238), _1009240))], (8240 ^ _779571) ^ [_916240, _916242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916240), _916242)), 8244 ^ _779571 : [(8247 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _916240), 8243 ^ [_916240, _916242]) = _916242)], (8245 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8243 ^ [_916240, _916242])))]]], (31118 ^ _779571) ^ [_1340117] : [31120 ^ _779571 : [(31123 ^ _779571) ^ [_1340227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31119 ^ [_1340117, _1340227]), _1340227))], (31121 ^ _779571) ^ [_1340193] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31119 ^ [_1340117, _1340193]), _1340117)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1340117)))], (17081 ^ _779571) ^ [_1073057, _1073059, _1073061, _1073063] : [class_Int_Onumber__ring(_1073057), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073057), hAPP(c_Int_Onumber__class_Onumber__of(_1073057), _1073059)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073057), _1073061), hAPP(c_Int_Onumber__class_Onumber__of(_1073057), _1073063))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073057), hAPP(c_Int_Onumber__class_Onumber__of(_1073057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073059), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1073063)))), _1073061))], (41905 ^ _779571) ^ [_1589494, _1589496, _1589498, _1589500, _1589502, _1589504, _1589506] : [-(c_Predicate_Opred__comp(_1589494, _1589496, _1589498, _1589500, _1589502, _1589504, _1589506)), 41906 ^ _779571 : [(41907 ^ _779571) ^ [_1589559] : [hBOOL(hAPP(hAPP(_1589500, _1589504), _1589559)), hBOOL(hAPP(hAPP(_1589502, _1589559), _1589506))]]], (18693 ^ _779571) ^ [_1100292, _1100294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1100292)), c_Int_OBit1(_1100294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100292), _1100294)))], (48738 ^ _779571) ^ [_1756801, _1756803, _1756805, _1756807] : [-(hAPP(hAPP(c_List_Odrop(_1756801), hAPP(c_Nat_OSuc, _1756803)), hAPP(hAPP(c_List_Olist_OCons(_1756801), _1756805), _1756807)) = hAPP(hAPP(c_List_Odrop(_1756801), _1756803), _1756807))], (18877 ^ _779571) ^ [_1103332, _1103334] : [class_Int_Onumber__ring(_1103332), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103332), _1103334), hAPP(c_Int_Onumber__class_Onumber__of(_1103332), c_Int_OBit1(c_Int_OPls))) = _1103334)], (16917 ^ _779571) ^ [_1069832, _1069834] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069832), _1069834)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1069832) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36234 ^ _779571) ^ [_1452354, _1452356] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452354, tc_HOL_Obool)), _1452356), c_Orderings_Obot__class_Obot(tc_fun(_1452354, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1452354, tc_HOL_Obool)))], (30698 ^ _779571) ^ [_1331022, _1331024, _1331026] : [class_Orderings_Oord(_1331022), 30701 ^ _779571 : [(30708 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331022), _1331026), _1331024)), -(hBOOL(hAPP(hAPP(c_member(_1331022), _1331024), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1331022), _1331026))))], (30702 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1331022), _1331024), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1331022), _1331026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331022), _1331026), _1331024)))]]], (18337 ^ _779571) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (10008 ^ _779571) ^ [_946222, _946224] : [class_Rings_Oring__1(_946222), -(hAPP(c_Int_Oring__1__class_Oof__int(_946222), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946224)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_946222), _946224))], (34124 ^ _779571) ^ [_1403468, _1403470, _1403472] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403468, tc_Nat_Onat), _1403470), _1403472) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403468, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1403468), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1403470)), _1403472)))], (10690 ^ _779571) ^ [_957495, _957497, _957499] : [10691 ^ _779571 : [(10694 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957497), _957499))], (10692 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957495)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957495), _957497)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957495), _957499))))], (25116 ^ _779571) ^ [_1219994] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219994), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1219994 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3200 ^ _779571) ^ [_828583, _828585, _828587, _828589, _828591, _828593, _828595, _828597] : [-(c_SetInterval_Oord_OatLeastAtMost(_828597, _828593, _828589, _828585) = c_SetInterval_Oord_OatLeastAtMost(_828595, _828591, _828587, _828583)), _828597 = _828595, _828593 = _828591, _828589 = _828587, _828585 = _828583], (16923 ^ _779571) ^ [_1069933, _1069935, _1069937] : [class_Int_Onumber__ring(_1069933), -(hAPP(c_Int_Onumber__class_Onumber__of(_1069933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1069935), _1069937)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069933), hAPP(c_Int_Onumber__class_Onumber__of(_1069933), _1069935)), hAPP(c_Int_Onumber__class_Onumber__of(_1069933), _1069937)))], (50762 ^ _779571) ^ [_1800157, _1800159, _1800161, _1800163] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800157)), _1800159) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800161)), _1800163), -(hAPP(hAPP(c_List_Ozip(_1800157, _1800161), hAPP(c_List_Orev(_1800157), _1800159)), hAPP(c_List_Orev(_1800161), _1800163)) = hAPP(c_List_Orev(tc_prod(_1800157, _1800161)), hAPP(hAPP(c_List_Ozip(_1800157, _1800161), _1800159), _1800163)))], (50320 ^ _779571) ^ [_1790436, _1790438, _1790440, _1790442, _1790444] : [class_Orderings_Olinorder(_1790436), c_List_Olinorder__class_Osorted(_1790436, hAPP(hAPP(c_List_Omap(_1790438, _1790436), _1790440), _1790442)), -(c_List_Olinorder__class_Osorted(_1790436, hAPP(hAPP(c_List_Omap(_1790438, _1790436), _1790440), c_List_Olinorder__class_Oinsort__insert__key(_1790438, _1790436, _1790440, _1790444, _1790442))))], (22810 ^ _779571) ^ [_1174948, _1174950, _1174952, _1174954] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1174948, _1174950), _1174952)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1174948, _1174950), _1174954)), -(_1174952 = _1174954)], (6572 ^ _779571) ^ [_886851, _886853, _886855] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886851), _886853), _886855)), -(c_Natural_Oevaln(_886851, _886853, 6575 ^ [_886851, _886853, _886855], _886855))], (49449 ^ _779571) ^ [_1772695, _1772697, _1772699] : [_1772695 = c_List_Olist_ONil(_1772697), -(c_List_Olast(_1772697, hAPP(hAPP(c_List_Olist_OCons(_1772697), _1772699), _1772695)) = _1772699)], (28940 ^ _779571) ^ [_1295122, _1295124, _1295126, _1295128, _1295130] : [28942 ^ _779571 : [(28945 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295122, tc_HOL_Obool)), hAPP(_1295128, 28941 ^ [_1295122, _1295124, _1295126, _1295128, _1295130])), _1295130))], (28943 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295124), 28941 ^ [_1295122, _1295124, _1295126, _1295128, _1295130]), _1295126)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295122, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295124, tc_fun(_1295122, tc_HOL_Obool)), _1295126), _1295128)), _1295130)))], (38557 ^ _779571) ^ [_1503906, _1503908, _1503910, _1503912, _1503914] : [c_Fun_Oinj__on(_1503906, _1503908, _1503910, c_Orderings_Otop__class_Otop(tc_fun(_1503906, tc_HOL_Obool))), 38560 ^ _779571 : [(38567 ^ _779571) ^ [] : [_1503912 = _1503914, -(hAPP(_1503910, _1503912) = hAPP(_1503910, _1503914))], (38561 ^ _779571) ^ [] : [hAPP(_1503910, _1503912) = hAPP(_1503910, _1503914), -(_1503912 = _1503914)]]], (32566 ^ _779571) ^ [_1373465, _1373467, _1373469] : [hAPP(c_Finite__Set_Ocard(_1373465), _1373467) = hAPP(c_Nat_OSuc, _1373469), 32571 ^ _779571 : [(32574 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1373465), 32569 ^ [_1373465, _1373467, _1373469]), 32570 ^ [_1373465, _1373467, _1373469]))], (32576 ^ _779571) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1373465), 32570 ^ [_1373465, _1373467, _1373469]) = _1373469)], (32578 ^ _779571) ^ [] : [_1373469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(32570 ^ [_1373465, _1373467, _1373469] = c_Orderings_Obot__class_Obot(tc_fun(_1373465, tc_HOL_Obool)))], (32572 ^ _779571) ^ [] : [-(_1373467 = hAPP(hAPP(c_Set_Oinsert(_1373465), 32569 ^ [_1373465, _1373467, _1373469]), 32570 ^ [_1373465, _1373467, _1373469]))]]], (6905 ^ _779571) ^ [_893501, _893503] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893501), hAPP(c_Nat_OSuc, _893503)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893501), _893503)))], (17043 ^ _779571) ^ [_1072313] : [_1072313 = 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), _1072313)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (41139 ^ _779571) ^ [_1562778, _1562780, _1562782] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562778, tc_HOL_Obool)), _1562780), _1562782) = hAPP(c_Set_OCollect(_1562778), hAPP(hAPP(c_COMBS(_1562778, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562778), c_fdisj), hAPP(hAPP(c_COMBC(_1562778, tc_fun(_1562778, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562778)), _1562780))), hAPP(hAPP(c_COMBC(_1562778, tc_fun(_1562778, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562778)), _1562782))))], (18303 ^ _779571) ^ [_1094096, _1094098, _1094100] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094096), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094098)), _1094100)) = 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), _1094096), _1094098))), _1094100))], (33039 ^ _779571) ^ [_1382070, _1382072, _1382074] : [class_Lattices_Olattice(_1382070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382070), _1382072)), -(_1382074 = c_Orderings_Obot__class_Obot(tc_fun(_1382070, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382070, tc_HOL_Obool)), _1382074), _1382072)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1382070), c_Big__Operators_Olattice__class_OSup__fin(_1382070, _1382074)), c_Big__Operators_Olattice__class_OSup__fin(_1382070, _1382072)) = c_Big__Operators_Olattice__class_OSup__fin(_1382070, _1382072))], (47023 ^ _779571) ^ [_1714620, _1714622, _1714624, _1714626] : [-(hBOOL(hAPP(hAPP(c_member(_1714620), _1714622), hAPP(c_List_Oset(_1714620), _1714624)))), hBOOL(hAPP(hAPP(c_member(_1714620), _1714622), hAPP(c_List_Oset(_1714620), c_List_Osublist(_1714620, _1714624, _1714626))))], (15834 ^ _779571) ^ [_1048566, _1048568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048566), _1048568)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048568), _1048566)) = _1048568)], (39866 ^ _779571) ^ [_1532705, _1532707, _1532709, _1532711] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1532705, _1532707, hAPP(hAPP(c_Set_Oinsert(_1532705), _1532709), c_Orderings_Obot__class_Obot(tc_fun(_1532705, tc_HOL_Obool)))), _1532711)), -(_1532709 = _1532711)], (35267 ^ _779571) ^ [_1429135, _1429137, _1429139] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1429135, tc_HOL_Obool)), _1429139), hAPP(c_Set_OPow(_1429135), _1429137))), -(hBOOL(hAPP(c_Predicate_OPowp(_1429135, hAPP(hAPP(c_COMBC(_1429135, tc_fun(_1429135, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429135)), _1429137)), _1429139)))], (22482 ^ _779571) ^ [_1168408, _1168410, _1168412, _1168414, _1168416] : [-(hAPP(c_Nat_Onat_Onat__rec(_1168408, _1168410, _1168412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168414)), _1168416)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1168408), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1168414))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1168408, _1168408), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1168408, tc_fun(_1168408, _1168408)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1168408, tc_fun(_1168408, _1168408)), tc_Int_Oint), c_If(_1168408)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1168408, _1168410, _1168412), _1168416))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1168408, _1168408), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1168408, _1168408), tc_Int_Oint), _1168412), 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)), _1168416))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1168408, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1168408, _1168410, _1168412)), 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)), _1168416))))))], (9894 ^ _779571) ^ [_944385] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _944385)), _944385) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44596 ^ _779571) ^ [_1654079, _1654081, _1654083, _1654085, _1654087] : [hBOOL(hAPP(hAPP(c_member(_1654079), _1654081), _1654083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654085, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654079, tc_fun(_1654085, tc_HOL_Obool)), _1654083), _1654087)), hAPP(_1654087, _1654081))))], (5348 ^ _779571) ^ [_862209, _862211] : [_862211 = _862209, -(c_List_Oappend(_862211) = c_List_Oappend(_862209))], (43479 ^ _779571) ^ [_1627277, _1627279, _1627281] : [c_Relation_Ototal__on(_1627277, _1627279, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1627277, _1627277), tc_HOL_Obool)), _1627281), c_Relation_OId(_1627277))), -(c_Relation_Ototal__on(_1627277, _1627279, _1627281))], (40819 ^ _779571) ^ [_1555369, _1555371, _1555373, _1555375, _1555377] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555369, _1555371)), _1555373), hAPP(hAPP(c_Product__Type_OSigma(_1555369, _1555371), _1555375), _1555377))), 40823 ^ _779571 : [(40829 ^ _779571) ^ [] : [-(_1555373 = hAPP(hAPP(c_Product__Type_OPair(_1555369, _1555371), 40822 ^ [_1555369, _1555371, _1555373, _1555375, _1555377]), 40825 ^ [_1555369, _1555371, _1555373, _1555375, _1555377]))], (40827 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555371), 40825 ^ [_1555369, _1555371, _1555373, _1555375, _1555377]), hAPP(_1555377, 40822 ^ [_1555369, _1555371, _1555373, _1555375, _1555377]))))], (40824 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555369), 40822 ^ [_1555369, _1555371, _1555373, _1555375, _1555377]), _1555375)))]]], (30235 ^ _779571) ^ [_1321608, _1321610, _1321612, _1321614, _1321616] : [-(hBOOL(hAPP(hAPP(c_member(_1321608), _1321610), hAPP(c_Set_Oimage(_1321612, _1321608, _1321614), _1321616)))), 30236 ^ _779571 : [(30237 ^ _779571) ^ [_1321678] : [hBOOL(hAPP(hAPP(c_member(_1321612), _1321678), _1321616)), _1321610 = hAPP(_1321614, _1321678)]]], (5749 ^ _779571) ^ [_871519, _871521, _871523] : [-(c_Hoare__Mirabelle_Ohoare__valids(_871519, _871521, _871523)), 5751 ^ _779571 : [(5752 ^ _779571) ^ [_871665] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871519)), _871665), _871521)), -(c_Hoare__Mirabelle_Otriple__valid(_871519, 5750 ^ [_871519, _871521, _871523], _871665))], (5761 ^ _779571) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_871519, 5750 ^ [_871519, _871521, _871523], 5757 ^ [_871519, _871521, _871523])], (5759 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871519)), 5757 ^ [_871519, _871521, _871523]), _871523)))]]], (11529 ^ _779571) ^ [_971135, _971137, _971139, _971141, _971143] : [c_Natural_Oevaln(_971135, _971137, _971139, _971141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971139), _971143)), -(c_Natural_Oevaln(_971135, _971137, _971143, _971141))], (49056 ^ _779571) ^ [_1763750, _1763752, _1763754] : [-(hAPP(c_List_Otl(_1763750), hAPP(hAPP(c_List_Oappend(_1763750), _1763752), _1763754)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1763750), _1763750, hAPP(c_List_Otl(_1763750), _1763754), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1763750), tc_List_Olist(_1763750)), _1763750), hAPP(hAPP(c_COMBC(tc_List_Olist(_1763750), tc_List_Olist(_1763750), tc_List_Olist(_1763750)), c_List_Oappend(_1763750)), _1763754))), _1763752))], (7409 ^ _779571) ^ [_902499, _902501] : [hBOOL(hAPP(_902499, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7415 ^ _779571 : [(7418 ^ _779571) ^ [] : [hBOOL(hAPP(_902499, hAPP(c_Nat_OSuc, 7414 ^ [_902499, _902501])))], (7416 ^ _779571) ^ [] : [-(hBOOL(hAPP(_902499, 7414 ^ [_902499, _902501])))]], -(hBOOL(hAPP(_902499, _902501)))], (49860 ^ _779571) ^ [_1781820, _1781822, _1781824, _1781826] : [-(c_List_Otranspose(_1781820, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1781822), tc_List_Olist(_1781820)), hAPP(c_List_Omap(_1781822, _1781820), _1781824)), _1781826)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1781822), tc_List_Olist(_1781820)), hAPP(c_List_Omap(_1781822, _1781820), _1781824)), c_List_Otranspose(_1781822, _1781826)))], (17067 ^ _779571) ^ [_1072716, _1072718, _1072720] : [class_Int_Onumber__ring(_1072716), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072716), hAPP(c_Groups_Ouminus__class_Ouminus(_1072716), hAPP(c_Int_Onumber__class_Onumber__of(_1072716), _1072718))), _1072720) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072716), hAPP(c_Int_Onumber__class_Onumber__of(_1072716), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1072718))), _1072720))], (46432 ^ _779571) ^ [_1697567, _1697569, _1697571, _1697573, _1697575, _1697577, _1697579, _1697581] : [-(hAPP(hAPP(c_List_Ozip(_1697567, _1697569), hAPP(hAPP(c_List_Omap(_1697571, _1697567), _1697573), _1697575)), hAPP(hAPP(c_List_Omap(_1697577, _1697569), _1697579), _1697581)) = hAPP(hAPP(c_List_Omap(tc_prod(_1697571, _1697577), tc_prod(_1697567, _1697569)), hAPP(c_Product__Type_Oprod_Oprod__case(_1697571, _1697577, tc_prod(_1697567, _1697569)), hAPP(hAPP(c_COMBC(_1697571, tc_fun(_1697577, _1697569), tc_fun(_1697577, tc_prod(_1697567, _1697569))), hAPP(hAPP(c_COMBB(tc_fun(_1697569, tc_prod(_1697567, _1697569)), tc_fun(tc_fun(_1697577, _1697569), tc_fun(_1697577, tc_prod(_1697567, _1697569))), _1697571), c_COMBB(_1697569, tc_prod(_1697567, _1697569), _1697577)), hAPP(hAPP(c_COMBB(_1697567, tc_fun(_1697569, tc_prod(_1697567, _1697569)), _1697571), c_Product__Type_OPair(_1697567, _1697569)), _1697573))), _1697579))), hAPP(hAPP(c_List_Ozip(_1697571, _1697577), _1697575), _1697581)))], (40887 ^ _779571) ^ [_1557479, _1557481, _1557483, _1557485, _1557487, _1557489, _1557491, _1557493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557479, _1557481)), _1557483), hAPP(c_Set_Oimage(tc_prod(_1557485, _1557487), tc_prod(_1557479, _1557481), c_Product__Type_Omap__pair(_1557485, _1557479, _1557487, _1557481, _1557489, _1557491)), _1557493))), 40892 ^ _779571 : [(40895 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557485, _1557487)), hAPP(hAPP(c_Product__Type_OPair(_1557485, _1557487), 40890 ^ [_1557479, _1557481, _1557483, _1557485, _1557487, _1557489, _1557491, _1557493]), 40891 ^ [_1557479, _1557481, _1557483, _1557485, _1557487, _1557489, _1557491, _1557493])), _1557493)))], (40893 ^ _779571) ^ [] : [-(_1557483 = hAPP(hAPP(c_Product__Type_OPair(_1557479, _1557481), hAPP(_1557489, 40890 ^ [_1557479, _1557481, _1557483, _1557485, _1557487, _1557489, _1557491, _1557493])), hAPP(_1557491, 40891 ^ [_1557479, _1557481, _1557483, _1557485, _1557487, _1557489, _1557491, _1557493])))]]], (2400 ^ _779571) ^ [_815811, _815813] : [_815813 = _815811, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_815813) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_815811))], (40736 ^ _779571) ^ [_1553311, _1553313, _1553315, _1553317, _1553319, _1553321] : [class_Groups_Ocomm__monoid__mult(_1553311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553313), _1553315)), 40746 ^ _779571 : [(40749 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553317), hAPP(_1553319, 40745 ^ [_1553311, _1553313, _1553315, _1553317, _1553319, _1553321])))], (40747 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553313), 40745 ^ [_1553311, _1553313, _1553315, _1553317, _1553319, _1553321]), _1553315)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1553311, _1553313, c_Groups_Otimes__class_Otimes(_1553311)), hAPP(hAPP(c_COMBS(_1553313, tc_fun(_1553317, tc_HOL_Obool), _1553311), hAPP(hAPP(c_COMBC(_1553313, _1553311, tc_fun(tc_fun(_1553317, tc_HOL_Obool), _1553311)), hAPP(hAPP(c_COMBB(tc_fun(_1553317, _1553311), tc_fun(_1553311, tc_fun(tc_fun(_1553317, tc_HOL_Obool), _1553311)), _1553313), c_Finite__Set_Ofold__image(_1553311, _1553317, c_Groups_Otimes__class_Otimes(_1553311))), _1553321)), c_Groups_Oone__class_Oone(_1553311))), _1553319)), c_Groups_Oone__class_Oone(_1553311)), _1553315) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1553311, tc_prod(_1553313, _1553317), c_Groups_Otimes__class_Otimes(_1553311)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553313, _1553317, _1553311), _1553321)), c_Groups_Oone__class_Oone(_1553311)), hAPP(hAPP(c_Product__Type_OSigma(_1553313, _1553317), _1553315), _1553319)))], (29668 ^ _779571) ^ [_1309733, _1309735] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309733, _1309735), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309733), _1309735))], (39852 ^ _779571) ^ [_1532390, _1532392, _1532394, _1532396] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1532390, _1532392, _1532394), _1532396)), _1532394 = c_Orderings_Obot__class_Obot(tc_fun(_1532390, tc_HOL_Obool))], (8136 ^ _779571) ^ [] : [-(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))], (46512 ^ _779571) ^ [_1699611, _1699613, _1699615, _1699617] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699611)), hAPP(hAPP(c_List_Omap(_1699613, _1699611), _1699615), _1699617)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699613)), _1699617))], (26670 ^ _779571) ^ [_1248605, _1248607, _1248609] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248605), _1248607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248605), _1248609))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248605)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248607), _1248609)))], (40200 ^ _779571) ^ [_1541700, _1541702] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1541700, _1541702), c_Orderings_Otop__class_Otop(tc_fun(_1541700, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1541702, tc_HOL_Obool), _1541700), c_Orderings_Otop__class_Otop(tc_fun(_1541702, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1541700, _1541702), tc_HOL_Obool)))], (22512 ^ _779571) ^ [_1169147, _1169149] : [22513 ^ _779571 : [(22516 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1169149), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22514 ^ _779571) ^ [] : [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), _1169147), _1169149)))]], -(c_Divides_OnegDivAlg(_1169147, _1169149) = 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), _1169147), _1169149)))], (43198 ^ _779571) ^ [_1620309, _1620311, _1620313, _1620315] : [-(hBOOL(hAPP(hAPP(c_member(_1620309), _1620311), hAPP(c_Relation_ODomain(_1620309, _1620309), _1620313)))), 43201 ^ _779571 : [(43208 ^ _779571) ^ [] : [_1620311 = _1620315, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620309, _1620309)), hAPP(hAPP(c_Product__Type_OPair(_1620309, _1620309), _1620311), _1620315)), c_Transitive__Closure_Ortrancl(_1620309, _1620313))))], (43202 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620309, _1620309)), hAPP(hAPP(c_Product__Type_OPair(_1620309, _1620309), _1620311), _1620315)), c_Transitive__Closure_Ortrancl(_1620309, _1620313))), -(_1620311 = _1620315)]]], (11479 ^ _779571) ^ [_970232, _970234, _970236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970232), _970234)), _970236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970232), _970236)))], (44307 ^ _779571) ^ [_1646006, _1646008, _1646010, _1646012, _1646014] : [c_Finite__Set_Ofun__left__comm(_1646006, _1646008, _1646010), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646006), _1646012)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1646006, _1646008, _1646010, _1646014, _1646012), hAPP(hAPP(c_Finite__Set_Ofold(_1646006, _1646008, _1646010), _1646014), _1646012))))], (32073 ^ _779571) ^ [_1363012, _1363014, _1363016, _1363018, _1363020, _1363022] : [hBOOL(hAPP(hAPP(_1363012, _1363014), _1363016)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363018, tc_fun(_1363020, tc_HOL_Obool))), _1363022), _1363012), _1363014), _1363016)))], (1302 ^ _779571) ^ [_798614, _798616] : [-(class_Lattices_Oboolean__algebra(_798614)), _798616 = _798614, class_Lattices_Oboolean__algebra(_798616)], (36186 ^ _779571) ^ [_1450979, _1450981, _1450983, _1450985] : [class_Lattices_Odistrib__lattice(_1450979), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1450979), _1450981), _1450983)), _1450985) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1450979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450979), _1450981), _1450985)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450979), _1450983), _1450985)))], (29662 ^ _779571) ^ [_1309670, _1309672] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309670), _1309672))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309670, _1309672) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (19881 ^ _779571) ^ [_1120936, _1120938, _1120940] : [class_Int_Onumber__ring(_1120936), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1120936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120936), _1120938), _1120940)), 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(_1120936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120936), hAPP(hAPP(c_Power_Opower__class_Opower(_1120936), _1120938), 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(_1120936), _1120940), 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(_1120936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120936), hAPP(c_Int_Onumber__class_Onumber__of(_1120936), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1120938)), _1120940)))], (43530 ^ _779571) ^ [_1628621, _1628623, _1628625] : [c_Wellfounded_Owf(_1628621, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628621, _1628621), tc_HOL_Obool), _1628623), _1628625)), -(c_Wellfounded_Owf(_1628621, _1628625))], (6534 ^ _779571) ^ [_886172, _886174] : [_886172 = _886174, -(hAPP(c_Com_Ocom_OBODY, _886172) = hAPP(c_Com_Ocom_OBODY, _886174))], (36594 ^ _779571) ^ [_1459312, _1459314, _1459316] : [class_Lattices_Osemilattice__inf(_1459312), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459312), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459312), _1459314), _1459316)), _1459314)))], (43742 ^ _779571) ^ [_1633875, _1633877, _1633879] : [c_Relation_Osingle__valued(_1633875, _1633877, _1633879), 43745 ^ _779571 : [(43746 ^ _779571) ^ [_1633996, _1633998] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633875, _1633877)), hAPP(hAPP(c_Product__Type_OPair(_1633875, _1633877), _1633998), _1633996)), _1633879)), 43749 ^ _779571 : [(43750 ^ _779571) ^ [_1634122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633875, _1633877)), hAPP(hAPP(c_Product__Type_OPair(_1633875, _1633877), _1633998), _1634122)), _1633879)), -(_1633996 = _1634122)]]]]], (41842 ^ _779571) ^ [_1588198, _1588200, _1588202] : [c_Wellfounded_Owf(_1588198, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588198, _1588198), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588198, _1588198), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588198, _1588198, _1588198), _1588200), _1588200)), hAPP(hAPP(c_Relation_Orel__comp(_1588198, _1588198, _1588198), _1588202), _1588200))), _1588202)), -(c_Wellfounded_Owf(_1588198, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588198, _1588198), tc_HOL_Obool)), _1588200), _1588202)))], (44654 ^ _779571) ^ [_1655638, _1655640, _1655642, _1655644, _1655646] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655638, tc_fun(_1655640, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1655638), _1655642), _1655644)), _1655646) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655640, tc_HOL_Obool)), hAPP(_1655646, _1655642)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655638, tc_fun(_1655640, tc_HOL_Obool)), _1655644), _1655646)))], (18771 ^ _779571) ^ [_1101588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1101588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1101588)))], (5829 ^ _779571) ^ [_872926, _872928] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _872926, _872928, _872926))], (31896 ^ _779571) ^ [_1358971, _1358973, _1358975, _1358977, _1358979] : [class_Rings_Oring(_1358971), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358973), _1358975)), hBOOL(hAPP(hAPP(c_member(_1358973), _1358977), _1358975)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358973, _1358971), _1358979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358973, tc_HOL_Obool)), _1358975), hAPP(hAPP(c_Set_Oinsert(_1358973), _1358977), c_Orderings_Obot__class_Obot(tc_fun(_1358973, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358971), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358973, _1358971), _1358979), _1358975)), hAPP(_1358979, _1358977)))], (48363 ^ _779571) ^ [_1746179, _1746181, _1746183] : [-(hAPP(hAPP(c_List_Otake(_1746179), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1746179), _1746181), _1746183)) = hAPP(hAPP(c_List_Olist_OCons(_1746179), _1746181), c_List_Olist_ONil(_1746179)))], (27836 ^ _779571) ^ [_1272528, _1272530, _1272532, _1272534] : [class_Lattices_Osemilattice__sup(_1272528), 27839 ^ _779571 : [(27848 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272528), _1272530), _1272532)), _1272534))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), _1272530), _1272534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), _1272532), _1272534))], (27840 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272528), _1272530), _1272532)), _1272534)), 27843 ^ _779571 : [(27846 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), _1272532), _1272534)))], (27844 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272528), _1272530), _1272534)))]]]]], (22382 ^ _779571) ^ [_1166016, _1166018] : [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(_1166018))), 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)), _1166016))))), -(hAPP(c_Nat_OSuc, _1166016) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166018))], (39860 ^ _779571) ^ [_1532547, _1532549, _1532551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532547, _1532547), tc_HOL_Obool)), _1532549), _1532551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532547, tc_HOL_Obool)), c_Wellfounded_Oacc(_1532547, _1532551)), c_Wellfounded_Oacc(_1532547, _1532549))))], (45959 ^ _779571) ^ [_1686043] : [-(hAPP(c_List_Omap(_1686043, _1686043), c_Fun_Oid(_1686043)) = c_Fun_Oid(tc_List_Olist(_1686043)))], (42577 ^ _779571) ^ [_1605020, _1605022, _1605024] : [hBOOL(hAPP(_1605020, _1605022)), -(hBOOL(hAPP(_1605020, c_Hilbert__Choice_OEps(_1605024, _1605020))))], (44422 ^ _779571) ^ [_1648361, _1648363, _1648365, _1648367, _1648369, _1648371] : [hBOOL(hAPP(hAPP(c_member(_1648361), _1648363), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648365, tc_fun(_1648361, tc_HOL_Obool)), _1648367), _1648369))), -(hBOOL(hAPP(hAPP(c_member(_1648361), _1648363), hAPP(_1648369, _1648371)))), hBOOL(hAPP(hAPP(c_member(_1648365), _1648371), _1648367))], (24299 ^ _779571) ^ [_1203025, _1203027, _1203029] : [class_Orderings_Olinorder(_1203025), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203025), _1203027), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203025), _1203027), _1203029)) = _1203027)], (29083 ^ _779571) ^ [_1298438, _1298440, _1298442, _1298444, _1298446] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298438, tc_fun(_1298440, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1298438), _1298442), _1298444)), _1298446) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298440, tc_HOL_Obool)), hAPP(_1298446, _1298442)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298438, tc_fun(_1298440, tc_HOL_Obool)), _1298444), _1298446)))], (20993 ^ _779571) ^ [_1140827, _1140829, _1140831, _1140833] : [class_Fields_Olinordered__field__inverse__zero(_1140827), 20996 ^ _779571 : [(20997 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140829), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140827), _1140831), _1140833))), 21000 ^ _779571 : [(21007 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), c_Groups_Ozero__class_Ozero(_1140827)), _1140833))), 21010 ^ _779571 : [(21017 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140833), c_Groups_Ozero__class_Ozero(_1140827)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140829), c_Groups_Ozero__class_Ozero(_1140827))))], (21011 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140833), c_Groups_Ozero__class_Ozero(_1140827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140827), _1140829), _1140833))))]]], (21001 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), c_Groups_Ozero__class_Ozero(_1140827)), _1140833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140827), _1140829), _1140833)), _1140831)))]]], (21023 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140829), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140827), _1140831), _1140833)))), 21026 ^ _779571 : [(21029 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140827), _1140829), _1140833)), _1140831))], (21027 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), c_Groups_Ozero__class_Ozero(_1140827)), _1140833)))]], 21030 ^ _779571 : [(21033 ^ _779571) ^ [] : [21034 ^ _779571 : [(21037 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140827), _1140829), _1140833)))], (21035 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140833), c_Groups_Ozero__class_Ozero(_1140827))))]], 21038 ^ _779571 : [(21041 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140829), c_Groups_Ozero__class_Ozero(_1140827)))], (21039 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140833), c_Groups_Ozero__class_Ozero(_1140827)))]]], (21031 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), c_Groups_Ozero__class_Ozero(_1140827)), _1140833))]]]]], (5276 ^ _779571) ^ [_861121, _861123] : [_861123 = _861121, -(c_List_Otl(_861123) = c_List_Otl(_861121))], (50815 ^ _779571) ^ [_1801776, _1801778, _1801780] : [50817 ^ _779571 : [(50820 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1801776), tc_List_Olist(_1801776), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1801776), tc_fun(tc_List_Olist(_1801776), tc_Nat_Onat), tc_fun(tc_List_Olist(_1801776), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1801776), tc_Nat_Onat), tc_fun(tc_List_Olist(_1801776), tc_HOL_Obool)), tc_List_Olist(_1801776)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1801776))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1801776)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1801776))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1801776)))), 50816 ^ [_1801776, _1801778, _1801780]))], (50818 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801776), tc_List_Olist(_1801776))), 50816 ^ [_1801776, _1801778, _1801780]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1801776), tc_List_Olist(_1801776))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1801776), tc_List_Olist(_1801776)), _1801778), _1801780)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801776))), _1801778) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801776))), _1801780), 50825 ^ _779571 : [(50832 ^ _779571) ^ [] : [_1801778 = _1801780, -(c_List_Oconcat(_1801776, _1801778) = c_List_Oconcat(_1801776, _1801780))], (50826 ^ _779571) ^ [] : [c_List_Oconcat(_1801776, _1801778) = c_List_Oconcat(_1801776, _1801780), -(_1801778 = _1801780)]]], (1522 ^ _779571) ^ [_801364, _801366] : [-(class_Groups_Oab__semigroup__add(_801364)), _801366 = _801364, class_Groups_Oab__semigroup__add(_801366)], (47991 ^ _779571) ^ [_1737575, _1737577, _1737579, _1737581, _1737583] : [hAPP(hAPP(c_List_Oappend(_1737575), _1737577), _1737579) = hAPP(hAPP(c_List_Oappend(_1737575), _1737581), _1737583), 47997 ^ _779571 : [(48000 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1737575), 47994 ^ [_1737575, _1737577, _1737579, _1737581, _1737583]), _1737579) = _1737583)], (47998 ^ _779571) ^ [] : [-(_1737577 = hAPP(hAPP(c_List_Oappend(_1737575), _1737581), 47994 ^ [_1737575, _1737577, _1737579, _1737581, _1737583]))]], 48001 ^ _779571 : [(48004 ^ _779571) ^ [] : [-(_1737579 = hAPP(hAPP(c_List_Oappend(_1737575), 47994 ^ [_1737575, _1737577, _1737579, _1737581, _1737583]), _1737583))], (48002 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1737575), _1737577), 47994 ^ [_1737575, _1737577, _1737579, _1737581, _1737583]) = _1737581)]]], (22846 ^ _779571) ^ [_1175596, _1175598] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175596, _1175598), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1175596), _1175598)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1175596, _1175598)))))], (47701 ^ _779571) ^ [_1730682, _1730684, _1730686, _1730688, _1730690, _1730692] : [-(_1730682 = _1730684), -(hAPP(hAPP(c_List_Olist__update(_1730686, hAPP(hAPP(c_List_Olist__update(_1730686, _1730688), _1730682), _1730690)), _1730684), _1730692) = hAPP(hAPP(c_List_Olist__update(_1730686, hAPP(hAPP(c_List_Olist__update(_1730686, _1730688), _1730684), _1730692)), _1730682), _1730690))], (51049 ^ _779571) ^ [_1807565, _1807567, _1807569, _1807571, _1807573] : [class_Orderings_Olinorder(_1807565), c_List_Olinorder__class_Osorted(_1807565, hAPP(c_List_Orev(_1807565), hAPP(hAPP(c_List_Omap(_1807567, _1807565), _1807569), _1807571))), -(hAPP(c_List_Ofilter(_1807567, hAPP(hAPP(c_COMBB(_1807565, tc_HOL_Obool, _1807567), hAPP(c_Orderings_Oord__class_Oless(_1807565), _1807573)), _1807569)), _1807571) = c_List_OtakeWhile(_1807567, hAPP(hAPP(c_COMBB(_1807565, tc_HOL_Obool, _1807567), hAPP(c_Orderings_Oord__class_Oless(_1807565), _1807573)), _1807569), _1807571))], (24791 ^ _779571) ^ [_1212684, _1212686, _1212688, _1212690, _1212692] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212684, _1212686, _1212684, _1212688), hAPP(c_Product__Type_OPair(_1212686, _1212684), _1212690)), _1212692) = hAPP(_1212692, _1212690))], (35245 ^ _779571) ^ [_1428541, _1428543] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428541), _1428543)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1428541, tc_HOL_Obool)), hAPP(c_Set_OPow(_1428541), _1428543))))], (35044 ^ _779571) ^ [_1423885, _1423887, _1423889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1423885, _1423885)), _1423887), c_Relation_OId__on(_1423885, _1423889))), 35048 ^ _779571 : [(35051 ^ _779571) ^ [] : [-(_1423887 = hAPP(hAPP(c_Product__Type_OPair(_1423885, _1423885), 35047 ^ [_1423885, _1423887, _1423889]), 35047 ^ [_1423885, _1423887, _1423889]))], (35049 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1423885), 35047 ^ [_1423885, _1423887, _1423889]), _1423889)))]]], (31464 ^ _779571) ^ [_1348989, _1348991, _1348993, _1348995, _1348997] : [class_Groups_Ocomm__monoid__add(_1348989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348991), _1348993)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348991, _1348989), hAPP(hAPP(c_COMBS(_1348991, _1348989, _1348989), hAPP(hAPP(c_COMBB(_1348989, tc_fun(_1348989, _1348989), _1348991), c_Groups_Oplus__class_Oplus(_1348989)), _1348995)), _1348997)), _1348993) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348989), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348991, _1348989), _1348995), _1348993)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348991, _1348989), _1348997), _1348993)))], (15616 ^ _779571) ^ [_1044412, _1044414, _1044416, _1044418, _1044420, _1044422] : [class_Rings_Oring(_1044412), 15619 ^ _779571 : [(15626 ^ _779571) ^ [] : [_1044418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044412), _1044420), _1044414)), _1044416)), _1044422), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), _1044414), _1044416)), _1044418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), _1044420), _1044416)), _1044422))], (15620 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), _1044414), _1044416)), _1044418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), _1044420), _1044416)), _1044422), -(_1044418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044412), _1044420), _1044414)), _1044416)), _1044422))]]], (48397 ^ _779571) ^ [_1747153, _1747155, _1747157, _1747159] : [_1747153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1747155), _1747153), hAPP(hAPP(c_List_Olist_OCons(_1747155), _1747157), _1747159)) = c_List_Olist_ONil(_1747155))], (3714 ^ _779571) ^ [_836766, _836768, _836770, _836772, _836774, _836776, _836778, _836780] : [-(c_Recdef_Osame__fst(_836780, _836776, _836772, _836768) = c_Recdef_Osame__fst(_836778, _836774, _836770, _836766)), _836780 = _836778, _836776 = _836774, _836772 = _836770, _836768 = _836766], (50608 ^ _779571) ^ [_1796976, _1796978, _1796980] : [_1796980 = hAPP(hAPP(c_List_Olist_OCons(_1796976), _1796978), c_List_Olist_ONil(_1796976)), -(hAPP(hAPP(c_List_Olist_OCons(_1796976), _1796978), c_List_Olist_ONil(_1796976)) = hAPP(c_List_Orev(_1796976), _1796980))], (24223 ^ _779571) ^ [_1201563, _1201565] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1201563)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1201565)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1201565))), 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, _1201563))), 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), _1201563)), c_Int_Onat)))))], (12049 ^ _779571) ^ [_980444, _980446] : [class_Rings_Olinordered__ring(_980444), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980444), c_Groups_Ozero__class_Ozero(_980444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980444), _980446), _980446))))], (35259 ^ _779571) ^ [_1428877, _1428879, _1428881, _1428883] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1428877, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428879, tc_fun(tc_fun(_1428877, tc_HOL_Obool), tc_HOL_Obool)), _1428881), hAPP(hAPP(c_COMBB(tc_fun(_1428877, tc_HOL_Obool), tc_fun(tc_fun(_1428877, tc_HOL_Obool), tc_HOL_Obool), _1428879), c_Set_OPow(_1428877)), _1428883))), hAPP(c_Set_OPow(_1428877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428879, tc_fun(_1428877, tc_HOL_Obool)), _1428881), _1428883)))))], (51495 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (33129 ^ _779571) ^ [_1383582, _1383584, _1383586] : [class_Lattices_Olattice(_1383582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383582), _1383584)), -(hBOOL(hAPP(hAPP(c_member(_1383582), _1383586), _1383584))), -(_1383584 = c_Orderings_Obot__class_Obot(tc_fun(_1383582, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1383582, hAPP(hAPP(c_Set_Oinsert(_1383582), _1383586), _1383584)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383582), _1383586), c_Big__Operators_Olattice__class_OSup__fin(_1383582, _1383584)))], (2552 ^ _779571) ^ [_818169, _818171, _818173, _818175] : [-(c_Divides_Odivmod__int(_818175, _818171) = c_Divides_Odivmod__int(_818173, _818169)), _818175 = _818173, _818171 = _818169], (50594 ^ _779571) ^ [_1796627, _1796629, _1796631, _1796633] : [_1796629 = hAPP(hAPP(c_List_Oappend(_1796627), hAPP(c_List_Orev(_1796627), _1796633)), hAPP(hAPP(c_List_Olist_OCons(_1796627), _1796631), c_List_Olist_ONil(_1796627))), -(hAPP(c_List_Orev(_1796627), _1796629) = hAPP(hAPP(c_List_Olist_OCons(_1796627), _1796631), _1796633))], (44816 ^ _779571) ^ [_1659973, _1659975, _1659977, _1659979, _1659981, _1659983] : [c_Relation_Osingle__valued(_1659973, _1659975, hAPP(c_Relation_Oconverse(_1659975, _1659973), _1659977)), -(_1659979 = c_Orderings_Obot__class_Obot(tc_fun(_1659981, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1659975, _1659973, _1659977), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659981, tc_fun(_1659975, tc_HOL_Obool)), _1659979), _1659983)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659981, tc_fun(_1659973, tc_HOL_Obool)), _1659979), hAPP(hAPP(c_COMBB(tc_fun(_1659975, tc_HOL_Obool), tc_fun(_1659973, tc_HOL_Obool), _1659981), c_Relation_OImage(_1659975, _1659973, _1659977)), _1659983)))], (9628 ^ _779571) ^ [_939480, _939482, _939484, _939486] : [class_Rings_Olinordered__ring__strict(_939480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939480), c_Groups_Ozero__class_Ozero(_939480)), _939482)), 9635 ^ _779571 : [(9642 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939480), _939484), _939486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939480), _939482), _939484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939480), _939482), _939486))))], (9636 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939480), _939482), _939484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939480), _939482), _939486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939480), _939484), _939486)))]]], (49953 ^ _779571) ^ [_1784164, _1784166, _1784168, _1784170, _1784172] : [class_Orderings_Olinorder(_1784164), -(c_List_Olinorder__class_Osorted(_1784164, hAPP(hAPP(c_List_Omap(_1784166, _1784164), _1784168), hAPP(c_List_Ofilter(_1784166, hAPP(hAPP(c_COMBC(_1784166, _1784164, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1784164, tc_fun(_1784164, tc_HOL_Obool), _1784166), c_fequal), _1784168)), hAPP(_1784170, _1784172))), _1784172))))], (13747 ^ _779571) ^ [_1010343, _1010345, _1010347, _1010349] : [class_Divides_Osemiring__div(_1010343), -(c_Divides_Odiv__class_Omod(_1010343, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010343), _1010345), _1010347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010343), _1010349), _1010347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010343), c_Divides_Odiv__class_Omod(_1010343, _1010345, _1010349)), _1010347))], (22214 ^ _779571) ^ [_1162956, _1162958] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162956), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162958)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162956)) = 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), _1162958), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1162956)))), 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)))], (23215 ^ _779571) ^ [_1182776, _1182778, _1182780, _1182782, _1182784] : [hAPP(c_Product__Type_Osnd(_1182776, _1182778), hAPP(hAPP(c_Product__Type_OPair(_1182776, _1182778), _1182780), _1182782)) = _1182784, -(_1182782 = _1182784)], (34992 ^ _779571) ^ [_1422601, _1422603, _1422605, _1422607] : [-(hAPP(c_Relation_OField(_1422601), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1422601, _1422601)), hAPP(hAPP(c_Product__Type_OPair(_1422601, _1422601), _1422603), _1422605)), _1422607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422601, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1422601), _1422603), hAPP(hAPP(c_Set_Oinsert(_1422601), _1422605), c_Orderings_Obot__class_Obot(tc_fun(_1422601, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1422601), _1422607)))], (10530 ^ _779571) ^ [_954794, _954796, _954798] : [class_Orderings_Oorder(_954794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954794), _954796), _954798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954794), _954798), _954796)), -(_954796 = _954798)], (36134 ^ _779571) ^ [_1449724, _1449726] : [class_Lattices_Obounded__lattice__top(_1449724), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449724), c_Orderings_Otop__class_Otop(_1449724)), _1449726) = _1449726)], (20725 ^ _779571) ^ [_1135738, _1135740, _1135742, _1135744, _1135746] : [class_Fields_Olinordered__field(_1135738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135738), c_Groups_Ozero__class_Ozero(_1135738)), _1135740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135738), _1135740), _1135742)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135738), c_Groups_Ozero__class_Ozero(_1135738)), _1135744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135738), _1135744), _1135746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135738), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135738), _1135740), _1135746)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135738), _1135742), _1135744))))], (29748 ^ _779571) ^ [_1311456, _1311458, _1311460, _1311462] : [-(hAPP(c_Set_Oimage(_1311456, _1311458, _1311460), _1311462) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1311456, tc_fun(_1311458, tc_HOL_Obool)), _1311462), hAPP(hAPP(c_COMBC(_1311456, tc_fun(_1311458, tc_HOL_Obool), tc_fun(_1311458, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1311458, tc_fun(tc_fun(_1311458, tc_HOL_Obool), tc_fun(_1311458, tc_HOL_Obool)), _1311456), c_Set_Oinsert(_1311458)), _1311460)), c_Orderings_Obot__class_Obot(tc_fun(_1311458, tc_HOL_Obool)))))], (6295 ^ _779571) ^ [_881716, _881718] : [hBOOL(hAPP(c_Com_OWT, _881718)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_881716, _881718))))], (39449 ^ _779571) ^ [_1522928, _1522930, _1522932, _1522934, _1522936] : [-(hAPP(c_Set_Ovimage(_1522928, _1522930, _1522932), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522930, tc_HOL_Obool)), _1522934), _1522936)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522928, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522928, _1522930, _1522932), _1522934)), hAPP(c_Set_Ovimage(_1522928, _1522930, _1522932), _1522936)))], (34813 ^ _779571) ^ [_1417762, _1417764, _1417766, _1417768] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1417762), _1417764)), 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)), _1417762), _1417766)), 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)), _1417764), _1417768)), 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)), _1417764), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1417766), _1417768))), c_FunDef_Omin__weak)))], (40993 ^ _779571) ^ [_1559817] : [-(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)), _1559817)))))], (48022 ^ _779571) ^ [_1738315, _1738317, _1738319, _1738321] : [hAPP(hAPP(c_List_Oappend(_1738315), _1738317), _1738319) = hAPP(hAPP(c_List_Oappend(_1738315), _1738317), _1738321), -(_1738319 = _1738321)], (9048 ^ _779571) ^ [_929537, _929539] : [class_Rings_Ocomm__ring__1(_929537), -(hAPP(c_Groups_Ouminus__class_Ouminus(_929537), _929539) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929537), hAPP(c_Groups_Ouminus__class_Ouminus(_929537), c_Groups_Oone__class_Oone(_929537))), _929539))], (51283 ^ _779571) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (46158 ^ _779571) ^ [_1691030, _1691032, _1691034] : [-(hAPP(c_Option_Omap(_1691030, _1691032), _1691034) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1691032), _1691030, c_Option_Ooption_ONone(_1691032), hAPP(hAPP(c_COMBB(_1691032, tc_Option_Ooption(_1691032), _1691030), c_Option_Ooption_OSome(_1691032)), _1691034)))], (7191 ^ _779571) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48914 ^ _779571) ^ [_1761032, _1761034, _1761036, _1761038, _1761040] : [-(hAPP(hAPP(c_List_Ozip(_1761032, _1761034), hAPP(hAPP(c_List_Oappend(_1761032), _1761036), _1761038)), _1761040) = hAPP(hAPP(c_List_Oappend(tc_prod(_1761032, _1761034)), hAPP(hAPP(c_List_Ozip(_1761032, _1761034), _1761036), hAPP(hAPP(c_List_Otake(_1761034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761032)), _1761036)), _1761040))), hAPP(hAPP(c_List_Ozip(_1761032, _1761034), _1761038), hAPP(hAPP(c_List_Odrop(_1761034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761032)), _1761036)), _1761040))))], (36106 ^ _779571) ^ [_1449302, _1449304, _1449306] : [class_Lattices_Obounded__lattice__top(_1449302), 36109 ^ _779571 : [(36118 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449302), _1449304), _1449306) = c_Orderings_Otop__class_Otop(_1449302)), _1449304 = c_Orderings_Otop__class_Otop(_1449302), _1449306 = c_Orderings_Otop__class_Otop(_1449302)], (36110 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449302), _1449304), _1449306) = c_Orderings_Otop__class_Otop(_1449302), 36113 ^ _779571 : [(36116 ^ _779571) ^ [] : [-(_1449306 = c_Orderings_Otop__class_Otop(_1449302))], (36114 ^ _779571) ^ [] : [-(_1449304 = c_Orderings_Otop__class_Otop(_1449302))]]]]], (9040 ^ _779571) ^ [_929413] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929413)) = _929413)], (15220 ^ _779571) ^ [_1037019, _1037021, _1037023, _1037025, _1037027] : [class_Groups_Ominus(_1037019), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037021, _1037019)), _1037023), _1037025), _1037027) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037019), hAPP(_1037023, _1037027)), hAPP(_1037025, _1037027)))], (50330 ^ _779571) ^ [_1790644, _1790646, _1790648, _1790650] : [c_List_Oupt(_1790644, _1790646) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1790648), _1790650), 50333 ^ _779571 : [(50338 ^ _779571) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790644), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1790646) = _1790650)], (50336 ^ _779571) ^ [] : [-(_1790644 = _1790648)], (50334 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790644), _1790646)))]]], (44570 ^ _779571) ^ [_1653109, _1653111, _1653113, _1653115, _1653117] : [hBOOL(hAPP(hAPP(c_member(_1653109), _1653111), _1653113)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1653115, tc_HOL_Obool)), hAPP(_1653117, _1653111)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653109, tc_fun(_1653115, tc_HOL_Obool)), _1653113), _1653117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653109, tc_fun(_1653115, tc_HOL_Obool)), _1653113), _1653117))], (51163 ^ _779571) ^ [_1809212, _1809214] : [class_Groups_Ouminus(_1809212), -(class_Groups_Ouminus(tc_fun(_1809214, _1809212)))], (19339 ^ _779571) ^ [_1111283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111283), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111283)), c_Int_OMin)))], (45620 ^ _779571) ^ [_1678265, _1678267, _1678269, _1678271, _1678273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1678265, tc_HOL_Obool)), _1678267), _1678269)), 45626 ^ _779571 : [(45631 ^ _779571) ^ [] : [hBOOL(hAPP(_1678273, 45625 ^ [_1678265, _1678267, _1678269, _1678271, _1678273]))], (45629 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1678271, 45625 ^ [_1678265, _1678267, _1678269, _1678271, _1678273])))], (45627 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678265), 45625 ^ [_1678265, _1678267, _1678269, _1678271, _1678273]), _1678267)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1678265, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678265, tc_HOL_Obool)), _1678267), hAPP(c_Set_OCollect(_1678265), _1678271))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678265, tc_HOL_Obool)), _1678269), hAPP(c_Set_OCollect(_1678265), _1678273)))))], (44528 ^ _779571) ^ [_1651946, _1651948, _1651950, _1651952] : [-(hAPP(c_Set_OPow(_1651946), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651948, tc_fun(_1651946, tc_HOL_Obool)), _1651950), _1651952)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651948, tc_fun(tc_fun(_1651946, tc_HOL_Obool), tc_HOL_Obool)), _1651950), hAPP(hAPP(c_COMBB(tc_fun(_1651946, tc_HOL_Obool), tc_fun(tc_fun(_1651946, tc_HOL_Obool), tc_HOL_Obool), _1651948), c_Set_OPow(_1651946)), _1651952)))], (40240 ^ _779571) ^ [_1542743, _1542745, _1542747, _1542749] : [c_Finite__Set_Ofolding__one(_1542743, _1542745, _1542747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542743), _1542749)), -(hAPP(_1542747, _1542749) = hAPP(c_Finite__Set_Ofold1(_1542743, _1542745), _1542749))], (41263 ^ _779571) ^ [_1566706, _1566708, _1566710, _1566712] : [-(hAPP(c_Relation_OImage(_1566706, _1566708, _1566710), hAPP(hAPP(c_Set_Oinsert(_1566706), _1566712), c_Orderings_Obot__class_Obot(tc_fun(_1566706, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1566708), hAPP(hAPP(c_COMBC(_1566708, tc_fun(tc_prod(_1566706, _1566708), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566706, _1566708), tc_fun(tc_fun(tc_prod(_1566706, _1566708), tc_HOL_Obool), tc_HOL_Obool), _1566708), c_member(tc_prod(_1566706, _1566708))), hAPP(c_Product__Type_OPair(_1566706, _1566708), _1566712))), _1566710)))], (41947 ^ _779571) ^ [_1590225, _1590227] : [c_Wellfounded_Owf(_1590225, _1590227), 41950 ^ _779571 : [(41951 ^ _779571) ^ [_1590294] : [-(hBOOL(hAPP(hAPP(c_member(_1590225), _1590294), c_Wellfounded_Oacc(_1590225, _1590227))))]]], (45129 ^ _779571) ^ [_1667087, _1667089, _1667091, _1667093] : [-(hAPP(c_Set_Ovimage(_1667087, _1667089, _1667091), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667089, tc_HOL_Obool), _1667093)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1667089, tc_HOL_Obool), tc_fun(_1667087, tc_HOL_Obool)), _1667093), c_Set_Ovimage(_1667087, _1667089, _1667091)))], (8163 ^ _779571) ^ [_914876, _914878, _914880] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914878)), _914880)) = 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), _914876), _914878))), _914880))], (35205 ^ _779571) ^ [_1427633, _1427635] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1427633, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1427633, tc_HOL_Obool))), hAPP(c_Set_OPow(_1427633), _1427635))))], (27998 ^ _779571) ^ [_1275564, _1275566, _1275568, _1275570] : [class_Lattices_Osemilattice__sup(_1275564), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275564), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275564), _1275566), _1275568)), _1275570) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275564), _1275566), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275564), _1275568), _1275570)))], (51313 ^ _779571) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (22360 ^ _779571) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10353 ^ _779571) ^ [_952046, _952048] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952046), _952048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952048), _952046)))], (51123 ^ _779571) ^ [_1808688, _1808690] : [-(class_Finite__Set_Ofinite(tc_fun(_1808688, _1808690))), class_Finite__Set_Ofinite(_1808688), class_Finite__Set_Ofinite(_1808690)], (7770 ^ _779571) ^ [_908295, _908297, _908299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908295), _908297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908299), _908297))))], (27780 ^ _779571) ^ [_1271508, _1271510, _1271512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271508, tc_HOL_Obool)), _1271510), _1271512)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271508, tc_HOL_Obool)), _1271510), _1271512) = _1271512)], (11797 ^ _779571) ^ [_975798, _975800, _975802, _975804, _975806] : [class_Rings_Oordered__semiring(_975798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975798), _975800), _975802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975798), _975804), _975806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975798), c_Groups_Ozero__class_Ozero(_975798)), _975802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975798), c_Groups_Ozero__class_Ozero(_975798)), _975804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975798), _975800), _975804)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975798), _975802), _975806))))], (48214 ^ _779571) ^ [_1742185, _1742187, _1742189, _1742191, _1742193] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742187)), _1742189)))), -(hAPP(hAPP(c_List_Olist__update(_1742187, hAPP(hAPP(c_List_Oappend(_1742187), _1742189), _1742191)), _1742185), _1742193) = hAPP(hAPP(c_List_Oappend(_1742187), _1742189), hAPP(hAPP(c_List_Olist__update(_1742187, _1742191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1742185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742187)), _1742189))), _1742193)))], (10359 ^ _779571) ^ [_952092, _952094, _952096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952092), _952094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952094), _952096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952092), _952096)))], (48858 ^ _779571) ^ [_1759625, _1759627, _1759629, _1759631, _1759633] : [-(hAPP(hAPP(c_List_Oappend(_1759625), _1759627), _1759629) = hAPP(hAPP(c_List_Oappend(_1759625), _1759631), _1759633)), 48861 ^ _779571 : [(48864 ^ _779571) ^ [] : [_1759627 = hAPP(hAPP(c_List_Otake(_1759625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759627)), _1759631), _1759629 = hAPP(hAPP(c_List_Oappend(_1759625), hAPP(hAPP(c_List_Odrop(_1759625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759627)), _1759631)), _1759633)], (48862 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759627)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759631))))]], 48869 ^ _779571 : [(48872 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Otake(_1759625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759631)), _1759627) = _1759631, hAPP(hAPP(c_List_Oappend(_1759625), hAPP(hAPP(c_List_Odrop(_1759625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759631)), _1759627)), _1759629) = _1759633], (48870 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759627)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759625)), _1759631)))]]], (14522 ^ _779571) ^ [_1024511] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024511, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1024511)], (46791 ^ _779571) ^ [_1708470, _1708472, _1708474, _1708476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708470)), _1708472)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708470)), _1708474))), _1708472 = hAPP(hAPP(c_List_Olist_OCons(_1708470), _1708476), _1708474)], (37495 ^ _779571) ^ [_1479877, _1479879, _1479881] : [class_Orderings_Olinorder(_1479877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479877), _1479879)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479877), _1479881)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479877, tc_HOL_Obool)), _1479879), _1479881) = c_Orderings_Obot__class_Obot(tc_fun(_1479877, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1479877), c_Big__Operators_Olattice_OSup__fin(_1479877, c_Orderings_Oord__class_Omax(_1479877), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479877, tc_HOL_Obool)), _1479879), _1479881))), c_Big__Operators_Olattice_OSup__fin(_1479877, c_Orderings_Oord__class_Omax(_1479877), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479877, tc_HOL_Obool)), _1479879), _1479881))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1479877), c_Big__Operators_Olattice_OSup__fin(_1479877, c_Orderings_Oord__class_Omax(_1479877), _1479879)), c_Big__Operators_Olattice_OSup__fin(_1479877, c_Orderings_Oord__class_Omax(_1479877), _1479881)))], (13312 ^ _779571) ^ [_1002376, _1002378, _1002380, _1002382, _1002384] : [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), _1002376), _1002378)), _1002380)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002376), _1002382)), _1002384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002380), _1002376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002384), _1002376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002378), _1002382)))], (19095 ^ _779571) ^ [_1106989, _1106991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1106989)), -(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)))), _1106991)), 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)))), _1106989)) = 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, _1106991, _1106989))))], (34493 ^ _779571) ^ [_1410761, _1410763, _1410765, _1410767, _1410769] : [class_Groups_Ocomm__monoid__mult(_1410761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410763), _1410765)), hBOOL(hAPP(hAPP(c_member(_1410763), _1410767), _1410765)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410763, _1410761), _1410769), _1410765) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410761), hAPP(_1410769, _1410767)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410763, _1410761), _1410769), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410763, tc_HOL_Obool)), _1410765), hAPP(hAPP(c_Set_Oinsert(_1410763), _1410767), c_Orderings_Obot__class_Obot(tc_fun(_1410763, tc_HOL_Obool)))))))], (47206 ^ _779571) ^ [_1719070] : [class_Groups_Omonoid__add(_1719070), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719070), c_List_Olist_ONil(_1719070)) = c_Groups_Ozero__class_Ozero(_1719070))], (51341 ^ _779571) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (48285 ^ _779571) ^ [_1744473, _1744475, _1744477, _1744479] : [-(hAPP(hAPP(c_List_Otake(_1744473), _1744475), hAPP(hAPP(c_List_Oappend(_1744473), _1744477), _1744479)) = hAPP(hAPP(c_List_Oappend(_1744473), hAPP(hAPP(c_List_Otake(_1744473), _1744475), _1744477)), hAPP(hAPP(c_List_Otake(_1744473), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1744475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744473)), _1744477))), _1744479)))], (28623 ^ _779571) ^ [_1287901, _1287903] : [class_Orderings_Olinorder(_1287901), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1287901, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287901), _1287903)) = hAPP(c_SetInterval_Oord__class_OatMost(_1287901), _1287903))], (50664 ^ _779571) ^ [_1798220, _1798222] : [hAPP(c_List_Orev(_1798220), _1798222) = c_List_Olist_ONil(_1798220), -(_1798222 = c_List_Olist_ONil(_1798220))], (32241 ^ _779571) ^ [_1366306, _1366308, _1366310, _1366312] : [hBOOL(hAPP(hAPP(_1366310, _1366312), _1366308)), -(hBOOL(hAPP(hAPP(c_member(_1366306), _1366308), c_SetInterval_Oord_OgreaterThan(_1366306, _1366310, _1366312))))], (49455 ^ _779571) ^ [_1772796, _1772798, _1772800] : [-(_1772796 = c_List_Olist_ONil(_1772798)), -(c_List_Olast(_1772798, hAPP(hAPP(c_List_Olist_OCons(_1772798), _1772800), _1772796)) = c_List_Olast(_1772798, _1772796))], (47455 ^ _779571) ^ [_1724463, _1724465, _1724467] : [47457 ^ _779571 : [(47460 ^ _779571) ^ [] : [hBOOL(hAPP(_1724467, hAPP(hAPP(c_List_Onth(_1724463), _1724465), 47456 ^ [_1724463, _1724465, _1724467])))], (47458 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47456 ^ [_1724463, _1724465, _1724467]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724463)), _1724465))))]], 47461 ^ _779571 : [(47462 ^ _779571) ^ [_1724665] : [hBOOL(hAPP(hAPP(c_member(_1724463), _1724665), hAPP(c_List_Oset(_1724463), _1724465))), -(hBOOL(hAPP(_1724467, _1724665)))]]], (12277 ^ _779571) ^ [_984532, _984534] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984532)), _984534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984532), _984534)))], (9822 ^ _779571) ^ [_943103, _943105, _943107, _943109] : [class_Rings_Olinordered__ring__strict(_943103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943103), _943105), _943107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943103), _943109), c_Groups_Ozero__class_Ozero(_943103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943103), _943109), _943107)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943103), _943109), _943105))))], (46815 ^ _779571) ^ [_1709018, _1709020, _1709022, _1709024, _1709026, _1709028] : [hBOOL(hAPP(hAPP(_1709018, _1709020), _1709022)), c_List_Olistrelp(_1709024, _1709018, _1709026, _1709028), -(c_List_Olistrelp(_1709024, _1709018, hAPP(hAPP(c_List_Olist_OCons(_1709024), _1709020), _1709026), hAPP(hAPP(c_List_Olist_OCons(_1709024), _1709022), _1709028)))], (38134 ^ _779571) ^ [_1495222, _1495224] : [class_Lattices_Olattice(_1495222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495222), _1495224)), -(_1495224 = c_Orderings_Obot__class_Obot(tc_fun(_1495222, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1495222), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1495222), 38147 ^ [_1495222, _1495224]), 38148 ^ [_1495222, _1495224])), hAPP(hAPP(c_Set_Oinsert(_1495222), 38147 ^ [_1495222, _1495224]), hAPP(hAPP(c_Set_Oinsert(_1495222), 38148 ^ [_1495222, _1495224]), c_Orderings_Obot__class_Obot(tc_fun(_1495222, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1495222), c_Big__Operators_Olattice__class_OInf__fin(_1495222, _1495224)), _1495224)))], (7620 ^ _779571) ^ [_905894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905894), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4310 ^ _779571) ^ [_846240, _846242] : [_846242 = _846240, -(c_Groups_Oabs__class_Oabs(_846242) = c_Groups_Oabs__class_Oabs(_846240))], (50218 ^ _779571) ^ [_1788790, _1788792, _1788794] : [class_Orderings_Olinorder(_1788790), 50221 ^ _779571 : [(50228 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1788790, _1788794), -(c_List_Olinorder__class_Osorted(_1788790, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1788790, _1788790, c_COMBI(_1788790)), _1788792), _1788794)))], (50222 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1788790, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1788790, _1788790, c_COMBI(_1788790)), _1788792), _1788794)), -(c_List_Olinorder__class_Osorted(_1788790, _1788794))]]], (41884 ^ _779571) ^ [_1589110, _1589112, _1589114] : [c_Wellfounded_Owf(_1589110, _1589112), -(c_Wellfounded_Owf(_1589110, c_Wellfounded_Omlex__prod(_1589110, _1589114, _1589112)))], (29784 ^ _779571) ^ [] : [-(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))))], (6213 ^ _779571) ^ [_880294, _880296, _880298] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880294, _880296, _880298))), -(hBOOL(hAPP(c_Com_OWT, _880298)))], (6385 ^ _779571) ^ [_883467, _883469, _883471] : [c_Com_Ocom_OLocal(_883467, _883469, _883471) = c_Com_Ocom_OSKIP], (10249 ^ _779571) ^ [_950289, _950291] : [class_Orderings_Opreorder(_950289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950289), _950291), _950291)))], (48798 ^ _779571) ^ [_1758159, _1758161, _1758163] : [-(hAPP(hAPP(c_List_Oappend(_1758159), hAPP(hAPP(c_List_Otake(_1758159), _1758161), _1758163)), hAPP(hAPP(c_List_Odrop(_1758159), _1758161), _1758163)) = _1758163)], (16024 ^ _779571) ^ [_1052813, _1052815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052815), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052813), _1052815)))], (43415 ^ _779571) ^ [_1625450, _1625452, _1625454, _1625456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625450, _1625450)), hAPP(hAPP(c_Product__Type_OPair(_1625450, _1625450), _1625452), _1625454)), c_Transitive__Closure_Ortrancl(_1625450, _1625456))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625450, _1625450)), hAPP(hAPP(c_Product__Type_OPair(_1625450, _1625450), _1625454), _1625452)), c_Transitive__Closure_Ortrancl(_1625450, hAPP(c_Relation_Oconverse(_1625450, _1625450), _1625456)))))], (7726 ^ _779571) ^ [_907477, _907479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _907477)), _907479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907477), _907479)))], (26042 ^ _779571) ^ [_1236773, _1236775, _1236777, _1236779] : [class_Rings_Oidom(_1236773), 26045 ^ _779571 : [(26046 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236773), _1236775), _1236777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236773), _1236775), _1236779))), -(_1236775 = c_Groups_Ozero__class_Ozero(_1236773)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236773), _1236777), _1236779)))], (26056 ^ _779571) ^ [] : [26057 ^ _779571 : [(26060 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236773), _1236777), _1236779))], (26058 ^ _779571) ^ [] : [_1236775 = c_Groups_Ozero__class_Ozero(_1236773)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236773), _1236775), _1236777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236773), _1236775), _1236779))))]]], (8020 ^ _779571) ^ [_912544, _912546] : [8021 ^ _779571 : [(8022 ^ _779571) ^ [_912592] : [_912544 = hAPP(c_Option_Ooption_OSome(_912546), _912592)]], _912544 = c_Option_Ooption_ONone(_912546)], (5046 ^ _779571) ^ [_857566, _857568, _857570, _857572] : [-(c_List_Olinorder__class_Osorted__list__of__set(_857572, _857568) = c_List_Olinorder__class_Osorted__list__of__set(_857570, _857566)), _857572 = _857570, _857568 = _857566], (24835 ^ _779571) ^ [_1213664, _1213666, _1213668] : [-(c_Nitpick_Otimes__frac(_1213664, _1213666, _1213668) = hAPP(hAPP(c_Nitpick_Ofrac(_1213664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1213664), _1213666)), hAPP(c_Nitpick_Onum(_1213664), _1213668))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1213664), _1213666)), hAPP(c_Nitpick_Odenom(_1213664), _1213668))))], (29634 ^ _779571) ^ [_1309136, _1309138, _1309140, _1309142, _1309144] : [_1309136 = c_Orderings_Obot__class_Obot(tc_fun(_1309138, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309138, tc_fun(_1309140, tc_HOL_Obool)), _1309136), hAPP(hAPP(c_COMBB(tc_fun(_1309140, tc_HOL_Obool), tc_fun(_1309140, tc_HOL_Obool), _1309138), hAPP(c_Set_Oinsert(_1309140), _1309142)), _1309144)) = c_Orderings_Obot__class_Obot(tc_fun(_1309140, tc_HOL_Obool)))], (43945 ^ _779571) ^ [_1639032, _1639034, _1639036, _1639038, _1639040, _1639042] : [c_Finite__Set_Ofun__left__comm__idem(_1639032, _1639034, _1639036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639032), _1639038)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1639032, _1639034, _1639036), _1639040), hAPP(hAPP(c_Set_Oinsert(_1639032), _1639042), _1639038)) = hAPP(hAPP(c_Finite__Set_Ofold(_1639032, _1639034, _1639036), hAPP(hAPP(_1639036, _1639042), _1639040)), _1639038))], (27794 ^ _779571) ^ [_1271796, _1271798, _1271800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271796, tc_HOL_Obool)), _1271798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271796, tc_HOL_Obool)), _1271798), _1271800))))], (40192 ^ _779571) ^ [_1541333, _1541335, _1541337, _1541339, _1541341] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1541333, _1541335), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541333, tc_HOL_Obool)), _1541337), _1541339)), _1541341) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1541333, _1541335), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1541333, _1541335), _1541337), _1541341)), hAPP(hAPP(c_Product__Type_OSigma(_1541333, _1541335), _1541339), _1541341)))], (44239 ^ _779571) ^ [_1644620, _1644622, _1644624, _1644626, _1644628, _1644630] : [c_Finite__Set_Ofun__left__comm(_1644620, _1644622, _1644624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644620), _1644626)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1644620, _1644622, _1644624), _1644628), hAPP(hAPP(c_Set_Oinsert(_1644620), _1644630), _1644626)) = hAPP(hAPP(_1644624, _1644630), hAPP(hAPP(c_Finite__Set_Ofold(_1644620, _1644622, _1644624), _1644628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1644620, tc_HOL_Obool)), _1644626), hAPP(hAPP(c_Set_Oinsert(_1644620), _1644630), c_Orderings_Obot__class_Obot(tc_fun(_1644620, tc_HOL_Obool)))))))], (50798 ^ _779571) ^ [_1801135, _1801137, _1801139] : [c_List_Oconcat(_1801135, _1801137) = c_List_Oconcat(_1801135, _1801139), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801135))), _1801137) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801135))), _1801139), 50808 ^ _779571 : [(50811 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1801135), tc_List_Olist(_1801135), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1801135), tc_fun(tc_List_Olist(_1801135), tc_Nat_Onat), tc_fun(tc_List_Olist(_1801135), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1801135), tc_Nat_Onat), tc_fun(tc_List_Olist(_1801135), tc_HOL_Obool)), tc_List_Olist(_1801135)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1801135))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1801135)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1801135))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1801135)))), 50807 ^ [_1801135, _1801137, _1801139]))], (50809 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801135), tc_List_Olist(_1801135))), 50807 ^ [_1801135, _1801137, _1801139]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1801135), tc_List_Olist(_1801135))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1801135), tc_List_Olist(_1801135)), _1801137), _1801139)))))]], -(_1801137 = _1801139)], (36622 ^ _779571) ^ [_1459864, _1459866, _1459868, _1459870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459864, tc_HOL_Obool)), _1459866), _1459868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459864, tc_HOL_Obool)), _1459866), _1459870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459864, tc_HOL_Obool)), _1459866), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459864, tc_HOL_Obool)), _1459868), _1459870))))], (38929 ^ _779571) ^ [_1511673, _1511675, _1511677, _1511679, _1511681] : [-(c_Fun_Oinj__on(_1511673, _1511675, _1511677, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1511673, tc_HOL_Obool)), _1511679), _1511681))), c_Fun_Oinj__on(_1511673, _1511675, _1511677, _1511679), c_Fun_Oinj__on(_1511673, _1511675, _1511677, _1511681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511675, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511673, _1511675, _1511677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511673, tc_HOL_Obool)), _1511679), _1511681))), hAPP(c_Set_Oimage(_1511673, _1511675, _1511677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511673, tc_HOL_Obool)), _1511681), _1511679))) = c_Orderings_Obot__class_Obot(tc_fun(_1511675, tc_HOL_Obool))], (11493 ^ _779571) ^ [_970494, _970496, _970498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970494), _970496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970498), _970496))))], (40687 ^ _779571) ^ [_1551924, _1551926, _1551928, _1551930] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1551926, _1551924), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551924, tc_prod(_1551926, _1551924), 40683 ^ [_1551924, _1551926, _1551928, _1551930]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551926, tc_fun(_1551924, tc_HOL_Obool)), _1551928), _1551930))), hAPP(hAPP(c_Product__Type_OSigma(_1551926, _1551924), _1551928), _1551930))))], (23899 ^ _779571) ^ [_1195230, _1195232, _1195234, _1195236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195230, tc_HOL_Obool)), _1195232), _1195234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195230, tc_HOL_Obool)), _1195234), _1195236)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195230, tc_HOL_Obool)), _1195234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195230, tc_HOL_Obool)), _1195236), _1195232)) = _1195232)], (9200 ^ _779571) ^ [_931864, _931866, _931868] : [class_Groups_Oordered__ab__group__add(_931864), 9203 ^ _779571 : [(9210 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931864), hAPP(c_Groups_Ouminus__class_Ouminus(_931864), _931868)), _931866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931864), hAPP(c_Groups_Ouminus__class_Ouminus(_931864), _931866)), _931868)))], (9204 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931864), hAPP(c_Groups_Ouminus__class_Ouminus(_931864), _931866)), _931868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931864), hAPP(c_Groups_Ouminus__class_Ouminus(_931864), _931868)), _931866)))]]], (38573 ^ _779571) ^ [_1504163, _1504165, _1504167, _1504169] : [c_Fun_Oinj__on(_1504163, _1504165, _1504167, c_Orderings_Otop__class_Otop(tc_fun(_1504163, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1504163, tc_fun(_1504169, _1504165), hAPP(hAPP(c_COMBB(_1504165, tc_fun(_1504169, _1504165), _1504163), c_COMBK(_1504165, _1504169)), _1504167), c_Orderings_Otop__class_Otop(tc_fun(_1504163, tc_HOL_Obool))))], (6015 ^ _779571) ^ [_876333, _876335] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_876333, _876335)], (39799 ^ _779571) ^ [_1530804, _1530806, _1530808, _1530810, _1530812, _1530814, _1530816] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530804, _1530806, _1530808, _1530810, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530804, tc_HOL_Obool)), _1530812), hAPP(hAPP(c_Set_Oinsert(_1530804), _1530814), c_Orderings_Obot__class_Obot(tc_fun(_1530804, tc_HOL_Obool))))), _1530816)), hBOOL(hAPP(hAPP(c_member(_1530804), _1530814), _1530812)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530804, _1530806, _1530808, _1530810, _1530812), hAPP(hAPP(_1530808, _1530814), _1530816))))], (692 ^ _779571) ^ [_790241, _790243, _790245, _790247, _790249, _790251, _790253, _790255] : [-(c_Finite__Set_Ofolding(_790253, _790249, _790245, _790241)), c_Finite__Set_Ofolding(_790255, _790251, _790247, _790243), _790255 = _790253, _790251 = _790249, _790247 = _790245, _790243 = _790241], (30614 ^ _779571) ^ [_1329467, _1329469, _1329471, _1329473] : [hBOOL(hAPP(hAPP(c_member(_1329467), _1329469), _1329471)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329467, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1329467), _1329469), _1329473)), _1329471) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329467, tc_HOL_Obool)), _1329473), _1329471))], (27738 ^ _779571) ^ [_1270605, _1270607, _1270609, _1270611] : [class_Lattices_Osemilattice__sup(_1270605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270605), _1270607), _1270609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270605), _1270607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270605), _1270611), _1270609))))], (5456 ^ _779571) ^ [_863907, _863909] : [_863909 = _863907, -(c_List_Orev(_863909) = c_List_Orev(_863907))], (49903 ^ _779571) ^ [_1783082, _1783084, _1783086, _1783088, _1783090] : [-(hAPP(hAPP(c_List_Omap(_1783082, _1783084), _1783086), hAPP(c_List_Ofilter(_1783082, _1783088), _1783090)) = c_List_Omap__filter(_1783082, _1783084, hAPP(hAPP(c_COMBC(_1783082, tc_Option_Ooption(_1783084), tc_Option_Ooption(_1783084)), hAPP(hAPP(c_COMBS(_1783082, tc_Option_Ooption(_1783084), tc_fun(tc_Option_Ooption(_1783084), tc_Option_Ooption(_1783084))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1783084), tc_fun(tc_Option_Ooption(_1783084), tc_Option_Ooption(_1783084))), _1783082), c_If(tc_Option_Ooption(_1783084))), _1783088)), hAPP(hAPP(c_COMBB(_1783084, tc_Option_Ooption(_1783084), _1783082), c_Option_Ooption_OSome(_1783084)), _1783086))), c_Option_Ooption_ONone(_1783084)), _1783090))], (33771 ^ _779571) ^ [_1396370, _1396372, _1396374] : [class_Orderings_Olinorder(_1396370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396370), _1396372)), -(_1396372 = c_Orderings_Obot__class_Obot(tc_fun(_1396370, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1396370, c_Orderings_Oord__class_Omin(_1396370), hAPP(hAPP(c_Set_Oinsert(_1396370), _1396374), _1396372)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396370), _1396374), c_Big__Operators_Olattice_OInf__fin(_1396370, c_Orderings_Oord__class_Omin(_1396370), _1396372)))], (33147 ^ _779571) ^ [_1383819, _1383821, _1383823] : [class_Orderings_Olinorder(_1383819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383819), _1383821)), -(hBOOL(hAPP(hAPP(c_member(_1383819), _1383823), _1383821))), -(_1383821 = c_Orderings_Obot__class_Obot(tc_fun(_1383819, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1383819, hAPP(hAPP(c_Set_Oinsert(_1383819), _1383823), _1383821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1383819), _1383823), c_Big__Operators_Olinorder__class_OMax(_1383819, _1383821)))], (7606 ^ _779571) ^ [_905737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905737), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29862 ^ _779571) ^ [_1313697, _1313699, _1313701, _1313703] : [c_Hoare__Mirabelle_Ohoare__derivs(_1313697, _1313699, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1313697)), _1313701), _1313703)), 29865 ^ _779571 : [(29868 ^ _779571) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1313697, _1313699, _1313703))], (29866 ^ _779571) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1313697, _1313699, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1313697)), _1313701), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1313697), tc_HOL_Obool)))))]]], (18127 ^ _779571) ^ [_1091411, _1091413] : [class_Int_Onumber__ring(_1091411), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091411), hAPP(c_Int_Onumber__class_Onumber__of(_1091411), c_Int_OMin)), _1091413) = hAPP(c_Groups_Ouminus__class_Ouminus(_1091411), _1091413))], (47743 ^ _779571) ^ [_1731634, _1731636, _1731638, _1731640] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731634, tc_HOL_Obool)), hAPP(c_List_Oset(_1731634), hAPP(hAPP(c_List_Olist__update(_1731634, _1731636), _1731638), _1731640))), hAPP(hAPP(c_Set_Oinsert(_1731634), _1731640), hAPP(c_List_Oset(_1731634), _1731636)))))], (42391 ^ _779571) ^ [_1601193, _1601195] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601193, _1601193)), _1601195)), c_Wellfounded_Oacyclic(_1601193, _1601195), -(c_Wellfounded_Owf(_1601193, _1601195))], (49279 ^ _779571) ^ [_1768920, _1768922, _1768924] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1768920)), _1768922), c_Wellfounded_Oacc(tc_List_Olist(_1768920), c_List_Olistrel1(_1768920, _1768924)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1768920)), _1768922), c_List_Olists(_1768920, c_Wellfounded_Oacc(_1768920, _1768924)))))], (19123 ^ _779571) ^ [_1107515, _1107517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1107515)), c_Int_OBit0(_1107517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107515), _1107517)))], (25940 ^ _779571) ^ [_1234289, _1234291, _1234293, _1234295, _1234297] : [class_Rings_Osemiring__0(_1234289), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234289), _1234291), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234293, _1234289), _1234295), _1234297)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234293, _1234289), hAPP(hAPP(c_COMBB(_1234289, _1234289, _1234293), hAPP(c_Groups_Otimes__class_Otimes(_1234289), _1234291)), _1234295)), _1234297))], (13284 ^ _779571) ^ [_1001904, _1001906, _1001908] : [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), _1001904), _1001906)), _1001908))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001908), _1001904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001906)))], (23283 ^ _779571) ^ [_1183922, _1183924, _1183926] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183922), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183924)), _1183926)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183922, _1183924), hAPP(c_Divides_OnegateSnd, _1183926))))], (41348 ^ _779571) ^ [_1569518] : [-(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)))), _1569518)) = 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), _1569518), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (39491 ^ _779571) ^ [_1523981, _1523983, _1523985, _1523987, _1523989] : [hAPP(_1523987, _1523983) = _1523989, -(hBOOL(hAPP(hAPP(c_member(_1523981), _1523983), hAPP(c_Set_Ovimage(_1523981, _1523985, _1523987), hAPP(hAPP(c_Set_Oinsert(_1523985), _1523989), c_Orderings_Obot__class_Obot(tc_fun(_1523985, tc_HOL_Obool)))))))], (48994 ^ _779571) ^ [_1762512, _1762514, _1762516] : [-(hAPP(hAPP(c_List_Odrop(_1762512), hAPP(c_Nat_OSuc, _1762514)), _1762516) = hAPP(hAPP(c_List_Odrop(_1762512), _1762514), hAPP(c_List_Otl(_1762512), _1762516)))], (39951 ^ _779571) ^ [_1534601, _1534603, _1534605, _1534607] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534601), _1534603)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534601), _1534605)), -(_1534605 = c_Orderings_Obot__class_Obot(tc_fun(_1534601, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1534601, tc_HOL_Obool), tc_fun(_1534601, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1534601, tc_HOL_Obool), tc_fun(_1534601, tc_HOL_Obool)), _1534603), _1534605)), c_Wellfounded_Omax__ext(_1534601, _1534607)))), 39965 ^ _779571 : [(39968 ^ _779571) ^ [_1535006] : [hBOOL(hAPP(hAPP(c_member(_1534601), _1535006), _1534605)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1534601, _1534601)), hAPP(hAPP(c_Product__Type_OPair(_1534601, _1534601), 39964 ^ [_1534601, _1534603, _1534605, _1534607]), _1535006)), _1534607))], (39966 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534601), 39964 ^ [_1534601, _1534603, _1534605, _1534607]), _1534603)))]]], (42654 ^ _779571) ^ [_1606850, _1606852] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1606850), _1606852)), 42660 ^ _779571 : [(42663 ^ _779571) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42661 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606850), 42659 ^ [_1606850, _1606852]), _1606852)))]], -(hAPP(c_Finite__Set_Ocard(_1606850), _1606852) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37311 ^ _779571) ^ [_1476388, _1476390, _1476392] : [class_Lattices_Olattice(_1476388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476388), _1476390)), -(_1476390 = c_Orderings_Obot__class_Obot(tc_fun(_1476388, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476388), _1476392)), -(_1476392 = c_Orderings_Obot__class_Obot(tc_fun(_1476388, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476388, tc_HOL_Obool)), _1476390), _1476392) = c_Orderings_Obot__class_Obot(tc_fun(_1476388, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1476388, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476388, tc_HOL_Obool)), _1476390), _1476392)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1476388), c_Big__Operators_Olattice__class_OSup__fin(_1476388, _1476390)), c_Big__Operators_Olattice__class_OSup__fin(_1476388, _1476392)))], (15680 ^ _779571) ^ [_1045735, _1045737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045737), _1045735)), -(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), _1045735), _1045737))))], (19475 ^ _779571) ^ [_1113635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113635), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1113635)), c_Int_OMin)))], (17237 ^ _779571) ^ [_1076037, _1076039] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076037), _1076039) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1076039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1076037 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12069 ^ _779571) ^ [_980824, _980826, _980828, _980830, _980832] : [class_Groups_Oordered__cancel__ab__semigroup__add(_980824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980824), _980826), _980828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980824), _980830), _980832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980824), _980826), _980830)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980824), _980828), _980832))))], (44792 ^ _779571) ^ [_1659469, _1659471, _1659473, _1659475, _1659477] : [class_Complete__Lattice_Ocomplete__lattice(_1659469), hBOOL(hAPP(hAPP(c_member(_1659471), _1659473), _1659475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659469), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659471, _1659469), _1659475), _1659477)), hAPP(_1659477, _1659473))))], (31051 ^ _779571) ^ [_1338679] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338679), c_Orderings_Obot__class_Obot(tc_fun(_1338679, tc_HOL_Obool)))))], (7331 ^ _779571) ^ [_901191, _901193, _901195] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_901191, _901193)), hAPP(c_Sum__Type_OInr(_901193, _901191), _901195)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12345 ^ _779571) ^ [_985700, _985702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985700)), _985702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985700), _985702)))], (25374 ^ _779571) ^ [_1224142, _1224144, _1224146] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224142), _1224144)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224144), _1224146)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224142), _1224146)))], (47889 ^ _779571) ^ [_1735154, _1735156, _1735158, _1735160, _1735162] : [-(hAPP(hAPP(c_List_Oappend(_1735154), _1735156), hAPP(hAPP(c_List_Olist_OCons(_1735154), _1735158), c_List_Olist_ONil(_1735154))) = hAPP(hAPP(c_List_Oappend(_1735154), _1735160), hAPP(hAPP(c_List_Olist_OCons(_1735154), _1735162), c_List_Olist_ONil(_1735154)))), _1735156 = _1735160, _1735158 = _1735162], (11280 ^ _779571) ^ [_966902, _966904, _966906] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966902), _966904)), _966906) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966902), _966906)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966904), _966906)))], (31698 ^ _779571) ^ [_1354843] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1354843), 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, _1354843)) = _1354843)], (7614 ^ _779571) ^ [_905803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _905803)), _905803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22801 ^ _779571) ^ [_1174762, _1174764, _1174766] : [22803 ^ _779571 : [(22806 ^ _779571) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1174762, _1174764), 22802 ^ [_1174762, _1174764, _1174766]))], (22804 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1174764, 22802 ^ [_1174762, _1174764, _1174766]), _1174766)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1174762, _1174764), _1174766)))], (1502 ^ _779571) ^ [_801114, _801116] : [-(class_Groups_Oab__semigroup__mult(_801114)), _801116 = _801114, class_Groups_Oab__semigroup__mult(_801116)], (35571 ^ _779571) ^ [_1436369, _1436371] : [-(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), _1436369), _1436371)), 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), _1436369), _1436371))], (26582 ^ _779571) ^ [_1247057, _1247059, _1247061, _1247063, _1247065] : [class_Divides_Osemiring__div(_1247057), -(_1247059 = c_Groups_Ozero__class_Ozero(_1247057)), -(_1247061 = c_Groups_Ozero__class_Ozero(_1247057)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1247057), _1247059), _1247063)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1247057), _1247061), _1247065)), 26601 ^ _779571 : [(26608 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247063), _1247061) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247059), _1247065), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), _1247063), _1247059) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), _1247065), _1247061))], (26602 ^ _779571) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), _1247063), _1247059) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), _1247065), _1247061), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247063), _1247061) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247059), _1247065))]]], (11410 ^ _779571) ^ [_968918, _968920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968918), _968920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968918), _968920)))], (44704 ^ _779571) ^ [_1656655, _1656657, _1656659, _1656661, _1656663, _1656665, _1656667] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656655, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656657, tc_fun(_1656655, tc_HOL_Obool)), _1656659), _1656661)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656663, tc_fun(_1656655, tc_HOL_Obool)), _1656665), _1656667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656657, tc_fun(_1656655, tc_HOL_Obool)), _1656659), hAPP(hAPP(c_COMBB(tc_fun(_1656663, tc_fun(_1656655, tc_HOL_Obool)), tc_fun(_1656655, tc_HOL_Obool), _1656657), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656663, tc_fun(_1656655, tc_HOL_Obool)), _1656665)), hAPP(hAPP(c_COMBC(_1656657, tc_fun(_1656663, tc_fun(_1656655, tc_HOL_Obool)), tc_fun(_1656663, tc_fun(_1656655, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1656655, tc_HOL_Obool), tc_fun(_1656655, tc_HOL_Obool)), tc_fun(tc_fun(_1656663, tc_fun(_1656655, tc_HOL_Obool)), tc_fun(_1656663, tc_fun(_1656655, tc_HOL_Obool))), _1656657), c_COMBB(tc_fun(_1656655, tc_HOL_Obool), tc_fun(_1656655, tc_HOL_Obool), _1656663)), hAPP(hAPP(c_COMBB(tc_fun(_1656655, tc_HOL_Obool), tc_fun(tc_fun(_1656655, tc_HOL_Obool), tc_fun(_1656655, tc_HOL_Obool)), _1656657), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656655, tc_HOL_Obool))), _1656661))), _1656667))))], (37722 ^ _779571) ^ [] : [-(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))], (5678 ^ _779571) ^ [_867212, _867214] : [_867214 = _867212, -(tc_Hoare__Mirabelle_Otriple(_867214) = tc_Hoare__Mirabelle_Otriple(_867212))], (13066 ^ _779571) ^ [_998359, _998361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998359)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998361)))), 13069 ^ _779571 : [(13072 ^ _779571) ^ [] : [-(_998361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13070 ^ _779571) ^ [] : [-(_998359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6118 ^ _779571) ^ [_878268, _878270] : [hAPP(c_Nat_OSuc, _878268) = hAPP(c_Nat_OSuc, _878270), -(_878268 = _878270)], (45662 ^ _779571) ^ [_1679266, _1679268, _1679270] : [-(c_Map_Omap__add(_1679266, _1679268, hAPP(c_COMBK(tc_Option_Ooption(_1679268), _1679266), c_Option_Ooption_ONone(_1679268)), _1679270) = _1679270)], (39727 ^ _779571) ^ [_1529367, _1529369, _1529371, _1529373] : [hBOOL(hAPP(hAPP(c_member(_1529367), _1529369), c_Map_Odom(_1529367, _1529371, _1529373))), hAPP(_1529373, _1529369) = c_Option_Ooption_ONone(_1529371)], (51403 ^ _779571) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (36342 ^ _779571) ^ [_1454596, _1454598, _1454600] : [class_Lattices_Osemilattice__inf(_1454596), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454596), _1454598), _1454600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454596), _1454600), _1454598))], (24413 ^ _779571) ^ [_1205179, _1205181, _1205183, _1205185] : [class_Orderings_Olinorder(_1205179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205179), _1205181), _1205183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205179), _1205181), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205179), _1205183), _1205185))))], (44936 ^ _779571) ^ [_1662659, _1662661, _1662663, _1662665] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662659, tc_fun(_1662661, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662659, tc_HOL_Obool), _1662663)), _1662665) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1662659, tc_HOL_Obool), tc_fun(_1662661, tc_HOL_Obool)), _1662663), hAPP(hAPP(c_COMBC(tc_fun(_1662659, tc_HOL_Obool), tc_fun(_1662659, tc_fun(_1662661, tc_HOL_Obool)), tc_fun(_1662661, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662659, tc_fun(_1662661, tc_HOL_Obool))), _1662665)))], (18889 ^ _779571) ^ [_1103534] : [class_Int_Onumber__ring(_1103534), -(c_Groups_Oone__class_Oone(_1103534) = hAPP(c_Int_Onumber__class_Onumber__of(_1103534), c_Int_OBit1(c_Int_OPls)))], (48902 ^ _779571) ^ [_1760712, _1760714, _1760716, _1760718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1760712), _1760714)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760716)), _1760718))), -(hAPP(hAPP(c_List_Otake(_1760716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1760712), _1760714)), _1760718) = hAPP(hAPP(c_List_Oappend(_1760716), hAPP(hAPP(c_List_Otake(_1760716), _1760712), _1760718)), hAPP(hAPP(c_List_Otake(_1760716), _1760714), hAPP(hAPP(c_List_Odrop(_1760716), _1760712), _1760718))))], (11685 ^ _779571) ^ [_973814, _973816, _973818] : [class_Groups_Oordered__comm__monoid__add(_973814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973814), c_Groups_Ozero__class_Ozero(_973814)), _973816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973814), c_Groups_Ozero__class_Ozero(_973814)), _973818)), 11696 ^ _779571 : [(11705 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973814), _973816), _973818) = c_Groups_Ozero__class_Ozero(_973814)), _973816 = c_Groups_Ozero__class_Ozero(_973814), _973818 = c_Groups_Ozero__class_Ozero(_973814)], (11697 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973814), _973816), _973818) = c_Groups_Ozero__class_Ozero(_973814), 11700 ^ _779571 : [(11703 ^ _779571) ^ [] : [-(_973818 = c_Groups_Ozero__class_Ozero(_973814))], (11701 ^ _779571) ^ [] : [-(_973816 = c_Groups_Ozero__class_Ozero(_973814))]]]]], (17837 ^ _779571) ^ [_1086607] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086607))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1086607)) = _1086607)], (50700 ^ _779571) ^ [_1798897, _1798899] : [-(hAPP(c_List_Orev(_1798897), _1798899) = hAPP(c_List_Ofoldl(tc_List_Olist(_1798897), _1798897, hAPP(c_COMBC(_1798897, tc_List_Olist(_1798897), tc_List_Olist(_1798897)), c_List_Olist_OCons(_1798897)), c_List_Olist_ONil(_1798897)), _1798899))], (7540 ^ _779571) ^ [_904557, _904559, _904561, _904563] : [class_Groups_Oordered__cancel__ab__semigroup__add(_904557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904557), _904559), _904561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904557), _904559), _904563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904557), _904561), _904563))))], (8368 ^ _779571) ^ [_918386, _918388, _918390] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918388), _918390)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918386), _918390)))], (18335 ^ _779571) ^ [_1094511] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1094511), c_Int_OPls) = _1094511)], (5718 ^ _779571) ^ [_870912, _870914, _870916] : [c_Hoare__Mirabelle_Otriple__valid(_870912, hAPP(c_Nat_OSuc, _870914), _870916), -(c_Hoare__Mirabelle_Otriple__valid(_870912, _870914, _870916))], (8364 ^ _779571) ^ [_918306] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918306), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _918306)], (13655 ^ _779571) ^ [_1008429, _1008431] : [class_Divides_Osemiring__div(_1008429), -(c_Divides_Odiv__class_Omod(_1008429, _1008431, c_Groups_Ozero__class_Ozero(_1008429)) = _1008431)], (3472 ^ _779571) ^ [_832917, _832919, _832921, _832923, _832925, _832927, _832929, _832931] : [-(c_Random__Sequence_Omap(_832931, _832927, _832923, _832919) = c_Random__Sequence_Omap(_832929, _832925, _832921, _832917)), _832931 = _832929, _832927 = _832925, _832923 = _832921, _832919 = _832917], (35478 ^ _779571) ^ [_1433854, _1433856, _1433858, _1433860, _1433862] : [hAPP(c_Set_Oimage(_1433854, _1433856, _1433858), c_Orderings_Otop__class_Otop(tc_fun(_1433854, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1433856, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1433856, _1433860, _1433862), c_Orderings_Otop__class_Otop(tc_fun(_1433856, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1433860, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1433854, _1433860, hAPP(c_Fun_Ocomp(_1433856, _1433860, _1433854, _1433862), _1433858)), c_Orderings_Otop__class_Otop(tc_fun(_1433854, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1433860, tc_HOL_Obool)))], (17937 ^ _779571) ^ [_1088296, _1088298] : [class_Int_Onumber__ring(_1088296), 17940 ^ _779571 : [(17947 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088298)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1088296), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088298)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088296), _1088298))], (17941 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088298))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1088296), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088298)) = c_Groups_Ozero__class_Ozero(_1088296))]]], (46322 ^ _779571) ^ [_1694598, _1694600, _1694602, _1694604] : [-(_1694598 = _1694600), 46325 ^ _779571 : [(46332 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1694602), _1694598), hAPP(c_List_Oset(_1694602), _1694604))), -(hBOOL(hAPP(hAPP(c_member(_1694602), _1694598), hAPP(c_List_Oset(_1694602), c_List_Oremove1(_1694602, _1694600, _1694604)))))], (46326 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1694602), _1694598), hAPP(c_List_Oset(_1694602), c_List_Oremove1(_1694602, _1694600, _1694604)))), -(hBOOL(hAPP(hAPP(c_member(_1694602), _1694598), hAPP(c_List_Oset(_1694602), _1694604))))]]], (17743 ^ _779571) ^ [_1085171, _1085173] : [-(c_Nitpick_Onat__lcm(_1085171, _1085173) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1085171), _1085173)), c_Nitpick_Onat__gcd(_1085171, _1085173)))], (44692 ^ _779571) ^ [_1656450, _1656452, _1656454, _1656456] : [_1656450 = c_Orderings_Obot__class_Obot(tc_fun(_1656452, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656452, tc_fun(_1656454, tc_HOL_Obool)), _1656450), hAPP(c_COMBK(tc_fun(_1656454, tc_HOL_Obool), _1656452), _1656456)) = c_Orderings_Otop__class_Otop(tc_fun(_1656454, tc_HOL_Obool)))], (17247 ^ _779571) ^ [_1076135, _1076137] : [17248 ^ _779571 : [(17251 ^ _779571) ^ [] : [_1076135 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17249 ^ _779571) ^ [] : [_1076137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076135), _1076137) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33635 ^ _779571) ^ [_1393614, _1393616, _1393618, _1393620] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1393614, _1393616)), c_Sum__Type_OPlus(_1393614, _1393616, _1393618, _1393620))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1393614), _1393618)))], (31616 ^ _779571) ^ [_1352961, _1352963, _1352965] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1352961), _1352963)), 31619 ^ _779571 : [(31639 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352961, tc_Nat_Onat), _1352965), _1352963) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 31640 ^ _779571 : [(31641 ^ _779571) ^ [_1353442] : [hBOOL(hAPP(hAPP(c_member(_1352961), _1353442), _1352963)), hAPP(_1352965, _1353442) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31649 ^ _779571 : [(31654 ^ _779571) ^ [] : [hAPP(_1352965, 31648 ^ [_1352961, _1352963, _1352965, _1353442]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31652 ^ _779571) ^ [] : [_1353442 = 31648 ^ [_1352961, _1352963, _1352965, _1353442]], (31650 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1352961), 31648 ^ [_1352961, _1352963, _1352965, _1353442]), _1352963)))]]]]], (31620 ^ _779571) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352961, tc_Nat_Onat), _1352965), _1352963) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31624 ^ _779571 : [(31629 ^ _779571) ^ [_1353281] : [hBOOL(hAPP(hAPP(c_member(_1352961), _1353281), _1352963)), -(31623 ^ [_1352961, _1352963, _1352965] = _1353281), -(hAPP(_1352965, _1353281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31627 ^ _779571) ^ [] : [-(hAPP(_1352965, 31623 ^ [_1352961, _1352963, _1352965]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31625 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1352961), 31623 ^ [_1352961, _1352963, _1352965]), _1352963)))]]]]], (48494 ^ _779571) ^ [_1749610, _1749612, _1749614, _1749616] : [hBOOL(hAPP(hAPP(c_member(_1749610), _1749612), c_Wellfounded_Oacc(_1749610, _1749614))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1749610)), _1749616), c_Wellfounded_Oacc(tc_List_Olist(_1749610), c_List_Olistrel1(_1749610, _1749614)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1749610)), hAPP(hAPP(c_List_Olist_OCons(_1749610), _1749612), _1749616)), c_Wellfounded_Oacc(tc_List_Olist(_1749610), c_List_Olistrel1(_1749610, _1749614)))))], (19239 ^ _779571) ^ [_1109515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1109515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1109515)))], (17295 ^ _779571) ^ [_1076893, _1076895] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076893)), _1076895) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076893), _1076895)))], (6466 ^ _779571) ^ [_884970, _884972, _884974, _884976, _884978] : [-(hBOOL(hAPP(_884970, _884972))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884974), _884972), _884976)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_884970, _884978, _884974)), _884972), _884976)))], (24623 ^ _779571) ^ [_1209516, _1209518, _1209520] : [class_Groups_Olinordered__ab__group__add(_1209516), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1209516), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209516), _1209518), _1209520)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209516), hAPP(c_Groups_Ouminus__class_Ouminus(_1209516), _1209518)), hAPP(c_Groups_Ouminus__class_Ouminus(_1209516), _1209520)))], (4784 ^ _779571) ^ [_853505, _853507, _853509, _853511, _853513, _853515] : [-(c_List_Olist_Olist__size(_853515, _853511, _853507) = c_List_Olist_Olist__size(_853513, _853509, _853505)), _853515 = _853513, _853511 = _853509, _853507 = _853505], (36746 ^ _779571) ^ [_1463045, _1463047, _1463049, _1463051, _1463053] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463045, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1463047, _1463045, _1463049), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463047, tc_HOL_Obool)), _1463051), _1463053))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463045, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1463047, _1463045, _1463049), _1463051)), hAPP(c_Set_Oimage(_1463047, _1463045, _1463049), _1463053)))))], (9718 ^ _779571) ^ [_941136, _941138, _941140, _941142] : [class_Rings_Olinordered__ring__strict(_941136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941136), _941138), c_Groups_Ozero__class_Ozero(_941136))), 9725 ^ _779571 : [(9732 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941136), _941142), _941140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941136), _941138), _941140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941136), _941138), _941142))))], (9726 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941136), _941138), _941140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941136), _941138), _941142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941136), _941142), _941140)))]]], (36956 ^ _779571) ^ [_1468075, _1468077, _1468079] : [class_Orderings_Oorder(_1468075), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468075, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1468075), _1468077)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1468075, _1468077, _1468079)) = c_Orderings_Obot__class_Obot(tc_fun(_1468075, tc_HOL_Obool)))], (18901 ^ _779571) ^ [_1103720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1103720)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103720), c_Int_OPls)))], (14662 ^ _779571) ^ [_1026821, _1026823] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026821), _1026823) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14663 ^ _779571 : [(14672 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1026821), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026823), _1026821))], (14666 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026821), _1026823))], (14664 ^ _779571) ^ [] : [_1026823 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (48331 ^ _779571) ^ [_1745457, _1745459, _1745461, _1745463, _1745465, _1745467] : [-(c_Map_Omap__add(_1745457, _1745459, _1745461, c_Map_Omap__upds(_1745457, _1745459, _1745463, _1745465, _1745467)) = c_Map_Omap__upds(_1745457, _1745459, c_Map_Omap__add(_1745457, _1745459, _1745461, _1745463), _1745465, _1745467))], (40100 ^ _779571) ^ [_1538573, _1538575, _1538577, _1538579, _1538581, _1538583] : [hBOOL(hAPP(hAPP(c_member(_1538573), _1538575), _1538577)), 40103 ^ _779571 : [(40110 ^ _779571) ^ [] : [_1538581 = _1538583, -(hAPP(hAPP(c_Product__Type_OSigma(_1538579, _1538573), _1538581), hAPP(c_COMBK(tc_fun(_1538573, tc_HOL_Obool), _1538579), _1538577)) = hAPP(hAPP(c_Product__Type_OSigma(_1538579, _1538573), _1538583), hAPP(c_COMBK(tc_fun(_1538573, tc_HOL_Obool), _1538579), _1538577)))], (40104 ^ _779571) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1538579, _1538573), _1538581), hAPP(c_COMBK(tc_fun(_1538573, tc_HOL_Obool), _1538579), _1538577)) = hAPP(hAPP(c_Product__Type_OSigma(_1538579, _1538573), _1538583), hAPP(c_COMBK(tc_fun(_1538573, tc_HOL_Obool), _1538579), _1538577)), -(_1538581 = _1538583)]]], (26398 ^ _779571) ^ [_1243253, _1243255, _1243257] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243253), _1243257))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243253, _1243255) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243257, _1243255))], (18291 ^ _779571) ^ [_1093868] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093868) = 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(_1093868)))))], (31940 ^ _779571) ^ [_1359995, _1359997, _1359999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359995), _1359997)), hBOOL(hAPP(hAPP(c_member(_1359995), _1359999), _1359997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1359995), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359995, tc_HOL_Obool)), _1359997), hAPP(hAPP(c_Set_Oinsert(_1359995), _1359999), c_Orderings_Obot__class_Obot(tc_fun(_1359995, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1359995), _1359997))))], (37527 ^ _779571) ^ [_1480586, _1480588, _1480590, _1480592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480586), _1480588)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480586), _1480590)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480586, tc_Nat_Onat), _1480592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480586, tc_HOL_Obool)), _1480588), _1480590)) = 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(_1480586, tc_Nat_Onat), _1480592), _1480588)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480586, tc_Nat_Onat), _1480592), _1480590))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480586, tc_Nat_Onat), _1480592), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480586, tc_HOL_Obool)), _1480588), _1480590))))], (47767 ^ _779571) ^ [_1732133, _1732135, _1732137, _1732139, _1732141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732133), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732135)), _1732137))), 47770 ^ _779571 : [(47777 ^ _779571) ^ [] : [-(_1732133 = _1732139), -(hAPP(hAPP(c_List_Onth(_1732135), hAPP(hAPP(c_List_Olist__update(_1732135, _1732137), _1732133), _1732141)), _1732139) = hAPP(hAPP(c_List_Onth(_1732135), _1732137), _1732139))], (47771 ^ _779571) ^ [] : [_1732133 = _1732139, -(hAPP(hAPP(c_List_Onth(_1732135), hAPP(hAPP(c_List_Olist__update(_1732135, _1732137), _1732133), _1732141)), _1732139) = _1732141)]]], (34545 ^ _779571) ^ [_1412023, _1412025, _1412027, _1412029, _1412031, _1412033, _1412035] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412023, tc_Option_Ooption(_1412025)), _1412027), _1412029), hAPP(c_Option_Ooption_OSome(_1412025), _1412031)), _1412033) = hAPP(c_Option_Ooption_OSome(_1412025), _1412035), 34550 ^ _779571 : [(34553 ^ _779571) ^ [] : [-(_1412031 = _1412035)], (34551 ^ _779571) ^ [] : [-(_1412033 = _1412029)]], 34554 ^ _779571 : [(34557 ^ _779571) ^ [] : [-(hAPP(_1412027, _1412033) = hAPP(c_Option_Ooption_OSome(_1412025), _1412035))], (34555 ^ _779571) ^ [] : [_1412033 = _1412029]]], (8980 ^ _779571) ^ [_928449, _928451] : [class_Rings_Ocomm__semiring__1(_928449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928449), _928451), c_Groups_Oone__class_Oone(_928449)) = _928451)], (39713 ^ _779571) ^ [_1529110, _1529112, _1529114, _1529116, _1529118] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529110, _1529112, _1529114, _1529116, c_Orderings_Obot__class_Obot(tc_fun(_1529110, tc_HOL_Obool))), _1529118)), -(_1529118 = _1529116)], (51443 ^ _779571) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (33495 ^ _779571) ^ [_1390371, _1390373, _1390375, _1390377, _1390379, _1390381, _1390383] : [-(c_Nitpick_Ofold__graph_H(_1390371, _1390373, _1390375, _1390377, _1390379, hAPP(hAPP(_1390375, _1390381), _1390383))), 33496 ^ _779571 : [(33503 ^ _779571) ^ [_1390600, _1390602] : [hAPP(hAPP(_1390375, _1390381), _1390383) = hAPP(hAPP(_1390375, _1390602), _1390600), hBOOL(hAPP(hAPP(c_member(_1390371), _1390602), _1390379)), c_Nitpick_Ofold__graph_H(_1390371, _1390373, _1390375, _1390377, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390371, tc_HOL_Obool)), _1390379), hAPP(hAPP(c_Set_Oinsert(_1390371), _1390602), c_Orderings_Obot__class_Obot(tc_fun(_1390371, tc_HOL_Obool)))), _1390600)], (33497 ^ _779571) ^ [] : [_1390379 = c_Orderings_Obot__class_Obot(tc_fun(_1390371, tc_HOL_Obool)), hAPP(hAPP(_1390375, _1390381), _1390383) = _1390377]]], (17223 ^ _779571) ^ [_1075758, _1075760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075758), _1075760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075758)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075760))))], (26968 ^ _779571) ^ [_1254541, _1254543, _1254545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1254541, 26969 ^ [_1254541, _1254543, _1254545])), hAPP(_1254543, 26969 ^ [_1254541, _1254543, _1254545]))), -(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), _1254543), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1254545))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1254541), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1254545))) = 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)), _1254543)), _1254541)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1254545)))], (48776 ^ _779571) ^ [_1757627, _1757629, _1757631, _1757633, _1757635] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1757627, _1757629)), _1757631), hAPP(hAPP(c_List_Ozip(_1757627, _1757629), _1757633), _1757635)) = hAPP(hAPP(c_List_Ozip(_1757627, _1757629), hAPP(hAPP(c_List_Odrop(_1757627), _1757631), _1757633)), hAPP(hAPP(c_List_Odrop(_1757629), _1757631), _1757635)))], (20747 ^ _779571) ^ [_1136161, _1136163, _1136165, _1136167, _1136169] : [class_Fields_Olinordered__field(_1136161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136161), c_Groups_Ozero__class_Ozero(_1136161)), _1136163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136161), _1136163), _1136165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136161), c_Groups_Ozero__class_Ozero(_1136161)), _1136167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136161), _1136167), _1136169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136161), _1136163), _1136169)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136161), _1136165), _1136167))))], (42417 ^ _779571) ^ [_1601557, _1601559, _1601561, _1601563, _1601565] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1601557), _1601559), _1601561), _1601563), _1601565) = c_New__DSequence_Oneg__single(_1601557, _1601559))], (36938 ^ _779571) ^ [_1467662, _1467664, _1467666] : [class_Orderings_Oorder(_1467662), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467662, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1467662, _1467664, _1467666)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1467662), _1467666)) = c_Orderings_Obot__class_Obot(tc_fun(_1467662, tc_HOL_Obool)))], (16479 ^ _779571) ^ [_1061429, _1061431, _1061433, _1061435] : [class_Rings_Ocomm__semiring__1(_1061429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1061429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061429), _1061431), _1061433)), _1061435) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061429), hAPP(hAPP(c_Power_Opower__class_Opower(_1061429), _1061431), _1061435)), hAPP(hAPP(c_Power_Opower__class_Opower(_1061429), _1061433), _1061435)))], (38589 ^ _779571) ^ [_1504485, _1504487, _1504489, _1504491, _1504493] : [c_Fun_Oinj__on(_1504485, _1504487, _1504489, c_Orderings_Otop__class_Otop(tc_fun(_1504485, tc_HOL_Obool))), 38592 ^ _779571 : [(38599 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504485), _1504491), _1504493)), -(hBOOL(hAPP(hAPP(c_member(_1504487), hAPP(_1504489, _1504491)), hAPP(c_Set_Oimage(_1504485, _1504487, _1504489), _1504493))))], (38593 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504487), hAPP(_1504489, _1504491)), hAPP(c_Set_Oimage(_1504485, _1504487, _1504489), _1504493))), -(hBOOL(hAPP(hAPP(c_member(_1504485), _1504491), _1504493)))]]], (1122 ^ _779571) ^ [_796364, _796366] : [-(class_Groups_Ogroup__add(_796364)), _796366 = _796364, class_Groups_Ogroup__add(_796366)], (16236 ^ _779571) ^ [_1057184, _1057186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1057186), _1057184))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1057186), _1057184) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057186), _1057184)), _1057184)))], (12409 ^ _779571) ^ [] : [-(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))))], (2274 ^ _779571) ^ [_813852, _813854, _813856, _813858, _813860, _813862, _813864, _813866, _813868, _813870] : [-(c_Option_Ooption_Ooption__rec(_813870, _813866, _813862, _813858, _813854) = c_Option_Ooption_Ooption__rec(_813868, _813864, _813860, _813856, _813852)), _813870 = _813868, _813866 = _813864, _813862 = _813860, _813858 = _813856, _813854 = _813852], (11168 ^ _779571) ^ [_964950, _964952, _964954] : [11169 ^ _779571 : [(11172 ^ _779571) ^ [] : [_964950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11170 ^ _779571) ^ [] : [_964952 = _964954]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964950), _964952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964950), _964954))], (10854 ^ _779571) ^ [_960037, _960039, _960041] : [class_Orderings_Opreorder(_960037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960037), _960039), _960041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960037), _960039), _960041)))], (50784 ^ _779571) ^ [_1800527, _1800529, _1800531] : [-(hAPP(c_List_Orev(_1800527), hAPP(hAPP(c_List_Otake(_1800527), _1800529), _1800531)) = hAPP(hAPP(c_List_Odrop(_1800527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800527)), _1800531)), _1800529)), hAPP(c_List_Orev(_1800527), _1800531)))], (30878 ^ _779571) ^ [_1335314, _1335316] : [_1335316 = c_Option_Ooption_ONone(_1335314), -(c_Option_Oset(_1335314, _1335316) = c_Orderings_Obot__class_Obot(tc_fun(_1335314, tc_HOL_Obool)))], (20769 ^ _779571) ^ [_1136584, _1136586, _1136588] : [class_Fields_Olinordered__field(_1136584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136584), c_Groups_Ozero__class_Ozero(_1136584)), _1136586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136584), _1136588), c_Groups_Ozero__class_Ozero(_1136584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136584), _1136586), _1136588)), c_Groups_Ozero__class_Ozero(_1136584))))], (31704 ^ _779571) ^ [_1354940, _1354942, _1354944, _1354946, _1354948] : [class_Groups_Ocomm__monoid__add(_1354940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354942), _1354944)), -(hBOOL(hAPP(hAPP(c_member(_1354942), _1354946), _1354944))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354942, _1354940), _1354948), hAPP(hAPP(c_Set_Oinsert(_1354942), _1354946), _1354944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354940), hAPP(_1354948, _1354946)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354942, _1354940), _1354948), _1354944)))], (43270 ^ _779571) ^ [_1621931, _1621933] : [-(c_Relation_Orefl__on(_1621931, c_Orderings_Otop__class_Otop(tc_fun(_1621931, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1621931, _1621931), tc_HOL_Obool)), _1621933), c_Relation_OId(_1621931))))], (1422 ^ _779571) ^ [_800114, _800116] : [-(class_Groups_Oordered__ab__semigroup__add(_800114)), _800116 = _800114, class_Groups_Oordered__ab__semigroup__add(_800116)], (49034 ^ _779571) ^ [_1763327, _1763329, _1763331] : [hAPP(c_List_Orotate(_1763327, _1763329), _1763331) = c_List_Olist_ONil(_1763327), -(_1763331 = c_List_Olist_ONil(_1763327))], (51523 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (22258 ^ _779571) ^ [_1163593, _1163595] : [hAPP(c_Code__Numeral_Oof__nat, _1163593) = hAPP(c_Code__Numeral_Oof__nat, _1163595), -(_1163593 = _1163595)], (26392 ^ _779571) ^ [_1243140, _1243142, _1243144] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243140, _1243142) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243144, _1243142), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243140), _1243144))))], (16579 ^ _779571) ^ [_1063199, _1063201] : [class_Groups_Oordered__ab__group__add__abs(_1063199), 16582 ^ _779571 : [(16589 ^ _779571) ^ [] : [_1063201 = c_Groups_Ozero__class_Ozero(_1063199), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063199), hAPP(c_Groups_Oabs__class_Oabs(_1063199), _1063201)), c_Groups_Ozero__class_Ozero(_1063199))))], (16583 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063199), hAPP(c_Groups_Oabs__class_Oabs(_1063199), _1063201)), c_Groups_Ozero__class_Ozero(_1063199))), -(_1063201 = c_Groups_Ozero__class_Ozero(_1063199))]]], (47985 ^ _779571) ^ [_1737355, _1737357, _1737359, _1737361, _1737363] : [-(hAPP(hAPP(c_List_Omap(_1737355, _1737357), _1737359), hAPP(hAPP(c_List_Oappend(_1737355), _1737361), _1737363)) = hAPP(hAPP(c_List_Oappend(_1737357), hAPP(hAPP(c_List_Omap(_1737355, _1737357), _1737359), _1737361)), hAPP(hAPP(c_List_Omap(_1737355, _1737357), _1737359), _1737363)))], (1542 ^ _779571) ^ [_801614, _801616] : [-(class_Rings_Ono__zero__divisors(_801614)), _801616 = _801614, class_Rings_Ono__zero__divisors(_801616)], (40186 ^ _779571) ^ [_1541190, _1541192, _1541194] : [c_Equiv__Relations_Oequiv(_1541190, _1541192, _1541194), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541190, _1541190), tc_HOL_Obool)), _1541194), hAPP(hAPP(c_Product__Type_OSigma(_1541190, _1541190), _1541192), hAPP(c_COMBK(tc_fun(_1541190, tc_HOL_Obool), _1541190), _1541192)))))], (17283 ^ _779571) ^ [_1076703] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076703) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1076703))], (47899 ^ _779571) ^ [_1735393, _1735395, _1735397, _1735399, _1735401] : [hAPP(hAPP(c_List_Olist_OCons(_1735393), _1735395), _1735397) = hAPP(hAPP(c_List_Oappend(_1735393), _1735399), _1735401), 47904 ^ _779571 : [(47907 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735393), _1735395), _1735397) = _1735401)], (47905 ^ _779571) ^ [] : [-(_1735399 = c_List_Olist_ONil(_1735393))]], 47909 ^ _779571 : [(47912 ^ _779571) ^ [] : [-(_1735397 = hAPP(hAPP(c_List_Oappend(_1735393), 47908 ^ [_1735393, _1735395, _1735397, _1735399, _1735401]), _1735401))], (47910 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735393), _1735395), 47908 ^ [_1735393, _1735395, _1735397, _1735399, _1735401]) = _1735399)]]], (27748 ^ _779571) ^ [_1270784, _1270786, _1270788, _1270790, _1270792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270784, tc_HOL_Obool)), _1270786), _1270788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270784, tc_HOL_Obool)), _1270790), _1270792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270784, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270784, tc_HOL_Obool)), _1270786), _1270790)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270784, tc_HOL_Obool)), _1270788), _1270792))))], (20057 ^ _779571) ^ [_1124462, _1124464] : [class_Rings_Odivision__ring(_1124462), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124462), _1124464), c_Groups_Oone__class_Oone(_1124462)) = _1124464)], (27193 ^ _779571) ^ [_1259056, _1259058, _1259060, _1259062] : [class_Groups_Ocomm__monoid__add(_1259056), 27196 ^ _779571 : [(27203 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1259058), _1259060))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1259056), _1259062), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259060), hAPP(c_Nat_OSuc, _1259058))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1259056), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1259056), _1259062), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259060), _1259058))), hAPP(_1259062, _1259058)))], (27197 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1259058), _1259060)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1259056), _1259062), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259060), hAPP(c_Nat_OSuc, _1259058))) = c_Groups_Ozero__class_Ozero(_1259056))]]], (10834 ^ _779571) ^ [_959781, _959783, _959785] : [class_Orderings_Olinorder(_959781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959781), _959783), _959785)), 10841 ^ _779571 : [(10848 ^ _779571) ^ [] : [_959783 = _959785, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959781), _959783), _959785))], (10842 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959781), _959783), _959785))), -(_959783 = _959785)]]], (28308 ^ _779571) ^ [_1281950] : [28310 ^ _779571 : [(28313 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28309 ^ [_1281950]))], (28311 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28309 ^ [_1281950]), _1281950)))]], -(c_Nat__Transfer_Onat__set(_1281950))], (22328 ^ _779571) ^ [_1165019, _1165021] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1165019)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1165021)), hAPP(c_Int_Onat, _1165019)) = hAPP(c_Int_Onat, _1165021))], (36390 ^ _779571) ^ [_1455652, _1455654, _1455656, _1455658] : [class_Lattices_Olattice(_1455652), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455652), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455652), _1455654), _1455656)), _1455658) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455652), _1455654), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455652), _1455656), _1455658)))], (18203 ^ _779571) ^ [_1092508] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1092508), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092508))], (25210 ^ _779571) ^ [_1221564, _1221566] : [_1221564 = _1221566, 25213 ^ _779571 : [(25216 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221566), _1221564)))], (25214 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1221564), _1221566)))]]], (19039 ^ _779571) ^ [_1105775, _1105777] : [class_Int_Onumber__ring(_1105775), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105775), c_Groups_Oone__class_Oone(_1105775)), hAPP(c_Int_Onumber__class_Onumber__of(_1105775), _1105777)) = hAPP(c_Int_Onumber__class_Onumber__of(_1105775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1105777)))], (49333 ^ _779571) ^ [_1770114, _1770116, _1770118, _1770120] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770114)), hAPP(hAPP(c_List_Olist_OCons(_1770114), _1770116), _1770118)), c_List_Olists(_1770114, _1770120)))), hBOOL(hAPP(hAPP(c_member(_1770114), _1770116), _1770120)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770114)), _1770118), c_List_Olists(_1770114, _1770120)))], (6359 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (49086 ^ _779571) ^ [_1764411, _1764413] : [class_Lattices_Oab__semigroup__idem__mult(_1764411), -(_1764413 = c_List_Olist_ONil(_1764411)), -(hAPP(c_Finite__Set_Ofold1(_1764411, c_Groups_Otimes__class_Otimes(_1764411)), hAPP(c_List_Oset(_1764411), _1764413)) = hAPP(c_List_Ofoldl(_1764411, _1764411, c_Groups_Otimes__class_Otimes(_1764411), hAPP(c_List_Ohd(_1764411), _1764413)), hAPP(c_List_Otl(_1764411), _1764413)))], (30098 ^ _779571) ^ [_1318929, _1318931, _1318933, _1318935, _1318937, _1318939, _1318941] : [hBOOL(hAPP(hAPP(c_member(_1318929), _1318931), hAPP(hAPP(_1318933, _1318935), _1318937))), -(hBOOL(hAPP(hAPP(c_member(_1318929), _1318931), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1318939, _1318941, tc_fun(_1318929, tc_HOL_Obool)), _1318933), hAPP(hAPP(c_Product__Type_OPair(_1318939, _1318941), _1318935), _1318937)))))], (16064 ^ _779571) ^ [_1053718, _1053720, _1053722, _1053724, _1053726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053718), _1053720)), -(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), _1053720), _1053722)), _1053724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053718), _1053722)), _1053726)) = 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), _1053720), _1053718)), _1053722)), _1053724)), _1053726))], (36302 ^ _779571) ^ [_1453794, _1453796, _1453798, _1453800] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453794, tc_HOL_Obool)), _1453796), _1453798), _1453800)), -(hBOOL(hAPP(_1453798, _1453800)))], (19401 ^ _779571) ^ [_1112260, _1112262] : [class_Int_Onumber__ring(_1112260), -(hAPP(c_Int_Onumber__class_Onumber__of(_1112260), c_Int_OBit0(_1112262)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112260), c_Groups_Ozero__class_Ozero(_1112260)), hAPP(c_Int_Onumber__class_Onumber__of(_1112260), _1112262))), hAPP(c_Int_Onumber__class_Onumber__of(_1112260), _1112262)))], (12127 ^ _779571) ^ [_981828, _981830] : [class_Groups_Oordered__ab__group__add(_981828), 12130 ^ _779571 : [(12137 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981828), c_Groups_Ozero__class_Ozero(_981828)), _981830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981828), hAPP(c_Groups_Ouminus__class_Ouminus(_981828), _981830)), c_Groups_Ozero__class_Ozero(_981828))))], (12131 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981828), hAPP(c_Groups_Ouminus__class_Ouminus(_981828), _981830)), c_Groups_Ozero__class_Ozero(_981828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981828), c_Groups_Ozero__class_Ozero(_981828)), _981830)))]]], (41350 ^ _779571) ^ [_1569559] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1569559) = 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), _1569559), c_Int_Onat)))))], (51595 ^ _779571) ^ [_1813501] : [hBOOL(hAPP(c_fNot, _1813501)), hBOOL(_1813501)], (38247 ^ _779571) ^ [_1497996, _1497998, _1498000] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497996), _1497998)), c_Fun_Oinj__on(_1497996, tc_fun(tc_fun(_1497996, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1497996, tc_fun(tc_prod(_1497996, _1497996), tc_HOL_Obool), tc_fun(tc_fun(_1497996, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497996, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1497996, _1497996), tc_HOL_Obool), tc_fun(tc_fun(_1497996, tc_HOL_Obool), tc_HOL_Obool)), _1497996), c_Equiv__Relations_Oquotient(_1497996)), hAPP(hAPP(c_COMBC(_1497996, tc_fun(_1497996, tc_HOL_Obool), tc_fun(_1497996, tc_HOL_Obool)), c_Set_Oinsert(_1497996)), c_Orderings_Obot__class_Obot(tc_fun(_1497996, tc_HOL_Obool))))), _1498000), _1497998), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1497996, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1497996), _1497998), _1498000)) = hAPP(c_Finite__Set_Ocard(_1497996), _1497998))], (40995 ^ _779571) ^ [_1559848, _1559850, _1559852, _1559854] : [c_Finite__Set_Ofun__left__comm__idem(_1559848, _1559850, _1559852), -(hAPP(c_Fun_Ocomp(_1559850, _1559850, _1559850, hAPP(_1559852, _1559854)), hAPP(_1559852, _1559854)) = hAPP(_1559852, _1559854))], (41581 ^ _779571) ^ [_1578915, _1578917, _1578919, _1578921, _1578923, _1578925, _1578927] : [class_Rings_Osemiring__0(_1578915), c_Fun_Oinj__on(tc_prod(_1578917, _1578919), _1578915, hAPP(c_Product__Type_Oprod_Oprod__case(_1578917, _1578919, _1578915), hAPP(hAPP(c_COMBC(_1578917, tc_fun(_1578919, _1578915), tc_fun(_1578919, _1578915)), hAPP(hAPP(c_COMBB(tc_fun(_1578915, _1578915), tc_fun(tc_fun(_1578919, _1578915), tc_fun(_1578919, _1578915)), _1578917), c_COMBB(_1578915, _1578915, _1578919)), hAPP(hAPP(c_COMBB(_1578915, tc_fun(_1578915, _1578915), _1578917), c_Groups_Otimes__class_Otimes(_1578915)), _1578921))), _1578923)), hAPP(hAPP(c_Product__Type_OSigma(_1578917, _1578919), _1578925), hAPP(c_COMBK(tc_fun(_1578919, tc_HOL_Obool), _1578917), _1578927))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1578915), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578917, _1578915), _1578921), _1578925)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578919, _1578915), _1578923), _1578927)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578915, _1578915), c_Fun_Oid(_1578915)), hAPP(c_Set_OCollect(_1578915), hAPP(hAPP(c_COMBB(tc_fun(_1578917, tc_HOL_Obool), tc_HOL_Obool, _1578915), c_HOL_OEx(_1578917)), hAPP(hAPP(c_COMBB(tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool)), tc_fun(_1578917, tc_HOL_Obool), _1578915), hAPP(c_COMBB(tc_fun(_1578919, tc_HOL_Obool), tc_HOL_Obool, _1578917), c_HOL_OEx(_1578919))), hAPP(hAPP(c_COMBC(_1578915, tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool)), tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578917, tc_fun(tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool))), tc_fun(tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool)), tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool))), _1578915), c_COMBS(_1578917, tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578917, tc_fun(_1578919, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1578917, tc_fun(tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool))), _1578915), hAPP(c_COMBB(tc_fun(_1578919, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool)), _1578917), c_COMBS(_1578919, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool)), tc_fun(_1578917, tc_fun(_1578919, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1578915), hAPP(c_COMBB(tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1578917), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578919), c_fconj))), hAPP(hAPP(c_COMBC(_1578915, tc_fun(_1578917, tc_fun(_1578919, _1578915)), tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578919, _1578915), tc_fun(_1578919, tc_HOL_Obool)), tc_fun(tc_fun(_1578917, tc_fun(_1578919, _1578915)), tc_fun(_1578917, tc_fun(_1578919, tc_HOL_Obool))), _1578915), c_COMBB(tc_fun(_1578919, _1578915), tc_fun(_1578919, tc_HOL_Obool), _1578917)), hAPP(hAPP(c_COMBB(tc_fun(_1578915, tc_HOL_Obool), tc_fun(tc_fun(_1578919, _1578915), tc_fun(_1578919, tc_HOL_Obool)), _1578915), c_COMBB(_1578915, tc_HOL_Obool, _1578919)), c_fequal))), hAPP(hAPP(c_COMBC(_1578917, tc_fun(_1578919, _1578915), tc_fun(_1578919, _1578915)), hAPP(hAPP(c_COMBB(tc_fun(_1578915, _1578915), tc_fun(tc_fun(_1578919, _1578915), tc_fun(_1578919, _1578915)), _1578917), c_COMBB(_1578915, _1578915, _1578919)), hAPP(hAPP(c_COMBB(_1578915, tc_fun(_1578915, _1578915), _1578917), c_Groups_Otimes__class_Otimes(_1578915)), _1578921))), _1578923)))))), hAPP(hAPP(c_COMBC(_1578917, tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578919, tc_HOL_Obool), tc_fun(_1578919, tc_HOL_Obool)), _1578917), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578919)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578917), c_fconj), hAPP(hAPP(c_COMBC(_1578917, tc_fun(_1578917, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578917)), _1578925)))), hAPP(hAPP(c_COMBC(_1578919, tc_fun(_1578919, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578919)), _1578927))))))))], (47330 ^ _779571) ^ [_1721306, _1721308] : [-(_1721308 = c_List_Olist_ONil(_1721306)), -(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(_1721306)), _1721308))))], (45682 ^ _779571) ^ [_1679697, _1679699, _1679701, _1679703, _1679705] : [-(hAPP(c_Map_Omap__add(_1679697, _1679699, _1679701, _1679703), _1679705) = c_Option_Ooption_ONone(_1679699)), hAPP(_1679703, _1679705) = c_Option_Ooption_ONone(_1679699), hAPP(_1679701, _1679705) = c_Option_Ooption_ONone(_1679699)], (37974 ^ _779571) ^ [_1492442, _1492444, _1492446, _1492448] : [c_Relation_Orefl__on(_1492442, _1492444, _1492446), hBOOL(hAPP(hAPP(c_member(_1492442), _1492448), _1492444)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492442, _1492442)), hAPP(hAPP(c_Product__Type_OPair(_1492442, _1492442), _1492448), _1492448)), _1492446)))], (7387 ^ _779571) ^ [_902218] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _902218))), -(hAPP(c_Com_Obody, _902218) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7390 ^ [_902218]))], (6424 ^ _779571) ^ [_884248, _884250, _884252] : [class_Rings_Osemiring__1(_884248), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_884248, _884250, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _884252) = _884252)], (37777 ^ _779571) ^ [_1487752, _1487754, _1487756, _1487758, _1487760] : [class_Groups_Ocomm__monoid__mult(_1487752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487754), _1487756)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487754), _1487758)), 37791 ^ _779571 : [(37794 ^ _779571) ^ [] : [hAPP(_1487760, 37790 ^ [_1487752, _1487754, _1487756, _1487758, _1487760]) = c_Groups_Oone__class_Oone(_1487752)], (37792 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487754), 37790 ^ [_1487752, _1487754, _1487756, _1487758, _1487760]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487754, tc_HOL_Obool)), _1487756), _1487758))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487754, _1487752), _1487760), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487754, tc_HOL_Obool)), _1487756), _1487758)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487752), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487754, _1487752), _1487760), _1487756)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487754, _1487752), _1487760), _1487758)))], (29296 ^ _779571) ^ [_1303124, _1303126, _1303128, _1303130] : [c_Orderings_Obot__class_Obot(tc_fun(_1303124, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303126, tc_fun(_1303124, tc_HOL_Obool)), _1303128), _1303130), 29299 ^ _779571 : [(29300 ^ _779571) ^ [_1303240] : [hBOOL(hAPP(hAPP(c_member(_1303126), _1303240), _1303128)), -(hAPP(_1303130, _1303240) = c_Orderings_Obot__class_Obot(tc_fun(_1303124, tc_HOL_Obool)))]]], (41159 ^ _779571) ^ [_1563262, _1563264, _1563266] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563262, tc_HOL_Obool)), _1563264), _1563266) = hAPP(c_Set_OCollect(_1563262), hAPP(hAPP(c_COMBS(_1563262, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563262), c_fconj), hAPP(hAPP(c_COMBC(_1563262, tc_fun(_1563262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563262)), _1563264))), hAPP(hAPP(c_COMBC(_1563262, tc_fun(_1563262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563262)), _1563266))))], (9010 ^ _779571) ^ [_928882, _928884] : [class_Groups_Ocomm__monoid__mult(_928882), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928882), c_Groups_Oone__class_Oone(_928882)), _928884) = _928884)], (11627 ^ _779571) ^ [_972725, _972727, _972729] : [class_Rings_Olinordered__idom(_972725), -(c_Groups_Osgn__class_Osgn(_972725, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972725), _972727), _972729)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972725), c_Groups_Osgn__class_Osgn(_972725, _972727)), c_Groups_Osgn__class_Osgn(_972725, _972729)))], (23809 ^ _779571) ^ [_1193337, _1193339, _1193341] : [class_Orderings_Olinorder(_1193337), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193337), _1193339), _1193341) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193337), _1193341), _1193339))], (23977 ^ _779571) ^ [_1196916, _1196918, _1196920] : [-(_1196916 = _1196918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196920, tc_HOL_Obool)), _1196916), _1196918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196920, tc_HOL_Obool)), _1196918), _1196916))], (51241 ^ _779571) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (50768 ^ _779571) ^ 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tc_fun(_1419079, tc_HOL_Obool)), _1419079), c_COMBC(_1419079, tc_fun(tc_prod(_1419079, _1419079), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419079, tc_prod(_1419079, _1419079)), tc_fun(_1419079, tc_fun(tc_fun(tc_prod(_1419079, _1419079), tc_HOL_Obool), tc_HOL_Obool)), _1419079), hAPP(c_COMBB(tc_prod(_1419079, _1419079), tc_fun(tc_fun(tc_prod(_1419079, _1419079), tc_HOL_Obool), tc_HOL_Obool), _1419079), c_member(tc_prod(_1419079, _1419079)))), c_Product__Type_OPair(_1419079, _1419079)))), _1419081), _1419083, _1419085))], (5620 ^ _779571) ^ [_866319, _866321, _866323, _866325, _866327, _866329] : [-(c_COMBB(_866329, _866325, _866321) = c_COMBB(_866327, _866323, _866319)), _866329 = _866327, _866325 = _866323, _866321 = _866319], (33605 ^ _779571) ^ [_1393020, _1393022, _1393024, _1393026] : [-(c_Sum__Type_OPlus(_1393020, _1393022, _1393024, _1393026) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(_1393020, _1393022), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1393020, tc_sum(_1393020, _1393022), c_Sum__Type_OInl(_1393020, _1393022)), _1393024)), hAPP(c_Set_Oimage(_1393022, tc_sum(_1393020, _1393022), c_Sum__Type_OInr(_1393022, _1393020)), _1393026)))], (32629 ^ _779571) ^ [_1374876, _1374878, _1374880, _1374882, _1374884, _1374886] : [hBOOL(hAPP(hAPP(c_member(_1374876), _1374878), c_SetInterval_Oord_OgreaterThanAtMost(_1374876, _1374880, _1374882, _1374884, _1374886))), 32632 ^ _779571 : [(32635 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1374880, _1374878), _1374886)))], (32633 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1374882, _1374884), _1374878)))]]], (22520 ^ _779571) ^ [_1169306, _1169308] : [-(c_Divides_OnegDivAlg(_1169306, _1169308) = hAPP(c_Divides_Oadjust(_1169308), c_Divides_OnegDivAlg(_1169306, 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)))), _1169308)))), -(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), _1169306), _1169308)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1169308), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12225 ^ _779571) ^ [_983506, _983508, _983510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983506), _983508)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983510), _983508))), 12228 ^ _779571 : [(12231 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983506), _983510)))], (12229 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983508)))]]], (43769 ^ _779571) ^ [_1634619, _1634621, _1634623, _1634625, _1634627, _1634629] : [c_Relation_Osingle__valued(_1634619, _1634621, _1634623), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634619, _1634621)), hAPP(hAPP(c_Product__Type_OPair(_1634619, _1634621), _1634625), _1634627)), _1634623)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634619, _1634621)), hAPP(hAPP(c_Product__Type_OPair(_1634619, _1634621), _1634625), _1634629)), _1634623)), -(_1634627 = _1634629)], (31013 ^ _779571) ^ [_1337924, _1337926] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1337924, _1337926)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1337924, _1337926), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337924), c_Orderings_Otop__class_Otop(tc_fun(_1337924, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337926), c_Orderings_Otop__class_Otop(tc_fun(_1337926, tc_HOL_Obool))))], (11939 ^ _779571) ^ [_978499, _978501, _978503] : [class_Rings_Oordered__cancel__semiring(_978499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978499), c_Groups_Ozero__class_Ozero(_978499)), _978501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978499), _978503), c_Groups_Ozero__class_Ozero(_978499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978499), _978503), _978501)), c_Groups_Ozero__class_Ozero(_978499))))], (15064 ^ _779571) ^ [_1034181, _1034183, _1034185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034181)), 15067 ^ _779571 : [(15068 ^ _779571) ^ [] : [-(_1034183 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1034185), _1034181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1034181), _1034183)), _1034185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1034181), hAPP(c_Nat_OSuc, _1034183))))], (15078 ^ _779571) ^ [] : [_1034183 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1034185), _1034181), 15081 ^ _779571 : [(15084 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1034181), hAPP(c_Nat_OSuc, _1034183)))))], (15082 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1034181), _1034183)), _1034185)))]]]]], (13424 ^ _779571) ^ [_1004437, _1004439] : [_1004437 = _1004439, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004437), _1004439)))], (40284 ^ _779571) ^ [_1543748, _1543750, _1543752, _1543754] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1543748, _1543750)), hAPP(hAPP(c_Product__Type_OSigma(_1543748, _1543750), _1543752), hAPP(c_COMBK(tc_fun(_1543750, tc_HOL_Obool), _1543748), _1543754)))), -(_1543752 = c_Orderings_Obot__class_Obot(tc_fun(_1543748, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543750), _1543754)))], (35827 ^ _779571) ^ [_1443051, _1443053, _1443055, _1443057] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1443051, tc_HOL_Obool)), _1443053), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1443051), _1443055), _1443057))), 35831 ^ _779571 : [(35834 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443051), 35830 ^ [_1443051, _1443053, _1443055, _1443057]), _1443055)))], (35832 ^ _779571) ^ [] : [-(_1443053 = hAPP(c_Relation_OImage(_1443051, _1443051, _1443057), hAPP(hAPP(c_Set_Oinsert(_1443051), 35830 ^ [_1443051, _1443053, _1443055, _1443057]), c_Orderings_Obot__class_Obot(tc_fun(_1443051, tc_HOL_Obool)))))]]], (8145 ^ _779571) ^ [_914519, _914521] : [8146 ^ _779571 : [(8147 ^ _779571) ^ [_914575] : [_914521 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914519), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _914575)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _914519), _914521)))], (30196 ^ _779571) ^ [_1320735, _1320737, _1320739, _1320741] : [hBOOL(hAPP(hAPP(c_member(_1320735), _1320737), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320735, tc_HOL_Obool)), _1320739), _1320741))), hBOOL(hAPP(hAPP(c_member(_1320735), _1320737), _1320741))], (40969 ^ _779571) ^ [_1559296] : [-(c_Finite__Set_Ofun__left__comm__idem(_1559296, tc_fun(_1559296, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1559296, tc_HOL_Obool), tc_fun(tc_fun(_1559296, tc_HOL_Obool), tc_fun(_1559296, tc_HOL_Obool)), _1559296), hAPP(c_COMBC(tc_fun(_1559296, tc_HOL_Obool), tc_fun(_1559296, tc_HOL_Obool), tc_fun(_1559296, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1559296, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1559296, tc_fun(_1559296, tc_HOL_Obool), tc_fun(_1559296, tc_HOL_Obool)), c_Set_Oinsert(_1559296)), c_Orderings_Obot__class_Obot(tc_fun(_1559296, tc_HOL_Obool))))))], (12792 ^ _779571) ^ [_993665, _993667, _993669, _993671] : [class_Rings_Olinordered__ring__strict(_993665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993665), _993667), c_Groups_Ozero__class_Ozero(_993665))), 12799 ^ _779571 : [(12806 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993665), _993671), _993669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993665), _993667), _993669)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993665), _993667), _993671))))], (12800 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993665), _993667), _993669)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993665), _993667), _993671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993665), _993671), _993669)))]]], (24789 ^ _779571) ^ [_1212638, _1212640, _1212642, _1212644] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212638, _1212640, _1212642, tc_prod(_1212640, _1212642)), _1212644), c_Product__Type_OPair(_1212640, _1212642)) = _1212644)], (49386 ^ _779571) ^ [_1771464, _1771466, _1771468] : [49387 ^ _779571 : [(49388 ^ _779571) ^ [_1771553, _1771555] : [_1771466 = hAPP(hAPP(c_List_Olist_OCons(_1771464), _1771555), _1771553)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1771464), tc_List_Olist(_1771464))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771464), tc_List_Olist(_1771464)), c_List_Olist_ONil(_1771464)), _1771466)), c_List_Olexord(_1771464, _1771468))))], (29244 ^ _779571) ^ [_1302219, _1302221, _1302223, _1302225] : [c_Orderings_Obot__class_Obot(tc_fun(_1302219, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1302221, _1302219, _1302223), _1302225), -(_1302225 = c_Orderings_Obot__class_Obot(tc_fun(_1302221, tc_HOL_Obool)))], (15516 ^ _779571) ^ [_1042352, _1042354, _1042356] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042354), _1042356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042352), _1042354)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042352), _1042356)))], (24583 ^ _779571) ^ [_1208588, _1208590, _1208592, _1208594, _1208596] : [-(hAPP(c_Product__Type_Osnd(_1208588, _1208590), hAPP(c_Product__Type_Oapfst(_1208592, _1208588, _1208590, _1208594), _1208596)) = hAPP(c_Product__Type_Osnd(_1208592, _1208590), _1208596))], (51413 ^ _779571) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (27658 ^ _779571) ^ [_1268831, _1268833] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1268831, _1268833)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1268833), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1268831), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46187 ^ _779571) ^ [_1691581, _1691583, _1691585] : [hBOOL(hAPP(c_List_Odistinct(_1691581), hAPP(hAPP(c_List_Omap(tc_prod(_1691581, _1691583), _1691581), c_Product__Type_Ofst(_1691581, _1691583)), _1691585))), -(hAPP(c_List_Oset(tc_prod(_1691581, _1691583)), _1691585) = hAPP(c_Set_OCollect(tc_prod(_1691581, _1691583)), hAPP(c_Product__Type_Oprod_Oprod__case(_1691581, _1691583, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1691581, tc_fun(_1691583, tc_Option_Ooption(_1691583)), tc_fun(_1691583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1691583), tc_HOL_Obool), tc_fun(tc_fun(_1691583, tc_Option_Ooption(_1691583)), tc_fun(_1691583, tc_HOL_Obool)), _1691581), c_COMBB(tc_Option_Ooption(_1691583), tc_HOL_Obool, _1691583)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1691583), tc_fun(tc_Option_Ooption(_1691583), tc_HOL_Obool), _1691581), c_fequal), c_Map_Omap__of(_1691581, _1691583, _1691585)))), c_Option_Ooption_OSome(_1691583)))))], (6389 ^ _779571) ^ [_883559, _883561, _883563] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_883559, _883561, _883563)], (49485 ^ _779571) ^ [_1773122, _1773124, _1773126] : [-(c_List_Olast(_1773122, hAPP(hAPP(c_List_Oappend(_1773122), _1773124), hAPP(hAPP(c_List_Olist_OCons(_1773122), _1773126), c_List_Olist_ONil(_1773122)))) = _1773126)], (35470 ^ _779571) ^ [_1433613, _1433615, _1433617, _1433619, _1433621, _1433623, _1433625, _1433627, _1433629, _1433631, _1433633] : [hAPP(_1433613, hAPP(_1433615, _1433617)) = hAPP(_1433619, hAPP(_1433621, _1433623)), -(hAPP(hAPP(c_Fun_Ocomp(_1433625, _1433627, _1433629, _1433613), _1433615), _1433617) = hAPP(hAPP(c_Fun_Ocomp(_1433631, _1433627, _1433633, _1433619), _1433621), _1433623))], (51507 ^ _779571) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (48750 ^ _779571) ^ [_1757110, _1757112] : [-(hAPP(c_List_Oset(_1757110), hAPP(c_List_Orotate1(_1757110), _1757112)) = hAPP(c_List_Oset(_1757110), _1757112))], (50670 ^ _779571) ^ [_1798311, _1798313] : [_1798313 = c_List_Olist_ONil(_1798311), -(hAPP(c_List_Orev(_1798311), _1798313) = c_List_Olist_ONil(_1798311))], (38779 ^ _779571) ^ [_1508361, _1508363, _1508365, _1508367, _1508369] : [c_Fun_Oinj__on(_1508361, _1508363, _1508365, c_Orderings_Otop__class_Otop(tc_fun(_1508361, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1508361, _1508363, _1508365), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508361, tc_HOL_Obool)), _1508367), _1508369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508363, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508361, _1508363, _1508365), _1508367)), hAPP(c_Set_Oimage(_1508361, _1508363, _1508365), _1508369)))], (872 ^ _779571) ^ [_793011, _793013, _793015, _793017, _793019, _793021] : [-(c_Finite__Set_Ofun__left__comm__idem(_793019, _793015, _793011)), c_Finite__Set_Ofun__left__comm__idem(_793021, _793017, _793013), _793021 = _793019, _793017 = _793015, _793013 = _793011], (47410 ^ _779571) ^ [_1722936] : [-(c_List_Olistset(_1722936, c_List_Olist_ONil(tc_fun(_1722936, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1722936)), c_List_Olist_ONil(_1722936)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1722936), tc_HOL_Obool))))], (29884 ^ _779571) ^ [_1314112, _1314114] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314112, _1314114, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314112), tc_HOL_Obool))))], (15236 ^ _779571) ^ [_1037355, _1037357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037355), _1037357)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037357)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037355)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037357), _1037355)))], (1312 ^ _779571) ^ [_798739, _798741] : [-(class_Lattices_Olattice(_798739)), _798741 = _798739, class_Lattices_Olattice(_798741)], (3866 ^ _779571) ^ [_839194, _839196, _839198, _839200] : [-(c_Lazy__Sequence_Osingle(_839200, _839196) = c_Lazy__Sequence_Osingle(_839198, _839194)), _839200 = _839198, _839196 = _839194], (48409 ^ _779571) ^ [_1747344, _1747346, _1747348, _1747350, _1747352, _1747354, _1747356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747344)), _1747346)), _1747348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747348), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747350)), _1747352))), -(c_Map_Omap__upds(_1747344, _1747350, _1747354, _1747346, hAPP(hAPP(c_List_Olist__update(_1747350, _1747352), _1747348), _1747356)) = c_Map_Omap__upds(_1747344, _1747350, _1747354, _1747346, _1747352))], (41061 ^ _779571) ^ [_1561555, _1561557] : [hAPP(c_Set_OCollect(_1561555), _1561557) = c_Orderings_Obot__class_Obot(tc_fun(_1561555, tc_HOL_Obool)), 41064 ^ _779571 : [(41065 ^ _779571) ^ [_1561640] : [hBOOL(hAPP(_1561557, _1561640))]]], (12299 ^ _779571) ^ [_984929, _984931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984929), _984931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984929), hAPP(c_Nat_OSuc, _984931))))], (29348 ^ _779571) ^ [_1304341, _1304343] : [class_Lattices_Obounded__lattice__bot(_1304341), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1304341), c_Orderings_Obot__class_Obot(_1304341)), _1304343) = _1304343)], (29950 ^ _779571) ^ [_1316150, _1316152] : [-(c_Option_Oset(_1316150, hAPP(c_Option_Ooption_OSome(_1316150), _1316152)) = hAPP(hAPP(c_Set_Oinsert(_1316150), _1316152), c_Orderings_Obot__class_Obot(tc_fun(_1316150, tc_HOL_Obool))))], (13036 ^ _779571) ^ [_997773, _997775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997773), _997775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _997773), c_Groups_Oone__class_Oone(tc_Int_Oint))), _997775)))], (20129 ^ _779571) ^ [_1125704, _1125706] : [c_Nat__Transfer_Ois__nat(_1125704), c_Nat__Transfer_Ois__nat(_1125706), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125704), _1125706)))], (36600 ^ _779571) ^ [_1459419, _1459421, _1459423] : [class_Lattices_Olattice(_1459419), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459419), _1459421), _1459423)), _1459421)))], (14808 ^ _779571) ^ [_1029160, _1029162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029160), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029162), _1029160)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029160), _1029162) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11953 ^ _779571) ^ [_978754, _978756, _978758] : [class_Rings_Oordered__cancel__semiring(_978754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978754), c_Groups_Ozero__class_Ozero(_978754)), _978756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978754), _978758), c_Groups_Ozero__class_Ozero(_978754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978754), _978756), _978758)), c_Groups_Ozero__class_Ozero(_978754))))], (26352 ^ _779571) ^ [_1242457] : [_1242457 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1242457), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (1232 ^ _779571) ^ [_797739, _797741] : [-(class_Orderings_Owellorder(_797739)), _797741 = _797739, class_Orderings_Owellorder(_797741)], (28109 ^ _779571) ^ [_1277948, _1277950, _1277952, _1277954] : [28110 ^ _779571 : [(28111 ^ _779571) ^ [_1278058] : [hBOOL(hAPP(hAPP(c_member(_1277948), _1278058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277948, tc_HOL_Obool)), _1277950), _1277952))), hBOOL(hAPP(_1277954, _1278058))]], 28119 ^ _779571 : [(28122 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1277954, 28118 ^ [_1277948, _1277950, _1277952, _1277954])))], (28120 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277948), 28118 ^ [_1277948, _1277950, _1277952, _1277954]), _1277950)))]], 28124 ^ _779571 : [(28127 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1277954, 28123 ^ [_1277948, _1277950, _1277952, _1277954])))], (28125 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277948), 28123 ^ [_1277948, _1277950, _1277952, _1277954]), _1277952)))]]], (26486 ^ _779571) ^ [_1244965, _1244967, _1244969] : [class_Rings_Odvd(_1244965), class_Rings_Osemiring__0(_1244965), 26493 ^ _779571 : [(26503 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1244967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244965), _1244969), 26510 ^ [_1244965, _1244967, _1244969])))), 26504 ^ _779571 : [(26505 ^ _779571) ^ [_1245294] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244965), _1244969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244965), _1245294), c_Groups_Ozero__class_Ozero(_1244965)))), hBOOL(hAPP(_1244967, _1245294))]]], (26494 ^ _779571) ^ [] : [26495 ^ _779571 : [(26496 ^ _779571) ^ [_1245157] : [hBOOL(hAPP(_1244967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244965), _1244969), _1245157)))]], 26498 ^ _779571 : [(26501 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1244967, 26497 ^ [_1244965, _1244967, _1244969])))], (26499 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244965), _1244969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244965), 26497 ^ [_1244965, _1244967, _1244969]), c_Groups_Ozero__class_Ozero(_1244965)))))]]]]], (24773 ^ _779571) ^ [_1212247, _1212249, _1212251, _1212253, _1212255, _1212257, _1212259, _1212261, _1212263] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212247, _1212249, _1212251, _1212253), hAPP(hAPP(c_Product__Type_Oscomp(_1212247, _1212255, _1212257, tc_prod(_1212249, _1212251)), _1212259), _1212261)), _1212263) = hAPP(hAPP(c_Product__Type_Oscomp(_1212247, _1212255, _1212257, _1212253), _1212259), hAPP(hAPP(c_COMBC(_1212255, tc_fun(_1212249, tc_fun(_1212251, _1212253)), tc_fun(_1212257, _1212253)), hAPP(hAPP(c_COMBB(tc_fun(_1212257, tc_prod(_1212249, _1212251)), tc_fun(tc_fun(_1212249, tc_fun(_1212251, _1212253)), tc_fun(_1212257, _1212253)), _1212255), c_Product__Type_Oscomp(_1212257, _1212249, _1212251, _1212253)), _1212261)), _1212263)))], (30064 ^ _779571) ^ [_1318280, _1318282, _1318284, _1318286] : [hBOOL(hAPP(hAPP(c_member(_1318280), _1318282), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318280, tc_HOL_Obool)), _1318284), _1318286))), 30067 ^ _779571 : [(30070 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1318280), _1318282), _1318286))], (30068 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318280), _1318282), _1318284)))]]], (37872 ^ _779571) ^ [_1490515, _1490517, _1490519] : [class_Lattices_Olattice(_1490515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490515), _1490517)), hBOOL(hAPP(hAPP(c_member(_1490515), _1490519), _1490517)), 37883 ^ _779571 : [(37890 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490515, tc_HOL_Obool)), _1490517), hAPP(hAPP(c_Set_Oinsert(_1490515), _1490519), c_Orderings_Obot__class_Obot(tc_fun(_1490515, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1490515, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1490515, _1490517) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1490515), _1490519), c_Big__Operators_Olattice__class_OInf__fin(_1490515, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490515, tc_HOL_Obool)), _1490517), hAPP(hAPP(c_Set_Oinsert(_1490515), _1490519), c_Orderings_Obot__class_Obot(tc_fun(_1490515, tc_HOL_Obool)))))))], (37884 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490515, tc_HOL_Obool)), _1490517), hAPP(hAPP(c_Set_Oinsert(_1490515), _1490519), c_Orderings_Obot__class_Obot(tc_fun(_1490515, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1490515, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1490515, _1490517) = _1490519)]]], (41237 ^ _779571) ^ [_1565771, _1565773, _1565775, _1565777] : [_1565771 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1565773, _1565775), 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)), _1565777))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565773), _1565771)))], (35627 ^ _779571) ^ [_1437918, _1437920, _1437922, _1437924, _1437926] : [c_Hoare__Mirabelle_Ohoare__derivs(_1437918, _1437920, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1437918)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1437918), c_Hoare__Mirabelle_Opeek__and(_1437918, _1437922, _1437924)), _1437926), _1437922)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1437918), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1437918, _1437920, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1437918)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1437918), _1437922), c_Com_Ocom_OWhile(_1437924, _1437926)), c_Hoare__Mirabelle_Opeek__and(_1437918, _1437922, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1437924)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1437918), tc_HOL_Obool)))))], (17345 ^ _779571) ^ [_1077772, _1077774, _1077776] : [class_Rings_Oring__1__no__zero__divisors(_1077772), -(_1077774 = c_Groups_Ozero__class_Ozero(_1077772)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077772), _1077774), _1077776) = c_Groups_Ozero__class_Ozero(_1077772)], (36224 ^ _779571) ^ [_1451972, _1451974, _1451976, _1451978] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451972, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451972, tc_HOL_Obool)), _1451974), _1451976)), _1451978) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451972, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451972, tc_HOL_Obool)), _1451974), _1451978)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451972, tc_HOL_Obool)), _1451976), _1451978)))], (41021 ^ _779571) ^ [_1560703, _1560705, _1560707] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560703), hAPP(c_Set_OCollect(_1560703), hAPP(hAPP(c_COMBS(_1560703, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560703), c_fdisj), _1560705)), _1560707))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560703), hAPP(c_Set_OCollect(_1560703), _1560705))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560703), hAPP(c_Set_OCollect(_1560703), _1560707)))], (28331 ^ _779571) ^ [_1282335, _1282337] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1282335, _1282337)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1282337)), _1282335))], (18883 ^ _779571) ^ [_1103433, _1103435] : [class_Int_Onumber__ring(_1103433), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103433), hAPP(c_Int_Onumber__class_Onumber__of(_1103433), c_Int_OBit1(c_Int_OPls))), _1103435) = _1103435)], (35609 ^ _779571) ^ [_1437606, _1437608, _1437610, _1437612, _1437614] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1437606, _1437608, _1437610), _1437612), _1437614)), 35612 ^ _779571 : [(35615 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1437610, _1437614)))], (35613 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1437608, _1437612), _1437614)))]]], (42515 ^ _779571) ^ [_1603696, _1603698, _1603700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1603696), c_Map_Odom(_1603696, _1603698, _1603700))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1603696), c_Orderings_Otop__class_Otop(tc_fun(_1603696, tc_HOL_Obool))))), -(hAPP(_1603700, 42522 ^ [_1603696, _1603698, _1603700]) = c_Option_Ooption_ONone(_1603698))], (31758 ^ _779571) ^ [_1355907, _1355909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1355907), _1355909))), 31761 ^ _779571 : [(31764 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1355907), _1355909)))], (31762 ^ _779571) ^ [] : [_1355909 = c_Orderings_Obot__class_Obot(tc_fun(_1355907, tc_HOL_Obool))]]], (39888 ^ _779571) ^ [_1533212, _1533214, _1533216] : [39890 ^ _779571 : [(39893 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1533212), 39889 ^ [_1533212, _1533214, _1533216]), c_Wellfounded_Oacc(_1533212, _1533216)))], (39891 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533212, _1533212)), hAPP(hAPP(c_Product__Type_OPair(_1533212, _1533212), 39889 ^ [_1533212, _1533214, _1533216]), _1533214)), _1533216)))]], -(hBOOL(hAPP(hAPP(c_member(_1533212), _1533214), c_Wellfounded_Oacc(_1533212, _1533216))))], (24887 ^ _779571) ^ [_1214996, _1214998, _1215000, _1215002, _1215004] : [-(hAPP(c_New__DSequence_Opos__bind(_1214996, _1214998, _1215000, _1215002), _1215004) = c_Lazy__Sequence_Obind(_1214996, _1214998, hAPP(_1215000, _1215004), hAPP(hAPP(c_COMBC(_1214996, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1214998)), _1215002), _1215004)))], (38501 ^ _779571) ^ [_1502983, _1502985, _1502987] : [c_Equiv__Relations_Oequivp(_1502983, _1502985), -(hBOOL(hAPP(hAPP(_1502985, _1502987), _1502987)))], (32549 ^ _779571) ^ [_1373057, _1373059, _1373061, _1373063, _1373065] : [class_Groups_Oordered__ab__semigroup__add(_1373057), class_Rings_Osemiring__1(_1373057), 32559 ^ _779571 : [(32562 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373057), hAPP(_1373063, 32558 ^ [_1373057, _1373059, _1373061, _1373063, _1373065])), _1373065))], (32560 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373059), 32558 ^ [_1373057, _1373059, _1373061, _1373063, _1373065]), _1373061)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373057), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373059, _1373057), _1373063), _1373061)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373057), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1373057), hAPP(c_Finite__Set_Ocard(_1373059), _1373061))), _1373065))))], (49670 ^ _779571) ^ [_1777148, _1777150, _1777152, _1777154] : [hAPP(hAPP(c_List_Oappend(_1777148), _1777150), hAPP(hAPP(c_List_Olist_OCons(_1777148), _1777152), c_List_Olist_ONil(_1777148))) = _1777154, 49673 ^ _779571 : [(49678 ^ _779571) ^ [] : [-(c_List_Olast(_1777148, _1777154) = _1777152)], (49676 ^ _779571) ^ [] : [-(c_List_Obutlast(_1777148, _1777154) = _1777150)], (49674 ^ _779571) ^ [] : [_1777154 = c_List_Olist_ONil(_1777148)]]], (40274 ^ _779571) ^ [_1543584, _1543586, _1543588, _1543590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1543584, _1543586)), hAPP(hAPP(c_Product__Type_OSigma(_1543584, _1543586), _1543588), hAPP(c_COMBK(tc_fun(_1543586, tc_HOL_Obool), _1543584), _1543590)))), -(_1543590 = c_Orderings_Obot__class_Obot(tc_fun(_1543586, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543584), _1543588)))], (14928 ^ _779571) ^ [_1031524, _1031526, _1031528] : [class_Divides_Osemiring__div(_1031524), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031524), _1031526), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031524), _1031528), _1031526))), c_Divides_Odiv__class_Omod(_1031524, _1031528, _1031526)) = _1031528)], (18395 ^ _779571) ^ [_1095346] : [class_Int_Onumber__ring(_1095346), -(c_Int_Oiszero(_1095346, hAPP(c_Int_Onumber__class_Onumber__of(_1095346), c_Int_OPls)))], (7159 ^ _779571) ^ [_897572, _897574, _897576, _897578] : [class_Groups_Oab__semigroup__add(_897572), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897572), _897574), _897576)), _897578) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897572), _897574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897572), _897576), _897578)))], (6017 ^ _779571) ^ [_876373, _876375] : [c_Com_Ocom_OSemi(_876373, _876375) = c_Com_Ocom_OSKIP], (18845 ^ _779571) ^ [_1102798] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1102798)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1102798))))], (18415 ^ _779571) ^ [_1095662] : [-(c_Int_Opred(_1095662) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1095662), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (44946 ^ _779571) ^ [_1663058, _1663060, _1663062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1663058, tc_HOL_Obool), tc_HOL_Obool)), _1663060), _1663062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663058, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663058, tc_HOL_Obool), _1663062)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663058, tc_HOL_Obool), _1663060))))], (37984 ^ _779571) ^ [_1492633, _1492635, _1492637] : [class_Lattices_Olattice(_1492633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492633), _1492635)), -(_1492635 = c_Orderings_Obot__class_Obot(tc_fun(_1492633, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1492633, hAPP(hAPP(c_Set_Oinsert(_1492633), _1492637), _1492635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492633), _1492637), c_Big__Operators_Olattice__class_OInf__fin(_1492633, _1492635)))], (49767 ^ _779571) ^ [_1779257, _1779259, _1779261, _1779263] : [-(hBOOL(hAPP(_1779257, _1779259))), -(c_List_Oremove1(_1779261, _1779259, hAPP(c_List_Ofilter(_1779261, _1779257), _1779263)) = hAPP(c_List_Ofilter(_1779261, _1779257), _1779263))], (22820 ^ _779571) ^ [_1175105, _1175107, _1175109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1175105, tc_fun(_1175105, tc_HOL_Obool))), _1175107), _1175109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1175105, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1175105, _1175109)), c_Wellfounded_Oaccp(_1175105, _1175107))))], (18733 ^ _779571) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (27590 ^ _779571) ^ [_1267503, _1267505] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1267503, _1267505)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1267505), _1267503)))], (12988 ^ _779571) ^ [_997106] : 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-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409285, _1409283), hAPP(hAPP(c_COMBC(_1409285, _1409283, _1409283), hAPP(hAPP(c_COMBS(_1409285, _1409283, tc_fun(_1409283, _1409283)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409283, tc_fun(_1409283, _1409283)), _1409285), c_If(_1409283)), hAPP(c_fequal, _1409289))), _1409291)), c_Groups_Oone__class_Oone(_1409283))), _1409287) = c_Groups_Oone__class_Oone(_1409283))], (34433 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1409285), _1409289), _1409287)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409285, _1409283), hAPP(hAPP(c_COMBC(_1409285, _1409283, _1409283), hAPP(hAPP(c_COMBS(_1409285, _1409283, tc_fun(_1409283, _1409283)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409283, tc_fun(_1409283, _1409283)), _1409285), c_If(_1409283)), hAPP(c_fequal, _1409289))), _1409291)), c_Groups_Oone__class_Oone(_1409283))), _1409287) = hAPP(_1409291, _1409289))]]], (43853 ^ _779571) ^ [_1637043, _1637045, _1637047, _1637049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637043, _1637043)), hAPP(hAPP(c_Product__Type_OPair(_1637043, _1637043), _1637045), _1637047)), c_Transitive__Closure_Otrancl(_1637043, _1637049))), 43857 ^ _779571 : [(43860 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637043, _1637043)), hAPP(hAPP(c_Product__Type_OPair(_1637043, _1637043), 43856 ^ [_1637043, _1637045, _1637047, _1637049]), _1637047)), c_Transitive__Closure_Ortrancl(_1637043, _1637049))))], (43858 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637043, _1637043)), hAPP(hAPP(c_Product__Type_OPair(_1637043, _1637043), _1637045), 43856 ^ [_1637043, _1637045, _1637047, _1637049])), _1637049)))]]], (48820 ^ _779571) ^ [_1758716, _1758718, _1758720, _1758722] : [_1758716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1758718), _1758716), hAPP(hAPP(c_List_Olist_OCons(_1758718), _1758720), _1758722)) = hAPP(hAPP(c_List_Olist_OCons(_1758718), _1758720), _1758722))], (35777 ^ _779571) ^ [_1441722, _1441724, _1441726] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1441722), _1441724), _1441726) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1441722, tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool)), _1441724), hAPP(hAPP(c_COMBC(_1441722, tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441722, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool)), _1441722), c_Set_Oinsert(tc_fun(_1441722, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1441722, tc_HOL_Obool), tc_fun(_1441722, tc_HOL_Obool), _1441722), c_Relation_OImage(_1441722, _1441722, _1441726)), hAPP(hAPP(c_COMBC(_1441722, tc_fun(_1441722, tc_HOL_Obool), tc_fun(_1441722, tc_HOL_Obool)), c_Set_Oinsert(_1441722)), c_Orderings_Obot__class_Obot(tc_fun(_1441722, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1441722, tc_HOL_Obool), tc_HOL_Obool)))))], (6693 ^ _779571) ^ [_889190, _889192, _889194, _889196, _889198] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889190, _889192, _889194)), _889196), _889198))), 6694 ^ _779571 : [(6701 ^ _779571) ^ [] : [-(hBOOL(hAPP(_889190, _889196))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889194), _889196), _889198))], (6695 ^ _779571) ^ [] : [hBOOL(hAPP(_889190, _889196)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889192), _889196), _889198))]]], (13839 ^ _779571) ^ [_1012149, _1012151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012151)), -(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, _1012149, _1012151))))], (11176 ^ _779571) ^ [_965111, _965113, _965115] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965111), _965113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965115), _965113), -(_965111 = _965115), -(_965113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35751 ^ _779571) ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924] : [class_Groups_Ocomm__monoid__add(_1440914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440916), _1440918)), 35761 ^ _779571 : [(35762 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440916), 35760 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924]), _1440918)))], (35767 ^ _779571) ^ [] : [35760 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924] = 35763 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924]], (35771 ^ _779571) ^ [] : [hAPP(_1440922, hAPP(_1440920, 35760 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924])) = c_Groups_Ozero__class_Ozero(_1440914)], (35769 ^ _779571) ^ [] : [-(hAPP(_1440920, 35760 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924]) = hAPP(_1440920, 35763 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924]))], (35765 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440916), 35763 ^ [_1440914, _1440916, _1440918, _1440920, _1440922, _1440924]), _1440918)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440924, _1440914), _1440922), hAPP(c_Set_Oimage(_1440916, _1440924, _1440920), _1440918)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440916, _1440914), hAPP(c_Fun_Ocomp(_1440924, _1440914, _1440916, _1440922), _1440920)), _1440918))], (43516 ^ _779571) ^ [_1628208, _1628210] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628208, _1628208), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1628210) = c_Relation_OId(_1628208))], (16158 ^ _779571) ^ [_1055757, _1055759] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055757), _1055759))), -(c_Nat__Transfer_Otsub(_1055759, _1055757) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8078 ^ _779571) ^ [_913516, _913518] : [c_Option_Ois__none(_913516, _913518), -(_913518 = c_Option_Ooption_ONone(_913516))], (38191 ^ _779571) ^ [_1496469, _1496471, _1496473, _1496475, _1496477] : [c_Finite__Set_Ofolding__idem(_1496469, _1496471, _1496473, _1496475), -(hAPP(c_Fun_Ocomp(_1496471, _1496471, _1496471, hAPP(_1496473, _1496477)), hAPP(_1496473, _1496477)) = hAPP(_1496473, _1496477))], (42837 ^ _779571) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (31504 ^ _779571) ^ [_1350850, _1350852] : [31505 ^ _779571 : [(31508 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1350850), _1350852)))], (31506 ^ _779571) ^ [] : [_1350852 = c_Orderings_Obot__class_Obot(tc_fun(_1350850, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1350850), _1350852) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13974 ^ _779571) ^ [_1014371, _1014373] : [class_Lattices_Oboolean__algebra(_1014371), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1014371), hAPP(c_Groups_Ouminus__class_Ouminus(_1014371), _1014373)) = _1014373)], (24009 ^ _779571) ^ [_1197520, _1197522, _1197524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197520, tc_HOL_Obool)), _1197522), _1197524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197520, tc_HOL_Obool)), _1197522), _1197524)))], (6055 ^ _779571) ^ [_877170, _877172, _877174, _877176, _877178, _877180] : [c_Com_Ocom_OCond(_877170, _877172, _877174) = c_Com_Ocom_OCond(_877176, _877178, _877180), 6058 ^ _779571 : [(6063 ^ _779571) ^ [] : [-(_877174 = _877180)], (6061 ^ _779571) ^ [] : [-(_877172 = _877178)], (6059 ^ _779571) ^ [] : [-(_877170 = _877176)]]], (24639 ^ _779571) ^ [_1209939] : [class_Orderings_Olinorder(_1209939), -(c_Orderings_Oord_Omin(_1209939, hAPP(c_COMBC(_1209939, _1209939, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1209939))) = c_Orderings_Oord__class_Omax(_1209939))], (22402 ^ _779571) ^ [_1166514, _1166516, _1166518, _1166520] : [-(hAPP(c_Nat_Onat_Onat__rec(_1166514, _1166516, _1166518), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166520)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1166514), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1166520))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1166514, _1166514), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1166514, tc_fun(_1166514, _1166514)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1166514, tc_fun(_1166514, _1166514)), tc_Int_Oint), c_If(_1166514)), c_Nat__Numeral_Oneg)), _1166516)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1166514, _1166514), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1166514, _1166514), tc_Int_Oint), _1166518), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1166514, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1166514, _1166516, _1166518)), c_Int_Onat)))))], (51445 ^ _779571) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (30632 ^ _779571) ^ [_1329858, _1329860, _1329862] : [class_Orderings_Oord(_1329858), 30635 ^ _779571 : [(30642 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329858), _1329860), _1329862)), -(hBOOL(hAPP(hAPP(c_member(_1329858), _1329860), hAPP(c_SetInterval_Oord__class_OlessThan(_1329858), _1329862))))], (30636 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329858), _1329860), hAPP(c_SetInterval_Oord__class_OlessThan(_1329858), _1329862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329858), _1329860), _1329862)))]]], (33289 ^ _779571) ^ [_1386724, _1386726] : [class_Orderings_Olinorder(_1386724), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386724), _1386726)), -(_1386726 = c_Orderings_Obot__class_Obot(tc_fun(_1386724, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1386724), c_Big__Operators_Olinorder__class_OMin(_1386724, _1386726)), _1386726)))], (24753 ^ _779571) ^ [_1211847, _1211849] : [-(c_Nitpick_Onumber__of__frac(_1211847, _1211849) = c_Nitpick_OAbs__Frac(_1211847, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1211849), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30423 ^ _779571) ^ [_1325196, _1325198, _1325200] : [hBOOL(hAPP(hAPP(c_member(_1325196), _1325198), c_Option_Oset(_1325196, _1325200))), -(_1325200 = hAPP(c_Option_Ooption_OSome(_1325196), _1325198))], (38395 ^ _779571) ^ [_1500810, _1500812, _1500814, _1500816] : [c_Fun_Oinj__on(_1500810, _1500812, _1500814, _1500816), -(hAPP(c_Finite__Set_Ocard(_1500812), hAPP(c_Set_Oimage(_1500810, _1500812, _1500814), _1500816)) = hAPP(c_Finite__Set_Ocard(_1500810), _1500816))], (29870 ^ _779571) ^ [_1313864, _1313866, _1313868, _1313870] : [c_Hoare__Mirabelle_Ohoare__derivs(_1313864, _1313866, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1313864)), _1313868), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1313864), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1313864, _1313866, _1313870), -(c_Hoare__Mirabelle_Ohoare__derivs(_1313864, _1313866, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1313864)), _1313868), _1313870)))], (6600 ^ _779571) ^ [_887368, _887370, _887372] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887368, _887370)), _887372), _887372))), 6601 ^ _779571 : [(6604 ^ _779571) ^ [_887468] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887370), _887372), _887468)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887368, _887370)), _887468), _887372))], (6602 ^ _779571) ^ [] : [-(hBOOL(hAPP(_887368, _887372)))]]], (6079 ^ _779571) ^ [_877561, _877563, _877565, _877567] : [c_Com_Ocom_OSemi(_877561, _877563) = c_Com_Ocom_OSemi(_877565, _877567), 6082 ^ _779571 : [(6085 ^ _779571) ^ [] : [-(_877563 = _877567)], (6083 ^ _779571) ^ [] : [-(_877561 = _877565)]]], (50997 ^ _779571) ^ [_1806578, _1806580, _1806582, _1806584] : [hBOOL(hAPP(_1806578, _1806580)), -(c_List_OtakeWhile(_1806582, _1806578, hAPP(hAPP(c_List_Olist_OCons(_1806582), _1806580), _1806584)) = hAPP(hAPP(c_List_Olist_OCons(_1806582), _1806580), c_List_OtakeWhile(_1806582, _1806578, _1806584)))], (15376 ^ _779571) ^ [_1039899] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039899) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6778 ^ _779571) ^ [_891134, _891136, _891138, _891140, _891142] : [c_Com_Ocom_OAss(_891134, _891136) = c_Com_Ocom_OCall(_891138, _891140, _891142)], (31219 ^ _779571) ^ [_1341891, _1341893, _1341895] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341891), _1341893)), 31222 ^ _779571 : [(31229 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341891), _1341895)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341891, tc_HOL_Obool)), _1341895), _1341893))))], (31223 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341891, tc_HOL_Obool)), _1341895), _1341893))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341891), _1341895)))]]], (45756 ^ _779571) ^ [_1681097, _1681099, _1681101, _1681103] : [c_Fun_Oinj__on(_1681097, tc_Option_Ooption(_1681099), _1681103, c_Map_Odom(_1681097, _1681099, _1681103)), -(c_Fun_Oinj__on(_1681097, tc_Option_Ooption(_1681099), c_Map_Omap__add(_1681097, _1681099, _1681101, _1681103), c_Map_Odom(_1681097, _1681099, _1681103)))], (11967 ^ _779571) ^ [_979009, _979011, _979013] : [class_Rings_Oordered__cancel__semiring(_979009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979009), c_Groups_Ozero__class_Ozero(_979009)), _979011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979009), c_Groups_Ozero__class_Ozero(_979009)), _979013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979009), c_Groups_Ozero__class_Ozero(_979009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979009), _979011), _979013))))], (17747 ^ _779571) ^ [_1085269] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085269))), -(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), _1085269)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18433 ^ _779571) ^ [_1095922] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095922), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095922), c_Int_OPls)))], (7496 ^ _779571) ^ [_903737, _903739, _903741, _903743, _903745] : [c_Sum__Type_OSuml(_903737, _903739, _903741, _903743) = c_Sum__Type_OSuml(_903737, _903739, _903741, _903745), -(_903743 = _903745)], (1222 ^ _779571) ^ [_797614, _797616] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_797614)), _797616 = _797614, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_797616)], (43756 ^ _779571) ^ [_1634249, _1634251, _1634253] : [43759 ^ _779571 : [(43765 ^ _779571) ^ [] : [43758 ^ [_1634249, _1634251, _1634253] = 43761 ^ [_1634249, _1634251, _1634253]], (43763 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634249, _1634251)), hAPP(hAPP(c_Product__Type_OPair(_1634249, _1634251), 43757 ^ [_1634249, _1634251, _1634253]), 43761 ^ [_1634249, _1634251, _1634253])), _1634253)))], (43760 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634249, _1634251)), hAPP(hAPP(c_Product__Type_OPair(_1634249, _1634251), 43757 ^ [_1634249, _1634251, _1634253]), 43758 ^ [_1634249, _1634251, _1634253])), _1634253)))]], -(c_Relation_Osingle__valued(_1634249, _1634251, _1634253))], (13868 ^ _779571) ^ [_1012622, _1012624] : [13869 ^ _779571 : [(13870 ^ _779571) ^ [_1012671] : [_1012622 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012624), _1012671)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012622, _1012624) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18073 ^ _779571) ^ [_1090694] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1090694), c_Int_OMin) = c_Int_Osucc(_1090694))], (27802 ^ _779571) ^ [_1271951, _1271953, _1271955] : [class_Lattices_Osemilattice__sup(_1271951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271951), _1271953), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271951), _1271953), _1271955))))], (27724 ^ _779571) ^ [_1270323, _1270325, _1270327, _1270329, _1270331] : [-(hAPP(c_Set_Oimage(_1270323, _1270325, _1270327), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270323, tc_HOL_Obool)), _1270329), _1270331)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270325, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1270323, _1270325, _1270327), _1270329)), hAPP(c_Set_Oimage(_1270323, _1270325, _1270327), _1270331)))], (6829 ^ _779571) ^ [_892130, _892132] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_892130, _892132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_892132)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5980 ^ _779571) ^ [_875692, _875694, _875696, _875698, _875700, _875702] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_875692, _875694, _875696), _875698, _875700, _875702)), 5981 ^ _779571 : [(5988 ^ _779571) ^ [] : [-(hBOOL(hAPP(_875692, _875698))), c_Natural_Oevaln(_875696, _875698, _875700, _875702)], (5982 ^ _779571) ^ [] : [hBOOL(hAPP(_875692, _875698)), c_Natural_Oevaln(_875694, _875698, _875700, _875702)]]], (29680 ^ _779571) ^ [_1309891, _1309893, _1309895, _1309897, _1309899] : [_1309891 = c_Orderings_Obot__class_Obot(tc_fun(_1309893, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309895, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309893, tc_fun(_1309895, tc_HOL_Obool)), _1309891), _1309897)), _1309899) = _1309899)], (27636 ^ _779571) ^ [_1268357, _1268359, _1268361, _1268363] : [class_Rings_Osemiring__1(_1268357), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1268359, _1268357), hAPP(c_COMBK(_1268357, _1268359), _1268361)), _1268363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268357), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268357), hAPP(c_Finite__Set_Ocard(_1268359), _1268363))), _1268361))], (31482 ^ _779571) ^ [_1349472, _1349474, _1349476, _1349478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349472, tc_fun(_1349474, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1349472, tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_fun(_1349474, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349474, tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_fun(_1349474, tc_HOL_Obool)), _1349472), c_COMBC(_1349474, tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349474, tc_prod(_1349472, _1349474)), tc_fun(_1349474, tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), _1349472), hAPP(c_COMBB(tc_prod(_1349472, _1349474), tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool), _1349474), c_member(tc_prod(_1349472, _1349474)))), c_Product__Type_OPair(_1349472, _1349474)))), _1349476)), hAPP(hAPP(c_COMBC(_1349472, tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_fun(_1349474, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349474, tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_fun(_1349474, tc_HOL_Obool)), _1349472), c_COMBC(_1349474, tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349474, tc_prod(_1349472, _1349474)), tc_fun(_1349474, tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool)), _1349472), hAPP(c_COMBB(tc_prod(_1349472, _1349474), tc_fun(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool), tc_HOL_Obool), _1349474), c_member(tc_prod(_1349472, _1349474)))), c_Product__Type_OPair(_1349472, _1349474)))), _1349478))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1349472, _1349474), tc_HOL_Obool)), _1349476), _1349478)))], (51151 ^ _779571) ^ [_1809054, _1809056] : [class_Orderings_Oord(_1809054), -(class_Orderings_Oord(tc_fun(_1809056, _1809054)))], (42361 ^ _779571) ^ [_1600667, _1600669, _1600671, _1600673] : [42362 ^ _779571 : [(42363 ^ _779571) ^ [_1600721] : [hBOOL(hAPP(hAPP(_1600671, _1600673), _1600721))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1600667, _1600669, _1600671), _1600673)))], (19325 ^ _779571) ^ [_1111014, _1111016] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1111014)), c_Int_OBit1(_1111016)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111014), _1111016)))], (49307 ^ _779571) ^ [_1769512, _1769514, _1769516, _1769518] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769512)), hAPP(hAPP(c_List_Oappend(_1769512), _1769514), _1769516)), c_List_Olists(_1769512, _1769518)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769512)), _1769514), c_List_Olists(_1769512, _1769518))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769512)), _1769516), c_List_Olists(_1769512, _1769518)))], (47565 ^ _779571) ^ [_1727144, _1727146, _1727148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727146)), _1727148))), -(hBOOL(hAPP(hAPP(c_member(_1727146), hAPP(hAPP(c_List_Onth(_1727146), _1727148), _1727144)), hAPP(c_List_Oset(_1727146), _1727148))))], (44249 ^ _779571) ^ [_1644891] : [class_Groups_Oab__semigroup__mult(_1644891), -(c_Finite__Set_Ofun__left__comm(_1644891, _1644891, c_Groups_Otimes__class_Otimes(_1644891)))], (3606 ^ _779571) ^ [_835068, _835070, _835072, _835074, _835076, _835078, _835080, _835082] : [-(c_Nitpick_Oprod(_835082, _835078, _835074, _835070) = c_Nitpick_Oprod(_835080, _835076, _835072, _835068)), _835082 = _835080, _835078 = _835076, _835074 = _835072, _835070 = _835068], (31978 ^ _779571) ^ [_1360863, _1360865, _1360867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360863), _1360865)), -(hAPP(c_Finite__Set_Ocard(_1360863), hAPP(hAPP(c_Set_Oinsert(_1360863), _1360867), _1360865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1360863), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360863, tc_HOL_Obool)), _1360865), hAPP(hAPP(c_Set_Oinsert(_1360863), _1360867), c_Orderings_Obot__class_Obot(tc_fun(_1360863, tc_HOL_Obool)))))))], (6165 ^ _779571) ^ [_879161, _879163, _879165, _879167] : [-(c_Nat_Onat_Onat__case(_879161, _879163, _879165, hAPP(c_Nat_OSuc, _879167)) = hAPP(_879165, _879167))], (30339 ^ _779571) ^ [_1323649, _1323651, _1323653] : [hBOOL(hAPP(hAPP(c_member(_1323649), _1323651), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323649, tc_HOL_Obool)), _1323653))), hBOOL(hAPP(hAPP(c_member(_1323649), _1323651), _1323653))], (14441 ^ _779571) ^ [_1023260] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023260, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51179 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (21541 ^ _779571) ^ [_1150389, _1150391, _1150393, _1150395] : [class_Fields_Olinordered__field(_1150389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150389), _1150391), c_Groups_Ozero__class_Ozero(_1150389))), 21548 ^ _779571 : [(21555 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150389), _1150395), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150389), _1150393), _1150391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150389), _1150393), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150389), _1150395), _1150391))))], (21549 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150389), _1150393), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150389), _1150395), _1150391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150389), _1150395), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150389), _1150393), _1150391))))]]], (8294 ^ _779571) ^ [_917280, _917282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917280)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917280), _917282)))], (68 ^ _779571) ^ [_780467, _780469] : [-(class_Fields_Olinordered__field__inverse__zero(_780467)), _780469 = _780467, class_Fields_Olinordered__field__inverse__zero(_780469)], (27105 ^ _779571) ^ [_1257109] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257109) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1257109))], (5096 ^ _779571) ^ [_858327, _858329] : [_858329 = _858327, -(c_Groups_Oplus__class_Oplus(_858329) = c_Groups_Oplus__class_Oplus(_858327))], (50750 ^ _779571) ^ [_1799902, _1799904, _1799906] : [_1799904 = _1799906, -(hAPP(c_List_Orev(_1799902), _1799904) = hAPP(c_List_Orev(_1799902), _1799906))], (43546 ^ _779571) ^ [_1628927, _1628929, _1628931] : [c_Relation_Ototal__on(_1628927, _1628929, _1628931), -(c_Relation_Ototal__on(_1628927, _1628929, hAPP(c_Relation_Oconverse(_1628927, _1628927), _1628931)))], (34646 ^ _779571) ^ [_1414182, _1414184, _1414186, _1414188, _1414190] : [hAPP(_1414182, _1414184) = hAPP(c_Option_Ooption_OSome(_1414186), _1414188), -(hBOOL(hAPP(hAPP(c_member(_1414186), _1414188), c_Map_Oran(_1414190, _1414186, _1414182))))], (7242 ^ _779571) ^ [_899303, _899305, _899307, _899309, _899311] : [-(c_Sum__Type_Osum_Osum__size(_899303, _899305, _899307, _899309, hAPP(c_Sum__Type_OInl(_899303, _899305), _899311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_899307, _899311)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37756 ^ _779571) ^ [_1487257, _1487259, _1487261, _1487263, _1487265] : [class_Groups_Ocomm__monoid__mult(_1487257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487259), _1487261)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487259), _1487263)), 37770 ^ _779571 : [(37773 ^ _779571) ^ [] : [hAPP(_1487265, 37769 ^ [_1487257, _1487259, _1487261, _1487263, _1487265]) = c_Groups_Oone__class_Oone(_1487257)], (37771 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487259), 37769 ^ [_1487257, _1487259, _1487261, _1487263, _1487265]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487259, tc_HOL_Obool)), _1487261), _1487263))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487259, _1487257), _1487265), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487259, tc_HOL_Obool)), _1487261), _1487263)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487257), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487259, _1487257), _1487265), _1487261)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487259, _1487257), _1487265), _1487263)))], (15262 ^ _779571) ^ [_1037839, _1037841, _1037843] : [class_Groups_Ogroup__add(_1037839), 15265 ^ _779571 : [(15272 ^ _779571) ^ [] : [_1037841 = _1037843, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037839), _1037841), _1037843) = c_Groups_Ozero__class_Ozero(_1037839))], (15266 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037839), _1037841), _1037843) = c_Groups_Ozero__class_Ozero(_1037839), -(_1037841 = _1037843)]]], (15332 ^ _779571) ^ [_1038975, _1038977, _1038979] : [class_Groups_Ogroup__add(_1038975), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038975), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038975), _1038977), _1038979)), _1038979) = _1038977)], (7105 ^ _779571) ^ [_896555, _896557, _896559, _896561] : [class_Groups_Ocancel__semigroup__add(_896555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896555), _896557), _896559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896555), _896557), _896561), -(_896559 = _896561)], (43734 ^ _779571) ^ [_1633724] : [-(c_Relation_Osingle__valued(_1633724, _1633724, c_Relation_OId(_1633724)))], (27546 ^ _779571) ^ [_1266522, _1266524, _1266526, _1266528] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1266522, tc_Nat_Onat), _1266524), _1266526) = hAPP(c_Nat_OSuc, _1266528), 27550 ^ _779571 : [(27553 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1266524, 27549 ^ [_1266522, _1266524, _1266526, _1266528]))))], (27551 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266522), 27549 ^ [_1266522, _1266524, _1266526, _1266528]), _1266526)))]]], (24659 ^ _779571) ^ [_1210202, _1210204, _1210206, _1210208] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1210202, _1210204, _1210206, _1210208) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1210202, _1210204), _1210206), _1210208)))], (27183 ^ _779571) ^ [_1258823, _1258825, _1258827, _1258829] : [class_Groups_Ocomm__monoid__add(_1258823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258825), _1258827)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258823), _1258829), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1258825), _1258827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1258823), hAPP(_1258829, _1258825)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258823), _1258829), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1258825)), _1258827))))], (43078 ^ _779571) ^ [_1617492, _1617494] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1617492, _1617492, _1617492), _1617494), c_Transitive__Closure_Ortrancl(_1617492, _1617494)) = hAPP(hAPP(c_Relation_Orel__comp(_1617492, _1617492, _1617492), c_Transitive__Closure_Ortrancl(_1617492, _1617494)), _1617494))], (46049 ^ _779571) ^ [_1688550, _1688552, _1688554, _1688556, _1688558] : [hAPP(hAPP(c_Option_Omap(_1688550, _1688552), _1688554), _1688556) = hAPP(c_Option_Ooption_OSome(_1688552), _1688558), 46053 ^ _779571 : [(46056 ^ _779571) ^ [] : [-(hAPP(_1688554, 46052 ^ [_1688550, _1688552, _1688554, _1688556, _1688558]) = _1688558)], (46054 ^ _779571) ^ [] : [-(_1688556 = hAPP(c_Option_Ooption_OSome(_1688550), 46052 ^ [_1688550, _1688552, _1688554, _1688556, _1688558]))]]], (20051 ^ _779571) ^ [_1124303, _1124305, _1124307, _1124309] : [class_Rings_Odivision__ring(_1124303), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124303), _1124305), _1124307)), _1124309) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124303), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124303), _1124305), _1124309)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124303), _1124307), _1124309)))], (8256 ^ _779571) ^ [_916483, _916485, _916487, _916489] : [class_Orderings_Oorder(_916483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916483), hAPP(_916485, 8261 ^ [_916483, _916485, _916487, _916489])), hAPP(_916485, hAPP(c_Nat_OSuc, 8261 ^ [_916483, _916485, _916487, _916489])))), 8264 ^ _779571 : [(8271 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916487), _916489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916483), hAPP(_916485, _916487)), hAPP(_916485, _916489))))], (8265 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916483), hAPP(_916485, _916487)), hAPP(_916485, _916489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916487), _916489)))]]], (5514 ^ _779571) ^ [_864766, _864768] : [_864768 = _864766, -(c_Nat_Osize__class_Osize(_864768) = c_Nat_Osize__class_Osize(_864766))], (18417 ^ _779571) ^ [_1095693] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095693), c_Int_OMin) = c_Int_Opred(_1095693))], (6197 ^ _779571) ^ [_879960, _879962] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_879960, _879962))), -(hBOOL(hAPP(c_Com_OWT, _879962)))], (7121 ^ _779571) ^ [_896899, _896901, _896903, _896905] : [class_Groups_Ocancel__semigroup__add(_896899), 7124 ^ _779571 : [(7131 ^ _779571) ^ [] : [_896901 = _896905, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896899), _896901), _896903) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896899), _896905), _896903))], (7125 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896899), _896901), _896903) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896899), _896905), _896903), -(_896901 = _896905)]]], (23691 ^ _779571) ^ [_1191001, _1191003, _1191005, _1191007] : [class_Groups_Oordered__ab__group__add(_1191001), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1191001), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191001), _1191003), _1191005)), _1191007) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1191001), _1191003), _1191007)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1191001), _1191005), _1191007)))], (43134 ^ _779571) ^ [_1618848, _1618850, _1618852, _1618854, _1618856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618848, _1618848)), hAPP(hAPP(c_Product__Type_OPair(_1618848, _1618848), _1618850), _1618852)), c_Transitive__Closure_Ortrancl(_1618848, _1618854))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618848, _1618848)), hAPP(hAPP(c_Product__Type_OPair(_1618848, _1618848), _1618852), _1618856)), _1618854)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618848, _1618848)), hAPP(hAPP(c_Product__Type_OPair(_1618848, _1618848), _1618850), _1618856)), c_Transitive__Closure_Otrancl(_1618848, _1618854))))], (2802 ^ _779571) ^ [_822076, _822078, _822080, _822082, _822084, _822086] : [-(c_Nitpick_Oof__frac(_822086, _822082, _822078) = c_Nitpick_Oof__frac(_822084, _822080, _822076)), _822086 = _822084, _822082 = _822080, _822078 = _822076], (13020 ^ _779571) ^ [_997535, _997537] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _997535) = _997537), _997535 = hAPP(c_Int_Onat, _997537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997537))], (51593 ^ _779571) ^ [] : [-(hBOOL(c_fTrue))], (41163 ^ _779571) ^ [_1563401, _1563403] : [-(hAPP(c_Set_OCollect(_1563401), hAPP(hAPP(c_COMBC(_1563401, _1563401, tc_HOL_Obool), c_fequal), _1563403)) = hAPP(hAPP(c_Set_Oinsert(_1563401), _1563403), c_Orderings_Obot__class_Obot(tc_fun(_1563401, tc_HOL_Obool))))], (44635 ^ _779571) ^ [_1655002, _1655004, _1655006, _1655008, _1655010] : [44637 ^ _779571 : [(44640 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1655002, tc_HOL_Obool)), _1655004), hAPP(_1655010, 44636 ^ [_1655002, _1655004, _1655006, _1655008, _1655010])))], (44638 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655006), 44636 ^ [_1655002, _1655004, _1655006, _1655008, _1655010]), _1655008)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1655002, tc_HOL_Obool)), _1655004), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655006, tc_fun(_1655002, tc_HOL_Obool)), _1655008), _1655010))))], (22238 ^ _779571) ^ [_1163325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1163325)), _1163325 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46913 ^ _779571) ^ [_1711060, _1711062, _1711064, _1711066, _1711068, _1711070] : [_1711060 = _1711062, -(hAPP(c_Map_Omap__of(_1711064, _1711066, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1711064, _1711066)), hAPP(hAPP(c_Product__Type_OPair(_1711064, _1711066), _1711060), _1711068)), _1711070)), _1711062) = hAPP(c_Option_Ooption_OSome(_1711066), _1711068))], (44051 ^ _779571) ^ [_1641165, _1641167, _1641169] : [class_Lattices_Olattice(_1641165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641165), _1641167)), -(c_Big__Operators_Olattice__class_OSup__fin(_1641165, hAPP(hAPP(c_Set_Oinsert(_1641165), _1641169), _1641167)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641165, _1641165, c_Lattices_Osemilattice__sup__class_Osup(_1641165)), _1641169), _1641167))], (24631 ^ _779571) ^ [_1209698, _1209700, _1209702, _1209704, _1209706, _1209708, _1209710] : [-(hAPP(c_Product__Type_Oapsnd(_1209698, _1209700, _1209702, _1209704), hAPP(c_Product__Type_Oapfst(_1209706, _1209702, _1209698, _1209708), _1209710)) = hAPP(c_Product__Type_Oapfst(_1209706, _1209702, _1209700, _1209708), hAPP(c_Product__Type_Oapsnd(_1209698, _1209700, _1209706, _1209704), _1209710)))], (41648 ^ _779571) ^ [_1581638, _1581640, _1581642, _1581644] : [-(c_Product__Type_Oapsnd(_1581638, _1581640, _1581642, _1581644) = c_Product__Type_Omap__pair(_1581642, _1581642, _1581638, _1581640, c_Fun_Oid(_1581642), _1581644))], (47733 ^ _779571) ^ [_1731401, _1731403, _1731405, _1731407, _1731409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731401, tc_HOL_Obool)), hAPP(c_List_Oset(_1731401), _1731403)), _1731405)), hBOOL(hAPP(hAPP(c_member(_1731401), _1731407), _1731405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731401, tc_HOL_Obool)), hAPP(c_List_Oset(_1731401), hAPP(hAPP(c_List_Olist__update(_1731401, _1731403), _1731409), _1731407))), _1731405)))], (48056 ^ _779571) ^ [_1738993, _1738995, _1738997, _1738999] : [-(c_Map_Omap__of(_1738993, _1738995, hAPP(hAPP(c_List_Oappend(tc_prod(_1738993, _1738995)), _1738997), _1738999)) = c_Map_Omap__add(_1738993, _1738995, c_Map_Omap__of(_1738993, _1738995, _1738999), c_Map_Omap__of(_1738993, _1738995, _1738997)))], (36692 ^ _779571) ^ [_1461900, _1461902, _1461904] : [class_Lattices_Oboolean__algebra(_1461900), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1461900), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461900), _1461902), _1461904)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461900), hAPP(c_Groups_Ouminus__class_Ouminus(_1461900), _1461902)), hAPP(c_Groups_Ouminus__class_Ouminus(_1461900), _1461904)))], (2260 ^ _779571) ^ [_813631, _813633, _813635, _813637, _813639, _813641] : [-(c_Option_Ooption_Ooption__size(_813641, _813637, _813633) = c_Option_Ooption_Ooption__size(_813639, _813635, _813631)), _813641 = _813639, _813637 = _813635, _813633 = _813631], (10323 ^ _779571) ^ [_951534] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _951534) = _951534)], (30812 ^ _779571) ^ [_1333843, _1333845, _1333847, _1333849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333843, tc_HOL_Obool)), _1333845), hAPP(hAPP(c_Set_Oinsert(_1333843), _1333847), _1333849))), 30815 ^ _779571 : [(30822 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333843), _1333847), _1333849))), 30825 ^ _779571 : [(30832 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333843), _1333847), _1333845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333843, tc_HOL_Obool)), _1333845), _1333849)))], (30826 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333843), _1333847), _1333845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333843, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333843, tc_HOL_Obool)), _1333845), hAPP(hAPP(c_Set_Oinsert(_1333843), _1333847), c_Orderings_Obot__class_Obot(tc_fun(_1333843, tc_HOL_Obool))))), _1333849)))]]], (30816 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333843), _1333847), _1333849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333843, tc_HOL_Obool)), _1333845), _1333849)))]]], (41610 ^ _779571) ^ [_1580931, _1580933] : [-(c_Product__Type_Omap__pair(_1580931, _1580931, _1580933, _1580933, c_COMBI(_1580931), c_COMBI(_1580933)) = c_Fun_Oid(tc_prod(_1580931, _1580933)))], (25170 ^ _779571) ^ [_1220863, _1220865, _1220867, _1220869] : [class_Rings_Ocomm__semiring__1(_1220863), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220863), _1220865), _1220867)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220863), hAPP(hAPP(c_Power_Opower__class_Opower(_1220863), _1220865), _1220869)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220863), _1220867), _1220869))))], (7476 ^ _779571) ^ [_903513, _903515] : [-(_903513 = _903515), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903513), _903515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903515), _903513)))], (21125 ^ _779571) ^ [_1143150, _1143152, _1143154, _1143156] : [class_Fields_Ofield(_1143150), -(_1143152 = c_Groups_Ozero__class_Ozero(_1143150)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1143150), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143150), _1143154), _1143152)), _1143156) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143150), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1143150), _1143154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143150), _1143152), _1143156))), _1143152))], (17393 ^ _779571) ^ [_1078761, _1078763] : [class_Groups_Omonoid__mult(_1078761), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078761), _1078763), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1078763)], (48293 ^ _779571) ^ [_1744708, _1744710, _1744712, _1744714, _1744716, _1744718] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744708)), _1744710) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744712)), _1744714), -(c_Map_Omap__upds(_1744708, _1744712, _1744716, _1744710, hAPP(hAPP(c_List_Oappend(_1744712), _1744714), _1744718)) = c_Map_Omap__upds(_1744708, _1744712, _1744716, _1744710, _1744714))], (46851 ^ _779571) ^ [_1709755, _1709757, _1709759, _1709761, _1709763] : [-(hAPP(hAPP(c_List_Olist_OCons(_1709755), _1709757), _1709759) = hAPP(hAPP(c_List_Olist_OCons(_1709755), _1709761), _1709763)), _1709757 = _1709761, _1709759 = _1709763], (20665 ^ _779571) ^ [_1134676, _1134678] : [c_Nat__Transfer_Ois__nat(_1134676), c_Nat__Transfer_Ois__nat(_1134678), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1134676, _1134678)))], (25958 ^ _779571) ^ [_1234974, _1234976, _1234978, _1234980, _1234982] : [class_Groups_Oab__group__add(_1234974), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234976, _1234974), hAPP(hAPP(c_COMBS(_1234976, _1234974, _1234974), hAPP(hAPP(c_COMBB(_1234974, tc_fun(_1234974, _1234974), _1234976), c_Groups_Ominus__class_Ominus(_1234974)), _1234978)), _1234980)), _1234982) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1234974), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234976, _1234974), _1234978), _1234982)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1234976, _1234974), _1234980), _1234982)))], (34589 ^ _779571) ^ [_1412978, _1412980, _1412982] : [34591 ^ _779571 : [(34594 ^ _779571) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1412982, 34590 ^ [_1412978, _1412980, _1412982]))], (34592 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412978), 34590 ^ [_1412978, _1412980, _1412982]), _1412980)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412978, tc_Int_Oint), _1412982), _1412980) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412978, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1412978), c_Int_Onat), _1412982)), _1412980)))], (16331 ^ _779571) ^ [_1058936] : [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), _1058936))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058936) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058936)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (37964 ^ _779571) ^ [_1492247, _1492249, _1492251, _1492253, _1492255] : [c_Relation_Orefl__on(_1492247, _1492249, _1492251), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492247, _1492247)), hAPP(hAPP(c_Product__Type_OPair(_1492247, _1492247), _1492253), _1492255)), _1492251)), -(hBOOL(hAPP(hAPP(c_member(_1492247), _1492253), _1492249)))], (31512 ^ _779571) ^ [_1350994, _1350996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1350994), _1350996))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1350994), _1350996)))], (17977 ^ _779571) ^ [_1088919, _1088921] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088919))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088919)), _1088921)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1088921))], (32287 ^ _779571) ^ [_1367099, _1367101, _1367103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367099)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1367101), _1367103)), 32294 ^ _779571 : [(32295 ^ _779571) ^ [_1367295] : [32297 ^ _779571 : [(32303 ^ _779571) ^ [] : [-(_1367295 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32299 ^ [_1367099, _1367101, _1367103, _1367295]), 32296 ^ [_1367099, _1367101, _1367103, _1367295]))], (32301 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32299 ^ [_1367099, _1367101, _1367103, _1367295]), _1367103)))], (32298 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32296 ^ [_1367099, _1367101, _1367103, _1367295]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1367099))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367295), _1367101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1367295), _1367099)), _1367101)))]]], (51285 ^ _779571) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (7899 ^ _779571) ^ [_910663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910663), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_910663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25670 ^ _779571) ^ [_1229074, _1229076] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229074)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229076))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229074), _1229076)))], (22109 ^ _779571) ^ [_1161300, _1161302] : [22110 ^ _779571 : [(22113 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1161302), _1161300))], (22111 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1161300), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1161300, _1161302) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (51393 ^ _779571) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (26014 ^ _779571) ^ [_1236253, _1236255] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236253), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236255))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1236253))), _1236255)))], (33269 ^ _779571) ^ [_1386390, _1386392] : [class_Orderings_Olinorder(_1386390), -(c_Big__Operators_Olinorder__class_OMin(_1386390, hAPP(hAPP(c_Set_Oinsert(_1386390), _1386392), c_Orderings_Obot__class_Obot(tc_fun(_1386390, tc_HOL_Obool)))) = _1386392)], (45209 ^ _779571) ^ [_1668983] : [class_Complete__Lattice_Ocomplete__lattice(_1668983), -(c_Complete__Lattice_OInf__class_OInf(_1668983, c_Orderings_Obot__class_Obot(tc_fun(_1668983, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1668983))], (6319 ^ _779571) ^ [_882101, _882103, _882105] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882101, _882103, _882105)))), hBOOL(hAPP(c_Com_OWT, _882103)), hBOOL(hAPP(c_Com_OWT, _882105))], (40226 ^ _779571) ^ [_1542377, _1542379, _1542381, _1542383, _1542385, _1542387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542377, _1542379)), hAPP(hAPP(c_Product__Type_OPair(_1542377, _1542379), _1542381), _1542383)), hAPP(hAPP(c_Product__Type_OSigma(_1542377, _1542379), _1542385), _1542387))), -(hBOOL(hAPP(hAPP(c_member(_1542379), _1542383), hAPP(_1542387, _1542381))))], (22946 ^ _779571) ^ [_1177259, _1177261] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177259))), 22949 ^ _779571 : [(22956 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177261))), -(c_Divides_Odivmod__int(_1177259, _1177261) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1177259), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1177261))))], (22950 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177261)), -(c_Divides_Odivmod__int(_1177259, _1177261) = c_Divides_OnegDivAlg(_1177259, _1177261))]]], (51217 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (19129 ^ _779571) ^ [_1107616, _1107618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107616), _1107618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1107616)), c_Int_OBit0(_1107618))))], (42221 ^ _779571) ^ [_1596784, _1596786, _1596788, _1596790, _1596792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596784, _1596786)), hAPP(hAPP(c_Product__Type_OPair(_1596784, _1596786), _1596788), _1596790)), _1596792)), -(hBOOL(hAPP(hAPP(c_member(_1596784), _1596788), hAPP(c_Relation_ODomain(_1596784, _1596786), _1596792))))], (11206 ^ _779571) ^ [_965612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965612)))], (36878 ^ _779571) ^ [_1466284, _1466286, _1466288] : [class_Orderings_Oorder(_1466284), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466284, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466284), _1466286)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1466284, _1466286), _1466288)) = c_Orderings_Obot__class_Obot(tc_fun(_1466284, tc_HOL_Obool)))], (15718 ^ _779571) ^ [_1046403, _1046405, _1046407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046403), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046405), _1046407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046403), _1046407)), _1046405)))], (35553 ^ _779571) ^ [_1435925, _1435927, _1435929, _1435931, _1435933, _1435935] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435925, tc_fun(_1435927, tc_HOL_Obool)), _1435929), hAPP(c_Fun_Ocomp(_1435931, tc_fun(_1435927, tc_HOL_Obool), _1435925, _1435933), _1435935)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435931, tc_fun(_1435927, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1435925, _1435931, _1435935), _1435929)), _1435933))], (1860 ^ _779571) ^ [_805743, _805745, _805747, _805749] : [-(v_R(_805747, _805743)), v_R(_805749, _805745), _805749 = _805747, _805745 = _805743], (3536 ^ _779571) ^ [_833923, _833925, _833927, _833929] : [-(c_Sum__Type_OInl(_833929, _833925) = c_Sum__Type_OInl(_833927, _833923)), _833929 = _833927, _833925 = _833923], (10255 ^ _779571) ^ [_950378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _950378)))], (29394 ^ _779571) ^ [_1305076, _1305078, _1305080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305076, tc_HOL_Obool)), _1305078), hAPP(hAPP(c_Set_Oinsert(_1305076), _1305080), c_Orderings_Obot__class_Obot(tc_fun(_1305076, tc_HOL_Obool))))), -(_1305078 = c_Orderings_Obot__class_Obot(tc_fun(_1305076, tc_HOL_Obool))), -(_1305078 = hAPP(hAPP(c_Set_Oinsert(_1305076), _1305080), c_Orderings_Obot__class_Obot(tc_fun(_1305076, tc_HOL_Obool))))], (47354 ^ _779571) ^ [_1721746, _1721748, _1721750] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1721746)), -(c_List_Osublist(_1721748, hAPP(hAPP(c_List_Olist_OCons(_1721748), _1721750), c_List_Olist_ONil(_1721748)), _1721746) = hAPP(hAPP(c_List_Olist_OCons(_1721748), _1721750), c_List_Olist_ONil(_1721748)))], (27792 ^ _779571) ^ [_1271748, _1271750, _1271752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271748, tc_HOL_Obool)), _1271750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271748, tc_HOL_Obool)), _1271752), _1271750))))], (13928 ^ _779571) ^ [_1013613, _1013615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013613)), -(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, _1013615, _1013613))))], (18383 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (42984 ^ _779571) ^ [_1615175, _1615177] : [-(c_Transitive__Closure_Otrancl(_1615175, _1615177) = hAPP(hAPP(c_Relation_Orel__comp(_1615175, _1615175, _1615175), c_Transitive__Closure_Ortrancl(_1615175, _1615177)), _1615177))], (12501 ^ _779571) ^ [_988240, _988242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988242)), -(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), _988240), _988242))))], (30026 ^ _779571) ^ [_1317582, _1317584, _1317586, _1317588, _1317590, _1317592] : [_1317582 = hAPP(_1317584, _1317586), hBOOL(hAPP(hAPP(c_member(_1317588), _1317586), _1317590)), -(hBOOL(hAPP(hAPP(c_member(_1317592), _1317582), hAPP(c_Set_Oimage(_1317588, _1317592, _1317584), _1317590))))], (12355 ^ _779571) ^ [_985864, _985866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985866)), -(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), _985864), _985866))))], (43862 ^ _779571) ^ [_1637303, _1637305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637303, _1637303)), _1637305), c_Relation_OId(_1637303))), -(_1637305 = hAPP(hAPP(c_Product__Type_OPair(_1637303, _1637303), 43865 ^ [_1637303, _1637305]), 43865 ^ [_1637303, _1637305]))], (41165 ^ _779571) ^ [_1563466, _1563468, _1563470] : [hBOOL(hAPP(_1563466, _1563468)), -(hAPP(c_Set_OCollect(_1563470), hAPP(hAPP(c_COMBS(_1563470, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563470), c_fconj), hAPP(c_fequal, _1563468))), _1563466)) = hAPP(hAPP(c_Set_Oinsert(_1563470), _1563468), c_Orderings_Obot__class_Obot(tc_fun(_1563470, tc_HOL_Obool))))], (31329 ^ _779571) ^ [_1345910, _1345912, _1345914, _1345916] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345910, tc_HOL_Obool)), _1345912), hAPP(hAPP(c_Set_Oinsert(_1345910), _1345914), _1345916)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345910, tc_HOL_Obool)), _1345912), _1345916))))], (49231 ^ _779571) ^ [_1767463, _1767465, _1767467, _1767469] : [class_Complete__Lattice_Ocomplete__lattice(_1767463), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767465, _1767463), hAPP(c_List_Oset(_1767465), _1767467)), _1767469) = hAPP(c_List_Ofoldl(_1767463, _1767465, hAPP(c_COMBC(_1767465, _1767463, _1767463), hAPP(hAPP(c_COMBB(_1767463, tc_fun(_1767463, _1767463), _1767465), c_Lattices_Osemilattice__sup__class_Osup(_1767463)), _1767469)), c_Orderings_Obot__class_Obot(_1767463)), _1767467))], (13799 ^ _779571) ^ [_1011411, _1011413] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011411), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011413)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011411, _1011413)))], (41935 ^ _779571) ^ [_1589996, _1589998, _1590000] : [c_Wellfounded_Owf(_1589996, _1589998), -(c_Wellfounded_Owf(_1589996, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1589996, _1589996), tc_HOL_Obool)), _1590000), _1589998)))], (47590 ^ _779571) ^ [_1727744, _1727746, _1727748, _1727750] : [_1727744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1727746), hAPP(hAPP(c_List_Olist_OCons(_1727746), _1727748), _1727750)), _1727744) = _1727748)], (19607 ^ _779571) ^ [_1115921] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1115921))), 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), _1115921), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (36052 ^ _779571) ^ [_1448146, _1448148, _1448150, _1448152, _1448154, _1448156] : [c_Equiv__Relations_Oequiv(_1448146, _1448148, _1448150), hBOOL(hAPP(hAPP(c_member(_1448146), _1448152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448146, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1448146, _1448146, _1448150), hAPP(hAPP(c_Set_Oinsert(_1448146), _1448154), c_Orderings_Obot__class_Obot(tc_fun(_1448146, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1448146, _1448146, _1448150), hAPP(hAPP(c_Set_Oinsert(_1448146), _1448156), c_Orderings_Obot__class_Obot(tc_fun(_1448146, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448146, _1448146)), hAPP(hAPP(c_Product__Type_OPair(_1448146, _1448146), _1448154), _1448156)), _1448150)))], (17203 ^ _779571) ^ [_1075381] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075381) = _1075381)], (37469 ^ _779571) ^ [_1479382, _1479384, _1479386] : [class_Orderings_Olinorder(_1479382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479382), _1479384)), -(_1479384 = c_Orderings_Obot__class_Obot(tc_fun(_1479382, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479382), _1479386)), -(_1479386 = c_Orderings_Obot__class_Obot(tc_fun(_1479382, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479382, tc_HOL_Obool)), _1479384), _1479386) = c_Orderings_Obot__class_Obot(tc_fun(_1479382, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1479382, c_Orderings_Oord__class_Omax(_1479382), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479382, tc_HOL_Obool)), _1479384), _1479386)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1479382), c_Big__Operators_Olattice_OSup__fin(_1479382, c_Orderings_Oord__class_Omax(_1479382), _1479384)), c_Big__Operators_Olattice_OSup__fin(_1479382, c_Orderings_Oord__class_Omax(_1479382), _1479386)))], (35569 ^ _779571) ^ [_1436268, _1436270, _1436272, _1436274] : [-(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), _1436268), _1436270)), 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), _1436272), _1436274)), 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), _1436268), _1436272)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436270), _1436274))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (42348 ^ _779571) ^ [_1600426, _1600428, _1600430, _1600432, _1600434] : [hBOOL(hAPP(hAPP(_1600426, _1600428), _1600430)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1600432, _1600434, _1600426), _1600428)))], (34267 ^ _779571) ^ [_1406163, _1406165, _1406167] : [class_Groups_Ocomm__monoid__mult(_1406163), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406165, _1406163), _1406167), c_Orderings_Obot__class_Obot(tc_fun(_1406165, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1406163))], (10544 ^ _779571) ^ [_955007, _955009, _955011, _955013] : [class_Orderings_Opreorder(_955007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955007), _955009), _955011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955007), _955011), _955013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955007), _955009), _955013)))], (24555 ^ _779571) ^ [_1207941, _1207943, _1207945] : [class_Orderings_Olinorder(_1207941), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207941), _1207943), _1207945) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207941), _1207945), _1207943))], (20797 ^ _779571) ^ [_1137094, _1137096, _1137098, _1137100] : [class_Fields_Olinordered__field(_1137094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137094), _1137096), _1137098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137094), _1137100), c_Groups_Ozero__class_Ozero(_1137094))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137094), c_Groups_Ozero__class_Ozero(_1137094)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137094), _1137096), _1137098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137094), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137094), _1137100), _1137096)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137094), _1137100), _1137098))))], (49526 ^ _779571) ^ [_1774098, _1774100, _1774102] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1774098)), _1774100), c_List_Olists(_1774098, _1774102))), -(_1774100 = c_List_Olist_ONil(_1774098)), 49535 ^ _779571 : [(49540 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1774098)), 49534 ^ [_1774098, _1774100, _1774102]), c_List_Olists(_1774098, _1774102))))], (49538 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774098), 49533 ^ [_1774098, _1774100, _1774102]), _1774102)))], (49536 ^ _779571) ^ [] : [-(_1774100 = hAPP(hAPP(c_List_Olist_OCons(_1774098), 49533 ^ [_1774098, _1774100, _1774102]), 49534 ^ [_1774098, _1774100, _1774102]))]]], (16381 ^ _779571) ^ [_1059706, _1059708, _1059710] : [class_Int_Onumber(_1059706), 16384 ^ _779571 : [(16391 ^ _779571) ^ [] : [_1059710 = hAPP(c_Int_Onumber__class_Onumber__of(_1059706), _1059708), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059706), _1059708) = _1059710)], (16385 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1059706), _1059708) = _1059710, -(_1059710 = hAPP(c_Int_Onumber__class_Onumber__of(_1059706), _1059708))]]], (42988 ^ _779571) ^ [_1615263, _1615265] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1615263, _1615263), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615263, _1615265)), c_Relation_OId(_1615263)) = c_Transitive__Closure_Ortrancl(_1615263, _1615265))], (30902 ^ _779571) ^ [_1335721, _1335723] : [30903 ^ _779571 : [(30906 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335723), _1335721))], (30904 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335721), _1335723)))]], -(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)))), _1335721, _1335723) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (19083 ^ _779571) ^ [_1106725, _1106727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1106725)), -(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)))), _1106727))), 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)))), _1106725)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1106727), _1106725))], (41868 ^ _779571) ^ [_1588778, _1588780, _1588782, _1588784] : [c_Wellfounded_Owf(_1588778, _1588780), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588778, _1588778)), hAPP(hAPP(c_Product__Type_OPair(_1588778, _1588778), _1588782), _1588784)), _1588780)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588778, _1588778)), hAPP(hAPP(c_Product__Type_OPair(_1588778, _1588778), _1588784), _1588782)), _1588780))], (50786 ^ _779571) ^ [_1800593, _1800595, _1800597] : [-(hAPP(c_List_Orev(_1800593), hAPP(hAPP(c_List_Odrop(_1800593), _1800595), _1800597)) = hAPP(hAPP(c_List_Otake(_1800593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800593)), _1800597)), _1800595)), hAPP(c_List_Orev(_1800593), _1800597)))], (18373 ^ _779571) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (51535 ^ _779571) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (31518 ^ _779571) ^ [_1351093, _1351095, _1351097] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351093), _1351095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1351093), _1351095)), hAPP(c_Finite__Set_Ocard(_1351093), hAPP(hAPP(c_Set_Oinsert(_1351093), _1351097), _1351095)))))], (48574 ^ _779571) ^ [_1752116, _1752118, _1752120, _1752122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752116), tc_List_Olist(_1752116))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752116), tc_List_Olist(_1752116)), _1752118), _1752120)), c_List_Olistrel(_1752116, _1752122))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752116), tc_List_Olist(_1752116))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752116), tc_List_Olist(_1752116)), _1752118), _1752120)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752116), c_List_Olistrel1(_1752116, _1752122)))))], (47181 ^ _779571) ^ [_1718587, _1718589, _1718591] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718587), tc_List_Olist(_1718587))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718587), tc_List_Olist(_1718587)), c_List_Olist_ONil(_1718587)), _1718589)), c_List_Olistrel(_1718587, _1718591))), -(_1718589 = c_List_Olist_ONil(_1718587))], (39425 ^ _779571) ^ [_1522396, _1522398, _1522400, _1522402, _1522404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522396, tc_HOL_Obool)), _1522398), _1522400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522402, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522402, _1522396, _1522404), _1522398)), hAPP(c_Set_Ovimage(_1522402, _1522396, _1522404), _1522400))))], (37192 ^ _779571) ^ [_1473444, _1473446, _1473448, _1473450] : [c_Equiv__Relations_Ocongruent(_1473444, _1473446, _1473448, _1473450), 37195 ^ _779571 : [(37196 ^ _779571) ^ [_1473589] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473444, _1473444)), _1473589), _1473448)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1473444, _1473444, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1473444, tc_fun(_1473444, _1473446), tc_fun(_1473444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473446, tc_HOL_Obool), tc_fun(tc_fun(_1473444, _1473446), tc_fun(_1473444, tc_HOL_Obool)), _1473444), c_COMBB(_1473446, tc_HOL_Obool, _1473444)), hAPP(hAPP(c_COMBB(_1473446, tc_fun(_1473446, tc_HOL_Obool), _1473444), c_fequal), _1473450))), _1473450)), _1473589)))]]], (37124 ^ _779571) ^ [_1472034, _1472036] : [class_Orderings_Oorder(_1472034), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472034, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1472034), _1472036)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472034), _1472036)) = hAPP(hAPP(c_Set_Oinsert(_1472034), _1472036), c_Orderings_Obot__class_Obot(tc_fun(_1472034, tc_HOL_Obool))))], (45043 ^ _779571) ^ [_1665229, _1665231] : [-(hAPP(c_Relation_OField(_1665229), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1665229, _1665229), tc_HOL_Obool), _1665231)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665229, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1665229, _1665229), tc_HOL_Obool), tc_fun(_1665229, tc_HOL_Obool), c_Relation_OField(_1665229)), _1665231)))], (18229 ^ _779571) ^ [_1092946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092946), 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), _1092946)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51573 ^ _779571) ^ [_1813122, _1813124, _1813126, _1813128, _1813130, _1813132] : [-(hAPP(hAPP(hAPP(c_COMBB(_1813122, _1813124, _1813126), _1813128), _1813130), _1813132) = hAPP(_1813128, hAPP(_1813130, _1813132)))], (30369 ^ _779571) ^ [_1324299, _1324301, _1324303] : [hBOOL(hAPP(hAPP(c_member(_1324299), _1324301), _1324303)), -(hBOOL(hAPP(_1324303, _1324301)))], (50977 ^ _779571) ^ [_1806238, _1806240, _1806242] : [-(c_List_OtakeWhile(_1806238, _1806240, _1806242) = hAPP(hAPP(c_List_Otake(_1806238), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806238)), c_List_OtakeWhile(_1806238, _1806240, _1806242))), _1806242))], (48580 ^ _779571) ^ [_1752327, _1752329, _1752331, _1752333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752327), tc_List_Olist(_1752327))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752327), tc_List_Olist(_1752327)), _1752329), _1752331)), c_List_Olistrel1(_1752327, _1752333))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752327), tc_List_Olist(_1752327))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752327), tc_List_Olist(_1752327)), _1752329), _1752331)), c_List_Olistrel(_1752327, c_Transitive__Closure_Ortrancl(_1752327, _1752333)))))], (36962 ^ _779571) ^ [_1468202, _1468204, _1468206, _1468208] : [class_Orderings_Oorder(_1468202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468202, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1468202, _1468204, _1468206)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1468202, _1468206, _1468208)) = c_Orderings_Obot__class_Obot(tc_fun(_1468202, tc_HOL_Obool)))], (36142 ^ _779571) ^ [_1449860, _1449862] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449860, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1449860, tc_HOL_Obool))), _1449862) = _1449862)], (14984 ^ _779571) ^ [_1032667, _1032669, _1032671, _1032673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032669), _1032671)), -(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), _1032671), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1032673, _1032667))), _1032669)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032671), _1032667))))], (6225 ^ _779571) ^ [_880509, _880511, _880513, _880515, _880517, _880519] : [c_Com_Ocom_OCall(_880509, _880511, _880513) = c_Com_Ocom_OCall(_880515, _880517, _880519), 6228 ^ _779571 : [(6233 ^ _779571) ^ [] : [-(_880513 = _880519)], (6231 ^ _779571) ^ [] : [-(_880511 = _880517)], (6229 ^ _779571) ^ [] : [-(_880509 = _880515)]]], (15044 ^ _779571) ^ [_1033839, _1033841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033841)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1033839, _1033841)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1033839), hAPP(c_Int_Onat, _1033841)))], (15378 ^ _779571) ^ [_1039925] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039925), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1039925)], (35002 ^ _779571) ^ [_1422990, _1422992, _1422994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1422990, _1422990), tc_HOL_Obool)), _1422992), _1422994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422990, tc_HOL_Obool)), hAPP(c_Relation_OField(_1422990), _1422992)), hAPP(c_Relation_OField(_1422990), _1422994))))], (38765 ^ _779571) ^ [_1508026, _1508028, _1508030, _1508032, _1508034, _1508036] : [c_Fun_Oinj__on(_1508026, _1508028, _1508030, _1508032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508026, tc_HOL_Obool)), _1508034), _1508032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508026, tc_HOL_Obool)), _1508036), _1508032)), -(hAPP(c_Set_Oimage(_1508026, _1508028, _1508030), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508026, tc_HOL_Obool)), _1508034), _1508036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508028, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508026, _1508028, _1508030), _1508034)), hAPP(c_Set_Oimage(_1508026, _1508028, _1508030), _1508036)))], (12167 ^ _779571) ^ [_982496, _982498] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982496), _982498) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _982496 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982498 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18155 ^ _779571) ^ [_1091861] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1091861, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16607 ^ _779571) ^ [_1063659, _1063661] : [class_Groups_Oordered__ab__group__add__abs(_1063659), 16610 ^ _779571 : [(16617 ^ _779571) ^ [] : [-(_1063661 = c_Groups_Ozero__class_Ozero(_1063659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063659), c_Groups_Ozero__class_Ozero(_1063659)), hAPP(c_Groups_Oabs__class_Oabs(_1063659), _1063661))))], (16611 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063659), c_Groups_Ozero__class_Ozero(_1063659)), hAPP(c_Groups_Oabs__class_Oabs(_1063659), _1063661))), _1063661 = c_Groups_Ozero__class_Ozero(_1063659)]]], (47789 ^ _779571) ^ [_1732576, _1732578, _1732580] : [class_Orderings_Olinorder(_1732576), hBOOL(hAPP(hAPP(c_member(_1732576), _1732578), hAPP(c_List_Oset(_1732576), _1732580))), -(c_List_Olinorder__class_Oinsort__insert__key(_1732576, _1732576, c_COMBI(_1732576), _1732578, _1732580) = _1732580)], (6873 ^ _779571) ^ [_893000, _893002, _893004] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893002), _893004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893000), _893004)))], (29728 ^ _779571) ^ [_1311057] : [class_Lattices_Oboolean__algebra(_1311057), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1311057), c_Orderings_Otop__class_Otop(_1311057)) = c_Orderings_Obot__class_Obot(_1311057))], (37082 ^ _779571) ^ [_1471070, _1471072, _1471074, _1471076, _1471078] : [class_Groups_Ocomm__monoid__add(_1471070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471072), _1471074)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471072, _1471070), _1471076), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471072, tc_HOL_Obool)), _1471074), _1471078)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471072, _1471070), hAPP(hAPP(c_COMBC(_1471072, _1471070, _1471070), hAPP(hAPP(c_COMBS(_1471072, _1471070, tc_fun(_1471070, _1471070)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1471070, tc_fun(_1471070, _1471070)), _1471072), c_If(_1471070)), hAPP(hAPP(c_COMBC(_1471072, tc_fun(_1471072, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471072)), _1471078))), _1471076)), c_Groups_Ozero__class_Ozero(_1471070))), _1471074))], (24645 ^ _779571) ^ [_1210040] : [class_Orderings_Oord(_1210040), -(c_Orderings_Oord__class_Omax(_1210040) = c_Orderings_Oord_Omax(_1210040, c_Orderings_Oord__class_Oless__eq(_1210040)))], (34996 ^ _779571) ^ [_1422816, _1422818] : [-(c_Relation_OId__on(_1422816, _1422818) = hAPP(c_Product__Type_Oprod_Oprod__case(_1422816, _1422816, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1422816, tc_HOL_Obool, tc_fun(_1422816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422816, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1422816, tc_HOL_Obool)), _1422816), c_COMBC(_1422816, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422816, tc_HOL_Obool), tc_fun(_1422816, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1422816), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1422816), c_fconj)), c_fequal))), _1422818)))], (34827 ^ _779571) ^ [_1418043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1418043)), -(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))), _1418043)), c_FunDef_Omax__weak)))], (48166 ^ _779571) ^ [_1741151, _1741153, _1741155, _1741157] : [-(hBOOL(hAPP(hAPP(c_member(_1741151), _1741153), hAPP(c_List_Oset(_1741151), _1741155)))), -(c_List_Oremove1(_1741151, _1741153, hAPP(hAPP(c_List_Oappend(_1741151), _1741155), _1741157)) = hAPP(hAPP(c_List_Oappend(_1741151), _1741155), c_List_Oremove1(_1741151, _1741153, _1741157)))], (42012 ^ _779571) ^ [_1591463, _1591465] : [c_FunDef_Oreduction__pair(_1591463, _1591465), 42015 ^ _779571 : [(42018 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1591463, _1591463, _1591463), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool), tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool)), _1591465)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool), tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool)), _1591465))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool), tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool)), _1591465))))], (42016 ^ _779571) ^ [] : [-(c_Wellfounded_Owf(_1591463, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool), tc_fun(tc_prod(_1591463, _1591463), tc_HOL_Obool)), _1591465)))]]], (41702 ^ _779571) ^ [_1583363, _1583365, _1583367, _1583369, _1583371, _1583373, _1583375] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583363, _1583365, _1583367), hAPP(hAPP(c_Relation_Orel__comp(_1583363, _1583369, _1583365), _1583371), _1583373)), _1583375) = hAPP(hAPP(c_Relation_Orel__comp(_1583363, _1583369, _1583367), _1583371), hAPP(hAPP(c_Relation_Orel__comp(_1583369, _1583365, _1583367), _1583373), _1583375)))], (13673 ^ _779571) ^ [_1008712, _1008714, _1008716] : [class_Divides_Osemiring__div(_1008712), -(c_Divides_Odiv__class_Omod(_1008712, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008712), _1008714), _1008716), _1008714) = c_Divides_Odiv__class_Omod(_1008712, _1008716, _1008714))], (29105 ^ _779571) ^ [_1298876, _1298878] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298876, 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(_1298876, tc_HOL_Obool)), tc_fun(_1298876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1298876, tc_HOL_Obool)), tc_fun(_1298876, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298876, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1298878)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298876, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1298878))], (46598 ^ _779571) ^ [_1701418, _1701420, _1701422, _1701424, _1701426] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701418)), _1701420) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701422)), _1701424), 46601 ^ _779571 : [(46610 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1701418, _1701422), _1701420), _1701424) = _1701426), hAPP(hAPP(c_List_Omap(tc_prod(_1701418, _1701422), _1701418), c_Product__Type_Ofst(_1701418, _1701422)), _1701426) = _1701420, hAPP(hAPP(c_List_Omap(tc_prod(_1701418, _1701422), _1701422), c_Product__Type_Osnd(_1701418, _1701422)), _1701426) = _1701424], (46602 ^ _779571) ^ [] : [hAPP(hAPP(c_List_Ozip(_1701418, _1701422), _1701420), _1701424) = _1701426, 46605 ^ _779571 : [(46608 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701418, _1701422), _1701422), c_Product__Type_Osnd(_1701418, _1701422)), _1701426) = _1701424)], (46606 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701418, _1701422), _1701418), c_Product__Type_Ofst(_1701418, _1701422)), _1701426) = _1701420)]]]]], (51277 ^ _779571) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11060 ^ _779571) ^ [_963053, _963055, _963057, _963059] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_963053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963053), _963055), _963057)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963053), _963059), _963057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963053), _963055), _963059)))], (16349 ^ _779571) ^ [_1059185, _1059187, _1059189] : [class_Rings_Oring__1(_1059185), -(hAPP(c_Int_Oring__1__class_Oof__int(_1059185), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059187), _1059189)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1059185), hAPP(c_Int_Oring__1__class_Oof__int(_1059185), _1059187)), _1059189))], (22740 ^ _779571) ^ [_1173654, _1173656] : [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), _1173654), _1173656))), 22743 ^ _779571 : [(22752 ^ _779571) ^ [] : [-(c_Divides_OnegDivAlg(_1173654, _1173656) = hAPP(c_Divides_Oadjust(_1173656), c_Divides_OnegDivAlg(_1173654, 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)))), _1173656)))), -(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), _1173654), _1173656)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1173656), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22744 ^ _779571) ^ [] : [22745 ^ _779571 : [(22748 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1173656), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22746 ^ _779571) ^ [] : [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), _1173654), _1173656)))]], -(c_Divides_OnegDivAlg(_1173654, _1173656) = 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), _1173654), _1173656)))]]], (18587 ^ _779571) ^ [_1098381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1098381)), -(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), _1098381))))], (49751 ^ _779571) ^ [_1779008, _1779010, _1779012, _1779014, _1779016, _1779018] : [class_Orderings_Olinorder(_1779008), -(hBOOL(hAPP(_1779010, _1779012))), -(hAPP(c_List_Ofilter(_1779014, _1779010), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1779014, _1779008, _1779016), _1779012), _1779018)) = hAPP(c_List_Ofilter(_1779014, _1779010), _1779018))], (41776 ^ _779571) ^ [_1586926, _1586928, _1586930] : [c_Wellfounded_Owf(_1586926, _1586928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586926, _1586926), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1586926, _1586926, _1586926), _1586928), _1586930)), _1586928)), -(c_FunDef_Oreduction__pair(_1586926, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1586926, _1586926), tc_HOL_Obool), tc_fun(tc_prod(_1586926, _1586926), tc_HOL_Obool)), _1586928), _1586930)))], (8092 ^ _779571) ^ [_913701, _913703] : [class_Rings_Olinordered__semidom(_913701), 8095 ^ _779571 : [(8102 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _913703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913701), c_Groups_Ozero__class_Ozero(_913701)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913701), _913703))))], (8096 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913701), c_Groups_Ozero__class_Ozero(_913701)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_913701), _913703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _913703)))]]], (3010 ^ _779571) ^ [_825602, _825604, _825606, _825608, _825610, _825612, _825614, _825616] : [-(c_New__DSequence_Oneg__bind(_825616, _825612, _825608, _825604) = c_New__DSequence_Oneg__bind(_825614, _825610, _825606, _825602)), _825616 = _825614, _825612 = _825610, _825608 = _825606, _825604 = _825602], (19431 ^ _779571) ^ [_1112866, _1112868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1112866)), c_Int_OBit0(_1112868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112866), _1112868)))], (21865 ^ _779571) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (1824 ^ _779571) ^ [_805201, _805203, _805205, _805207] : [-(v_P(_805205, _805201)), v_P(_805207, _805203), _805207 = _805205, _805203 = _805201], (6173 ^ _779571) ^ [_879394, _879396, _879398, _879400, _879402, _879404, _879406, _879408, _879410, _879412, _879414, _879416] : [-(c_Com_Ocom_Ocom__rec(_879394, _879396, _879398, _879400, _879402, _879404, _879406, _879408, _879410, c_Com_Ocom_OCond(_879412, _879414, _879416)) = hAPP(hAPP(hAPP(hAPP(hAPP(_879404, _879412), _879414), _879416), c_Com_Ocom_Ocom__rec(_879394, _879396, _879398, _879400, _879402, _879404, _879406, _879408, _879410, _879414)), c_Com_Ocom_Ocom__rec(_879394, _879396, _879398, _879400, _879402, _879404, _879406, _879408, _879410, _879416)))], (25288 ^ _779571) ^ [_1222829, _1222831] : [_1222829 = _1222831, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222829), _1222831)))], (26244 ^ _779571) ^ [_1240516, _1240518, _1240520, _1240522] : [class_Rings_Ocomm__semiring__1(_1240516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240518), _1240520)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240516), hAPP(hAPP(c_Power_Opower__class_Opower(_1240516), _1240522), _1240518)), hAPP(hAPP(c_Power_Opower__class_Opower(_1240516), _1240522), _1240520))))], (18325 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (5966 ^ _779571) ^ [_875460, _875462, _875464, _875466, _875468, _875470] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_875460, _875462, _875464), _875466, _875468, _875470), 5971 ^ _779571 : [(5974 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_875462, _875466, _875468, _875470))], (5972 ^ _779571) ^ [] : [-(hBOOL(hAPP(_875460, _875466)))]], 5975 ^ _779571 : [(5978 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_875464, _875466, _875468, _875470))], (5976 ^ _779571) ^ [] : [hBOOL(hAPP(_875460, _875466))]]], (49052 ^ _779571) ^ [_1763654, _1763656, _1763658] : [-(hAPP(c_List_Orotate(_1763654, hAPP(c_Nat_OSuc, _1763656)), _1763658) = hAPP(c_List_Orotate1(_1763654), hAPP(c_List_Orotate(_1763654, _1763656), _1763658)))], (19715 ^ _779571) ^ [] : [-(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))))], (19221 ^ _779571) ^ [_1109194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109194), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1109194)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24657 ^ _779571) ^ [_1210174] : [-(c_Nitpick_Ozero__frac(_1210174) = c_Nitpick_OAbs__Frac(_1210174, 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))))], (51663 ^ _779571) ^ [_1814320, _1814322] : [hBOOL(hAPP(hAPP(c_fimplies, _1814320), _1814322)), hBOOL(_1814320), -(hBOOL(_1814322))], (27952 ^ _779571) ^ [_1274580] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1274580) = c_Orderings_Oord__class_Omax(_1274580)), class_Lattices_Osemilattice__sup(_1274580), class_Orderings_Olinorder(_1274580)], (12676 ^ _779571) ^ [_991435, _991437, _991439, _991441] : [class_Rings_Olinordered__semiring__strict(_991435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991435), _991437), _991439)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991435), _991441), _991439))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991435), c_Groups_Ozero__class_Ozero(_991435)), _991439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991435), _991437), _991441)))], (23255 ^ _779571) ^ [_1183514, _1183516, _1183518, _1183520, _1183522, _1183524] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183514, _1183516), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183518), _1183520))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183514, _1183516), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183522), _1183524))), -(_1183516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1183518 = _1183522)], (2376 ^ _779571) ^ [_815441, _815443, _815445, _815447, _815449, _815451] : [-(c_Random_Ominus__shift(_815451, _815447, _815443) = c_Random_Ominus__shift(_815449, _815445, _815441)), _815451 = _815449, _815447 = _815445, _815443 = _815441], (2490 ^ _779571) ^ [_817254, _817256] : [_817256 = _817254, -(c_Natural_Oevalc(_817256) = c_Natural_Oevalc(_817254))], (31041 ^ _779571) ^ [_1338484, _1338486] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338484), c_Orderings_Otop__class_Otop(tc_fun(_1338484, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338486), c_Orderings_Otop__class_Otop(tc_fun(_1338486, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1338484, _1338486)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1338484, _1338486), tc_HOL_Obool)))))], (12958 ^ _779571) ^ [_996631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _996631)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_996631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11186 ^ _779571) ^ [_965223, _965225, _965227] : [11187 ^ _779571 : [(11190 ^ _779571) ^ [] : [_965225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11188 ^ _779571) ^ [] : [_965223 = _965227]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965223), _965225) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965227), _965225))], (47695 ^ _779571) ^ [_1730449, _1730451, _1730453, _1730455, _1730457, _1730459, _1730461] : [-(hAPP(hAPP(c_List_Ozip(_1730449, _1730451), hAPP(hAPP(c_List_Olist__update(_1730449, _1730453), _1730455), _1730457)), hAPP(hAPP(c_List_Olist__update(_1730451, _1730459), _1730455), _1730461)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1730449, _1730451), hAPP(hAPP(c_List_Ozip(_1730449, _1730451), _1730453), _1730459)), _1730455), hAPP(hAPP(c_Product__Type_OPair(_1730449, _1730451), _1730457), _1730461)))], (18483 ^ _779571) ^ [_1096755, _1096757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096755)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096755), _1096757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096755), c_Int_OPls)))], (41929 ^ _779571) ^ [_1589907, _1589909] : [c_Wellfounded_Owf(_1589907, _1589909), -(c_Wellfounded_Owf(tc_fun(_1589907, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1589907, _1589909)))], (34114 ^ _779571) ^ [_1403265, _1403267, _1403269, _1403271] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1403265), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403267, tc_Int_Oint), _1403269), _1403271)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403267, _1403265), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1403265, _1403267), c_Int_Oring__1__class_Oof__int(_1403265)), _1403269)), _1403271)), class_Groups_Ocomm__monoid__mult(_1403265), class_Rings_Oring__1(_1403265)], (36884 ^ _779571) ^ [_1466415, _1466417, _1466419, _1466421] : [class_Orderings_Oorder(_1466415), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466415, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1466415, _1466417, _1466419)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1466415, _1466419, _1466421)) = c_Orderings_Obot__class_Obot(tc_fun(_1466415, tc_HOL_Obool)))], (11671 ^ _779571) ^ [_973559, _973561, _973563] : [class_Groups_Oordered__comm__monoid__add(_973559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973559), c_Groups_Ozero__class_Ozero(_973559)), _973561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973559), c_Groups_Ozero__class_Ozero(_973559)), _973563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973559), c_Groups_Ozero__class_Ozero(_973559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973559), _973561), _973563))))], (46783 ^ _779571) ^ [_1707796, _1707798, _1707800, _1707802] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707796), tc_List_Olist(_1707796))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707796), tc_List_Olist(_1707796)), _1707800), _1707802)), c_List_Olistrel(_1707796, _1707798))), -(c_List_Olistrelp(_1707796, hAPP(hAPP(c_COMBC(_1707796, tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_fun(_1707796, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707796, tc_fun(tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_fun(_1707796, tc_HOL_Obool)), _1707796), c_COMBC(_1707796, tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707796, tc_prod(_1707796, _1707796)), tc_fun(_1707796, tc_fun(tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_HOL_Obool)), _1707796), hAPP(c_COMBB(tc_prod(_1707796, _1707796), tc_fun(tc_fun(tc_prod(_1707796, _1707796), tc_HOL_Obool), tc_HOL_Obool), _1707796), c_member(tc_prod(_1707796, _1707796)))), c_Product__Type_OPair(_1707796, _1707796)))), _1707798), _1707800, _1707802))], (43895 ^ _779571) ^ [_1637907, _1637909, _1637911, _1637913] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1637907, _1637909, _1637911), _1637913), c_Orderings_Obot__class_Obot(tc_fun(_1637907, tc_HOL_Obool))) = _1637913)], (8076 ^ _779571) ^ [_913471, _913473] : [c_Option_Ois__none(_913471, hAPP(c_Option_Ooption_OSome(_913471), _913473))], (19205 ^ _779571) ^ [_1108902, _1108904] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1108902)), _1108904) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1108902), _1108904)))], (34799 ^ _779571) ^ [_1417481, _1417483, _1417485, _1417487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1417481), _1417483)), 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)), _1417485), _1417481)), 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)), _1417487), _1417483)), 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)), _1417485), _1417487)), _1417483)), c_FunDef_Omax__weak)))], (34833 ^ _779571) ^ [_1418138] : [-(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)), _1418138), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (46809 ^ _779571) ^ [_1708851, _1708853, _1708855] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1708851, tc_HOL_Obool)), hAPP(c_List_Oset(_1708851), _1708853)), hAPP(c_List_Oset(_1708851), hAPP(hAPP(c_List_Olist_OCons(_1708851), _1708855), _1708853)))))], (38211 ^ _779571) ^ [_1496855, _1496857, _1496859, _1496861, _1496863, _1496865] : [c_Finite__Set_Ofolding__idem(_1496855, _1496857, _1496859, _1496861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496855), _1496863)), -(hAPP(_1496861, hAPP(hAPP(c_Set_Oinsert(_1496855), _1496865), _1496863)) = hAPP(c_Fun_Ocomp(_1496857, _1496857, _1496857, hAPP(_1496861, _1496863)), hAPP(_1496859, _1496865)))], (7294 ^ _779571) ^ [_900378, _900380, _900382, _900384] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _900378), _900380, hAPP(c_Nat_OSuc, _900382), _900384), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900378)), _900380, _900382, _900384))], (17881 ^ _779571) ^ [_1087273, _1087275] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087273) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087275)), 17884 ^ _779571 : [(17887 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087275)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17885 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087273))))]], 17888 ^ _779571 : [(17891 ^ _779571) ^ [] : [17892 ^ _779571 : [(17895 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087273) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17893 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087275))))]], 17896 ^ _779571 : [(17899 ^ _779571) ^ [] : [_1087273 = _1087275], (17897 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087275)))]]], (17889 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087273)))]]], (51251 ^ _779571) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (22608 ^ _779571) ^ [_1170833] : [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), _1170833))), 22611 ^ _779571 : [(22618 ^ _779571) ^ [] : [-(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), _1170833)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170833)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170833)), 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), _1170833)))))], (22612 ^ _779571) ^ [] : [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), _1170833))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170833)) = 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)))]]], (23797 ^ _779571) ^ [_1193103, _1193105, _1193107] : [class_Orderings_Olinorder(_1193103), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193103), _1193105), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193103), _1193105), _1193107)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193103), _1193105), _1193107))], (28473 ^ _779571) ^ [_1285242, _1285244, _1285246] : [class_Orderings_Olinorder(_1285242), 28476 ^ _779571 : [(28483 ^ _779571) ^ [] : [_1285244 = _1285246, -(hAPP(c_SetInterval_Oord__class_OatMost(_1285242), _1285244) = hAPP(c_SetInterval_Oord__class_OatMost(_1285242), _1285246))], (28477 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1285242), _1285244) = hAPP(c_SetInterval_Oord__class_OatMost(_1285242), _1285246), -(_1285244 = _1285246)]]], (46037 ^ _779571) ^ [_1688196, _1688198, _1688200, _1688202, _1688204, _1688206] : [-(hAPP(hAPP(c_Option_Omap(_1688196, _1688198), _1688200), hAPP(hAPP(c_Option_Omap(_1688202, _1688196), _1688204), _1688206)) = hAPP(hAPP(c_Option_Omap(_1688202, _1688198), hAPP(c_Fun_Ocomp(_1688196, _1688198, _1688202, _1688200), _1688204)), _1688206))], (41688 ^ _779571) ^ [_1582840, _1582842, _1582844, _1582846, _1582848, _1582850, _1582852, _1582854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582840, _1582842)), hAPP(hAPP(c_Product__Type_OPair(_1582840, _1582842), _1582844), _1582846)), _1582848)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582842, _1582850)), hAPP(hAPP(c_Product__Type_OPair(_1582842, _1582850), _1582846), _1582852)), _1582854)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582840, _1582850)), hAPP(hAPP(c_Product__Type_OPair(_1582840, _1582850), _1582844), _1582852)), hAPP(hAPP(c_Relation_Orel__comp(_1582840, _1582842, _1582850), _1582848), _1582854))))], (37202 ^ _779571) ^ [_1473820, _1473822, _1473824, _1473826] : [37204 ^ _779571 : [(37207 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1473820, _1473820, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1473820, tc_fun(_1473820, _1473822), tc_fun(_1473820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473822, tc_HOL_Obool), tc_fun(tc_fun(_1473820, _1473822), tc_fun(_1473820, tc_HOL_Obool)), _1473820), c_COMBB(_1473822, tc_HOL_Obool, _1473820)), hAPP(hAPP(c_COMBB(_1473822, tc_fun(_1473822, tc_HOL_Obool), _1473820), c_fequal), _1473826))), _1473826)), 37203 ^ [_1473820, _1473822, _1473824, _1473826]))], (37205 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473820, _1473820)), 37203 ^ [_1473820, _1473822, _1473824, _1473826]), _1473824)))]], -(c_Equiv__Relations_Ocongruent(_1473820, _1473822, _1473824, _1473826))], (24815 ^ _779571) ^ [_1213333, _1213335, _1213337, _1213339, _1213341] : [-(_1213333 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1213335, _1213337, _1213339, _1213341), _1213333) = c_Lazy__Sequence_Obind(_1213335, _1213337, hAPP(_1213339, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1213333), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1213335, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1213337)), _1213341), _1213333)))], (22270 ^ _779571) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (18369 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (12281 ^ _779571) ^ [_984611, _984613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984611), _984613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984611)), _984613)))], (51673 ^ _779571) ^ [_1814459] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _1814459), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, v_n, _1814459))], (29120 ^ _779571) ^ [_1299466, _1299468, _1299470] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299466), _1299468))), 29123 ^ _779571 : [(29130 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299470), _1299468))), -(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)), _1299466)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299470), _1299468)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29124 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299470), _1299468)), -(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)), _1299466)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299470), _1299468)) = 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))))]]], (24759 ^ _779571) ^ [_1212010, _1212012, _1212014, _1212016, _1212018] : [_1212010 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1212012, _1212014, _1212010, _1212016), _1212018) = hAPP(c_Product__Type_OPair(_1212012, _1212014), _1212018))], (10351 ^ _779571) ^ [_952022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952022), _952022)))], (40766 ^ _779571) ^ [_1554205, _1554207] : [class_Groups_Oab__semigroup__mult(_1554205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554205), _1554207)), -(_1554207 = c_Orderings_Obot__class_Obot(tc_fun(_1554205, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1554205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1554205), 40779 ^ [_1554205, _1554207]), 40780 ^ [_1554205, _1554207])), hAPP(hAPP(c_Set_Oinsert(_1554205), 40779 ^ [_1554205, _1554207]), hAPP(hAPP(c_Set_Oinsert(_1554205), 40780 ^ [_1554205, _1554207]), c_Orderings_Obot__class_Obot(tc_fun(_1554205, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1554205), hAPP(c_Finite__Set_Ofold1(_1554205, c_Groups_Otimes__class_Otimes(_1554205)), _1554207)), _1554207)))], (33407 ^ _779571) ^ [_1388553, _1388555, _1388557] : [class_Orderings_Olinorder(_1388553), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388553), _1388555)), 33414 ^ _779571 : [(33421 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388553, tc_HOL_Obool)), _1388555), hAPP(hAPP(c_Set_Oinsert(_1388553), _1388557), c_Orderings_Obot__class_Obot(tc_fun(_1388553, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1388553, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1388553, hAPP(hAPP(c_Set_Oinsert(_1388553), _1388557), _1388555)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388553), _1388557), c_Big__Operators_Olinorder__class_OMin(_1388553, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388553, tc_HOL_Obool)), _1388555), hAPP(hAPP(c_Set_Oinsert(_1388553), _1388557), c_Orderings_Obot__class_Obot(tc_fun(_1388553, tc_HOL_Obool)))))))], (33415 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388553, tc_HOL_Obool)), _1388555), hAPP(hAPP(c_Set_Oinsert(_1388553), _1388557), c_Orderings_Obot__class_Obot(tc_fun(_1388553, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1388553, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1388553, hAPP(hAPP(c_Set_Oinsert(_1388553), _1388557), _1388555)) = _1388557)]]], (46534 ^ _779571) ^ [_1700089, _1700091] : [hAPP(c_Finite__Set_Ocard(_1700089), hAPP(c_List_Oset(_1700089), _1700091)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700089)), _1700091), -(hBOOL(hAPP(c_List_Odistinct(_1700089), _1700091)))], (24581 ^ _779571) ^ [_1208534, _1208536, _1208538, _1208540, _1208542] : [-(hAPP(c_Product__Type_Ofst(_1208534, _1208536), hAPP(c_Product__Type_Oapfst(_1208538, _1208534, _1208536, _1208540), _1208542)) = hAPP(_1208540, hAPP(c_Product__Type_Ofst(_1208538, _1208536), _1208542)))], (46797 ^ _779571) ^ [_1708606, _1708608, _1708610, _1708612] : [hBOOL(hAPP(hAPP(c_member(_1708606), _1708608), hAPP(c_List_Oset(_1708606), hAPP(hAPP(c_List_Olist_OCons(_1708606), _1708610), _1708612)))), -(_1708608 = _1708610), -(hBOOL(hAPP(hAPP(c_member(_1708606), _1708608), hAPP(c_List_Oset(_1708606), _1708612))))], (23791 ^ _779571) ^ [_1192978, _1192980, _1192982] : [class_Orderings_Olinorder(_1192978), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192978), _1192980), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192978), _1192980), _1192982)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192978), _1192980), _1192982))], (9054 ^ _779571) ^ [_929652] : [class_Rings_Oring__1(_929652), -(hAPP(c_Int_Oring__1__class_Oof__int(_929652), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_929652))], (44940 ^ _779571) ^ [_1662806, _1662808, _1662810, _1662812] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1662806, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662808, tc_fun(_1662806, tc_HOL_Obool), _1662810), _1662812)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662808, tc_fun(_1662806, tc_HOL_Obool)), _1662812), _1662810))], (30397 ^ _779571) ^ [_1324752, _1324754, _1324756, _1324758] : [_1324752 = _1324754, 30400 ^ _779571 : [(30407 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324756), _1324754), _1324758)), -(hBOOL(hAPP(hAPP(c_member(_1324756), _1324752), _1324758)))], (30401 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324756), _1324752), _1324758)), -(hBOOL(hAPP(hAPP(c_member(_1324756), _1324754), _1324758)))]]], (7776 ^ _779571) ^ [_908406, _908408, _908410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908406), _908408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908408), _908410))))], (14838 ^ _779571) ^ [_1029689, _1029691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029691, _1029689)), _1029689)))], (41752 ^ _779571) ^ [_1584902, _1584904, _1584906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584902, _1584902), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584902, _1584902, _1584902), _1584904), _1584906)), _1584904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1584902, _1584904)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1584902, _1584906)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1584902, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1584902, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1584902, tc_HOL_Obool), tc_fun(_1584902, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1584902, _1584904))))], (6277 ^ _779571) ^ [_881428, _881430, _881432] : [hBOOL(hAPP(c_Com_OWT, _881428)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_881430, _881432, _881428))))], (33455 ^ _779571) ^ [_1389423, _1389425] : [class_Orderings_Olinorder(_1389423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389423), _1389425)), -(_1389425 = c_Orderings_Obot__class_Obot(tc_fun(_1389423, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1389423), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1389423), 33468 ^ [_1389423, _1389425]), 33469 ^ [_1389423, _1389425])), hAPP(hAPP(c_Set_Oinsert(_1389423), 33468 ^ [_1389423, _1389425]), hAPP(hAPP(c_Set_Oinsert(_1389423), 33469 ^ [_1389423, _1389425]), c_Orderings_Obot__class_Obot(tc_fun(_1389423, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1389423), c_Big__Operators_Olinorder__class_OMin(_1389423, _1389425)), _1389425)))], (51331 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11463 ^ _779571) ^ [_969930, _969932, _969934, _969936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969930), _969932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969934), _969936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969930), _969934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969932), _969936))))], (42954 ^ _779571) ^ [_1613897, _1613899, _1613901, _1613903] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1613897, tc_fun(_1613897, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1613897, tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_fun(_1613897, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613897, tc_fun(tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_fun(_1613897, tc_HOL_Obool)), _1613897), c_COMBC(_1613897, tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613897, tc_prod(_1613897, _1613897)), tc_fun(_1613897, tc_fun(tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_HOL_Obool)), _1613897), hAPP(c_COMBB(tc_prod(_1613897, _1613897), tc_fun(tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool), tc_HOL_Obool), _1613897), c_member(tc_prod(_1613897, _1613897)))), c_Product__Type_OPair(_1613897, _1613897)))), _1613899)), c_fequal), _1613901), _1613903)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613897, _1613897)), hAPP(hAPP(c_Product__Type_OPair(_1613897, _1613897), _1613901), _1613903)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1613897, _1613897), tc_HOL_Obool)), _1613899), c_Relation_OId(_1613897)))))], (33335 ^ _779571) ^ [_1387445, _1387447, _1387449] : [class_Orderings_Olinorder(_1387445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387445), _1387447)), -(_1387447 = c_Orderings_Obot__class_Obot(tc_fun(_1387445, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1387445, hAPP(hAPP(c_Set_Oinsert(_1387445), _1387449), _1387447)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387445), _1387449), c_Big__Operators_Olinorder__class_OMin(_1387445, _1387447)))], (30682 ^ _779571) ^ [_1330754, _1330756, _1330758] : [class_Orderings_Oord(_1330754), 30685 ^ _779571 : [(30692 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330754), _1330758), _1330756)), -(hBOOL(hAPP(hAPP(c_member(_1330754), _1330756), hAPP(c_SetInterval_Oord__class_OatLeast(_1330754), _1330758))))], (30686 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330754), _1330756), hAPP(c_SetInterval_Oord__class_OatLeast(_1330754), _1330758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330754), _1330758), _1330756)))]]], (19443 ^ _779571) ^ [_1113089, _1113091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1113089)), c_Int_OBit0(_1113091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113089), _1113091)))], (16569 ^ _779571) ^ [_1063044, _1063046] : [class_Groups_Oordered__ab__group__add__abs(_1063044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063044), c_Groups_Ozero__class_Ozero(_1063044)), _1063046)), -(hAPP(c_Groups_Oabs__class_Oabs(_1063044), _1063046) = _1063046)], (12311 ^ _779571) ^ [_985148, _985150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985148), _985150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985148)), _985150)))], (15852 ^ _779571) ^ [_1048937, _1048939, _1048941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048941), _1048939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048937), _1048939)), _1048941)))], (48160 ^ _779571) ^ [_1741004, _1741006, _1741008, _1741010] : [hBOOL(hAPP(hAPP(c_member(_1741004), _1741006), hAPP(c_List_Oset(_1741004), _1741008))), -(c_List_Oremove1(_1741004, _1741006, hAPP(hAPP(c_List_Oappend(_1741004), _1741008), _1741010)) = hAPP(hAPP(c_List_Oappend(_1741004), c_List_Oremove1(_1741004, _1741006, _1741008)), _1741010))], (50788 ^ _779571) ^ [_1800659, _1800661, _1800663] : [-(hAPP(c_List_Orotate(_1800659, _1800661), hAPP(c_List_Orev(_1800659), _1800663)) = hAPP(c_List_Orev(_1800659), hAPP(c_List_Orotate(_1800659, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800659)), _1800663)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1800661, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800659)), _1800663)))), _1800663)))], (51355 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (19561 ^ _779571) ^ [_1115117] : [-(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)))), _1115117) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1115117)))], (49150 ^ _779571) ^ [_1765834, _1765836] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765834), _1765836) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49153 ^ _779571 : [(49156 ^ _779571) ^ [_1765948] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1765948), hAPP(c_List_Oset(tc_Nat_Onat), _1765836))), -(_1765948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49154 ^ _779571) ^ [] : [-(_1765834 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49020 ^ _779571) ^ [_1763044, _1763046, _1763048] : [hBOOL(hAPP(c_List_Odistinct(_1763044), hAPP(c_List_Orotate(_1763044, _1763046), _1763048))), -(hBOOL(hAPP(c_List_Odistinct(_1763044), _1763048)))], (36734 ^ _779571) ^ [_1462801, _1462803, _1462805, _1462807] : [hBOOL(hAPP(hAPP(c_member(_1462801), _1462803), _1462805)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462801, tc_HOL_Obool)), _1462805), hAPP(hAPP(c_Set_Oinsert(_1462801), _1462803), _1462807)) = hAPP(hAPP(c_Set_Oinsert(_1462801), _1462803), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462801, tc_HOL_Obool)), _1462805), _1462807)))], (14373 ^ _779571) ^ [_1022142, _1022144] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022142)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022144)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022142), _1022144))], (6813 ^ _779571) ^ [_891781] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _891781)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23767 ^ _779571) ^ [_1192406, _1192408, _1192410, _1192412] : [class_Orderings_Olinorder(_1192406), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192406), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192406), _1192408), _1192410)), _1192412) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192406), _1192408), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192406), _1192410), _1192412)))], (51301 ^ _779571) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (45139 ^ _779571) ^ [_1667478, _1667480, _1667482] : [-(hAPP(c_Relation_ORange(_1667478, _1667480), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1667478, _1667480), tc_HOL_Obool), _1667482)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1667478, _1667480), tc_HOL_Obool), tc_fun(_1667480, tc_HOL_Obool)), _1667482), c_Relation_ORange(_1667478, _1667480)))], (22364 ^ _779571) ^ [_1165662, _1165664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1165662)), hAPP(c_Code__Numeral_Oof__nat, _1165664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1165662), _1165664)))], (17537 ^ _779571) ^ [_1081307, _1081309, _1081311, _1081313] : [class_Rings_Olinordered__semidom(_1081307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081307), hAPP(hAPP(c_Power_Opower__class_Opower(_1081307), _1081309), _1081311)), hAPP(hAPP(c_Power_Opower__class_Opower(_1081307), _1081313), _1081311))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081307), c_Groups_Ozero__class_Ozero(_1081307)), _1081313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081307), _1081309), _1081313)))], (36680 ^ _779571) ^ [_1461642, _1461644, _1461646] : [class_Lattices_Oboolean__algebra(_1461642), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1461642), _1461644), _1461646) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461642), _1461644), hAPP(c_Groups_Ouminus__class_Ouminus(_1461642), _1461646)))], (42239 ^ _779571) ^ [_1597127, _1597129] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1597127, _1597129), 42240 ^ [_1597127, _1597129])), -(c_Wellfounded_OwfP(_1597127, _1597129))], (29810 ^ _779571) ^ [_1312612, _1312614, _1312616] : [class_Orderings_Olinorder(_1312612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312612), _1312614), _1312616)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312612, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1312612, _1312614), _1312616)), hAPP(hAPP(c_Set_Oinsert(_1312612), _1312616), c_Orderings_Obot__class_Obot(tc_fun(_1312612, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1312612, _1312614, _1312616))], (29530 ^ _779571) ^ [_1307315, _1307317] : [class_Orderings_Oorder(_1307315), -(c_SetInterval_Oord__class_OatLeastAtMost(_1307315, _1307317, _1307317) = hAPP(hAPP(c_Set_Oinsert(_1307315), _1307317), c_Orderings_Obot__class_Obot(tc_fun(_1307315, tc_HOL_Obool))))], (49775 ^ _779571) ^ [_1779364, _1779366, _1779368, _1779370] : [-(hAPP(c_List_Ofilter(_1779364, _1779366), hAPP(c_List_Ofilter(_1779364, _1779368), _1779370)) = hAPP(c_List_Ofilter(_1779364, hAPP(hAPP(c_COMBS(_1779364, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1779364), c_fconj), _1779368)), _1779366)), _1779370))], (6103 ^ _779571) ^ [_878002, _878004, _878006, _878008, _878010] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_878002, _878004), _878006, _878008, _878010), 6107 ^ _779571 : [(6110 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_878004, 6106 ^ [_878002, _878004, _878006, _878008, _878010], _878008, _878010))], (6108 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_878002, _878006, _878008, 6106 ^ [_878002, _878004, _878006, _878008, _878010]))]]], (27718 ^ _779571) ^ [_1270232] : [c_Nat__Transfer_Onat__set(_1270232), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1270232) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1270232)))], (23415 ^ _779571) ^ [_1186111, _1186113] : [-(c_Divides_Odivmod__nat(_1186113, _1186111) = 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), _1186113), _1186111), _1186111))), -(_1186111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186113), _1186111)))], (32039 ^ _779571) ^ [_1362287, _1362289, _1362291, _1362293] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362287, _1362287)), hAPP(hAPP(c_Product__Type_OPair(_1362287, _1362287), _1362289), _1362291)), hAPP(c_Wellfounded_Omeasure(_1362287), _1362293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1362293, _1362289)), hAPP(_1362293, _1362291))))], (1442 ^ _779571) ^ [_800364, _800366] : [-(class_Groups_Ocancel__ab__semigroup__add(_800364)), _800366 = _800364, class_Groups_Ocancel__ab__semigroup__add(_800366)], (7308 ^ _779571) ^ [_900644, _900646, _900648, _900650, _900652, _900654] : [-(c_Nitpick_Opair__box_Opair__box__rec(_900644, _900646, _900648, _900650, c_Nitpick_Opair__box_OPairBox(_900644, _900646, _900652, _900654)) = hAPP(hAPP(_900650, _900652), _900654))], (24807 ^ _779571) ^ [] : [-(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)))], (9940 ^ _779571) ^ [_945122, _945124] : [9941 ^ _779571 : [(9944 ^ _779571) ^ [] : [_945122 = _945124], (9942 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945122), _945124))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _945124), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42548 ^ _779571) ^ [_1604523, _1604525] : [-(c_Hilbert__Choice_OEps(_1604523, hAPP(c_fequal, _1604525)) = _1604525)], (51397 ^ _779571) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (48790 ^ _779571) ^ [_1757906, _1757908] : [-(hAPP(hAPP(c_List_Odrop(_1757906), _1757908), c_List_Olist_ONil(_1757906)) = c_List_Olist_ONil(_1757906))], (49201 ^ _779571) ^ [_1766806, _1766808, _1766810] : [class_Lattices_Olattice(_1766806), -(c_Big__Operators_Olattice__class_OInf__fin(_1766806, hAPP(c_List_Oset(_1766806), hAPP(hAPP(c_List_Olist_OCons(_1766806), _1766808), _1766810))) = hAPP(c_List_Ofoldl(_1766806, _1766806, c_Lattices_Osemilattice__inf__class_Oinf(_1766806), _1766808), _1766810))], (18723 ^ _779571) ^ [_1100839, _1100841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100839), _1100841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100839)), c_Int_OBit1(_1100841))))], (14574 ^ _779571) ^ [_1025369, _1025371, _1025373, _1025375] : [class_Divides_Osemiring__div(_1025369), 14577 ^ _779571 : [(14584 ^ _779571) ^ [] : [-(_1025371 = c_Groups_Ozero__class_Ozero(_1025369)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025369), _1025371), _1025373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025369), _1025371), _1025375)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025369), _1025373), _1025375))], (14578 ^ _779571) ^ [] : [_1025371 = c_Groups_Ozero__class_Ozero(_1025369), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025369), _1025371), _1025373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025369), _1025371), _1025375)) = c_Groups_Ozero__class_Ozero(_1025369))]]], (6065 ^ _779571) ^ [_877317, _877319, _877321, _877323, _877325, _877327] : [-(c_Com_Ocom_OCond(_877317, _877319, _877321) = c_Com_Ocom_OCond(_877323, _877325, _877327)), _877317 = _877323, _877319 = _877325, _877321 = _877327], (40098 ^ _779571) ^ [_1538524, _1538526, _1538528] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538524, _1538526), c_Orderings_Obot__class_Obot(tc_fun(_1538524, tc_HOL_Obool))), _1538528) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1538524, _1538526), tc_HOL_Obool)))], (16042 ^ _779571) ^ [_1053178, _1053180, _1053182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053178), _1053180)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053182), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053180), _1053178))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053182), _1053178)), hAPP(c_Nat_OSuc, _1053180)))], (14696 ^ _779571) ^ [_1027357, _1027359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027357)), 14699 ^ _779571 : [(14706 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027357), _1027359)), -(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), _1027359), _1027357))))], (14700 ^ _779571) ^ [] : [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), _1027359), _1027357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027357), _1027359)))]]], (46144 ^ _779571) ^ [_1690724, _1690726, _1690728] : [-(c_Map_Odom(_1690724, _1690726, c_Map_Omap__of(_1690724, _1690726, _1690728)) = hAPP(c_Set_Oimage(tc_prod(_1690724, _1690726), _1690724, c_Product__Type_Ofst(_1690724, _1690726)), hAPP(c_List_Oset(tc_prod(_1690724, _1690726)), _1690728)))], (44540 ^ _779571) ^ [_1652278, _1652280, _1652282, _1652284] : [44542 ^ _779571 : [(44545 ^ _779571) ^ [] : [hAPP(_1652284, 44541 ^ [_1652278, _1652280, _1652282, _1652284]) = c_Orderings_Otop__class_Otop(tc_fun(_1652278, tc_HOL_Obool))], (44543 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652280), 44541 ^ [_1652278, _1652280, _1652282, _1652284]), _1652282)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1652278, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652280, tc_fun(_1652278, tc_HOL_Obool)), _1652282), _1652284))], (11981 ^ _779571) ^ [_979264, _979266, _979268] : [class_Rings_Olinordered__ring__strict(_979264), 11984 ^ _779571 : [(11999 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979264), _979266), _979268)), c_Groups_Ozero__class_Ozero(_979264)))), 12000 ^ _779571 : [(12007 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), _979266), c_Groups_Ozero__class_Ozero(_979264))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), c_Groups_Ozero__class_Ozero(_979264)), _979268))], (12001 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), c_Groups_Ozero__class_Ozero(_979264)), _979266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), _979268), c_Groups_Ozero__class_Ozero(_979264)))]]], (11985 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979264), _979266), _979268)), c_Groups_Ozero__class_Ozero(_979264))), 11990 ^ _779571 : [(11993 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), _979268), c_Groups_Ozero__class_Ozero(_979264))))], (11991 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), c_Groups_Ozero__class_Ozero(_979264)), _979266)))]], 11994 ^ _779571 : [(11997 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), c_Groups_Ozero__class_Ozero(_979264)), _979268)))], (11995 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979264), _979266), c_Groups_Ozero__class_Ozero(_979264))))]]]]], (16507 ^ _779571) ^ [_1062006, _1062008, _1062010] : [-(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, _1062006, _1062008)), _1062010), _1062008) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1062006), _1062010), _1062008))], (24697 ^ _779571) ^ [_1210836, _1210838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210836)), hAPP(c_Code__Numeral_Onat__of, _1210838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1210836), _1210838)))], (39020 ^ _779571) ^ [_1513796, _1513798, _1513800] : [-(c_Fun_Oinj__on(_1513796, tc_sum(_1513798, _1513796), c_Sum__Type_OInr(_1513796, _1513798), _1513800))], (29360 ^ _779571) ^ [_1304531, _1304533, _1304535] : [class_Lattices_Obounded__lattice__bot(_1304531), 29363 ^ _779571 : [(29372 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1304531), _1304533), _1304535) = c_Orderings_Obot__class_Obot(_1304531)), _1304533 = c_Orderings_Obot__class_Obot(_1304531), _1304535 = c_Orderings_Obot__class_Obot(_1304531)], (29364 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1304531), _1304533), _1304535) = c_Orderings_Obot__class_Obot(_1304531), 29367 ^ _779571 : [(29370 ^ _779571) ^ [] : [-(_1304535 = c_Orderings_Obot__class_Obot(_1304531))], (29368 ^ _779571) ^ [] : [-(_1304533 = c_Orderings_Obot__class_Obot(_1304531))]]]]], (39509 ^ _779571) ^ [_1524411, _1524413, _1524415, _1524417, _1524419] : [hAPP(c_Set_Oimage(_1524411, _1524413, _1524415), c_Orderings_Otop__class_Otop(tc_fun(_1524411, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1524413, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524411, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1524411, _1524413, _1524415), _1524417)), _1524419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524413, tc_HOL_Obool)), _1524417), hAPP(c_Set_Oimage(_1524411, _1524413, _1524415), _1524419))))], (4022 ^ _779571) ^ [_841516, _841518, _841520, _841522, _841524, _841526] : [-(c_Set_Ovimage(_841526, _841522, _841518) = c_Set_Ovimage(_841524, _841520, _841516)), _841526 = _841524, _841522 = _841520, _841518 = _841516], (12592 ^ _779571) ^ [_989849, _989851, _989853] : [class_Groups_Oordered__comm__monoid__add(_989849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989849), _989851), c_Groups_Ozero__class_Ozero(_989849))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989849), _989853), c_Groups_Ozero__class_Ozero(_989849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989849), _989851), _989853)), c_Groups_Ozero__class_Ozero(_989849))))], (42083 ^ _779571) ^ [_1593268, _1593270] : [-(c_List_Olex(_1593268, _1593270) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1593268), tc_List_Olist(_1593268)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1593268, _1593270)))], (29087 ^ _779571) ^ [_1298533, _1298535] : [class_Lattices_Oboolean__algebra(_1298533), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1298533), hAPP(c_Groups_Ouminus__class_Ouminus(_1298533), _1298535)), _1298535) = c_Orderings_Otop__class_Otop(_1298533))], (35549 ^ _779571) ^ [] : [-(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))))))], (17759 ^ _779571) ^ [_1085420] : [class_Power_Opower(_1085420), -(c_Power_Opower__class_Opower(_1085420) = c_Power_Opower_Opower(_1085420, c_Groups_Oone__class_Oone(_1085420), c_Groups_Otimes__class_Otimes(_1085420)))], (2562 ^ _779571) ^ [_818318, _818320, _818322, _818324] : [-(c_Divides_OposDivAlg(_818324, _818320) = c_Divides_OposDivAlg(_818322, _818318)), _818324 = _818322, _818320 = _818318], (23773 ^ _779571) ^ [_1192549, _1192551, _1192553, _1192555] : [class_Orderings_Olinorder(_1192549), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192549), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192549), _1192551), _1192553)), _1192555) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192549), _1192551), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192549), _1192553), _1192555)))], (18931 ^ _779571) ^ [_1104154] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1104154)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1104154)))], (35908 ^ _779571) ^ [_1444856, _1444858, _1444860, _1444862, _1444864, _1444866, _1444868] : [c_Equiv__Relations_Oequiv(_1444856, _1444858, _1444860), hBOOL(hAPP(hAPP(c_member(tc_fun(_1444856, tc_HOL_Obool)), _1444862), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1444856), _1444858), _1444860))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1444856, tc_HOL_Obool)), _1444864), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1444856), _1444858), _1444860))), hBOOL(hAPP(hAPP(c_member(_1444856), _1444866), _1444862)), hBOOL(hAPP(hAPP(c_member(_1444856), _1444868), _1444864)), 35927 ^ _779571 : [(35934 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1444856, _1444856)), hAPP(hAPP(c_Product__Type_OPair(_1444856, _1444856), _1444866), _1444868)), _1444860)), -(_1444862 = _1444864)], (35928 ^ _779571) ^ [] : [_1444862 = _1444864, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1444856, _1444856)), hAPP(hAPP(c_Product__Type_OPair(_1444856, _1444856), _1444866), _1444868)), _1444860)))]]], (8054 ^ _779571) ^ [_913037] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_913037)), c_Option_Ooption_ONone(_913037)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31454 ^ _779571) ^ [_1348424, _1348426, _1348428, _1348430, _1348432, _1348434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1348426, _1348428)), hAPP(hAPP(c_Product__Type_OPair(_1348426, _1348428), _1348432), _1348434)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1348424, tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1348424, tc_HOL_Obool))), _1348430))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1348424, tc_fun(_1348426, tc_fun(_1348428, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1348424, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_fun(_1348426, tc_fun(_1348428, tc_HOL_Obool)), _1348424), hAPP(c_COMBC(_1348426, tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348428, tc_fun(tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), _1348426), c_COMBC(_1348428, tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348428, tc_prod(_1348426, _1348428)), tc_fun(_1348428, tc_fun(tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_HOL_Obool)), _1348426), hAPP(c_COMBB(tc_prod(_1348426, _1348428), tc_fun(tc_fun(tc_prod(_1348426, _1348428), tc_HOL_Obool), tc_HOL_Obool), _1348428), c_member(tc_prod(_1348426, _1348428)))), c_Product__Type_OPair(_1348426, _1348428))))), _1348430)), _1348432), _1348434)))], (29152 ^ _779571) ^ [_1300281, _1300283, _1300285] : [hAPP(hAPP(c_Set_Oinsert(_1300281), _1300283), c_Orderings_Obot__class_Obot(tc_fun(_1300281, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1300281), _1300285), c_Orderings_Obot__class_Obot(tc_fun(_1300281, tc_HOL_Obool))), -(_1300283 = _1300285)], (42219 ^ _779571) ^ [_1596746] : [-(c_Wellfounded_OwfP(_1596746, hAPP(c_COMBK(tc_fun(_1596746, tc_HOL_Obool), _1596746), hAPP(c_COMBK(tc_HOL_Obool, _1596746), c_fFalse))))], (35862 ^ _779571) ^ [_1443851, _1443853, _1443855, _1443857] : [c_Equiv__Relations_Oequiv(_1443851, _1443853, _1443855), hBOOL(hAPP(hAPP(c_member(_1443851), _1443857), _1443853)), -(hBOOL(hAPP(hAPP(c_member(_1443851), _1443857), hAPP(c_Relation_OImage(_1443851, _1443851, _1443855), hAPP(hAPP(c_Set_Oinsert(_1443851), _1443857), c_Orderings_Obot__class_Obot(tc_fun(_1443851, tc_HOL_Obool)))))))], (7061 ^ _779571) ^ [_895904] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _895904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _895904)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6347 ^ _779571) ^ [_882535, _882537] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_882535, _882537)))), hBOOL(hAPP(c_Com_OWT, _882535)), hBOOL(hAPP(c_Com_OWT, _882537))], (18803 ^ _779571) ^ [_1102097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1102097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1102097))))], (7193 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51421 ^ _779571) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (50944 ^ _779571) ^ [_1805471, _1805473, _1805475, _1805477, _1805479] : [-(hAPP(hAPP(c_List_Ozip(_1805471, _1805473), _1805475), c_List_OtakeWhile(_1805473, _1805477, _1805479)) = c_List_OtakeWhile(tc_prod(_1805471, _1805473), hAPP(c_Fun_Ocomp(_1805473, tc_HOL_Obool, tc_prod(_1805471, _1805473), _1805477), c_Product__Type_Osnd(_1805471, _1805473)), hAPP(hAPP(c_List_Ozip(_1805471, _1805473), _1805475), _1805479)))], (38855 ^ _779571) ^ [_1509940, _1509942, _1509944, _1509946, _1509948, _1509950] : [c_Fun_Oinj__on(_1509940, _1509942, _1509944, _1509946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509942, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509940, _1509942, _1509944), _1509946)), _1509948)), c_Fun_Oinj__on(_1509942, _1509940, _1509950, _1509948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509940, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509942, _1509940, _1509950), _1509948)), _1509946)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509940), _1509946)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509942), _1509948)), -(hAPP(c_Finite__Set_Ocard(_1509940), _1509946) = hAPP(c_Finite__Set_Ocard(_1509942), _1509948))], (30435 ^ _779571) ^ [_1325427, _1325429] : [hAPP(c_Int_ORep__Integ, _1325427) = hAPP(c_Int_ORep__Integ, _1325429), -(_1325427 = _1325429)], (48483 ^ _779571) ^ [_1749291, _1749293, _1749295, _1749297, _1749299] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749291), tc_List_Olist(_1749291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1749291), tc_List_Olist(_1749291)), hAPP(hAPP(c_List_Oappend(_1749291), _1749293), _1749295)), hAPP(hAPP(c_List_Oappend(_1749291), _1749293), _1749297))), c_List_Olexord(_1749291, _1749299))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749291, _1749291)), hAPP(hAPP(c_Product__Type_OPair(_1749291, _1749291), 48488 ^ [_1749291, _1749293, _1749295, _1749297, _1749299]), 48488 ^ [_1749291, _1749293, _1749295, _1749297, _1749299])), _1749299))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749291), tc_List_Olist(_1749291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1749291), tc_List_Olist(_1749291)), _1749295), _1749297)), c_List_Olexord(_1749291, _1749299))))], (30465 ^ _779571) ^ [_1325976, _1325978, _1325980, _1325982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1325976, tc_HOL_Obool)), _1325978), _1325980)), hBOOL(hAPP(hAPP(c_member(_1325976), _1325982), _1325978)), -(hBOOL(hAPP(hAPP(c_member(_1325976), _1325982), _1325980)))], (12515 ^ _779571) ^ [_988485, _988487] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988485)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988487)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988485), _988487)))], (43325 ^ _779571) ^ [_1623321, _1623323, _1623325, _1623327, _1623329] : [-(hAPP(c_Relation_Oconverse(_1623321, _1623323), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1623325, tc_fun(tc_prod(_1623321, _1623323), tc_HOL_Obool)), _1623327), _1623329)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1623325, tc_fun(tc_prod(_1623323, _1623321), tc_HOL_Obool)), _1623327), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1623321, _1623323), tc_HOL_Obool), tc_fun(tc_prod(_1623323, _1623321), tc_HOL_Obool), _1623325), c_Relation_Oconverse(_1623321, _1623323)), _1623329)))], (14870 ^ _779571) ^ [_1030373, _1030375, _1030377, _1030379] : [class_Divides_Osemiring__div(_1030373), -(_1030375 = c_Groups_Ozero__class_Ozero(_1030373)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030373), _1030377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030373), _1030379), _1030375))), _1030375) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030373), _1030379), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030373), _1030377), _1030375)))], (12287 ^ _779571) ^ [_984710, _984712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984710)), _984712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984710), _984712)))], (10778 ^ _779571) ^ [_959028, _959030, _959032, _959034] : [class_Orderings_Opreorder(_959028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959028), _959030), _959032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959028), _959032), _959034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959028), _959030), _959034)))], (45710 ^ _779571) ^ [_1680127, _1680129, _1680131, _1680133] : [-(c_Map_Odom(_1680127, _1680129, c_Map_Omap__add(_1680127, _1680129, _1680131, _1680133)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1680127, tc_HOL_Obool)), c_Map_Odom(_1680127, _1680129, _1680133)), c_Map_Odom(_1680127, _1680129, _1680131)))], (50556 ^ _779571) ^ [_1795497, _1795499] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1795497)), c_List_Otranspose__rel(_1795497)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1795497)), c_List_Olist_ONil(_1795497)), _1795499))), -(c_List_Otranspose(_1795497, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1795497)), c_List_Olist_ONil(_1795497)), _1795499)) = c_List_Otranspose(_1795497, _1795499))], (17745 ^ _779571) ^ [_1085214, _1085216] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1085214), _1085216) = 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), _1085214)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1085216)))))], (840 ^ _779571) ^ [_792533, _792535, _792537, _792539, _792541, _792543, _792545, _792547] : [-(c_List_Olistrelp(_792545, _792541, _792537, _792533)), c_List_Olistrelp(_792547, _792543, _792539, _792535), _792547 = _792545, _792543 = _792541, _792539 = _792537, _792535 = _792533], (19613 ^ _779571) ^ [_1116052, _1116054] : [class_Rings_Olinordered__idom(_1116052), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116052), c_Groups_Ozero__class_Ozero(_1116052)), hAPP(hAPP(c_Power_Opower__class_Opower(_1116052), _1116054), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (6911 ^ _779571) ^ [_893645, _893647] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893645), _893647) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6916 ^ _779571 : [(6919 ^ _779571) ^ [] : [-(_893647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6917 ^ _779571) ^ [] : [-(_893645 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6920 ^ _779571 : [(6923 ^ _779571) ^ [] : [-(_893647 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6921 ^ _779571) ^ [] : [-(_893645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5950 ^ _779571) ^ [_875164, _875166, _875168, _875170, _875172, _875174] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_875164, _875166, _875168), _875170, _875172, _875174)), 5951 ^ _779571 : [(5958 ^ _779571) ^ [] : [-(hBOOL(hAPP(_875164, _875170))), c_Natural_Oevaln(_875168, _875170, _875172, _875174)], (5952 ^ _779571) ^ [] : [hBOOL(hAPP(_875164, _875170)), c_Natural_Oevaln(_875166, _875170, _875172, _875174)]]], (44985 ^ _779571) ^ [_1664081, _1664083, _1664085] : [class_Complete__Lattice_Ocomplete__lattice(_1664081), 44988 ^ _779571 : [(44989 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664081), _1664083), c_Complete__Lattice_OInf__class_OInf(_1664081, _1664085))), 44992 ^ _779571 : [(44993 ^ _779571) ^ [_1664239] : [hBOOL(hAPP(hAPP(c_member(_1664081), _1664239), _1664085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664081), _1664083), _1664239)))]]], (44999 ^ _779571) ^ [] : [45001 ^ _779571 : [(45004 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664081), _1664083), 45000 ^ [_1664081, _1664083, _1664085]))], (45002 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664081), 45000 ^ [_1664081, _1664083, _1664085]), _1664085)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664081), _1664083), c_Complete__Lattice_OInf__class_OInf(_1664081, _1664085))))]]], (19793 ^ _779571) ^ [_1119130, _1119132, _1119134] : [class_Rings_Olinordered__idom(_1119130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119130), hAPP(hAPP(c_Power_Opower__class_Opower(_1119130), _1119132), 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(_1119130), _1119134), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1119130)))], (48696 ^ _779571) ^ [_1755736, _1755738] : [-(hAPP(c_List_Orotate1(_1755736), _1755738) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1755736), _1755736, c_List_Olist_ONil(_1755736), hAPP(hAPP(c_COMBB(tc_List_Olist(_1755736), tc_fun(tc_List_Olist(_1755736), tc_List_Olist(_1755736)), _1755736), hAPP(c_COMBC(tc_List_Olist(_1755736), tc_List_Olist(_1755736), tc_List_Olist(_1755736)), c_List_Oappend(_1755736))), hAPP(hAPP(c_COMBC(_1755736, tc_List_Olist(_1755736), tc_List_Olist(_1755736)), c_List_Olist_OCons(_1755736)), c_List_Olist_ONil(_1755736)))), _1755738))], (42149 ^ _779571) ^ [_1594760, _1594762, _1594764, _1594766, _1594768] : [-(hAPP(c_Relation_ORange(_1594760, _1594762), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1594760, _1594762)), hAPP(hAPP(c_Product__Type_OPair(_1594760, _1594762), _1594764), _1594766)), _1594768)) = hAPP(hAPP(c_Set_Oinsert(_1594762), _1594766), hAPP(c_Relation_ORange(_1594760, _1594762), _1594768)))], (2076 ^ _779571) ^ [_810485, _810487, _810489, _810491, _810493, _810495, _810497, _810499, _810501, _810503] : [-(c_Sum__Type_Osum_Osum__size(_810503, _810499, _810495, _810491, _810487) = c_Sum__Type_Osum_Osum__size(_810501, _810497, _810493, _810489, _810485)), _810503 = _810501, _810499 = _810497, _810495 = _810493, _810491 = _810489, _810487 = _810485], (43026 ^ _779571) ^ [_1616219, _1616221] : [-(c_Relation_Orefl__on(_1616219, c_Orderings_Otop__class_Otop(tc_fun(_1616219, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616219, _1616221)))], (17661 ^ _779571) ^ [_1083587, _1083589, _1083591, _1083593] : [class_Rings_Olinordered__semidom(_1083587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083587), c_Groups_Oone__class_Oone(_1083587)), _1083589)), 17668 ^ _779571 : [(17675 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083591), _1083593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083587), hAPP(hAPP(c_Power_Opower__class_Opower(_1083587), _1083589), _1083591)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083587), _1083589), _1083593))))], (17669 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083587), hAPP(hAPP(c_Power_Opower__class_Opower(_1083587), _1083589), _1083591)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083587), _1083589), _1083593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083591), _1083593)))]]], (29448 ^ _779571) ^ [_1305910, _1305912, _1305914, _1305916] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305910, tc_HOL_Obool)), _1305912), hAPP(hAPP(c_Set_Oinsert(_1305910), _1305914), _1305916)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305910, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305910, tc_HOL_Obool)), _1305912), _1305916)), hAPP(hAPP(c_Set_Oinsert(_1305910), _1305914), c_Orderings_Obot__class_Obot(tc_fun(_1305910, tc_HOL_Obool)))))], (40539 ^ _779571) ^ [_1549237, _1549239, _1549241] : [class_Orderings_Olinorder(_1549237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549237), _1549239)), -(_1549239 = c_Orderings_Obot__class_Obot(tc_fun(_1549237, tc_HOL_Obool))), 40550 ^ _779571 : [(40560 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1549237), hAPP(c_Finite__Set_Ofold1(_1549237, c_Orderings_Oord__class_Omin(_1549237)), _1549239)), _1549241))), 40561 ^ _779571 : [(40562 ^ _779571) ^ [_1549626] : [hBOOL(hAPP(hAPP(c_member(_1549237), _1549626), _1549239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1549237), _1549626), _1549241))]]], (40551 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1549237), hAPP(c_Finite__Set_Ofold1(_1549237, c_Orderings_Oord__class_Omin(_1549237)), _1549239)), _1549241)), 40555 ^ _779571 : [(40558 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1549237), 40554 ^ [_1549237, _1549239, _1549241]), _1549241)))], (40556 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549237), 40554 ^ [_1549237, _1549239, _1549241]), _1549239)))]]]]], (23739 ^ _779571) ^ [_1191867, _1191869, _1191871, _1191873] : [class_Orderings_Olinorder(_1191867), 23742 ^ _779571 : [(23751 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191867), _1191871), _1191873)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), _1191871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), _1191873))], (23743 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191867), _1191871), _1191873))), 23746 ^ _779571 : [(23749 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), _1191873)))], (23747 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191867), _1191869), _1191871)))]]]]], (32482 ^ _779571) ^ [_1371428, _1371430, _1371432, _1371434, _1371436] : [c_Finite__Set_Ofolding__one(_1371428, _1371430, _1371432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371428), _1371434)), 32489 ^ _779571 : [(32496 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371428, tc_HOL_Obool)), _1371434), hAPP(hAPP(c_Set_Oinsert(_1371428), _1371436), c_Orderings_Obot__class_Obot(tc_fun(_1371428, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371428, tc_HOL_Obool))), -(hAPP(_1371432, hAPP(hAPP(c_Set_Oinsert(_1371428), _1371436), _1371434)) = hAPP(hAPP(_1371430, _1371436), hAPP(_1371432, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371428, tc_HOL_Obool)), _1371434), hAPP(hAPP(c_Set_Oinsert(_1371428), _1371436), c_Orderings_Obot__class_Obot(tc_fun(_1371428, tc_HOL_Obool)))))))], (32490 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371428, tc_HOL_Obool)), _1371434), hAPP(hAPP(c_Set_Oinsert(_1371428), _1371436), c_Orderings_Obot__class_Obot(tc_fun(_1371428, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371428, tc_HOL_Obool)), -(hAPP(_1371432, hAPP(hAPP(c_Set_Oinsert(_1371428), _1371436), _1371434)) = _1371436)]]], (10002 ^ _779571) ^ [_946087, _946089, _946091] : [class_Rings_Oring__1(_946087), -(hAPP(c_Int_Oring__1__class_Oof__int(_946087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _946089), _946091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946087), hAPP(c_Int_Oring__1__class_Oof__int(_946087), _946089)), hAPP(c_Int_Oring__1__class_Oof__int(_946087), _946091)))], (4440 ^ _779571) ^ [_848287, _848289] : [_848289 = _848287, -(c_Random_Orange(_848289) = c_Random_Orange(_848287))], (51515 ^ _779571) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (8614 ^ _779571) ^ [_921886, _921888, _921890] : [class_Orderings_Olinorder(_921886), 8617 ^ _779571 : [(8618 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921886), _921888), _921890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921886), _921890), _921888))), -(_921888 = _921890)], (8628 ^ _779571) ^ [] : [8629 ^ _779571 : [(8632 ^ _779571) ^ [] : [_921888 = _921890], (8630 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921886), _921890), _921888))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921886), _921888), _921890))]]], (38154 ^ _779571) ^ [_1495666, _1495668, _1495670, _1495672] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495666), _1495668)), c_Equiv__Relations_Oequiv(_1495666, _1495668, _1495670), 38164 ^ _779571 : [(38167 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1495672), hAPP(c_Finite__Set_Ocard(_1495666), 38163 ^ [_1495666, _1495668, _1495670, _1495672])))], (38165 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1495666, tc_HOL_Obool)), 38163 ^ [_1495666, _1495668, _1495670, _1495672]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495666), _1495668), _1495670))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1495672), hAPP(c_Finite__Set_Ocard(_1495666), _1495668))))], (44448 ^ _779571) ^ [_1649109, _1649111, _1649113, _1649115, _1649117, _1649119] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649109, tc_fun(_1649111, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649113, tc_fun(_1649109, tc_HOL_Obool)), _1649115), _1649117)), _1649119) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649113, tc_fun(_1649111, tc_HOL_Obool)), _1649115), hAPP(hAPP(c_COMBC(_1649113, tc_fun(_1649109, tc_fun(_1649111, tc_HOL_Obool)), tc_fun(_1649111, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649109, tc_HOL_Obool), tc_fun(tc_fun(_1649109, tc_fun(_1649111, tc_HOL_Obool)), tc_fun(_1649111, tc_HOL_Obool)), _1649113), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649109, tc_fun(_1649111, tc_HOL_Obool))), _1649117)), _1649119)))], (28515 ^ _779571) ^ [_1285889, _1285891, _1285893, _1285895] : [c_Hoare__Mirabelle_Ohoare__derivs(_1285889, _1285891, _1285893), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1285889), tc_HOL_Obool)), _1285895), _1285893)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1285889, _1285891, _1285895))], (34405 ^ _779571) ^ [_1408745, _1408747, _1408749, _1408751, _1408753] : [class_Groups_Ocomm__monoid__mult(_1408745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408747), _1408749)), 34412 ^ _779571 : [(34419 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408747), _1408751), _1408749))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408747, _1408745), hAPP(hAPP(c_COMBC(_1408747, _1408745, _1408745), hAPP(hAPP(c_COMBS(_1408747, _1408745, tc_fun(_1408745, _1408745)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1408745, tc_fun(_1408745, _1408745)), _1408747), c_If(_1408745)), hAPP(hAPP(c_COMBC(_1408747, _1408747, tc_HOL_Obool), c_fequal), _1408751))), _1408753)), c_Groups_Oone__class_Oone(_1408745))), _1408749) = c_Groups_Oone__class_Oone(_1408745))], (34413 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1408747), _1408751), _1408749)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408747, _1408745), hAPP(hAPP(c_COMBC(_1408747, _1408745, _1408745), hAPP(hAPP(c_COMBS(_1408747, _1408745, tc_fun(_1408745, _1408745)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1408745, tc_fun(_1408745, _1408745)), _1408747), c_If(_1408745)), hAPP(hAPP(c_COMBC(_1408747, _1408747, tc_HOL_Obool), c_fequal), _1408751))), _1408753)), c_Groups_Oone__class_Oone(_1408745))), _1408749) = hAPP(_1408753, _1408751))]]], (46211 ^ _779571) ^ [_1692249, _1692251, _1692253, _1692255] : [hBOOL(hAPP(c_List_Odistinct(_1692249), hAPP(hAPP(c_List_Omap(tc_prod(_1692249, _1692251), _1692249), c_Product__Type_Ofst(_1692249, _1692251)), _1692253))), hBOOL(hAPP(c_List_Odistinct(_1692249), hAPP(hAPP(c_List_Omap(tc_prod(_1692249, _1692251), _1692249), c_Product__Type_Ofst(_1692249, _1692251)), _1692255))), 46218 ^ _779571 : [(46225 ^ _779571) ^ [] : [hAPP(c_List_Oset(tc_prod(_1692249, _1692251)), _1692253) = hAPP(c_List_Oset(tc_prod(_1692249, _1692251)), _1692255), -(c_Map_Omap__of(_1692249, _1692251, _1692253) = c_Map_Omap__of(_1692249, _1692251, _1692255))], (46219 ^ _779571) ^ [] : [c_Map_Omap__of(_1692249, _1692251, _1692253) = c_Map_Omap__of(_1692249, _1692251, _1692255), -(hAPP(c_List_Oset(tc_prod(_1692249, _1692251)), _1692253) = hAPP(c_List_Oset(tc_prod(_1692249, _1692251)), _1692255))]]], (19609 ^ _779571) ^ [_1115965, _1115967] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115965)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115967))) = 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), _1115965), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115967))))], (49285 ^ _779571) ^ [_1769063, _1769065] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769063)), c_List_Olist_ONil(_1769063)), c_List_Olists(_1769063, _1769065))))], (16415 ^ _779571) ^ [_1060257, _1060259] : [class_Groups_Oordered__ab__group__add__abs(_1060257), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060257), _1060259), hAPP(c_Groups_Oabs__class_Oabs(_1060257), _1060259))))], (22676 ^ _779571) ^ [_1171931] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1171931) = 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)))], (50710 ^ _779571) ^ [_1799118, _1799120] : [hBOOL(hAPP(c_List_Odistinct(_1799118), _1799120)), -(hBOOL(hAPP(c_List_Odistinct(_1799118), hAPP(c_List_Orev(_1799118), _1799120))))], (18493 ^ _779571) ^ [_1096885, _1096887] : [18494 ^ _779571 : [(18497 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096885), c_Int_OPls))], (18495 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096885), _1096887))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096885)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096887))))], (10488 ^ _779571) ^ [_954137, _954139, _954141, _954143] : [class_Orderings_Oorder(_954137), _954139 = _954141, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954137), _954143), _954141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954137), _954143), _954139)))], (4584 ^ _779571) ^ [_850501, _850503, _850505, _850507, _850509, _850511] : [-(c_Finite__Set_Ofold(_850511, _850507, _850503) = c_Finite__Set_Ofold(_850509, _850505, _850501)), _850511 = _850509, _850507 = _850505, _850503 = _850501], (22436 ^ _779571) ^ [_1167232, _1167234] : [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(_1167234))), 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), _1167232)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167232)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167234))))], (28010 ^ _779571) ^ [_1275850, _1275852, _1275854, _1275856] : [class_Lattices_Olattice(_1275850), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275850), _1275852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275850), _1275854), _1275856)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275850), _1275854), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275850), _1275852), _1275856)))], (5354 ^ _779571) ^ [_862294, _862296] : [_862296 = _862294, -(c_List_Onth(_862296) = c_List_Onth(_862294))], (17303 ^ _779571) ^ [_1077080, _1077082] : [_1077080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1077082), _1077080) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9008 ^ _779571) ^ [_928856] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _928856) = _928856)], (23079 ^ _779571) ^ [_1179866, _1179868, _1179870, _1179872, _1179874, _1179876] : [hAPP(hAPP(c_Product__Type_OPair(_1179866, _1179868), _1179870), _1179872) = hAPP(hAPP(c_Product__Type_OPair(_1179866, _1179868), _1179874), _1179876), 23082 ^ _779571 : [(23085 ^ _779571) ^ [] : [-(_1179872 = _1179876)], (23083 ^ _779571) ^ [] : [-(_1179870 = _1179874)]]], (24755 ^ _779571) ^ [_1211884, _1211886, _1211888] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1211884), _1211886), _1211888) = c_Nitpick_OAbs__Frac(_1211884, c_Nitpick_Onorm__frac(_1211886, _1211888)))], (41001 ^ _779571) ^ [_1559965, _1559967, _1559969] : [-(hAPP(hAPP(c_Set_Oinsert(_1559965), _1559967), _1559969) = hAPP(c_Set_OCollect(_1559965), hAPP(hAPP(c_COMBS(_1559965, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559965), c_fdisj), hAPP(hAPP(c_COMBC(_1559965, _1559965, tc_HOL_Obool), c_fequal), _1559967))), hAPP(hAPP(c_COMBC(_1559965, tc_fun(_1559965, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559965)), _1559969))))], (22994 ^ _779571) ^ [_1178154, _1178156, _1178158, _1178160, _1178162] : [hBOOL(hAPP(hAPP(_1178154, _1178156), _1178158)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1178160, _1178162, tc_HOL_Obool), _1178154), hAPP(hAPP(c_Product__Type_OPair(_1178160, _1178162), _1178156), _1178158))))], (6819 ^ _779571) ^ [_891902, _891904, _891906] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_891902, _891904, _891906)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_891906)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48006 ^ _779571) ^ [_1737906, _1737908, _1737910, _1737912, _1737914] : [-(hAPP(hAPP(c_List_Oappend(_1737906), _1737908), _1737910) = hAPP(hAPP(c_List_Oappend(_1737906), _1737912), _1737914)), 48007 ^ _779571 : [(48014 ^ _779571) ^ [_1738130] : [hAPP(hAPP(c_List_Oappend(_1737906), _1737908), _1738130) = _1737912, _1737910 = hAPP(hAPP(c_List_Oappend(_1737906), _1738130), _1737914)], (48008 ^ _779571) ^ [_1738018] : [_1737908 = hAPP(hAPP(c_List_Oappend(_1737906), _1737912), _1738018), hAPP(hAPP(c_List_Oappend(_1737906), _1738018), _1737910) = _1737914]]], (41612 ^ _779571) ^ [_1580972, _1580974] : [-(c_Product__Type_Omap__pair(_1580972, _1580972, _1580974, _1580974, c_Fun_Oid(_1580972), c_Fun_Oid(_1580974)) = c_Fun_Oid(tc_prod(_1580972, _1580974)))], (45606 ^ _779571) ^ [_1677982, _1677984, _1677986, _1677988, _1677990, _1677992, _1677994, _1677996] : [c_Finite__Set_Ofolding__image__simple__idem(_1677982, _1677984, _1677986, _1677988, _1677990, _1677992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677984), _1677994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1677984, tc_HOL_Obool)), _1677996), _1677994)), -(hAPP(hAPP(_1677986, hAPP(_1677992, _1677996)), hAPP(_1677992, _1677994)) = hAPP(_1677992, _1677994))], (46126 ^ _779571) ^ [_1690221, _1690223, _1690225, _1690227] : [c_Map_Omap__of(_1690221, _1690223, _1690225) = c_Map_Omap__of(_1690221, _1690223, _1690227), -(hAPP(c_Set_Oimage(tc_prod(_1690221, _1690223), _1690221, c_Product__Type_Ofst(_1690221, _1690223)), hAPP(c_List_Oset(tc_prod(_1690221, _1690223)), _1690225)) = hAPP(c_Set_Oimage(tc_prod(_1690221, _1690223), _1690221, c_Product__Type_Ofst(_1690221, _1690223)), hAPP(c_List_Oset(tc_prod(_1690221, _1690223)), _1690227)))], (46919 ^ _779571) ^ [_1711203, _1711205, _1711207, _1711209, _1711211, _1711213] : [-(_1711203 = _1711205), -(hAPP(c_Map_Omap__of(_1711207, _1711209, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1711207, _1711209)), hAPP(hAPP(c_Product__Type_OPair(_1711207, _1711209), _1711203), _1711211)), _1711213)), _1711205) = hAPP(c_Map_Omap__of(_1711207, _1711209, _1711213), _1711205))], (22886 ^ _779571) ^ [_1176370, _1176372] : [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), _1176370), _1176372))), 22889 ^ _779571 : [(22896 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176372), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22899 ^ _779571 : [(22908 ^ _779571) ^ [] : [-(c_Nitpick_Onorm__frac(_1176370, _1176372) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1176370), _1176372)), 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), _1176370))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176372)))), -(_1176370 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1176372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22900 ^ _779571) ^ [] : [22901 ^ _779571 : [(22904 ^ _779571) ^ [] : [_1176372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22902 ^ _779571) ^ [] : [_1176370 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1176370, _1176372) = 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)))]]], (22890 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176372), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1176370, _1176372) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176370), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176372)))]]], (30487 ^ _779571) ^ [_1326428, _1326430, _1326432, _1326434, _1326436] : [hBOOL(hAPP(hAPP(c_member(_1326428), _1326430), c_SetInterval_Oord_OatLeastAtMost(_1326428, _1326432, _1326434, _1326436))), 30490 ^ _779571 : [(30493 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1326432, _1326430), _1326436)))], (30491 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1326432, _1326434), _1326430)))]]], (6155 ^ _779571) ^ [_878918, _878920, _878922, _878924, _878926, _878928, _878930, _878932, _878934, _878936, _878938, _878940] : [-(c_Com_Ocom_Ocom__case(_878918, _878920, _878922, _878924, _878926, _878928, _878930, _878932, _878934, c_Com_Ocom_OCond(_878936, _878938, _878940)) = hAPP(hAPP(hAPP(_878928, _878936), _878938), _878940))], (29438 ^ _779571) ^ [_1305747, _1305749, _1305751] : [class_Orderings_Oorder(_1305747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305747), _1305749), _1305751)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1305747, _1305751, _1305749) = c_Orderings_Obot__class_Obot(tc_fun(_1305747, tc_HOL_Obool)))], (45967 ^ _779571) ^ [_1686255, _1686257, _1686259, _1686261, _1686263, _1686265] : [-(hAPP(hAPP(c_List_Omap(_1686255, _1686257), _1686259), hAPP(hAPP(c_List_Omap(_1686261, _1686255), _1686263), _1686265)) = hAPP(hAPP(c_List_Omap(_1686261, _1686257), hAPP(c_Fun_Ocomp(_1686255, _1686257, _1686261, _1686259), _1686263)), _1686265))], (14544 ^ _779571) ^ [_1024951, _1024953, _1024955, _1024957] : [class_Divides_Osemiring__div(_1024951), -(_1024953 = c_Groups_Ozero__class_Ozero(_1024951)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024951), _1024955), _1024953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024951), _1024957), _1024953)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024951), _1024955), _1024957))], (6831 ^ _779571) ^ [_892168, _892170, _892172] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_892168, _892170)), _892172), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892172), _892168), hAPP(_892170, _892172)))))], (37940 ^ _779571) ^ [_1491817, _1491819, _1491821] : [class_Lattices_Olattice(_1491817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491817), _1491819)), hBOOL(hAPP(hAPP(c_member(_1491817), _1491821), _1491819)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1491817), _1491821), c_Big__Operators_Olattice__class_OInf__fin(_1491817, _1491819)) = c_Big__Operators_Olattice__class_OInf__fin(_1491817, _1491819))], (51213 ^ _779571) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (17231 ^ _779571) ^ [_1075915, _1075917] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075915)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075917)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1075915), _1075917)))], (16561 ^ _779571) ^ [_1062908, _1062910] : [16562 ^ _779571 : [(16565 ^ _779571) ^ [] : [_1062910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16563 ^ _779571) ^ [] : [-(_1062908 = 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), _1062908)), _1062910))))], (3824 ^ _779571) ^ [_838577, _838579] : [_838579 = _838577, -(tc_Lazy__Sequence_Olazy__sequence(_838579) = tc_Lazy__Sequence_Olazy__sequence(_838577))], (51223 ^ _779571) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (34733 ^ _779571) ^ [_1416291, _1416293, _1416295, _1416297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1416291), _1416293)), -(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), _1416291), _1416295)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1416293), _1416297))), c_FunDef_Opair__less)))], (30973 ^ _779571) ^ [_1337196, _1337198] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1337196, _1337198))))], (32917 ^ _779571) ^ [_1380160, _1380162, _1380164] : [class_Orderings_Olinorder(_1380160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380160), _1380162)), hBOOL(hAPP(hAPP(c_member(_1380160), _1380164), _1380162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380160), _1380164), c_Big__Operators_Olinorder__class_OMax(_1380160, _1380162))))], (41039 ^ _779571) ^ [_1561084] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1561084, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561084), hAPP(c_COMBK(tc_HOL_Obool, _1561084), c_fTrue)))], (26975 ^ _779571) ^ [_1254774, _1254776, _1254778] : [class_Fields_Ofield(_1254774), -(_1254776 = c_Groups_Oone__class_Oone(_1254774)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254774), hAPP(c_Power_Opower__class_Opower(_1254774), _1254776)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254778)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254774), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254774), hAPP(hAPP(c_Power_Opower__class_Opower(_1254774), _1254776), _1254778)), c_Groups_Oone__class_Oone(_1254774))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254774), _1254776), c_Groups_Oone__class_Oone(_1254774))))], (30142 ^ _779571) ^ [_1319884, _1319886, _1319888, _1319890] : [hBOOL(hAPP(hAPP(c_member(_1319884), _1319886), hAPP(hAPP(c_Set_Oinsert(_1319884), _1319888), _1319890))), -(_1319886 = _1319888), -(hBOOL(hAPP(hAPP(c_member(_1319884), _1319886), _1319890)))], (13054 ^ _779571) ^ [_998128, _998130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _998130), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998128), _998130)))], (21357 ^ _779571) ^ [_1147004, _1147006] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147004), _1147006), hAPP(c_Int_Onumber__class_Onumber__of(_1147004), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1147004), _1147006)), class_Fields_Ofield__inverse__zero(_1147004), class_Int_Onumber__ring(_1147004)], (47831 ^ _779571) ^ [_1733388, _1733390, _1733392, _1733394] : [-(c_List_Osublist(_1733388, hAPP(hAPP(c_List_Olist_OCons(_1733388), _1733390), _1733392), _1733394) = hAPP(hAPP(c_List_Oappend(_1733388), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1733388)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1733394)), hAPP(hAPP(c_List_Olist_OCons(_1733388), _1733390), c_List_Olist_ONil(_1733388))), c_List_Olist_ONil(_1733388))), c_List_Osublist(_1733388, _1733392, 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)), _1733394)))))], (30088 ^ _779571) ^ [_1318732, _1318734, _1318736, _1318738, _1318740, _1318742] : [hBOOL(hAPP(hAPP(c_member(_1318732), _1318734), _1318736)), hBOOL(hAPP(hAPP(_1318738, _1318734), _1318740)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318732, tc_fun(_1318742, tc_HOL_Obool)), _1318736), _1318738), _1318740)))], (44516 ^ _779571) ^ [_1651586, _1651588, _1651590, _1651592, _1651594, _1651596] : [class_Complete__Lattice_Ocomplete__lattice(_1651586), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651588, _1651586), _1651590), hAPP(hAPP(c_COMBB(tc_fun(_1651592, _1651586), _1651586, _1651588), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651592, _1651586), _1651594)), _1651596)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651592, _1651586), _1651594), hAPP(hAPP(c_COMBB(tc_fun(_1651588, _1651586), _1651586, _1651592), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651588, _1651586), _1651590)), hAPP(c_COMBC(_1651588, _1651592, _1651586), _1651596))))], (49183 ^ _779571) ^ [_1766447, _1766449] : [class_Complete__Lattice_Ocomplete__lattice(_1766447), -(c_Complete__Lattice_OSup__class_OSup(_1766447, hAPP(c_List_Oset(_1766447), _1766449)) = hAPP(c_List_Ofoldl(_1766447, _1766447, c_Lattices_Osemilattice__sup__class_Osup(_1766447), c_Orderings_Obot__class_Obot(_1766447)), _1766449))], (30788 ^ _779571) ^ [_1333203, _1333205, _1333207, _1333209] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333203, tc_HOL_Obool)), _1333205), hAPP(hAPP(c_Set_Oinsert(_1333203), _1333207), _1333209)))), 30791 ^ _779571 : [(30794 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333203, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333203, tc_HOL_Obool)), _1333205), hAPP(hAPP(c_Set_Oinsert(_1333203), _1333207), c_Orderings_Obot__class_Obot(tc_fun(_1333203, tc_HOL_Obool))))), _1333209))], (30792 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333203), _1333207), _1333205)))]], 30795 ^ _779571 : [(30798 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333203, tc_HOL_Obool)), _1333205), _1333209))], (30796 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333203), _1333207), _1333205))]]], (39234 ^ _779571) ^ [_1518097, _1518099, _1518101, _1518103, _1518105] : [-(hAPP(c_Fun_Othe__inv__into(_1518097, _1518099, _1518101, _1518103), _1518105) = c_HOL_OThe(_1518097, hAPP(hAPP(c_COMBS(_1518097, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518097), c_fconj), hAPP(hAPP(c_COMBC(_1518097, tc_fun(_1518097, tc_HOL_Obool), tc_HOL_Obool), c_member(_1518097)), _1518101))), hAPP(hAPP(c_COMBC(_1518097, _1518099, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1518099, tc_fun(_1518099, tc_HOL_Obool), _1518097), c_fequal), _1518103)), _1518105))))], (22394 ^ _779571) ^ [_1166283, _1166285] : [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(_1166283))), 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)), _1166285))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166283) = hAPP(c_Nat_OSuc, _1166285))], (49656 ^ _779571) ^ [_1776853, _1776855] : [-(c_List_Obutlast(_1776853, _1776855) = hAPP(hAPP(c_List_Otake(_1776853), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776853)), _1776855)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1776855))], (15876 ^ _779571) ^ [_1049451, _1049453] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1049451, _1049453) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049451), _1049453)), _1049453)))], (33765 ^ _779571) ^ [_1396257, _1396259] : [class_Orderings_Olinorder(_1396257), -(c_Big__Operators_Olattice_OSup__fin(_1396257, c_Orderings_Oord__class_Omax(_1396257), hAPP(hAPP(c_Set_Oinsert(_1396257), _1396259), c_Orderings_Obot__class_Obot(tc_fun(_1396257, tc_HOL_Obool)))) = _1396259)], (8992 ^ _779571) ^ [_928639, _928641] : [class_Groups_Oone(_928639), 8995 ^ _779571 : [(9002 ^ _779571) ^ [] : [_928641 = c_Groups_Oone__class_Oone(_928639), -(c_Groups_Oone__class_Oone(_928639) = _928641)], (8996 ^ _779571) ^ [] : [c_Groups_Oone__class_Oone(_928639) = _928641, -(_928641 = c_Groups_Oone__class_Oone(_928639))]]], (37407 ^ _779571) ^ [_1478167, _1478169, _1478171] : [class_Orderings_Olinorder(_1478167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478167), _1478169)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478167), _1478171)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478167, tc_HOL_Obool)), _1478169), _1478171) = c_Orderings_Obot__class_Obot(tc_fun(_1478167, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1478167), c_Big__Operators_Olinorder__class_OMax(_1478167, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478167, tc_HOL_Obool)), _1478169), _1478171))), c_Big__Operators_Olinorder__class_OMax(_1478167, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478167, tc_HOL_Obool)), _1478169), _1478171))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1478167), c_Big__Operators_Olinorder__class_OMax(_1478167, _1478169)), c_Big__Operators_Olinorder__class_OMax(_1478167, _1478171)))], (7329 ^ _779571) ^ [_901150, _901152, _901154] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_901150, _901152)), hAPP(c_Sum__Type_OInl(_901150, _901152), _901154)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10102 ^ _779571) ^ [_947903, _947905] : [-(c_Int_Onat__aux(_947903, _947905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _947903)), _947905))], (36748 ^ _779571) ^ [_1463129, _1463131, _1463133] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463129, tc_HOL_Obool)), _1463131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463129, tc_HOL_Obool)), _1463133), _1463131)) = c_Orderings_Obot__class_Obot(tc_fun(_1463129, tc_HOL_Obool)))], (35442 ^ _779571) ^ [_1432890, _1432892, _1432894, _1432896, _1432898, _1432900, _1432902] : [hAPP(c_Fun_Ocomp(_1432890, _1432892, _1432894, _1432896), _1432898) = _1432900, -(hAPP(_1432896, hAPP(_1432898, _1432902)) = hAPP(_1432900, _1432902))], (43234 ^ _779571) ^ [_1621068, _1621070, _1621072, _1621074] : [c_Wellfounded_Owf(_1621068, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1621068, _1621068)), hAPP(hAPP(c_Product__Type_OPair(_1621068, _1621068), _1621070), _1621072)), _1621074)), 43237 ^ _779571 : [(43240 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621068, _1621068)), hAPP(hAPP(c_Product__Type_OPair(_1621068, _1621068), _1621072), _1621070)), c_Transitive__Closure_Ortrancl(_1621068, _1621074)))], (43238 ^ _779571) ^ [] : [-(c_Wellfounded_Owf(_1621068, _1621074))]]], (45975 ^ _779571) ^ [_1686508, _1686510, _1686512, _1686514, _1686516] : [-(c_Map_Omap__comp(_1686508, _1686510, _1686512, _1686514, hAPP(c_COMBK(tc_Option_Ooption(_1686508), _1686512), c_Option_Ooption_ONone(_1686508)), _1686516) = c_Option_Ooption_ONone(_1686510))], (34783 ^ _779571) ^ [_1417234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1417234)), -(_1417234 = 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))), _1417234)), c_FunDef_Omax__strict)))], (1252 ^ _779571) ^ [_797989, _797991] : [-(class_Lattices_Obounded__lattice__top(_797989)), _797991 = _797989, class_Lattices_Obounded__lattice__top(_797991)], (5102 ^ _779571) ^ [_858412, _858414, _858416, _858418] : [-(c_List_Oupt(_858418, _858414) = c_List_Oupt(_858416, _858412)), _858418 = _858416, _858414 = _858412], (22304 ^ _779571) ^ [_1164399, _1164401] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164399), hAPP(c_Nat_OSuc, _1164401)) = 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), _1164399), _1164401)))], (43100 ^ _779571) ^ [_1618010, _1618012] : [-(hAPP(c_Relation_OImage(_1618010, _1618010, c_Relation_OId(_1618010)), _1618012) = _1618012)], (15878 ^ _779571) ^ [_1049498, _1049500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1049498), _1049500)), -(c_Nat__Transfer_Otsub(_1049500, _1049498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049500), _1049498))], (36210 ^ _779571) ^ [_1451615, _1451617, _1451619] : [class_Lattices_Olattice(_1451615), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451615), _1451617), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451615), _1451617), _1451619)) = _1451617)], (20853 ^ _779571) ^ [_1138193, _1138195, _1138197, _1138199] : [class_Fields_Olinordered__field(_1138193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138193), _1138195), c_Groups_Ozero__class_Ozero(_1138193))), 20860 ^ _779571 : [(20867 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138193), _1138199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138193), _1138197), _1138195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138193), _1138197), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138193), _1138199), _1138195))))], (20861 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138193), _1138197), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138193), _1138199), _1138195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138193), _1138199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138193), _1138197), _1138195))))]]], (4884 ^ _779571) ^ [_855035, _855037, _855039, _855041, _855043, _855045, _855047, _855049] : [-(c_List_Omap__filter(_855049, _855045, _855041, _855037) = c_List_Omap__filter(_855047, _855043, _855039, _855035)), _855049 = _855047, _855045 = _855043, _855041 = _855039, _855037 = _855035], (25100 ^ _779571) ^ [_1219682, _1219684, _1219686, _1219688] : [class_Groups_Oordered__ab__group__add__abs(_1219682), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219682), c_Groups_Ozero__class_Ozero(_1219682)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1219684, _1219682), hAPP(hAPP(c_COMBB(_1219682, _1219682, _1219684), c_Groups_Oabs__class_Oabs(_1219682)), _1219686)), _1219688))))], (46316 ^ _779571) ^ [_1694475, _1694477, _1694479, _1694481] : [-(hBOOL(hAPP(hAPP(c_member(_1694475), _1694477), hAPP(c_List_Oset(_1694475), _1694479)))), hBOOL(hAPP(hAPP(c_member(_1694475), _1694477), hAPP(c_List_Oset(_1694475), c_List_Oremove1(_1694475, _1694481, _1694479))))], (20145 ^ _779571) ^ [_1125924, _1125926, _1125928] : [class_Fields_Olinordered__field__inverse__zero(_1125924), 20148 ^ _779571 : [(20163 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125924), _1125926), _1125928)))), 20164 ^ _779571 : [(20171 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), _1125926), c_Groups_Ozero__class_Ozero(_1125924))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), _1125928), c_Groups_Ozero__class_Ozero(_1125924)))], (20165 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), _1125926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), _1125928))]]], (20149 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125924), _1125926), _1125928))), 20154 ^ _779571 : [(20157 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), _1125928)))], (20155 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), c_Groups_Ozero__class_Ozero(_1125924)), _1125926)))]], 20158 ^ _779571 : [(20161 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), _1125928), c_Groups_Ozero__class_Ozero(_1125924))))], (20159 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125924), _1125926), c_Groups_Ozero__class_Ozero(_1125924))))]]]]], (6738 ^ _779571) ^ [_890147, _890149, _890151] : [hAPP(c_Com_Ocom_OBODY, _890147) = c_Com_Ocom_OSemi(_890149, _890151)], (27478 ^ _779571) ^ [_1265219, _1265221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1265219), _1265221)), -(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)), _1265219)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265221))))], (27858 ^ _779571) ^ [_1272908, _1272910, _1272912, _1272914] : [class_Lattices_Osemilattice__sup(_1272908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272908), _1272910), _1272912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272908), _1272910), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272908), _1272912), _1272914))))], (37998 ^ _779571) ^ [_1492841, _1492843, _1492845] : [class_Lattices_Olattice(_1492841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492841), _1492843)), -(_1492845 = c_Orderings_Obot__class_Obot(tc_fun(_1492841, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492841, tc_HOL_Obool)), _1492845), _1492843)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492841), c_Big__Operators_Olattice__class_OInf__fin(_1492841, _1492845)), c_Big__Operators_Olattice__class_OInf__fin(_1492841, _1492843)) = c_Big__Operators_Olattice__class_OInf__fin(_1492841, _1492843))], (18927 ^ _779571) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (5360 ^ _779571) ^ [_862379, _862381, _862383, _862385, _862387, _862389, _862391, _862393, _862395, _862397] : [-(c_Map_Omap__upds(_862397, _862393, _862389, _862385, _862381) = c_Map_Omap__upds(_862395, _862391, _862387, _862383, _862379)), _862397 = _862395, _862393 = _862391, _862389 = _862387, _862385 = _862383, _862381 = _862379], (30351 ^ _779571) ^ [_1323926, _1323928, _1323930] : [_1323928 = _1323930, -(hAPP(hAPP(c_COMBC(_1323926, tc_fun(_1323926, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323926)), _1323928) = hAPP(hAPP(c_COMBC(_1323926, tc_fun(_1323926, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323926)), _1323930))], (8372 ^ _779571) ^ [_918470, _918472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918470), _918472))), -(_918470 = _918472), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918472), _918470)))], (29820 ^ _779571) ^ [_1312825, _1312827, _1312829] : [class_Orderings_Olinorder(_1312825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1312825), _1312827), _1312829)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312825, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1312825), _1312827), c_Orderings_Obot__class_Obot(tc_fun(_1312825, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1312825, _1312827, _1312829)) = c_SetInterval_Oord__class_OatLeastAtMost(_1312825, _1312827, _1312829))], (51215 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (8249 ^ _779571) ^ [_916388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _916388)), -(_916388 = hAPP(c_Nat_OSuc, 8252 ^ [_916388]))], (29754 ^ _779571) ^ [_1311620, _1311622, _1311624] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1311620, _1311622) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1311624), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 29757 ^ _779571 : [(29760 ^ _779571) ^ [] : [-(_1311622 = _1311624)], (29758 ^ _779571) ^ [] : [-(_1311620 = _1311622)]]], (46867 ^ _779571) ^ [_1710113, _1710115, _1710117, _1710119] : [_1710113 = _1710115, -(c_List_Oremove1(_1710117, _1710113, hAPP(hAPP(c_List_Olist_OCons(_1710117), _1710115), _1710119)) = _1710119)], (6436 ^ _779571) ^ [_884519, _884521, _884523] : [-(hAPP(c_Nat_Onat_Onat__rec(_884519, _884521, _884523), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _884521)], (37243 ^ _779571) ^ [_1474951, _1474953, _1474955, _1474957, _1474959] : [class_Groups_Ocomm__monoid__mult(_1474951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474953), _1474955)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474953), _1474957)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474953, tc_HOL_Obool)), _1474955), _1474957) = c_Orderings_Obot__class_Obot(tc_fun(_1474953, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1474953, _1474951), _1474959), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474953, tc_HOL_Obool)), _1474955), _1474957)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1474951), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1474953, _1474951), _1474959), _1474955)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1474953, _1474951), _1474959), _1474957)))], (6839 ^ _779571) ^ [_892342, _892344, _892346, _892348] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_892342, _892344), _892346, _892348, hAPP(hAPP(hAPP(c_Natural_Oupdate, _892346), _892342), hAPP(_892344, _892346))))], (42006 ^ _779571) ^ [_1591341] : [class_Orderings_Owellorder(_1591341), -(c_Wellfounded_Owf(_1591341, hAPP(c_Set_OCollect(tc_prod(_1591341, _1591341)), hAPP(c_Product__Type_Oprod_Oprod__case(_1591341, _1591341, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1591341)))))], (49098 ^ _779571) ^ [_1764631, _1764633, _1764635, _1764637] : [-(hAPP(c_List_Ofoldl(_1764631, _1764633, _1764635, _1764637), c_List_Olist_ONil(_1764633)) = _1764637)], (4556 ^ _779571) ^ [_850097, _850099] : [_850099 = _850097, -(c_List_Orotate1(_850099) = c_List_Orotate1(_850097))], (39549 ^ _779571) ^ [_1525231, _1525233, _1525235, _1525237] : [-(hAPP(c_Set_Ovimage(_1525231, _1525233, _1525235), _1525237) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525233, tc_fun(_1525231, tc_HOL_Obool)), _1525237), hAPP(hAPP(c_COMBB(tc_fun(_1525233, tc_HOL_Obool), tc_fun(_1525231, tc_HOL_Obool), _1525233), c_Set_Ovimage(_1525231, _1525233, _1525235)), hAPP(hAPP(c_COMBC(_1525233, tc_fun(_1525233, tc_HOL_Obool), tc_fun(_1525233, tc_HOL_Obool)), c_Set_Oinsert(_1525233)), c_Orderings_Obot__class_Obot(tc_fun(_1525233, tc_HOL_Obool))))))], (7043 ^ _779571) ^ [_895627, _895629] : [class_Groups_Olinordered__ab__group__add(_895627), 7046 ^ _779571 : [(7053 ^ _779571) ^ [] : [_895629 = c_Groups_Ozero__class_Ozero(_895627), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895627), _895629), _895629) = c_Groups_Ozero__class_Ozero(_895627))], (7047 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895627), _895629), _895629) = c_Groups_Ozero__class_Ozero(_895627), -(_895629 = c_Groups_Ozero__class_Ozero(_895627))]]], (39302 ^ _779571) ^ [_1519409, _1519411, _1519413, _1519415, _1519417] : [c_Fun_Oinj__on(_1519409, _1519411, _1519413, _1519415), hBOOL(hAPP(hAPP(c_member(_1519411), _1519417), hAPP(c_Set_Oimage(_1519409, _1519411, _1519413), _1519415))), -(hAPP(_1519413, hAPP(c_Fun_Othe__inv__into(_1519409, _1519411, _1519415, _1519413), _1519417)) = _1519417)], (19071 ^ _779571) ^ [_1106492, _1106494] : [-(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), _1106492)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1106494)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106492))) = 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), _1106494)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106492)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38038 ^ _779571) ^ [_1493504, _1493506] : [class_Lattices_Olattice(_1493504), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493504), _1493506)), -(_1493506 = c_Orderings_Obot__class_Obot(tc_fun(_1493504, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493504), c_Big__Operators_Olattice__class_OInf__fin(_1493504, _1493506)), c_Big__Operators_Olattice__class_OSup__fin(_1493504, _1493506))))], (19559 ^ _779571) ^ [] : [-(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))))))], (40656 ^ _779571) ^ [_1551408, _1551410, _1551412] : [class_Groups_Oab__semigroup__mult(_1551408), -(_1551410 = c_Orderings_Obot__class_Obot(tc_fun(_1551408, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551408), _1551410)), -(hBOOL(hAPP(hAPP(c_member(_1551408), _1551412), _1551410))), -(hAPP(c_Finite__Set_Ofold1(_1551408, c_Groups_Otimes__class_Otimes(_1551408)), hAPP(hAPP(c_Set_Oinsert(_1551408), _1551412), _1551410)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1551408), _1551412), hAPP(c_Finite__Set_Ofold1(_1551408, c_Groups_Otimes__class_Otimes(_1551408)), _1551410)))], (6393 ^ _779571) ^ [_883636, _883638, _883640] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_883636, _883638, _883640))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _883638))))], (34174 ^ _779571) ^ [_1404443, _1404445, _1404447, _1404449, _1404451] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404443, _1404445), _1404447), _1404449), _1404451), _1404449) = _1404451)], (6151 ^ _779571) ^ [_878805, _878807, _878809, _878811, _878813, _878815, _878817, _878819, _878821] : [-(c_Com_Ocom_Ocom__case(_878805, _878807, _878809, _878811, _878813, _878815, _878817, _878819, _878821, c_Com_Ocom_OSKIP) = _878807)], (5765 ^ _779571) ^ [_871920, _871922, _871924, _871926, _871928, _871930] : [c_Natural_Oevaln(_871920, _871922, _871924, _871926), c_Natural_Oevaln(_871928, _871926, _871924, _871930), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_871920, _871928), _871922, _871924, _871930))], (7594 ^ _779571) ^ [_905604] : [-(_905604 = 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)), _905604)))], (33549 ^ _779571) ^ [_1391845, _1391847, _1391849, _1391851] : [33550 ^ _779571 : [(33553 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391849), _1391851)))], (33551 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391845), _1391847)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1391845, _1391849)), c_Sum__Type_OPlus(_1391845, _1391849, _1391847, _1391851)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44744 ^ _779571) ^ [_1658214, _1658216, _1658218, _1658220, _1658222] : [_1658214 = c_Orderings_Obot__class_Obot(tc_fun(_1658216, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658216, tc_fun(_1658218, tc_HOL_Obool)), _1658214), hAPP(hAPP(c_COMBC(_1658216, tc_fun(_1658218, tc_HOL_Obool), tc_fun(_1658218, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1658218, tc_HOL_Obool), tc_fun(tc_fun(_1658218, tc_HOL_Obool), tc_fun(_1658218, tc_HOL_Obool)), _1658216), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658218, tc_HOL_Obool))), _1658220)), _1658222)) = c_Orderings_Otop__class_Otop(tc_fun(_1658218, tc_HOL_Obool)))], (21785 ^ _779571) ^ [_1155121, _1155123, _1155125, _1155127] : [class_Fields_Olinordered__field__inverse__zero(_1155121), class_Int_Onumber(_1155121), 21792 ^ _779571 : [(21793 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155121), _1155125), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)))), 21796 ^ _779571 : [(21803 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), c_Groups_Ozero__class_Ozero(_1155121)), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)))), 21806 ^ _779571 : [(21813 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)), c_Groups_Ozero__class_Ozero(_1155121)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155123), c_Groups_Ozero__class_Ozero(_1155121))))], (21807 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)), c_Groups_Ozero__class_Ozero(_1155121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155121), _1155123), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)))))]]], (21797 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), c_Groups_Ozero__class_Ozero(_1155121)), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155121), _1155123), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))), _1155125)))]]], (21819 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155121), _1155125), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))))), 21822 ^ _779571 : [(21825 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155121), _1155123), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))), _1155125))], (21823 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), c_Groups_Ozero__class_Ozero(_1155121)), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))))]], 21826 ^ _779571 : [(21829 ^ _779571) ^ [] : [21830 ^ _779571 : [(21833 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155121), _1155123), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127))))], (21831 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)), c_Groups_Ozero__class_Ozero(_1155121))))]], 21834 ^ _779571 : [(21837 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), _1155123), c_Groups_Ozero__class_Ozero(_1155121)))], (21835 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)), c_Groups_Ozero__class_Ozero(_1155121)))]]], (21827 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155121), c_Groups_Ozero__class_Ozero(_1155121)), hAPP(c_Int_Onumber__class_Onumber__of(_1155121), _1155127)))]]]]], (7422 ^ _779571) ^ [_902728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902728), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37678 ^ _779571) ^ [_1485063, _1485065, _1485067, _1485069, _1485071, _1485073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485063, _1485065)), hAPP(hAPP(c_Product__Type_OPair(_1485063, _1485065), _1485071), _1485073)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool)), _1485067), _1485069))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485063, tc_fun(_1485065, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1485063, tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_fun(_1485065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485065, tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_fun(_1485065, tc_HOL_Obool)), _1485063), c_COMBC(_1485065, tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485065, tc_prod(_1485063, _1485065)), tc_fun(_1485065, tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), _1485063), hAPP(c_COMBB(tc_prod(_1485063, _1485065), tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool), _1485065), c_member(tc_prod(_1485063, _1485065)))), c_Product__Type_OPair(_1485063, _1485065)))), _1485067)), hAPP(hAPP(c_COMBC(_1485063, tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_fun(_1485065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485065, tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_fun(_1485065, tc_HOL_Obool)), _1485063), c_COMBC(_1485065, tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485065, tc_prod(_1485063, _1485065)), tc_fun(_1485065, tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool)), _1485063), hAPP(c_COMBB(tc_prod(_1485063, _1485065), tc_fun(tc_fun(tc_prod(_1485063, _1485065), tc_HOL_Obool), tc_HOL_Obool), _1485065), c_member(tc_prod(_1485063, _1485065)))), c_Product__Type_OPair(_1485063, _1485065)))), _1485069)), _1485071), _1485073)))], (51383 ^ _779571) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (39691 ^ _779571) ^ [_1528682, _1528684, _1528686, _1528688, _1528690] : [class_Groups_Oab__semigroup__mult(_1528682), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1528682, _1528682, c_Groups_Otimes__class_Otimes(_1528682), _1528684, _1528686), _1528688)), hBOOL(hAPP(hAPP(c_member(_1528682), _1528690), _1528686)), -(hBOOL(hAPP(hAPP(c_member(_1528682), _1528684), _1528686))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1528682, _1528682, c_Groups_Otimes__class_Otimes(_1528682), _1528690, hAPP(hAPP(c_Set_Oinsert(_1528682), _1528684), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528682, tc_HOL_Obool)), _1528686), hAPP(hAPP(c_Set_Oinsert(_1528682), _1528690), c_Orderings_Obot__class_Obot(tc_fun(_1528682, tc_HOL_Obool)))))), _1528688)))], (15177 ^ _779571) ^ [_1036171, _1036173, _1036175] : [class_Fields_Olinordered__field__inverse__zero(_1036171), 15183 ^ _779571 : [(15188 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036171), 15182 ^ [_1036171, _1036173, _1036175]), _1036173)), _1036175))], (15186 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036171), 15182 ^ [_1036171, _1036173, _1036175]), c_Groups_Oone__class_Oone(_1036171))))], (15184 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036171), c_Groups_Ozero__class_Ozero(_1036171)), 15182 ^ [_1036171, _1036173, _1036175])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036171), _1036173), _1036175)))], (24859 ^ _779571) ^ [_1214264, _1214266, _1214268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1214264), c_Nitpick_Oplus__frac(_1214264, _1214266, c_Nitpick_Ouminus__frac(_1214264, _1214268)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1214264, _1214266, _1214268))], (27726 ^ _779571) ^ [_1270397] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1270397)) = _1270397)], (11869 ^ _779571) ^ [_977182, _977184, _977186, _977188] : [class_Rings_Oordered__comm__semiring(_977182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977182), _977184), _977186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977182), c_Groups_Ozero__class_Ozero(_977182)), _977188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977182), _977188), _977184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977182), _977188), _977186))))], (49026 ^ _779571) ^ [_1763147, _1763149, _1763151] : [hBOOL(hAPP(c_List_Odistinct(_1763147), _1763151)), -(hBOOL(hAPP(c_List_Odistinct(_1763147), hAPP(c_List_Orotate(_1763147, _1763149), _1763151))))], (18675 ^ _779571) ^ [_1099967, _1099969] : [_1099967 = _1099969, -(c_Int_OBit1(_1099967) = c_Int_OBit1(_1099969))], (17275 ^ _779571) ^ [_1076566, _1076568] : [17276 ^ _779571 : [(17279 ^ _779571) ^ [] : [_1076568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17277 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1076566))]], -(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), _1076566), _1076568))))], (44952 ^ _779571) ^ [_1663207] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663207, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1663207, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1663207, tc_HOL_Obool)))], (15054 ^ _779571) ^ [_1034010, _1034012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034012)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1034010), hAPP(c_Int_Onat, _1034012)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034010, _1034012)))], (35257 ^ _779571) ^ [_1428797, _1428799, _1428801] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1428797, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1428797, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1428797), _1428799)), hAPP(c_Set_OPow(_1428797), _1428801))), hAPP(c_Set_OPow(_1428797), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428797, tc_HOL_Obool)), _1428799), _1428801)))))], (38235 ^ _779571) ^ [_1497348, _1497350] : [c_Equiv__Relations_Oequiv(_1497348, c_Orderings_Otop__class_Otop(tc_fun(_1497348, tc_HOL_Obool)), _1497350), -(c_Equiv__Relations_Oequivp(_1497348, hAPP(hAPP(c_COMBC(_1497348, tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_fun(_1497348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497348, tc_fun(tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_fun(_1497348, tc_HOL_Obool)), _1497348), c_COMBC(_1497348, tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497348, tc_prod(_1497348, _1497348)), tc_fun(_1497348, tc_fun(tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_HOL_Obool)), _1497348), hAPP(c_COMBB(tc_prod(_1497348, _1497348), tc_fun(tc_fun(tc_prod(_1497348, _1497348), tc_HOL_Obool), tc_HOL_Obool), _1497348), c_member(tc_prod(_1497348, _1497348)))), c_Product__Type_OPair(_1497348, _1497348)))), _1497350)))], (40268 ^ _779571) ^ [_1543403, _1543405, _1543407, _1543409, _1543411, _1543413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543403, _1543405), tc_HOL_Obool)), _1543407), hAPP(hAPP(c_Product__Type_OSigma(_1543403, _1543405), _1543409), hAPP(c_COMBK(tc_fun(_1543405, tc_HOL_Obool), _1543403), _1543411)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1543405, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1543403, _1543405, _1543407), _1543413)), _1543411)))], (8760 ^ _779571) ^ [_924347, _924349] : [class_Rings_Ocomm__semiring__1(_924347), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924347), _924349), _924349) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924347), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924347), c_Groups_Oone__class_Oone(_924347)), c_Groups_Oone__class_Oone(_924347))), _924349))], (18217 ^ _779571) ^ [_1092736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092736)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1092736) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (48792 ^ _779571) ^ [_1757943, _1757945, _1757947, _1757949] : [-(hAPP(hAPP(c_List_Odrop(_1757943), _1757945), hAPP(hAPP(c_List_Oappend(_1757943), _1757947), _1757949)) = hAPP(hAPP(c_List_Oappend(_1757943), hAPP(hAPP(c_List_Odrop(_1757943), _1757945), _1757947)), hAPP(hAPP(c_List_Odrop(_1757943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1757945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757943)), _1757947))), _1757949)))], (47057 ^ _779571) ^ [_1715602, _1715604, _1715606, _1715608, _1715610] : [class_Rings_Osemiring__0(_1715602), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715602), hAPP(hAPP(c_List_Omap(_1715604, _1715602), hAPP(hAPP(c_COMBB(_1715602, _1715602, _1715604), hAPP(c_Groups_Otimes__class_Otimes(_1715602), _1715606)), _1715608)), _1715610)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1715602), _1715606), hAPP(c_List_Omonoid__add__class_Olistsum(_1715602), hAPP(hAPP(c_List_Omap(_1715604, _1715602), _1715608), _1715610))))], (34881 ^ _779571) ^ [_1419722, _1419724, _1419726, _1419728] : [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), _1419722), _1419724)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1419726), _1419728))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419722), _1419728) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419726), _1419724))], (18731 ^ _779571) ^ [_1100989] : [c_Int_OBit1(_1100989) = c_Int_OPls], (30965 ^ _779571) ^ [_1337073] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1337073))))], (29716 ^ _779571) ^ [_1310780, _1310782, _1310784, _1310786, _1310788] : [_1310780 = c_Orderings_Obot__class_Obot(tc_fun(_1310782, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310782, tc_fun(_1310784, tc_HOL_Obool)), _1310780), hAPP(hAPP(c_COMBB(tc_fun(_1310784, tc_HOL_Obool), tc_fun(_1310784, tc_HOL_Obool), _1310782), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310784, tc_HOL_Obool)), _1310786)), _1310788)) = c_Orderings_Obot__class_Obot(tc_fun(_1310784, tc_HOL_Obool)))], (28547 ^ _779571) ^ [_1286469, _1286471] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1286469), _1286471) = 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)), _1286469)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1286471))))], (24989 ^ _779571) ^ [_1217640, _1217642] : [-(c_Divides_Odivmod__nat(_1217640, _1217642) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1217640, _1217642)))], (2730 ^ _779571) ^ [_820950, _820952, _820954, _820956, _820958, _820960, _820962, _820964] : [-(c_Random_Oiterate(_820964, _820960, _820956, _820952) = c_Random_Oiterate(_820962, _820958, _820954, _820950)), _820964 = _820962, _820960 = _820958, _820956 = _820954, _820952 = _820950], (30311 ^ _779571) ^ [_1323142, _1323144, _1323146, _1323148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323142, tc_HOL_Obool)), _1323144), _1323146)), hBOOL(hAPP(hAPP(c_member(_1323142), _1323148), _1323144)), -(hBOOL(hAPP(hAPP(c_member(_1323142), _1323148), _1323146)))], (18471 ^ _779571) ^ [_1096530, _1096532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096530)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096532)))), 18474 ^ _779571 : [(18477 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1096532))], (18475 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096530), _1096532)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096530), _1096532))], (46364 ^ _779571) ^ [_1695490, _1695492, _1695494, _1695496, _1695498] : [-(hBOOL(hAPP(hAPP(c_member(_1695490), _1695492), hAPP(c_List_Oset(_1695490), _1695494)))), -(hAPP(c_Map_Omap__of(_1695490, _1695496, hAPP(hAPP(c_List_Ozip(_1695490, _1695496), _1695494), hAPP(hAPP(c_List_Omap(_1695490, _1695496), _1695498), _1695494))), _1695492) = c_Option_Ooption_ONone(_1695496))], (47396 ^ _779571) ^ [_1722466, _1722468, _1722470] : [-(hAPP(c_Map_Omap__of(_1722466, _1722468, c_List_Olist_ONil(tc_prod(_1722466, _1722468))), _1722470) = c_Option_Ooption_ONone(_1722468))], (24025 ^ _779571) ^ [_1197785, _1197787, _1197789] : [24026 ^ _779571 : [(24029 ^ _779571) ^ [] : [_1197787 = _1197789], (24027 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197785, tc_HOL_Obool)), _1197787), _1197789))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197785, tc_HOL_Obool)), _1197787), _1197789)))], (7327 ^ _779571) ^ [_901109, _901111, _901113, _901115] : [hAPP(c_Sum__Type_OInr(_901109, _901111), _901113) = hAPP(c_Sum__Type_OInl(_901111, _901109), _901115)], (19487 ^ _779571) ^ [_1113847, _1113849] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1113847)), c_Int_OBit1(_1113849)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1113847), c_Int_Osucc(_1113849))))], (5610 ^ _779571) ^ [_866170, _866172, _866174, _866176] : [-(c_COMBK(_866176, _866172) = c_COMBK(_866174, _866170)), _866176 = _866174, _866172 = _866170], (36642 ^ _779571) ^ [_1460328, _1460330, _1460332] : [-(hAPP(c_Set_OPow(_1460328), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460328, tc_HOL_Obool)), _1460330), _1460332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1460328, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1460328), _1460330)), hAPP(c_Set_OPow(_1460328), _1460332)))], (38427 ^ _779571) ^ [_1501477, _1501479, _1501481, _1501483] : [38429 ^ _779571 : [(38433 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501477), 38431 ^ [_1501477, _1501479, _1501481, _1501483]), _1501483)))], (38435 ^ _779571) ^ [] : [-(hAPP(_1501481, 38428 ^ [_1501477, _1501479, _1501481, _1501483]) = hAPP(_1501481, 38431 ^ [_1501477, _1501479, _1501481, _1501483]))], (38437 ^ _779571) ^ [] : [38428 ^ [_1501477, _1501479, _1501481, _1501483] = 38431 ^ [_1501477, _1501479, _1501481, _1501483]], (38430 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501477), 38428 ^ [_1501477, _1501479, _1501481, _1501483]), _1501483)))]], -(c_Fun_Oinj__on(_1501477, _1501479, _1501481, _1501483))], (19717 ^ _779571) ^ [_1117743, _1117745] : [class_Rings_Oring__1__no__zero__divisors(_1117743), 19720 ^ _779571 : [(19721 ^ _779571) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1117743), _1117745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1117743), -(_1117745 = c_Groups_Oone__class_Oone(_1117743)), -(_1117745 = hAPP(c_Groups_Ouminus__class_Ouminus(_1117743), c_Groups_Oone__class_Oone(_1117743)))], (19731 ^ _779571) ^ [] : [19732 ^ _779571 : [(19735 ^ _779571) ^ [] : [_1117745 = hAPP(c_Groups_Ouminus__class_Ouminus(_1117743), c_Groups_Oone__class_Oone(_1117743))], (19733 ^ _779571) ^ [] : [_1117745 = c_Groups_Oone__class_Oone(_1117743)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1117743), _1117745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1117743))]]], (26206 ^ _779571) ^ [_1239785, _1239787, _1239789] : [class_Divides_Oring__div(_1239785), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239785), _1239787), _1239789)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239785), hAPP(c_Groups_Ouminus__class_Ouminus(_1239785), _1239789)), _1239787) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239785), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239785), _1239789), _1239787)))], (21297 ^ _779571) ^ [_1145916, _1145918, _1145920] : [class_Fields_Olinordered__field(_1145916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145916), _1145918), _1145920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145916), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145916), _1145918), _1145920)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145916), c_Groups_Oone__class_Oone(_1145916)), c_Groups_Oone__class_Oone(_1145916)))), _1145920)))], (29852 ^ _779571) ^ [_1313526] : [-(hAPP(c_Finite__Set_Ocard(_1313526), c_Orderings_Obot__class_Obot(tc_fun(_1313526, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17399 ^ _779571) ^ [_1078852, _1078854, _1078856] : [class_Rings_Olinordered__semidom(_1078852), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078852), c_Groups_Ozero__class_Ozero(_1078852)), _1078854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078852), c_Groups_Ozero__class_Ozero(_1078852)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078852), _1078854), _1078856))))], (35229 ^ _779571) ^ [_1428187, _1428189, _1428191] : [hAPP(c_Set_Oimage(_1428189, tc_fun(_1428189, tc_HOL_Obool), _1428187), _1428191) = hAPP(c_Set_OPow(_1428189), _1428191)], (16601 ^ _779571) ^ [_1063555, _1063557] : [class_Groups_Oordered__ab__group__add__abs(_1063555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063555), hAPP(c_Groups_Oabs__class_Oabs(_1063555), _1063557)), c_Groups_Ozero__class_Ozero(_1063555)))], (4466 ^ _779571) ^ [_848678, _848680, _848682, _848684] : [-(c_List_Olex(_848684, _848680) = c_List_Olex(_848682, _848678)), _848684 = _848682, _848680 = _848678], (18735 ^ _779571) ^ [_1101044] : [c_Int_OMin = c_Int_OBit1(_1101044), -(c_Int_OMin = _1101044)], (26324 ^ _779571) ^ [_1241902, _1241904, _1241906] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241902), _1241904)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1241904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241902), _1241906)))))], (47987 ^ _779571) ^ [_1737429, _1737431, _1737433] : [-(hAPP(c_List_Oset(_1737429), hAPP(hAPP(c_List_Oappend(_1737429), _1737431), _1737433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1737429, tc_HOL_Obool)), hAPP(c_List_Oset(_1737429), _1737431)), hAPP(c_List_Oset(_1737429), _1737433)))], (7357 ^ _779571) ^ [_901688, _901690, _901692, _901694] : [_901692 = _901694, -(hAPP(c_Sum__Type_OInr(_901688, _901690), _901692) = hAPP(c_Sum__Type_OInr(_901688, _901690), _901694))], (51385 ^ _779571) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (36740 ^ _779571) ^ [_1462966, _1462968, _1462970, _1462972] : [-(hBOOL(hAPP(hAPP(c_member(_1462966), _1462968), _1462970))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462966, tc_HOL_Obool)), _1462970), hAPP(hAPP(c_Set_Oinsert(_1462966), _1462968), _1462972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462966, tc_HOL_Obool)), _1462970), _1462972))], (30321 ^ _779571) ^ [_1323345, _1323347, _1323349] : [hBOOL(hAPP(hAPP(c_member(_1323345), _1323347), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323345, tc_HOL_Obool)), _1323349))), hBOOL(hAPP(hAPP(c_member(_1323345), _1323347), _1323349))], (19177 ^ _779571) ^ [_1108479] : [_1108479 = c_Int_OPls, -(c_Int_OBit0(_1108479) = c_Int_OPls)], (6585 ^ _779571) ^ [_887070, _887072, _887074, _887076] : [-(c_Hoare__Mirabelle_Otriple__valid(_887070, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887070), _887072), hAPP(c_Com_Ocom_OBODY, _887074)), _887076)))], (22334 ^ _779571) ^ [_1165124, _1165126] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1165124))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1165126)), hAPP(c_Int_Onat, _1165124)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1165126), _1165124)), 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)))], (47930 ^ _779571) ^ [_1736057, _1736059, _1736061, _1736063, _1736065] : [hAPP(hAPP(c_List_Oappend(_1736057), _1736059), _1736061) = hAPP(hAPP(c_List_Olist_OCons(_1736057), _1736063), _1736065), 47935 ^ _779571 : [(47938 ^ _779571) ^ [] : [-(_1736061 = hAPP(hAPP(c_List_Olist_OCons(_1736057), _1736063), _1736065))], (47936 ^ _779571) ^ [] : [-(_1736059 = c_List_Olist_ONil(_1736057))]], 47940 ^ _779571 : [(47943 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1736057), 47939 ^ [_1736057, _1736059, _1736061, _1736063, _1736065]), _1736061) = _1736065)], (47941 ^ _779571) ^ [] : [-(_1736059 = hAPP(hAPP(c_List_Olist_OCons(_1736057), _1736063), 47939 ^ [_1736057, _1736059, _1736061, _1736063, _1736065]))]]], (18333 ^ _779571) ^ [_1094485] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1094485) = c_Int_OPls)], (24575 ^ _779571) ^ [_1208379, _1208381, _1208383, _1208385, _1208387, _1208389] : [hAPP(_1208385, hAPP(c_Product__Type_Ofst(_1208379, _1208383), _1208387)) = hAPP(_1208389, hAPP(c_Product__Type_Ofst(_1208379, _1208383), _1208387)), -(hAPP(c_Product__Type_Oapfst(_1208379, _1208381, _1208383, _1208385), _1208387) = hAPP(c_Product__Type_Oapfst(_1208379, _1208381, _1208383, _1208389), _1208387))], (23863 ^ _779571) ^ [_1194392, _1194394, _1194396] : [class_Int_Onumber(_1194392), class_Orderings_Oord(_1194392), 23870 ^ _779571 : [(23877 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194392), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194394)), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194396)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194392), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194394)), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194396)) = hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194396))], (23871 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194392), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194394)), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194396))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194392), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194394)), hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194396)) = hAPP(c_Int_Onumber__class_Onumber__of(_1194392), _1194394))]]], (41680 ^ _779571) ^ [_1582256, _1582258] : [41681 ^ _779571 : [(41682 ^ _779571) ^ [_1582320, _1582322] : [_1582258 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1582256, _1582320), 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)), _1582322)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1582256), _1582258)))], (29646 ^ _779571) ^ [_1309401, _1309403] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309403, _1309401) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309401), _1309403)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309403), _1309401)))], (51447 ^ _779571) ^ [_1811818, _1811820] : [-(class_Finite__Set_Ofinite(tc_sum(_1811818, _1811820))), class_Finite__Set_Ofinite(_1811818), class_Finite__Set_Ofinite(_1811820)], (16501 ^ _779571) ^ [_1061915, _1061917] : [class_Rings_Ocomm__semiring__1(_1061915), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1061915), _1061917), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1061917)], (6556 ^ _779571) ^ [_886568] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _886568)], (48736 ^ _779571) ^ [_1756757, _1756759] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756757)), hAPP(c_List_Orotate1(_1756757), _1756759)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756757)), _1756759))], (6430 ^ _779571) ^ [_884335, _884337, _884339, _884341, _884343, _884345, _884347, _884349, _884351, _884353, _884355] : [-(c_Com_Ocom_Ocom__case(_884335, _884337, _884339, _884341, _884343, _884345, _884347, _884349, _884351, c_Com_Ocom_OAss(_884353, _884355)) = hAPP(hAPP(_884339, _884353), _884355))], (29266 ^ _779571) ^ [_1302641, _1302643] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302641, tc_HOL_Obool)), _1302643), _1302643) = c_Orderings_Obot__class_Obot(tc_fun(_1302641, tc_HOL_Obool)))], (33367 ^ _779571) ^ [_1387967, _1387969, _1387971] : [class_Orderings_Olinorder(_1387967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387967), _1387969)), -(_1387969 = c_Orderings_Obot__class_Obot(tc_fun(_1387967, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387967), _1387971)), -(_1387971 = c_Orderings_Obot__class_Obot(tc_fun(_1387967, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1387967, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387967, tc_HOL_Obool)), _1387969), _1387971)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387967), c_Big__Operators_Olinorder__class_OMin(_1387967, _1387969)), c_Big__Operators_Olinorder__class_OMin(_1387967, _1387971)))], (6971 ^ _779571) ^ [_894480, _894482, _894484, _894486] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_894480, _894482), _894484, _894486, hAPP(hAPP(hAPP(c_Natural_Oupdate, _894484), _894480), hAPP(_894482, _894484))))], (45528 ^ _779571) ^ [_1676293, _1676295] : [-(c_Wellfounded_Owf(_1676293, _1676295)), 45531 ^ _779571 : [(45534 ^ _779571) ^ [_1676513] : [hBOOL(hAPP(hAPP(c_member(_1676293), _1676513), 45529 ^ [_1676293, _1676295])), 45538 ^ _779571 : [(45541 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676293), 45537 ^ [_1676293, _1676295, _1676513]), 45529 ^ [_1676293, _1676295])))], (45539 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1676293, _1676293)), hAPP(hAPP(c_Product__Type_OPair(_1676293, _1676293), 45537 ^ [_1676293, _1676295, _1676513]), _1676513)), _1676295)))]]], (45532 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676293), 45530 ^ [_1676293, _1676295]), 45529 ^ [_1676293, _1676295])))]]], (1994 ^ _779571) ^ [_809178, _809180, _809182, _809184, _809186, _809188] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_809188, _809184, _809180) = c_Hoare__Mirabelle_Otriple_Otriple__size(_809186, _809182, _809178)), _809188 = _809186, _809184 = _809182, _809180 = _809178], (5112 ^ _779571) ^ [_858561, _858563] : [_858563 = _858561, -(c_List_Omonoid__add__class_Olistsum(_858563) = c_List_Omonoid__add__class_Olistsum(_858561))], (45704 ^ _779571) ^ [_1680063, _1680065, _1680067, _1680069, _1680071] : [-(hBOOL(hAPP(hAPP(c_member(_1680063), _1680065), c_Map_Odom(_1680063, _1680067, _1680069)))), -(hAPP(c_Map_Omap__add(_1680063, _1680067, _1680069, _1680071), _1680065) = hAPP(_1680071, _1680065))], (27610 ^ _779571) ^ [_1267831, _1267833] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1267831, _1267833)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1267831), hAPP(c_Nat_OSuc, _1267833)))], (50676 ^ _779571) ^ [_1798423, _1798425] : [c_List_Olist_ONil(_1798423) = hAPP(c_List_Orev(_1798423), _1798425), -(_1798425 = c_List_Olist_ONil(_1798423))], (31165 ^ _779571) ^ [_1341020, _1341022, _1341024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341020), _1341022)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341020), _1341024)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341020), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341020, tc_HOL_Obool)), _1341022), _1341024))))], (4046 ^ _779571) ^ [_841886, _841888, _841890, _841892] : [-(c_Relation_ODomain(_841892, _841888) = c_Relation_ODomain(_841890, _841886)), _841892 = _841890, _841888 = _841886], (30919 ^ _779571) ^ [_1336099, _1336101, _1336103, _1336105, _1336107, _1336109, _1336111] : [hBOOL(hAPP(hAPP(c_member(_1336099), _1336101), _1336103)), c_Nitpick_Ofold__graph_H(_1336099, _1336105, _1336107, _1336109, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336099, tc_HOL_Obool)), _1336103), hAPP(hAPP(c_Set_Oinsert(_1336099), _1336101), c_Orderings_Obot__class_Obot(tc_fun(_1336099, tc_HOL_Obool)))), _1336111), -(c_Nitpick_Ofold__graph_H(_1336099, _1336105, _1336107, _1336109, _1336103, hAPP(hAPP(_1336107, _1336101), _1336111)))], (15828 ^ _779571) ^ [_1048429, _1048431, _1048433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048429), _1048431)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048433), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048431), _1048429)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048433), _1048431)), _1048429))], (29037 ^ _779571) ^ [_1297466, _1297468, _1297470, _1297472] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297466, tc_HOL_Obool)), _1297468), hAPP(hAPP(c_Set_Oinsert(_1297466), _1297470), _1297472)) = hAPP(hAPP(c_Set_Oinsert(_1297466), _1297470), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297466, tc_HOL_Obool)), _1297468), _1297472)))], (40198 ^ _779571) ^ [_1541641, _1541643] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541641, _1541641), tc_HOL_Obool)), c_Relation_OId__on(_1541641, _1541643)), hAPP(hAPP(c_Product__Type_OSigma(_1541641, _1541641), _1541643), hAPP(c_COMBK(tc_fun(_1541641, tc_HOL_Obool), _1541641), _1541643)))))], (12896 ^ _779571) ^ [_995612, _995614] : [class_Rings_Olinordered__idom(_995612), 12899 ^ _779571 : [(12906 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995612), _995614), c_Groups_Ozero__class_Ozero(_995612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995612), c_Groups_Osgn__class_Osgn(_995612, _995614)), c_Groups_Ozero__class_Ozero(_995612))))], (12900 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995612), c_Groups_Osgn__class_Osgn(_995612, _995614)), c_Groups_Ozero__class_Ozero(_995612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995612), _995614), c_Groups_Ozero__class_Ozero(_995612))))]]], (46710 ^ _779571) ^ [_1704597, _1704599, _1704601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1704597), _1704599)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1704597)), hAPP(c_Set_OCollect(tc_List_Olist(_1704597)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1704597), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1704597)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704597), tc_fun(_1704597, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1704597, tc_HOL_Obool), tc_fun(tc_fun(_1704597, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1704597)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1704597, tc_HOL_Obool))), c_List_Oset(_1704597))), _1704599))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704597), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1704597)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1704597)))), _1704601))))))], (17853 ^ _779571) ^ [_1086839] : [-(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, _1086839))))))], (560 ^ _779571) ^ [_788229, _788231, _788233, _788235, _788237, _788239, _788241, _788243, _788245, _788247, _788249, _788251, _788253, _788255] : [-(c_Predicate_Opred__comp(_788253, _788249, _788245, _788241, _788237, _788233, _788229)), c_Predicate_Opred__comp(_788255, _788251, _788247, _788243, _788239, _788235, _788231), _788255 = _788253, _788251 = _788249, _788247 = _788245, _788243 = _788241, _788239 = _788237, _788235 = _788233, _788231 = _788229], (9914 ^ _779571) ^ [_944710, _944712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944710)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944712))))], (44786 ^ _779571) ^ [_1659361, _1659363, _1659365, _1659367, _1659369] : [-(_1659361 = c_Orderings_Obot__class_Obot(tc_fun(_1659363, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659365, tc_HOL_Obool)), _1659367), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659363, tc_fun(_1659365, tc_HOL_Obool)), _1659361), _1659369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659363, tc_fun(_1659365, tc_HOL_Obool)), _1659361), hAPP(hAPP(c_COMBB(tc_fun(_1659365, tc_HOL_Obool), tc_fun(_1659365, tc_HOL_Obool), _1659363), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659365, tc_HOL_Obool)), _1659367)), _1659369)))], (38016 ^ _779571) ^ [_1493155, _1493157, _1493159] : [class_Lattices_Olattice(_1493155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493155), _1493157)), -(_1493157 = c_Orderings_Obot__class_Obot(tc_fun(_1493155, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493155), _1493159)), -(_1493159 = c_Orderings_Obot__class_Obot(tc_fun(_1493155, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1493155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493155, tc_HOL_Obool)), _1493157), _1493159)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493155), c_Big__Operators_Olattice__class_OInf__fin(_1493155, _1493157)), c_Big__Operators_Olattice__class_OInf__fin(_1493155, _1493159)))], (18659 ^ _779571) ^ [_1099640, _1099642] : [class_Int_Onumber__ring(_1099640), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099640), c_Groups_Oone__class_Oone(_1099640)), hAPP(c_Int_Onumber__class_Onumber__of(_1099640), _1099642)) = hAPP(c_Int_Onumber__class_Onumber__of(_1099640), 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), _1099642))))], (51381 ^ _779571) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (48622 ^ _779571) ^ [_1753572, _1753574, _1753576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1753572, _1753572), tc_HOL_Obool)), _1753574), _1753576)), c_Relation_Orefl__on(_1753572, c_Orderings_Otop__class_Otop(tc_fun(_1753572, tc_HOL_Obool)), _1753576), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1753572), tc_List_Olist(_1753572)), tc_HOL_Obool)), c_List_Olistrel1(_1753572, _1753574)), c_List_Olistrel(_1753572, _1753576))))], (24711 ^ _779571) ^ [_1211099, _1211101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211099)), hAPP(c_Code__Numeral_Onat__of, _1211101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1211099), _1211101)))], (24221 ^ _779571) ^ [_1201525, _1201527] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1201525), _1201527) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1201525, 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)))), _1201527))))], (47596 ^ _779571) ^ [_1727851, _1727853, _1727855, _1727857] : [-(_1727851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1727853), hAPP(hAPP(c_List_Olist_OCons(_1727853), _1727855), _1727857)), _1727851) = hAPP(hAPP(c_List_Onth(_1727853), _1727857), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1727851), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (27492 ^ _779571) ^ [_1265514, _1265516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1265514), _1265516)), -(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)), _1265514)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265516))))], (44549 ^ _779571) ^ [_1652529, _1652531, _1652533, _1652535] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652529, tc_fun(_1652531, tc_HOL_Obool)), _1652533), _1652535) = c_Orderings_Otop__class_Otop(tc_fun(_1652531, tc_HOL_Obool)), 44552 ^ _779571 : [(44553 ^ _779571) ^ [_1652645] : [hBOOL(hAPP(hAPP(c_member(_1652529), _1652645), _1652533)), -(hAPP(_1652535, _1652645) = c_Orderings_Otop__class_Otop(tc_fun(_1652531, tc_HOL_Obool)))]]], (31277 ^ _779571) ^ [_1345109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345109), c_Orderings_Otop__class_Otop(tc_fun(_1345109, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1345109)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1345109), tc_HOL_Obool)))))], (15394 ^ _779571) ^ [_1040193, _1040195] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1040193)), hAPP(c_Nat_OSuc, _1040195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040193), _1040195))], (23927 ^ _779571) ^ [_1195913, _1195915, _1195917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195913, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195913, tc_HOL_Obool)), _1195915)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1195913, tc_HOL_Obool)), _1195917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195913, tc_HOL_Obool)), _1195917), _1195915)))], (36632 ^ _779571) ^ [_1460083, _1460085, _1460087, _1460089, _1460091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460083, tc_HOL_Obool)), _1460085), _1460087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460083, tc_HOL_Obool)), _1460089), _1460091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460083, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460083, tc_HOL_Obool)), _1460085), _1460089)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460083, tc_HOL_Obool)), _1460087), _1460091))))], (22320 ^ _779571) ^ [_1164793] : [-(c_Quickcheck_Obeyond(_1164793, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (29306 ^ _779571) ^ [_1303353, _1303355, _1303357, _1303359] : [29308 ^ _779571 : [(29311 ^ _779571) ^ [] : [hAPP(_1303359, 29307 ^ [_1303353, _1303355, _1303357, _1303359]) = c_Orderings_Obot__class_Obot(tc_fun(_1303353, tc_HOL_Obool))], (29309 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303355), 29307 ^ [_1303353, _1303355, _1303357, _1303359]), _1303357)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1303353, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303355, tc_fun(_1303353, tc_HOL_Obool)), _1303357), _1303359))], (50732 ^ _779571) ^ [_1799593, _1799595, _1799597] : [hAPP(c_List_Orev(_1799593), _1799595) = _1799597, -(_1799595 = hAPP(c_List_Orev(_1799593), _1799597))], (812 ^ _779571) ^ [_792139, _792141] : [-(c_Nat__Transfer_Onat__set(_792139)), _792141 = _792139, c_Nat__Transfer_Onat__set(_792141)], (33963 ^ _779571) ^ [_1399664, _1399666, _1399668] : [class_Orderings_Olinorder(_1399664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399664), _1399666)), 33970 ^ _779571 : [(33977 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399664, tc_HOL_Obool)), _1399666), hAPP(hAPP(c_Set_Oinsert(_1399664), _1399668), c_Orderings_Obot__class_Obot(tc_fun(_1399664, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1399664, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1399664, c_Orderings_Oord__class_Omax(_1399664), hAPP(hAPP(c_Set_Oinsert(_1399664), _1399668), _1399666)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1399664), _1399668), c_Big__Operators_Olattice_OSup__fin(_1399664, c_Orderings_Oord__class_Omax(_1399664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399664, tc_HOL_Obool)), _1399666), hAPP(hAPP(c_Set_Oinsert(_1399664), _1399668), c_Orderings_Obot__class_Obot(tc_fun(_1399664, tc_HOL_Obool)))))))], (33971 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399664, tc_HOL_Obool)), _1399666), hAPP(hAPP(c_Set_Oinsert(_1399664), _1399668), c_Orderings_Obot__class_Obot(tc_fun(_1399664, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1399664, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1399664, c_Orderings_Oord__class_Omax(_1399664), hAPP(hAPP(c_Set_Oinsert(_1399664), _1399668), _1399666)) = _1399668)]]], (42258 ^ _779571) ^ [_1597438, _1597440] : [-(hAPP(c_Relation_ODomain(_1597438, _1597440), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1597438, _1597440), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1597438, tc_HOL_Obool)))], (40004 ^ _779571) ^ [_1536114, _1536116, _1536118, _1536120, _1536122] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1536114, _1536116, hAPP(hAPP(c_Set_Oinsert(_1536114), _1536118), _1536120)), _1536122)), 40009 ^ _779571 : [(40014 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1536114), 40007 ^ [_1536114, _1536116, _1536118, _1536120, _1536122]), 40008 ^ [_1536114, _1536116, _1536118, _1536120, _1536122]))], (40012 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1536114, _1536114, _1536116, 40007 ^ [_1536114, _1536116, _1536118, _1536120, _1536122], 40008 ^ [_1536114, _1536116, _1536118, _1536120, _1536122]), _1536122)))], (40010 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1536114), _1536118), _1536120) = hAPP(hAPP(c_Set_Oinsert(_1536114), 40007 ^ [_1536114, _1536116, _1536118, _1536120, _1536122]), 40008 ^ [_1536114, _1536116, _1536118, _1536120, _1536122]))]]], (35519 ^ _779571) ^ [_1434935, _1434937, _1434939, _1434941, _1434943, _1434945] : [hBOOL(hAPP(hAPP(c_member(_1434935), _1434937), _1434939)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1434935, _1434941)), hAPP(hAPP(c_Product__Type_OPair(_1434935, _1434941), _1434937), _1434943)), _1434945)), -(hBOOL(hAPP(hAPP(c_member(_1434941), _1434943), hAPP(c_Relation_OImage(_1434935, _1434941, _1434945), _1434939))))], (42942 ^ _779571) ^ [_1613358, _1613360, _1613362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613358, _1613358), tc_HOL_Obool)), _1613360), _1613362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613358, _1613358), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1613358, _1613358, _1613358), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1613358, _1613358), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613358, _1613360)), _1613362)), _1613360)), _1613362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613358, _1613358), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613358, _1613360)), _1613362)))], (36476 ^ _779571) ^ [_1457284, _1457286, _1457288, _1457290] : [class_Lattices_Osemilattice__inf(_1457284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457284), _1457286), _1457288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457284), _1457286), _1457290)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457284), _1457286), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457284), _1457288), _1457290))))], (44495 ^ _779571) ^ [_1651067, _1651069, _1651071, _1651073, _1651075] : [hBOOL(hAPP(hAPP(c_member(_1651067), _1651069), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651071, tc_fun(_1651067, tc_HOL_Obool)), _1651073), _1651075))), 44498 ^ _779571 : [(44499 ^ _779571) ^ [_1651191] : [hBOOL(hAPP(hAPP(c_member(_1651071), _1651191), _1651073)), -(hBOOL(hAPP(hAPP(c_member(_1651067), _1651069), hAPP(_1651075, _1651191))))]]], (10327 ^ _779571) ^ [_951600] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951600), _951600))))], (19527 ^ _779571) ^ [_1114608, _1114610] : [class_Rings_Oring__1__no__zero__divisors(_1114608), 19530 ^ _779571 : [(19537 ^ _779571) ^ [] : [_1114610 = c_Groups_Ozero__class_Ozero(_1114608), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114608), _1114610), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1114608))], (19531 ^ _779571) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1114608), _1114610), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1114608), -(_1114610 = c_Groups_Ozero__class_Ozero(_1114608))]]], (23893 ^ _779571) ^ [_1195011, _1195013, _1195015, _1195017, _1195019] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1195011, _1195013, _1195015), _1195017), _1195019) = hAPP(hAPP(_1195017, hAPP(c_Product__Type_Ofst(_1195011, _1195013), _1195019)), hAPP(c_Product__Type_Osnd(_1195011, _1195013), _1195019)))], (42972 ^ _779571) ^ [_1614870, _1614872, _1614874] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614870, _1614870)), hAPP(hAPP(c_Product__Type_OPair(_1614870, _1614870), _1614872), _1614872)), c_Transitive__Closure_Ortrancl(_1614870, _1614874))))], (45803 ^ _779571) ^ [_1682471, _1682473, _1682475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1682471), _1682473))), -(c_Smallcheck_Osmall_H(_1682475, _1682471, _1682473) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1682475, _1682471, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1682473), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1682475, _1682473)))], (17707 ^ _779571) ^ [_1084513, _1084515, _1084517] : [class_Rings_Olinordered__semidom(_1084513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084513), c_Groups_Ozero__class_Ozero(_1084513)), _1084515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084513), _1084515), c_Groups_Oone__class_Oone(_1084513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084513), _1084515), hAPP(hAPP(c_Power_Opower__class_Opower(_1084513), _1084515), _1084517))), hAPP(hAPP(c_Power_Opower__class_Opower(_1084513), _1084515), _1084517))))], (50236 ^ _779571) ^ [_1789067, _1789069, _1789071] : [class_Orderings_Olinorder(_1789067), c_List_Olinorder__class_Osorted(_1789067, _1789069), -(c_List_Olinorder__class_Osorted(_1789067, c_List_Oremove1(_1789067, _1789071, _1789069)))], (9420 ^ _779571) ^ [_935902, _935904] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935902), _935904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _935902)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _935904)))], (35968 ^ _779571) ^ [_1446100, _1446102, _1446104, _1446106, _1446108] : [hAPP(c_Relation_OImage(_1446100, _1446100, _1446102), hAPP(hAPP(c_Set_Oinsert(_1446100), _1446104), c_Orderings_Obot__class_Obot(tc_fun(_1446100, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1446100, _1446100, _1446102), hAPP(hAPP(c_Set_Oinsert(_1446100), _1446106), c_Orderings_Obot__class_Obot(tc_fun(_1446100, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1446100, _1446108, _1446102), hBOOL(hAPP(hAPP(c_member(_1446100), _1446106), _1446108)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446100, _1446100)), hAPP(hAPP(c_Product__Type_OPair(_1446100, _1446100), _1446104), _1446106)), _1446102)))], (23064 ^ _779571) ^ [_1179514, _1179516, _1179518] : [hBOOL(hAPP(_1179514, 23065 ^ [_1179514, _1179516, _1179518])), 23068 ^ _779571 : [(23069 ^ _779571) ^ [_1179625, _1179627] : [-(hBOOL(hAPP(_1179514, hAPP(hAPP(c_Product__Type_OPair(_1179516, _1179518), _1179627), _1179625))))]]], (34537 ^ _779571) ^ [_1411824, _1411826, _1411828, _1411830, _1411832, _1411834] : [-(hBOOL(hAPP(hAPP(c_member(_1411824), _1411826), _1411828))), -(hAPP(c_Set_Oimage(_1411824, tc_Option_Ooption(_1411830), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1411824, tc_Option_Ooption(_1411830)), _1411832), _1411826), hAPP(c_Option_Ooption_OSome(_1411830), _1411834))), _1411828) = hAPP(c_Set_Oimage(_1411824, tc_Option_Ooption(_1411830), _1411832), _1411828))], (6742 ^ _779571) ^ [_890246, _890248, _890250, _890252] : [c_Com_Ocom_OLocal(_890246, _890248, _890250) = hAPP(c_Com_Ocom_OBODY, _890252)], (5302 ^ _779571) ^ [_861504, _861506, _861508, _861510, _861512, _861514, _861516, _861518] : [-(c_Fun_Ocomp(_861518, _861514, _861510, _861506) = c_Fun_Ocomp(_861516, _861512, _861508, _861504)), _861518 = _861516, _861514 = _861512, _861510 = _861508, _861506 = _861504], (6209 ^ _779571) ^ [_880170, _880172, _880174, _880176, _880178, _880180] : [c_Com_Ocom_OCall(_880170, _880172, _880174) = c_Com_Ocom_OLocal(_880176, _880178, _880180)], (15526 ^ _779571) ^ [_1042631, _1042633, _1042635] : [-(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, _1042631, _1042633)), _1042635), _1042633) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042631), _1042635), _1042633))], (12451 ^ _779571) ^ [_987479, _987481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987481)), 12458 ^ _779571 : [(12465 ^ _779571) ^ [] : [_987479 = _987481, -(hAPP(c_Int_Onat, _987479) = hAPP(c_Int_Onat, _987481))], (12459 ^ _779571) ^ [] : [hAPP(c_Int_Onat, _987479) = hAPP(c_Int_Onat, _987481), -(_987479 = _987481)]]], (40592 ^ _779571) ^ [_1550166, _1550168, _1550170] : [class_Orderings_Olinorder(_1550166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550166), _1550168)), -(_1550168 = c_Orderings_Obot__class_Obot(tc_fun(_1550166, tc_HOL_Obool))), 40603 ^ _779571 : [(40613 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550166), hAPP(c_Finite__Set_Ofold1(_1550166, c_Orderings_Oord__class_Omin(_1550166)), _1550168)), _1550170))), 40614 ^ _779571 : [(40615 ^ _779571) ^ [_1550555] : [hBOOL(hAPP(hAPP(c_member(_1550166), _1550555), _1550168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550166), _1550555), _1550170))]]], (40604 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550166), hAPP(c_Finite__Set_Ofold1(_1550166, c_Orderings_Oord__class_Omin(_1550166)), _1550168)), _1550170)), 40608 ^ _779571 : [(40611 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550166), 40607 ^ [_1550166, _1550168, _1550170]), _1550170)))], (40609 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550166), 40607 ^ [_1550166, _1550168, _1550170]), _1550168)))]]]]], (5705 ^ _779571) ^ [_870531, _870533, _870535, _870537, _870539] : [5708 ^ _779571 : [(5714 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_870539, 5706 ^ [_870531, _870533, _870535, _870537, _870539]), 5710 ^ [_870531, _870533, _870535, _870537, _870539]))], (5712 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_870537, 5707 ^ [_870531, _870533, _870535, _870537, _870539], _870533, 5710 ^ [_870531, _870533, _870535, _870537, _870539]))], (5709 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_870535, 5706 ^ [_870531, _870533, _870535, _870537, _870539]), 5707 ^ [_870531, _870533, _870535, _870537, _870539])))]], -(c_Hoare__Mirabelle_Otriple__valid(_870531, _870533, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_870531), _870535), _870537), _870539)))], (41896 ^ _779571) ^ [_1589316, _1589318, _1589320, _1589322, _1589324, _1589326, _1589328] : [c_Predicate_Opred__comp(_1589316, _1589318, _1589320, _1589322, _1589324, _1589326, _1589328), 41900 ^ _779571 : [(41903 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1589324, 41899 ^ [_1589316, _1589318, _1589320, _1589322, _1589324, _1589326, _1589328]), _1589328)))], (41901 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1589322, _1589326), 41899 ^ [_1589316, _1589318, _1589320, _1589322, _1589324, _1589326, _1589328])))]]], (25976 ^ _779571) ^ [_1235507, _1235509, _1235511, _1235513] : [class_Groups_Oordered__ab__group__add__abs(_1235507), -(hAPP(c_Groups_Oabs__class_Oabs(_1235507), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235509, _1235507), hAPP(hAPP(c_COMBB(_1235507, _1235507, _1235509), c_Groups_Oabs__class_Oabs(_1235507)), _1235511)), _1235513)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235509, _1235507), hAPP(hAPP(c_COMBB(_1235507, _1235507, _1235509), c_Groups_Oabs__class_Oabs(_1235507)), _1235511)), _1235513))], (17211 ^ _779571) ^ [_1075527, _1075529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075527), _1075529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075529))))], (26026 ^ _779571) ^ [_1236481, _1236483, _1236485] : [class_Orderings_Olinorder(_1236481), 26029 ^ _779571 : [(26036 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236481), _1236483), _1236485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236481, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1236481), _1236483)), hAPP(c_SetInterval_Oord__class_OlessThan(_1236481), _1236485))))], (26030 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236481, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1236481), _1236483)), hAPP(c_SetInterval_Oord__class_OlessThan(_1236481), _1236485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236481), _1236483), _1236485)))]]], (51253 ^ _779571) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (25682 ^ _779571) ^ [_1229290, _1229292, _1229294] : [class_Rings_Ocomm__semiring__1(_1229290), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229290), _1229292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229290), _1229292), _1229294))))], (19141 ^ _779571) ^ [_1107839, _1107841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107839), _1107841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1107839)), c_Int_OBit0(_1107841))))], (51311 ^ _779571) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (23665 ^ _779571) ^ [_1190507, _1190509, _1190511, _1190513, _1190515] : [class_Orderings_Olinorder(_1190507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190507), _1190509), _1190511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190507), _1190513), _1190515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190507), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190507), _1190509), _1190513)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190507), _1190511), _1190515))))], (33925 ^ _779571) ^ [_1398927, _1398929, _1398931] : [class_Orderings_Olinorder(_1398927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398927), _1398929)), -(hBOOL(hAPP(hAPP(c_member(_1398927), _1398931), _1398929))), -(_1398929 = c_Orderings_Obot__class_Obot(tc_fun(_1398927, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1398927, c_Orderings_Oord__class_Omax(_1398927), hAPP(hAPP(c_Set_Oinsert(_1398927), _1398931), _1398929)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1398927), _1398931), c_Big__Operators_Olattice_OSup__fin(_1398927, c_Orderings_Oord__class_Omax(_1398927), _1398929)))], (17355 ^ _779571) ^ [_1077931, _1077933, _1077935] : [class_Groups_Omonoid__mult(_1077931), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077931), hAPP(hAPP(c_Power_Opower__class_Opower(_1077931), _1077933), _1077935)), _1077933) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077931), _1077933), hAPP(hAPP(c_Power_Opower__class_Opower(_1077931), _1077933), _1077935)))], (27011 ^ _779571) ^ [_1255471, _1255473] : [27013 ^ _779571 : [(27016 ^ _779571) ^ [] : [hBOOL(hAPP(_1255473, 27012 ^ [_1255471, _1255473]))], (27014 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27012 ^ [_1255471, _1255473]), _1255471)))]], 27017 ^ _779571 : [(27018 ^ _779571) ^ [_1255621] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1255621), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1255471))), -(hBOOL(hAPP(_1255473, _1255621)))]]], (51407 ^ _779571) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (31023 ^ _779571) ^ [_1338139, _1338141, _1338143] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338139), hAPP(hAPP(c_Set_Oinsert(_1338139), _1338141), _1338143))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338139), _1338143)))], (38683 ^ _779571) ^ [_1506310, _1506312] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506310), c_Orderings_Otop__class_Otop(tc_fun(_1506310, tc_HOL_Obool)))), c_Fun_Oinj__on(_1506310, _1506310, _1506312, c_Orderings_Otop__class_Otop(tc_fun(_1506310, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1506310, _1506310, _1506312), c_Orderings_Otop__class_Otop(tc_fun(_1506310, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1506310, tc_HOL_Obool)))], (34793 ^ _779571) ^ [_1417344, _1417346, _1417348, _1417350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1417344), _1417346)), -(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), _1417344), _1417348)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1417346), _1417350))), c_FunDef_Opair__leq)))], (47961 ^ _779571) ^ [_1736697, _1736699, _1736701, _1736703, _1736705, _1736707, _1736709] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1736697, _1736697)), hAPP(hAPP(c_Product__Type_OPair(_1736697, _1736697), _1736699), _1736701)), _1736703)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736697), tc_List_Olist(_1736697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736697), tc_List_Olist(_1736697)), hAPP(hAPP(c_List_Oappend(_1736697), _1736705), hAPP(hAPP(c_List_Olist_OCons(_1736697), _1736699), _1736707))), hAPP(hAPP(c_List_Oappend(_1736697), _1736705), hAPP(hAPP(c_List_Olist_OCons(_1736697), _1736701), _1736709)))), c_List_Olexord(_1736697, _1736703))))], (46939 ^ _779571) ^ [_1711779, _1711781, _1711783, _1711785, _1711787, _1711789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711779), tc_List_Olist(_1711779))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711779), tc_List_Olist(_1711779)), hAPP(hAPP(c_List_Olist_OCons(_1711779), _1711781), _1711783)), hAPP(hAPP(c_List_Olist_OCons(_1711779), _1711785), _1711787))), c_List_Olex(_1711779, _1711789))), 46944 ^ _779571 : [(46947 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711779)), _1711783) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711779)), _1711787))], (46945 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1711779, _1711779)), hAPP(hAPP(c_Product__Type_OPair(_1711779, _1711779), _1711781), _1711785)), _1711789)))]], 46948 ^ _779571 : [(46951 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711779), tc_List_Olist(_1711779))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711779), tc_List_Olist(_1711779)), _1711783), _1711787)), c_List_Olex(_1711779, _1711789))))], (46949 ^ _779571) ^ [] : [-(_1711781 = _1711785)]]], (29772 ^ _779571) ^ [_1311900] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1311900, _1311900) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1311900), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27389 ^ _779571) ^ [_1263161, _1263163, _1263165, _1263167] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1263161), _1263163)), 27392 ^ _779571 : [(27393 ^ _779571) ^ [_1263315] : [27395 ^ _779571 : [(27401 ^ _779571) ^ [] : [-(_1263315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27397 ^ [_1263161, _1263163, _1263165, _1263167, _1263315]), 27394 ^ [_1263161, _1263163, _1263165, _1263167, _1263315]))], (27399 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27397 ^ [_1263161, _1263163, _1263165, _1263167, _1263315]), _1263165)))], (27396 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27394 ^ [_1263161, _1263163, _1263165, _1263167, _1263315]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1263163))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1263161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1263315), _1263167))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1263161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1263315), _1263163)), _1263167))))]]], (51329 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (16148 ^ _779571) ^ [_1055555, _1055557] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055555, _1055557) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1055555), _1055557)), _1055557)))], (28874 ^ _779571) ^ [_1293471, _1293473, _1293475, _1293477, _1293479, _1293481] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293471, tc_fun(_1293473, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293475, tc_fun(_1293471, tc_HOL_Obool)), _1293477), _1293479)), _1293481) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293475, tc_fun(_1293473, tc_HOL_Obool)), _1293477), hAPP(hAPP(c_COMBC(_1293475, tc_fun(_1293471, tc_fun(_1293473, tc_HOL_Obool)), tc_fun(_1293473, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293471, tc_HOL_Obool), tc_fun(tc_fun(_1293471, tc_fun(_1293473, tc_HOL_Obool)), tc_fun(_1293473, tc_HOL_Obool)), _1293475), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293471, tc_fun(_1293473, tc_HOL_Obool))), _1293479)), _1293481)))], (5672 ^ _779571) ^ [_867131, _867133] : [_867133 = _867131, -(c_member(_867133) = c_member(_867131))], (27786 ^ _779571) ^ [_1271625, _1271627, _1271629] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271625, tc_HOL_Obool)), _1271627), _1271629) = _1271629, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271625, tc_HOL_Obool)), _1271627), _1271629)))], (13797 ^ _779571) ^ [_1011368, _1011370] : [-(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, _1011368, _1011370)), _1011370) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011368), _1011370))], (40861 ^ _779571) ^ [_1556592, _1556594, _1556596, _1556598, _1556600, _1556602, _1556604, _1556606, _1556608, _1556610, _1556612] : [-(hAPP(c_Product__Type_Omap__pair(_1556592, _1556594, _1556596, _1556598, _1556600, _1556602), hAPP(c_Product__Type_Omap__pair(_1556604, _1556592, _1556606, _1556596, _1556608, _1556610), _1556612)) = hAPP(c_Product__Type_Omap__pair(_1556604, _1556594, _1556606, _1556598, hAPP(c_Fun_Ocomp(_1556592, _1556594, _1556604, _1556600), _1556608), hAPP(c_Fun_Ocomp(_1556596, _1556598, _1556606, _1556602), _1556610)), _1556612))], (51201 ^ _779571) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (9336 ^ _779571) ^ [_934114] : [class_Rings_Ozero__neq__one(_934114), c_Groups_Ozero__class_Ozero(_934114) = c_Groups_Oone__class_Oone(_934114)], (22920 ^ _779571) ^ [_1176889, _1176891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176889)), 22923 ^ _779571 : [(22930 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176891))), 22933 ^ _779571 : [(22940 ^ _779571) ^ [] : [-(_1176889 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1176889, _1176891) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176889), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176891))))], (22934 ^ _779571) ^ [] : [_1176889 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1176889, _1176891) = 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)))]]], (22924 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176891)), -(c_Divides_Odivmod__int(_1176889, _1176891) = c_Divides_OposDivAlg(_1176889, _1176891))]]], (6748 ^ _779571) ^ [_890408, _890410, _890412, _890414] : [hAPP(c_Com_Ocom_OBODY, _890408) = c_Com_Ocom_OCall(_890410, _890412, _890414)], (19299 ^ _779571) ^ [_1110540, _1110542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110540)), c_Int_OBit0(_1110542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110540), _1110542)))], (35607 ^ _779571) ^ [_1437547] : [-(c_Nitpick_Onum(_1437547) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1437547, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1437547)))], (12994 ^ _779571) ^ [_997185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _997185)))], (43439 ^ _779571) ^ [_1626222, _1626224, _1626226, _1626228, _1626230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626222, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1626224, _1626222, _1626226), _1626228)), _1626230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626224, tc_HOL_Obool)), _1626228), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1626224, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1626222, _1626224, hAPP(c_Relation_Oconverse(_1626224, _1626222), _1626226)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1626222, tc_HOL_Obool)), _1626230))))))], (14491 ^ _779571) ^ [_1024054, _1024056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024054), 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)), _1024056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024054), _1024056)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24881 ^ _779571) ^ [_1214805, _1214807] : [-(hAPP(c_New__DSequence_Opos__empty(_1214805), _1214807) = c_Lazy__Sequence_Oempty(_1214805))], (10207 ^ _779571) ^ [_949513, _949515, _949517, _949519, _949521, _949523] : [class_Rings_Olinordered__semiring__1__strict(_949513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949513), _949515), _949517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949513), _949519), _949517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949513), c_Groups_Ozero__class_Ozero(_949513)), _949521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949513), c_Groups_Ozero__class_Ozero(_949513)), _949523)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949513), _949521), _949523) = c_Groups_Oone__class_Oone(_949513), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949513), _949521), _949515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949513), _949523), _949519))), _949517)))], (8705 ^ _779571) ^ [_923293, _923295] : [-(hBOOL(hAPP(_923293, hAPP(c_Int_Onat, _923295)))), 8709 ^ _779571 : [(8712 ^ _779571) ^ [] : [hBOOL(hAPP(_923293, 8708 ^ [_923293, _923295]))], (8710 ^ _779571) ^ [] : [-(_923295 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8708 ^ [_923293, _923295]))]], 8713 ^ _779571 : [(8716 ^ _779571) ^ [] : [hBOOL(hAPP(_923293, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8714 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923295), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14606 ^ _779571) ^ [_1025894, _1025896, _1025898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025894), _1025896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025898), _1025896)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025898), _1025894))))], (13492 ^ _779571) ^ [_1005572, _1005574, _1005576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005572)), 13495 ^ _779571 : [(13502 ^ _779571) ^ [] : [_1005574 = _1005576, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005572), _1005574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005572), _1005576))], (13496 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005572), _1005574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005572), _1005576), -(_1005574 = _1005576)]]], (44716 ^ _779571) ^ [_1657346, _1657348, _1657350, _1657352, _1657354] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657346, tc_fun(_1657348, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657346, tc_HOL_Obool)), _1657350), _1657352)), _1657354) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657348, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657346, tc_fun(_1657348, tc_HOL_Obool)), _1657350), _1657354)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657346, tc_fun(_1657348, tc_HOL_Obool)), _1657352), _1657354)))], (50702 ^ _779571) ^ [_1798952, _1798954, _1798956] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1798952), tc_List_Olist(_1798952), c_List_Oappend(_1798952), _1798954), _1798956) = hAPP(hAPP(c_List_Oappend(_1798952), _1798954), c_List_Oconcat(_1798952, _1798956)))], (4920 ^ _779571) ^ [_855591, _855593, _855595, _855597, _855599, _855601] : [-(c_List_Osublist(_855601, _855597, _855593) = c_List_Osublist(_855599, _855595, _855591)), _855601 = _855599, _855597 = _855595, _855593 = _855591], (17681 ^ _779571) ^ [_1083962, _1083964, _1083966] : [class_Rings_Olinordered__idom(_1083962), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083962), c_Groups_Ozero__class_Ozero(_1083962)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083962), hAPP(c_Groups_Oabs__class_Oabs(_1083962), _1083964)), _1083966))))], (49461 ^ _779571) ^ [_1772862, _1772864, _1772866] : [_1772862 = c_List_Olist_ONil(_1772864), -(c_List_Olast(_1772864, hAPP(hAPP(c_List_Olist_OCons(_1772864), _1772866), _1772862)) = _1772866)], (29192 ^ _779571) ^ [_1301133] : [c_Orderings_Otop__class_Otop(tc_fun(_1301133, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1301133, tc_HOL_Obool))], (43645 ^ _779571) ^ [_1631639] : [-(c_Nat_Ofunpow(_1631639) = c_Nat_Ocompow(_1631639, _1631639))], (37617 ^ _779571) ^ [_1482848, _1482850, _1482852, _1482854, _1482856, _1482858, _1482860, _1482862, _1482864, _1482866, _1482868] : [c_Equiv__Relations_Oequiv(_1482848, _1482850, _1482852), c_Equiv__Relations_Oequiv(_1482854, _1482856, _1482858), c_Equiv__Relations_Ocongruent2(_1482848, _1482854, tc_fun(_1482860, tc_HOL_Obool), _1482852, _1482858, _1482862), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482848, tc_HOL_Obool)), _1482864), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482848), _1482850), _1482852))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482854, tc_HOL_Obool)), _1482866), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482854), _1482856), _1482858))), 37639 ^ _779571 : [(37645 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1482860, tc_HOL_Obool)), hAPP(hAPP(_1482862, 37638 ^ [_1482848, _1482850, _1482852, _1482854, _1482856, _1482858, _1482860, _1482862, _1482864, _1482866, _1482868]), 37641 ^ [_1482848, _1482850, _1482852, _1482854, _1482856, _1482858, _1482860, _1482862, _1482864, _1482866, _1482868])), _1482868))], (37643 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482854), 37641 ^ [_1482848, _1482850, _1482852, _1482854, _1482856, _1482858, _1482860, _1482862, _1482864, _1482866, _1482868]), _1482856)))], (37640 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482848), 37638 ^ [_1482848, _1482850, _1482852, _1482854, _1482856, _1482858, _1482860, _1482862, _1482864, _1482866, _1482868]), _1482850)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1482860, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482848, tc_fun(_1482860, tc_HOL_Obool)), _1482864), hAPP(hAPP(c_COMBB(tc_fun(_1482854, tc_fun(_1482860, tc_HOL_Obool)), tc_fun(_1482860, tc_HOL_Obool), _1482848), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482854, tc_fun(_1482860, tc_HOL_Obool)), _1482866)), _1482862))), _1482868)))], (37279 ^ _779571) ^ [_1475741, _1475743, _1475745] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475741), _1475743)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475741), _1475745)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475741, tc_HOL_Obool)), _1475743), _1475745) = c_Orderings_Obot__class_Obot(tc_fun(_1475741, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1475741), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475741, tc_HOL_Obool)), _1475743), _1475745)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1475741), _1475743)), hAPP(c_Finite__Set_Ocard(_1475741), _1475745)))], (41481 ^ _779571) ^ [_1574749, _1574751, _1574753] : [class_Lattices_Odistrib__lattice(_1574749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574749), _1574751)), -(_1574751 = c_Orderings_Obot__class_Obot(tc_fun(_1574749, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574749), _1574753)), -(_1574753 = c_Orderings_Obot__class_Obot(tc_fun(_1574749, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574749), c_Big__Operators_Olattice__class_OInf__fin(_1574749, _1574751)), c_Big__Operators_Olattice__class_OInf__fin(_1574749, _1574753)) = c_Big__Operators_Olattice__class_OInf__fin(_1574749, hAPP(c_Set_OCollect(_1574749), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_HOL_Obool), tc_HOL_Obool, _1574749), c_HOL_OEx(_1574749)), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool)), tc_fun(_1574749, tc_HOL_Obool), _1574749), hAPP(c_COMBB(tc_fun(_1574749, tc_HOL_Obool), tc_HOL_Obool, _1574749), c_HOL_OEx(_1574749))), hAPP(hAPP(c_COMBC(_1574749, tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool)), tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_fun(tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool))), tc_fun(tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool)), tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool))), _1574749), c_COMBS(_1574749, tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_fun(_1574749, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1574749, tc_fun(tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool))), _1574749), hAPP(c_COMBB(tc_fun(_1574749, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool)), _1574749), c_COMBS(_1574749, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool)), tc_fun(_1574749, tc_fun(_1574749, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1574749), hAPP(c_COMBB(tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1574749), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574749), c_fconj))), hAPP(hAPP(c_COMBC(_1574749, tc_fun(_1574749, tc_fun(_1574749, _1574749)), tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1574749, _1574749), tc_fun(_1574749, tc_HOL_Obool)), tc_fun(tc_fun(_1574749, tc_fun(_1574749, _1574749)), tc_fun(_1574749, tc_fun(_1574749, tc_HOL_Obool))), _1574749), c_COMBB(tc_fun(_1574749, _1574749), tc_fun(_1574749, tc_HOL_Obool), _1574749)), hAPP(hAPP(c_COMBB(tc_fun(_1574749, tc_HOL_Obool), tc_fun(tc_fun(_1574749, _1574749), tc_fun(_1574749, tc_HOL_Obool)), _1574749), c_COMBB(_1574749, tc_HOL_Obool, _1574749)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1574749)))))), hAPP(hAPP(c_COMBC(_1574749, tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1574749, tc_HOL_Obool), tc_fun(_1574749, tc_HOL_Obool)), _1574749), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1574749)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574749), c_fconj), hAPP(hAPP(c_COMBC(_1574749, tc_fun(_1574749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574749)), _1574751)))), hAPP(hAPP(c_COMBC(_1574749, tc_fun(_1574749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574749)), _1574753))))))))], (25826 ^ _779571) ^ [_1231883, _1231885, _1231887] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1231885), _1231887))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231883), _1231887)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231883), _1231885)))], (9986 ^ _779571) ^ [_945810, _945812, _945814] : [class_Rings_Olinordered__idom(_945810), 9989 ^ _779571 : [(9996 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945812), _945814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945810), hAPP(c_Int_Oring__1__class_Oof__int(_945810), _945812)), hAPP(c_Int_Oring__1__class_Oof__int(_945810), _945814))))], (9990 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945810), hAPP(c_Int_Oring__1__class_Oof__int(_945810), _945812)), hAPP(c_Int_Oring__1__class_Oof__int(_945810), _945814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945812), _945814)))]]], (11855 ^ _779571) ^ [_976913, _976915, _976917, _976919] : [class_Rings_Oordered__ring(_976913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976913), _976915), _976917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976913), _976919), c_Groups_Ozero__class_Ozero(_976913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976913), _976917), _976919)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976913), _976915), _976919))))], (22988 ^ _779571) ^ [_1178025, _1178027, _1178029, _1178031, _1178033] : [hBOOL(hAPP(hAPP(_1178025, _1178027), _1178029)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1178031, _1178033, tc_HOL_Obool), _1178025), hAPP(hAPP(c_Product__Type_OPair(_1178031, _1178033), _1178027), _1178029))))], (48066 ^ _779571) ^ [_1739344, _1739346, _1739348] : [_1739344 = _1739346, -(_1739344 = hAPP(hAPP(c_List_Oappend(_1739348), c_List_Olist_ONil(_1739348)), _1739346))], (50756 ^ _779571) ^ [_1800003, _1800005, _1800007, _1800009, _1800011] : [-(hAPP(c_List_Ofoldl(_1800003, _1800005, _1800007, _1800009), _1800011) = c_List_Ofoldr(_1800005, _1800003, hAPP(c_COMBC(_1800003, _1800005, _1800003), _1800007), hAPP(c_List_Orev(_1800005), _1800011), _1800009))], (3986 ^ _779571) ^ [_841006, _841008] : [_841008 = _841006, -(c_Set_OBall(_841008) = c_Set_OBall(_841006))], (498 ^ _779571) ^ [_787222, _787224, _787226, _787228, _787230, _787232] : [-(c_Big__Operators_Osemilattice__big(_787230, _787226, _787222)), c_Big__Operators_Osemilattice__big(_787232, _787228, _787224), _787232 = _787230, _787228 = _787226, _787224 = _787222], (9034 ^ _779571) ^ [_929302, _929304] : [class_Rings_Oring__1(_929302), -(hAPP(c_Int_Oring__1__class_Oof__int(_929302), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929304)) = hAPP(c_Groups_Ouminus__class_Ouminus(_929302), hAPP(c_Int_Oring__1__class_Oof__int(_929302), _929304)))], (31127 ^ _779571) ^ [_1340308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1340308)), 31131 ^ _779571 : [(31132 ^ _779571) ^ [_1340388] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1340388), _1340308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1340388), 31130 ^ [_1340308])))]]], (45827 ^ _779571) ^ [_1682871, _1682873, _1682875, _1682877] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1682873, _1682871)), _1682875), _1682877) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1682873), hAPP(hAPP(c_COMBC(_1682873, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1682871, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1682873), c_Smallcheck_Osmall__class_Osmall(_1682871)), hAPP(hAPP(c_COMBB(tc_fun(_1682871, tc_prod(_1682873, _1682871)), tc_fun(_1682871, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1682873), hAPP(c_COMBB(tc_prod(_1682873, _1682871), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1682871), _1682875)), c_Product__Type_OPair(_1682873, _1682871)))), _1682877)), _1682877)), class_Smallcheck_Osmall(_1682871), class_Smallcheck_Osmall(_1682873)], (19521 ^ _779571) ^ [_1114511] : [class_Rings_Osemiring__1(_1114511), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114511), c_Groups_Ozero__class_Ozero(_1114511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1114511))], (48704 ^ _779571) ^ [_1756023, _1756025, _1756027, _1756029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756023), _1756025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1756027, tc_HOL_Obool)), hAPP(c_List_Oset(_1756027), hAPP(hAPP(c_List_Odrop(_1756027), _1756025), _1756029))), hAPP(c_List_Oset(_1756027), hAPP(hAPP(c_List_Odrop(_1756027), _1756023), _1756029)))))], (1292 ^ _779571) ^ [_798489, _798491] : [-(class_Lattices_Odistrib__lattice(_798489)), _798491 = _798489, class_Lattices_Odistrib__lattice(_798491)], (42526 ^ _779571) ^ [_1603848, _1603850, _1603852, _1603854, _1603856, _1603858] : [42529 ^ _779571 : [(42532 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1603854), _1603856), hAPP(hAPP(_1603858, 42527 ^ [_1603848, _1603850, _1603852, _1603854, _1603856, _1603858]), 42528 ^ [_1603848, _1603850, _1603852, _1603854, _1603856, _1603858])))], (42530 ^ _779571) ^ [] : [-(_1603848 = hAPP(hAPP(c_Product__Type_OPair(_1603850, _1603852), 42527 ^ [_1603848, _1603850, _1603852, _1603854, _1603856, _1603858]), 42528 ^ [_1603848, _1603850, _1603852, _1603854, _1603856, _1603858]))]], -(hBOOL(hAPP(hAPP(c_member(_1603854), _1603856), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1603850, _1603852, tc_fun(_1603854, tc_HOL_Obool)), _1603858), _1603848))))], (20227 ^ _779571) ^ [_1127373, _1127375, _1127377, _1127379] : [class_Fields_Olinordered__field__inverse__zero(_1127373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127373), _1127375), _1127377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127373), _1127379), c_Groups_Ozero__class_Ozero(_1127373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127373), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127373), _1127377), _1127379)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127373), _1127375), _1127379))))], (2434 ^ _779571) ^ [_816346, _816348, _816350, _816352, _816354, _816356, _816358, _816360] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_816360, _816356, _816352, _816348) = c_Nat_Osemiring__1__class_Oof__nat__aux(_816358, _816354, _816350, _816346)), _816360 = _816358, _816356 = _816354, _816352 = _816350, _816348 = _816346], (41503 ^ _779571) ^ [_1575848, _1575850, _1575852] : [class_Lattices_Odistrib__lattice(_1575848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575848), _1575850)), -(_1575850 = c_Orderings_Obot__class_Obot(tc_fun(_1575848, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1575848), _1575852), c_Big__Operators_Olattice__class_OInf__fin(_1575848, _1575850)) = c_Big__Operators_Olattice__class_OInf__fin(_1575848, hAPP(c_Set_OCollect(_1575848), hAPP(hAPP(c_COMBB(tc_fun(_1575848, tc_HOL_Obool), tc_HOL_Obool, _1575848), c_HOL_OEx(_1575848)), hAPP(hAPP(c_COMBC(_1575848, tc_fun(_1575848, tc_HOL_Obool), tc_fun(_1575848, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575848, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1575848, tc_HOL_Obool), tc_fun(_1575848, tc_HOL_Obool)), _1575848), c_COMBS(_1575848, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575848, tc_HOL_Obool), tc_fun(_1575848, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1575848), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575848), c_fconj)), hAPP(hAPP(c_COMBC(_1575848, tc_fun(_1575848, _1575848), tc_fun(_1575848, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575848, tc_HOL_Obool), tc_fun(tc_fun(_1575848, _1575848), tc_fun(_1575848, tc_HOL_Obool)), _1575848), c_COMBB(_1575848, tc_HOL_Obool, _1575848)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1575848), _1575852))))), hAPP(hAPP(c_COMBC(_1575848, tc_fun(_1575848, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575848)), _1575850))))))], (7628 ^ _779571) ^ [_905976, _905978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905978), hAPP(c_Nat_OSuc, _905976))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905976), _905978))], (39719 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (6853 ^ _779571) ^ [_892622, _892624, _892626] : [_892622 = _892626, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892622), _892624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892626), _892624))], (1322 ^ _779571) ^ [_798864, _798866] : [-(class_Orderings_Otop(_798864)), _798866 = _798864, class_Orderings_Otop(_798866)], (41215 ^ _779571) ^ [_1564656, _1564658, _1564660] : [-(c_Map_Odom(_1564656, _1564658, _1564660) = hAPP(c_Set_OCollect(_1564656), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564656), c_fNot), hAPP(hAPP(c_COMBC(_1564656, tc_Option_Ooption(_1564658), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1564658), tc_fun(tc_Option_Ooption(_1564658), tc_HOL_Obool), _1564656), c_fequal), _1564660)), c_Option_Ooption_ONone(_1564658)))))], (36316 ^ _779571) ^ [_1454123, _1454125, _1454127, _1454129] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454123, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454123, tc_HOL_Obool)), _1454125), _1454127)), _1454129) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454123, tc_HOL_Obool)), _1454125), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454123, tc_HOL_Obool)), _1454127), _1454129)))], (28880 ^ _779571) ^ [_1293828, _1293830, _1293832, _1293834, _1293836] : [class_Complete__Lattice_Ocomplete__lattice(_1293828), 28883 ^ _779571 : [(28884 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293830, _1293828), _1293832), _1293834)), _1293836)), 28887 ^ _779571 : [(28888 ^ _779571) ^ [_1294009] : [hBOOL(hAPP(hAPP(c_member(_1293830), _1294009), _1293832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293828), hAPP(_1293834, _1294009)), _1293836)))]]], (28894 ^ _779571) ^ [] : [28896 ^ _779571 : [(28899 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293828), hAPP(_1293834, 28895 ^ [_1293828, _1293830, _1293832, _1293834, _1293836])), _1293836))], (28897 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293830), 28895 ^ [_1293828, _1293830, _1293832, _1293834, _1293836]), _1293832)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293830, _1293828), _1293832), _1293834)), _1293836)))]]], (43477 ^ _779571) ^ [_1627083, _1627085, _1627087] : [-(hAPP(c_Relation_Oconverse(_1627083, _1627085), _1627087) = hAPP(c_Set_OCollect(tc_prod(_1627085, _1627083)), hAPP(c_Product__Type_Oprod_Oprod__case(_1627085, _1627083, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1627085, tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_fun(_1627083, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1627083, tc_fun(tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_fun(_1627083, tc_HOL_Obool)), _1627085), c_COMBC(_1627083, tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1627083, tc_prod(_1627083, _1627085)), tc_fun(_1627083, tc_fun(tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_HOL_Obool)), _1627085), hAPP(c_COMBB(tc_prod(_1627083, _1627085), tc_fun(tc_fun(tc_prod(_1627083, _1627085), tc_HOL_Obool), tc_HOL_Obool), _1627083), c_member(tc_prod(_1627083, _1627085)))), hAPP(c_COMBC(_1627083, _1627085, tc_prod(_1627083, _1627085)), c_Product__Type_OPair(_1627083, _1627085))))), _1627087))))], (12976 ^ _779571) ^ [_996914] : [hAPP(c_Int_Onat, _996914) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996914), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42207 ^ _779571) ^ [_1596534, _1596536] : [c_Wellfounded_OwfP(_1596534, _1596536), -(c_Wellfounded_Owf(_1596534, hAPP(c_Set_OCollect(tc_prod(_1596534, _1596534)), hAPP(c_Product__Type_Oprod_Oprod__case(_1596534, _1596534, tc_HOL_Obool), _1596536))))], (26752 ^ _779571) ^ [_1250046, _1250048, _1250050, _1250052] : [class_Groups_Oab__group__add(_1250046), 26755 ^ _779571 : [(26762 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1250048), _1250050))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1250046), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1250046, _1250046), hAPP(hAPP(c_COMBB(_1250046, tc_fun(_1250046, _1250046), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1250046)), _1250052)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1250046, tc_Nat_Onat), _1250052), 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, _1250048, _1250050)) = c_Groups_Ozero__class_Ozero(_1250046))], (26756 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1250048), _1250050)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1250046), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1250046, _1250046), hAPP(hAPP(c_COMBB(_1250046, tc_fun(_1250046, _1250046), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1250046)), _1250052)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1250046, tc_Nat_Onat), _1250052), 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, _1250048, _1250050)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1250046), hAPP(_1250052, _1250048)), hAPP(_1250052, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1250050), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (12431 ^ _779571) ^ [_987128] : [hBOOL(hAPP(_987128, 12432 ^ [_987128])), 12435 ^ _779571 : [(12436 ^ _779571) ^ [_987222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987222)), -(hBOOL(hAPP(_987128, hAPP(c_Int_Onat, _987222))))]]], (24363 ^ _779571) ^ [_1204329, _1204331, _1204333] : [class_Orderings_Olinorder(_1204329), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204329), _1204331), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1204329), _1204331), _1204333))))], (30967 ^ _779571) ^ [_1337101, _1337103] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1337101), _1337103))))], (48377 ^ _779571) ^ [_1746578, _1746580, _1746582, _1746584, _1746586] : [-(c_Map_Odom(_1746578, _1746580, c_Map_Omap__upds(_1746578, _1746580, _1746582, _1746584, _1746586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1746578, tc_HOL_Obool)), hAPP(c_List_Oset(_1746578), hAPP(hAPP(c_List_Otake(_1746578), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746580)), _1746586)), _1746584))), c_Map_Odom(_1746578, _1746580, _1746582)))], (17701 ^ _779571) ^ [_1084348, _1084350, _1084352] : [class_Rings_Oring__1(_1084348), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084348), hAPP(c_Groups_Ouminus__class_Ouminus(_1084348), _1084350)), _1084352) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084348), hAPP(hAPP(c_Power_Opower__class_Opower(_1084348), hAPP(c_Groups_Ouminus__class_Ouminus(_1084348), c_Groups_Oone__class_Oone(_1084348))), _1084352)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084348), _1084350), _1084352)))], (41059 ^ _779571) ^ [_1561501] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1561501, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561501), hAPP(c_COMBK(tc_HOL_Obool, _1561501), c_fFalse)))], (42667 ^ _779571) ^ [_1607071, _1607073, _1607075, _1607077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1607071, tc_HOL_Obool), tc_fun(_1607071, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1607071, tc_HOL_Obool), tc_fun(_1607071, tc_HOL_Obool)), _1607073), _1607075)), c_Wellfounded_Omax__ext(_1607071, _1607077))), 42670 ^ _779571 : [(42673 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1607071), _1607075)))], (42675 ^ _779571) ^ [] : [_1607075 = c_Orderings_Obot__class_Obot(tc_fun(_1607071, tc_HOL_Obool))], (42677 ^ _779571) ^ [_1607365] : [hBOOL(hAPP(hAPP(c_member(_1607071), _1607365), _1607073)), 42681 ^ _779571 : [(42684 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607071, _1607071)), hAPP(hAPP(c_Product__Type_OPair(_1607071, _1607071), _1607365), 42680 ^ [_1607071, _1607073, _1607075, _1607077, _1607365])), _1607077)))], (42682 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607071), 42680 ^ [_1607071, _1607073, _1607075, _1607077, _1607365]), _1607075)))]]], (42671 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1607071), _1607073)))]]], (43712 ^ _779571) ^ [_1633361, _1633363] : [-(c_Relation_Osingle__valued(_1633361, _1633361, c_Relation_OId__on(_1633361, _1633363)))], (44846 ^ _779571) ^ [_1660599, _1660601] : [class_Complete__Lattice_Ocomplete__lattice(_1660599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660599), _1660601)), -(c_Complete__Lattice_OSup__class_OSup(_1660599, _1660601) = hAPP(hAPP(c_Finite__Set_Ofold(_1660599, _1660599, c_Lattices_Osemilattice__sup__class_Osup(_1660599)), c_Orderings_Obot__class_Obot(_1660599)), _1660601))], (33539 ^ _779571) ^ [_1391640, _1391642, _1391644, _1391646] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1391640, _1391644)), c_Sum__Type_OPlus(_1391640, _1391644, _1391642, _1391646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1391640), _1391642)), hAPP(c_Finite__Set_Ocard(_1391644), _1391646))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391640), _1391642)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391644), _1391646))], (5815 ^ _779571) ^ [_872693, _872695, _872697, _872699, _872701, _872703] : [hBOOL(hAPP(_872693, _872695)), c_Natural_Oevaln(_872697, _872695, _872699, _872701), c_Natural_Oevaln(c_Com_Ocom_OWhile(_872693, _872697), _872701, _872699, _872703), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_872693, _872697), _872695, _872699, _872703))], (9870 ^ _779571) ^ [_943938, _943940, _943942, _943944, _943946, _943948] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_943938), -(_943940 = c_Groups_Ozero__class_Ozero(_943938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943938), _943942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943938), _943940), _943946)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943938), _943944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943938), _943940), _943948)), _943942 = _943944, -(_943946 = _943948)], (41640 ^ _779571) ^ [_1581490, _1581492, _1581494, _1581496] : [c_Finite__Set_Ofolding(_1581490, _1581492, _1581494, _1581496), -(hAPP(_1581496, c_Orderings_Obot__class_Obot(tc_fun(_1581490, tc_HOL_Obool))) = c_Fun_Oid(_1581492))], (4518 ^ _779571) ^ [_849498, _849500, _849502, _849504] : [-(c_Transitive__Closure_Ortrancl(_849504, _849500) = c_Transitive__Closure_Ortrancl(_849502, _849498)), _849504 = _849502, _849500 = _849498], (7400 ^ _779571) ^ [_902433] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _902433))))], (3946 ^ _779571) ^ [_840402, _840404, _840406, _840408] : [-(c_Transitive__Closure_Otrancl(_840408, _840404) = c_Transitive__Closure_Otrancl(_840406, _840402)), _840408 = _840406, _840404 = _840402], (15438 ^ _779571) ^ [_1040916, _1040918, _1040920] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040916), _1040918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040920), _1040918)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040916), _1040920))], (34616 ^ _779571) ^ [_1413657, _1413659, _1413661, _1413663, _1413665] : [hBOOL(hAPP(hAPP(c_member(_1413657), _1413659), _1413661)), -(hAPP(c_Map_Orestrict__map(_1413657, _1413663, _1413665, _1413661), _1413659) = hAPP(_1413665, _1413659))], (30910 ^ _779571) ^ [_1335869, _1335871, _1335873] : [30912 ^ _779571 : [(30915 ^ _779571) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1335873, 30911 ^ [_1335869, _1335871, _1335873]))], (30913 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335869), 30911 ^ [_1335869, _1335871, _1335873]), _1335871)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335869, tc_Int_Oint), _1335873), _1335871) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335869, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1335869), c_Int_Onat), _1335873)), _1335871)))], (24987 ^ _779571) ^ [_1217534, _1217536, _1217538, _1217540] : [-(c_HOL_OThe(tc_prod(_1217534, _1217536), hAPP(c_Product__Type_Oprod_Oprod__case(_1217534, _1217536, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1217534, tc_fun(_1217536, tc_HOL_Obool), tc_fun(_1217536, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1217536, tc_HOL_Obool), tc_fun(_1217536, tc_HOL_Obool)), _1217534), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1217536)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1217534), c_fconj), hAPP(c_fequal, _1217538)))), hAPP(c_fequal, _1217540)))) = hAPP(hAPP(c_Product__Type_OPair(_1217534, _1217536), _1217538), _1217540))], (29752 ^ _779571) ^ [] : [-(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))))], (39108 ^ _779571) ^ [_1515342, _1515344, _1515346, _1515348, _1515350, _1515352] : [c_Typedef_Otype__definition(_1515342, _1515344, _1515346, _1515348, _1515350), -(hBOOL(hAPP(hAPP(c_member(_1515344), hAPP(_1515346, _1515352)), _1515350)))], (36216 ^ _779571) ^ [_1451724, _1451726, _1451728] : [class_Lattices_Olattice(_1451724), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451724), _1451726), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451724), _1451726), _1451728)) = _1451726)], (5578 ^ _779571) ^ [_865702, _865704, _865706, _865708] : [-(tc_sum(_865708, _865704) = tc_sum(_865706, _865702)), _865708 = _865706, _865704 = _865702], (20689 ^ _779571) ^ [_1135060, _1135062, _1135064] : [class_Fields_Olinordered__field(_1135060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135060), _1135062), c_Groups_Ozero__class_Ozero(_1135060))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135060), c_Groups_Ozero__class_Ozero(_1135060)), _1135064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135060), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135060), _1135062), _1135064)), c_Groups_Ozero__class_Ozero(_1135060))))], (17531 ^ _779571) ^ [_1081168, _1081170, _1081172] : [class_Rings_Olinordered__idom(_1081168), -(hAPP(c_Groups_Oabs__class_Oabs(_1081168), hAPP(hAPP(c_Power_Opower__class_Opower(_1081168), hAPP(c_Groups_Ouminus__class_Ouminus(_1081168), _1081170)), _1081172)) = hAPP(c_Groups_Oabs__class_Oabs(_1081168), hAPP(hAPP(c_Power_Opower__class_Opower(_1081168), _1081170), _1081172)))], (49425 ^ _779571) ^ [_1772361, _1772363, _1772365] : [_1772361 = c_List_Olist_ONil(_1772363), -(c_List_Olast(_1772363, hAPP(hAPP(c_List_Oappend(_1772363), _1772365), _1772361)) = c_List_Olast(_1772363, _1772365))], (49473 ^ _779571) ^ [_1773013, _1773015, _1773017, _1773019] : [-(_1773013 = c_List_Olist_ONil(_1773015)), -(c_List_Olast(_1773017, hAPP(hAPP(c_List_Omap(_1773015, _1773017), _1773019), _1773013)) = hAPP(_1773019, c_List_Olast(_1773015, _1773013)))], (44656 ^ _779571) ^ [_1655715, _1655717, _1655719, _1655721] : [class_Complete__Lattice_Ocomplete__lattice(_1655715), -(_1655717 = c_Orderings_Obot__class_Obot(tc_fun(_1655719, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655719, _1655715), _1655717), hAPP(c_COMBK(_1655715, _1655719), _1655721)) = _1655721)], (49100 ^ _779571) ^ [_1764670, _1764672, _1764674] : [class_Groups_Oab__semigroup__add(_1764670), -(c_List_Ofoldr(_1764670, _1764670, c_Groups_Oplus__class_Oplus(_1764670), _1764672, _1764674) = hAPP(c_List_Ofoldl(_1764670, _1764670, c_Groups_Oplus__class_Oplus(_1764670), _1764674), _1764672))], (24929 ^ _779571) ^ [_1215767, _1215769, _1215771, _1215773, _1215775, _1215777, _1215779] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1215767, _1215769, _1215771, _1215773), _1215775), _1215777), _1215779) = c_New__DSequence_Opos__bind(_1215767, _1215769, hAPP(hAPP(hAPP(_1215771, _1215775), _1215777), _1215779), hAPP(hAPP(c_COMBC(_1215767, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1215769))), hAPP(hAPP(c_COMBC(_1215767, 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(_1215769)))), hAPP(hAPP(c_COMBC(_1215767, 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(_1215769))))), _1215773), _1215775)), _1215777)), _1215779)))], (28451 ^ _779571) ^ [_1284946, _1284948] : [c_Nat__Transfer_Onat__set(_1284946), c_Nat__Transfer_Onat__set(_1284948), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1284946), _1284948)))], (18653 ^ _779571) ^ [_1099513, _1099515] : [class_Int_Onumber__ring(_1099513), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099513), hAPP(c_Int_Onumber__class_Onumber__of(_1099513), _1099515)), c_Groups_Oone__class_Oone(_1099513)) = hAPP(c_Int_Onumber__class_Onumber__of(_1099513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (47063 ^ _779571) ^ [_1715785, _1715787, _1715789, _1715791, _1715793] : [class_Groups_Ocomm__monoid__add(_1715785), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715785), hAPP(hAPP(c_List_Omap(_1715787, _1715785), hAPP(hAPP(c_COMBS(_1715787, _1715785, _1715785), hAPP(hAPP(c_COMBB(_1715785, tc_fun(_1715785, _1715785), _1715787), c_Groups_Oplus__class_Oplus(_1715785)), _1715789)), _1715791)), _1715793)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1715785), hAPP(c_List_Omonoid__add__class_Olistsum(_1715785), hAPP(hAPP(c_List_Omap(_1715787, _1715785), _1715789), _1715793))), hAPP(c_List_Omonoid__add__class_Olistsum(_1715785), hAPP(hAPP(c_List_Omap(_1715787, _1715785), _1715791), _1715793))))], (23627 ^ _779571) ^ [_1189848, _1189850, _1189852] : [class_Orderings_Olinorder(_1189848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189848), _1189850), _1189852)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189848), _1189852), _1189850) = _1189850)], (30072 ^ _779571) ^ [_1318455, _1318457, _1318459] : [-(hBOOL(hAPP(hAPP(c_member(_1318455), _1318457), _1318459))), -(hBOOL(hAPP(hAPP(c_member(_1318455), _1318457), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1318455, tc_HOL_Obool)), _1318459))))], (2688 ^ _779571) ^ [_820333, _820335, _820337, _820339] : [-(c_Orderings_Oord_Omax(_820339, _820335) = c_Orderings_Oord_Omax(_820337, _820333)), _820339 = _820337, _820335 = _820333], (2672 ^ _779571) ^ [_820099, _820101] : [_820101 = _820099, -(c_New__DSequence_Opos__not__seq(_820101) = c_New__DSequence_Opos__not__seq(_820099))], (46004 ^ _779571) ^ [_1687215, _1687217, _1687219, _1687221] : [hAPP(c_List_Oset(_1687215), _1687217) = c_Map_Odom(_1687215, _1687219, _1687221), -(c_Map_Omap__of(_1687215, _1687219, hAPP(hAPP(c_List_Omap(_1687215, tc_prod(_1687215, _1687219)), hAPP(hAPP(c_COMBS(_1687215, _1687219, tc_prod(_1687215, _1687219)), c_Product__Type_OPair(_1687215, _1687219)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1687219), _1687219, _1687215), c_Option_Othe(_1687219)), _1687221))), _1687217)) = _1687221)], (39040 ^ _779571) ^ [_1514109, _1514111, _1514113, _1514115, _1514117, _1514119, _1514121, _1514123] : [c_Finite__Set_Ofolding__image(_1514109, _1514111, _1514113, _1514115, _1514117), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514111), _1514119)), -(hAPP(hAPP(_1514117, hAPP(hAPP(c_COMBS(_1514111, _1514109, _1514109), hAPP(hAPP(c_COMBB(_1514109, tc_fun(_1514109, _1514109), _1514111), _1514113), _1514121)), _1514123)), _1514119) = hAPP(hAPP(_1514113, hAPP(hAPP(_1514117, _1514121), _1514119)), hAPP(hAPP(_1514117, _1514123), _1514119)))], (51509 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (41770 ^ _779571) ^ [_1586297, _1586299, _1586301, _1586303, _1586305, _1586307, _1586309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586297, _1586301)), hAPP(hAPP(c_Product__Type_OPair(_1586297, _1586301), _1586307), _1586309)), hAPP(hAPP(c_Relation_Orel__comp(_1586297, _1586299, _1586301), _1586303), _1586305))), -(c_Predicate_Opred__comp(_1586297, _1586299, _1586301, hAPP(hAPP(c_COMBC(_1586297, tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_fun(_1586299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586299, tc_fun(tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_fun(_1586299, tc_HOL_Obool)), _1586297), c_COMBC(_1586299, tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586299, tc_prod(_1586297, _1586299)), tc_fun(_1586299, tc_fun(tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_HOL_Obool)), _1586297), hAPP(c_COMBB(tc_prod(_1586297, _1586299), tc_fun(tc_fun(tc_prod(_1586297, _1586299), tc_HOL_Obool), tc_HOL_Obool), _1586299), c_member(tc_prod(_1586297, _1586299)))), c_Product__Type_OPair(_1586297, _1586299)))), _1586303), hAPP(hAPP(c_COMBC(_1586299, tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_fun(_1586301, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586301, tc_fun(tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_fun(_1586301, tc_HOL_Obool)), _1586299), c_COMBC(_1586301, tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586301, tc_prod(_1586299, _1586301)), tc_fun(_1586301, tc_fun(tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_HOL_Obool)), _1586299), hAPP(c_COMBB(tc_prod(_1586299, _1586301), tc_fun(tc_fun(tc_prod(_1586299, _1586301), tc_HOL_Obool), tc_HOL_Obool), _1586301), c_member(tc_prod(_1586299, _1586301)))), c_Product__Type_OPair(_1586299, _1586301)))), _1586305), _1586307, _1586309))], (23425 ^ _779571) ^ [_1186176, _1186178, _1186180, _1186182] : [_1186176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186178), _1186180)), _1186182), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186176, _1186178), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1186180), _1186182)))), 23432 ^ _779571 : [(23435 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186182), _1186178))], (23433 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186178)))]], 23440 ^ _779571 : [(23443 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186178), _1186182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186182), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23441 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186178))]]], (16911 ^ _779571) ^ [_1069697, _1069699, _1069701] : [class_Int_Onumber__ring(_1069697), -(hAPP(c_Int_Onumber__class_Onumber__of(_1069697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069699), _1069701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069697), hAPP(c_Int_Onumber__class_Onumber__of(_1069697), _1069699)), hAPP(c_Int_Onumber__class_Onumber__of(_1069697), _1069701)))], (5556 ^ _779571) ^ [_865383, _865385] : [_865385 = _865383, -(tc_List_Olist(_865385) = tc_List_Olist(_865383))], (45113 ^ _779571) ^ [_1666584, _1666586] : [class_Complete__Lattice_Ocomplete__lattice(_1666584), -(c_Complete__Lattice_OSup__class_OSup(_1666584, _1666586) = c_Complete__Lattice_OInf__class_OInf(_1666584, hAPP(c_Set_OCollect(_1666584), hAPP(hAPP(c_COMBB(tc_fun(_1666584, tc_HOL_Obool), tc_HOL_Obool, _1666584), c_HOL_OAll(_1666584)), hAPP(hAPP(c_COMBB(tc_fun(_1666584, tc_HOL_Obool), tc_fun(_1666584, tc_HOL_Obool), _1666584), hAPP(c_COMBS(_1666584, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1666584), c_fimplies), hAPP(hAPP(c_COMBC(_1666584, tc_fun(_1666584, tc_HOL_Obool), tc_HOL_Obool), c_member(_1666584)), _1666586)))), hAPP(c_COMBC(_1666584, _1666584, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1666584)))))))], (36314 ^ _779571) ^ [_1454050, _1454052, _1454054, _1454056] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454050, tc_HOL_Obool)), _1454052), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454050, tc_HOL_Obool)), _1454054), _1454056)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454050, tc_HOL_Obool)), _1454054), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454050, tc_HOL_Obool)), _1454052), _1454056)))], (51175 ^ _779571) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (48542 ^ _779571) ^ [_1751050, _1751052, _1751054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751050), tc_List_Olist(_1751050))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751050), tc_List_Olist(_1751050)), c_List_Olist_ONil(_1751050)), _1751052)), c_List_Olistrel1(_1751050, _1751054)))], (49467 ^ _779571) ^ [_1772961, _1772963, _1772965] : [-(_1772961 = c_List_Olist_ONil(_1772963)), -(c_List_Olast(_1772963, hAPP(hAPP(c_List_Olist_OCons(_1772963), _1772965), _1772961)) = c_List_Olast(_1772963, _1772961))], (15038 ^ _779571) ^ [_1033732, _1033734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1033732)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033732), _1033734)), _1033732) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37954 ^ _779571) ^ [_1492052, _1492054, _1492056, _1492058, _1492060] : [c_Relation_Orefl__on(_1492052, _1492054, _1492056), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492052, _1492052)), hAPP(hAPP(c_Product__Type_OPair(_1492052, _1492052), _1492058), _1492060)), _1492056)), -(hBOOL(hAPP(hAPP(c_member(_1492052), _1492060), _1492054)))], (48800 ^ _779571) ^ [_1758231, _1758233, _1758235, _1758237] : [hAPP(hAPP(c_List_Oappend(_1758231), _1758233), _1758235) = _1758237, 48803 ^ _779571 : [(48806 ^ _779571) ^ [] : [-(_1758235 = hAPP(hAPP(c_List_Odrop(_1758231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758231)), _1758233)), _1758237))], (48804 ^ _779571) ^ [] : [-(_1758233 = hAPP(hAPP(c_List_Otake(_1758231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758231)), _1758233)), _1758237))]]], (4256 ^ _779571) ^ [_845305, _845307, _845309, _845311, _845313, _845315, _845317, _845319, _845321, _845323, _845325, _845327] : [-(c_Product__Type_Omap__pair(_845327, _845323, _845319, _845315, _845311, _845307) = c_Product__Type_Omap__pair(_845325, _845321, _845317, _845313, _845309, _845305)), _845327 = _845325, _845323 = _845321, _845319 = _845317, _845315 = _845313, _845311 = _845309, _845307 = _845305], (2962 ^ _779571) ^ [_824830, _824832, _824834, _824836, _824838, _824840, _824842, _824844] : [-(c_Lazy__Sequence_Ohb__bind(_824844, _824840, _824836, _824832) = c_Lazy__Sequence_Ohb__bind(_824842, _824838, _824834, _824830)), _824844 = _824842, _824840 = _824838, _824836 = _824834, _824832 = _824830], (28629 ^ _779571) ^ [_1288012, _1288014, _1288016] : [class_Groups_Ocomm__monoid__add(_1288012), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1288012), _1288014), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288016))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288012), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1288012), _1288014), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1288016))), hAPP(_1288014, hAPP(c_Nat_OSuc, _1288016))))], (41836 ^ _779571) ^ [_1587999, _1588001, _1588003] : [c_Wellfounded_Owf(_1587999, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587999, _1587999), tc_HOL_Obool)), _1588001), _1588003)), -(c_Wellfounded_Owf(_1587999, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587999, _1587999), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587999, _1587999), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587999, _1587999, _1587999), _1588001), _1588001)), hAPP(hAPP(c_Relation_Orel__comp(_1587999, _1587999, _1587999), _1588003), _1588001))), _1588003)))], (39358 ^ _779571) ^ [_1520848, _1520850] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520848), _1520850))), -(hAPP(c_Finite__Set_Ocard(_1520848), _1520850) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6540 ^ _779571) ^ [_886278, _886280, _886282] : [c_Com_Ocom_OAss(_886278, _886280) = hAPP(c_Com_Ocom_OBODY, _886282)], (45360 ^ _779571) ^ [_1672354, _1672356, _1672358] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1672354, tc_HOL_Obool)), _1672356), _1672358))), 45366 ^ _779571 : [(45370 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1672354, tc_HOL_Obool)), 45368 ^ [_1672354, _1672356, _1672358]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1672354, tc_HOL_Obool)), _1672356), _1672358))))], (45372 ^ _779571) ^ [] : [45365 ^ [_1672354, _1672356, _1672358] = 45368 ^ [_1672354, _1672356, _1672358]], (45374 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1672354, tc_HOL_Obool)), 45365 ^ [_1672354, _1672356, _1672358]), 45368 ^ [_1672354, _1672356, _1672358]) = c_Orderings_Obot__class_Obot(tc_fun(_1672354, tc_HOL_Obool))], (45367 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1672354, tc_HOL_Obool)), 45365 ^ [_1672354, _1672356, _1672358]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1672354, tc_HOL_Obool)), _1672356), _1672358))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1672354, tc_HOL_Obool)), _1672356), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672354, tc_HOL_Obool), _1672358)) = c_Orderings_Obot__class_Obot(tc_fun(_1672354, tc_HOL_Obool)))], (23707 ^ _779571) ^ [_1191339, _1191341, _1191343, _1191345] : [class_Orderings_Olinorder(_1191339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191339), _1191341), _1191343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191339), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191339), _1191345), _1191341)), _1191343)))], (3444 ^ _779571) ^ [_832475, _832477, _832479, _832481, _832483, _832485] : [-(c_Hoare__Mirabelle_Opeek__and(_832485, _832481, _832477) = c_Hoare__Mirabelle_Opeek__and(_832483, _832479, _832475)), _832485 = _832483, _832481 = _832479, _832477 = _832475], (29550 ^ _779571) ^ [_1307724] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307724, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1307724, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1307724, tc_HOL_Obool)))], (15440 ^ _779571) ^ [_1040967, _1040969, _1040971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040967), _1040969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040967), _1040971)), 15447 ^ _779571 : [(15454 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040969), _1040971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040969), _1040967)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040971), _1040967))))], (15448 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040969), _1040967)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040971), _1040967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040969), _1040971)))]]], (3678 ^ _779571) ^ [_836226, _836228, _836230, _836232, _836234, _836236] : [-(c_Wellfounded_Omlex__prod(_836236, _836232, _836228) = c_Wellfounded_Omlex__prod(_836234, _836230, _836226)), _836236 = _836234, _836232 = _836230, _836228 = _836226], (1572 ^ _779571) ^ [_801989, _801991] : [-(class_Groups_Osemigroup__add(_801989)), _801991 = _801989, class_Groups_Osemigroup__add(_801991)], (48586 ^ _779571) ^ [_1752561, _1752563, _1752565, _1752567, _1752569, _1752571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752561), tc_List_Olist(_1752561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752561), tc_List_Olist(_1752561)), hAPP(hAPP(c_List_Olist_OCons(_1752561), _1752563), _1752565)), hAPP(hAPP(c_List_Olist_OCons(_1752561), _1752567), _1752569))), c_List_Olistrel1(_1752561, _1752571))), 48591 ^ _779571 : [(48594 ^ _779571) ^ [] : [-(_1752565 = _1752569)], (48592 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752561, _1752561)), hAPP(hAPP(c_Product__Type_OPair(_1752561, _1752561), _1752563), _1752567)), _1752571)))]], 48595 ^ _779571 : [(48598 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752561), tc_List_Olist(_1752561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752561), tc_List_Olist(_1752561)), _1752565), _1752569)), c_List_Olistrel1(_1752561, _1752571))))], (48596 ^ _779571) ^ [] : [-(_1752563 = _1752567)]]], (47861 ^ _779571) ^ [_1734328, _1734330, _1734332, _1734334, _1734336, _1734338] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734328)), _1734330) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734332)), _1734334), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734328)), _1734336) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734332)), _1734338), -(hAPP(hAPP(c_List_Ozip(_1734328, _1734332), hAPP(hAPP(c_List_Oappend(_1734328), _1734330), _1734336)), hAPP(hAPP(c_List_Oappend(_1734332), _1734334), _1734338)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1734328, _1734332)), hAPP(hAPP(c_List_Ozip(_1734328, _1734332), _1734330), _1734334)), hAPP(hAPP(c_List_Ozip(_1734328, _1734332), _1734336), _1734338)))], (26292 ^ _779571) ^ [_1241350, _1241352, _1241354] : [-(_1241350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26295 ^ _779571 : [(26302 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241350), _1241352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241350), _1241354))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241352), _1241354)))], (26296 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241352), _1241354)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241350), _1241352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241350), _1241354))))]]], (19455 ^ _779571) ^ [_1113297, _1113299] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1113297)), _1113299) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1113297), _1113299))), _1113299))], (48248 ^ _779571) ^ [_1743272, _1743274, _1743276, _1743278] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743272), tc_List_Olist(_1743272))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743272), tc_List_Olist(_1743272)), _1743274), _1743276)), c_List_Olexord(_1743272, _1743278))), 48253 ^ _779571 : [(48256 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1743272), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743272)), _1743274)), _1743276) = _1743274)], (48254 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743272)), _1743274)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743272)), _1743276))))]], 48258 ^ _779571 : [(48263 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743272, _1743272)), hAPP(hAPP(c_Product__Type_OPair(_1743272, _1743272), hAPP(hAPP(c_List_Onth(_1743272), _1743274), 48257 ^ [_1743272, _1743274, _1743276, _1743278])), hAPP(hAPP(c_List_Onth(_1743272), _1743276), 48257 ^ [_1743272, _1743274, _1743276, _1743278]))), _1743278)))], (48261 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1743272), 48257 ^ [_1743272, _1743274, _1743276, _1743278]), _1743274) = hAPP(hAPP(c_List_Otake(_1743272), 48257 ^ [_1743272, _1743274, _1743276, _1743278]), _1743276))], (48259 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48257 ^ [_1743272, _1743274, _1743276, _1743278]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743272)), _1743274)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743272)), _1743276)))))]]], (15460 ^ _779571) ^ [_1041320, _1041322, _1041324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041320), _1041322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041320), _1041324)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041322), _1041320)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041324), _1041320)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041322), _1041324))], (15362 ^ _779571) ^ [_1039616, _1039618, _1039620, _1039622, _1039624, _1039626] : [class_Divides_Oring__div(_1039616), c_Divides_Odiv__class_Omod(_1039616, _1039618, _1039620) = c_Divides_Odiv__class_Omod(_1039616, _1039622, _1039620), c_Divides_Odiv__class_Omod(_1039616, _1039624, _1039620) = c_Divides_Odiv__class_Omod(_1039616, _1039626, _1039620), -(c_Divides_Odiv__class_Omod(_1039616, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039616), _1039618), _1039624), _1039620) = c_Divides_Odiv__class_Omod(_1039616, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039616), _1039622), _1039626), _1039620))], (32675 ^ _779571) ^ [_1375705] : [class_Rings_Osemiring__1(_1375705), -(hBOOL(hAPP(hAPP(c_member(_1375705), c_Groups_Ozero__class_Ozero(_1375705)), c_Nat_Osemiring__1__class_ONats(_1375705))))], (14890 ^ _779571) ^ [_1030729, _1030731, _1030733] : [class_Divides_Osemiring__div(_1030729), -(_1030731 = c_Groups_Ozero__class_Ozero(_1030729)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030729), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030729), _1030731), _1030733)), _1030731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030729), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030729), _1030733), _1030731)), c_Groups_Oone__class_Oone(_1030729)))], (40142 ^ _779571) ^ [_1539791, _1539793, _1539795, _1539797] : [40143 ^ _779571 : [(40146 ^ _779571) ^ [] : [_1539797 = c_Orderings_Obot__class_Obot(tc_fun(_1539793, tc_HOL_Obool))], (40144 ^ _779571) ^ [] : [_1539795 = c_Orderings_Obot__class_Obot(tc_fun(_1539791, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1539791, _1539793), _1539795), hAPP(c_COMBK(tc_fun(_1539793, tc_HOL_Obool), _1539791), _1539797)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1539791, _1539793), tc_HOL_Obool)))], (15338 ^ _779571) ^ [_1039084, _1039086, _1039088] : [class_Groups_Oab__group__add(_1039084), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1039084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039084), _1039086), _1039088)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039084), _1039088), _1039086))], (22322 ^ _779571) ^ [_1164819, _1164821, _1164823] : [class_Int_Onumber__ring(_1164819), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164819), hAPP(c_Int_Onumber__class_Onumber__of(_1164819), _1164821)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1164823))) = hAPP(hAPP(c_HOL_OLet(_1164819, _1164819), hAPP(hAPP(c_Power_Opower__class_Opower(_1164819), hAPP(c_Int_Onumber__class_Onumber__of(_1164819), _1164821)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1164823))), hAPP(hAPP(c_COMBS(_1164819, _1164819, _1164819), c_Groups_Otimes__class_Otimes(_1164819)), c_COMBI(_1164819))))], (18113 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16485 ^ _779571) ^ [_1061588, _1061590] : [class_Rings_Olinordered__idom(_1061588), -(hAPP(c_Groups_Oabs__class_Oabs(_1061588), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1061588), _1061590)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1061588), _1061590))], (6817 ^ _779571) ^ [_891853, _891855] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_891853, _891855)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891853)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891855))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41758 ^ _779571) ^ [_1585273, _1585275, _1585277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585273, _1585273), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1585273, _1585273, _1585273), _1585275), _1585277)), _1585275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1585273, _1585275)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1585273, _1585277)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1585273, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1585273, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1585273, tc_HOL_Obool), tc_fun(_1585273, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1585273, _1585275))))], (31207 ^ _779571) ^ [_1341725, _1341727] : [class_Finite__Set_Ofinite(_1341725), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341725), _1341727)))], (16905 ^ _779571) ^ [_1069562, _1069564, _1069566] : [class_Int_Onumber__ring(_1069562), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069562), hAPP(c_Int_Onumber__class_Onumber__of(_1069562), _1069564)), hAPP(c_Int_Onumber__class_Onumber__of(_1069562), _1069566)) = hAPP(c_Int_Onumber__class_Onumber__of(_1069562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069564), _1069566)))], (15686 ^ _779571) ^ [_1045840, _1045842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045842), _1045840)), _1045842)))], (46482 ^ _779571) ^ [_1698952, _1698954, _1698956, _1698958, _1698960, _1698962] : [class_Orderings_Olinorder(_1698952), -(hAPP(_1698954, _1698956) = hAPP(_1698954, _1698958)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698960, _1698952, _1698954), _1698958), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698960, _1698952, _1698954), _1698956), _1698962)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698960, _1698952, _1698954), _1698956), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698960, _1698952, _1698954), _1698958), _1698962)))], (26916 ^ _779571) ^ [_1253546, _1253548] : [26918 ^ _779571 : [(26921 ^ _779571) ^ [] : [hBOOL(hAPP(_1253548, 26917 ^ [_1253546, _1253548]))], (26919 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26917 ^ [_1253546, _1253548]), _1253546)))]], 26922 ^ _779571 : [(26923 ^ _779571) ^ [_1253697] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1253697), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1253546))), -(hBOOL(hAPP(_1253548, _1253697)))]]], (51315 ^ _779571) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (6019 ^ _779571) ^ [_876416, _876418, _876420] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_876416, _876418, _876420)], (43373 ^ _779571) ^ [_1624594, _1624596, _1624598] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624594, _1624596)), hAPP(c_Relation_Oconverse(_1624596, _1624594), _1624598))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624596, _1624594)), _1624598)))], (34638 ^ _779571) ^ [_1414077, _1414079, _1414081, _1414083, _1414085] : [-(hBOOL(hAPP(hAPP(c_member(_1414077), _1414079), _1414081))), -(hAPP(c_Map_Orestrict__map(_1414077, _1414083, _1414085, _1414081), _1414079) = c_Option_Ooption_ONone(_1414083))], (26450 ^ _779571) ^ [_1244186, _1244188] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1244186)), _1244188)), 26453 ^ _779571 : [(26460 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244186))), -(_1244188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26454 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244186)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244186), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244188))))]]], (22840 ^ _779571) ^ [_1175481, _1175483, _1175485, _1175487] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175481, _1175483), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175485), _1175487))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1175481), _1175483) = _1175485)], (35466 ^ _779571) ^ [_1433479, _1433481, _1433483, _1433485, _1433487, _1433489, _1433491] : [-(hAPP(c_Product__Type_Oapfst(_1433479, _1433481, _1433483, _1433485), hAPP(c_Product__Type_Oapfst(_1433487, _1433479, _1433483, _1433489), _1433491)) = hAPP(c_Product__Type_Oapfst(_1433487, _1433481, _1433483, hAPP(c_Fun_Ocomp(_1433479, _1433481, _1433487, _1433485), _1433489)), _1433491))], (35587 ^ _779571) ^ [_1436893, _1436895, _1436897, _1436899] : [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), _1436893), _1436895)), 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), _1436897), _1436899)), 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), _1436893), _1436899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436897), _1436895))))], (13418 ^ _779571) ^ [_1004391, _1004393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004391), _1004393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004393), _1004391)))], (14429 ^ _779571) ^ [_1023102, _1023104] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023102, _1023104)) = _1023104, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1023102), _1023104) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12275 ^ _779571) ^ [_984486, _984488] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984486), hAPP(c_Nat_OSuc, _984488)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984486), _984488)))], (4282 ^ _779571) ^ [_845790, _845792, _845794, _845796, _845798, _845800, _845802, _845804] : [-(c_Wellfounded_Olex__prod(_845804, _845800, _845796, _845792) = c_Wellfounded_Olex__prod(_845802, _845798, _845794, _845790)), _845804 = _845802, _845800 = _845798, _845796 = _845794, _845792 = _845790], (4914 ^ _779571) ^ [_855506, _855508] : [_855508 = _855506, -(c_Option_Ooption_ONone(_855508) = c_Option_Ooption_ONone(_855506))], (43497 ^ _779571) ^ [_1627734, _1627736, _1627738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627734, _1627734)), _1627736), c_Transitive__Closure_Ortrancl(_1627734, _1627738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627734, _1627734)), _1627736), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1627734, _1627734), tc_HOL_Obool), 43500 ^ [_1627734, _1627736, _1627738]), _1627738))))], (18451 ^ _779571) ^ [_1096201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096201), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096201) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29274 ^ _779571) ^ [_1302779, _1302781, _1302783] : [class_Orderings_Obot(_1302779), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1302781, _1302779)), _1302783) = c_Orderings_Obot__class_Obot(_1302779))], (47262 ^ _779571) ^ [_1720070, _1720072, _1720074] : [-(hAPP(hAPP(c_List_Ozip(_1720070, _1720072), c_List_Olist_ONil(_1720070)), _1720074) = c_List_Olist_ONil(tc_prod(_1720070, _1720072)))], (22362 ^ _779571) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (32825 ^ _779571) ^ [_1378540] : [class_Rings_Oring__1(_1378540), -(hBOOL(hAPP(hAPP(c_member(_1378540), c_Groups_Ozero__class_Ozero(_1378540)), c_Int_Oring__1__class_OInts(_1378540))))], (30517 ^ _779571) ^ [_1327159, _1327161, _1327163, _1327165] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327159, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1327159, tc_fun(_1327159, tc_HOL_Obool), tc_HOL_Obool), c_member(_1327159)), _1327161)), hAPP(hAPP(c_COMBC(_1327159, tc_fun(_1327159, tc_HOL_Obool), tc_HOL_Obool), c_member(_1327159)), _1327163)), _1327165)), -(hBOOL(hAPP(hAPP(c_member(_1327159), _1327165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327159, tc_HOL_Obool)), _1327161), _1327163))))], (46444 ^ _779571) ^ [_1697977, _1697979, _1697981, _1697983, _1697985, _1697987, _1697989, _1697991] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697977)), _1697979) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697981)), _1697983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697977)), _1697985) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697981)), _1697983), -(hBOOL(hAPP(hAPP(c_member(_1697981), _1697987), hAPP(c_List_Oset(_1697981), _1697983)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1697981, tc_Option_Ooption(_1697977)), c_Map_Omap__of(_1697981, _1697977, hAPP(hAPP(c_List_Ozip(_1697981, _1697977), _1697983), _1697979))), _1697987), hAPP(c_Option_Ooption_OSome(_1697977), _1697989)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1697981, tc_Option_Ooption(_1697977)), c_Map_Omap__of(_1697981, _1697977, hAPP(hAPP(c_List_Ozip(_1697981, _1697977), _1697983), _1697985))), _1697987), hAPP(c_Option_Ooption_OSome(_1697977), _1697991)), -(c_Map_Omap__of(_1697981, _1697977, hAPP(hAPP(c_List_Ozip(_1697981, _1697977), _1697983), _1697979)) = c_Map_Omap__of(_1697981, _1697977, hAPP(hAPP(c_List_Ozip(_1697981, _1697977), _1697983), _1697985)))], (50975 ^ _779571) ^ [_1806188, _1806190, _1806192] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806188)), c_List_OtakeWhile(_1806188, _1806190, _1806192))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806188)), _1806192))))], (6211 ^ _779571) ^ [_880235, _880237, _880239, _880241, _880243, _880245] : [c_Com_Ocom_OLocal(_880235, _880237, _880239) = c_Com_Ocom_OCall(_880241, _880243, _880245)], (15092 ^ _779571) ^ [_1034667, _1034669] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034667))), -(c_SMT_Oz3div(_1034669, _1034667) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034669), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1034667))))], (34763 ^ _779571) ^ [_1416912, _1416914, _1416916, _1416918] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1416912), _1416914)), 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)), _1416916), _1416912)), 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)), _1416918), _1416914)), 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)), _1416916), _1416918)), _1416914)), c_FunDef_Omax__strict)))], (49905 ^ _779571) ^ [_1783208, _1783210, _1783212, _1783214, _1783216] : [class_Orderings_Olinorder(_1783208), hBOOL(hAPP(hAPP(c_member(_1783210), _1783212), hAPP(c_List_Oset(_1783210), _1783214))), c_List_Olinorder__class_Osorted(_1783208, hAPP(hAPP(c_List_Omap(_1783210, _1783208), _1783216), _1783214)), hAPP(c_List_Ohd(_1783210), hAPP(c_List_Ofilter(_1783210, hAPP(hAPP(c_COMBB(_1783208, tc_HOL_Obool, _1783210), hAPP(c_fequal, hAPP(_1783216, _1783212))), _1783216)), _1783214)) = _1783212, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1783210, _1783208, _1783216), _1783212), c_List_Oremove1(_1783210, _1783212, _1783214)) = _1783214)], (5924 ^ _779571) ^ [_874685, _874687, _874689, _874691] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_874685, _874687), _874689, _874691, _874689)), 5925 ^ _779571 : [(5928 ^ _779571) ^ [_874772] : [c_Natural_Oevaln(_874687, _874689, _874691, _874772), c_Natural_Oevaln(c_Com_Ocom_OWhile(_874685, _874687), _874772, _874691, _874689)], (5926 ^ _779571) ^ [] : [-(hBOOL(hAPP(_874685, _874689)))]]], (3218 ^ _779571) ^ [_828884, _828886, _828888, _828890, _828892, _828894, _828896, _828898] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_828898, _828894, _828890, _828886) = c_SetInterval_Oord_OgreaterThanLessThan(_828896, _828892, _828888, _828884)), _828898 = _828896, _828894 = _828892, _828890 = _828888, _828886 = _828884], (40689 ^ _779571) ^ [_1552010, _1552012, _1552014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552010, _1552010), tc_HOL_Obool)), _1552012), hAPP(hAPP(c_Product__Type_OSigma(_1552010, _1552010), _1552014), hAPP(c_COMBK(tc_fun(_1552010, tc_HOL_Obool), _1552010), _1552014)))), 40695 ^ _779571 : [(40698 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1552010, _1552010)), hAPP(hAPP(c_Product__Type_OPair(_1552010, _1552010), 40694 ^ [_1552010, _1552012, _1552014]), 40694 ^ [_1552010, _1552012, _1552014])), _1552012))], (40696 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552010), 40694 ^ [_1552010, _1552012, _1552014]), _1552014)))]], -(c_Relation_Orefl__on(_1552010, _1552014, _1552012))], (48990 ^ _779571) ^ [_1762406, _1762408, _1762410] : [-(hAPP(c_List_Otl(_1762406), hAPP(hAPP(c_List_Odrop(_1762406), _1762408), _1762410)) = hAPP(hAPP(c_List_Odrop(_1762406), _1762408), hAPP(c_List_Otl(_1762406), _1762410)))], (10634 ^ _779571) ^ [_956514, _956516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956514)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _956516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956514), _956516)))], (6185 ^ _779571) ^ [_879693, _879695, _879697, _879699, _879701, _879703, _879705, _879707, _879709, _879711, _879713, _879715] : [-(c_Com_Ocom_Ocom__case(_879693, _879695, _879697, _879699, _879701, _879703, _879705, _879707, _879709, c_Com_Ocom_OLocal(_879711, _879713, _879715)) = hAPP(hAPP(hAPP(_879699, _879711), _879713), _879715))], (13827 ^ _779571) ^ [_1011959, _1011961] : [class_Divides_Osemiring__div(_1011959), -(c_Divides_Odiv__class_Omod(_1011959, _1011961, c_Groups_Oone__class_Oone(_1011959)) = c_Groups_Ozero__class_Ozero(_1011959))], (30261 ^ _779571) ^ [_1322150, _1322152, _1322154, _1322156] : [hBOOL(hAPP(hAPP(c_member(_1322150), _1322152), _1322154)), -(hBOOL(hAPP(hAPP(c_member(_1322150), _1322152), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322150, tc_HOL_Obool)), _1322156), _1322154))))], (41714 ^ _779571) ^ [_1583705, _1583707, _1583709, _1583711, _1583713, _1583715] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583705, _1583707, _1583709), _1583711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583707, _1583709), tc_HOL_Obool)), _1583713), _1583715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583705, _1583709), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583705, _1583707, _1583709), _1583711), _1583713)), hAPP(hAPP(c_Relation_Orel__comp(_1583705, _1583707, _1583709), _1583711), _1583715)))], (19953 ^ _779571) ^ [] : [-(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)))], (39431 ^ _779571) ^ [_1522571, _1522573, _1522575, _1522577, _1522579] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522571, _1522573, _1522575), _1522577), _1522579)), -(hBOOL(hAPP(_1522577, hAPP(_1522575, _1522579))))], (47366 ^ _779571) ^ [_1721938, _1721940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721938)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721940))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721938), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721940)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721938)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721938)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1721940))))], (3956 ^ _779571) ^ [_840551, _840553] : [_840553 = _840551, -(c_Relation_OId(_840553) = c_Relation_OId(_840551))], (5546 ^ _779571) ^ [_865234, _865236, _865238, _865240] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_865240, _865236) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_865238, _865234)), _865240 = _865238, _865236 = _865234], (9092 ^ _779571) ^ [_930273, _930275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930273)), 9095 ^ _779571 : [(9104 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930273), _930275) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _930273 = c_Groups_Oone__class_Oone(tc_Int_Oint), _930275 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9096 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930273), _930275) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9099 ^ _779571 : [(9102 ^ _779571) ^ [] : [-(_930275 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9100 ^ _779571) ^ [] : [-(_930273 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (48516 ^ _779571) ^ [_1750144, _1750146] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1750144), tc_List_Olist(_1750144)), tc_HOL_Obool)), c_List_Olistrel(_1750144, _1750146)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750144), c_List_Olistrel1(_1750144, _1750146)))))], (3382 ^ _779571) ^ [_831536, _831538] : [_831538 = _831536, -(c_Power_Opower__class_Opower(_831538) = c_Power_Opower__class_Opower(_831536))], (22404 ^ _779571) ^ [_1166645, _1166647] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1166645)), hAPP(c_Code__Numeral_Oof__nat, _1166647)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1166645), _1166647)))], (50722 ^ _779571) ^ [_1799391, _1799393] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799391)), hAPP(c_List_Orev(_1799391), _1799393)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799391)), _1799393))], (8842 ^ _779571) ^ [_925746, _925748, _925750] : [class_Rings_Oring(_925746), -(hAPP(c_Groups_Ouminus__class_Ouminus(_925746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925746), _925748), _925750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925746), _925748), hAPP(c_Groups_Ouminus__class_Ouminus(_925746), _925750)))], (40202 ^ _779571) ^ [_1541788, _1541790, _1541792, _1541794, _1541796, _1541798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541788, _1541790)), hAPP(hAPP(c_Product__Type_OPair(_1541788, _1541790), _1541792), _1541794)), hAPP(hAPP(c_Product__Type_OSigma(_1541788, _1541790), _1541796), _1541798))), 40205 ^ _779571 : [(40208 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541790), _1541794), hAPP(_1541798, _1541792))))], (40206 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541788), _1541792), _1541796)))]]], (44956 ^ _779571) ^ [_1663310, _1663312] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1663310, tc_HOL_Obool), tc_HOL_Obool)), _1663312), hAPP(c_Set_OPow(_1663310), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663310, tc_HOL_Obool), _1663312)))))], (18809 ^ _779571) ^ [_1102198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1102198)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102198), c_Int_OMin)))], (44111 ^ _779571) ^ [_1642287, _1642289, _1642291] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1642287), _1642289)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1642287, tc_HOL_Obool)), _1642291), _1642289) = hAPP(hAPP(c_Finite__Set_Ofold(_1642287, tc_fun(_1642287, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1642287, tc_HOL_Obool), tc_fun(tc_fun(_1642287, tc_HOL_Obool), tc_fun(_1642287, tc_HOL_Obool)), _1642287), hAPP(c_COMBC(tc_fun(_1642287, tc_HOL_Obool), tc_fun(_1642287, tc_HOL_Obool), tc_fun(_1642287, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1642287, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1642287, tc_fun(_1642287, tc_HOL_Obool), tc_fun(_1642287, tc_HOL_Obool)), c_Set_Oinsert(_1642287)), c_Orderings_Obot__class_Obot(tc_fun(_1642287, tc_HOL_Obool))))), _1642291), _1642289))], (36686 ^ _779571) ^ [_1461761, _1461763, _1461765] : [class_Lattices_Oboolean__algebra(_1461761), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1461761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461761), _1461763), _1461765)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461761), hAPP(c_Groups_Ouminus__class_Ouminus(_1461761), _1461763)), hAPP(c_Groups_Ouminus__class_Ouminus(_1461761), _1461765)))], (4678 ^ _779571) ^ [_851922, _851924, _851926, _851928, _851930, _851932] : [-(c_Big__Operators_Olattice_OSup__fin(_851932, _851928, _851924) = c_Big__Operators_Olattice_OSup__fin(_851930, _851926, _851922)), _851932 = _851930, _851928 = _851926, _851924 = _851922], (32721 ^ _779571) ^ [_1376508, _1376510] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376508), _1376510)), -(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)))), _1376510, _1376508) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33245 ^ _779571) ^ [_1385884, _1385886, _1385888] : [class_Orderings_Olinorder(_1385884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385884), _1385886)), hBOOL(hAPP(hAPP(c_member(_1385884), _1385888), _1385886)), 33256 ^ _779571 : [(33263 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385884, tc_HOL_Obool)), _1385886), hAPP(hAPP(c_Set_Oinsert(_1385884), _1385888), c_Orderings_Obot__class_Obot(tc_fun(_1385884, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1385884, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1385884, _1385886) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385884), _1385888), c_Big__Operators_Olinorder__class_OMin(_1385884, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385884, tc_HOL_Obool)), _1385886), hAPP(hAPP(c_Set_Oinsert(_1385884), _1385888), c_Orderings_Obot__class_Obot(tc_fun(_1385884, tc_HOL_Obool)))))))], (33257 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385884, tc_HOL_Obool)), _1385886), hAPP(hAPP(c_Set_Oinsert(_1385884), _1385888), c_Orderings_Obot__class_Obot(tc_fun(_1385884, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1385884, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1385884, _1385886) = _1385888)]]], (26444 ^ _779571) ^ [_1244042, _1244044] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244042), _1244044)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1244044), _1244042)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244044)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244042)))], (11298 ^ _779571) ^ [_967186, _967188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967186), _967188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967186), hAPP(c_Nat_OSuc, _967188))))], (36430 ^ _779571) ^ [_1456432, _1456434, _1456436, _1456438] : [class_Lattices_Osemilattice__inf(_1456432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456432), _1456434), _1456436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456432), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456432), _1456438), _1456434)), _1456436)))], (28565 ^ _779571) ^ [_1286785, _1286787] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1286785)), _1286787) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1286785, _1286787))], (8308 ^ _779571) ^ [_917514, _917516] : [class_Orderings_Opreorder(_917514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917514), _917516), _917516))], (40294 ^ _779571) ^ [_1543927, _1543929, _1543931, _1543933] : [_1543927 = c_Orderings_Obot__class_Obot(tc_fun(_1543929, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1543931, _1543929), _1543931, c_Product__Type_Ofst(_1543931, _1543929)), hAPP(hAPP(c_Product__Type_OSigma(_1543931, _1543929), _1543933), hAPP(c_COMBK(tc_fun(_1543929, tc_HOL_Obool), _1543931), _1543927))) = c_Orderings_Obot__class_Obot(tc_fun(_1543931, tc_HOL_Obool)))], (27249 ^ _779571) ^ [_1260202, _1260204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260202)), 27258 ^ _779571 : [(27261 ^ _779571) ^ [] : [hBOOL(hAPP(_1260204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27254 ^ [_1260202, _1260204]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27255 ^ [_1260202, _1260204]), _1260202))))], (27259 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1260204, 27254 ^ [_1260202, _1260204])))]], 27262 ^ _779571 : [(27265 ^ _779571) ^ [] : [hBOOL(hAPP(_1260204, 27254 ^ [_1260202, _1260204]))], (27263 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1260204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27254 ^ [_1260202, _1260204]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27255 ^ [_1260202, _1260204]), _1260202)))))]], 27266 ^ _779571 : [(27276 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1260204, 27283 ^ [_1260202, _1260204]))), 27277 ^ _779571 : [(27278 ^ _779571) ^ [_1260749] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1260749), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1260202))), hBOOL(hAPP(_1260204, _1260749))]]], (27267 ^ _779571) ^ [] : [27268 ^ _779571 : [(27269 ^ _779571) ^ [_1260634] : [hBOOL(hAPP(_1260204, _1260634))]], 27271 ^ _779571 : [(27274 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1260204, 27270 ^ [_1260202, _1260204])))], (27272 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27270 ^ [_1260202, _1260204]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1260202))))]]]]], (42272 ^ _779571) ^ [_1597732, _1597734, _1597736, _1597738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597732, _1597734), tc_HOL_Obool)), _1597736), _1597738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597732, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597732, _1597734), _1597736)), hAPP(c_Relation_ODomain(_1597732, _1597734), _1597738))))], (23046 ^ _779571) ^ [_1179074, _1179076] : [-(_1179074 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23049 ^ _779571 : [(23056 ^ _779571) ^ [] : [-(_1179076 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1179074, _1179076) = 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, _1179076))), 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)), _1179076)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179074))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179076), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179074), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1179074, _1179076)), 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), _1179076))))), c_Divides_Opdivmod(_1179074, _1179076)))))], (23050 ^ _779571) ^ [] : [_1179076 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1179074, _1179076) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179074))]]], (12398 ^ _779571) ^ [_986573] : [hBOOL(hAPP(_986573, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12399 ^ [_986573]))), 12402 ^ _779571 : [(12403 ^ _779571) ^ [_986673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986673)), -(hBOOL(hAPP(_986573, _986673)))]]], (10680 ^ _779571) ^ [_957318, _957320, _957322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957318), _957320)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957318), _957322))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957320), _957322)))], (21369 ^ _779571) ^ [_1147183, _1147185, _1147187, _1147189] : [class_Fields_Olinordered__field__inverse__zero(_1147183), 21372 ^ _779571 : [(21373 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147185), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147183), _1147187), _1147189))), 21376 ^ _779571 : [(21383 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), c_Groups_Ozero__class_Ozero(_1147183)), _1147189))), 21386 ^ _779571 : [(21393 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), _1147189), c_Groups_Ozero__class_Ozero(_1147183)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147185), c_Groups_Ozero__class_Ozero(_1147183))))], (21387 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), _1147189), c_Groups_Ozero__class_Ozero(_1147183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147183), _1147185), _1147189))))]]], (21377 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), c_Groups_Ozero__class_Ozero(_1147183)), _1147189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147183), _1147185), _1147189)), _1147187)))]]], (21399 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147185), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147183), _1147187), _1147189)))), 21402 ^ _779571 : [(21405 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147183), _1147185), _1147189)), _1147187))], (21403 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), c_Groups_Ozero__class_Ozero(_1147183)), _1147189)))]], 21406 ^ _779571 : [(21409 ^ _779571) ^ [] : [21410 ^ _779571 : [(21413 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147183), _1147185), _1147189)))], (21411 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), _1147189), c_Groups_Ozero__class_Ozero(_1147183))))]], 21414 ^ _779571 : [(21417 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147183), _1147185), c_Groups_Ozero__class_Ozero(_1147183)))], (21415 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), _1147189), c_Groups_Ozero__class_Ozero(_1147183)))]]], (21407 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147183), c_Groups_Ozero__class_Ozero(_1147183)), _1147189))]]]]], (34777 ^ _779571) ^ [_1417189] : [-(_1417189 = 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)), _1417189), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (8074 ^ _779571) ^ [_913422, _913424, _913426, _913428] : [-(c_Option_Ooption_Ooption__rec(_913422, _913424, _913426, _913428, c_Option_Ooption_ONone(_913424)) = _913426)], (12648 ^ _779571) ^ [_990897, _990899, _990901, _990903] : [class_Rings_Olinordered__semiring__strict(_990897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990897), _990899), _990901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990897), _990899), _990903))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990897), c_Groups_Ozero__class_Ozero(_990897)), _990899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990897), _990901), _990903)))], (34656 ^ _779571) ^ [_1414463, _1414465, _1414467, _1414469, _1414471, _1414473] : [hBOOL(hAPP(hAPP(c_member(_1414463), _1414465), _1414467)), -(c_Map_Orestrict__map(_1414463, _1414469, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414463, tc_Option_Ooption(_1414469)), _1414471), _1414465), _1414473), _1414467) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414463, tc_Option_Ooption(_1414469)), c_Map_Orestrict__map(_1414463, _1414469, _1414471, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414463, tc_HOL_Obool)), _1414467), hAPP(hAPP(c_Set_Oinsert(_1414463), _1414465), c_Orderings_Obot__class_Obot(tc_fun(_1414463, tc_HOL_Obool)))))), _1414465), _1414473))], (44906 ^ _779571) ^ [_1661809, _1661811, _1661813, _1661815, _1661817] : [44908 ^ _779571 : [(44911 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1661815, 44907 ^ [_1661809, _1661811, _1661813, _1661815, _1661817]), _1661817))], (44909 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661809), 44907 ^ [_1661809, _1661811, _1661813, _1661815, _1661817]), _1661813)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661809, tc_fun(_1661811, tc_HOL_Obool)), _1661813), _1661815), _1661817)))], (30327 ^ _779571) ^ [_1323463, _1323465, _1323467] : [-(hBOOL(hAPP(hAPP(c_member(_1323463), _1323465), _1323467))), -(hBOOL(hAPP(hAPP(c_member(_1323463), _1323465), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323463, tc_HOL_Obool)), _1323467))))], (1212 ^ _779571) ^ [_797489, _797491] : [-(class_Rings_Oidom(_797489)), _797491 = _797489, class_Rings_Oidom(_797491)], (1022 ^ _779571) ^ [_795114, _795116] : [-(class_Rings_Olinordered__ring__strict(_795114)), _795116 = _795114, class_Rings_Olinordered__ring__strict(_795116)], (7796 ^ _779571) ^ [_908839, _908841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908839), _908841)), _908839))], (30152 ^ _779571) ^ [_1320018, _1320020, _1320022, _1320024] : [30153 ^ _779571 : [(30156 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1320018), _1320020), _1320024))], (30154 ^ _779571) ^ [] : [_1320020 = _1320022]], -(hBOOL(hAPP(hAPP(c_member(_1320018), _1320020), hAPP(hAPP(c_Set_Oinsert(_1320018), _1320022), _1320024))))], (51211 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (29740 ^ _779571) ^ [_1311239] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1311239), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1311239)), c_Option_Ooption_ONone(_1311239)), hAPP(c_Set_Oimage(_1311239, tc_Option_Ooption(_1311239), c_Option_Ooption_OSome(_1311239)), c_Orderings_Otop__class_Otop(tc_fun(_1311239, tc_HOL_Obool)))))], (47087 ^ _779571) ^ [_1716447, _1716449] : [class_Groups_Ocomm__monoid__add(_1716447), hBOOL(hAPP(c_List_Odistinct(_1716447), _1716449)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716447), _1716449) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1716447, _1716447), c_COMBI(_1716447)), hAPP(c_List_Oset(_1716447), _1716449)))], (51225 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (28431 ^ _779571) ^ [_1284556, _1284558, _1284560] : [class_Orderings_Olinorder(_1284556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284556), _1284558), _1284560)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284556, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1284556, _1284558, _1284560)), hAPP(c_SetInterval_Oord__class_OatLeast(_1284556), _1284560)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1284556), _1284558))], (41816 ^ _779571) ^ [_1587631, _1587633] : [-(c_Wellfounded_Owf(_1587631, hAPP(c_Wellfounded_Omeasure(_1587631), _1587633)))], (37819 ^ _779571) ^ [_1488742, _1488744, _1488746, _1488748, _1488750] : [class_Groups_Ocomm__monoid__add(_1488742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488744), _1488746)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488744), _1488748)), 37833 ^ _779571 : [(37836 ^ _779571) ^ [] : [hAPP(_1488750, 37832 ^ [_1488742, _1488744, _1488746, _1488748, _1488750]) = c_Groups_Ozero__class_Ozero(_1488742)], (37834 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488744), 37832 ^ [_1488742, _1488744, _1488746, _1488748, _1488750]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488744, tc_HOL_Obool)), _1488746), _1488748))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488744, _1488742), _1488750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488744, tc_HOL_Obool)), _1488746), _1488748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1488742), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488744, _1488742), _1488750), _1488746)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488744, _1488742), _1488750), _1488748)))], (12524 ^ _779571) ^ [_988659, _988661] : [12525 ^ _779571 : [(12526 ^ _779571) ^ [_988712] : [_988661 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _988659), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988712))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988659), _988661)))], (29406 ^ _779571) ^ [_1305309, _1305311, _1305313] : [class_Orderings_Oorder(_1305309), 29409 ^ _779571 : [(29416 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305309), _1305311), _1305313))), -(c_Orderings_Obot__class_Obot(tc_fun(_1305309, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1305309, _1305311, _1305313))], (29410 ^ _779571) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1305309, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1305309, _1305311, _1305313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305309), _1305311), _1305313))]]], (2108 ^ _779571) ^ [_811023, _811025, _811027, _811029, _811031, _811033, _811035, _811037, _811039, _811041] : [-(c_Nitpick_Opair__box_Opair__box__rec(_811041, _811037, _811033, _811029, _811025) = c_Nitpick_Opair__box_Opair__box__rec(_811039, _811035, _811031, _811027, _811023)), _811041 = _811039, _811037 = _811035, _811033 = _811031, _811029 = _811027, _811025 = _811023], (17119 ^ _779571) ^ [_1073802, _1073804, _1073806, _1073808] : 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c_List_Olist_ONil(_1720491))], (51203 ^ _779571) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51351 ^ _779571) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (7969 ^ _779571) ^ [_911765, _911767, _911769] : [-(c_Option_Ooption_Ooption__size(_911765, _911767, hAPP(c_Option_Ooption_OSome(_911765), _911769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_911767, _911769)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19057 ^ _779571) ^ [_1106146, _1106148] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106146, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106148)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106146, 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)))), _1106148)))], (41858 ^ _779571) ^ [_1588564, _1588566, _1588568, _1588570] : [c_Wellfounded_Owf(_1588564, _1588566), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588564, _1588564)), hAPP(hAPP(c_Product__Type_OPair(_1588564, _1588564), _1588568), _1588570)), _1588566)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588564, _1588564)), hAPP(hAPP(c_Product__Type_OPair(_1588564, _1588564), _1588570), _1588568)), _1588566))], (11378 ^ _779571) ^ [_968437, _968439] : [11379 ^ _779571 : [(11382 ^ _779571) ^ [] : [_968437 = _968439], (11380 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968437), _968439))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968437), _968439)))], (22190 ^ _779571) ^ [_1162515] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1162515)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1162515)], (46047 ^ _779571) ^ [_1688450, _1688452, _1688454, _1688456, _1688458] : [-(c_Map_Odom(_1688450, _1688452, hAPP(hAPP(c_COMBS(_1688450, tc_Option_Ooption(_1688454), tc_Option_Ooption(_1688452)), hAPP(hAPP(c_COMBB(tc_fun(_1688454, _1688452), tc_fun(tc_Option_Ooption(_1688454), tc_Option_Ooption(_1688452)), _1688450), c_Option_Omap(_1688454, _1688452)), _1688456)), _1688458)) = c_Map_Odom(_1688450, _1688454, _1688458))], (11150 ^ _779571) ^ [_964691, _964693] : [11151 ^ _779571 : [(11154 ^ _779571) ^ [] : [_964693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11152 ^ _779571) ^ [] : [_964691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964691), _964693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13298 ^ _779571) ^ [_1002137, _1002139, _1002141] : [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), _1002137), _1002139)), _1002141)), 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)), _1002141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002139), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23525 ^ _779571) ^ [_1188130, _1188132, _1188134, _1188136] : [class_Orderings_Olinorder(_1188130), 23528 ^ _779571 : [(23529 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188130), _1188132), _1188134)), _1188136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), _1188132), _1188136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), _1188134), _1188136)))], (23539 ^ _779571) ^ [] : [23540 ^ _779571 : [(23543 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), _1188134), _1188136))], (23541 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), _1188132), _1188136))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188130), _1188132), _1188134)), _1188136)))]]], (2048 ^ _779571) ^ [_810011, _810013] : [_810013 = _810011, -(c_HOL_Obool_Obool__size(_810013) = c_HOL_Obool_Obool__size(_810011))], (50368 ^ _779571) ^ [_1791347, _1791349] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1791347), hAPP(c_List_Onth(_1791347), _1791349)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791347)), _1791349))) = _1791349)], (32819 ^ _779571) ^ [_1378433, _1378435] : [class_Lattices_Olattice(_1378433), -(c_Big__Operators_Olattice__class_OSup__fin(_1378433, hAPP(hAPP(c_Set_Oinsert(_1378433), _1378435), c_Orderings_Obot__class_Obot(tc_fun(_1378433, tc_HOL_Obool)))) = _1378435)], (51503 ^ _779571) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (44117 ^ _779571) ^ [_1642554, _1642556, _1642558, _1642560, _1642562] : [c_Finite__Set_Ofolding__one(_1642554, _1642556, _1642558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642554), _1642560)), -(hBOOL(hAPP(hAPP(c_member(_1642554), _1642562), _1642560))), -(hAPP(_1642558, hAPP(hAPP(c_Set_Oinsert(_1642554), _1642562), _1642560)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642554, _1642554, _1642556), _1642562), _1642560))], (32464 ^ _779571) ^ [_1371183, _1371185, _1371187, _1371189, _1371191] : [c_Finite__Set_Ofolding__one(_1371183, _1371185, _1371187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371183), _1371189)), -(hBOOL(hAPP(hAPP(c_member(_1371183), _1371191), _1371189))), -(_1371189 = c_Orderings_Obot__class_Obot(tc_fun(_1371183, tc_HOL_Obool))), -(hAPP(_1371187, hAPP(hAPP(c_Set_Oinsert(_1371183), _1371191), _1371189)) = hAPP(hAPP(_1371185, _1371191), hAPP(_1371187, _1371189)))], (33641 ^ _779571) ^ [_1393727, _1393729, _1393731, _1393733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1393727, _1393729)), c_Sum__Type_OPlus(_1393727, _1393729, _1393731, _1393733))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1393729), _1393733)))], (10379 ^ _779571) ^ [_952404, _952406] : [class_Rings_Olinordered__idom(_952404), -(c_Groups_Osgn__class_Osgn(_952404, c_Groups_Osgn__class_Osgn(_952404, _952406)) = c_Groups_Osgn__class_Osgn(_952404, _952406))], (41209 ^ _779571) ^ [_1564440, _1564442] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1564440, tc_HOL_Obool)), _1564442) = hAPP(c_Set_OCollect(_1564440), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564440), c_fNot), hAPP(hAPP(c_COMBC(_1564440, tc_fun(_1564440, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564440)), _1564442))))], (29015 ^ _779571) ^ [_1296935, _1296937, _1296939, _1296941, _1296943] : [-(hAPP(c_Set_Oimage(_1296935, _1296937, _1296939), hAPP(hAPP(c_Set_Oinsert(_1296935), _1296941), _1296943)) = hAPP(hAPP(c_Set_Oinsert(_1296937), hAPP(_1296939, _1296941)), hAPP(c_Set_Oimage(_1296935, _1296937, _1296939), _1296943)))], (12095 ^ _779571) ^ [_981286, _981288] : [class_Groups_Oordered__ab__group__add(_981286), 12098 ^ _779571 : [(12105 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981286), _981288), c_Groups_Ozero__class_Ozero(_981286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981286), c_Groups_Ozero__class_Ozero(_981286)), hAPP(c_Groups_Ouminus__class_Ouminus(_981286), _981288))))], (12099 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981286), c_Groups_Ozero__class_Ozero(_981286)), hAPP(c_Groups_Ouminus__class_Ouminus(_981286), _981288))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981286), _981288), c_Groups_Ozero__class_Ozero(_981286))))]]], (36324 ^ _779571) ^ [_1454287, _1454289] : [class_Lattices_Osemilattice__inf(_1454287), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454287), _1454289), _1454289) = _1454289)], (17971 ^ _779571) ^ [_1088846, _1088848] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088846)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088846)), _1088848) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088846)), _1088848)))], (50588 ^ _779571) ^ [_1796478, _1796480, _1796482, _1796484] : [hAPP(c_List_Orev(_1796478), _1796480) = hAPP(hAPP(c_List_Olist_OCons(_1796478), _1796482), _1796484), -(_1796480 = hAPP(hAPP(c_List_Oappend(_1796478), hAPP(c_List_Orev(_1796478), _1796484)), hAPP(hAPP(c_List_Olist_OCons(_1796478), _1796482), c_List_Olist_ONil(_1796478))))], (41704 ^ _779571) ^ [_1583438, _1583440, _1583442, _1583444, _1583446, _1583448, _1583450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583438, _1583440), tc_HOL_Obool)), _1583442), _1583444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583440, _1583446), tc_HOL_Obool)), _1583448), _1583450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583438, _1583446), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583438, _1583440, _1583446), _1583442), _1583448)), hAPP(hAPP(c_Relation_Orel__comp(_1583438, _1583440, _1583446), _1583444), _1583450))))], (29073 ^ _779571) ^ [_1298212, _1298214] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298212, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298212, tc_HOL_Obool)), _1298214)), _1298214) = c_Orderings_Otop__class_Otop(tc_fun(_1298212, tc_HOL_Obool)))], (19673 ^ _779571) ^ [_1117065, _1117067, _1117069] : [class_Rings_Olinordered__idom(_1117065), 19676 ^ _779571 : [(19685 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117065), hAPP(hAPP(c_Power_Opower__class_Opower(_1117065), _1117067), 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(_1117065), _1117069), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1117065)), _1117067 = c_Groups_Ozero__class_Ozero(_1117065), _1117069 = c_Groups_Ozero__class_Ozero(_1117065)], (19677 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117065), hAPP(hAPP(c_Power_Opower__class_Opower(_1117065), _1117067), 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(_1117065), _1117069), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1117065), 19680 ^ _779571 : [(19683 ^ _779571) ^ [] : [-(_1117069 = c_Groups_Ozero__class_Ozero(_1117065))], (19681 ^ _779571) ^ [] : [-(_1117067 = c_Groups_Ozero__class_Ozero(_1117065))]]]]], (3830 ^ _779571) ^ [_838662, _838664, _838666, _838668] : [-(c_New__DSequence_Oneg__single(_838668, _838664) = c_New__DSequence_Oneg__single(_838666, _838662)), _838668 = _838666, _838664 = _838662], (16881 ^ _779571) ^ [_1068992, _1068994, _1068996] : [class_Int_Onumber__ring(_1068992), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068992), hAPP(c_Int_Onumber__class_Onumber__of(_1068992), _1068994)), hAPP(c_Int_Onumber__class_Onumber__of(_1068992), _1068996)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068992), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068994), _1068996)))], (16030 ^ _779571) ^ [_1052918, _1052920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052918), _1052920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052918), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052920), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23125 ^ _779571) ^ [_1180799, _1180801, _1180803, _1180805, _1180807, _1180809, _1180811, _1180813] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180799, _1180801, _1180803), _1180805), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180807, _1180809, tc_prod(_1180799, _1180801)), _1180811), _1180813)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180807, _1180809, _1180803), hAPP(hAPP(c_COMBB(tc_fun(_1180809, tc_prod(_1180799, _1180801)), tc_fun(_1180809, _1180803), _1180807), hAPP(c_COMBB(tc_prod(_1180799, _1180801), _1180803, _1180809), hAPP(c_Product__Type_Oprod_Oprod__case(_1180799, _1180801, _1180803), _1180805))), _1180811)), _1180813))], (50645 ^ _779571) ^ [_1797808, _1797810] : [c_List_Oconcat(_1797808, _1797810) = c_List_Olist_ONil(_1797808), 50648 ^ _779571 : [(50649 ^ _779571) ^ [_1797899] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1797808)), _1797899), hAPP(c_List_Oset(tc_List_Olist(_1797808)), _1797810))), -(_1797899 = c_List_Olist_ONil(_1797808))]]], (49959 ^ _779571) ^ [_1784327, _1784329] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1784327, _1784329)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1784329), _1784327))], (38467 ^ _779571) ^ [_1502318] : [-(c_Equiv__Relations_Oequivp(_1502318, c_fequal))], (29962 ^ _779571) ^ [_1316372, _1316374] : [29963 ^ _779571 : [(29966 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1316374), _1316372))], (29964 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1316372), _1316374)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1316372, _1316374))], (1612 ^ _779571) ^ [_802489, _802491] : [-(class_Rings_Ozero__neq__one(_802489)), _802491 = _802489, class_Rings_Ozero__neq__one(_802491)], (36788 ^ _779571) ^ [_1464304, _1464306, _1464308] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464304, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464304, tc_HOL_Obool)), _1464306), _1464308)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464304, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464304, tc_HOL_Obool)), _1464306)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464304, tc_HOL_Obool)), _1464308)))], (27159 ^ _779571) ^ [_1258311, _1258313, _1258315, _1258317, _1258319] : [class_Groups_Oab__group__add(_1258311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1258313), _1258315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1258315), _1258317)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1258311), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258311), _1258319), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1258313), _1258317))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258311), _1258319), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1258313), _1258315))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258311), _1258319), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1258315), _1258317)))], (20815 ^ _779571) ^ [_1137453, _1137455, _1137457, _1137459] : [class_Fields_Olinordered__field(_1137453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137453), _1137455), _1137457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137453), c_Groups_Ozero__class_Ozero(_1137453)), _1137459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137453), c_Groups_Ozero__class_Ozero(_1137453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137453), _1137457), _1137455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137453), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137453), _1137459), _1137457)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137453), _1137459), _1137455))))], (43584 ^ _779571) ^ [_1629977, _1629979] : [-(hAPP(hAPP(c_Nat_Ocompow(_1629977, _1629977), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629979) = c_Fun_Oid(_1629977))], (11220 ^ _779571) ^ [_965817, _965819, _965821] : [class_Groups_Oordered__ab__group__add(_965817), 11223 ^ _779571 : [(11230 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965817), _965821), hAPP(c_Groups_Ouminus__class_Ouminus(_965817), _965819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965817), _965819), hAPP(c_Groups_Ouminus__class_Ouminus(_965817), _965821))))], (11224 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965817), _965819), hAPP(c_Groups_Ouminus__class_Ouminus(_965817), _965821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965817), _965821), hAPP(c_Groups_Ouminus__class_Ouminus(_965817), _965819))))]]], (37798 ^ _779571) ^ [_1488247, _1488249, _1488251, _1488253, _1488255] : [class_Groups_Ocomm__monoid__add(_1488247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488249), _1488251)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488249), _1488253)), 37812 ^ _779571 : [(37815 ^ _779571) ^ [] : [hAPP(_1488255, 37811 ^ [_1488247, _1488249, _1488251, _1488253, _1488255]) = c_Groups_Ozero__class_Ozero(_1488247)], (37813 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488249), 37811 ^ [_1488247, _1488249, _1488251, _1488253, _1488255]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488249, tc_HOL_Obool)), _1488251), _1488253))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488249, _1488247), _1488255), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488249, tc_HOL_Obool)), _1488251), _1488253)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1488247), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488249, _1488247), _1488255), _1488251)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488249, _1488247), _1488255), _1488253)))], (23315 ^ _779571) ^ [_1184321, _1184323, _1184325, _1184327] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184321, _1184323), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184325), _1184327))), -(_1184323 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1184321), _1184323) = _1184325)], (28957 ^ _779571) ^ [_1295712, _1295714, _1295716, _1295718, _1295720] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295712, tc_fun(_1295714, tc_HOL_Obool)), _1295716), hAPP(hAPP(c_COMBS(_1295712, tc_fun(_1295714, tc_HOL_Obool), tc_fun(_1295714, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295714, tc_HOL_Obool), tc_fun(tc_fun(_1295714, tc_HOL_Obool), tc_fun(_1295714, tc_HOL_Obool)), _1295712), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295714, tc_HOL_Obool))), _1295718)), _1295720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295714, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295712, tc_fun(_1295714, tc_HOL_Obool)), _1295716), _1295718)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295712, tc_fun(_1295714, tc_HOL_Obool)), _1295716), _1295720)))], (7764 ^ _779571) ^ [_908172, _908174, _908176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908172), _908174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908172), _908176)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908174), _908176))))], (8084 ^ _779571) ^ [_913593, _913595] : [_913595 = c_Option_Ooption_ONone(_913593), -(c_Option_Ois__none(_913593, _913595))], (926 ^ _779571) ^ [_793818, _793820, _793822, _793824, _793826, _793828, _793830, _793832] : [-(c_Fun_Oinj__on(_793830, _793826, _793822, _793818)), c_Fun_Oinj__on(_793832, _793828, _793824, _793820), _793832 = _793830, _793828 = _793826, _793824 = _793822, _793820 = _793818], (50730 ^ _779571) ^ [_1799540, _1799542] : [-(hAPP(c_List_Orev(_1799540), hAPP(c_List_Orev(_1799540), _1799542)) = _1799542)], (17293 ^ _779571) ^ [_1076861] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076861) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076861)))], (36098 ^ _779571) ^ [_1449139, _1449141, _1449143] : [36099 ^ _779571 : [(36102 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449139), _1449143))], (36100 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449139), _1449141))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1449139), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449139, tc_HOL_Obool)), _1449141), _1449143))))], (24783 ^ _779571) ^ [_1212515, _1212517, _1212519, _1212521, _1212523, _1212525, _1212527] : [_1212515 = _1212517, -(hAPP(c_Sum__Type_Osum_Osum__case(_1212519, _1212521, _1212523, _1212525, _1212527), _1212515) = hAPP(c_Sum__Type_Osum_Osum__case(_1212519, _1212521, _1212523, _1212525, _1212527), _1212517))], (43379 ^ _779571) ^ [_1624709, _1624711, _1624713] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624711, _1624709)), _1624713)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624709, _1624711)), hAPP(c_Relation_Oconverse(_1624711, _1624709), _1624713))))], (30566 ^ _779571) ^ [_1328416, _1328418, _1328420, _1328422] : [-(hBOOL(hAPP(hAPP(c_member(_1328416), _1328418), _1328420))), 30569 ^ _779571 : [(30576 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328416, tc_HOL_Obool)), _1328420), _1328422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328416, tc_HOL_Obool)), _1328420), hAPP(hAPP(c_Set_Oinsert(_1328416), _1328418), _1328422))))], (30570 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328416, tc_HOL_Obool)), _1328420), hAPP(hAPP(c_Set_Oinsert(_1328416), _1328418), _1328422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328416, tc_HOL_Obool)), _1328420), _1328422)))]]], (47033 ^ _779571) ^ [_1714848, _1714850, _1714852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1714848), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714850), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1714850)), _1714852)))), -(hBOOL(hAPP(hAPP(c_member(_1714850), hAPP(c_Random_Opick(_1714850, _1714852), _1714848)), hAPP(c_List_Oset(_1714850), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1714850), _1714850), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1714850)), _1714852)))))], (9766 ^ _779571) ^ [_942027, _942029, _942031, _942033] : [class_Rings_Olinordered__semiring__strict(_942027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942027), _942029), _942031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942027), c_Groups_Ozero__class_Ozero(_942027)), _942033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942027), _942029), _942033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942027), _942031), _942033))))], (51075 ^ _779571) ^ [_1808056, _1808058] : [class_Complete__Lattice_Ocomplete__lattice(_1808056), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1808058, _1808056)))], (42546 ^ _779571) ^ [_1604442, _1604444, _1604446] : [-(c_Hilbert__Choice_OEps(tc_prod(_1604442, _1604444), hAPP(c_Product__Type_Oprod_Oprod__case(_1604442, _1604444, tc_HOL_Obool), _1604446)) = c_Hilbert__Choice_OEps(tc_prod(_1604442, _1604444), hAPP(hAPP(c_COMBS(tc_prod(_1604442, _1604444), _1604444, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1604442, tc_fun(_1604444, tc_HOL_Obool), tc_prod(_1604442, _1604444)), _1604446), c_Product__Type_Ofst(_1604442, _1604444))), c_Product__Type_Osnd(_1604442, _1604444))))], (40991 ^ _779571) ^ [_1559786] : [-(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)), _1559786)))))], (9436 ^ _779571) ^ [_936215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _936215)), -(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, _936215))))], (31984 ^ _779571) ^ [_1361040, _1361042, _1361044] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1361040), _1361042)), hBOOL(hAPP(hAPP(c_member(_1361040), _1361044), _1361042)), -(hAPP(c_Finite__Set_Ocard(_1361040), _1361042) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1361040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361040, tc_HOL_Obool)), _1361042), hAPP(hAPP(c_Set_Oinsert(_1361040), _1361044), c_Orderings_Obot__class_Obot(tc_fun(_1361040, tc_HOL_Obool)))))))], (41614 ^ _779571) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (22918 ^ _779571) ^ [] : [-(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)))))], (13793 ^ _779571) ^ [_1011266, _1011268, _1011270] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011266), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011268, _1011270)), _1011270) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011266), _1011268), _1011270))], (34678 ^ _779571) ^ [_1415153, _1415155, _1415157, _1415159, _1415161, _1415163] : [class_Groups_Oordered__ab__group__add(_1415153), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415155), _1415157)), 34688 ^ _779571 : [(34691 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415153), c_Groups_Ozero__class_Ozero(_1415153)), hAPP(_1415159, 34687 ^ [_1415153, _1415155, _1415157, _1415159, _1415161, _1415163])))], (34689 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415155), 34687 ^ [_1415153, _1415155, _1415157, _1415159, _1415161, _1415163]), _1415157)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415155, _1415153), _1415159), _1415157) = _1415161, hBOOL(hAPP(hAPP(c_member(_1415155), _1415163), _1415157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415153), hAPP(_1415159, _1415163)), _1415161)))], (28549 ^ _779571) ^ [_1286515, _1286517] : [c_Nat__Transfer_Onat__set(_1286515), c_Nat__Transfer_Onat__set(_1286517), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1286515), _1286517) = 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), _1286515)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1286517))))], (28129 ^ _779571) ^ [_1278347, _1278349, _1278351, _1278353] : [28143 ^ _779571 : [(28146 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1278353, 28142 ^ [_1278347, _1278349, _1278351, _1278353])))], (28144 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278347), 28142 ^ [_1278347, _1278349, _1278351, _1278353]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278347, tc_HOL_Obool)), _1278349), _1278351))))]], 28130 ^ _779571 : [(28137 ^ _779571) ^ [_1278556] : [hBOOL(hAPP(hAPP(c_member(_1278347), _1278556), _1278351)), hBOOL(hAPP(_1278353, _1278556))], (28131 ^ _779571) ^ [_1278460] : [hBOOL(hAPP(hAPP(c_member(_1278347), _1278460), _1278349)), hBOOL(hAPP(_1278353, _1278460))]]], (8720 ^ _779571) ^ [_923568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _923568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _923568)))], (13490 ^ _779571) ^ [_1005501, _1005503, _1005505, _1005507] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005501), _1005503)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005505), _1005503)), _1005507)) = 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), _1005501), _1005505)), _1005503)), _1005507))], (46526 ^ _779571) ^ [_1699923, _1699925] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1699923), hAPP(c_List_Oset(_1699923), _1699925))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699923)), _1699925))))], (750 ^ _779571) ^ [_791132, _791134, _791136, _791138, _791140, _791142] : [-(c_Relation_Osingle__valued(_791140, _791136, _791132)), c_Relation_Osingle__valued(_791142, _791138, _791134), _791142 = _791140, _791138 = _791136, _791134 = _791132], (40122 ^ _779571) ^ [_1539234, _1539236, _1539238, _1539240] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1539234, _1539236)), hAPP(hAPP(c_Product__Type_OSigma(_1539234, _1539236), _1539238), hAPP(c_COMBK(tc_fun(_1539236, tc_HOL_Obool), _1539234), _1539240))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1539234), _1539238)), hAPP(c_Finite__Set_Ocard(_1539236), _1539240)))], (33849 ^ _779571) ^ [_1397709, _1397711, _1397713] : [class_Orderings_Olinorder(_1397709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397709), _1397711)), hBOOL(hAPP(hAPP(c_member(_1397709), _1397713), _1397711)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1397709), _1397713), c_Big__Operators_Olattice_OSup__fin(_1397709, c_Orderings_Oord__class_Omax(_1397709), _1397711)) = _1397713)], (17925 ^ _779571) ^ [_1088155] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088155))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088155)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30014 ^ _779571) ^ [_1317360, _1317362, _1317364, _1317366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317360, tc_HOL_Obool)), _1317362), _1317364)), hBOOL(hAPP(hAPP(c_member(_1317360), _1317366), _1317362)), -(hBOOL(hAPP(hAPP(c_member(_1317360), _1317366), _1317364)))], (44442 ^ _779571) ^ [_1648810, _1648812, _1648814, _1648816, _1648818] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648810, tc_HOL_Obool)), _1648812), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648814, tc_fun(_1648810, tc_HOL_Obool)), _1648816), _1648818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648814, tc_fun(_1648810, tc_HOL_Obool)), _1648816), hAPP(hAPP(c_COMBB(tc_fun(_1648810, tc_HOL_Obool), tc_fun(_1648810, tc_HOL_Obool), _1648814), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648810, tc_HOL_Obool)), _1648812)), _1648818)))], (42770 ^ _779571) ^ [_1609483, _1609485, _1609487] : [class_Orderings_Olinorder(_1609483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609483), _1609485)), 42780 ^ _779571 : [(42783 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609483), 42779 ^ [_1609483, _1609485, _1609487]), _1609487))], (42781 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609483), 42779 ^ [_1609483, _1609485, _1609487]), _1609485)))]], hBOOL(hAPP(hAPP(c_member(_1609483), _1609487), _1609485)), -(c_Big__Operators_Olinorder__class_OMax(_1609483, _1609485) = _1609487)], (24335 ^ _779571) ^ [_1203879] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203879) = _1203879)], (24871 ^ _779571) ^ [_1214510, _1214512, _1214514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1214510), c_Nitpick_Oplus__frac(_1214510, _1214512, c_Nitpick_Ouminus__frac(_1214510, _1214514)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1214510, _1214512, _1214514))], (45660 ^ _779571) ^ [_1679209, _1679211, _1679213, _1679215, _1679217] : [-(hAPP(c_Map_Omap__add(_1679209, _1679211, _1679213, _1679215), _1679217) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1679211), _1679211, hAPP(_1679213, _1679217), c_Option_Ooption_OSome(_1679211)), hAPP(_1679215, _1679217)))], (47404 ^ _779571) ^ [_1722644, _1722646, _1722648, _1722650, _1722652] : [-(_1722644 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1722646, _1722648, _1722650, _1722644), _1722652) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1722648), _1722646), tc_prod(_1722648, _1722646), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722648), _1722646), c_List_Olist_ONil(_1722648)), _1722652), hAPP(c_Product__Type_Oprod_Oprod__case(_1722648, _1722646, tc_prod(tc_List_Olist(_1722648), _1722646)), hAPP(hAPP(c_COMBC(_1722648, tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646)), tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1722648), _1722646), tc_prod(tc_List_Olist(_1722648), _1722646)), tc_fun(tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646)), tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646))), _1722648), c_COMBB(tc_prod(tc_List_Olist(_1722648), _1722646), tc_prod(tc_List_Olist(_1722648), _1722646), _1722646)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1722648), tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646))), tc_fun(tc_prod(tc_List_Olist(_1722648), _1722646), tc_prod(tc_List_Olist(_1722648), _1722646)), _1722648), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1722648), _1722646, tc_prod(tc_List_Olist(_1722648), _1722646))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1722648), tc_List_Olist(_1722648)), tc_fun(tc_List_Olist(_1722648), tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646))), _1722648), hAPP(c_COMBB(tc_List_Olist(_1722648), tc_fun(_1722646, tc_prod(tc_List_Olist(_1722648), _1722646)), tc_List_Olist(_1722648)), c_Product__Type_OPair(tc_List_Olist(_1722648), _1722646))), c_List_Olist_OCons(_1722648))))), c_Lazy__Sequence_Oanamorph(_1722646, _1722648, _1722650, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1722644), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1722650, _1722652)))], (43965 ^ _779571) ^ [_1639478, _1639480, _1639482, _1639484, _1639486] : [class_Complete__Lattice_Ocomplete__lattice(_1639478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639480), _1639482)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1639478), _1639484), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1639480, _1639478), _1639482), _1639486)) = hAPP(hAPP(c_Finite__Set_Ofold(_1639480, _1639478, hAPP(hAPP(c_COMBB(_1639478, tc_fun(_1639478, _1639478), _1639480), c_Lattices_Osemilattice__sup__class_Osup(_1639478)), _1639486)), _1639484), _1639482))], (49032 ^ _779571) ^ [_1763256, _1763258, _1763260, _1763262] : [-(hAPP(c_List_Orotate(_1763256, _1763258), hAPP(c_List_Orotate(_1763256, _1763260), _1763262)) = hAPP(c_List_Orotate(_1763256, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1763258), _1763260)), _1763262))], (7696 ^ _779571) ^ [_907066, _907068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907066), _907068)), -(hAPP(c_Nat_OSuc, _907066) = _907068), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _907066)), _907068)))], (23269 ^ _779571) ^ [_1183718, _1183720, _1183722, _1183724, _1183726, _1183728] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183718, _1183720), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183722), _1183724))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183718, _1183720), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183726), _1183728))), -(_1183720 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1183724 = _1183728)], (6825 ^ _779571) ^ [_892041, _892043, _892045] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_892041, _892043, _892045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_892043)), c_Com_Ocom_Ocom__size(_892045))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31241 ^ _779571) ^ [_1342347, _1342349, _1342351, _1342353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1342347, _1342349)), hAPP(hAPP(c_Product__Type_OPair(_1342347, _1342349), _1342351), _1342353)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1342347, _1342349), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1342347, tc_fun(_1342349, tc_HOL_Obool))), _1342351), _1342353)))], (51333 ^ _779571) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (49925 ^ _779571) ^ [_1783690] : [class_Orderings_Olinorder(_1783690), -(c_List_Olinorder__class_Osorted(_1783690, c_List_Olist_ONil(_1783690)))], (32347 ^ _779571) ^ [_1368281, _1368283] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1368281), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368283))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368281), _1368283)))], (10303 ^ _779571) ^ [_951236] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951236), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _951236)], (34483 ^ _779571) ^ [_1410492, _1410494, _1410496, _1410498, _1410500] : [class_Groups_Ocomm__monoid__mult(_1410492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410494), _1410496)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410494, _1410492), _1410498), hAPP(hAPP(c_Set_Oinsert(_1410494), _1410500), _1410496)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410492), hAPP(_1410498, _1410500)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410494, _1410492), _1410498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410494, tc_HOL_Obool)), _1410496), hAPP(hAPP(c_Set_Oinsert(_1410494), _1410500), c_Orderings_Obot__class_Obot(tc_fun(_1410494, tc_HOL_Obool)))))))], (10986 ^ _779571) ^ [_961986, _961988, _961990] : [class_Orderings_Oorder(_961986), 10989 ^ _779571 : [(10998 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961986), _961988), _961990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961986), _961988), _961990)), -(_961988 = _961990)], (10990 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961986), _961988), _961990)), 10993 ^ _779571 : [(10996 ^ _779571) ^ [] : [_961988 = _961990], (10994 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961986), _961988), _961990)))]]]]], (22312 ^ _779571) ^ [_1164571, _1164573, _1164575] : [class_Int_Onumber__ring(_1164571), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164571), _1164573), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1164575))) = hAPP(hAPP(c_HOL_OLet(_1164571, _1164571), hAPP(hAPP(c_Power_Opower__class_Opower(_1164571), _1164573), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1164575))), hAPP(hAPP(c_COMBS(_1164571, _1164571, _1164571), c_Groups_Otimes__class_Otimes(_1164571)), c_COMBI(_1164571))))], (24851 ^ _779571) ^ [_1214024, _1214026, _1214028, _1214030, _1214032, _1214034, _1214036] : [-(c_New__Random__Sequence_Opos__decr__bind(_1214024, _1214026, _1214028, _1214030, _1214032, _1214034, _1214036) = c_New__DSequence_Opos__decr__bind(_1214024, _1214026, hAPP(hAPP(hAPP(_1214028, _1214032), _1214034), _1214036), hAPP(hAPP(c_COMBC(_1214024, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1214026))), hAPP(hAPP(c_COMBC(_1214024, 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(_1214026)))), hAPP(hAPP(c_COMBC(_1214024, 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(_1214026))))), _1214030), _1214032)), _1214034)), _1214036)))], (14868 ^ _779571) ^ [_1030326, _1030328] : [-(_1030326 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030328), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030326), _1030328))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030326, _1030328)))], (51265 ^ _779571) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (29780 ^ _779571) ^ [_1312033] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1312033)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1312033)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1312033), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (26830 ^ _779571) ^ [_1251792, _1251794, _1251796] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251792, tc_Nat_Onat), _1251794), _1251796)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251792, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1251792), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1251794)), _1251796))], (51371 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (8677 ^ _779571) ^ [_922785, _922787, _922789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922785), _922787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _922789)), -(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), _922789)), _922785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922789)), _922787))))], (46370 ^ _779571) ^ [_1695573, _1695575, _1695577, _1695579] : [hBOOL(hAPP(c_List_Odistinct(_1695573), _1695575)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1695573, _1695577)), hAPP(hAPP(c_List_Ozip(_1695573, _1695577), _1695575), _1695579))))], (17339 ^ _779571) ^ [_1077655, _1077657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077655)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1077655)), _1077657) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077655), _1077657)))], (18393 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (14712 ^ _779571) ^ [_1027607, _1027609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027607)), 14715 ^ _779571 : [(14724 ^ _779571) ^ [] : [-(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), _1027607), _1027609)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027609), _1027607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027609))], (14716 ^ _779571) ^ [] : [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), _1027607), _1027609))), 14719 ^ _779571 : [(14722 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027609)))], (14720 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027609), _1027607)))]]]]], (49138 ^ _779571) ^ [_1765567, _1765569, _1765571] : [class_Groups_Omonoid__add(_1765567), -(hAPP(c_List_Ofoldl(_1765567, _1765567, c_Groups_Oplus__class_Oplus(_1765567), _1765569), _1765571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1765567), _1765569), c_List_Ofoldr(_1765567, _1765567, c_Groups_Oplus__class_Oplus(_1765567), _1765571, c_Groups_Ozero__class_Ozero(_1765567))))], (26438 ^ _779571) ^ [_1243949] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1243949) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243949), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8754 ^ _779571) ^ [_924202, _924204, _924206] : [class_Rings_Ocomm__semiring__1(_924202), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924202), _924204), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924202), _924206), _924204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924202), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924202), _924206), c_Groups_Oone__class_Oone(_924202))), _924204))], (25354 ^ _779571) ^ [_1223844, _1223846] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223844), _1223846)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223846), _1223844)), -(_1223844 = _1223846)], (22290 ^ _779571) ^ [_1164159, _1164161] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164159), _1164161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164159)), _1164161)))], (31766 ^ _779571) ^ [_1356048, _1356050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1356048), _1356050)))), -(_1356050 = c_Orderings_Obot__class_Obot(tc_fun(_1356048, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356048), _1356050))], (32444 ^ _779571) ^ [_1370824, _1370826, _1370828, _1370830] : [c_Finite__Set_Ofolding__one(_1370824, _1370826, _1370828), -(hAPP(_1370828, hAPP(hAPP(c_Set_Oinsert(_1370824), _1370830), c_Orderings_Obot__class_Obot(tc_fun(_1370824, tc_HOL_Obool)))) = _1370830)], (13661 ^ _779571) ^ [_1008516, _1008518] : [class_Divides_Osemiring__div(_1008516), -(c_Divides_Odiv__class_Omod(_1008516, _1008518, _1008518) = c_Groups_Ozero__class_Ozero(_1008516))], (11252 ^ _779571) ^ [_966383, _966385, _966387] : [class_Groups_Oordered__ab__group__add(_966383), 11255 ^ _779571 : [(11262 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966383), _966387), _966385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966383), hAPP(c_Groups_Ouminus__class_Ouminus(_966383), _966385)), hAPP(c_Groups_Ouminus__class_Ouminus(_966383), _966387))))], (11256 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966383), hAPP(c_Groups_Ouminus__class_Ouminus(_966383), _966385)), hAPP(c_Groups_Ouminus__class_Ouminus(_966383), _966387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966383), _966387), _966385)))]]], (41824 ^ _779571) ^ [_1587769, _1587771] : [c_Wellfounded_Owf(_1587769, hAPP(hAPP(c_Relation_Orel__comp(_1587769, _1587769, _1587769), _1587771), _1587771)), -(c_Wellfounded_Owf(_1587769, _1587771))], (13060 ^ _779571) ^ [_998233, _998235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998233), _998235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _998235), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51025 ^ _779571) ^ [_1806985, _1806987, _1806989, _1806991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1806985), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806987)), c_List_OtakeWhile(_1806987, _1806989, _1806991)))), -(hAPP(hAPP(c_List_Onth(_1806987), c_List_OtakeWhile(_1806987, _1806989, _1806991)), _1806985) = hAPP(hAPP(c_List_Onth(_1806987), _1806991), _1806985))], (43955 ^ _779571) ^ [_1639255, _1639257, _1639259, _1639261, _1639263, _1639265] : [c_Finite__Set_Ofun__left__comm__idem(_1639255, _1639257, _1639259), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639255), _1639261)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1639255, _1639257, _1639259), _1639263), hAPP(hAPP(c_Set_Oinsert(_1639255), _1639265), _1639261)) = hAPP(hAPP(_1639259, _1639265), hAPP(hAPP(c_Finite__Set_Ofold(_1639255, _1639257, _1639259), _1639263), _1639261)))], (51059 ^ _779571) ^ [_1807812] : [c_List_Onat__list(_1807812), -(c_List_Oembed__list(c_List_Oreturn__list(_1807812)) = _1807812)], (39142 ^ _779571) ^ [_1516103, _1516105, _1516107, _1516109, _1516111] : [class_Groups_Ocomm__monoid__mult(_1516103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516105), _1516107)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516105), _1516109)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516105, tc_HOL_Obool)), _1516107), _1516109) = c_Orderings_Obot__class_Obot(tc_fun(_1516105, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516103, _1516105, c_Groups_Otimes__class_Otimes(_1516103)), _1516111), c_Groups_Oone__class_Oone(_1516103)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1516105, tc_HOL_Obool)), _1516107), _1516109)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1516103), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516103, _1516105, c_Groups_Otimes__class_Otimes(_1516103)), _1516111), c_Groups_Oone__class_Oone(_1516103)), _1516107)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516103, _1516105, c_Groups_Otimes__class_Otimes(_1516103)), _1516111), c_Groups_Oone__class_Oone(_1516103)), _1516109)))], (48918 ^ _779571) ^ [_1761246, _1761248, _1761250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761246), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761248)), _1761250))), -(_1761250 = hAPP(hAPP(c_List_Oappend(_1761248), hAPP(hAPP(c_List_Otake(_1761248), _1761246), _1761250)), hAPP(hAPP(c_List_Olist_OCons(_1761248), hAPP(hAPP(c_List_Onth(_1761248), _1761250), _1761246)), hAPP(hAPP(c_List_Odrop(_1761248), hAPP(c_Nat_OSuc, _1761246)), _1761250))))], (2944 ^ _779571) ^ [_824529, _824531, _824533, _824535, _824537, _824539, _824541, _824543] : [-(c_New__DSequence_Oneg__decr__bind(_824543, _824539, _824535, _824531) = c_New__DSequence_Oneg__decr__bind(_824541, _824537, _824533, _824529)), _824543 = _824541, _824539 = _824537, _824535 = _824533, _824531 = _824529], (39352 ^ _779571) ^ [_1520721, _1520723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520721), _1520723)), -(hAPP(c_Finite__Set_Ocard(_1520721), _1520723) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1520721, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1520721), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1520723))], (51499 ^ _779571) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (46789 ^ _779571) ^ [_1708179, _1708181, _1708183] : [-(hAPP(c_List_Olexn(_1708179, _1708181), hAPP(c_Nat_OSuc, _1708183)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1708179), tc_List_Olist(_1708179)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1708179, tc_List_Olist(_1708179)), tc_prod(_1708179, tc_List_Olist(_1708179))), tc_prod(tc_List_Olist(_1708179), tc_List_Olist(_1708179)), c_Product__Type_Omap__pair(tc_prod(_1708179, tc_List_Olist(_1708179)), tc_List_Olist(_1708179), tc_prod(_1708179, tc_List_Olist(_1708179)), tc_List_Olist(_1708179), hAPP(c_Product__Type_Oprod_Oprod__case(_1708179, tc_List_Olist(_1708179), tc_List_Olist(_1708179)), c_List_Olist_OCons(_1708179)), hAPP(c_Product__Type_Oprod_Oprod__case(_1708179, tc_List_Olist(_1708179), tc_List_Olist(_1708179)), c_List_Olist_OCons(_1708179)))), c_Wellfounded_Olex__prod(_1708179, tc_List_Olist(_1708179), _1708181, hAPP(c_List_Olexn(_1708179, _1708181), _1708183)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1708179), tc_List_Olist(_1708179))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1708179), tc_List_Olist(_1708179), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708179), tc_fun(tc_List_Olist(_1708179), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708179), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1708179), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708179), tc_HOL_Obool)), tc_List_Olist(_1708179)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1708179))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708179)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708179), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1708179)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1708179)))), hAPP(c_Nat_OSuc, _1708183))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708179), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1708179)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1708179)))), hAPP(c_Nat_OSuc, _1708183)))))))], (44866 ^ _779571) ^ [_1660976, _1660978, _1660980, _1660982] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1660976, tc_HOL_Obool)), _1660978), _1660980)), hBOOL(hAPP(hAPP(c_member(_1660976), _1660982), _1660978)), -(hBOOL(hAPP(hAPP(c_member(_1660976), _1660982), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1660976, tc_HOL_Obool), _1660980))))], (30929 ^ _779571) ^ [_1336350, _1336352, _1336354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336350, tc_HOL_Obool)), _1336352), hAPP(hAPP(c_Set_Oinsert(_1336350), _1336354), c_Orderings_Obot__class_Obot(tc_fun(_1336350, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1336350, _1336354, _1336352) = _1336354)], (43665 ^ _779571) ^ [_1632109, _1632111, _1632113, _1632115, _1632117] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632109, _1632109)), hAPP(hAPP(c_Product__Type_OPair(_1632109, _1632109), _1632111), _1632113)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632109, _1632109), tc_HOL_Obool), _1632115), _1632117))), 43670 ^ _779571 : [(43673 ^ _779571) ^ [] : [-(_1632111 = _1632113)], (43671 ^ _779571) ^ [] : [-(_1632115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43676 ^ _779571 : [(43681 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632109, _1632109)), hAPP(hAPP(c_Product__Type_OPair(_1632109, _1632109), 43674 ^ [_1632109, _1632111, _1632113, _1632115, _1632117]), _1632113)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632109, _1632109), tc_HOL_Obool), 43675 ^ [_1632109, _1632111, _1632113, _1632115, _1632117]), _1632117))))], (43679 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632109, _1632109)), hAPP(hAPP(c_Product__Type_OPair(_1632109, _1632109), _1632111), 43674 ^ [_1632109, _1632111, _1632113, _1632115, _1632117])), _1632117)))], (43677 ^ _779571) ^ [] : [-(_1632115 = hAPP(c_Nat_OSuc, 43675 ^ [_1632109, _1632111, _1632113, _1632115, _1632117]))]]], (43801 ^ _779571) ^ [_1635292, _1635294, _1635296, _1635298, _1635300] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635292, _1635292)), hAPP(hAPP(c_Product__Type_OPair(_1635292, _1635292), _1635294), _1635296)), c_Transitive__Closure_Ortrancl(_1635292, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1635292, _1635292), tc_HOL_Obool)), _1635298), _1635300)))), 43807 ^ _779571 : [(43813 ^ _779571) ^ [] : [43806 ^ [_1635292, _1635294, _1635296, _1635298, _1635300] = 43809 ^ [_1635292, _1635294, _1635296, _1635298, _1635300]], (43811 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635292, _1635292)), hAPP(hAPP(c_Product__Type_OPair(_1635292, _1635292), 43806 ^ [_1635292, _1635294, _1635296, _1635298, _1635300]), 43809 ^ [_1635292, _1635294, _1635296, _1635298, _1635300])), _1635300)))], (43808 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635292, _1635292)), hAPP(hAPP(c_Product__Type_OPair(_1635292, _1635292), _1635294), 43806 ^ [_1635292, _1635294, _1635296, _1635298, _1635300])), c_Transitive__Closure_Ortrancl(_1635292, _1635298))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635292, _1635292)), hAPP(hAPP(c_Product__Type_OPair(_1635292, _1635292), _1635294), _1635296)), c_Transitive__Closure_Ortrancl(_1635292, _1635298))))], (36504 ^ _779571) ^ [_1457782, _1457784, _1457786] : [class_Lattices_Osemilattice__inf(_1457782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457782), _1457784), _1457786)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1457782), _1457786), _1457784) = _1457784)], (3526 ^ _779571) ^ [_833774, _833776, _833778, _833780] : [-(c_Sum__Type_OInr(_833780, _833776) = c_Sum__Type_OInr(_833778, _833774)), _833780 = _833778, _833776 = _833774], (15790 ^ _779571) ^ [_1047770, _1047772, _1047774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047770), _1047772)), 15793 ^ _779571 : [(15800 ^ _779571) ^ [] : [_1047772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047774), _1047770), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047772), _1047770) = _1047774)], (15794 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047772), _1047770) = _1047774, -(_1047772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047774), _1047770))]]], (40948 ^ _779571) ^ [_1558795, _1558797, _1558799, _1558801, _1558803, _1558805, _1558807, _1558809] : [c_Finite__Set_Ofolding__image__simple(_1558795, _1558797, _1558799, _1558801, _1558803, _1558805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558797), _1558807)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558797), _1558809)), 40962 ^ _779571 : [(40965 ^ _779571) ^ [] : [hAPP(_1558803, 40961 ^ [_1558795, _1558797, _1558799, _1558801, _1558803, _1558805, _1558807, _1558809]) = _1558801], (40963 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558797), 40961 ^ [_1558795, _1558797, _1558799, _1558801, _1558803, _1558805, _1558807, _1558809]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1558797, tc_HOL_Obool)), _1558807), _1558809))))]], -(hAPP(_1558805, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1558797, tc_HOL_Obool)), _1558807), _1558809)) = hAPP(hAPP(_1558799, hAPP(_1558805, _1558807)), hAPP(_1558805, _1558809)))], (11386 ^ _779571) ^ [_968574, _968576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968574), _968576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968574), _968576)))], (34559 ^ _779571) ^ [_1412301, _1412303, _1412305, _1412307, _1412309, _1412311, _1412313] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412301, tc_Option_Ooption(_1412303)), _1412305), _1412307), hAPP(c_Option_Ooption_OSome(_1412303), _1412309)), _1412311) = hAPP(c_Option_Ooption_OSome(_1412303), _1412313)), 34560 ^ _779571 : [(34567 ^ _779571) ^ [] : [-(_1412311 = _1412307), hAPP(_1412305, _1412311) = hAPP(c_Option_Ooption_OSome(_1412303), _1412313)], (34561 ^ _779571) ^ [] : [_1412311 = _1412307, _1412309 = _1412313]]], (51559 ^ _779571) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (45674 ^ _779571) ^ [_1679552, _1679554, _1679556, _1679558, _1679560] : [hAPP(c_Map_Omap__add(_1679552, _1679554, _1679556, _1679558), _1679560) = c_Option_Ooption_ONone(_1679554), 45677 ^ _779571 : [(45680 ^ _779571) ^ [] : [-(hAPP(_1679556, _1679560) = c_Option_Ooption_ONone(_1679554))], (45678 ^ _779571) ^ [] : [-(hAPP(_1679558, _1679560) = c_Option_Ooption_ONone(_1679554))]]], (45787 ^ _779571) ^ [_1681928, _1681930, _1681932] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1681928), c_Map_Odom(_1681928, _1681930, c_Map_Omap__of(_1681928, _1681930, _1681932)))))], (18711 ^ _779571) ^ [_1100616, _1100618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100616), _1100618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100616)), c_Int_OBit1(_1100618))))], (1352 ^ _779571) ^ [_799239, _799241] : [-(class_Finite__Set_Ofinite(_799239)), _799241 = _799239, class_Finite__Set_Ofinite(_799241)], (29674 ^ _779571) ^ [_1309825, _1309827] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309825), _1309827))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309825, _1309827))], (29692 ^ _779571) ^ [_1310169, _1310171, _1310173, _1310175, _1310177] : [_1310169 = c_Orderings_Obot__class_Obot(tc_fun(_1310171, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310173, tc_HOL_Obool)), _1310175), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310171, tc_fun(_1310173, tc_HOL_Obool)), _1310169), _1310177)) = _1310175)], (23213 ^ _779571) ^ [_1182732, _1182734, _1182736, _1182738] : [-(hAPP(c_Product__Type_Osnd(_1182732, _1182734), hAPP(hAPP(c_Product__Type_OPair(_1182732, _1182734), _1182736), _1182738)) = _1182738)], (43387 ^ _779571) ^ [_1624905, _1624907, _1624909, _1624911, _1624913] : [-(hAPP(c_Relation_Oconverse(_1624905, _1624907), hAPP(hAPP(c_Relation_Orel__comp(_1624905, _1624909, _1624907), _1624911), _1624913)) = hAPP(hAPP(c_Relation_Orel__comp(_1624907, _1624909, _1624905), hAPP(c_Relation_Oconverse(_1624909, _1624907), _1624913)), hAPP(c_Relation_Oconverse(_1624905, _1624909), _1624911)))], (48379 ^ _779571) ^ [_1746654, _1746656, _1746658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746654)), _1746656)), _1746658)), -(hAPP(hAPP(c_List_Otake(_1746654), _1746658), _1746656) = _1746656)], (43605 ^ _779571) ^ [_1630497, _1630499, _1630501] : [c_Relation_Ototal__on(_1630497, _1630499, _1630501), 43608 ^ _779571 : [(43609 ^ _779571) ^ [_1630641] : [hBOOL(hAPP(hAPP(c_member(_1630497), _1630641), _1630499)), 43612 ^ _779571 : [(43613 ^ _779571) ^ [_1630781] : [hBOOL(hAPP(hAPP(c_member(_1630497), _1630781), _1630499)), -(_1630641 = _1630781), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630497, _1630497)), hAPP(hAPP(c_Product__Type_OPair(_1630497, _1630497), _1630641), _1630781)), _1630501))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630497, _1630497)), hAPP(hAPP(c_Product__Type_OPair(_1630497, _1630497), _1630781), _1630641)), _1630501)))]]]]], (38261 ^ _779571) ^ [_1498397, _1498399] : [class_Groups_Oordered__ab__group__add(_1498397), -(c_Fun_Oinj__on(_1498397, _1498397, c_Groups_Ouminus__class_Ouminus(_1498397), _1498399))], (48940 ^ _779571) ^ [_1761832, _1761834, _1761836, _1761838] : [-(_1761832 = c_List_Olist_ONil(_1761834)), -(hAPP(c_List_Ohd(_1761836), hAPP(hAPP(c_List_Omap(_1761834, _1761836), _1761838), _1761832)) = hAPP(_1761838, hAPP(c_List_Ohd(_1761834), _1761832)))], (6219 ^ _779571) ^ [_880385, _880387, _880389] : [hBOOL(hAPP(c_Com_OWT, _880389)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880385, _880387, _880389))))], (50152 ^ _779571) ^ [_1787759, _1787761, _1787763] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1787759), c_List_Oupt(_1787761, _1787763)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787761), _1787759), _1787763))], (48393 ^ _779571) ^ [_1746967, _1746969, _1746971, _1746973, _1746975, _1746977, _1746979] : [-(c_Map_Omap__upds(_1746967, _1746969, _1746971, hAPP(hAPP(c_List_Olist_OCons(_1746967), _1746973), _1746975), hAPP(hAPP(c_List_Olist_OCons(_1746969), _1746977), _1746979)) = c_Map_Omap__upds(_1746967, _1746969, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1746967, tc_Option_Ooption(_1746969)), _1746971), _1746973), hAPP(c_Option_Ooption_OSome(_1746969), _1746977)), _1746975, _1746979))], (31994 ^ _779571) ^ [_1361269, _1361271, _1361273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1361269), _1361271)), hBOOL(hAPP(hAPP(c_member(_1361269), _1361273), _1361271)), -(hAPP(c_Finite__Set_Ocard(_1361269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361269, tc_HOL_Obool)), _1361271), hAPP(hAPP(c_Set_Oinsert(_1361269), _1361273), c_Orderings_Obot__class_Obot(tc_fun(_1361269, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1361269), _1361271)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33587 ^ _779571) ^ [_1392686, _1392688, _1392690, _1392692] : [c_Sum__Type_OPlus(_1392686, _1392688, _1392690, _1392692) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1392686, _1392688), tc_HOL_Obool)), 33590 ^ _779571 : [(33593 ^ _779571) ^ [] : [-(_1392692 = c_Orderings_Obot__class_Obot(tc_fun(_1392688, tc_HOL_Obool)))], (33591 ^ _779571) ^ [] : [-(_1392690 = c_Orderings_Obot__class_Obot(tc_fun(_1392686, tc_HOL_Obool)))]]], (44954 ^ _779571) ^ [_1663249, _1663251, _1663253] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663249, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1663249, tc_HOL_Obool)), _1663251), _1663253)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1663249, tc_HOL_Obool)), _1663251), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663249, tc_HOL_Obool), _1663253)))], (51003 ^ _779571) ^ [_1806705, _1806707, _1806709, _1806711] : [-(hBOOL(hAPP(_1806705, _1806707))), -(c_List_OtakeWhile(_1806709, _1806705, hAPP(hAPP(c_List_Olist_OCons(_1806709), _1806707), _1806711)) = c_List_Olist_ONil(_1806709))], (22358 ^ _779571) ^ [_1165531, _1165533, _1165535] : [-(hAPP(c_Divides_Oadjust(_1165531), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1165533), _1165535)) = 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), _1165535), _1165531)), 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)))), _1165533)), 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)))), _1165533)), _1165535))))], (41149 ^ _779571) ^ [_1563059, _1563061, _1563063, _1563065] : [-(hBOOL(hAPP(hAPP(c_member(_1563059), _1563061), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563059, tc_HOL_Obool)), _1563063), hAPP(c_Set_OCollect(_1563059), _1563065))))), hBOOL(hAPP(hAPP(c_member(_1563059), _1563061), _1563063)), hBOOL(hAPP(_1563065, _1563061))], (51387 ^ _779571) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (41848 ^ _779571) ^ [] : [-(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)))))], (8382 ^ _779571) ^ [_918523, _918525, _918527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918523), _918525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918523), _918527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918525), _918527))))], (18957 ^ _779571) ^ [] : [-(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)))))], (36854 ^ _779571) ^ [_1465696, _1465698, _1465700, _1465702] : [class_Orderings_Oorder(_1465696), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465696, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1465696, _1465698), _1465700)), c_SetInterval_Oord__class_OatLeastAtMost(_1465696, _1465700, _1465702)) = c_Orderings_Obot__class_Obot(tc_fun(_1465696, tc_HOL_Obool)))], (39475 ^ _779571) ^ [_1523548, _1523550, _1523552, _1523554] : [hAPP(c_Set_Oimage(_1523548, _1523550, _1523552), c_Orderings_Otop__class_Otop(tc_fun(_1523548, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523550, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1523548, _1523550, _1523552), hAPP(c_Set_Ovimage(_1523548, _1523550, _1523552), _1523554)) = _1523554)], (28333 ^ _779571) ^ [_1282376, _1282378, _1282380, _1282382] : [class_Orderings_Olinorder(_1282376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282376), _1282378), _1282380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282376), _1282380), _1282382)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282376, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1282376, _1282378), _1282380)), c_SetInterval_Oord__class_OatLeastAtMost(_1282376, _1282380, _1282382)) = c_SetInterval_Oord__class_OatLeastAtMost(_1282376, _1282378, _1282382))], (3140 ^ _779571) ^ [_827711, _827713] : [_827713 = _827711, -(c_DSequence_Oempty(_827713) = c_DSequence_Oempty(_827711))], (40875 ^ _779571) ^ [_1557055, _1557057, _1557059, _1557061, _1557063, _1557065] : [-(c_Product__Type_Omap__pair(_1557055, _1557057, _1557059, _1557061, _1557063, _1557065) = hAPP(c_Product__Type_Oprod_Oprod__case(_1557055, _1557059, tc_prod(_1557057, _1557061)), hAPP(hAPP(c_COMBC(_1557055, tc_fun(_1557059, _1557061), tc_fun(_1557059, tc_prod(_1557057, _1557061))), hAPP(hAPP(c_COMBB(tc_fun(_1557061, tc_prod(_1557057, _1557061)), tc_fun(tc_fun(_1557059, _1557061), tc_fun(_1557059, tc_prod(_1557057, _1557061))), _1557055), c_COMBB(_1557061, tc_prod(_1557057, _1557061), _1557059)), hAPP(hAPP(c_COMBB(_1557057, tc_fun(_1557061, tc_prod(_1557057, _1557061)), _1557055), c_Product__Type_OPair(_1557057, _1557061)), _1557063))), _1557065)))], (42878 ^ _779571) ^ [_1611698, _1611700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1611698, _1611698)), _1611700)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1611698, _1611698)), c_Transitive__Closure_Otrancl(_1611698, _1611700))))], (15518 ^ _779571) ^ [_1042409, _1042411, _1042413] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042409), _1042411)), _1042413) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042409), _1042413)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042411), _1042413)))], (39407 ^ _779571) ^ [_1521939, _1521941, _1521943, _1521945, _1521947, _1521949] : [hAPP(_1521939, _1521941) = _1521943, hBOOL(hAPP(hAPP(c_member(_1521945), _1521943), _1521947)), -(hBOOL(hAPP(hAPP(c_member(_1521949), _1521941), hAPP(c_Set_Ovimage(_1521949, _1521945, _1521939), _1521947))))], (2356 ^ _779571) ^ [_815143, _815145, _815147, _815149] : [-(c_Nat__Transfer_Otsub(_815149, _815145) = c_Nat__Transfer_Otsub(_815147, _815143)), _815149 = _815147, _815145 = _815143], (13667 ^ _779571) ^ [_1008603, _1008605, _1008607] : [class_Divides_Osemiring__div(_1008603), -(c_Divides_Odiv__class_Omod(_1008603, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008603), _1008605), _1008607), _1008607) = c_Divides_Odiv__class_Omod(_1008603, _1008605, _1008607))], (27582 ^ _779571) ^ [_1267333, _1267335] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1267333, _1267335)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1267335), _1267333)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (12536 ^ _779571) ^ [_988833, _988835, _988837] : [class_Groups_Oordered__comm__monoid__add(_988833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988833), c_Groups_Ozero__class_Ozero(_988833)), _988835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988833), c_Groups_Ozero__class_Ozero(_988833)), _988837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988833), c_Groups_Ozero__class_Ozero(_988833)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988833), _988835), _988837))))], (24961 ^ _779571) ^ [_1216943, _1216945, _1216947, _1216949, _1216951] : [hBOOL(hAPP(_1216943, hAPP(hAPP(c_Product__Type_OPair(_1216945, _1216947), _1216949), _1216951))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1216945, _1216947, tc_HOL_Obool, _1216943), _1216949), _1216951)))], (12530 ^ _779571) ^ [] : [-(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))], (35575 ^ _779571) ^ [_1436480, _1436482, _1436484, _1436486] : [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), _1436480), _1436482)), 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), _1436484), _1436486)), 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), _1436480), _1436486)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436484), _1436482))))], (49343 ^ _779571) ^ [_1770349, _1770351, _1770353] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770349)), _1770351), c_List_Olists(_1770349, _1770353))), 49346 ^ _779571 : [(49347 ^ _779571) ^ [_1770457] : [hBOOL(hAPP(hAPP(c_member(_1770349), _1770457), hAPP(c_List_Oset(_1770349), _1770351))), -(hBOOL(hAPP(hAPP(c_member(_1770349), _1770457), _1770353)))]]], (49010 ^ _779571) ^ [_1762819, _1762821, _1762823, _1762825, _1762827] : [-(hAPP(c_List_Orotate(_1762819, _1762821), hAPP(hAPP(c_List_Omap(_1762823, _1762819), _1762825), _1762827)) = hAPP(hAPP(c_List_Omap(_1762823, _1762819), _1762825), hAPP(c_List_Orotate(_1762823, _1762821), _1762827)))], (18017 ^ _779571) ^ [_1089511, _1089513, _1089515] : [18019 ^ _779571 : [(18022 ^ _779571) ^ [] : [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(_1089513, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18018 ^ [_1089511, _1089513, _1089515]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1089513, 18018 ^ [_1089511, _1089513, _1089515])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18020 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18018 ^ [_1089511, _1089513, _1089515]), _1089511)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1089513, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1089515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089515), hAPP(_1089513, _1089511))), 18032 ^ _779571 : [(18035 ^ _779571) ^ [] : [-(hAPP(_1089513, 18031 ^ [_1089511, _1089513, _1089515]) = _1089515)], (18033 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18031 ^ [_1089511, _1089513, _1089515]), _1089511)))]]], (31534 ^ _779571) ^ [_1351367, _1351369, _1351371] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351367), _1351369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351367, tc_HOL_Obool)), _1351371), _1351369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1351367), _1351369)), hAPP(c_Finite__Set_Ocard(_1351367), _1351371))), -(_1351371 = _1351369)], (30475 ^ _779571) ^ [_1326176, _1326178] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326176, tc_HOL_Obool)), _1326178)), -(hBOOL(hAPP(hAPP(c_member(_1326176), _1326178), c_Orderings_Obot__class_Obot(tc_fun(_1326176, tc_HOL_Obool)))))], (6740 ^ _779571) ^ [_890195, _890197, _890199] : [c_Com_Ocom_OSemi(_890195, _890197) = hAPP(c_Com_Ocom_OBODY, _890199)], (44780 ^ _779571) ^ [_1659228, _1659230, _1659232, _1659234, _1659236] : [_1659228 = c_Orderings_Obot__class_Obot(tc_fun(_1659230, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659232, tc_HOL_Obool)), _1659234), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659230, tc_fun(_1659232, tc_HOL_Obool)), _1659228), _1659236)) = _1659234)], (19317 ^ _779571) ^ [_1110864, _1110866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110864), _1110866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110864)), c_Int_OBit0(_1110866))))], (43627 ^ _779571) ^ [_1630986, _1630988, _1630990] : [43629 ^ _779571 : [(43630 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630986), 43628 ^ [_1630986, _1630988, _1630990]), _1630988)))], (43635 ^ _779571) ^ [] : [43628 ^ [_1630986, _1630988, _1630990] = 43631 ^ [_1630986, _1630988, _1630990]], (43639 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630986, _1630986)), hAPP(hAPP(c_Product__Type_OPair(_1630986, _1630986), 43631 ^ [_1630986, _1630988, _1630990]), 43628 ^ [_1630986, _1630988, _1630990])), _1630990))], (43637 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630986, _1630986)), hAPP(hAPP(c_Product__Type_OPair(_1630986, _1630986), 43628 ^ [_1630986, _1630988, _1630990]), 43631 ^ [_1630986, _1630988, _1630990])), _1630990))], (43633 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630986), 43631 ^ [_1630986, _1630988, _1630990]), _1630988)))]], -(c_Relation_Ototal__on(_1630986, _1630988, _1630990))], (36750 ^ _779571) ^ [_1463183, _1463185, _1463187] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463183, tc_HOL_Obool)), _1463185), _1463187) = c_Orderings_Obot__class_Obot(tc_fun(_1463183, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463183, tc_HOL_Obool)), _1463185), _1463187) = _1463185)], (39266 ^ _779571) ^ [_1518747, _1518749, _1518751, _1518753] : [class_Groups_Ocomm__monoid__add(_1518747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518749), _1518751)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1518749, _1518747), _1518753), _1518751) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518747, _1518749, c_Groups_Oplus__class_Oplus(_1518747)), _1518753), c_Groups_Ozero__class_Ozero(_1518747)), _1518751))], (6815 ^ _779571) ^ [_891810, _891812, _891814] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_891810, _891812, _891814)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891814)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45795 ^ _779571) ^ [_1682326, _1682328] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1682326, _1682328) = c_Smallcheck_Ofull__small_H(_1682326, hAPP(c_Code__Numeral_Oint__of, _1682328), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1682328))))], (22762 ^ _779571) ^ [_1174001, _1174003, _1174005, _1174007] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1174001, _1174003), _1174005)), hBOOL(hAPP(hAPP(_1174003, _1174007), _1174005)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1174001, _1174003), _1174007)))], (7452 ^ _779571) ^ [_903242, _903244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903242), _903244)), _903242 = _903244], (48158 ^ _779571) ^ [_1740954, _1740956] : [-(hAPP(hAPP(c_List_Oappend(_1740954), c_List_Olist_ONil(_1740954)), _1740956) = _1740956)], (46428 ^ _779571) ^ [_1697321, _1697323, _1697325, _1697327, _1697329, _1697331] : [-(hAPP(hAPP(c_List_Ozip(_1697321, _1697323), _1697325), hAPP(hAPP(c_List_Omap(_1697327, _1697323), _1697329), _1697331)) = hAPP(hAPP(c_List_Omap(tc_prod(_1697321, _1697327), tc_prod(_1697321, _1697323)), hAPP(c_Product__Type_Oprod_Oprod__case(_1697321, _1697327, tc_prod(_1697321, _1697323)), hAPP(hAPP(c_COMBC(_1697321, tc_fun(_1697327, _1697323), tc_fun(_1697327, tc_prod(_1697321, _1697323))), hAPP(hAPP(c_COMBB(tc_fun(_1697323, tc_prod(_1697321, _1697323)), tc_fun(tc_fun(_1697327, _1697323), tc_fun(_1697327, tc_prod(_1697321, _1697323))), _1697321), c_COMBB(_1697323, tc_prod(_1697321, _1697323), _1697327)), c_Product__Type_OPair(_1697321, _1697323))), _1697329))), hAPP(hAPP(c_List_Ozip(_1697321, _1697327), _1697325), _1697331)))], (6101 ^ _779571) ^ [_877944, _877946, _877948, _877950, _877952, _877954] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_877944, _877946, _877948, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877944), _877950), _877952), _877954)) = hAPP(hAPP(hAPP(_877948, _877950), _877952), _877954))], (36360 ^ _779571) ^ [_1454955, _1454957, _1454959] : [class_Lattices_Osemilattice__inf(_1454955), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454955), _1454957), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454955), _1454957), _1454959)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454955), _1454957), _1454959))], (35805 ^ _779571) ^ [_1442440, _1442442, _1442444, _1442446] : [hBOOL(hAPP(hAPP(c_member(_1442440), _1442442), _1442444)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1442440, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442440, _1442440, _1442446), hAPP(hAPP(c_Set_Oinsert(_1442440), _1442442), c_Orderings_Obot__class_Obot(tc_fun(_1442440, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442440), _1442444), _1442446))))], (24741 ^ _779571) ^ [_1211593, _1211595] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1211593), _1211595) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211593)), hAPP(c_Code__Numeral_Onat__of, _1211595))))], (23895 ^ _779571) ^ [_1195070, _1195072, _1195074, _1195076, _1195078, _1195080] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1195070, _1195072), _1195072, _1195074), hAPP(hAPP(c_COMBB(_1195076, tc_fun(_1195072, _1195074), tc_prod(_1195070, _1195072)), _1195078), hAPP(hAPP(c_COMBB(_1195070, _1195076, tc_prod(_1195070, _1195072)), _1195080), c_Product__Type_Ofst(_1195070, _1195072)))), c_Product__Type_Osnd(_1195070, _1195072)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1195070, _1195072, _1195074), hAPP(hAPP(c_COMBB(_1195076, tc_fun(_1195072, _1195074), _1195070), _1195078), _1195080)))], (24805 ^ _779571) ^ [_1213165, _1213167, _1213169] : [-(c_Product__Type_Ointernal__split(_1213165, _1213167, _1213169) = c_Product__Type_Oprod_Oprod__case(_1213165, _1213167, _1213169))], (41618 ^ _779571) ^ [_1581061, _1581063] : [-(hAPP(c_Fun_Oid(_1581061), _1581063) = _1581063)], (47338 ^ _779571) ^ [_1721429, _1721431, _1721433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721429), tc_List_Olist(_1721429))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721429), tc_List_Olist(_1721429)), c_List_Olist_ONil(_1721429)), _1721431)), c_List_Olex(_1721429, _1721433)))], (5508 ^ _779571) ^ [_864681, _864683] : [_864683 = _864681, -(c_List_Oreturn__list(_864683) = c_List_Oreturn__list(_864681))], (48734 ^ _779571) ^ [_1756702, _1756704, _1756706] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756702)), hAPP(hAPP(c_List_Odrop(_1756702), _1756704), _1756706)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756702)), _1756706)), _1756704))], (48646 ^ _779571) ^ [_1754168, _1754170, _1754172, _1754174, _1754176, _1754178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1754168, _1754168)), hAPP(hAPP(c_Product__Type_OPair(_1754168, _1754168), _1754170), _1754172)), c_Transitive__Closure_Ortrancl(_1754168, _1754174))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754168), tc_List_Olist(_1754168))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754168), tc_List_Olist(_1754168)), _1754176), _1754178)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1754168), c_List_Olistrel1(_1754168, _1754174)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754168), tc_List_Olist(_1754168))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754168), tc_List_Olist(_1754168)), hAPP(hAPP(c_List_Olist_OCons(_1754168), _1754170), _1754176)), hAPP(hAPP(c_List_Olist_OCons(_1754168), _1754172), _1754178))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1754168), c_List_Olistrel1(_1754168, _1754174)))))], (41133 ^ _779571) ^ [_1562699] : [class_Orderings_Olinorder(_1562699), -(c_Finite__Set_Ofun__left__comm__idem(_1562699, _1562699, c_Orderings_Oord__class_Omin(_1562699)))], (5540 ^ _779571) ^ [_865149, _865151] : [_865151 = _865149, -(c_Finite__Set_Ocard(_865151) = c_Finite__Set_Ocard(_865149))], (35500 ^ _779571) ^ [_1434453, _1434455, _1434457, _1434459, _1434461] : [hBOOL(hAPP(hAPP(c_member(_1434453), _1434455), hAPP(c_Relation_OImage(_1434457, _1434453, _1434459), _1434461))), 35504 ^ _779571 : [(35507 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1434457, _1434453)), hAPP(hAPP(c_Product__Type_OPair(_1434457, _1434453), 35503 ^ [_1434453, _1434455, _1434457, _1434459, _1434461]), _1434455)), _1434459)))], (35505 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434457), 35503 ^ [_1434453, _1434455, _1434457, _1434459, _1434461]), _1434461)))]]], (8918 ^ _779571) ^ [_927368, _927370, _927372] : [class_Groups_Ogroup__add(_927368), 8921 ^ _779571 : [(8928 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927368), _927372) = _927370, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927368), _927370) = _927372)], (8922 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927368), _927370) = _927372, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927368), _927372) = _927370)]]], (312 ^ _779571) ^ [_784241, _784243, _784245, _784247, _784249, _784251, _784253, _784255] : [-(c_Equiv__Relations_Ocongruent(_784253, _784249, _784245, _784241)), c_Equiv__Relations_Ocongruent(_784255, _784251, _784247, _784243), _784255 = _784253, _784251 = _784249, _784247 = _784245, _784243 = _784241], (27516 ^ _779571) ^ [_1265921, _1265923, _1265925, _1265927, _1265929] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265921, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265921, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1265923, _1265921, _1265925), _1265927)), hAPP(c_Set_Oimage(_1265923, _1265921, _1265925), _1265929))), hAPP(c_Set_Oimage(_1265923, _1265921, _1265925), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265923, tc_HOL_Obool)), _1265927), _1265929)))))], (22166 ^ _779571) ^ [_1162135] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1162135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1162135)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34293 ^ _779571) ^ [_1406520, _1406522, _1406524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406520), _1406522)), 34296 ^ _779571 : [(34297 ^ _779571) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406520, tc_Nat_Onat), _1406524), _1406522) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 34300 ^ _779571 : [(34301 ^ _779571) ^ [_1406682] : [hBOOL(hAPP(hAPP(c_member(_1406520), _1406682), _1406522)), -(hAPP(_1406524, _1406682) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (34307 ^ _779571) ^ [] : [34309 ^ _779571 : [(34312 ^ _779571) ^ [] : [hAPP(_1406524, 34308 ^ [_1406520, _1406522, _1406524]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34310 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406520), 34308 ^ [_1406520, _1406522, _1406524]), _1406522)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406520, tc_Nat_Onat), _1406524), _1406522) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17011 ^ _779571) ^ [_1071809, _1071811] : [class_Groups_Oabs__if(_1071809), 17014 ^ _779571 : [(17021 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071809), _1071811), c_Groups_Ozero__class_Ozero(_1071809)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1071809), _1071811) = _1071811)], (17015 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071809), _1071811), c_Groups_Ozero__class_Ozero(_1071809))), -(hAPP(c_Groups_Oabs__class_Oabs(_1071809), _1071811) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071809), _1071811))]]], (44666 ^ _779571) ^ [_1655867, _1655869, _1655871, _1655873, _1655875] : [_1655867 = c_Orderings_Obot__class_Obot(tc_fun(_1655869, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655871, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655869, tc_fun(_1655871, tc_HOL_Obool)), _1655867), _1655873)), _1655875) = _1655875)], (26718 ^ _779571) ^ [_1249434, _1249436, _1249438, _1249440] : [class_Orderings_Oorder(_1249434), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1249434, 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)))), _1249436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249434), hAPP(_1249436, _1249438)), hAPP(_1249436, _1249440)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249438), _1249440)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249440), _1249438)))], (42425 ^ _779571) ^ [_1601752, _1601754, _1601756] : [-(hAPP(c_New__DSequence_Opos__single(_1601752, _1601754), _1601756) = c_Lazy__Sequence_Osingle(_1601752, _1601754))], (29554 ^ _779571) ^ [_1307794, _1307796, _1307798] : [class_Orderings_Oorder(_1307794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307794), _1307796), _1307798)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1307794, _1307798, _1307796) = c_Orderings_Obot__class_Obot(tc_fun(_1307794, tc_HOL_Obool)))], (39437 ^ _779571) ^ [_1522678, _1522680, _1522682, _1522684, _1522686] : [hBOOL(hAPP(_1522684, hAPP(_1522682, _1522686))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522678, _1522680, _1522682), _1522684), _1522686)))], (15656 ^ _779571) ^ [_1045271, _1045273, _1045275] : [class_Groups_Ogroup__add(_1045271), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045271), _1045273), hAPP(c_Groups_Ouminus__class_Ouminus(_1045271), _1045275)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045271), _1045273), _1045275))], (36790 ^ _779571) ^ [_1464377, _1464379, _1464381] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464377, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464377, tc_HOL_Obool)), _1464379), _1464381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464377, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464377, tc_HOL_Obool)), _1464379)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464377, tc_HOL_Obool)), _1464381)))], (24889 ^ _779571) ^ [_1215055, _1215057, _1215059, _1215061, _1215063, _1215065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215055, tc_fun(_1215057, tc_HOL_Obool))), _1215059), _1215061)), hBOOL(hAPP(hAPP(_1215059, _1215063), _1215065)), -(hBOOL(hAPP(hAPP(_1215061, _1215063), _1215065)))], (46045 ^ _779571) ^ [_1688414] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1688414)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1688414), tc_HOL_Obool))))], (29548 ^ _779571) ^ [_1307683] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307683, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1307683, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1307683, tc_HOL_Obool)))], (46564 ^ _779571) ^ [_1700738, _1700740, _1700742, _1700744] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700738)), _1700740) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700742)), _1700744), -(hAPP(hAPP(c_List_Omap(tc_prod(_1700738, _1700742), _1700742), c_Product__Type_Osnd(_1700738, _1700742)), hAPP(hAPP(c_List_Ozip(_1700738, _1700742), _1700740), _1700744)) = _1700744)], (37926 ^ _779571) ^ [_1491588, _1491590, _1491592] : [class_Lattices_Olattice(_1491588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491588), _1491590)), hBOOL(hAPP(hAPP(c_member(_1491588), _1491592), _1491590)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1491588), _1491592), c_Big__Operators_Olattice__class_OInf__fin(_1491588, _1491590)) = _1491592)], (33011 ^ _779571) ^ [_1381654, _1381656, _1381658] : [class_Lattices_Olattice(_1381654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381654), _1381656)), -(_1381656 = c_Orderings_Obot__class_Obot(tc_fun(_1381654, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1381654, hAPP(hAPP(c_Set_Oinsert(_1381654), _1381658), _1381656)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1381654), _1381658), c_Big__Operators_Olattice__class_OSup__fin(_1381654, _1381656)))], (25580 ^ _779571) ^ [_1227510, _1227512] : [class_Rings_Ocomm__semiring__1(_1227510), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227510), _1227512), _1227512)))], (18857 ^ _779571) ^ [_1102994] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1102994)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1102994))))], (27504 ^ _779571) ^ [_1265745, _1265747] : [_1265745 = _1265747, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265745) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1265747))], (43058 ^ _779571) ^ [_1616956, _1616958, _1616960] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616956, _1616956), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616956, _1616956), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616956, _1616958)), c_Transitive__Closure_Ortrancl(_1616956, _1616960))), c_Transitive__Closure_Ortrancl(_1616956, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616956, _1616956), tc_HOL_Obool)), _1616958), _1616960)))))], (46273 ^ _779571) ^ [_1693689, _1693691] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1693689, _1693691) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1693689), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1693691), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (4598 ^ _779571) ^ [_850722, _850724, _850726, _850728] : [-(c_Complete__Lattice_OSup__class_OSup(_850728, _850724) = c_Complete__Lattice_OSup__class_OSup(_850726, _850722)), _850728 = _850726, _850724 = _850722], (14554 ^ _779571) ^ [_1025113, _1025115, _1025117] : [class_Divides_Osemiring__div(_1025113), -(_1025115 = c_Groups_Ozero__class_Ozero(_1025113)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025113), _1025115), _1025117)), _1025115) = _1025117)], (49225 ^ _779571) ^ [_1767328, _1767330, _1767332] : [class_Orderings_Olinorder(_1767328), -(c_Big__Operators_Olattice_OSup__fin(_1767328, c_Orderings_Oord__class_Omax(_1767328), hAPP(c_List_Oset(_1767328), hAPP(hAPP(c_List_Olist_OCons(_1767328), _1767330), _1767332))) = hAPP(c_List_Ofoldl(_1767328, _1767328, c_Orderings_Oord__class_Omax(_1767328), _1767330), _1767332))], (38749 ^ _779571) ^ [_1507742, _1507744, _1507746, _1507748] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507742), _1507744)), 38752 ^ _779571 : [(38759 ^ _779571) ^ [] : [hAPP(c_Finite__Set_Ocard(_1507746), hAPP(c_Set_Oimage(_1507742, _1507746, _1507748), _1507744)) = hAPP(c_Finite__Set_Ocard(_1507742), _1507744), -(c_Fun_Oinj__on(_1507742, _1507746, _1507748, _1507744))], (38753 ^ _779571) ^ [] : [c_Fun_Oinj__on(_1507742, _1507746, _1507748, _1507744), -(hAPP(c_Finite__Set_Ocard(_1507746), hAPP(c_Set_Oimage(_1507742, _1507746, _1507748), _1507744)) = hAPP(c_Finite__Set_Ocard(_1507742), _1507744))]]], (44081 ^ _779571) ^ [_1641720, _1641722, _1641724] : [class_Orderings_Olinorder(_1641720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641720), _1641722)), -(c_Big__Operators_Olinorder__class_OMax(_1641720, hAPP(hAPP(c_Set_Oinsert(_1641720), _1641724), _1641722)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641720, _1641720, c_Orderings_Oord__class_Omax(_1641720)), _1641724), _1641722))], (10716 ^ _779571) ^ [_958014, _958016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _958014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _958016)), 10723 ^ _779571 : [(10730 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _958014), _958016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _958014)), hAPP(c_Int_Onat, _958016))))], (10724 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _958014)), hAPP(c_Int_Onat, _958016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _958014), _958016)))]]], (11416 ^ _779571) ^ [_969015, _969017] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969015), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969017), _969015))))], (40480 ^ _779571) ^ [_1548152, _1548154, _1548156] : [class_Orderings_Olinorder(_1548152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548152), _1548154)), hBOOL(hAPP(hAPP(c_member(_1548152), _1548156), _1548154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1548152), hAPP(c_Finite__Set_Ofold1(_1548152, c_Orderings_Oord__class_Omin(_1548152)), _1548154)), _1548156)))], (23933 ^ _779571) ^ [_1196060, _1196062, _1196064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196060, tc_HOL_Obool)), _1196064), _1196062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196060, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1196060, tc_HOL_Obool)), _1196062)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1196060, tc_HOL_Obool)), _1196064))))], (46043 ^ _779571) ^ [_1688370] : [-(hAPP(c_Option_Omap(_1688370, _1688370), c_COMBI(_1688370)) = c_Fun_Oid(tc_Option_Ooption(_1688370)))], (19351 ^ _779571) ^ [_1111479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1111479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1111479))))], (19857 ^ _779571) ^ [_1120564, _1120566] : [-(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), _1120564)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1120566))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1120564))) = 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), _1120566)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120564)))], (5996 ^ _779571) ^ [_875985, _875987, _875989, _875991, _875993] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_875985, _875987), _875989, _875991, _875993), 6000 ^ _779571 : [(6003 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_875987, 5999 ^ [_875985, _875987, _875989, _875991, _875993], _875991, _875993))], (6001 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_875985, _875989, _875991, 5999 ^ [_875985, _875987, _875989, _875991, _875993]))]]], (23651 ^ _779571) ^ [_1190258, _1190260, _1190262, _1190264] : [class_Orderings_Olinorder(_1190258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190258), _1190260), _1190262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190258), _1190260), _1190264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190258), _1190260), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190258), _1190262), _1190264))))], (22412 ^ _779571) ^ [_1166811, _1166813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1166811), _1166813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1166811)), hAPP(c_Code__Numeral_Oof__nat, _1166813))))], (39026 ^ _779571) ^ [_1513887, _1513889, _1513891] : [-(c_Fun_Oinj__on(_1513887, tc_sum(_1513887, _1513889), c_Sum__Type_OInl(_1513887, _1513889), _1513891))], (47360 ^ _779571) ^ [_1721871, _1721873, _1721875] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1721871))), -(c_List_Osublist(_1721873, hAPP(hAPP(c_List_Olist_OCons(_1721873), _1721875), c_List_Olist_ONil(_1721873)), _1721871) = c_List_Olist_ONil(_1721873))], (50790 ^ _779571) ^ [_1800732, _1800734, _1800736, _1800738] : [-(c_List_Otranspose(_1800732, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1800732)), hAPP(hAPP(c_List_Olist_OCons(_1800732), _1800734), _1800736)), _1800738)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1800732)), hAPP(hAPP(c_List_Olist_OCons(_1800732), _1800734), c_List_Oconcat(_1800732, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800732), tc_List_Olist(_1800732)), c_List_Olist_Olist__case(tc_List_Olist(_1800732), _1800732, c_List_Olist_ONil(_1800732), hAPP(hAPP(c_COMBB(tc_List_Olist(_1800732), tc_fun(tc_List_Olist(_1800732), tc_List_Olist(_1800732)), _1800732), c_COMBK(tc_List_Olist(_1800732), tc_List_Olist(_1800732))), hAPP(hAPP(c_COMBC(_1800732, tc_List_Olist(_1800732), tc_List_Olist(_1800732)), c_List_Olist_OCons(_1800732)), c_List_Olist_ONil(_1800732))))), _1800738)))), c_List_Otranspose(_1800732, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1800732)), _1800736), c_List_Oconcat(tc_List_Olist(_1800732), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800732), tc_List_Olist(tc_List_Olist(_1800732))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1800732)), _1800732, c_List_Olist_ONil(tc_List_Olist(_1800732)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1800732), tc_List_Olist(tc_List_Olist(_1800732))), _1800732), hAPP(hAPP(c_COMBC(tc_List_Olist(_1800732), tc_List_Olist(tc_List_Olist(_1800732)), tc_List_Olist(tc_List_Olist(_1800732))), c_List_Olist_OCons(tc_List_Olist(_1800732))), c_List_Olist_ONil(tc_List_Olist(_1800732)))))), _1800738))))))], (26230 ^ _779571) ^ [_1240249, _1240251, _1240253, _1240255, _1240257] : [class_Rings_Ocomm__semiring__1(_1240249), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240249), _1240251), _1240253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240255), _1240257)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240249), hAPP(hAPP(c_Power_Opower__class_Opower(_1240249), _1240251), _1240255)), hAPP(hAPP(c_Power_Opower__class_Opower(_1240249), _1240253), _1240257))))], (23861 ^ _779571) ^ [_1194346, _1194348, _1194350] : [-(hAPP(c_Product__Type_Ofst(_1194346, _1194348), _1194350) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194346, _1194348, _1194346), c_COMBK(_1194346, _1194348)), _1194350))], (9262 ^ _779571) ^ [_933045, _933047] : [class_Rings_Ocomm__semiring__1(_933045), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), _933047), c_Groups_Ozero__class_Ozero(_933045)) = c_Groups_Ozero__class_Ozero(_933045))], (2042 ^ _779571) ^ [_809926, _809928] : [_809928 = _809926, -(c_Nat_Onat_Onat__size(_809928) = c_Nat_Onat_Onat__size(_809926))], (47622 ^ _779571) ^ [_1728397, _1728399, _1728401] : [-(hAPP(c_List_Oset(_1728397), c_List_Osublist(_1728397, _1728399, _1728401)) = hAPP(c_Set_OCollect(_1728397), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1728397), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1728397, 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)), _1728397), 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)), _1728397), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1728397, tc_fun(tc_Nat_Onat, _1728397), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1728397, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1728397), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1728397), c_COMBB(_1728397, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1728397), _1728399))))), 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(_1728397)), _1728399)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1728401))))))], (4578 ^ _779571) ^ [_850416, _850418] : [_850418 = _850416, -(c_Groups_Otimes__class_Otimes(_850418) = c_Groups_Otimes__class_Otimes(_850416))], (13880 ^ _779571) ^ [_1012823, _1012825] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1012823), _1012825) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012823, _1012825) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (38441 ^ _779571) ^ [_1501869, _1501871, _1501873, _1501875, _1501877] : [c_Fun_Oinj__on(_1501869, _1501871, _1501873, _1501875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501869, tc_HOL_Obool)), _1501877), _1501875)), -(c_Fun_Oinj__on(_1501869, _1501871, _1501873, _1501877))], (46024 ^ _779571) ^ [_1687763, _1687765, _1687767, _1687769, _1687771] : [46026 ^ _779571 : [(46029 ^ _779571) ^ [] : [hAPP(_1687767, 46025 ^ [_1687763, _1687765, _1687767, _1687769, _1687771]) = hAPP(_1687771, 46025 ^ [_1687763, _1687765, _1687767, _1687769, _1687771])], (46027 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1687763), 46025 ^ [_1687763, _1687765, _1687767, _1687769, _1687771]), hAPP(c_List_Oset(_1687763), _1687769))))]], -(hAPP(hAPP(c_List_Omap(_1687763, _1687765), _1687767), _1687769) = hAPP(hAPP(c_List_Omap(_1687763, _1687765), _1687771), _1687769))], (7246 ^ _779571) ^ [_899407, _899409, _899411] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _899407))), _899409), _899411)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _899407)), _899409), _899411)))], (21057 ^ _779571) ^ [_1141944, _1141946, _1141948, _1141950] : [class_Fields_Ofield__inverse__zero(_1141944), -(_1141946 = c_Groups_Ozero__class_Ozero(_1141944)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141944), _1141948), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141944), _1141950), _1141946)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141944), _1141950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141944), _1141948), _1141946))), _1141946))], (3310 ^ _779571) ^ [_830386, _830388, _830390, _830392, _830394, _830396] : [-(c_SetInterval_Oord_OatMost(_830396, _830392, _830388) = c_SetInterval_Oord_OatMost(_830394, _830390, _830386)), _830396 = _830394, _830392 = _830390, _830388 = _830386], (30481 ^ _779571) ^ [_1326287, _1326289] : [hBOOL(hAPP(hAPP(c_member(_1326287), _1326289), c_Orderings_Obot__class_Obot(tc_fun(_1326287, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326287, tc_HOL_Obool)), _1326289)))], (5382 ^ _779571) ^ [_862768, _862770, _862772, _862774, _862776, _862778, _862780, _862782] : [-(c_Map_Omap__add(_862782, _862778, _862774, _862770) = c_Map_Omap__add(_862780, _862776, _862772, _862768)), _862782 = _862780, _862778 = _862776, _862774 = _862772, _862770 = _862768], (24633 ^ _779571) ^ [_1209765, _1209767] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1209765)), _1209767) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1209765), 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), _1209765)), _1209767))], (13430 ^ _779571) ^ [_1004524, _1004526, _1004528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004524), _1004526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004526), _1004528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004524), _1004528)))], (49096 ^ _779571) ^ [_1764571, _1764573, _1764575, _1764577] : [-(c_List_Olist_Olist__size(_1764571, _1764573, hAPP(hAPP(c_List_Olist_OCons(_1764571), _1764575), _1764577)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1764573, _1764575)), c_List_Olist_Olist__size(_1764571, _1764573, _1764577))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40753 ^ _779571) ^ [_1553868, _1553870, _1553872, _1553874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553868), _1553870)), 40759 ^ _779571 : [(40762 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553872), hAPP(_1553874, 40758 ^ [_1553868, _1553870, _1553872, _1553874])))], (40760 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553868), 40758 ^ [_1553868, _1553870, _1553872, _1553874]), _1553870)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1553868, _1553872)), hAPP(hAPP(c_Product__Type_OSigma(_1553868, _1553872), _1553870), _1553874)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1553868, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1553872, tc_HOL_Obool), tc_Nat_Onat, _1553868), c_Finite__Set_Ocard(_1553872)), _1553874)), _1553870))], (43975 ^ _779571) ^ [_1639709, _1639711, _1639713, _1639715, _1639717] : [c_Finite__Set_Ofolding__one__idem(_1639709, _1639711, _1639713), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639709), _1639715)), -(hAPP(_1639713, hAPP(hAPP(c_Set_Oinsert(_1639709), _1639717), _1639715)) = hAPP(hAPP(c_Finite__Set_Ofold(_1639709, _1639709, _1639711), _1639717), _1639715))], (14600 ^ _779571) ^ [_1025789, _1025791, _1025793] : [class_Divides_Osemiring__div(_1025789), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025789), c_Divides_Odiv__class_Omod(_1025789, _1025791, _1025793)), _1025793) = c_Groups_Ozero__class_Ozero(_1025789))], (17771 ^ _779571) ^ [_1085627, _1085629] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085627)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085627)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085629)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085627)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085629))))], (48544 ^ _779571) ^ [_1751124, _1751126, _1751128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751124), tc_List_Olist(_1751124))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751124), tc_List_Olist(_1751124)), _1751126), c_List_Olist_ONil(_1751124))), c_List_Olistrel1(_1751124, _1751128)))], (49130 ^ _779571) ^ [_1765407, _1765409, _1765411, _1765413, _1765415, _1765417] : [-(hAPP(c_List_Ofoldl(_1765407, _1765409, _1765411, _1765413), hAPP(hAPP(c_List_Oappend(_1765409), _1765415), _1765417)) = hAPP(c_List_Ofoldl(_1765407, _1765409, _1765411, hAPP(c_List_Ofoldl(_1765407, _1765409, _1765411, _1765413), _1765415)), _1765417))], (2152 ^ _779571) ^ [_811801, _811803, _811805, _811807, _811809, _811811, _811813, _811815] : [-(c_Nitpick_Opair__box_OPairBox(_811815, _811811, _811807, _811803) = c_Nitpick_Opair__box_OPairBox(_811813, _811809, _811805, _811801)), _811815 = _811813, _811811 = _811809, _811807 = _811805, _811803 = _811801], (47805 ^ _779571) ^ [_1732876, _1732878, _1732880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1732878))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1732878), _1732876), _1732880)) = 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), _1732878)), _1732880)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1732878), _1732876)))], (7911 ^ _779571) ^ [_910843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _910843)), -(_910843 = hAPP(c_Nat_OSuc, 7914 ^ [_910843]))], (23957 ^ _779571) ^ [_1196559, _1196561, _1196563] : [_1196559 = _1196561, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196563, tc_HOL_Obool)), _1196561), _1196559)))], (51243 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (21051 ^ _779571) ^ [_1141865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141865)), -(c_Nat__Transfer_Ois__nat(_1141865))], (23305 ^ _779571) ^ [_1184195, _1184197, _1184199, _1184201] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184195, _1184197), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184199), _1184201))), -(_1184197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184195, _1184197) = _1184201)], (43536 ^ _779571) ^ [_1628724, _1628726, _1628728, _1628730] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1628724, _1628726), tc_fun(_1628724, _1628726)), _1628728), c_Fun_Ocomp(_1628726, _1628726, _1628724, _1628730)) = c_Fun_Ocomp(_1628726, _1628726, _1628724, hAPP(hAPP(c_Nat_Ocompow(_1628726, _1628726), _1628728), _1628730)))], (27425 ^ _779571) ^ [_1263947, _1263949] : [class_Orderings_Oorder(_1263947), 27432 ^ _779571 : [(27437 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263947), hAPP(_1263949, 27430 ^ [_1263947, _1263949])), hAPP(_1263949, 27431 ^ [_1263947, _1263949])))], (27435 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27431 ^ [_1263947, _1263949]), 27430 ^ [_1263947, _1263949]))], (27433 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27430 ^ [_1263947, _1263949]), 27431 ^ [_1263947, _1263949])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1263947, 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)))), _1263949))], (39809 ^ _779571) ^ [_1531077, _1531079, _1531081, _1531083, _1531085] : [_1531077 = c_Option_Ooption_ONone(_1531079), -(c_Map_Odom(_1531081, _1531079, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1531081, tc_Option_Ooption(_1531079)), _1531083), _1531085), _1531077)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531081, tc_HOL_Obool)), c_Map_Odom(_1531081, _1531079, _1531083)), hAPP(hAPP(c_Set_Oinsert(_1531081), _1531085), c_Orderings_Obot__class_Obot(tc_fun(_1531081, tc_HOL_Obool)))))], (24107 ^ _779571) ^ [_1199378, _1199380, _1199382, _1199384, _1199386] : [hBOOL(hAPP(hAPP(_1199378, _1199380), _1199382)), -(hBOOL(hAPP(hAPP(_1199378, hAPP(c_Product__Type_Osnd(_1199384, _1199386), hAPP(hAPP(c_Product__Type_OPair(_1199384, _1199386), _1199382), _1199380))), hAPP(c_Product__Type_Ofst(_1199384, _1199386), hAPP(hAPP(c_Product__Type_OPair(_1199384, _1199386), _1199382), _1199380)))))], (34575 ^ _779571) ^ [_1412618, _1412620, _1412622, _1412624, _1412626] : [hAPP(_1412618, _1412620) = hAPP(c_Option_Ooption_OSome(_1412622), _1412624), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412626, tc_Option_Ooption(_1412622)), _1412618), _1412620), hAPP(c_Option_Ooption_OSome(_1412622), _1412624)) = _1412618)], (23963 ^ _779571) ^ [_1196658, _1196660, _1196662] : [_1196658 = _1196660, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196662, tc_HOL_Obool)), _1196658), _1196660)))], (21493 ^ _779571) ^ [_1149470, _1149472, _1149474, _1149476] : [class_Fields_Olinordered__field(_1149470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149470), c_Groups_Ozero__class_Ozero(_1149470)), _1149472)), 21500 ^ _779571 : [(21507 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149470), _1149474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149470), _1149476), _1149472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149470), _1149474), _1149472)), _1149476)))], (21501 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149470), _1149474), _1149472)), _1149476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149470), _1149474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149470), _1149476), _1149472))))]]], (18999 ^ _779571) ^ [_1105156, _1105158] : [class_Int_Onumber__ring(_1105156), class_Rings_Olinordered__idom(_1105156), 19006 ^ _779571 : [(19013 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105158), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105156), hAPP(c_Int_Onumber__class_Onumber__of(_1105156), _1105158)), c_Groups_Oone__class_Oone(_1105156))))], (19007 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105156), hAPP(c_Int_Onumber__class_Onumber__of(_1105156), _1105158)), c_Groups_Oone__class_Oone(_1105156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105158), c_Int_OBit1(c_Int_OPls))))]]], (4412 ^ _779571) ^ [_847837, _847839, _847841, _847843] : [-(c_Random_Oselect(_847843, _847839) = c_Random_Oselect(_847841, _847837)), _847843 = _847841, _847839 = _847837], (7015 ^ _779571) ^ [_895196, _895198] : [class_Rings_Ocomm__semiring__1(_895196), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_895196), _895198), c_Groups_Ozero__class_Ozero(_895196)) = _895198)], (51291 ^ _779571) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (7272 ^ _779571) ^ [_899924, _899926, _899928, _899930, _899932, _899934] : [-(c_Nitpick_Opair__box_OPairBox(_899924, _899926, _899928, _899930) = c_Nitpick_Opair__box_OPairBox(_899924, _899926, _899932, _899934)), _899928 = _899932, _899930 = _899934], (38267 ^ _779571) ^ [_1498480, _1498482, _1498484, _1498486, _1498488] : [c_Fun_Oinj__on(_1498480, _1498482, _1498484, _1498486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1498480, tc_HOL_Obool)), _1498488), _1498486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1498482, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1498480, _1498482, _1498484), _1498488)), hAPP(c_Set_Oimage(_1498480, _1498482, _1498484), _1498486))))], (35982 ^ _779571) ^ [_1446433, _1446435, _1446437, _1446439, _1446441] : [c_Equiv__Relations_Oequiv(_1446433, _1446435, _1446437), hBOOL(hAPP(hAPP(c_member(_1446433), _1446439), _1446435)), hBOOL(hAPP(hAPP(c_member(_1446433), _1446441), _1446435)), 35993 ^ _779571 : [(36000 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446433, _1446433)), hAPP(hAPP(c_Product__Type_OPair(_1446433, _1446433), _1446439), _1446441)), _1446437)), -(hAPP(c_Relation_OImage(_1446433, _1446433, _1446437), hAPP(hAPP(c_Set_Oinsert(_1446433), _1446439), c_Orderings_Obot__class_Obot(tc_fun(_1446433, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1446433, _1446433, _1446437), hAPP(hAPP(c_Set_Oinsert(_1446433), _1446441), c_Orderings_Obot__class_Obot(tc_fun(_1446433, tc_HOL_Obool)))))], (35994 ^ _779571) ^ [] : [hAPP(c_Relation_OImage(_1446433, _1446433, _1446437), hAPP(hAPP(c_Set_Oinsert(_1446433), _1446439), c_Orderings_Obot__class_Obot(tc_fun(_1446433, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1446433, _1446433, _1446437), hAPP(hAPP(c_Set_Oinsert(_1446433), _1446441), c_Orderings_Obot__class_Obot(tc_fun(_1446433, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446433, _1446433)), hAPP(hAPP(c_Product__Type_OPair(_1446433, _1446433), _1446439), _1446441)), _1446437)))]]], (30078 ^ _779571) ^ [_1318515, _1318517, _1318519, _1318521, _1318523, _1318525] : [hBOOL(hAPP(hAPP(c_member(_1318515), _1318517), _1318519)), hBOOL(hAPP(hAPP(c_member(_1318521), _1318523), hAPP(_1318525, _1318517))), -(hBOOL(hAPP(hAPP(c_member(_1318521), _1318523), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318515, tc_fun(_1318521, tc_HOL_Obool)), _1318519), _1318525))))], (49112 ^ _779571) ^ [_1764920, _1764922, _1764924, _1764926] : [class_Groups_Osemigroup__add(_1764920), -(hAPP(c_List_Ofoldl(_1764920, _1764920, c_Groups_Oplus__class_Oplus(_1764920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1764920), _1764922), _1764924)), _1764926) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1764920), _1764922), hAPP(c_List_Ofoldl(_1764920, _1764920, c_Groups_Oplus__class_Oplus(_1764920), _1764924), _1764926)))], (50636 ^ _779571) ^ [_1797602, _1797604] : [50638 ^ _779571 : [(50641 ^ _779571) ^ [] : [50637 ^ [_1797602, _1797604] = c_List_Olist_ONil(_1797602)], (50639 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1797602)), 50637 ^ [_1797602, _1797604]), hAPP(c_List_Oset(tc_List_Olist(_1797602)), _1797604))))]], -(c_List_Olist_ONil(_1797602) = c_List_Oconcat(_1797602, _1797604))], (5662 ^ _779571) ^ [_866982, _866984, _866986, _866988] : [-(hAPP(_866988, _866984) = hAPP(_866986, _866982)), _866988 = _866986, _866984 = _866982], (16745 ^ _779571) ^ [_1066253, _1066255, _1066257] : [class_Int_Onumber(_1066253), class_Orderings_Olinorder(_1066253), 16752 ^ _779571 : [(16759 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066253), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066257)), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066255)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066253), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066255)), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066257))))], (16753 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066253), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066255)), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066257))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066253), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066257)), hAPP(c_Int_Onumber__class_Onumber__of(_1066253), _1066255)))]]], (42136 ^ _779571) ^ [_1594443, _1594445, _1594447, _1594449] : [hBOOL(hAPP(hAPP(c_member(_1594443), _1594445), hAPP(c_Relation_ORange(_1594447, _1594443), _1594449))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594447, _1594443)), hAPP(hAPP(c_Product__Type_OPair(_1594447, _1594443), 42139 ^ [_1594443, _1594445, _1594447, _1594449]), _1594445)), _1594449)))], (13709 ^ _779571) ^ [_1009504, _1009506, _1009508, _1009510, _1009512, _1009514] : [class_Divides_Osemiring__div(_1009504), c_Divides_Odiv__class_Omod(_1009504, _1009506, _1009508) = c_Divides_Odiv__class_Omod(_1009504, _1009510, _1009508), c_Divides_Odiv__class_Omod(_1009504, _1009512, _1009508) = c_Divides_Odiv__class_Omod(_1009504, _1009514, _1009508), -(c_Divides_Odiv__class_Omod(_1009504, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009504), _1009506), _1009512), _1009508) = c_Divides_Odiv__class_Omod(_1009504, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009504), _1009510), _1009514), _1009508))], (51231 ^ _779571) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (6754 ^ _779571) ^ [_890514, _890516] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_890514, _890516))))], (18339 ^ _779571) ^ [] : [c_Int_OPls = c_Int_OMin], (35026 ^ _779571) ^ [_1423527, _1423529, _1423531, _1423533] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1423527, _1423527)), hAPP(hAPP(c_Product__Type_OPair(_1423527, _1423527), _1423529), _1423531)), c_Relation_OId__on(_1423527, _1423533))), 35029 ^ _779571 : [(35032 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1423527), _1423529), _1423533)))], (35030 ^ _779571) ^ [] : [-(_1423529 = _1423531)]]], (42550 ^ _779571) ^ [_1604554, _1604556] : [-(c_Hilbert__Choice_OEps(_1604554, hAPP(hAPP(c_COMBC(_1604554, _1604554, tc_HOL_Obool), c_fequal), _1604556)) = _1604556)], (18521 ^ _779571) ^ [_1097360, _1097362] : [class_Int_Onumber__ring(_1097360), class_Rings_Olinordered__idom(_1097360), 18528 ^ _779571 : [(18535 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1097362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097360), c_Groups_Ozero__class_Ozero(_1097360)), hAPP(c_Int_Onumber__class_Onumber__of(_1097360), _1097362))))], (18529 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097360), c_Groups_Ozero__class_Ozero(_1097360)), hAPP(c_Int_Onumber__class_Onumber__of(_1097360), _1097362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1097362)))]]], (42595 ^ _779571) ^ [_1605351, _1605353, _1605355, _1605357] : [-(c_Hilbert__Choice_OEps(tc_prod(_1605351, _1605353), hAPP(c_Product__Type_Oprod_Oprod__case(_1605351, _1605353, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1605351, tc_fun(_1605353, tc_HOL_Obool), tc_fun(_1605353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1605353, tc_HOL_Obool), tc_fun(_1605353, tc_HOL_Obool)), _1605351), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1605353)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1605351), c_fconj), hAPP(c_fequal, _1605355)))), hAPP(c_fequal, _1605357)))) = hAPP(hAPP(c_Product__Type_OPair(_1605351, _1605353), _1605355), _1605357))], (23024 ^ _779571) ^ [_1178769, _1178771] : [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), _1178769), _1178771))), 23027 ^ _779571 : [(23034 ^ _779571) ^ [] : [-(_1178771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1178769, _1178771) = c_Nitpick_Onat__gcd(_1178771, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1178769, _1178771)))], (23028 ^ _779571) ^ [] : [_1178771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1178769, _1178771) = _1178769)]]], (47610 ^ _779571) ^ [_1728183, _1728185, _1728187, _1728189] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1728183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1728185), hAPP(hAPP(c_List_Olist_OCons(_1728185), _1728187), _1728189)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1728183)) = hAPP(hAPP(c_List_Onth(_1728185), _1728189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1728183)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43056 ^ _779571) ^ [_1616909, _1616911] : [-(c_Transitive__Closure_Ortrancl(_1616909, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616909, _1616909), tc_HOL_Obool)), _1616911), c_Relation_OId(_1616909))) = c_Transitive__Closure_Ortrancl(_1616909, _1616911))], (51293 ^ _779571) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (26086 ^ _779571) ^ [_1237489, _1237491, _1237493] : [class_Divides_Osemiring__div(_1237489), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237489), _1237491), _1237493)), -(c_Divides_Odiv__class_Omod(_1237489, _1237493, _1237491) = c_Groups_Ozero__class_Ozero(_1237489))], (27524 ^ _779571) ^ [_1266136, _1266138] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1266136), _1266138) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1266136, _1266138))], (36384 ^ _779571) ^ [_1455509, _1455511, _1455513, _1455515] : [class_Lattices_Osemilattice__inf(_1455509), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455509), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455509), _1455511), _1455513)), _1455515) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455509), _1455511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455509), _1455513), _1455515)))], (12832 ^ _779571) ^ [_994427, _994429, _994431] : [class_Rings_Olinordered__ring__strict(_994427), 12835 ^ _779571 : [(12844 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_994427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994427), _994429), _994429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994427), _994431), _994431))), c_Groups_Ozero__class_Ozero(_994427)))), _994429 = c_Groups_Ozero__class_Ozero(_994427), _994431 = c_Groups_Ozero__class_Ozero(_994427)], (12836 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_994427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994427), _994429), _994429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994427), _994431), _994431))), c_Groups_Ozero__class_Ozero(_994427))), 12839 ^ _779571 : [(12842 ^ _779571) ^ [] : [-(_994431 = c_Groups_Ozero__class_Ozero(_994427))], (12840 ^ _779571) ^ [] : [-(_994429 = c_Groups_Ozero__class_Ozero(_994427))]]]]], (39196 ^ _779571) ^ [_1517238, _1517240, _1517242, _1517244, _1517246] : [c_Fun_Oinj__on(_1517238, _1517240, _1517242, _1517244), hBOOL(hAPP(hAPP(c_member(_1517238), _1517246), _1517244)), -(hAPP(c_Fun_Othe__inv__into(_1517238, _1517240, _1517244, _1517242), hAPP(_1517242, _1517246)) = _1517246)], (45650 ^ _779571) ^ [_1678956, _1678958, _1678960, _1678962] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1678956, _1678958)), _1678960), hAPP(c_Relation_Oconverse(_1678958, _1678956), _1678962))), 45655 ^ _779571 : [(45658 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678958, _1678956)), hAPP(hAPP(c_Product__Type_OPair(_1678958, _1678956), 45653 ^ [_1678956, _1678958, _1678960, _1678962]), 45654 ^ [_1678956, _1678958, _1678960, _1678962])), _1678962)))], (45656 ^ _779571) ^ [] : [-(_1678960 = hAPP(hAPP(c_Product__Type_OPair(_1678956, _1678958), 45654 ^ [_1678956, _1678958, _1678960, _1678962]), 45653 ^ [_1678956, _1678958, _1678960, _1678962]))]]], (51565 ^ _779571) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (45145 ^ _779571) ^ [_1667665, _1667667, _1667669] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667665, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1667665, tc_HOL_Obool), tc_HOL_Obool)), _1667667), _1667669)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1667665, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667665, tc_HOL_Obool), _1667667)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667665, tc_HOL_Obool), _1667669)))], (43595 ^ _779571) ^ [_1630229, _1630231, _1630233] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630229, _1630229)), _1630231), c_Transitive__Closure_Otrancl(_1630229, _1630233)))), 43596 ^ _779571 : [(43597 ^ _779571) ^ [_1630308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1630308)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1630229, _1630229)), _1630231), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630229, _1630229), tc_HOL_Obool), _1630308), _1630233)))]]], (40164 ^ _779571) ^ [_1540638, _1540640, _1540642, _1540644, _1540646] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1540638, _1540640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540638, tc_HOL_Obool)), _1540642), _1540644)), _1540646) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540638, _1540640), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1540638, _1540640), _1540642), _1540646)), hAPP(hAPP(c_Product__Type_OSigma(_1540638, _1540640), _1540644), _1540646)))], (35450 ^ _779571) ^ [_1433061, _1433063, _1433065, _1433067, _1433069, _1433071, _1433073] : [-(hAPP(c_Fun_Ocomp(_1433061, _1433063, _1433065, _1433067), hAPP(c_Fun_Ocomp(_1433069, _1433061, _1433065, _1433071), _1433073)) = hAPP(c_Fun_Ocomp(_1433069, _1433063, _1433065, hAPP(c_Fun_Ocomp(_1433061, _1433063, _1433069, _1433067), _1433071)), _1433073))], (42288 ^ _779571) ^ [_1598135, _1598137, _1598139, _1598141] : [hBOOL(hAPP(hAPP(c_member(_1598135), _1598137), hAPP(c_Relation_ODomain(_1598135, _1598139), _1598141))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598135, _1598139)), hAPP(hAPP(c_Product__Type_OPair(_1598135, _1598139), _1598137), 42291 ^ [_1598135, _1598137, _1598139, _1598141])), _1598141)))], (19449 ^ _779571) ^ [_1113190, _1113192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113190), _1113192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1113190)), c_Int_OBit0(_1113192))))], (5002 ^ _779571) ^ [_856890, _856892, _856894, _856896] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_856896, _856892) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_856894, _856890)), _856896 = _856894, _856892 = _856890], (254 ^ _779571) ^ [_783302, _783304] : [-(c_Nat__Transfer_Ois__nat(_783302)), _783304 = _783302, c_Nat__Transfer_Ois__nat(_783304)], (26368 ^ _779571) ^ [_1242716, _1242718, _1242720] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242716), _1242718)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242716), _1242720))), -(_1242716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1242718), _1242720)))], (44267 ^ _779571) ^ [_1645218, _1645220, _1645222, _1645224, _1645226, _1645228, _1645230] : [c_Finite__Set_Ofun__left__comm(_1645218, _1645220, _1645222), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1645218, _1645220, _1645222, _1645224, _1645226), _1645228)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1645218, _1645220, _1645222, _1645224, _1645226), _1645230)), -(_1645230 = _1645228)], (6027 ^ _779571) ^ [_876623, _876625] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_876623, _876625)], (42974 ^ _779571) ^ [_1614919, _1614921] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614919, _1614919)), hAPP(hAPP(c_Product__Type_OPair(_1614919, _1614919), _1614921), _1614921)), c_Relation_OId(_1614919))))], (2 ^ _779571) ^ [_779598] : [-(_779598 = _779598)], (42151 ^ _779571) ^ [_1594831, _1594833, _1594835, _1594837] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594831, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594833, _1594831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594833, _1594831), tc_HOL_Obool)), _1594835), _1594837))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1594831, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594833, _1594831), _1594835)), hAPP(c_Relation_ORange(_1594833, _1594831), _1594837)))))], (22091 ^ _779571) ^ [_1161093, _1161095] : [_1161093 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1161093, _1161095) = _1161095)], (45195 ^ _779571) ^ [_1668654, _1668656, _1668658, _1668660, _1668662] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668654, tc_fun(_1668656, tc_HOL_Obool)), _1668658), hAPP(hAPP(c_COMBS(_1668654, tc_fun(_1668656, tc_HOL_Obool), tc_fun(_1668656, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668656, tc_HOL_Obool), tc_fun(tc_fun(_1668656, tc_HOL_Obool), tc_fun(_1668656, tc_HOL_Obool)), _1668654), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668656, tc_HOL_Obool))), _1668660)), _1668662)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668656, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668656, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668654, tc_fun(_1668656, tc_HOL_Obool), _1668660), _1668658))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668656, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668654, tc_fun(_1668656, tc_HOL_Obool), _1668662), _1668658))))], (48728 ^ _779571) ^ [_1756571, _1756573, _1756575, _1756577, _1756579] : [hAPP(hAPP(c_List_Odrop(_1756571), _1756573), _1756575) = hAPP(hAPP(c_List_Olist_OCons(_1756571), _1756577), _1756579), -(hAPP(hAPP(c_List_Onth(_1756571), _1756575), _1756573) = _1756577)], (4004 ^ _779571) ^ [_841261, _841263] : [_841263 = _841261, -(c_Set_OPow(_841263) = c_Set_OPow(_841261))], (18205 ^ _779571) ^ [_1092540] : [-(c_Int_Osucc(_1092540) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092540), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33647 ^ _779571) ^ [_1393840, _1393842] : [-(c_Sum__Type_OPlus(_1393840, _1393842, c_Orderings_Otop__class_Otop(tc_fun(_1393840, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1393842, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1393840, _1393842), tc_HOL_Obool)))], (49487 ^ _779571) ^ [_1773170, _1773172, _1773174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773170), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773172)), _1773174))), -(c_List_Olast(_1773172, hAPP(hAPP(c_List_Odrop(_1773172), _1773170), _1773174)) = c_List_Olast(_1773172, _1773174))], (12323 ^ _779571) ^ [_985356, _985358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985356), _985358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985356)), _985358)))], (51437 ^ _779571) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (39346 ^ _779571) ^ [_1520579, _1520581] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520579), _1520581)), -(hAPP(c_Finite__Set_Ocard(_1520579), _1520581) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1520579, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1520579), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1520581))], (30666 ^ _779571) ^ [_1330486, _1330488, _1330490] : [class_Orderings_Oord(_1330486), 30669 ^ _779571 : [(30676 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330486), _1330488), _1330490)), -(hBOOL(hAPP(hAPP(c_member(_1330486), _1330488), hAPP(c_SetInterval_Oord__class_OatMost(_1330486), _1330490))))], (30670 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330486), _1330488), hAPP(c_SetInterval_Oord__class_OatMost(_1330486), _1330490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330486), _1330488), _1330490)))]]], (38919 ^ _779571) ^ [_1511406, _1511408, _1511410, _1511412, _1511414] : [c_Fun_Oinj__on(_1511406, _1511408, _1511410, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1511406, tc_HOL_Obool)), _1511412), _1511414)), 38922 ^ _779571 : [(38927 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511408, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511406, _1511408, _1511410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511406, tc_HOL_Obool)), _1511412), _1511414))), hAPP(c_Set_Oimage(_1511406, _1511408, _1511410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511406, tc_HOL_Obool)), _1511414), _1511412))) = c_Orderings_Obot__class_Obot(tc_fun(_1511408, tc_HOL_Obool)))], (38925 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1511406, _1511408, _1511410, _1511414))], (38923 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1511406, _1511408, _1511410, _1511412))]]], (31138 ^ _779571) ^ [_1340495] : [31140 ^ _779571 : [(31143 ^ _779571) ^ [_1340605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31139 ^ [_1340495, _1340605]), _1340605))], (31141 ^ _779571) ^ [_1340571] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31139 ^ [_1340495, _1340571]), _1340495)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1340495)))], (46257 ^ _779571) ^ [_1693309, _1693311, _1693313, _1693315, _1693317] : [hBOOL(hAPP(c_List_Odistinct(_1693309), hAPP(hAPP(c_List_Omap(tc_prod(_1693309, _1693311), _1693309), c_Product__Type_Ofst(_1693309, _1693311)), _1693313))), 46260 ^ _779571 : [(46267 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693309, _1693311)), hAPP(hAPP(c_Product__Type_OPair(_1693309, _1693311), _1693317), _1693315)), hAPP(c_List_Oset(tc_prod(_1693309, _1693311)), _1693313))), -(hAPP(c_Option_Ooption_OSome(_1693311), _1693315) = hAPP(c_Map_Omap__of(_1693309, _1693311, _1693313), _1693317))], (46261 ^ _779571) ^ [] : [hAPP(c_Option_Ooption_OSome(_1693311), _1693315) = hAPP(c_Map_Omap__of(_1693309, _1693311, _1693313), _1693317), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693309, _1693311)), hAPP(hAPP(c_Product__Type_OPair(_1693309, _1693311), _1693317), _1693315)), hAPP(c_List_Oset(tc_prod(_1693309, _1693311)), _1693313))))]]], (44588 ^ _779571) ^ [_1653747, _1653749, _1653751, _1653753, _1653755, _1653757] : [-(hAPP(c_Set_Ovimage(_1653747, _1653749, _1653751), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653753, tc_fun(_1653749, tc_HOL_Obool)), _1653755), _1653757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653753, tc_fun(_1653747, tc_HOL_Obool)), _1653755), hAPP(hAPP(c_COMBB(tc_fun(_1653749, tc_HOL_Obool), tc_fun(_1653747, tc_HOL_Obool), _1653753), c_Set_Ovimage(_1653747, _1653749, _1653751)), _1653757)))], (51483 ^ _779571) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (43090 ^ _779571) ^ [_1617818] : [-(c_Transitive__Closure_Ortrancl(_1617818, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1617818, _1617818), tc_HOL_Obool))) = c_Relation_OId(_1617818))], (15326 ^ _779571) ^ [_1038866, _1038868, _1038870] : [class_Groups_Ogroup__add(_1038866), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038866), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038866), _1038868), _1038870)), _1038870) = _1038868)], (29580 ^ _779571) ^ [_1308176, _1308178, _1308180] : [class_Orderings_Oorder(_1308176), 29583 ^ _779571 : [(29590 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308176), _1308178), _1308180))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1308176, _1308178, _1308180) = c_Orderings_Obot__class_Obot(tc_fun(_1308176, tc_HOL_Obool)))], (29584 ^ _779571) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1308176, _1308178, _1308180) = c_Orderings_Obot__class_Obot(tc_fun(_1308176, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308176), _1308178), _1308180))]]], (51183 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (48046 ^ _779571) ^ [_1738784, _1738786, _1738788, _1738790, _1738792, _1738794] : [hAPP(hAPP(c_List_Oappend(_1738784), _1738786), _1738788) = _1738790, _1738792 = hAPP(hAPP(c_List_Oappend(_1738784), _1738788), _1738794), -(hAPP(hAPP(c_List_Oappend(_1738784), _1738786), _1738792) = hAPP(hAPP(c_List_Oappend(_1738784), _1738790), 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c_Nat_Osemiring__1__class_ONats(_830828))], (41652 ^ _779571) ^ [_1581724, _1581726, _1581728, _1581730] : [class_Groups_Ocomm__monoid__add(_1581724), c_Fun_Oinj__on(_1581726, _1581724, _1581728, _1581730), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1581726, _1581724), _1581728), _1581730) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1581724, _1581724), c_Fun_Oid(_1581724)), hAPP(c_Set_Oimage(_1581726, _1581724, _1581728), _1581730)))], (22035 ^ _779571) ^ [_1159970, _1159972, _1159974, _1159976] : [class_Fields_Olinordered__field__inverse__zero(_1159970), class_Int_Onumber(_1159970), 22042 ^ _779571 : [(22043 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159970), _1159972), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))), _1159976)), 22046 ^ _779571 : [(22053 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)))), 22056 ^ _779571 : [(22063 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)), c_Groups_Ozero__class_Ozero(_1159970)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), _1159976)))], (22057 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)), c_Groups_Ozero__class_Ozero(_1159970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159970), _1159976), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))), _1159972)))]]], (22047 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), _1159972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159970), _1159976), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)))))]]], (22069 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159970), _1159972), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))), _1159976))), 22072 ^ _779571 : [(22075 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), _1159972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159970), _1159976), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))))], (22073 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))))]], 22076 ^ _779571 : [(22079 ^ _779571) ^ [] : [22080 ^ _779571 : [(22083 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159970), _1159976), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974))), _1159972))], (22081 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)), c_Groups_Ozero__class_Ozero(_1159970))))]], 22084 ^ _779571 : [(22087 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), _1159976))], (22085 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)), c_Groups_Ozero__class_Ozero(_1159970)))]]], (22077 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159970), c_Groups_Ozero__class_Ozero(_1159970)), hAPP(c_Int_Onumber__class_Onumber__of(_1159970), _1159974)))]]]]], (16295 ^ _779571) ^ [_1058230, _1058232, _1058234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1058232), 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), _1058232), _1058234))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1058230))), _1058234)))], (36402 ^ _779571) ^ [_1455938, _1455940, _1455942, _1455944, _1455946] : [class_Lattices_Olattice(_1455938), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455940, _1455938)), _1455942), _1455944), _1455946) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455938), hAPP(_1455942, _1455946)), hAPP(_1455944, _1455946)))], (45692 ^ _779571) ^ [_1679880, _1679882, _1679884, _1679886, _1679888] : [hBOOL(hAPP(hAPP(c_member(_1679880), _1679882), c_Map_Odom(_1679880, _1679884, _1679886))), -(hAPP(c_Map_Omap__add(_1679880, _1679884, _1679888, _1679886), _1679882) = hAPP(_1679886, _1679882))], (38363 ^ _779571) ^ [_1500208, _1500210, _1500212, _1500214, _1500216, _1500218] : [c_Fun_Oinj__on(_1500208, _1500210, hAPP(c_Fun_Ocomp(_1500212, _1500210, _1500208, _1500214), _1500216), _1500218), -(c_Fun_Oinj__on(_1500212, _1500210, _1500214, hAPP(c_Set_Oimage(_1500208, _1500212, _1500216), _1500218)))], (19171 ^ _779571) ^ [_1108404] : [c_Int_OBit0(_1108404) = c_Int_OPls, -(_1108404 = c_Int_OPls)], (36722 ^ _779571) ^ [_1462542, _1462544, _1462546, _1462548] : [hBOOL(hAPP(hAPP(c_member(_1462542), _1462544), _1462546)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462542, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1462542), _1462544), _1462548)), _1462546) = hAPP(hAPP(c_Set_Oinsert(_1462542), _1462544), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462542, tc_HOL_Obool)), _1462548), _1462546)))], (2720 ^ _779571) ^ [_820801, _820803, _820805, _820807] : [-(c_Nitpick_Onorm__frac(_820807, _820803) = c_Nitpick_Onorm__frac(_820805, _820801)), _820807 = _820805, _820803 = _820801], (10233 ^ _779571) ^ [_950042, _950044] : [class_Rings_Olinordered__idom(_950042), 10236 ^ _779571 : [(10243 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950042), c_Groups_Ozero__class_Ozero(_950042)), _950044)), -(c_Groups_Osgn__class_Osgn(_950042, _950044) = c_Groups_Oone__class_Oone(_950042))], (10237 ^ _779571) ^ [] : [c_Groups_Osgn__class_Osgn(_950042, _950044) = c_Groups_Oone__class_Oone(_950042), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950042), c_Groups_Ozero__class_Ozero(_950042)), _950044)))]]], (6023 ^ _779571) ^ [_876514, _876516, _876518, _876520, _876522] : [c_Com_Ocom_OSemi(_876514, _876516) = c_Com_Ocom_OCond(_876518, _876520, _876522)], (11523 ^ _779571) ^ [_971012, _971014, _971016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _971012), _971014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _971016), _971012)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _971016), _971014))))], (32727 ^ _779571) ^ [_1376622, _1376624] : [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)))), _1376622, _1376624) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376622), _1376624)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376624), _1376622)))], (30429 ^ _779571) ^ [_1325301, _1325303, _1325305] : [_1325305 = hAPP(c_Option_Ooption_OSome(_1325301), _1325303), -(hBOOL(hAPP(hAPP(c_member(_1325301), _1325303), c_Option_Oset(_1325301, _1325305))))], (26466 ^ _779571) ^ [_1244398, _1244400] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1244398)), _1244400))), 26469 ^ _779571 : [(26472 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244398), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244400)))], (26470 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244398)))]], 26473 ^ _779571 : [(26476 ^ _779571) ^ [] : [_1244400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26474 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244398))]]], (51541 ^ _779571) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (12662 ^ _779571) ^ [_991166, _991168, _991170, _991172] : [class_Rings_Olinordered__semiring(_991166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991166), _991168), _991170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991166), _991168), _991172))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991166), c_Groups_Ozero__class_Ozero(_991166)), _991168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991166), _991170), _991172)))], (51521 ^ _779571) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (42870 ^ _779571) ^ [_1611536, _1611538] : [-(hAPP(c_Relation_ORange(_1611536, _1611536), c_Transitive__Closure_Otrancl(_1611536, _1611538)) = hAPP(c_Relation_ORange(_1611536, _1611536), _1611538))], (8880 ^ _779571) ^ [_926743, _926745, _926747, _926749] : [class_Groups_Oab__semigroup__mult(_926743), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926743), _926745), _926747)), _926749) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926743), _926745), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926743), _926747), _926749)))], (31175 ^ _779571) ^ [_1341199, _1341201, _1341203] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341199), _1341201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341199, tc_HOL_Obool)), _1341203), _1341201)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341199), _1341203)))], (29924 ^ _779571) ^ [_1315007, _1315009, _1315011, _1315013, _1315015] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1315007, _1315009, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315007)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315007), hAPP(hAPP(c_COMBC(_1315007, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1315007), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1315011)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1315013)), _1315015))), c_Com_Ocom_OAss(_1315013, _1315015)), _1315011)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315007), tc_HOL_Obool)))))], (48760 ^ _779571) ^ [_1757331, _1757333] : [hBOOL(hAPP(c_List_Odistinct(_1757331), hAPP(c_List_Orotate1(_1757331), _1757333))), -(hBOOL(hAPP(c_List_Odistinct(_1757331), _1757333)))], (24561 ^ _779571) ^ [_1208050, _1208052] : [class_Orderings_Olinorder(_1208050), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208050), _1208052), _1208052) = _1208052)], (25886 ^ _779571) ^ [_1232974, _1232976, _1232978, _1232980] : [class_Rings_Ocomm__ring__1(_1232974), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232974), _1232976), _1232978)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232974), _1232976), _1232980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232974), _1232976), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1232974), _1232978), _1232980))))], (43714 ^ _779571) ^ [_1633390, _1633392, _1633394, _1633396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633390, _1633392), tc_HOL_Obool)), _1633394), _1633396)), c_Relation_Osingle__valued(_1633390, _1633392, _1633396), -(c_Relation_Osingle__valued(_1633390, _1633392, _1633394))], (7858 ^ _779571) ^ [_909951, _909953] : [class_Groups_Olinordered__ab__group__add(_909951), 7861 ^ _779571 : [(7868 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909951), c_Groups_Ozero__class_Ozero(_909951)), _909953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909951), c_Groups_Ozero__class_Ozero(_909951)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909951), _909953), _909953))))], (7862 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909951), c_Groups_Ozero__class_Ozero(_909951)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909951), _909953), _909953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909951), c_Groups_Ozero__class_Ozero(_909951)), _909953)))]]], (1672 ^ _779571) ^ [_803239, _803241] : [-(class_Rings_Osemiring__0(_803239)), _803241 = _803239, class_Rings_Osemiring__0(_803241)], (24033 ^ _779571) ^ [_1197962, _1197964, _1197966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197962, tc_HOL_Obool)), _1197964), _1197966)), 24036 ^ _779571 : [(24039 ^ _779571) ^ [] : [_1197964 = _1197966], (24037 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197962, tc_HOL_Obool)), _1197964), _1197966)))]]], (17807 ^ _779571) ^ [_1086218] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086218)))], (47707 ^ _779571) ^ [_1730762, _1730764, _1730766, _1730768, _1730770] : [-(hAPP(hAPP(c_List_Olist__update(_1730762, hAPP(hAPP(c_List_Olist__update(_1730762, _1730764), _1730766), _1730768)), _1730766), _1730770) = hAPP(hAPP(c_List_Olist__update(_1730762, _1730764), _1730766), _1730770))], (30169 ^ _779571) ^ [_1320285, _1320287] : [_1320287 = c_Orderings_Obot__class_Obot(tc_fun(_1320285, tc_HOL_Obool)), 30172 ^ _779571 : [(30173 ^ _779571) ^ [_1320365] : [hBOOL(hAPP(hAPP(c_member(_1320285), _1320365), _1320287))]]], (6371 ^ _779571) ^ [_883045, _883047, _883049, _883051, _883053, _883055] : [c_Com_Ocom_OCond(_883045, _883047, _883049) = c_Com_Ocom_OLocal(_883051, _883053, _883055)], (13809 ^ _779571) ^ [_1011600, _1011602, _1011604] : [class_Divides_Osemiring__div(_1011600), -(c_Divides_Odiv__class_Omod(_1011600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011600), _1011602), _1011604), _1011602) = c_Groups_Ozero__class_Ozero(_1011600))], (24229 ^ _779571) ^ [_1201779, _1201781, _1201783, _1201785] : [class_Groups_Oordered__ab__group__add(_1201779), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201779), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201779), _1201781), _1201783)), _1201785) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201779), _1201781), _1201785)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201779), _1201783), _1201785)))], (7153 ^ _779571) ^ [_897429, _897431, _897433, _897435] : [class_Rings_Ocomm__semiring__1(_897429), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897429), _897431), _897433)), _897435) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897429), _897431), _897435)), _897433))], (1402 ^ _779571) ^ [_799864, _799866] : [-(class_Groups_Olinordered__ab__semigroup__add(_799864)), _799866 = _799864, class_Groups_Olinordered__ab__semigroup__add(_799866)], (5236 ^ _779571) ^ [_860501, _860503, _860505, _860507] : [-(c_Wellfounded_Oaccp(_860507, _860503) = c_Wellfounded_Oaccp(_860505, _860501)), _860507 = _860505, _860503 = _860501], (34176 ^ _779571) ^ [_1404489, _1404491, _1404493, _1404495, _1404497, _1404499] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404489, _1404491), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404489, _1404491), _1404493), _1404495), _1404497)), _1404495), _1404499) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404489, _1404491), _1404493), _1404495), _1404499))], (47109 ^ _779571) ^ [_1716907, _1716909, _1716911, _1716913] : [class_Groups_Ocomm__monoid__add(_1716907), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1716907), _1716909), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1716911, _1716913))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1716907), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1716907), _1716909), c_List_Oupto(_1716911, _1716913))))], (23617 ^ _779571) ^ [_1189687, _1189689, _1189691] : [class_Orderings_Olinorder(_1189687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189687), _1189689), _1189691)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189687), _1189689), _1189691) = _1189689)], (39340 ^ _779571) ^ [_1520340, _1520342, _1520344, _1520346] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520340), _1520342)), -(hAPP(c_Set_Oimage(_1520340, _1520344, _1520346), _1520342) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1520344, tc_HOL_Obool), _1520340, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520344, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1520340, tc_fun(_1520344, tc_HOL_Obool), tc_fun(_1520344, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1520344, tc_fun(tc_fun(_1520344, tc_HOL_Obool), tc_fun(_1520344, tc_HOL_Obool)), _1520340), c_Set_Oinsert(_1520344)), _1520346)), c_Orderings_Obot__class_Obot(tc_fun(_1520344, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1520344, tc_HOL_Obool))), _1520342))], (48078 ^ _779571) ^ [_1739556, _1739558, _1739560] : [_1739558 = c_List_Olist_ONil(_1739556), -(hAPP(hAPP(c_List_Oappend(_1739556), _1739558), _1739560) = _1739560)], (25586 ^ _779571) ^ [_1227599, _1227601, _1227603, _1227605] : [class_Rings_Ocomm__semiring__1(_1227599), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227599), _1227601), _1227603)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227599), _1227603), _1227605)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227599), _1227601), _1227605)))], (28987 ^ _779571) ^ [_1296446, _1296448, _1296450] : [class_Orderings_Otop(_1296446), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1296448, _1296446)), _1296450) = c_Orderings_Otop__class_Otop(_1296446))], (47342 ^ _779571) ^ [_1721571, _1721573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1721571), _1721573)), -(c_List_Oupto(_1721571, _1721573) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1721571), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1721571), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1721573)))], (22264 ^ _779571) ^ [_1163678, _1163680] : [_1163678 = _1163680, -(hAPP(c_Code__Numeral_Oof__nat, _1163678) = hAPP(c_Code__Numeral_Oof__nat, _1163680))], (25066 ^ _779571) ^ [_1219039, _1219041] : [-(_1219039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25069 ^ _779571 : [(25076 ^ _779571) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1219041) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219039), _1219041)), _1219039)))], (25070 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219039), _1219041)), _1219039)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1219041) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (40851 ^ _779571) ^ [_1556183, _1556185, _1556187, _1556189, _1556191, _1556193, _1556195, _1556197, _1556199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556183, _1556185)), hAPP(hAPP(c_Product__Type_OPair(_1556183, _1556185), _1556187), _1556189)), _1556191)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556193, _1556195)), hAPP(hAPP(c_Product__Type_OPair(_1556193, _1556195), hAPP(_1556197, _1556187)), hAPP(_1556199, _1556189))), hAPP(c_Set_Oimage(tc_prod(_1556183, _1556185), tc_prod(_1556193, _1556195), c_Product__Type_Omap__pair(_1556183, _1556193, _1556185, _1556195, _1556197, _1556199)), _1556191))))], (35203 ^ _779571) ^ [_1427576] : [-(hAPP(c_Set_OPow(_1427576), c_Orderings_Obot__class_Obot(tc_fun(_1427576, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1427576, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1427576, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427576, tc_HOL_Obool), tc_HOL_Obool))))], (29079 ^ _779571) ^ [_1298348, _1298350] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298348, tc_HOL_Obool)), _1298350) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298348, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1298348, tc_HOL_Obool))), _1298350))], (25814 ^ _779571) ^ [_1231679, _1231681] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231679), _1231681)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231679)), _1231681)))], (46865 ^ _779571) ^ [_1710030, _1710032, _1710034, _1710036, _1710038] : [-(hAPP(hAPP(c_List_Omap(_1710030, _1710032), _1710034), hAPP(hAPP(c_List_Olist_OCons(_1710030), _1710036), _1710038)) = hAPP(hAPP(c_List_Olist_OCons(_1710032), hAPP(_1710034, _1710036)), hAPP(hAPP(c_List_Omap(_1710030, _1710032), _1710034), _1710038)))], (51343 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (24075 ^ _779571) ^ [_1198707] : [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), _1198707))), -(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), _1198707)) = 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), _1198707))))], (24973 ^ _779571) ^ [_1217193, _1217195, _1217197, _1217199, _1217201] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1217193, _1217195, tc_HOL_Obool, _1217197), _1217199), _1217201)), -(hBOOL(hAPP(_1217197, hAPP(hAPP(c_Product__Type_OPair(_1217193, _1217195), _1217199), _1217201))))], (26308 ^ _779571) ^ [_1241627, _1241629, _1241631] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241627), _1241629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241627), _1241631))), -(_1241627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241629), _1241631)))], (43844 ^ _779571) ^ [_1636783, _1636785, _1636787, _1636789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636783, _1636783)), hAPP(hAPP(c_Product__Type_OPair(_1636783, _1636783), _1636785), _1636787)), c_Transitive__Closure_Otrancl(_1636783, _1636789))), 43848 ^ _779571 : [(43851 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636783, _1636783)), hAPP(hAPP(c_Product__Type_OPair(_1636783, _1636783), 43847 ^ [_1636783, _1636785, _1636787, _1636789]), _1636787)), _1636789)))], (43849 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636783, _1636783)), hAPP(hAPP(c_Product__Type_OPair(_1636783, _1636783), _1636785), 43847 ^ [_1636783, _1636785, _1636787, _1636789])), c_Transitive__Closure_Ortrancl(_1636783, _1636789))))]]], (2502 ^ _779571) ^ [_817424, _817426, _817428, _817430] : [-(c_Nitpick_Onat__gcd(_817430, _817426) = c_Nitpick_Onat__gcd(_817428, _817424)), _817430 = _817428, _817426 = _817424], (23239 ^ _779571) ^ [_1183359] : [-(_1183359 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1183359), 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)))))], (50716 ^ _779571) ^ [_1799223, _1799225, _1799227] : [-(c_List_Oconcat(_1799223, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1799223)), _1799225), _1799227)) = hAPP(hAPP(c_List_Oappend(_1799223), c_List_Oconcat(_1799223, _1799225)), c_List_Oconcat(_1799223, _1799227)))], (26614 ^ _779571) ^ [_1247650, _1247652, _1247654, _1247656] : [class_Divides_Osemiring__div(_1247650), -(_1247652 = c_Groups_Ozero__class_Ozero(_1247650)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1247650), _1247652), _1247654)), 26625 ^ _779571 : [(26632 ^ _779571) ^ [] : [_1247654 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247650), _1247656), _1247652), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247650), _1247654), _1247652) = _1247656)], (26626 ^ _779571) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247650), _1247654), _1247652) = _1247656, -(_1247654 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247650), _1247656), _1247652))]]], (11392 ^ _779571) ^ [_968671, _968673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968671), _968673)), -(_968671 = _968673), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968671), _968673)))], (25138 ^ _779571) ^ [_1220327, _1220329, _1220331] : [class_Rings_Olinordered__idom(_1220327), 25141 ^ _779571 : [(25148 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220327), _1220329), _1220331)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220327), hAPP(c_Groups_Oabs__class_Oabs(_1220327), _1220329)), _1220331)))], (25142 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220327), hAPP(c_Groups_Oabs__class_Oabs(_1220327), _1220329)), _1220331)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220327), _1220329), _1220331)))]]], (6203 ^ _779571) ^ [_880051, _880053, _880055] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880051, _880053, _880055))), -(hBOOL(hAPP(c_Com_OWT, _880055)))], (4154 ^ _779571) ^ [_843614, _843616, _843618, _843620, _843622, _843624, _843626, _843628, _843630, _843632, _843634, _843636] : [-(c_Map_Omap__comp(_843636, _843632, _843628, _843624, _843620, _843616) = c_Map_Omap__comp(_843634, _843630, _843626, _843622, _843618, _843614)), _843636 = _843634, _843632 = _843630, _843628 = _843626, _843624 = _843622, _843620 = _843618, _843616 = _843614], (44672 ^ _779571) ^ [_1656000, _1656002, _1656004, _1656006, _1656008] : [-(_1656000 = c_Orderings_Obot__class_Obot(tc_fun(_1656002, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656004, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656002, tc_fun(_1656004, tc_HOL_Obool)), _1656000), _1656006)), _1656008) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656002, tc_fun(_1656004, tc_HOL_Obool)), _1656000), hAPP(hAPP(c_COMBC(_1656002, tc_fun(_1656004, tc_HOL_Obool), tc_fun(_1656004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1656004, tc_HOL_Obool), tc_fun(tc_fun(_1656004, tc_HOL_Obool), tc_fun(_1656004, tc_HOL_Obool)), _1656002), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656004, tc_HOL_Obool))), _1656006)), _1656008)))], (4692 ^ _779571) ^ [_852143, _852145, _852147, _852149] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_852149, _852145) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_852147, _852143)), _852149 = _852147, _852145 = _852143], (27462 ^ _779571) ^ [_1264808, _1264810, _1264812, _1264814, _1264816] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264808, tc_HOL_Obool)), _1264810), hAPP(c_Set_Oimage(_1264812, _1264808, _1264814), _1264816)))), 27463 ^ _779571 : [(27464 ^ _779571) ^ [_1264888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264812, tc_HOL_Obool)), _1264888), _1264816)), _1264810 = hAPP(c_Set_Oimage(_1264812, _1264808, _1264814), _1264888)]]], (11473 ^ _779571) ^ [_970121, _970123, _970125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970121), _970123)), _970125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970123), _970125)))], (13896 ^ _779571) ^ [_1013071, _1013073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013071), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13899 ^ _779571 : [(13902 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013071), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013073, _1013071))))], (13900 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013073, _1013071)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25738 ^ _779571) ^ [_1230298, _1230300, _1230302, _1230304] : [class_Rings_Ocomm__semiring__1(_1230298), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230298), _1230300), _1230302)), _1230304)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230298), _1230300), _1230304)))], (47651 ^ _779571) ^ [_1729639, _1729641, _1729643, _1729645, _1729647] : [class_Orderings_Olinorder(_1729639), -(hBOOL(hAPP(hAPP(c_member(_1729639), hAPP(_1729641, _1729643)), hAPP(c_Set_Oimage(_1729645, _1729639, _1729641), hAPP(c_List_Oset(_1729645), _1729647))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1729645, _1729639, _1729641, _1729643, _1729647) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1729645, _1729639, _1729641), _1729643), _1729647))], (58 ^ _779571) ^ [_780342, _780344] : [-(class_Rings_Odivision__ring(_780342)), _780344 = _780342, class_Rings_Odivision__ring(_780344)], (44750 ^ _779571) ^ [_1658421, _1658423, _1658425, _1658427, _1658429] : [-(_1658421 = c_Orderings_Obot__class_Obot(tc_fun(_1658423, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658423, tc_fun(_1658425, tc_HOL_Obool)), _1658421), hAPP(hAPP(c_COMBC(_1658423, tc_fun(_1658425, tc_HOL_Obool), tc_fun(_1658425, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1658425, tc_HOL_Obool), tc_fun(tc_fun(_1658425, tc_HOL_Obool), tc_fun(_1658425, tc_HOL_Obool)), _1658423), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658425, tc_HOL_Obool))), _1658427)), _1658429)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658425, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658423, tc_fun(_1658425, tc_HOL_Obool)), _1658421), _1658427)), _1658429))], (39036 ^ _779571) ^ [] : [-(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))))], (19745 ^ _779571) ^ [_1118197, _1118199, _1118201] : [class_Rings_Oring__1(_1118197), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118197), hAPP(c_Groups_Ouminus__class_Ouminus(_1118197), _1118199)), 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)))), _1118201)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1118197), _1118199), 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)))), _1118201)))], (22826 ^ _779571) ^ [_1175242, _1175244, _1175246] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175242, _1175244), _1175246)), -(c_Divides_Odivmod__nat(_1175242, _1175244) = _1175246)], (29136 ^ _779571) ^ [_1299735, _1299737, _1299739, _1299741] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299735, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29137 ^ [_1299735, _1299737, _1299739, _1299741])), _1299737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299735, 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), 29137 ^ [_1299735, _1299737, _1299739, _1299741]), _1299739))), _1299741), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299735, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299735, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299741))], (2184 ^ _779571) ^ [_812323, _812325, _812327, _812329, _812331, _812333] : [-(c_Sum__Type_OProjr(_812333, _812329, _812325) = c_Sum__Type_OProjr(_812331, _812327, _812323)), _812333 = _812331, _812329 = _812327, _812325 = _812323], (6799 ^ _779571) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25530 ^ _779571) ^ [_1226696, _1226698, _1226700] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226696), _1226698)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226698), _1226696))), 25545 ^ _779571 : [(25548 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226700), _1226696))], (25546 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226696), _1226700)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226698), _1226700)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226700), _1226698)))], (41982 ^ _779571) ^ [_1590903, _1590905, _1590907] : [c_Wellfounded_Owf(_1590903, _1590905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590903, tc_HOL_Obool)), _1590907), hAPP(c_Relation_OImage(_1590903, _1590903, _1590905), _1590907))), -(_1590907 = c_Orderings_Obot__class_Obot(tc_fun(_1590903, tc_HOL_Obool)))], (39162 ^ _779571) ^ [_1516595, _1516597, _1516599, _1516601, _1516603, _1516605, _1516607] : [c_Finite__Set_Ofolding__image__simple(_1516595, _1516597, _1516599, _1516601, _1516603, _1516605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516597), _1516607)), -(hAPP(_1516605, _1516607) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516595, _1516597, _1516599), _1516603), _1516601), _1516607))], (34644 ^ _779571) ^ [_1414138, _1414140, _1414142, _1414144] : [-(hAPP(c_Map_Orestrict__map(_1414138, _1414140, _1414142, c_Orderings_Obot__class_Obot(tc_fun(_1414138, tc_HOL_Obool))), _1414144) = c_Option_Ooption_ONone(_1414140))], (14940 ^ _779571) ^ [_1031808, _1031810, _1031812] : [hBOOL(hAPP(_1031808, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1031810), _1031812))), 14943 ^ _779571 : [(14950 ^ _779571) ^ [] : [-(_1031812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14953 ^ _779571 : [(14954 ^ _779571) ^ [_1032060, _1032062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032060), _1031812)), _1031810 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031812), _1032062)), _1032060), -(hBOOL(hAPP(_1031808, _1032062)))]]], (14944 ^ _779571) ^ [] : [_1031812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1031808, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (21337 ^ _779571) ^ [_1146702, _1146704] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146702), _1146704), hAPP(c_Int_Onumber__class_Onumber__of(_1146702), c_Int_OBit1(c_Int_OPls))) = _1146704), class_Fields_Ofield(_1146702), class_Int_Onumber__ring(_1146702)], (41013 ^ _779571) ^ [_1560508, _1560510, _1560512] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1560508), hAPP(c_Set_OCollect(_1560508), hAPP(hAPP(c_COMBS(_1560508, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560508), c_fdisj), _1560510)), _1560512)))), 41016 ^ _779571 : [(41019 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560508), hAPP(c_Set_OCollect(_1560508), _1560512))))], (41017 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560508), hAPP(c_Set_OCollect(_1560508), _1560510))))]]], (50190 ^ _779571) ^ [_1788370, _1788372] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1788370), _1788372) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1788370, _1788372)))], (45314 ^ _779571) ^ [_1671212, _1671214, _1671216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1671212, tc_HOL_Obool)), _1671214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1671212), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671212, tc_HOL_Obool), _1671214))), 45324 ^ _779571 : [(45327 ^ _779571) ^ [] : [hAPP(c_Finite__Set_Ocard(_1671212), 45323 ^ [_1671212, _1671214, _1671216]) = _1671216], (45325 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1671212, tc_HOL_Obool)), 45323 ^ [_1671212, _1671214, _1671216]), _1671214)))]], 45331 ^ _779571 : [(45335 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1671212, tc_HOL_Obool)), 45333 ^ [_1671212, _1671214, _1671216]), _1671214)))], (45337 ^ _779571) ^ [] : [45330 ^ [_1671212, _1671214, _1671216] = 45333 ^ [_1671212, _1671214, _1671216]], (45339 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671212, tc_HOL_Obool)), 45330 ^ [_1671212, _1671214, _1671216]), 45333 ^ [_1671212, _1671214, _1671216]) = c_Orderings_Obot__class_Obot(tc_fun(_1671212, tc_HOL_Obool))], (45332 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1671212, tc_HOL_Obool)), 45330 ^ [_1671212, _1671214, _1671216]), _1671214)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1671216), hAPP(c_Finite__Set_Ocard(tc_fun(_1671212, tc_HOL_Obool)), _1671214)) = hAPP(c_Finite__Set_Ocard(_1671212), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671212, tc_HOL_Obool), _1671214)))], (22164 ^ _779571) ^ [_1162098] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1162098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1162098)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14343 ^ _779571) ^ [_1021512, _1021514, _1021516] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021512), _1021514)), _1021516) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021512), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021514), _1021516))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021512), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021514, _1021516))), _1021516)))], (36366 ^ _779571) ^ [_1455080, _1455082, _1455084, _1455086] : [class_Lattices_Osemilattice__inf(_1455080), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455080), _1455082), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455080), _1455084), _1455086)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455080), _1455084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455080), _1455082), _1455086)))], (30104 ^ _779571) ^ [_1319100, _1319102, _1319104, _1319106, _1319108, _1319110, _1319112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1319100, _1319102)), hAPP(hAPP(c_Product__Type_OPair(_1319100, _1319102), _1319104), _1319106)), _1319108)), -(hBOOL(hAPP(hAPP(c_member(_1319110), hAPP(hAPP(_1319112, _1319104), _1319106)), hAPP(c_Set_Oimage(tc_prod(_1319100, _1319102), _1319110, hAPP(c_Product__Type_Oprod_Oprod__case(_1319100, _1319102, _1319110), _1319112)), _1319108))))], (39739 ^ _779571) ^ [_1529533, _1529535, _1529537, _1529539, _1529541] : [hAPP(_1529533, _1529535) = hAPP(c_Option_Ooption_OSome(_1529537), _1529539), -(hBOOL(hAPP(hAPP(c_member(_1529541), _1529535), c_Map_Odom(_1529541, _1529537, _1529533))))], (948 ^ _779571) ^ [_794171, _794173, _794175, _794177] : [-(c_List_Olinorder__class_Osorted(_794175, _794171)), c_List_Olinorder__class_Osorted(_794177, _794173), _794177 = _794175, _794173 = _794171], (50280 ^ _779571) ^ [_1789695, _1789697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789695)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789697))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789695), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789697)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789695)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789695)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1789697))))], (42153 ^ _779571) ^ [_1594913, _1594915, _1594917, _1594919] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594913, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594913, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594915, _1594913), _1594917)), hAPP(c_Relation_ORange(_1594915, _1594913), _1594919))), hAPP(c_Relation_ORange(_1594915, _1594913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1594915, _1594913), tc_HOL_Obool)), _1594917), _1594919)))))], (30554 ^ _779571) ^ [_1328181, _1328183, _1328185] : [hBOOL(hAPP(hAPP(c_member(_1328181), _1328183), hAPP(hAPP(c_Set_Oinsert(_1328181), _1328185), c_Orderings_Obot__class_Obot(tc_fun(_1328181, tc_HOL_Obool))))), -(_1328183 = _1328185)], (23345 ^ _779571) ^ [_1184769, _1184771] : [-(_1184769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1184771, _1184769), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1184771), _1184769)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184771, _1184769)))))], (10736 ^ _779571) ^ [_958329, _958331, _958333, _958335] : [class_Orderings_Oorder(_958329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958329), _958331), _958333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958329), _958335), _958331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958329), _958335), _958333)))], (26790 ^ _779571) ^ [_1250943, _1250945, _1250947, _1250949, _1250951] : [class_Orderings_Oorder(_1250943), 26793 ^ _779571 : [(26806 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250943, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1250943, _1250945, _1250947)), c_SetInterval_Oord__class_OatLeastAtMost(_1250943, _1250949, _1250951)))), 26807 ^ _779571 : [(26810 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250949), _1250945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250947), _1250951))], (26808 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250945), _1250947)))]]], (26794 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250943, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1250943, _1250945, _1250947)), c_SetInterval_Oord__class_OatLeastAtMost(_1250943, _1250949, _1250951))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250945), _1250947)), 26801 ^ _779571 : [(26804 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250947), _1250951)))], (26802 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250943), _1250949), _1250945)))]]]]], (51185 ^ _779571) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (34855 ^ _779571) ^ [] : [-(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)))], (41051 ^ _779571) ^ [_1561303, _1561305, _1561307, _1561309, _1561311] : [c_Finite__Set_Ofun__left__comm__idem(_1561303, _1561305, _1561307), -(c_Finite__Set_Ofun__left__comm__idem(_1561309, _1561305, hAPP(hAPP(c_COMBB(_1561303, tc_fun(_1561305, _1561305), _1561309), _1561307), _1561311)))], (6542 ^ _779571) ^ [_886326, _886328, _886330] : [hAPP(c_Com_Ocom_OBODY, _886326) = c_Com_Ocom_OAss(_886328, _886330)], (39236 ^ _779571) ^ [_1518197, _1518199, _1518201, _1518203, _1518205, _1518207] : [class_Groups_Oab__semigroup__mult(_1518197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518199), _1518201)), -(hBOOL(hAPP(hAPP(c_member(_1518199), _1518203), _1518201))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518197, _1518199, c_Groups_Otimes__class_Otimes(_1518197)), _1518205), _1518207), hAPP(hAPP(c_Set_Oinsert(_1518199), _1518203), _1518201)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1518197), hAPP(_1518205, _1518203)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518197, _1518199, c_Groups_Otimes__class_Otimes(_1518197)), _1518205), _1518207), _1518201)))], (40162 ^ _779571) ^ [_1540528, _1540530, _1540532, _1540534, _1540536] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1540528, _1540530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540528, tc_HOL_Obool)), _1540532), _1540534)), hAPP(c_COMBK(tc_fun(_1540530, tc_HOL_Obool), _1540528), _1540536)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540528, _1540530), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1540528, _1540530), _1540532), hAPP(c_COMBK(tc_fun(_1540530, tc_HOL_Obool), _1540528), _1540536))), hAPP(hAPP(c_Product__Type_OSigma(_1540528, _1540530), _1540534), hAPP(c_COMBK(tc_fun(_1540530, tc_HOL_Obool), _1540528), _1540536))))], (47914 ^ _779571) ^ [_1735686, _1735688, _1735690, _1735692, _1735694] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735686), _1735688), _1735690) = hAPP(hAPP(c_List_Oappend(_1735686), _1735692), _1735694)), 47915 ^ _779571 : [(47922 ^ _779571) ^ [_1735869] : [hAPP(hAPP(c_List_Olist_OCons(_1735686), _1735688), _1735869) = _1735692, _1735690 = hAPP(hAPP(c_List_Oappend(_1735686), _1735869), _1735694)], (47916 ^ _779571) ^ [] : [_1735692 = c_List_Olist_ONil(_1735686), hAPP(hAPP(c_List_Olist_OCons(_1735686), _1735688), _1735690) = _1735694]]], (10054 ^ _779571) ^ [_947019, _947021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _947019)), _947021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947019), hAPP(c_Int_Onat, _947021))))], (49634 ^ _779571) ^ [_1776293, _1776295, _1776297] : [-(hAPP(hAPP(c_List_Odrop(_1776293), _1776295), c_List_Obutlast(_1776293, _1776297)) = c_List_Obutlast(_1776293, hAPP(hAPP(c_List_Odrop(_1776293), _1776295), _1776297)))], (41788 ^ _779571) ^ [_1587165, _1587167, _1587169, _1587171, _1587173, _1587175, _1587177, _1587179] : [hBOOL(hAPP(hAPP(_1587165, _1587167), _1587169)), hBOOL(hAPP(hAPP(_1587171, _1587169), _1587173)), -(c_Predicate_Opred__comp(_1587175, _1587177, _1587179, _1587165, _1587171, _1587167, _1587173))], (48467 ^ _779571) ^ [_1748823, _1748825, _1748827, _1748829, _1748831, _1748833] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748823), tc_List_Olist(_1748823))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748823), tc_List_Olist(_1748823)), hAPP(hAPP(c_List_Oappend(_1748823), _1748825), hAPP(hAPP(c_List_Olist_OCons(_1748823), _1748827), c_List_Olist_ONil(_1748823)))), hAPP(hAPP(c_List_Oappend(_1748823), _1748829), hAPP(hAPP(c_List_Olist_OCons(_1748823), _1748831), c_List_Olist_ONil(_1748823))))), c_List_Olistrel1(_1748823, _1748833)))), 48468 ^ _779571 : [(48475 ^ _779571) ^ [] : [_1748825 = _1748829, hBOOL(hAPP(hAPP(c_member(tc_prod(_1748823, _1748823)), hAPP(hAPP(c_Product__Type_OPair(_1748823, _1748823), _1748827), _1748831)), _1748833))], (48469 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748823), tc_List_Olist(_1748823))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748823), tc_List_Olist(_1748823)), _1748825), _1748829)), c_List_Olistrel1(_1748823, _1748833))), _1748827 = _1748831]]], (35211 ^ _779571) ^ [_1427786, _1427788, _1427790] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1427786, tc_HOL_Obool)), _1427788), hAPP(c_Set_OPow(_1427786), _1427790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427786, tc_HOL_Obool)), _1427788), _1427790)))], (2914 ^ _779571) ^ [_823940, _823942, _823944, _823946, _823948, _823950, _823952, _823954, _823956, _823958, _823960, _823962, _823964, _823966] : [-(c_New__Random__Sequence_Oneg__decr__bind(_823966, _823962, _823958, _823954, _823950, _823946, _823942) = c_New__Random__Sequence_Oneg__decr__bind(_823964, _823960, _823956, _823952, _823948, _823944, _823940)), _823966 = _823964, _823962 = _823960, _823958 = _823956, _823954 = _823952, _823950 = _823948, _823946 = _823944, _823942 = _823940], (51145 ^ _779571) ^ [_1808975, _1808977] : [class_Orderings_Otop(_1808975), -(class_Orderings_Otop(tc_fun(_1808977, _1808975)))], (34632 ^ _779571) ^ [_1413964, _1413966, _1413968, _1413970, _1413972] : [hBOOL(hAPP(hAPP(c_member(_1413964), _1413966), _1413968)), -(hAPP(c_Map_Orestrict__map(_1413964, _1413970, _1413972, _1413968), _1413966) = hAPP(_1413972, _1413966))], (32010 ^ _779571) ^ [_1361663, _1361665, _1361667, _1361669, _1361671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1361663, _1361665)), hAPP(hAPP(c_Product__Type_OPair(_1361663, _1361665), _1361669), _1361671)), _1361667)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1361663, _1361665, _1361667), _1361669), _1361671)))], (29143 ^ _779571) ^ [_1300015, _1300017, _1300019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300015, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1300015, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29144 ^ [_1300015, _1300017, _1300019])), _1300017)), _1300019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300015, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1300015, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1300017)), _1300019)))], (10048 ^ _779571) ^ [_946914, _946916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _946914), hAPP(c_Int_Onat, _946916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946914)), _946916)))], (19419 ^ _779571) ^ [_1112643, _1112645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112643)), c_Int_OBit1(_1112645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112643), _1112645)))], (7137 ^ _779571) ^ [_897164, _897166, _897168, _897170] : [class_Groups_Ocancel__semigroup__add(_897164), 7140 ^ _779571 : [(7147 ^ _779571) ^ [] : [_897168 = _897170, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897164), _897166), _897168) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897164), _897166), _897170))], (7141 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897164), _897166), _897168) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897164), _897166), _897170), -(_897168 = _897170)]]], (43504 ^ _779571) ^ [_1627893, _1627895, _1627897] : [43505 ^ _779571 : [(43506 ^ _779571) ^ [_1627969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627893, _1627893)), _1627895), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1627893, _1627893), tc_HOL_Obool), _1627969), _1627897)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627893, _1627893)), _1627895), c_Transitive__Closure_Ortrancl(_1627893, _1627897))))], (25638 ^ _779571) ^ [_1228487, _1228489, _1228491, _1228493] : [class_Divides_Osemiring__div(_1228487), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228487), _1228489), _1228491)), 25645 ^ _779571 : [(25652 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228487), _1228489), _1228493)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228487), _1228489), c_Divides_Odiv__class_Omod(_1228487, _1228493, _1228491))))], (25646 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228487), _1228489), c_Divides_Odiv__class_Omod(_1228487, _1228493, _1228491))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228487), _1228489), _1228493)))]]], (18157 ^ _779571) ^ [_1091903, _1091905] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1091903), _1091905) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18162 ^ _779571 : [(18165 ^ _779571) ^ [] : [-(_1091905 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18163 ^ _779571) ^ [] : [-(_1091903 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18166 ^ _779571 : [(18169 ^ _779571) ^ [] : [-(_1091905 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18167 ^ _779571) ^ [] : [-(_1091903 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (7424 ^ _779571) ^ [_902756] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902756), hAPP(c_Nat_OSuc, _902756))))], (4388 ^ _779571) ^ [_847467, _847469, _847471, _847473, _847475, _847477] : [-(c_List_Oset__Cons(_847477, _847473, _847469) = c_List_Oset__Cons(_847475, _847471, _847467)), _847477 = _847475, _847473 = _847471, _847469 = _847467], (18321 ^ _779571) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (22546 ^ _779571) ^ [_1169776, _1169778, _1169780] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1169776, _1169778, _1169780, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1169778)], (27229 ^ _779571) ^ [_1259794, _1259796, _1259798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259794)), 27232 ^ _779571 : [(27233 ^ _779571) ^ [_1259928] : [27235 ^ _779571 : [(27241 ^ _779571) ^ [] : [-(_1259928 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27237 ^ [_1259794, _1259796, _1259798, _1259928]), 27234 ^ [_1259794, _1259796, _1259798, _1259928]))], (27239 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27237 ^ [_1259794, _1259796, _1259798, _1259928]), _1259796)))], (27236 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27234 ^ [_1259794, _1259796, _1259798, _1259928]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1259794))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259798), _1259928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259928), _1259794))))]]], (32400 ^ _779571) ^ [_1369868, _1369870, _1369872, _1369874, _1369876] : [c_Finite__Set_Ofolding__one(_1369868, _1369870, _1369872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369868), _1369874)), hBOOL(hAPP(hAPP(c_member(_1369868), _1369876), _1369874)), 32411 ^ _779571 : [(32418 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369868, tc_HOL_Obool)), _1369874), hAPP(hAPP(c_Set_Oinsert(_1369868), _1369876), c_Orderings_Obot__class_Obot(tc_fun(_1369868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369868, tc_HOL_Obool))), -(hAPP(_1369872, _1369874) = hAPP(hAPP(_1369870, _1369876), hAPP(_1369872, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369868, tc_HOL_Obool)), _1369874), hAPP(hAPP(c_Set_Oinsert(_1369868), _1369876), c_Orderings_Obot__class_Obot(tc_fun(_1369868, tc_HOL_Obool)))))))], (32412 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369868, tc_HOL_Obool)), _1369874), hAPP(hAPP(c_Set_Oinsert(_1369868), _1369876), c_Orderings_Obot__class_Obot(tc_fun(_1369868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369868, tc_HOL_Obool)), -(hAPP(_1369872, _1369874) = _1369876)]]], (3398 ^ _779571) ^ [_831770, _831772, _831774, _831776, _831778, _831780, _831782, _831784] : [-(c_Sum__Type_OPlus(_831784, _831780, _831776, _831772) = c_Sum__Type_OPlus(_831782, _831778, _831774, _831770)), _831784 = _831782, _831780 = _831778, _831776 = _831774, _831772 = _831770], (6518 ^ _779571) ^ [_885921, _885923, _885925, _885927] : [-(c_Com_Ocom_OAss(_885921, _885923) = c_Com_Ocom_OAss(_885925, _885927)), _885921 = _885925, _885923 = _885927], (27796 ^ _779571) ^ [_1271844, _1271846, _1271848] : [class_Lattices_Olattice(_1271844), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271844), _1271846), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271844), _1271846), _1271848))))], (41358 ^ _779571) ^ [_1569835, _1569837] : [c_Predicate_Oreflp(_1569835, _1569837), -(c_Relation_Orefl__on(_1569835, c_Orderings_Otop__class_Otop(tc_fun(_1569835, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569835, _1569835)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569835, _1569835, tc_HOL_Obool), _1569837))))], (2904 ^ _779571) ^ [_823791, _823793, _823795, _823797] : [-(c_Nitpick_Ouminus__frac(_823797, _823793) = c_Nitpick_Ouminus__frac(_823795, _823791)), _823797 = _823795, _823793 = _823791], (26404 ^ _779571) ^ [_1243372, _1243374, _1243376] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243374), _1243376))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243372), _1243374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243376), _1243374)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243372), _1243376)))], (32359 ^ _779571) ^ [_1368510, _1368512, _1368514, _1368516] : [hBOOL(hAPP(hAPP(c_member(_1368510), _1368512), c_SetInterval_Oord_OatMost(_1368510, _1368514, _1368516))), -(hBOOL(hAPP(hAPP(_1368514, _1368512), _1368516)))], (22097 ^ _779571) ^ [_1161170, _1161172] : [-(_1161170 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1161170, _1161172) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1161170), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1161172)))], (19913 ^ _779571) ^ [_1121672, _1121674] : [class_Int_Onumber__ring(_1121672), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121672), hAPP(c_Int_Onumber__class_Onumber__of(_1121672), 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)))), _1121674)) = c_Groups_Oone__class_Oone(_1121672))], (14528 ^ _779571) ^ [_1024622, _1024624, _1024626] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024622), _1024624)), _1024626) = 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), _1024622), _1024626)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024624), _1024626))), 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, _1024622, _1024626)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024624, _1024626))), _1024626)))], (19183 ^ _779571) ^ [_1108572] : [c_Int_OPls = c_Int_OBit0(_1108572), -(c_Int_OPls = _1108572)], (19975 ^ _779571) ^ [_1122723, _1122725] : [class_Fields_Olinordered__field__inverse__zero(_1122723), class_Int_Onumber__ring(_1122723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122723), c_Groups_Ozero__class_Ozero(_1122723)), _1122725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122723), c_Groups_Ozero__class_Ozero(_1122723)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122723), _1122725), hAPP(c_Int_Onumber__class_Onumber__of(_1122723), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (18615 ^ _779571) ^ [_1098866, _1098868] : [class_Int_Onumber__ring(_1098866), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098866), c_Int_Opred(_1098868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098866), hAPP(c_Groups_Ouminus__class_Ouminus(_1098866), c_Groups_Oone__class_Oone(_1098866))), hAPP(c_Int_Onumber__class_Onumber__of(_1098866), _1098868)))], (7381 ^ _779571) ^ [_902164] : [-(hAPP(c_Com_Obody, _902164) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _902164))))], (22232 ^ _779571) ^ [_1163293] : [-(_1163293 = 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)), _1163293)))], (48132 ^ _779571) ^ [_1740508, _1740510, _1740512] : [_1740512 = c_List_Olist_ONil(_1740510), -(_1740508 = hAPP(hAPP(c_List_Oappend(_1740510), _1740508), _1740512))], (39551 ^ _779571) ^ [_1525322, _1525324, _1525326, _1525328, _1525330] : [c_Fun_Oinj__on(_1525322, _1525324, _1525326, c_Orderings_Otop__class_Otop(tc_fun(_1525322, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525324, tc_HOL_Obool)), _1525328), hAPP(c_Set_Oimage(_1525322, _1525324, _1525326), _1525330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525322, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1525322, _1525324, _1525326), _1525328)), _1525330)))], (8191 ^ _779571) ^ [_915361, _915363, _915365] : [class_Rings_Olinordered__semidom(_915361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915361), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915361), _915363)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915361), _915365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915363), _915365)))], (51209 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (48954 ^ _779571) ^ [_1762061, _1762063, _1762065] : [-(_1762061 = c_List_Olist_ONil(_1762063)), -(hAPP(c_List_Ohd(_1762063), hAPP(hAPP(c_List_Oappend(_1762063), _1762061), _1762065)) = hAPP(c_List_Ohd(_1762063), _1762061))], (12353 ^ _779571) ^ [_985832] : [-(hAPP(c_Nat_OSuc, _985832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985832), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42246 ^ _779571) ^ [_1597245, _1597247] : [-(hAPP(c_Relation_ODomain(_1597245, _1597245), c_Relation_OId__on(_1597245, _1597247)) = _1597247)], (46833 ^ _779571) ^ [_1709397, _1709399, _1709401, _1709403, _1709405, _1709407] : [-(c_List_Olistrelp(_1709397, _1709399, hAPP(hAPP(c_List_Olist_OCons(_1709397), _1709401), _1709403), hAPP(hAPP(c_List_Olist_OCons(_1709397), _1709405), _1709407))), hBOOL(hAPP(hAPP(_1709399, _1709401), _1709405)), c_List_Olistrelp(_1709397, _1709399, _1709403, _1709407)], (45668 ^ _779571) ^ [_1679401, _1679403, _1679405, _1679407, _1679409, _1679411] : [hAPP(_1679401, _1679403) = hAPP(c_Option_Ooption_OSome(_1679405), _1679407), -(hAPP(c_Map_Omap__add(_1679409, _1679405, _1679411, _1679401), _1679403) = hAPP(c_Option_Ooption_OSome(_1679405), _1679407))], (3180 ^ _779571) ^ [_828285, _828287, _828289, _828291] : [-(c_Com_Ocom_OAss(_828291, _828287) = c_Com_Ocom_OAss(_828289, _828285)), _828291 = _828289, _828287 = _828285], (4356 ^ _779571) ^ [_846945, _846947, _846949, _846951, _846953, _846955] : [-(c_Relation_OImage(_846955, _846951, _846947) = c_Relation_OImage(_846953, _846949, _846945)), _846955 = _846953, _846951 = _846949, _846947 = _846945], (25034 ^ _779571) ^ [_1218552, _1218554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218552)), 25037 ^ _779571 : [(25044 ^ _779571) ^ [] : [_1218554 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218554), _1218552)), _1218552)))], (25038 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218554), _1218552)), _1218552)), -(_1218554 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (43385 ^ _779571) ^ [_1624830, _1624832, _1624834, _1624836] : [-(hAPP(c_Relation_Oconverse(_1624830, _1624832), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1624830, _1624832), tc_HOL_Obool)), _1624834), _1624836)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1624832, _1624830), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1624830, _1624832), _1624834)), hAPP(c_Relation_Oconverse(_1624830, _1624832), _1624836)))], (15114 ^ _779571) ^ [_1034994, _1034996] : [-(_1034994 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15117 ^ _779571 : [(15124 ^ _779571) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034996, _1034994) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034996), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1034994)) = 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), _1034996), _1034994))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15118 ^ _779571) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034996, _1034994) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034996), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1034994)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034996), _1034994)))]]], (27415 ^ _779571) ^ [_1263728, _1263730, _1263732, _1263734] : [class_Groups_Ocomm__monoid__add(_1263728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1263730), _1263732)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1263728), _1263734), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1263730, _1263732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1263728), hAPP(_1263734, _1263730)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1263728), _1263734), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1263730, _1263732))))], (30560 ^ _779571) ^ [_1328296, _1328298, _1328300] : [_1328298 = _1328300, -(hBOOL(hAPP(hAPP(c_member(_1328296), _1328298), hAPP(hAPP(c_Set_Oinsert(_1328296), _1328300), c_Orderings_Obot__class_Obot(tc_fun(_1328296, tc_HOL_Obool))))))], (12860 ^ _779571) ^ [_994966, _994968, _994970] : [class_Rings_Olinordered__idom(_994966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994966), c_Groups_Ozero__class_Ozero(_994966)), _994968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994966), c_Groups_Ozero__class_Ozero(_994966)), _994970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994966), _994970), c_Groups_Oone__class_Oone(_994966))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994966), _994970), _994968)), _994968)))], (17831 ^ _779571) ^ [_1086526] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086526)), -(hAPP(c_Int_Onat, _1086526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11200 ^ _779571) ^ [_965495, _965497, _965499] : [_965497 = _965499, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965495)), _965497) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965495)), _965499))], (42478 ^ _779571) ^ [_1602794, _1602796, _1602798, _1602800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1602794), _1602796)), 42484 ^ _779571 : [(42487 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1602798), hAPP(_1602800, 42483 ^ [_1602794, _1602796, _1602798, _1602800])))], (42485 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602794), 42483 ^ [_1602794, _1602796, _1602798, _1602800]), _1602796)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1602798), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1602794, tc_fun(_1602798, tc_HOL_Obool)), _1602796), _1602800))))], (9152 ^ _779571) ^ [_931123, _931125] : [class_Groups_Ogroup__add(_931123), 9155 ^ _779571 : [(9162 ^ _779571) ^ [] : [_931125 = c_Groups_Ozero__class_Ozero(_931123), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931123), _931125) = c_Groups_Ozero__class_Ozero(_931123))], (9156 ^ _779571) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_931123), _931125) = c_Groups_Ozero__class_Ozero(_931123), -(_931125 = c_Groups_Ozero__class_Ozero(_931123))]]], (47378 ^ _779571) ^ [_1722155, _1722157] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1722155), tc_List_Olist(_1722155), c_List_Olistrel(_1722155, _1722157)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1722155)), c_List_Olist_ONil(_1722155)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1722155), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1722155)), c_List_Olist_ONil(_1722155)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1722155), tc_HOL_Obool))))], (25128 ^ _779571) ^ [_1220162, _1220164, _1220166] : [class_Rings_Olinordered__idom(_1220162), hAPP(c_Groups_Oabs__class_Oabs(_1220162), _1220164) = hAPP(c_Groups_Oabs__class_Oabs(_1220162), _1220166), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220162), _1220164), _1220166)))], (15350 ^ _779571) ^ [_1039338, _1039340, _1039342, _1039344] : [class_Divides_Oring__div(_1039338), -(c_Divides_Odiv__class_Omod(_1039338, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039338), _1039340), _1039342), _1039344) = c_Divides_Odiv__class_Omod(_1039338, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039338), c_Divides_Odiv__class_Omod(_1039338, _1039340, _1039344)), _1039342), _1039344))], (39976 ^ _779571) ^ [_1535232, _1535234, _1535236, _1535238, _1535240, _1535242] : [c_Hoare__Mirabelle_Ohoare__derivs(_1535232, _1535234, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1535232)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1535232), _1535236), _1535238), _1535240)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1535232), tc_HOL_Obool)))), 39983 ^ _779571 : [(39986 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1535242, 39981 ^ [_1535232, _1535234, _1535236, _1535238, _1535240, _1535242]), 39982 ^ [_1535232, _1535234, _1535236, _1535238, _1535240, _1535242]))], (39984 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1535240, 39981 ^ [_1535232, _1535234, _1535236, _1535238, _1535240, _1535242]), 39982 ^ [_1535232, _1535234, _1535236, _1535238, _1535240, _1535242])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1535232, _1535234, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1535232)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1535232), _1535236), _1535238), _1535242)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1535232), tc_HOL_Obool)))))], (47559 ^ _779571) ^ [_1727023, _1727025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727023), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1727025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1727025), _1727023)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1727025))))], (6339 ^ _779571) ^ [_882418, _882420] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_882418, _882420))), 6342 ^ _779571 : [(6345 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882420)))], (6343 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882418)))]]], (33477 ^ _779571) ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946] : [c_Nitpick_Ofold__graph_H(_1389934, _1389936, _1389938, _1389940, _1389942, hAPP(hAPP(_1389938, _1389944), _1389946)), 33482 ^ _779571 : [(33485 ^ _779571) ^ [] : [-(hAPP(hAPP(_1389938, _1389944), _1389946) = _1389940)], (33483 ^ _779571) ^ [] : [-(_1389942 = c_Orderings_Obot__class_Obot(tc_fun(_1389934, tc_HOL_Obool)))]], 33488 ^ _779571 : [(33493 ^ _779571) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1389934, _1389936, _1389938, _1389940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389934, tc_HOL_Obool)), _1389942), hAPP(hAPP(c_Set_Oinsert(_1389934), 33486 ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946]), c_Orderings_Obot__class_Obot(tc_fun(_1389934, tc_HOL_Obool)))), 33487 ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946]))], (33491 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389934), 33486 ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946]), _1389942)))], (33489 ^ _779571) ^ [] : [-(hAPP(hAPP(_1389938, _1389944), _1389946) = hAPP(hAPP(_1389938, 33486 ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946]), 33487 ^ [_1389934, _1389936, _1389938, _1389940, _1389942, _1389944, _1389946]))]]], (17623 ^ _779571) ^ [_1082868, _1082870, _1082872] : [class_Rings_Olinordered__semidom(_1082868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082868), c_Groups_Oone__class_Oone(_1082868)), _1082870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082868), c_Groups_Oone__class_Oone(_1082868)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082868), _1082870), hAPP(c_Nat_OSuc, _1082872)))))], (45961 ^ _779571) ^ [_1686078] : [-(hAPP(c_List_Omap(_1686078, _1686078), c_COMBI(_1686078)) = c_Fun_Oid(tc_List_Olist(_1686078)))], (15806 ^ _779571) ^ [_1048029, _1048031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048029), _1048031)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048031), _1048029)), _1048029) = _1048031)], (40869 ^ _779571) ^ [_1556894, _1556896, _1556898] : [-(hAPP(c_Product__Type_Omap__pair(_1556894, _1556894, _1556896, _1556896, c_COMBI(_1556894), c_COMBI(_1556896)), _1556898) = _1556898)], (35223 ^ _779571) ^ [_1428042, _1428044, _1428046] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1428042, tc_HOL_Obool)), _1428044), hAPP(c_Set_OPow(_1428042), _1428046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428042, tc_HOL_Obool)), _1428044), _1428046)))], (19787 ^ _779571) ^ [_1118987, _1118989, _1118991] : [class_Rings_Olinordered__idom(_1118987), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118987), c_Groups_Ozero__class_Ozero(_1118987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118987), hAPP(hAPP(c_Power_Opower__class_Opower(_1118987), _1118989), 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(_1118987), _1118991), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (23471 ^ _779571) ^ [_1187047, _1187049, _1187051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187047, tc_HOL_Obool)), _1187049), _1187051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187047, tc_HOL_Obool)), _1187051), _1187049)), -(_1187049 = _1187051)], (50838 ^ _779571) ^ [_1802503, _1802505, _1802507, _1802509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802503), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802505)), _1802507))), -(hAPP(c_List_Orev(_1802505), hAPP(hAPP(c_List_Olist__update(_1802505, _1802507), _1802503), _1802509)) = hAPP(hAPP(c_List_Olist__update(_1802505, hAPP(c_List_Orev(_1802505), _1802507)), 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(_1802505)), _1802507)), _1802503)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1802509))], (38795 ^ _779571) ^ [_1508757, _1508759, _1508761, _1508763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1508757), hAPP(c_Set_Oimage(_1508759, _1508757, _1508761), _1508763))), hAPP(c_Finite__Set_Ocard(_1508759), _1508763))), c_Fun_Oinj__on(_1508759, _1508757, _1508761, _1508763)], (9380 ^ _779571) ^ [_934979, _934981, _934983, _934985] : [class_Rings_Ocomm__semiring__1(_934979), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934979), _934981), _934983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934979), _934985), _934983)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934979), _934981), _934985)), _934983))], (39423 ^ _779571) ^ [_1522312, _1522314, _1522316, _1522318, _1522320, _1522322] : [-(hAPP(c_Set_Ovimage(_1522312, _1522314, _1522316), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522318, tc_fun(_1522314, tc_HOL_Obool)), _1522320), _1522322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522318, tc_fun(_1522312, tc_HOL_Obool)), _1522320), hAPP(hAPP(c_COMBB(tc_fun(_1522314, tc_HOL_Obool), tc_fun(_1522312, tc_HOL_Obool), _1522318), c_Set_Ovimage(_1522312, _1522314, _1522316)), _1522322)))], (33557 ^ _779571) ^ [_1391963, _1391965, _1391967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1391963, tc_HOL_Obool), tc_fun(_1391963, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1391963, tc_HOL_Obool), tc_fun(_1391963, tc_HOL_Obool)), _1391965), _1391967)), c_Wellfounded_Ofinite__psubset(_1391963))), 33560 ^ _779571 : [(33563 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391963), _1391967)))], (33561 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1391963, tc_HOL_Obool)), _1391965), _1391967)))]]], (8362 ^ _779571) ^ [_918280] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918280) = _918280)], (38719 ^ _779571) ^ [_1507041, _1507043, _1507045, _1507047, _1507049, _1507051] : [c_Fun_Oinj__on(_1507041, _1507043, _1507045, _1507047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507041, tc_HOL_Obool)), _1507049), _1507047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507041, tc_HOL_Obool)), _1507051), _1507047)), -(hAPP(c_Set_Oimage(_1507041, _1507043, _1507045), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507041, tc_HOL_Obool)), _1507049), _1507051)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507043, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1507041, _1507043, _1507045), _1507049)), hAPP(c_Set_Oimage(_1507041, _1507043, _1507045), _1507051)))], (42110 ^ _779571) ^ [_1593863, _1593865] : [-(hAPP(c_Relation_ORange(_1593863, _1593863), c_Relation_OId__on(_1593863, _1593865)) = _1593865)], (40176 ^ _779571) ^ [_1540987, _1540989, _1540991, _1540993] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540987), _1540989)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540991), _1540993)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1540987, _1540991)), hAPP(hAPP(c_Product__Type_OSigma(_1540987, _1540991), _1540989), hAPP(c_COMBK(tc_fun(_1540991, tc_HOL_Obool), _1540987), _1540993)))))], (19153 ^ _779571) ^ [_1108062, _1108064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108062), _1108064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1108062)), c_Int_OBit0(_1108064))))], (42619 ^ _779571) ^ [_1606044, _1606046, _1606048] : [-(hBOOL(hAPP(hAPP(c_member(_1606044), _1606046), c_Wellfounded_Oacc(_1606044, _1606048)))), 42623 ^ _779571 : [(42626 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1606044), 42622 ^ [_1606044, _1606046, _1606048]), c_Wellfounded_Oacc(_1606044, _1606048)))], (42624 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606044, _1606044)), hAPP(hAPP(c_Product__Type_OPair(_1606044, _1606044), 42622 ^ [_1606044, _1606046, _1606048]), _1606046)), _1606048)))]]], (44362 ^ _779571) ^ [_1647081, _1647083, _1647085, _1647087] : [class_Complete__Lattice_Ocomplete__lattice(_1647081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1647083), _1647085)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647083, _1647081), _1647085), _1647087) = hAPP(hAPP(c_Finite__Set_Ofold(_1647083, _1647081, hAPP(hAPP(c_COMBB(_1647081, tc_fun(_1647081, _1647081), _1647083), c_Lattices_Osemilattice__inf__class_Oinf(_1647081)), _1647087)), c_Orderings_Otop__class_Otop(_1647081)), _1647085))], (16531 ^ _779571) ^ [_1062392, _1062394] : [class_Int_Onumber__ring(_1062392), class_Rings_Olinordered__idom(_1062392), 16538 ^ _779571 : [(16545 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062392), hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394)), c_Groups_Ozero__class_Ozero(_1062392)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1062392), hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394)) = hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394))], (16539 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062392), hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394)), c_Groups_Ozero__class_Ozero(_1062392))), -(hAPP(c_Groups_Oabs__class_Oabs(_1062392), hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1062392), hAPP(c_Int_Onumber__class_Onumber__of(_1062392), _1062394)))]]], (20019 ^ _779571) ^ [] : [-(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))], (16813 ^ _779571) ^ [_1067702, _1067704, _1067706, _1067708] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067702), hAPP(c_Int_Onumber__class_Onumber__of(_1067702), _1067704)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067702), _1067706), _1067708)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067702), hAPP(c_Int_Onumber__class_Onumber__of(_1067702), _1067704)), _1067706)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067702), hAPP(c_Int_Onumber__class_Onumber__of(_1067702), _1067704)), _1067708))), class_Int_Onumber(_1067702), class_Rings_Oring(_1067702)], (2350 ^ _779571) ^ [_815058, _815060] : [_815060 = _815058, -(c_Int_Osucc(_815060) = c_Int_Osucc(_815058))], (37106 ^ _779571) ^ [_1471716, _1471718, _1471720, _1471722, _1471724] : [c_Equiv__Relations_Oequiv(_1471716, _1471718, _1471720), hBOOL(hAPP(hAPP(c_member(tc_fun(_1471716, tc_HOL_Obool)), _1471722), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471716), _1471718), _1471720))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1471716, tc_HOL_Obool)), _1471724), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471716), _1471718), _1471720))), -(_1471722 = _1471724), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471716, tc_HOL_Obool)), _1471722), _1471724) = c_Orderings_Obot__class_Obot(tc_fun(_1471716, tc_HOL_Obool)))], (4864 ^ _779571) ^ [_854737, _854739, _854741, _854743] : [-(c_Random_Oselect__weight(_854743, _854739) = c_Random_Oselect__weight(_854741, _854737)), _854743 = _854741, _854739 = _854737], (36308 ^ _779571) ^ [_1453905, _1453907] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453905, tc_HOL_Obool)), _1453907), _1453907) = _1453907)], (24847 ^ _779571) ^ [_1213928, _1213930] : [-(c_Nitpick_Oinverse__frac(_1213928, _1213930) = hAPP(hAPP(c_Nitpick_Ofrac(_1213928), hAPP(c_Nitpick_Odenom(_1213928), _1213930)), hAPP(c_Nitpick_Onum(_1213928), _1213930)))], (31319 ^ _779571) ^ [_1345698, _1345700, _1345702, _1345704, _1345706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345698), _1345700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345702, tc_HOL_Obool)), _1345704), hAPP(c_Set_Oimage(_1345698, _1345702, _1345706), _1345700))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345702), _1345704)))], (45434 ^ _779571) ^ [_1674087, _1674089, _1674091, _1674093] : [class_Orderings_Olinorder(_1674087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1674087), _1674089)), 45444 ^ _779571 : [(45447 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1674087), 45443 ^ [_1674087, _1674089, _1674091, _1674093]), _1674091))], (45445 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1674087), 45443 ^ [_1674087, _1674089, _1674091, _1674093]), _1674089)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1674087), hAPP(hAPP(c_Finite__Set_Ofold(_1674087, _1674087, c_Orderings_Oord__class_Omax(_1674087)), _1674093), _1674089)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1674087), _1674091), _1674093))))], (12634 ^ _779571) ^ [_990628, _990630, _990632, _990634] : [class_Rings_Olinordered__semiring__strict(_990628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990628), _990630), _990632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990628), _990634), _990632))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990628), c_Groups_Ozero__class_Ozero(_990628)), _990632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990628), _990630), _990634)))], (23919 ^ _779571) ^ [_1195696, _1195698, _1195700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195696, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195696, tc_HOL_Obool)), _1195698), _1195700)), _1195698)))], (34108 ^ _779571) ^ [_1403150, _1403152, _1403154] : [class_Groups_Ocomm__monoid__mult(_1403150), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403152, _1403150), hAPP(c_COMBK(_1403150, _1403152), c_Groups_Oone__class_Oone(_1403150))), _1403154) = c_Groups_Oone__class_Oone(_1403150))], (32365 ^ _779571) ^ [_1368619, _1368621, _1368623, _1368625] : [hBOOL(hAPP(hAPP(_1368623, _1368621), _1368625)), -(hBOOL(hAPP(hAPP(c_member(_1368619), _1368621), c_SetInterval_Oord_OatMost(_1368619, _1368623, _1368625))))], (11633 ^ _779571) ^ [_972852, _972854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _972852), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _972852), _972854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _972852))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _972854))))], (23969 ^ _779571) ^ [_1196775, _1196777, _1196779] : [_1196775 = _1196777, 23972 ^ _779571 : [(23975 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196779, tc_HOL_Obool)), _1196777), _1196775)))], (23973 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196779, tc_HOL_Obool)), _1196775), _1196777)))]]], (44970 ^ _779571) ^ [_1663687, _1663689, _1663691] : [44972 ^ _779571 : [(44975 ^ _779571) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663687, tc_HOL_Obool)), 44971 ^ [_1663687, _1663689, _1663691]), _1663691) = c_Orderings_Obot__class_Obot(tc_fun(_1663687, tc_HOL_Obool))], (44973 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1663687, tc_HOL_Obool)), 44971 ^ [_1663687, _1663689, _1663691]), _1663689)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663687, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663687, tc_HOL_Obool), _1663689)), _1663691) = c_Orderings_Obot__class_Obot(tc_fun(_1663687, tc_HOL_Obool)))], (14423 ^ _779571) ^ [_1023029, _1023031, _1023033] : [-(_1023029 = 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), _1023029), _1023031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023029), _1023033)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1023031), _1023033))], (14417 ^ _779571) ^ [_1022920, _1022922, _1022924] : [_1022920 = 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), _1022920), _1022922)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022920), _1022924)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34350 ^ _779571) ^ [_1407719, _1407721, _1407723, _1407725, _1407727] : [class_Rings_Ocomm__semiring__1(_1407719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407721), _1407723)), hBOOL(hAPP(hAPP(c_member(_1407721), _1407725), _1407723)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1407719), hAPP(_1407727, _1407725)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407721, _1407719), _1407727), _1407723))))], (6124 ^ _779571) ^ [_878353, _878355] : [_878353 = _878355, -(hAPP(c_Nat_OSuc, _878353) = hAPP(c_Nat_OSuc, _878355))], (30181 ^ _779571) ^ [_1320525, _1320527] : [-(_1320527 = c_Orderings_Obot__class_Obot(tc_fun(_1320525, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1320525), 30184 ^ [_1320525, _1320527]), _1320527)))], (50260 ^ _779571) ^ [_1789402, _1789404, _1789406] : [class_Orderings_Olinorder(_1789402), c_List_Olinorder__class_Osorted(_1789402, _1789404), -(c_List_Olinorder__class_Osorted(_1789402, hAPP(hAPP(c_List_Otake(_1789402), _1789406), _1789404)))], (42093 ^ _779571) ^ [_1593456, _1593458, _1593460, _1593462] : [42095 ^ _779571 : [(42098 ^ _779571) ^ [] : [c_Wellfounded_Owf(_1593458, hAPP(_1593460, 42094 ^ [_1593456, _1593458, _1593460, _1593462]))], (42096 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1593456, 42094 ^ [_1593456, _1593458, _1593460, _1593462])))]], -(c_Wellfounded_Owf(tc_prod(_1593462, _1593458), c_Recdef_Osame__fst(_1593462, _1593458, _1593456, _1593460)))], (9238 ^ _779571) ^ [_932569, _932571, _932573] : [class_Groups_Ogroup__add(_932569), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932569), _932571), _932573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932569), hAPP(c_Groups_Ouminus__class_Ouminus(_932569), _932573)), hAPP(c_Groups_Ouminus__class_Ouminus(_932569), _932571)))], (1732 ^ _779571) ^ [_803989, _803991] : [-(class_Power_Opower(_803989)), _803991 = _803989, class_Power_Opower(_803991)], (2036 ^ _779571) ^ [_809841, _809843] : [_809843 = _809841, -(c_Com_Ocom_Ocom__size(_809843) = c_Com_Ocom_Ocom__size(_809841))], (45774 ^ _779571) ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681550, _1681552)), _1681554), hAPP(hAPP(c_Relation_Orel__comp(_1681550, _1681556, _1681552), _1681558), _1681560))), 45780 ^ _779571 : [(45785 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681556, _1681552)), hAPP(hAPP(c_Product__Type_OPair(_1681556, _1681552), 45778 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560]), 45779 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560])), _1681560)))], (45783 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681550, _1681556)), hAPP(hAPP(c_Product__Type_OPair(_1681550, _1681556), 45777 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560]), 45778 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560])), _1681558)))], (45781 ^ _779571) ^ [] : [-(_1681554 = hAPP(hAPP(c_Product__Type_OPair(_1681550, _1681552), 45777 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560]), 45779 ^ [_1681550, _1681552, _1681554, _1681556, _1681558, _1681560]))]]], (38943 ^ _779571) ^ [_1512012, _1512014, _1512016, _1512018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512012), _1512014)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512016), _1512018)), 38950 ^ _779571 : [(38951 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1512012), _1512014)), hAPP(c_Finite__Set_Ocard(_1512016), _1512018)))), 38952 ^ _779571 : [(38953 ^ _779571) ^ [_1512223] : [c_Fun_Oinj__on(_1512012, _1512016, _1512223, _1512014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512016, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512012, _1512016, _1512223), _1512014)), _1512018))]]], (38961 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1512012), _1512014)), hAPP(c_Finite__Set_Ocard(_1512016), _1512018))), 38965 ^ _779571 : [(38968 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512016, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512012, _1512016, 38964 ^ [_1512012, _1512014, _1512016, _1512018]), _1512014)), _1512018)))], (38966 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1512012, _1512016, 38964 ^ [_1512012, _1512014, _1512016, _1512018], _1512014))]]]]], (17513 ^ _779571) ^ [_1080787, _1080789, _1080791] : [class_Groups_Omonoid__mult(_1080787), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1080787), _1080789), hAPP(c_Nat_OSuc, _1080791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080787), hAPP(hAPP(c_Power_Opower__class_Opower(_1080787), _1080789), _1080791)), _1080789))], (28004 ^ _779571) ^ [_1275707, _1275709, _1275711, _1275713] : [class_Lattices_Osemilattice__sup(_1275707), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275707), _1275709), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275707), _1275711), _1275713)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275707), _1275711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275707), _1275709), _1275713)))], (32502 ^ _779571) ^ [_1371910, _1371912, _1371914, _1371916, _1371918, _1371920, _1371922, _1371924] : [c_Finite__Set_Ofolding__image__simple(_1371910, _1371912, _1371914, _1371916, _1371918, _1371920), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371912), _1371922)), -(hAPP(_1371920, hAPP(hAPP(c_Set_Oinsert(_1371912), _1371924), _1371922)) = hAPP(hAPP(_1371914, hAPP(_1371918, _1371924)), hAPP(_1371920, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371912, tc_HOL_Obool)), _1371922), hAPP(hAPP(c_Set_Oinsert(_1371912), _1371924), c_Orderings_Obot__class_Obot(tc_fun(_1371912, tc_HOL_Obool)))))))], (12369 ^ _779571) ^ [_986085] : [-(hBOOL(hAPP(_986085, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12376 ^ [_986085])))), 12370 ^ _779571 : [(12371 ^ _779571) ^ [_986137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986137)), hBOOL(hAPP(_986085, _986137))]]], (27614 ^ _779571) ^ [_1267934, _1267936, _1267938] : [-(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)), _1267934)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1267936, _1267938)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1267936), _1267934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1267938), _1267934)))], (51571 ^ _779571) ^ [_1813084, _1813086, _1813088, _1813090] : [-(hAPP(hAPP(c_COMBK(_1813084, _1813086), _1813088), _1813090) = _1813088)], (28148 ^ _779571) ^ [_1278750, _1278752, _1278754, _1278756] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278750, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278750, tc_HOL_Obool)), _1278752), _1278754)), _1278756) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278750, tc_HOL_Obool)), _1278752), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278750, tc_HOL_Obool)), _1278754), _1278756)))], (30963 ^ _779571) ^ [_1337045] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1337045))))], (48196 ^ _779571) ^ [_1741760, _1741762, _1741764, _1741766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741762)), _1741764))), -(hAPP(hAPP(c_List_Onth(_1741762), hAPP(hAPP(c_List_Oappend(_1741762), _1741764), _1741766)), _1741760) = hAPP(hAPP(c_List_Onth(_1741762), _1741764), _1741760))], (4422 ^ _779571) ^ [_847986, _847988, _847990, _847992, _847994, _847996, _847998, _848000] : [-(c_Product__Type_Oscomp(_848000, _847996, _847992, _847988) = c_Product__Type_Oscomp(_847998, _847994, _847990, _847986)), _848000 = _847998, _847996 = _847994, _847992 = _847990, _847988 = _847986], (35563 ^ _779571) ^ [_1436142, _1436144] : [-(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), _1436142), _1436144)), 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), _1436144), _1436142)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (2390 ^ _779571) ^ [_815662, _815664, _815666, _815668] : [-(c_Random_Oinc__shift(_815668, _815664) = c_Random_Oinc__shift(_815666, _815662)), _815668 = _815666, _815664 = _815662], (25440 ^ _779571) ^ [_1225226, _1225228] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225226), _1225228))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225226), _1225228)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225228), _1225226)))], (28803 ^ _779571) ^ [_1291547, _1291549, _1291551, _1291553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291547, _1291549)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291551, _1291553)))), 28804 ^ _779571 : [(28807 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291551), _1291547)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291549), _1291553))], (28805 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1291547), _1291549)))]]], (31309 ^ _779571) ^ [_1345574, _1345576, _1345578, _1345580] : [class_Groups_Ocomm__monoid__add(_1345574), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345576), _1345578))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345576, _1345574), _1345580), _1345578) = c_Groups_Ozero__class_Ozero(_1345574))], (44522 ^ _779571) ^ [_1651795, _1651797, _1651799, _1651801, _1651803, _1651805] : [class_Complete__Lattice_Ocomplete__lattice(_1651795), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651797, tc_fun(_1651799, _1651795)), _1651801), _1651803), _1651805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651797, _1651795), _1651801), hAPP(hAPP(c_COMBC(_1651797, _1651799, _1651795), _1651803), _1651805)))], (7798 ^ _779571) ^ [_908875, _908877, _908879] : [class_Groups_Oordered__comm__monoid__add(_908875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908875), _908877), c_Groups_Ozero__class_Ozero(_908875))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908875), _908879), c_Groups_Ozero__class_Ozero(_908875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908875), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908875), _908877), _908879)), c_Groups_Ozero__class_Ozero(_908875))))], (40494 ^ _779571) ^ [_1548389, _1548391, _1548393] : [class_Lattices_Oab__semigroup__idem__mult(_1548389), -(_1548391 = c_Orderings_Obot__class_Obot(tc_fun(_1548389, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548389), _1548391)), -(hAPP(c_Finite__Set_Ofold1(_1548389, c_Groups_Otimes__class_Otimes(_1548389)), hAPP(hAPP(c_Set_Oinsert(_1548389), _1548393), _1548391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1548389), _1548393), hAPP(c_Finite__Set_Ofold1(_1548389, c_Groups_Otimes__class_Otimes(_1548389)), _1548391)))], (17217 ^ _779571) ^ [_1075653, _1075655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075653)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075653), _1075655)))], (5430 ^ _779571) ^ [_863524, _863526] : [_863526 = _863524, -(c_List_Odistinct(_863526) = c_List_Odistinct(_863524))], (22430 ^ _779571) ^ [_1167087, _1167089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167087)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167089))), -(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(_1167089))), 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), _1167087)), c_Int_Onat))))))], (3672 ^ _779571) ^ [_836141, _836143] : [_836143 = _836141, -(c_Int_Oint__ge__less__than2(_836143) = c_Int_Oint__ge__less__than2(_836141))], (45343 ^ _779571) ^ [_1671994, _1671996] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1671994, tc_HOL_Obool), _1671996) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1671994, tc_HOL_Obool), tc_fun(_1671994, tc_HOL_Obool)), _1671996), c_COMBI(tc_fun(_1671994, tc_HOL_Obool))))], (1472 ^ _779571) ^ [_800739, _800741] : [-(class_Groups_Ocancel__semigroup__add(_800739)), _800741 = _800739, class_Groups_Ocancel__semigroup__add(_800741)], (15524 ^ _779571) ^ [_1042580, _1042582, _1042584] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042580), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042582, _1042584)), _1042584) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042580), _1042582), _1042584))], (48562 ^ _779571) ^ [_1751652, _1751654, _1751656, _1751658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751652), tc_List_Olist(_1751652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751652), tc_List_Olist(_1751652)), _1751654), _1751656)), c_List_Olistrel1(_1751652, hAPP(c_Relation_Oconverse(_1751652, _1751652), _1751658)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751652), tc_List_Olist(_1751652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751652), tc_List_Olist(_1751652)), _1751654), _1751656)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1751652), tc_List_Olist(_1751652)), c_List_Olistrel1(_1751652, _1751658)))))], (30724 ^ _779571) ^ [_1331481, _1331483, _1331485, _1331487, _1331489, _1331491] : [hBOOL(hAPP(hAPP(c_member(_1331481), _1331483), _1331485)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331481, tc_fun(_1331487, tc_HOL_Obool)), _1331485), hAPP(hAPP(c_COMBB(tc_fun(_1331487, tc_HOL_Obool), tc_fun(_1331487, tc_HOL_Obool), _1331481), hAPP(c_Set_Oinsert(_1331487), _1331489)), _1331491)) = hAPP(hAPP(c_Set_Oinsert(_1331487), _1331489), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1331481, tc_fun(_1331487, tc_HOL_Obool)), _1331485), _1331491)))], (39711 ^ _779571) ^ [_1529068, _1529070, _1529072, _1529074] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529068, _1529070, _1529072, _1529074, c_Orderings_Obot__class_Obot(tc_fun(_1529068, tc_HOL_Obool))), _1529074)))], (41338 ^ _779571) ^ [_1569052, _1569054, _1569056, _1569058, _1569060, _1569062] : [-(hBOOL(hAPP(hAPP(c_member(_1569052), _1569054), _1569056))), -(hAPP(c_Fun_Ooverride__on(_1569052, _1569058, _1569060, _1569062, _1569056), _1569054) = hAPP(_1569060, _1569054))], (46290 ^ _779571) ^ [_1694058, _1694060] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1694058, _1694060) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1694058), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1694060)))], (16036 ^ _779571) ^ [_1053029, _1053031, _1053033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053029), _1053031)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053031), _1053029))), _1053033) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1053031)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053029), _1053033)))], (23989 ^ _779571) ^ [_1197126, _1197128, _1197130, _1197132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1197126, tc_HOL_Obool)), _1197128), _1197130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197126, tc_HOL_Obool)), _1197130), _1197132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1197126, tc_HOL_Obool)), _1197128), _1197132)))], (14393 ^ _779571) ^ [_1022478, _1022480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022478)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022478), _1022480)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1022478)), hAPP(c_Int_Onat, _1022480)))], (28605 ^ _779571) ^ [_1287568, _1287570] : [class_Orderings_Olinorder(_1287568), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1287568, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1287568), _1287570)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1287568), _1287570))], (32831 ^ _779571) ^ [_1378635, _1378637, _1378639] : [class_Rings_Oring__1(_1378635), hBOOL(hAPP(hAPP(c_member(_1378635), _1378637), c_Int_Oring__1__class_OInts(_1378635))), hBOOL(hAPP(hAPP(c_member(_1378635), _1378639), c_Int_Oring__1__class_OInts(_1378635))), -(hBOOL(hAPP(hAPP(c_member(_1378635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1378635), _1378637), _1378639)), c_Int_Oring__1__class_OInts(_1378635))))], (49981 ^ _779571) ^ [_1784667, _1784669, _1784671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1784667), _1784669)), _1784671)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1784669), c_List_Oupt(_1784667, _1784671)) = c_List_Oupt(_1784667, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1784667), _1784669)))], (24743 ^ _779571) ^ [_1211639, _1211641] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1211639), _1211641) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211639)), hAPP(c_Code__Numeral_Onat__of, _1211641))))], (48387 ^ _779571) ^ [_1746828, _1746830, _1746832, _1746834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746828), _1746830)), -(hAPP(hAPP(c_List_Onth(_1746832), hAPP(hAPP(c_List_Otake(_1746832), _1746830), _1746834)), _1746828) = hAPP(hAPP(c_List_Onth(_1746832), _1746834), _1746828))], (2466 ^ _779571) ^ [_816868, _816870, _816872, _816874, _816876, _816878, _816880, _816882] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_816882, _816878, _816874, _816870) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_816880, _816876, _816872, _816868)), _816882 = _816880, _816878 = _816876, _816874 = _816872, _816870 = _816868], (9704 ^ _779571) ^ [_940881, _940883, _940885] : [class_Rings_Olinordered__semiring__strict(_940881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940881), c_Groups_Ozero__class_Ozero(_940881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940881), _940883), _940885))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940881), c_Groups_Ozero__class_Ozero(_940881)), _940885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940881), c_Groups_Ozero__class_Ozero(_940881)), _940883)))], (36156 ^ _779571) ^ [_1450347, _1450349, _1450351, _1450353] : [hBOOL(hAPP(hAPP(c_member(_1450347), _1450349), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450347, tc_HOL_Obool)), _1450351), _1450353))), 36159 ^ _779571 : [(36162 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450347), _1450349), _1450353)))], (36160 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450347), _1450349), _1450351)))]]], (24685 ^ _779571) ^ [_1210629] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1210629)) = _1210629)], (48220 ^ _779571) ^ [_1742303, _1742305, _1742307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742303), tc_List_Olist(_1742303))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742303), tc_List_Olist(_1742303)), _1742305), c_List_Olist_ONil(_1742303))), c_List_Olexord(_1742303, _1742307)))], (30748 ^ _779571) ^ [_1332298, _1332300, _1332302, _1332304, _1332306] : [hBOOL(hAPP(hAPP(c_member(_1332298), _1332300), _1332302)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332304, tc_HOL_Obool)), hAPP(_1332306, _1332300)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332298, tc_fun(_1332304, tc_HOL_Obool)), _1332302), _1332306)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332298, tc_fun(_1332304, tc_HOL_Obool)), _1332302), _1332306))], (40623 ^ _779571) ^ [_1550716, _1550718, _1550720] : [class_Orderings_Olinorder(_1550716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550716), _1550718)), -(_1550718 = c_Orderings_Obot__class_Obot(tc_fun(_1550716, tc_HOL_Obool))), 40634 ^ _779571 : [(40635 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550716), _1550720), hAPP(c_Finite__Set_Ofold1(_1550716, c_Orderings_Oord__class_Omin(_1550716)), _1550718))), 40638 ^ _779571 : [(40639 ^ _779571) ^ [_1551009] : [hBOOL(hAPP(hAPP(c_member(_1550716), _1551009), _1550718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550716), _1550720), _1551009)))]]], (40645 ^ _779571) ^ [] : [40647 ^ _779571 : [(40650 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550716), _1550720), 40646 ^ [_1550716, _1550718, _1550720]))], (40648 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550716), 40646 ^ [_1550716, _1550718, _1550720]), _1550718)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1550716), _1550720), hAPP(c_Finite__Set_Ofold1(_1550716, c_Orderings_Oord__class_Omin(_1550716)), _1550718))))]]], (26890 ^ _779571) ^ [_1252904, _1252906, _1252908, _1252910] : [class_Groups_Ocomm__monoid__add(_1252904), 26893 ^ _779571 : [(26900 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252906)), _1252908))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252904), _1252910), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1252908, hAPP(c_Nat_OSuc, _1252906))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252904), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252904), _1252910), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1252908, _1252906))), hAPP(_1252910, hAPP(c_Nat_OSuc, _1252906))))], (26894 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252906)), _1252908)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252904), _1252910), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1252908, hAPP(c_Nat_OSuc, _1252906))) = c_Groups_Ozero__class_Ozero(_1252904))]]], (41217 ^ _779571) ^ [_1564733, _1564735] : [-(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), _1564733)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1564735))))))], (1892 ^ _779571) ^ [_806979, _806981, _806983, _806985, _806987, _806989, _806991, _806993] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_806993, _806989, _806985, _806981) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_806991, _806987, _806983, _806979)), _806993 = _806991, _806989 = _806987, _806985 = _806983, _806981 = _806979], (17633 ^ _779571) ^ [_1083057, _1083059, _1083061, _1083063] : [class_Rings_Olinordered__semidom(_1083057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083059), _1083061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083057), c_Groups_Oone__class_Oone(_1083057)), _1083063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083057), hAPP(hAPP(c_Power_Opower__class_Opower(_1083057), _1083063), _1083059)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083057), _1083063), _1083061))))], (29188 ^ _779571) ^ [_1301029, _1301031, _1301033] : [hAPP(hAPP(c_Set_Oinsert(_1301029), _1301031), _1301033) = c_Orderings_Obot__class_Obot(tc_fun(_1301029, tc_HOL_Obool))], (47693 ^ _779571) ^ [_1730409, _1730411, _1730413] : [-(hAPP(hAPP(c_List_Olist__update(_1730409, c_List_Olist_ONil(_1730409)), _1730411), _1730413) = c_List_Olist_ONil(_1730409))], (47430 ^ _779571) ^ [_1723817, _1723819, _1723821, _1723823] : [-(hAPP(hAPP(c_List_Onth(_1723817), hAPP(hAPP(c_List_Olist_OCons(_1723817), _1723819), _1723821)), hAPP(c_Nat_OSuc, _1723823)) = hAPP(hAPP(c_List_Onth(_1723817), _1723821), _1723823))], (6130 ^ _779571) ^ [_878453] : [hAPP(c_Nat_OSuc, _878453) = _878453], (29656 ^ _779571) ^ [_1309578, _1309580] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309578, _1309580) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1309578), _1309580))], (28244 ^ _779571) ^ [_1280696, _1280698, _1280700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280696, tc_HOL_Obool)), _1280698), _1280700)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280696, tc_HOL_Obool)), _1280698), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280696, tc_HOL_Obool)), _1280700), _1280698)) = _1280700)], (12317 ^ _779571) ^ [_985253, _985255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985253), _985255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985253), hAPP(c_Nat_OSuc, _985255))))], (34387 ^ _779571) ^ [_1408412, _1408414, _1408416, _1408418, _1408420] : [class_Groups_Ocomm__monoid__mult(_1408412), class_Rings_Odvd(_1408412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408414), _1408416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408414, tc_HOL_Obool)), _1408418), _1408416)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1408412), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408414, _1408412), _1408420), _1408418)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408414, _1408412), _1408420), _1408416))))], (8179 ^ _779571) ^ [_915170, _915172] : [class_Rings_Olinordered__semidom(_915170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915170), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915170), _915172)), c_Groups_Ozero__class_Ozero(_915170)))], (41634 ^ _779571) ^ [_1581377, _1581379, _1581381] : [-(hAPP(c_Fun_Ocomp(_1581377, _1581379, _1581377, _1581381), c_Fun_Oid(_1581377)) = _1581381)], (25310 ^ _779571) ^ [_1223148, _1223150] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223148), _1223150)), 25315 ^ _779571 : [(25318 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223150), _1223148))], (25316 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223148), _1223150)))]], -(_1223148 = _1223150)], (40232 ^ _779571) ^ [_1542538, _1542540, _1542542, _1542544, _1542546, _1542548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542538, _1542540)), hAPP(hAPP(c_Product__Type_OPair(_1542538, _1542540), _1542542), _1542544)), hAPP(hAPP(c_Product__Type_OSigma(_1542538, _1542540), _1542546), _1542548))), 40235 ^ _779571 : [(40238 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542540), _1542544), hAPP(_1542548, _1542542))))], (40236 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542538), _1542542), _1542546)))]]], (16665 ^ _779571) ^ [_1064799, _1064801, _1064803] : [class_Groups_Oordered__ab__group__add__abs(_1064799), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064799), hAPP(c_Groups_Oabs__class_Oabs(_1064799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064799), hAPP(c_Groups_Oabs__class_Oabs(_1064799), _1064801)), hAPP(c_Groups_Oabs__class_Oabs(_1064799), _1064803)))), hAPP(c_Groups_Oabs__class_Oabs(_1064799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064799), _1064801), _1064803)))))], (27490 ^ _779571) ^ [_1265435, _1265437, _1265439, _1265441, _1265443, _1265445] : [-(hAPP(c_Set_Oimage(_1265435, _1265437, _1265439), hAPP(c_Set_Oimage(_1265441, _1265435, _1265443), _1265445)) = hAPP(c_Set_Oimage(_1265441, _1265437, hAPP(hAPP(c_COMBB(_1265435, _1265437, _1265441), _1265439), _1265443)), _1265445))], (34190 ^ _779571) ^ [_1404827, _1404829, _1404831, _1404833, _1404835, _1404837] : [_1404827 = _1404829, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404831, _1404833), _1404835), _1404829), _1404837), _1404827) = _1404837)], (30538 ^ _779571) ^ [_1327795, _1327797, _1327799, _1327801, _1327803] : [-(hBOOL(hAPP(hAPP(c_member(_1327795), _1327797), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327799, tc_fun(_1327795, tc_HOL_Obool)), _1327801), _1327803)))), 30539 ^ _779571 : [(30540 ^ _779571) ^ [_1327877] : [hBOOL(hAPP(hAPP(c_member(_1327799), _1327877), _1327801)), hBOOL(hAPP(hAPP(c_member(_1327795), _1327797), hAPP(_1327803, _1327877)))]]], (11008 ^ _779571) ^ [_962322, _962324, _962326] : [class_Orderings_Olinorder(_962322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962322), _962324), _962326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962322), _962326), _962324)))], (47524 ^ _779571) ^ [_1726142, _1726144, _1726146] : [_1726142 = _1726144, 47527 ^ _779571 : [(47530 ^ _779571) ^ [_1726290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726146)), _1726142))), -(hAPP(hAPP(c_List_Onth(_1726146), _1726142), _1726290) = hAPP(hAPP(c_List_Onth(_1726146), _1726144), _1726290))], (47528 ^ _779571) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726146)), _1726142) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726146)), _1726144))]]], (1692 ^ _779571) ^ [_803489, _803491] : [-(class_Orderings_Oorder(_803489)), _803491 = _803489, class_Orderings_Oorder(_803491)], (24733 ^ _779571) ^ [_1211458] : [class_Orderings_Olinorder(_1211458), -(c_Orderings_Oord_Omax(_1211458, hAPP(c_COMBC(_1211458, _1211458, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1211458))) = c_Orderings_Oord__class_Omin(_1211458))], (40977 ^ _779571) ^ [_1559468, _1559470, _1559472] : [hBOOL(hAPP(_1559468, _1559470)), -(hBOOL(hAPP(hAPP(c_member(_1559472), _1559470), hAPP(c_Set_OCollect(_1559472), _1559468))))], (47729 ^ _779571) ^ [_1731279, _1731281, _1731283, _1731285] : [-(hAPP(hAPP(c_List_Olist__update(_1731279, hAPP(hAPP(c_List_Olist_OCons(_1731279), _1731281), _1731283)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1731285) = hAPP(hAPP(c_List_Olist_OCons(_1731279), _1731285), _1731283))], (48232 ^ _779571) ^ [_1742713, _1742715, _1742717, _1742719] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742713), tc_List_Olist(_1742713))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742713), tc_List_Olist(_1742713)), _1742715), _1742717)), c_List_Olex(_1742713, _1742719)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742713), tc_List_Olist(_1742713))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742713), tc_List_Olist(_1742713)), _1742715), _1742717)), c_List_Olexord(_1742713, _1742719))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742713)), _1742715) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742713)), _1742717)], (43036 ^ _779571) ^ [_1616443, _1616445, _1616447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616443, _1616443), tc_HOL_Obool)), _1616445), _1616447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616443, _1616443), tc_HOL_Obool)), _1616447), c_Transitive__Closure_Ortrancl(_1616443, _1616445))), -(c_Transitive__Closure_Ortrancl(_1616443, _1616447) = c_Transitive__Closure_Ortrancl(_1616443, _1616445))], (39775 ^ _779571) ^ [_1530301, _1530303] : [-(c_Map_Odom(_1530301, _1530303, hAPP(c_COMBK(tc_Option_Ooption(_1530303), _1530301), c_Option_Ooption_ONone(_1530303))) = c_Orderings_Obot__class_Obot(tc_fun(_1530301, tc_HOL_Obool)))], (39028 ^ _779571) ^ [_1513922, _1513924] : [-(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)), _1513922), _1513924))], (19263 ^ _779571) ^ [_1109925, _1109927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1109925)), c_Int_OBit1(_1109927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109925), _1109927)))], (8860 ^ _779571) ^ [_926229, _926231, _926233, _926235, _926237] : [class_Rings_Ocomm__semiring__1(_926229), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), _926231), _926233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), _926235), _926237)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), _926231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), _926233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926229), _926235), _926237))))], (47436 ^ _779571) ^ [_1723971, _1723973, _1723975, _1723977, _1723979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723971), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723973)), _1723975))), -(hAPP(hAPP(c_List_Onth(_1723977), hAPP(hAPP(c_List_Omap(_1723973, _1723977), _1723979), _1723975)), _1723971) = hAPP(_1723979, hAPP(hAPP(c_List_Onth(_1723973), _1723975), _1723971)))], (37916 ^ _779571) ^ [_1491391, _1491393, _1491395, _1491397, _1491399] : [c_Relation_Orefl__on(_1491391, _1491393, _1491395), c_Relation_Orefl__on(_1491391, _1491397, _1491399), -(c_Relation_Orefl__on(_1491391, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491391, tc_HOL_Obool)), _1491393), _1491397), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1491391, _1491391), tc_HOL_Obool)), _1491395), _1491399)))], (50956 ^ _779571) ^ [_1805804, _1805806, _1805808] : [c_List_OtakeWhile(_1805804, _1805806, _1805808) = _1805808, 50959 ^ _779571 : [(50960 ^ _779571) ^ [_1805891] : [hBOOL(hAPP(hAPP(c_member(_1805804), _1805891), hAPP(c_List_Oset(_1805804), _1805808))), -(hBOOL(hAPP(_1805806, _1805891)))]]], (41009 ^ _779571) ^ [_1560381, _1560383, _1560385, _1560387] : [-(hAPP(c_Set_Ovimage(_1560381, _1560383, _1560385), hAPP(c_Set_OCollect(_1560383), _1560387)) = hAPP(c_Set_OCollect(_1560381), hAPP(hAPP(c_COMBB(_1560383, tc_HOL_Obool, _1560381), _1560387), _1560385)))], (1082 ^ _779571) ^ [_795864, _795866] : [-(class_Rings_Olinordered__idom(_795864)), _795866 = _795864, class_Rings_Olinordered__idom(_795866)], (49118 ^ _779571) ^ [_1765071, _1765073, _1765075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1765071), _1765073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1765071), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765073), _1765075))))], (33427 ^ _779571) ^ [_1389023, _1389025] : [class_Groups_Olinordered__ab__group__add(_1389023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389023), _1389025)), -(_1389025 = c_Orderings_Obot__class_Obot(tc_fun(_1389023, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1389023), c_Big__Operators_Olinorder__class_OMax(_1389023, _1389025)) = c_Big__Operators_Olinorder__class_OMin(_1389023, hAPP(c_Set_Oimage(_1389023, _1389023, c_Groups_Ouminus__class_Ouminus(_1389023)), _1389025)))], (27660 ^ _779571) ^ [_1268878, _1268880, _1268882, _1268884, _1268886] : [c_Hoare__Mirabelle_Ohoare__valids(_1268878, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1268878), tc_HOL_Obool)), _1268880), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1268878), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), hAPP(hAPP(c_COMBB(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1268878)), _1268882)), c_Com_Ocom_OBODY)), _1268884)), _1268886)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1268878), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), hAPP(hAPP(c_COMBB(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1268878)), _1268882)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1268884)), _1268886)), -(c_Hoare__Mirabelle_Ohoare__valids(_1268878, _1268880, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1268878), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), hAPP(hAPP(c_COMBB(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1268878, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1268878))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1268878)), _1268882)), c_Com_Ocom_OBODY)), _1268884)), _1268886)))], (32789 ^ _779571) ^ [_1377820, _1377822, _1377824] : [class_Orderings_Olinorder(_1377820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377820), _1377822)), hBOOL(hAPP(hAPP(c_member(_1377820), _1377824), _1377822)), 32800 ^ _779571 : [(32807 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377820, tc_HOL_Obool)), _1377822), hAPP(hAPP(c_Set_Oinsert(_1377820), _1377824), c_Orderings_Obot__class_Obot(tc_fun(_1377820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377820, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1377820, _1377822) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377820), _1377824), c_Big__Operators_Olinorder__class_OMax(_1377820, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377820, tc_HOL_Obool)), _1377822), hAPP(hAPP(c_Set_Oinsert(_1377820), _1377824), c_Orderings_Obot__class_Obot(tc_fun(_1377820, tc_HOL_Obool)))))))], (32801 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377820, tc_HOL_Obool)), _1377822), hAPP(hAPP(c_Set_Oinsert(_1377820), _1377824), c_Orderings_Obot__class_Obot(tc_fun(_1377820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377820, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1377820, _1377822) = _1377824)]]], (3782 ^ _779571) ^ [_837890, _837892] : [_837892 = _837890, -(c_New__Random__Sequence_Oneg__single(_837892) = c_New__Random__Sequence_Oneg__single(_837890))], (2648 ^ _779571) ^ [_819713, _819715] : [_819715 = _819713, -(c_Nitpick_Ozero__frac(_819715) = c_Nitpick_Ozero__frac(_819713))], (15130 ^ _779571) ^ [_1035268, _1035270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1035268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035268), _1035270)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1035270), _1035268) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035270), _1035268)), _1035268)))], (26216 ^ _779571) ^ [_1239982, _1239984, _1239986, _1239988, _1239990] : [class_Rings_Ocomm__semiring__1(_1239982), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239982), hAPP(hAPP(c_Power_Opower__class_Opower(_1239982), _1239984), _1239986)), _1239988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1239990), _1239986)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239982), hAPP(hAPP(c_Power_Opower__class_Opower(_1239982), _1239984), _1239990)), _1239988)))], (31097 ^ _779571) ^ [_1339665, _1339667, _1339669, _1339671, _1339673, _1339675, _1339677] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339665, tc_fun(_1339667, tc_fun(_1339669, tc_HOL_Obool))), _1339671), _1339673), _1339675), _1339677))), 31098 ^ _779571 : [(31099 ^ _779571) ^ [_1339750] : [hBOOL(hAPP(hAPP(c_member(_1339665), _1339750), _1339671)), hBOOL(hAPP(hAPP(hAPP(_1339673, _1339750), _1339675), _1339677))]]], (8972 ^ _779571) ^ [_928325] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928325), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _928325)], (47697 ^ _779571) ^ [_1730541, _1730543, _1730545, _1730547, _1730549, _1730551] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1730541, _1730543), hAPP(hAPP(c_List_Ozip(_1730541, _1730543), _1730545), _1730547)), _1730549), _1730551) = hAPP(hAPP(c_List_Ozip(_1730541, _1730543), hAPP(hAPP(c_List_Olist__update(_1730541, _1730545), _1730549), hAPP(c_Product__Type_Ofst(_1730541, _1730543), _1730551))), hAPP(hAPP(c_List_Olist__update(_1730543, _1730547), _1730549), hAPP(c_Product__Type_Osnd(_1730541, _1730543), _1730551))))], (30977 ^ _779571) ^ [_1337258] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337258), c_Orderings_Obot__class_Obot(tc_fun(_1337258, tc_HOL_Obool)))))], (30866 ^ _779571) ^ [_1335115, _1335117, _1335119, _1335121] : [-(hBOOL(hAPP(hAPP(c_member(_1335115), _1335117), _1335119))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335115, tc_Nat_Onat), _1335121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335115, tc_HOL_Obool)), _1335119), hAPP(hAPP(c_Set_Oinsert(_1335115), _1335117), c_Orderings_Obot__class_Obot(tc_fun(_1335115, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335115, tc_Nat_Onat), _1335121), _1335119))], (39603 ^ _779571) ^ [_1526690, _1526692, _1526694] : [class_Lattices_Olattice(_1526690), hAPP(_1526692, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1526690), 39608 ^ [_1526690, _1526692, _1526694]), 39609 ^ [_1526690, _1526692, _1526694])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1526690), hAPP(_1526692, 39608 ^ [_1526690, _1526692, _1526694])), hAPP(_1526692, 39609 ^ [_1526690, _1526692, _1526694])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526690), _1526694)), -(_1526694 = c_Orderings_Obot__class_Obot(tc_fun(_1526690, tc_HOL_Obool))), -(hAPP(_1526692, c_Big__Operators_Olattice__class_OInf__fin(_1526690, _1526694)) = c_Big__Operators_Olattice__class_OInf__fin(_1526690, hAPP(c_Set_Oimage(_1526690, _1526690, _1526692), _1526694)))], (11911 ^ _779571) ^ [_977989, _977991, _977993] : [class_Rings_Oordered__ring(_977989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977989), _977991), c_Groups_Ozero__class_Ozero(_977989))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977989), _977993), c_Groups_Ozero__class_Ozero(_977989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977989), c_Groups_Ozero__class_Ozero(_977989)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977989), _977991), _977993))))], (35537 ^ _779571) ^ [_1435446, _1435448, _1435450, _1435452, _1435454] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1435450, _1435446)), hAPP(hAPP(c_Product__Type_OPair(_1435450, _1435446), _1435454), _1435448)), _1435452)), -(hBOOL(hAPP(hAPP(c_member(_1435446), _1435448), hAPP(c_Relation_OImage(_1435450, _1435446, _1435452), hAPP(hAPP(c_Set_Oinsert(_1435450), _1435454), c_Orderings_Obot__class_Obot(tc_fun(_1435450, tc_HOL_Obool)))))))], (41722 ^ _779571) ^ [_1583997, _1583999, _1584001, _1584003] : [hAPP(hAPP(c_Relation_Orel__comp(_1583997, _1583997, _1583997), _1583999), _1584001) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583997, _1583997), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583997, _1583997, _1583997), _1584003), _1584001) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583997, _1583997), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1583997, _1583997, _1583997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583997, _1583997), tc_HOL_Obool)), _1583999), _1584003)), _1584001) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583997, _1583997), tc_HOL_Obool)))], (41798 ^ _779571) ^ [_1587348] : [-(c_Wellfounded_Owf(_1587348, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587348, _1587348), tc_HOL_Obool))))], (50626 ^ _779571) ^ [_1797396, _1797398] : [c_List_Olist_ONil(_1797396) = c_List_Oconcat(_1797396, _1797398), 50629 ^ _779571 : [(50630 ^ _779571) ^ [_1797487] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1797396)), _1797487), hAPP(c_List_Oset(tc_List_Olist(_1797396)), _1797398))), -(_1797487 = c_List_Olist_ONil(_1797396))]]], (7584 ^ _779571) ^ [_905413, _905415, _905417, _905419] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_905413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905413), _905415), _905417)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905413), _905415), _905419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905413), _905417), _905419)))], (12970 ^ _779571) ^ [_996811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996811), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _996811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43395 ^ _779571) ^ [_1625074, _1625076] : [c_Wellfounded_Oacyclic(_1625074, _1625076), -(c_Wellfounded_Oacyclic(_1625074, hAPP(c_Relation_Oconverse(_1625074, _1625074), _1625076)))], (46700 ^ _779571) ^ [_1704380, _1704382, _1704384, _1704386] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704380)), _1704382) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704384)), _1704386), hBOOL(hAPP(c_List_Odistinct(_1704380), _1704382)), -(c_Map_Odom(_1704380, _1704384, c_Map_Omap__of(_1704380, _1704384, hAPP(hAPP(c_List_Ozip(_1704380, _1704384), _1704382), _1704386))) = hAPP(c_List_Oset(_1704380), _1704382))], (11402 ^ _779571) ^ [_968783, _968785] : [11403 ^ _779571 : [(11406 ^ _779571) ^ [] : [_968783 = _968785], (11404 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968783), _968785))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968783), _968785)))], (6560 ^ _779571) ^ [_886638] : [hAPP(c_Nat_OSuc, _886638) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34469 ^ _779571) ^ [_1410242, _1410244, _1410246, _1410248, _1410250] : [class_Groups_Ocomm__monoid__mult(_1410242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410244), _1410246)), -(hBOOL(hAPP(hAPP(c_member(_1410244), _1410248), _1410246))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410244, _1410242), _1410250), hAPP(hAPP(c_Set_Oinsert(_1410244), _1410248), _1410246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410242), hAPP(_1410250, _1410248)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410244, _1410242), _1410250), _1410246)))], (6766 ^ _779571) ^ [_890798, _890800, _890802] : [-(c_Nat_Onat_Onat__case(_890798, _890800, _890802, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _890800)], (48090 ^ _779571) ^ [_1739770, _1739772, _1739774] : [_1739774 = c_List_Olist_ONil(_1739770), -(hAPP(hAPP(c_List_Oappend(_1739770), _1739772), _1739774) = _1739772)], (35347 ^ _779571) ^ [_1430843, _1430845, _1430847, _1430849] : [c_Finite__Set_Ofolding__one__idem(_1430843, _1430845, _1430847), -(hAPP(hAPP(_1430845, _1430849), _1430849) = _1430849)], (41189 ^ _779571) ^ [_1563967, _1563969, _1563971] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1563967, tc_HOL_Obool)), _1563969), _1563971) = hAPP(c_Set_OCollect(_1563967), hAPP(hAPP(c_COMBS(_1563967, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563967), c_fconj), hAPP(hAPP(c_COMBC(_1563967, tc_fun(_1563967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563967)), _1563969))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563967), c_fNot), hAPP(hAPP(c_COMBC(_1563967, tc_fun(_1563967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563967)), _1563971)))))], (3082 ^ _779571) ^ [_826806, _826808] : [_826808 = _826806, -(c_DSequence_Ounion(_826808) = c_DSequence_Ounion(_826806))], (38401 ^ _779571) ^ [_1500929, _1500931, _1500933, _1500935, _1500937] : [c_Fun_Oinj__on(_1500929, _1500931, _1500933, _1500935), -(c_Fun_Oinj__on(_1500929, _1500931, _1500933, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500929, tc_HOL_Obool)), _1500935), _1500937)))], (51263 ^ _779571) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (7994 ^ _779571) ^ [_912205, _912207] : [-(hAPP(c_Option_Othe(_912205), hAPP(c_Option_Ooption_OSome(_912205), _912207)) = _912207)], (46434 ^ _779571) ^ [_1697738, _1697740, _1697742] : [class_Orderings_Olinorder(_1697738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1697738), _1697740)), -(c_List_Olinorder__class_Osorted__list__of__set(_1697738, hAPP(hAPP(c_Set_Oinsert(_1697738), _1697742), _1697740)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697738, _1697738, c_COMBI(_1697738)), _1697742), c_List_Olinorder__class_Osorted__list__of__set(_1697738, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1697738, tc_HOL_Obool)), _1697740), hAPP(hAPP(c_Set_Oinsert(_1697738), _1697742), c_Orderings_Obot__class_Obot(tc_fun(_1697738, tc_HOL_Obool)))))))], (19293 ^ _779571) ^ [_1110436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1110436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1110436))))], (14507 ^ _779571) ^ [_1024270, _1024272] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024270, _1024272) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1024270 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024272), 14510 ^ [_1024270, _1024272]))], (22310 ^ _779571) ^ [_1164527, _1164529] : [-(c_Divides_Odivmod__nat(_1164527, _1164529) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1164527), _1164529)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1164527, _1164529)))], (12532 ^ _779571) ^ [] : [-(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)))], (23135 ^ _779571) ^ [_1181059, _1181061] : [-(_1181059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1181061, _1181059) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1181061), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1181059)))], (16639 ^ _779571) ^ [_1064182, _1064184, _1064186, _1064188, _1064190] : [class_Rings_Olinordered__idom(_1064182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064182), hAPP(c_Groups_Oabs__class_Oabs(_1064182), _1064184)), _1064186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064182), hAPP(c_Groups_Oabs__class_Oabs(_1064182), _1064188)), _1064190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064182), hAPP(c_Groups_Oabs__class_Oabs(_1064182), _1064184)), hAPP(c_Groups_Oabs__class_Oabs(_1064182), _1064188))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064182), _1064186), _1064190))))], (47320 ^ _779571) ^ [_1721133, _1721135] : [-(c_List_Osublist(_1721133, _1721135, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1721133))], (10088 ^ _779571) ^ [_947649] : [class_Rings_Olinordered__semidom(_947649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947649), c_Groups_Ozero__class_Ozero(_947649)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947649), c_Groups_Oone__class_Oone(_947649)), c_Groups_Oone__class_Oone(_947649)))))], (13703 ^ _779571) ^ [_1009369, _1009371, _1009373, _1009375] : [class_Divides_Osemiring__div(_1009369), -(c_Divides_Odiv__class_Omod(_1009369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009369), c_Divides_Odiv__class_Omod(_1009369, _1009371, _1009373)), _1009375), _1009373) = c_Divides_Odiv__class_Omod(_1009369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009369), _1009371), _1009375), _1009373))], (19827 ^ _779571) ^ [_1119864, _1119866, _1119868] : [class_Rings_Olinordered__idom(_1119864), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119864), c_Groups_Ozero__class_Ozero(_1119864)), hAPP(hAPP(c_Power_Opower__class_Opower(_1119864), _1119866), 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)))), _1119868)))))], (50562 ^ _779571) ^ [_1795656] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1795656)), c_List_Otranspose__rel(_1795656)), c_List_Olist_ONil(tc_List_Olist(_1795656)))), -(c_List_Otranspose(_1795656, c_List_Olist_ONil(tc_List_Olist(_1795656))) = c_List_Olist_ONil(tc_List_Olist(_1795656)))], (22388 ^ _779571) ^ [_1166160, _1166162] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166160) = hAPP(c_Nat_OSuc, _1166162), -(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(_1166160))), 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)), _1166162))))))], (2788 ^ _779571) ^ [_821855, _821857, _821859, _821861, _821863, _821865] : [-(c_Nitpick_Otimes__frac(_821865, _821861, _821857) = c_Nitpick_Otimes__frac(_821863, _821859, _821855)), _821865 = _821863, _821861 = _821859, _821857 = _821855], (36232 ^ _779571) ^ [_1452308, _1452310] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452308, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1452308, tc_HOL_Obool))), _1452310) = c_Orderings_Obot__class_Obot(tc_fun(_1452308, tc_HOL_Obool)))], (18959 ^ _779571) ^ [_1104537, _1104539] : [class_Int_Onumber__ring(_1104537), class_Rings_Olinordered__idom(_1104537), 18966 ^ _779571 : [(18973 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104539), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104537), hAPP(c_Int_Onumber__class_Onumber__of(_1104537), _1104539)), c_Groups_Oone__class_Oone(_1104537))))], (18967 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104537), hAPP(c_Int_Onumber__class_Onumber__of(_1104537), _1104539)), c_Groups_Oone__class_Oone(_1104537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104539), c_Int_OBit1(c_Int_OPls))))]]], (48208 ^ _779571) ^ [_1742016, _1742018, _1742020, _1742022, _1742024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742018)), _1742020))), -(hAPP(hAPP(c_List_Olist__update(_1742018, hAPP(hAPP(c_List_Oappend(_1742018), _1742020), _1742022)), _1742016), _1742024) = hAPP(hAPP(c_List_Oappend(_1742018), hAPP(hAPP(c_List_Olist__update(_1742018, _1742020), _1742016), _1742024)), _1742022))], (15018 ^ _779571) ^ [_1033323, _1033325, _1033327] : [-(hBOOL(hAPP(_1033323, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1033325, _1033327)))), 15021 ^ _779571 : [(15024 ^ _779571) ^ [] : [hBOOL(hAPP(_1033323, _1033325))], (15022 ^ _779571) ^ [] : [-(_1033327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15025 ^ _779571 : [(15030 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15028 ^ [_1033323, _1033325, _1033327]), _1033327)))], (15032 ^ _779571) ^ [] : [-(_1033325 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033327), 15027 ^ [_1033323, _1033325, _1033327])), 15028 ^ [_1033323, _1033325, _1033327]))], (15034 ^ _779571) ^ [] : [hBOOL(hAPP(_1033323, 15028 ^ [_1033323, _1033325, _1033327]))], (15026 ^ _779571) ^ [] : [_1033327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (46688 ^ _779571) ^ [_1704165, _1704167, _1704169] : [hBOOL(hAPP(hAPP(c_member(_1704165), _1704167), hAPP(c_List_Oset(_1704165), _1704169))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704165)), c_List_Oremove1(_1704165, _1704167, _1704169)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704165)), _1704169)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (34261 ^ _779571) ^ [_1406054, _1406056, _1406058] : [class_Groups_Ocomm__monoid__mult(_1406054), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406056, _1406054), _1406058), c_Orderings_Obot__class_Obot(tc_fun(_1406056, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1406054))], (44925 ^ _779571) ^ [_1662309, _1662311, _1662313, _1662315, _1662317, _1662319, _1662321] : [44927 ^ _779571 : [(44930 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1662317, 44926 ^ [_1662309, _1662311, _1662313, _1662315, _1662317, _1662319, _1662321]), _1662319), _1662321))], (44928 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1662309), 44926 ^ [_1662309, _1662311, _1662313, _1662315, _1662317, _1662319, _1662321]), _1662315)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662309, tc_fun(_1662311, tc_fun(_1662313, tc_HOL_Obool))), _1662315), _1662317), _1662319), _1662321)))], (27037 ^ _779571) ^ [_1255976, _1255978, _1255980, _1255982, _1255984] : [class_Orderings_Olinorder(_1255976), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255976, _1255978), _1255980) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255976, _1255982), _1255984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255976), _1255978), _1255980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255976), _1255982), _1255984)), -(_1255980 = _1255984)], (26378 ^ _779571) ^ [_1242848, _1242850, _1242852] : [26379 ^ _779571 : [(26382 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1242850), _1242852))], (26380 ^ _779571) ^ [] : [_1242848 = 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), _1242848), _1242850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242848), _1242852))))], (46953 ^ _779571) ^ [_1712177, _1712179, _1712181, _1712183, _1712185, _1712187] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712177), tc_List_Olist(_1712177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712177), tc_List_Olist(_1712177)), hAPP(hAPP(c_List_Olist_OCons(_1712177), _1712179), _1712181)), hAPP(hAPP(c_List_Olist_OCons(_1712177), _1712183), _1712185))), c_List_Olex(_1712177, _1712187)))), 46954 ^ _779571 : [(46961 ^ _779571) ^ [] : [_1712179 = _1712183, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712177), tc_List_Olist(_1712177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712177), tc_List_Olist(_1712177)), _1712181), _1712185)), c_List_Olex(_1712177, _1712187)))], (46955 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712177, _1712177)), hAPP(hAPP(c_Product__Type_OPair(_1712177, _1712177), _1712179), _1712183)), _1712187)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712177)), _1712181) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712177)), _1712185)]]], (46039 ^ _779571) ^ [_1688264, _1688266, _1688268, _1688270, _1688272] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688264), tc_Option_Ooption(_1688266), tc_Option_Ooption(_1688268), hAPP(c_Option_Omap(_1688264, _1688266), _1688270)), hAPP(c_Option_Omap(_1688268, _1688264), _1688272)) = hAPP(c_Option_Omap(_1688268, _1688266), hAPP(c_Fun_Ocomp(_1688264, _1688266, _1688268, _1688270), _1688272)))], (34587 ^ _779571) ^ [_1412918, _1412920, _1412922, _1412924] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412918, tc_Option_Ooption(_1412920)), hAPP(c_COMBK(tc_Option_Ooption(_1412920), _1412918), c_Option_Ooption_ONone(_1412920))), _1412922), c_Option_Ooption_ONone(_1412920)), _1412924) = c_Option_Ooption_ONone(_1412920))], (14922 ^ _779571) ^ [_1031391, _1031393, _1031395] : [class_Divides_Osemiring__div(_1031391), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031391), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031391), _1031393), _1031395)), _1031395)), c_Divides_Odiv__class_Omod(_1031391, _1031393, _1031395)) = _1031393)], (29614 ^ _779571) ^ [_1308712, _1308714, _1308716, _1308718] : [-(_1308712 = c_Orderings_Obot__class_Obot(tc_fun(_1308714, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1308714, _1308716, hAPP(c_COMBK(_1308716, _1308714), _1308718)), _1308712) = hAPP(hAPP(c_Set_Oinsert(_1308716), _1308718), c_Orderings_Obot__class_Obot(tc_fun(_1308716, tc_HOL_Obool))))], (20255 ^ _779571) ^ [_1127911, _1127913, _1127915, _1127917] : [class_Fields_Olinordered__field(_1127911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127911), _1127913), _1127915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127911), c_Groups_Ozero__class_Ozero(_1127911)), _1127917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127911), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127911), _1127913), _1127917)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127911), _1127915), _1127917))))], (14758 ^ _779571) ^ [_1028339, _1028341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028339), _1028341)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028339), _1028341) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40120 ^ _779571) ^ [_1539151, _1539153, _1539155, _1539157, _1539159] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1539151, _1539153), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1539151, tc_HOL_Obool)), _1539155), _1539157)), _1539159) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1539151, _1539153), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539151, _1539153), _1539155), _1539159)), hAPP(hAPP(c_Product__Type_OSigma(_1539151, _1539153), _1539157), _1539159)))], (27774 ^ _779571) ^ [_1271369, _1271371, _1271373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271369, tc_HOL_Obool)), _1271371), _1271373)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271369, tc_HOL_Obool)), _1271371), _1271373) = _1271373)], (34196 ^ _779571) ^ [_1404936, _1404938, _1404940, _1404942, _1404944, _1404946] : [-(_1404936 = _1404938), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404940, _1404942), _1404944), _1404938), _1404946), _1404936) = hAPP(_1404944, _1404936))], (18253 ^ _779571) ^ [_1093247, _1093249] : [class_Int_Onumber__ring(_1093247), 18256 ^ _779571 : [(18263 ^ _779571) ^ [] : [c_Int_Oiszero(_1093247, hAPP(c_Int_Onumber__class_Onumber__of(_1093247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093249), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1093247), _1093249) = c_Groups_Ozero__class_Ozero(_1093247))], (18257 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1093247), _1093249) = c_Groups_Ozero__class_Ozero(_1093247), -(c_Int_Oiszero(_1093247, hAPP(c_Int_Onumber__class_Onumber__of(_1093247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093249), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (44960 ^ _779571) ^ [_1663419, _1663421, _1663423] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663419, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663419, tc_HOL_Obool), _1663421)), _1663423) = c_Orderings_Obot__class_Obot(tc_fun(_1663419, tc_HOL_Obool)), 44963 ^ _779571 : [(44964 ^ _779571) ^ [_1663554] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1663419, tc_HOL_Obool)), _1663554), _1663421)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663419, tc_HOL_Obool)), _1663554), _1663423) = c_Orderings_Obot__class_Obot(tc_fun(_1663419, tc_HOL_Obool)))]]], (38469 ^ _779571) ^ [_1502356, _1502358] : [c_Equiv__Relations_Oequivp(_1502356, _1502358), 38472 ^ _779571 : [(38479 ^ _779571) ^ [_1502549, _1502551] : [hAPP(_1502358, _1502551) = hAPP(_1502358, _1502549), -(hBOOL(hAPP(hAPP(_1502358, _1502551), _1502549)))], (38473 ^ _779571) ^ [_1502450, _1502452] : [hBOOL(hAPP(hAPP(_1502358, _1502452), _1502450)), -(hAPP(_1502358, _1502452) = hAPP(_1502358, _1502450))]]], (11348 ^ _779571) ^ [] : [-(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))))], (6728 ^ _779571) ^ [_889900] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _889900), _889900)))], (45451 ^ _779571) ^ [_1674451, _1674453, _1674455, _1674457] : [class_Orderings_Olinorder(_1674451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1674451), _1674453)), 45461 ^ _779571 : [(45464 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1674451), _1674455), 45460 ^ [_1674451, _1674453, _1674455, _1674457]))], (45462 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1674451), 45460 ^ [_1674451, _1674453, _1674455, _1674457]), _1674453)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1674451), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1674451), _1674455), _1674457)), hAPP(hAPP(c_Finite__Set_Ofold(_1674451, _1674451, c_Orderings_Oord__class_Omin(_1674451)), _1674457), _1674453))))], (15600 ^ _779571) ^ [_1044015, _1044017, _1044019, _1044021, _1044023, _1044025] : [class_Rings_Oring(_1044015), 15603 ^ _779571 : [(15610 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044015), _1044017), _1044023)), _1044019)), _1044021) = _1044025, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), _1044017), _1044019)), _1044021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), _1044023), _1044019)), _1044025))], (15604 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), _1044017), _1044019)), _1044021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), _1044023), _1044019)), _1044025), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044015), _1044017), _1044023)), _1044019)), _1044021) = _1044025)]]], (17507 ^ _779571) ^ [_1080656, _1080658, _1080660] : [class_Power_Opower(_1080656), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1080656), _1080658), hAPP(c_Nat_OSuc, _1080660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080656), _1080658), hAPP(hAPP(c_Power_Opower__class_Opower(_1080656), _1080658), _1080660)))], (24585 ^ _779571) ^ [_1208639, _1208641, _1208643] : [class_Int_Onumber(_1208639), class_Orderings_Oord(_1208639), 24592 ^ _779571 : [(24599 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208639), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208641)), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208643)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208639), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208641)), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208643)) = hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208641))], (24593 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208639), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208641)), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208643))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208639), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208641)), hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208643)) = hAPP(c_Int_Onumber__class_Onumber__of(_1208639), _1208643))]]], (13042 ^ _779571) ^ [_997897, _997899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _997897), c_Groups_Oone__class_Oone(tc_Int_Oint))), _997899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997897), _997899)))], (32045 ^ _779571) ^ [_1362434, _1362436, _1362438, _1362440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1362440, _1362436)), hAPP(_1362440, _1362438))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1362434, _1362434)), hAPP(hAPP(c_Product__Type_OPair(_1362434, _1362434), _1362436), _1362438)), hAPP(c_Wellfounded_Omeasure(_1362434), _1362440))))], (29698 ^ _779571) ^ [_1310302, _1310304, _1310306, _1310308, _1310310] : [-(_1310302 = c_Orderings_Obot__class_Obot(tc_fun(_1310304, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310306, tc_HOL_Obool)), _1310308), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310304, tc_fun(_1310306, tc_HOL_Obool)), _1310302), _1310310)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310304, tc_fun(_1310306, tc_HOL_Obool)), _1310302), hAPP(hAPP(c_COMBB(tc_fun(_1310306, tc_HOL_Obool), tc_fun(_1310306, tc_HOL_Obool), _1310304), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310306, tc_HOL_Obool)), _1310308)), _1310310)))], (35436 ^ _779571) ^ [_1432694, _1432696, _1432698, _1432700, _1432702, _1432704] : [-(hAPP(c_Relation_OImage(_1432694, _1432696, _1432698), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432700, tc_fun(_1432694, tc_HOL_Obool)), _1432702), _1432704)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432700, tc_fun(_1432696, tc_HOL_Obool)), _1432702), hAPP(hAPP(c_COMBB(tc_fun(_1432694, tc_HOL_Obool), tc_fun(_1432696, tc_HOL_Obool), _1432700), c_Relation_OImage(_1432694, _1432696, _1432698)), _1432704)))], (42798 ^ _779571) ^ [_1610056, _1610058, _1610060, _1610062, _1610064, _1610066, _1610068, _1610070] : [class_Groups_Ocomm__monoid__add(_1610056), c_Fun_Oinj__on(_1610058, _1610060, _1610062, _1610064), _1610066 = hAPP(c_Set_Oimage(_1610058, _1610060, _1610062), _1610064), 42812 ^ _779571 : [(42815 ^ _779571) ^ [] : [hAPP(_1610068, 42811 ^ [_1610056, _1610058, _1610060, _1610062, _1610064, _1610066, _1610068, _1610070]) = hAPP(_1610070, hAPP(_1610062, 42811 ^ [_1610056, _1610058, _1610060, _1610062, _1610064, _1610066, _1610068, _1610070]))], (42813 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610058), 42811 ^ [_1610056, _1610058, _1610060, _1610062, _1610064, _1610066, _1610068, _1610070]), _1610064)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1610060, _1610056), _1610070), _1610066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1610058, _1610056), _1610068), _1610064))], (8689 ^ _779571) ^ [_923030, _923032] : [hBOOL(hAPP(_923030, hAPP(c_Int_Onat, _923032))), 8692 ^ _779571 : [(8699 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923032), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_923030, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8693 ^ _779571) ^ [_923130] : [_923032 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923130), -(hBOOL(hAPP(_923030, _923130)))]]], (17433 ^ _779571) ^ [_1079487, _1079489, _1079491] : [class_Power_Opower(_1079487), class_Rings_Omult__zero(_1079487), class_Rings_Ono__zero__divisors(_1079487), class_Rings_Ozero__neq__one(_1079487), 17448 ^ _779571 : [(17457 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1079487), _1079489), _1079491) = c_Groups_Ozero__class_Ozero(_1079487)), _1079489 = c_Groups_Ozero__class_Ozero(_1079487), -(_1079491 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17449 ^ _779571) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1079487), _1079489), _1079491) = c_Groups_Ozero__class_Ozero(_1079487), 17452 ^ _779571 : [(17455 ^ _779571) ^ [] : [_1079491 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17453 ^ _779571) ^ [] : [-(_1079489 = c_Groups_Ozero__class_Ozero(_1079487))]]]]], (4608 ^ _779571) ^ [_850871, _850873, _850875, _850877] : [-(c_Complete__Lattice_OInf__class_OInf(_850877, _850873) = c_Complete__Lattice_OInf__class_OInf(_850875, _850871)), _850877 = _850875, _850873 = _850871], (49263 ^ _779571) ^ [_1768203, _1768205, _1768207, _1768209, _1768211] : [-(c_Map_Omap__upds(_1768203, _1768205, _1768207, _1768209, _1768211) = hAPP(c_List_Ofoldl(tc_fun(_1768203, tc_Option_Ooption(_1768205)), tc_prod(_1768203, _1768205), hAPP(hAPP(c_COMBB(tc_fun(_1768203, tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205)))), tc_fun(tc_prod(_1768203, _1768205), tc_fun(_1768203, tc_Option_Ooption(_1768205))), tc_fun(_1768203, tc_Option_Ooption(_1768205))), c_Product__Type_Oprod_Oprod__case(_1768203, _1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205)))), hAPP(hAPP(c_COMBC(tc_fun(_1768203, tc_Option_Ooption(_1768205)), tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768203, tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205))))), hAPP(hAPP(c_COMBB(tc_fun(_1768203, tc_fun(tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205))))), tc_fun(tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768203, tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205))))), tc_fun(_1768203, tc_Option_Ooption(_1768205))), c_COMBC(_1768203, tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205))))), hAPP(hAPP(c_COMBB(tc_fun(_1768203, tc_fun(tc_Option_Ooption(_1768205), tc_fun(_1768203, tc_Option_Ooption(_1768205)))), tc_fun(_1768203, tc_fun(tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205))))), tc_fun(_1768203, tc_Option_Ooption(_1768205))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1768205), tc_fun(_1768203, tc_Option_Ooption(_1768205))), tc_fun(tc_fun(_1768205, tc_Option_Ooption(_1768205)), tc_fun(_1768205, tc_fun(_1768203, tc_Option_Ooption(_1768205)))), _1768203), c_COMBB(tc_Option_Ooption(_1768205), tc_fun(_1768203, tc_Option_Ooption(_1768205)), _1768205))), c_Fun_Ofun__upd(_1768203, tc_Option_Ooption(_1768205))))), c_Option_Ooption_OSome(_1768205))), _1768207), hAPP(hAPP(c_List_Ozip(_1768203, _1768205), _1768209), _1768211)))], (13753 ^ _779571) ^ [_1010486, _1010488, _1010490, _1010492] : [class_Divides_Osemiring__div(_1010486), -(c_Divides_Odiv__class_Omod(_1010486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010486), c_Divides_Odiv__class_Omod(_1010486, _1010488, _1010490)), _1010492), _1010490) = c_Divides_Odiv__class_Omod(_1010486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010486), _1010488), _1010492), _1010490))], (41650 ^ _779571) ^ [_1581681, _1581683] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1581681, _1581683, tc_prod(_1581681, _1581683)), c_Product__Type_OPair(_1581681, _1581683)) = c_Fun_Oid(tc_prod(_1581681, _1581683)))], (25294 ^ _779571) ^ [_1222916, _1222918] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222916), _1222918)), 25297 ^ _779571 : [(25304 ^ _779571) ^ [] : [_1222918 = _1222916, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222918), _1222916)))], (25298 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222918), _1222916)), -(_1222918 = _1222916)]]], (37014 ^ _779571) ^ [_1469278, _1469280, _1469282, _1469284, _1469286] : [class_Groups_Ocomm__monoid__add(_1469278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469280), _1469282)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469280), _1469284)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469278), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469280, _1469278), _1469286), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469280, tc_HOL_Obool)), _1469282), _1469284))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469280, _1469278), _1469286), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469280, tc_HOL_Obool)), _1469282), _1469284))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469278), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469280, _1469278), _1469286), _1469282)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469280, _1469278), _1469286), _1469284)))], (51287 ^ _779571) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (48096 ^ _779571) ^ [_1739889, _1739891, _1739893] : [hAPP(hAPP(c_List_Oappend(_1739889), _1739891), _1739893) = c_List_Olist_ONil(_1739889), 48099 ^ _779571 : [(48102 ^ _779571) ^ [] : [-(_1739893 = c_List_Olist_ONil(_1739889))], (48100 ^ _779571) ^ [] : [-(_1739891 = c_List_Olist_ONil(_1739889))]]], (17005 ^ _779571) ^ [_1071696, _1071698] : [class_Groups_Oordered__ab__group__add__abs(_1071696), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071696), hAPP(c_Groups_Ouminus__class_Ouminus(_1071696), hAPP(c_Groups_Oabs__class_Oabs(_1071696), _1071698))), c_Groups_Ozero__class_Ozero(_1071696))))], (40070 ^ _779571) ^ [_1537963, _1537965, _1537967] : [class_Orderings_Olinorder(_1537963), -(_1537965 = c_Orderings_Obot__class_Obot(tc_fun(_1537963, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537963, tc_HOL_Obool)), _1537965), _1537967)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537963), _1537967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1537963), hAPP(c_Finite__Set_Ofold1(_1537963, c_Orderings_Oord__class_Omin(_1537963)), _1537967)), hAPP(c_Finite__Set_Ofold1(_1537963, c_Orderings_Oord__class_Omin(_1537963)), _1537965))))], (45957 ^ _779571) ^ [_1686007, _1686009] : [-(hAPP(hAPP(c_List_Omap(_1686007, _1686007), c_COMBI(_1686007)), _1686009) = _1686009)], (20873 ^ _779571) ^ [_1138574, _1138576, _1138578, _1138580] : [class_Fields_Olinordered__field(_1138574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138574), c_Groups_Ozero__class_Ozero(_1138574)), _1138576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138574), _1138578), _1138576)), _1138580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138574), _1138578), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138574), _1138580), _1138576))))], (35836 ^ _779571) ^ [_1443279, _1443281, _1443283, _1443285, _1443287] : [c_Equiv__Relations_Oequiv(_1443279, _1443281, _1443283), hBOOL(hAPP(hAPP(c_member(_1443279), _1443285), _1443281)), hBOOL(hAPP(hAPP(c_member(_1443279), _1443287), _1443281)), 35847 ^ _779571 : [(35854 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1443279, _1443279)), hAPP(hAPP(c_Product__Type_OPair(_1443279, _1443279), _1443285), _1443287)), _1443283)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1443279), hAPP(hAPP(c_Set_Oinsert(_1443279), _1443285), c_Orderings_Obot__class_Obot(tc_fun(_1443279, tc_HOL_Obool)))), _1443283) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1443279), hAPP(hAPP(c_Set_Oinsert(_1443279), _1443287), c_Orderings_Obot__class_Obot(tc_fun(_1443279, tc_HOL_Obool)))), _1443283))], (35848 ^ _779571) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1443279), hAPP(hAPP(c_Set_Oinsert(_1443279), _1443285), c_Orderings_Obot__class_Obot(tc_fun(_1443279, tc_HOL_Obool)))), _1443283) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1443279), hAPP(hAPP(c_Set_Oinsert(_1443279), _1443287), c_Orderings_Obot__class_Obot(tc_fun(_1443279, tc_HOL_Obool)))), _1443283), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443279, _1443279)), hAPP(hAPP(c_Product__Type_OPair(_1443279, _1443279), _1443285), _1443287)), _1443283)))]]], (23163 ^ _779571) ^ [_1181508, _1181510] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1181508, _1181510) = 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), _1181508), _1181510)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1181508, _1181510)))], (9926 ^ _779571) ^ [] : [-(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))))], (22186 ^ _779571) ^ [_1162451] : [c_Code__Numeral_OSuc__code__numeral(_1162451) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (8734 ^ _779571) ^ [_923786] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _923786)) = 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), _923786)))], (22500 ^ _779571) ^ [_1168927, _1168929] : [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), _1168927))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168929), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168927))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168929), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168927))), 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), _1168929))), c_COMBI(tc_Int_Oint))))], (6175 ^ _779571) ^ [_879491, _879493, _879495, _879497, _879499, _879501, _879503, _879505, _879507, _879509, _879511] : [-(c_Com_Ocom_Ocom__rec(_879491, _879493, _879495, _879497, _879499, _879501, _879503, _879505, _879507, c_Com_Ocom_OWhile(_879509, _879511)) = hAPP(hAPP(hAPP(_879503, _879509), _879511), c_Com_Ocom_Ocom__rec(_879491, _879493, _879495, _879497, _879499, _879501, _879503, _879505, _879507, _879511)))], (29242 ^ _779571) ^ [_1302154, _1302156, _1302158] : [-(hAPP(c_Set_Oimage(_1302154, _1302156, _1302158), c_Orderings_Obot__class_Obot(tc_fun(_1302154, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1302156, tc_HOL_Obool)))], (43570 ^ _779571) ^ [_1629538, _1629540, _1629542, _1629544, _1629546, _1629548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629538, _1629538)), hAPP(hAPP(c_Product__Type_OPair(_1629538, _1629538), _1629540), _1629542)), _1629544)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1629538, _1629538)), hAPP(hAPP(c_Product__Type_OPair(_1629538, _1629538), _1629542), _1629546)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629538, _1629538), tc_HOL_Obool), _1629548), _1629544))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629538, _1629538)), hAPP(hAPP(c_Product__Type_OPair(_1629538, _1629538), _1629540), _1629546)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1629538, _1629538), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1629548)), _1629544))))], (27612 ^ _779571) ^ [_1267873, _1267875, _1267877] : [-(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)), _1267873)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1267875), _1267877)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1267875), _1267873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1267877), _1267873)))], (29564 ^ _779571) ^ [_1307957, _1307959, _1307961] : [class_Orderings_Oorder(_1307957), 29567 ^ _779571 : [(29574 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307957), _1307959), _1307961))), -(c_Orderings_Obot__class_Obot(tc_fun(_1307957, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1307957, _1307959, _1307961))], (29568 ^ _779571) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1307957, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1307957, _1307959, _1307961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307957), _1307959), _1307961))]]], (25484 ^ _779571) ^ [_1225924, _1225926, _1225928] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225924), _1225926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225926), _1225924))), _1225926 = _1225928, 25495 ^ _779571 : [(25498 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225928), _1225924))], (25496 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225924), _1225928)))]]], (28022 ^ _779571) ^ [_1276136, _1276138, _1276140] : [class_Lattices_Osemilattice__sup(_1276136), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276136), _1276138), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276136), _1276138), _1276140)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276136), _1276138), _1276140))], (31460 ^ _779571) ^ [_1348913, _1348915, _1348917, _1348919] : [-(c_Nitpick_Ofold__graph_H(_1348913, _1348915, _1348917, _1348919, c_Orderings_Obot__class_Obot(tc_fun(_1348913, tc_HOL_Obool)), _1348919))], (51099 ^ _779571) ^ [_1808372, _1808374] : [class_Lattices_Olattice(_1808372), -(class_Lattices_Osemilattice__inf(tc_fun(_1808374, _1808372)))], (31658 ^ _779571) ^ [_1353795, _1353797, _1353799, _1353801, _1353803] : [class_Groups_Ocomm__monoid__add(_1353795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353797), _1353799)), 31665 ^ _779571 : [(31672 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1353797), _1353801), _1353799))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353797, _1353795), hAPP(hAPP(c_COMBC(_1353797, _1353795, _1353795), hAPP(hAPP(c_COMBS(_1353797, _1353795, tc_fun(_1353795, _1353795)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1353795, tc_fun(_1353795, _1353795)), _1353797), c_If(_1353795)), hAPP(c_fequal, _1353801))), _1353803)), c_Groups_Ozero__class_Ozero(_1353795))), _1353799) = c_Groups_Ozero__class_Ozero(_1353795))], (31666 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1353797), _1353801), _1353799)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353797, _1353795), hAPP(hAPP(c_COMBC(_1353797, _1353795, _1353795), hAPP(hAPP(c_COMBS(_1353797, _1353795, tc_fun(_1353795, _1353795)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1353795, tc_fun(_1353795, _1353795)), _1353797), c_If(_1353795)), hAPP(c_fequal, _1353801))), _1353803)), c_Groups_Ozero__class_Ozero(_1353795))), _1353799) = hAPP(_1353803, _1353801))]]], (42091 ^ _779571) ^ [_1593413, _1593415] : [-(hAPP(c_List_Olexn(_1593413, _1593415), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1593413), tc_List_Olist(_1593413)), tc_HOL_Obool)))], (42309 ^ _779571) ^ [_1598740, _1598742] : [c_Wellfounded_Owf(_1598740, _1598742), -(c_Wellfounded_OwfP(_1598740, c_FunDef_Oin__rel(_1598740, _1598740, _1598742)))], (14862 ^ _779571) ^ [_1030131, _1030133, _1030135] : [-(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), _1030131), _1030133)), _1030133)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030131, _1030133))), _1030135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030131), _1030135))], (43580 ^ _779571) ^ [_1629851, _1629853, _1629855] : [-(hAPP(hAPP(c_Nat_Ocompow(_1629851, _1629851), hAPP(c_Nat_OSuc, _1629853)), _1629855) = hAPP(c_Fun_Ocomp(_1629851, _1629851, _1629851, _1629855), hAPP(hAPP(c_Nat_Ocompow(_1629851, _1629851), _1629853), _1629855)))], (2632 ^ _779571) ^ [_819479, _819481] : [_819481 = _819479, -(c_Int_Opred(_819481) = c_Int_Opred(_819479))], (8536 ^ _779571) ^ [_920895, _920897, _920899] : [class_Orderings_Opreorder(_920895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920895), _920897), _920899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920895), _920899), _920897))], (30226 ^ _779571) ^ [_1321424, _1321426, _1321428, _1321430, _1321432] : [hBOOL(hAPP(hAPP(c_member(_1321424), _1321426), hAPP(c_Set_Oimage(_1321428, _1321424, _1321430), _1321432))), 30230 ^ _779571 : [(30233 ^ _779571) ^ [] : [-(_1321426 = hAPP(_1321430, 30229 ^ [_1321424, _1321426, _1321428, _1321430, _1321432]))], (30231 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321428), 30229 ^ [_1321424, _1321426, _1321428, _1321430, _1321432]), _1321432)))]]], (44372 ^ _779571) ^ [_1647296, _1647298, _1647300, _1647302, _1647304, _1647306, _1647308, _1647310] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647296, tc_fun(_1647298, tc_fun(_1647300, tc_HOL_Obool))), _1647302), _1647304), _1647306), _1647308)), -(hBOOL(hAPP(hAPP(hAPP(_1647304, _1647310), _1647306), _1647308))), hBOOL(hAPP(hAPP(c_member(_1647296), _1647310), _1647302))], (10100 ^ _779571) ^ [] : [-(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))], (26818 ^ _779571) ^ [_1251446, _1251448, _1251450, _1251452] : [class_Groups_Ocomm__monoid__add(_1251446), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1251446), _1251448), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1251450), hAPP(c_Nat_OSuc, _1251452))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1251446), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1251446, tc_Nat_Onat), _1251448), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1251450, _1251452)))], (20325 ^ _779571) ^ [_1129200, _1129202, _1129204] : [class_Fields_Olinordered__field__inverse__zero(_1129200), 20328 ^ _779571 : [(20343 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129200), _1129202), _1129204)), c_Groups_Ozero__class_Ozero(_1129200)))), 20344 ^ _779571 : [(20351 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), _1129202), c_Groups_Ozero__class_Ozero(_1129200))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), c_Groups_Ozero__class_Ozero(_1129200)), _1129204))], (20345 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), c_Groups_Ozero__class_Ozero(_1129200)), _1129202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), _1129204), c_Groups_Ozero__class_Ozero(_1129200)))]]], (20329 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129200), _1129202), _1129204)), c_Groups_Ozero__class_Ozero(_1129200))), 20334 ^ _779571 : [(20337 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), _1129204), c_Groups_Ozero__class_Ozero(_1129200))))], (20335 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129200), c_Groups_Ozero__class_Ozero(_1129200)), _1129202)))]], 20338 ^ 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286823, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1286823), _1286825)), hAPP(c_SetInterval_Oord__class_OatLeast(_1286823), _1286827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286823), _1286827), _1286825)))]]], (37701 ^ _779571) ^ [_1486070, _1486072, _1486074, _1486076, _1486078] : [class_Fields_Ofield(_1486070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486072), _1486074)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486072), _1486076)), 37715 ^ _779571 : [(37718 ^ _779571) ^ [] : [-(hAPP(_1486078, 37714 ^ [_1486070, _1486072, _1486074, _1486076, _1486078]) = c_Groups_Ozero__class_Ozero(_1486070))], (37716 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486072), 37714 ^ [_1486070, _1486072, _1486074, _1486076, _1486078]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486072, tc_HOL_Obool)), _1486074), _1486076))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1486072, 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_1705947] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705941), tc_List_Olist(_1705941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705941), tc_List_Olist(_1705941)), _1705943), _1705945)), c_List_Olistrel(_1705941, _1705947)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705941)), _1705943) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705941)), _1705945), 46746 ^ _779571 : [(46749 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1705941, _1705941, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1705941, tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_fun(_1705941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1705941, tc_fun(tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_fun(_1705941, tc_HOL_Obool)), _1705941), c_COMBC(_1705941, tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1705941, tc_prod(_1705941, _1705941)), tc_fun(_1705941, tc_fun(tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_HOL_Obool)), _1705941), hAPP(c_COMBB(tc_prod(_1705941, _1705941), tc_fun(tc_fun(tc_prod(_1705941, _1705941), tc_HOL_Obool), tc_HOL_Obool), _1705941), c_member(tc_prod(_1705941, _1705941)))), c_Product__Type_OPair(_1705941, _1705941)))), _1705947)), 46745 ^ [_1705941, _1705943, _1705945, _1705947]))], (46747 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1705941, _1705941)), 46745 ^ [_1705941, _1705943, _1705945, _1705947]), hAPP(c_List_Oset(tc_prod(_1705941, _1705941)), hAPP(hAPP(c_List_Ozip(_1705941, _1705941), _1705943), _1705945)))))]]], (15712 ^ _779571) ^ [_1046286, _1046288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046286), _1046288)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046286), _1046288) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15568 ^ _779571) ^ [_1043449, _1043451, _1043453] : [class_Groups_Oordered__ab__group__add(_1043449), 15571 ^ _779571 : [(15578 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043449), _1043451), _1043453)), c_Groups_Ozero__class_Ozero(_1043449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043449), _1043451), _1043453)))], (15572 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043449), _1043451), _1043453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043449), _1043451), _1043453)), c_Groups_Ozero__class_Ozero(_1043449))))]]], (48524 ^ _779571) ^ [_1750432, _1750434, _1750436, _1750438, _1750440] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750432), tc_List_Olist(_1750432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750432), tc_List_Olist(_1750432)), _1750434), _1750436)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750432), c_List_Olistrel1(_1750432, _1750438)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750432), tc_List_Olist(_1750432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750432), tc_List_Olist(_1750432)), hAPP(hAPP(c_List_Olist_OCons(_1750432), _1750440), _1750434)), hAPP(hAPP(c_List_Olist_OCons(_1750432), _1750440), _1750436))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1750432), c_List_Olistrel1(_1750432, _1750438)))))], (51501 ^ _779571) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27472 ^ _779571) ^ [_1265053, _1265055, _1265057, _1265059, _1265061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265053, tc_HOL_Obool)), _1265055), _1265057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265059, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1265053, _1265059, _1265061), _1265055)), hAPP(c_Set_Oimage(_1265053, _1265059, _1265061), _1265057))))], (41698 ^ _779571) ^ [_1583127, _1583129, _1583131, _1583133, _1583135, _1583137, _1583139] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583127, _1583129, _1583131), _1583133), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583135, tc_fun(tc_prod(_1583129, _1583131), tc_HOL_Obool)), _1583137), _1583139)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583135, tc_fun(tc_prod(_1583127, _1583131), tc_HOL_Obool)), _1583137), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1583129, _1583131), tc_HOL_Obool), tc_fun(tc_prod(_1583127, _1583131), tc_HOL_Obool), _1583135), hAPP(c_Relation_Orel__comp(_1583127, _1583129, _1583131), _1583133)), _1583139)))], (45762 ^ _779571) ^ [_1681222, _1681224, _1681226, _1681228] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1681222, tc_HOL_Obool)), c_Map_Odom(_1681222, _1681224, _1681226)), c_Map_Odom(_1681222, _1681224, _1681228)) = c_Orderings_Obot__class_Obot(tc_fun(_1681222, tc_HOL_Obool)), -(c_Map_Omap__add(_1681222, _1681224, _1681226, _1681228) = c_Map_Omap__add(_1681222, _1681224, _1681228, _1681226))], (29382 ^ _779571) ^ [_1304858, _1304860, _1304862] : [class_Groups_Ocomm__monoid__add(_1304858), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304860, _1304858), _1304862), c_Orderings_Obot__class_Obot(tc_fun(_1304860, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1304858))], (2098 ^ _779571) ^ [_810874, _810876, _810878, _810880] : [-(tc_Nitpick_Opair__box(_810880, _810876) = tc_Nitpick_Opair__box(_810878, _810874)), _810880 = _810878, _810876 = _810874], (16086 ^ _779571) ^ [_1054280, _1054282, _1054284, _1054286, _1054288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054280), _1054282)), 16089 ^ _779571 : [(16096 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054286), 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), _1054282), _1054280)), _1054284)), _1054288))), -(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), _1054280), _1054284)), _1054286)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054282), _1054284)), _1054288))))], (16090 ^ _779571) ^ [] : [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), _1054280), _1054284)), _1054286)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054282), _1054284)), _1054288))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054286), 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), _1054282), _1054280)), _1054284)), _1054288))))]]], (6029 ^ _779571) ^ [_876663, _876665] : [c_Com_Ocom_OWhile(_876663, _876665) = c_Com_Ocom_OSKIP], (46298 ^ _779571) ^ [_1694184] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1694184)), -(c_List_Onat__list(_1694184))], (37583 ^ _779571) ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890] : [c_Equiv__Relations_Oequiv(_1481878, _1481880, _1481882), c_Equiv__Relations_Ocongruent(_1481878, tc_fun(_1481884, tc_HOL_Obool), _1481882, _1481886), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481878, tc_fun(_1481884, tc_HOL_Obool)), _1481888), _1481886) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481878, tc_fun(_1481884, tc_HOL_Obool)), _1481890), _1481886), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481878, tc_HOL_Obool)), _1481888), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481878), _1481880), _1481882))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481878, tc_HOL_Obool)), _1481890), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481878), _1481880), _1481882))), 37605 ^ _779571 : [(37609 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481878), 37607 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890]), _1481880)))], (37611 ^ _779571) ^ [] : [-(hAPP(_1481886, 37604 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890]) = hAPP(_1481886, 37607 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890]))], (37613 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481878, _1481878)), hAPP(hAPP(c_Product__Type_OPair(_1481878, _1481878), 37604 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890]), 37607 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890])), _1481882))], (37606 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481878), 37604 ^ [_1481878, _1481880, _1481882, _1481884, _1481886, _1481888, _1481890]), _1481880)))]], -(_1481888 = _1481890)], (3936 ^ _779571) ^ [_840253, _840255, _840257, _840259] : [-(c_Relation_OId__on(_840259, _840255) = c_Relation_OId__on(_840257, _840253)), _840259 = _840257, _840255 = _840253], (7732 ^ _779571) ^ [_907580, _907582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _907580)), hAPP(c_Nat_OSuc, _907582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907580), _907582)))], (28389 ^ _779571) ^ [_1283483, _1283485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1283483)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1283483, _1283485)))], (51425 ^ _779571) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (36828 ^ _779571) ^ [_1465157, _1465159, _1465161] : [class_Lattices_Olattice(_1465157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465157), _1465159)), hBOOL(hAPP(hAPP(c_member(_1465157), _1465161), _1465159)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465157), _1465161), c_Big__Operators_Olattice__class_OSup__fin(_1465157, _1465159)) = _1465161)], (49592 ^ _779571) ^ [_1775619, _1775621] : [-(_1775619 = c_List_Olist_ONil(_1775621)), hBOOL(hAPP(c_List_Odistinct(_1775621), _1775619)), -(hBOOL(hAPP(c_List_Odistinct(_1775621), c_List_Obutlast(_1775621, _1775619))))], (51375 ^ _779571) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (44568 ^ _779571) ^ [_1652988, _1652990, _1652992, _1652994, _1652996] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652988, tc_fun(_1652990, tc_HOL_Obool)), _1652992), hAPP(hAPP(c_COMBS(_1652988, tc_fun(_1652990, tc_HOL_Obool), tc_fun(_1652990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1652990, tc_HOL_Obool), tc_fun(tc_fun(_1652990, tc_HOL_Obool), tc_fun(_1652990, tc_HOL_Obool)), _1652988), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652990, tc_HOL_Obool))), _1652994)), _1652996)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652990, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652988, tc_fun(_1652990, tc_HOL_Obool)), _1652992), _1652994)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652988, tc_fun(_1652990, tc_HOL_Obool)), _1652992), _1652996)))], (37649 ^ _779571) ^ [_1483850, _1483852, _1483854, _1483856, _1483858, _1483860, _1483862] : [c_Equiv__Relations_Oequiv(_1483850, _1483852, _1483854), c_Equiv__Relations_Ocongruent(_1483850, tc_fun(_1483856, tc_HOL_Obool), _1483854, _1483858), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483850, tc_HOL_Obool)), _1483860), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483850), _1483852), _1483854))), 37663 ^ _779571 : [(37666 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1483856, tc_HOL_Obool)), hAPP(_1483858, 37662 ^ [_1483850, _1483852, _1483854, _1483856, _1483858, _1483860, _1483862])), _1483862))], (37664 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483850), 37662 ^ [_1483850, _1483852, _1483854, _1483856, _1483858, _1483860, _1483862]), _1483852)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1483856, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483850, tc_fun(_1483856, tc_HOL_Obool)), _1483860), _1483858)), _1483862)))], (43319 ^ _779571) ^ [_1623208, _1623210, _1623212] : [c_Equiv__Relations_Oequiv(_1623208, _1623210, _1623212), -(hAPP(hAPP(c_Relation_Orel__comp(_1623208, _1623208, _1623208), hAPP(c_Relation_Oconverse(_1623208, _1623208), _1623212)), _1623212) = _1623212)], (19695 ^ _779571) ^ [_1117440, _1117442] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1117440), hAPP(c_Int_Onumber__class_Onumber__of(_1117440), _1117442)), 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(_1117440), hAPP(c_Int_Onumber__class_Onumber__of(_1117440), _1117442)), hAPP(c_Int_Onumber__class_Onumber__of(_1117440), _1117442))), class_Groups_Omonoid__mult(_1117440), class_Int_Onumber(_1117440)], (19195 ^ _779571) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (36192 ^ _779571) ^ [_1451138, _1451140, _1451142, _1451144] : [class_Lattices_Odistrib__lattice(_1451138), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451138), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451138), _1451140), _1451142)), _1451144) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451138), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451138), _1451140), _1451144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451138), _1451142), _1451144)))], (8986 ^ _779571) ^ [_928544, _928546] : [class_Groups_Omonoid__mult(_928544), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928544), _928546), c_Groups_Oone__class_Oone(_928544)) = _928546)], (8948 ^ _779571) ^ [_927938, _927940, _927942] : [class_Groups_Ogroup__add(_927938), 8951 ^ _779571 : [(8958 ^ _779571) ^ [] : [_927942 = hAPP(c_Groups_Ouminus__class_Ouminus(_927938), _927940), -(_927940 = hAPP(c_Groups_Ouminus__class_Ouminus(_927938), _927942))], (8952 ^ _779571) ^ [] : [_927940 = hAPP(c_Groups_Ouminus__class_Ouminus(_927938), _927942), -(_927942 = hAPP(c_Groups_Ouminus__class_Ouminus(_927938), _927940))]]], (40831 ^ _779571) ^ [_1555671, _1555673, _1555675, _1555677, _1555679, _1555681] : [hAPP(c_Set_Oimage(_1555671, _1555673, _1555675), c_Orderings_Otop__class_Otop(tc_fun(_1555671, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1555673, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1555677, _1555679, _1555681), c_Orderings_Otop__class_Otop(tc_fun(_1555677, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1555679, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1555671, _1555677), tc_prod(_1555673, _1555679), c_Product__Type_Omap__pair(_1555671, _1555673, _1555677, _1555679, _1555675, _1555681)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1555671, _1555677), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1555673, _1555679), tc_HOL_Obool)))], (43030 ^ _779571) ^ [_1616300, _1616302, _1616304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616300, _1616300), tc_HOL_Obool)), _1616302), _1616304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1616300, _1616300), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1616300, _1616302)), c_Transitive__Closure_Ortrancl(_1616300, _1616304))))], (1112 ^ _779571) ^ [_796239, _796241] : [-(class_Rings_Ocomm__ring__1(_796239)), _796241 = _796239, class_Rings_Ocomm__ring__1(_796241)], (36842 ^ _779571) ^ [_1465404, _1465406, _1465408] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465404, tc_HOL_Obool)), _1465406), _1465408) = c_Orderings_Obot__class_Obot(tc_fun(_1465404, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465404, tc_HOL_Obool)), _1465406), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1465404, tc_HOL_Obool)), _1465408))))], (10094 ^ _779571) ^ [_947764, _947766] : [class_Rings_Osemiring__1(_947764), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_947764), hAPP(c_Nat_OSuc, _947766)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947764), c_Groups_Oone__class_Oone(_947764)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_947764), _947766)))], (42305 ^ _779571) ^ [_1598605, _1598607, _1598609, _1598611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598605, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598605, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1598605, _1598607), _1598609)), hAPP(c_Relation_ODomain(_1598605, _1598607), _1598611))), hAPP(c_Relation_ODomain(_1598605, _1598607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1598605, _1598607), tc_HOL_Obool)), _1598609), _1598611)))))], (36348 ^ _779571) ^ [_1454705, _1454707, _1454709] : [class_Lattices_Osemilattice__inf(_1454705), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454705), _1454707), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454705), _1454707), _1454709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454705), _1454707), _1454709))], (6744 ^ _779571) ^ [_890300, _890302, _890304, _890306] : [c_Com_Ocom_OCall(_890300, _890302, _890304) = hAPP(c_Com_Ocom_OBODY, _890306)], (51239 ^ _779571) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (27329 ^ _779571) ^ [_1261753, _1261755, _1261757, _1261759] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1261753), _1261755)), 27332 ^ _779571 : [(27333 ^ _779571) ^ [_1261911] : [27335 ^ _779571 : [(27341 ^ _779571) ^ [] : [-(_1261911 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27337 ^ [_1261753, _1261755, _1261757, _1261759, _1261911]), 27334 ^ [_1261753, _1261755, _1261757, _1261759, _1261911]))], (27339 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27337 ^ [_1261753, _1261755, _1261757, _1261759, _1261911]), _1261757)))], (27336 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27334 ^ [_1261753, _1261755, _1261757, _1261759, _1261911]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1261755))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1261753), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261911), _1261759)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1261753), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261911), _1261755)), _1261759)))]]], (51353 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (6801 ^ _779571) ^ [_891607, _891609, _891611] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_891607, _891609, _891611)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26162 ^ _779571) ^ [_1238877, _1238879, _1238881] : [class_Divides_Osemiring__div(_1238877), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238877), _1238879), _1238881)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238877), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238877), _1238881), _1238879)), _1238879) = _1238881)], (39777 ^ _779571) ^ [_1530345, _1530347, _1530349] : [-(c_Map_Odom(_1530345, _1530347, hAPP(hAPP(c_COMBB(_1530347, tc_Option_Ooption(_1530347), _1530345), c_Option_Ooption_OSome(_1530347)), _1530349)) = c_Orderings_Otop__class_Otop(tc_fun(_1530345, tc_HOL_Obool)))], (6486 ^ _779571) ^ [_885328, _885330, _885332, _885334, _885336] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_885328, _885330, _885332)), _885334), _885336)), 6491 ^ _779571 : [(6494 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885330), _885334), _885336)))], (6492 ^ _779571) ^ [] : [-(hBOOL(hAPP(_885328, _885334)))]], 6495 ^ _779571 : [(6498 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885332), _885334), _885336)))], (6496 ^ _779571) ^ [] : [hBOOL(hAPP(_885328, _885334))]]], (13482 ^ _779571) ^ [_1005358, _1005360, _1005362] : [13483 ^ _779571 : [(13486 ^ _779571) ^ [] : [_1005360 = _1005362], (13484 ^ _779571) ^ [] : [_1005358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005358), _1005360) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005358), _1005362))], (40877 ^ _779571) ^ [_1557178, _1557180, _1557182, _1557184, _1557186, _1557188, _1557190, _1557192, _1557194, _1557196] : [hAPP(c_Set_Oimage(_1557178, _1557180, _1557182), _1557184) = _1557186, hAPP(c_Set_Oimage(_1557188, _1557190, _1557192), _1557194) = _1557196, -(hAPP(c_Set_Oimage(tc_prod(_1557178, _1557188), tc_prod(_1557180, _1557190), c_Product__Type_Omap__pair(_1557178, _1557180, _1557188, _1557190, _1557182, _1557192)), hAPP(hAPP(c_Product__Type_OSigma(_1557178, _1557188), _1557184), hAPP(c_COMBK(tc_fun(_1557188, tc_HOL_Obool), _1557178), _1557194))) = hAPP(hAPP(c_Product__Type_OSigma(_1557180, _1557190), _1557186), hAPP(c_COMBK(tc_fun(_1557190, tc_HOL_Obool), _1557180), _1557196)))], (4338 ^ _779571) ^ [_846644, _846646, _846648, _846650, _846652, _846654, _846656, _846658] : [-(c_Nitpick_Osetsum_H(_846658, _846654, _846650, _846646) = c_Nitpick_Osetsum_H(_846656, _846652, _846648, _846644)), _846658 = _846656, _846654 = _846652, _846650 = _846648, _846646 = _846644], (2582 ^ _779571) ^ [_818616, _818618, _818620, _818622, _818624, _818626, _818628, _818630, _818632, _818634] : [-(c_Product__Type_Oprod_Oprod__size(_818634, _818630, _818626, _818622, _818618) = c_Product__Type_Oprod_Oprod__size(_818632, _818628, _818624, _818620, _818616)), _818634 = _818632, _818630 = _818628, _818626 = _818624, _818622 = _818620, _818618 = _818616], (2198 ^ _779571) ^ [_812544, _812546, _812548, _812550, _812552, _812554, _812556, _812558, _812560, _812562, _812564, _812566] : [-(c_Sum__Type_Osum_Osum__rec(_812566, _812562, _812558, _812554, _812550, _812546) = c_Sum__Type_Osum_Osum__rec(_812564, _812560, _812556, _812552, _812548, _812544)), _812566 = _812564, _812562 = _812560, _812558 = _812556, _812554 = _812552, _812550 = _812548, _812546 = _812544], (33799 ^ _779571) ^ [_1396810, _1396812, _1396814] : [class_Orderings_Olinorder(_1396810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396810), _1396812)), -(_1396814 = c_Orderings_Obot__class_Obot(tc_fun(_1396810, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1396810, tc_HOL_Obool)), _1396814), _1396812)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396810), c_Big__Operators_Olattice_OInf__fin(_1396810, c_Orderings_Oord__class_Omin(_1396810), _1396814)), c_Big__Operators_Olattice_OInf__fin(_1396810, c_Orderings_Oord__class_Omin(_1396810), _1396812)) = c_Big__Operators_Olattice_OInf__fin(_1396810, c_Orderings_Oord__class_Omin(_1396810), _1396812))], (19591 ^ _779571) ^ [_1115632, _1115634] : [class_Rings_Olinordered__idom(_1115632), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1115632), hAPP(c_Groups_Oabs__class_Oabs(_1115632), _1115634)), 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(_1115632), _1115634), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (24827 ^ _779571) ^ [_1213526, _1213528, _1213530, _1213532, _1213534] : [-(_1213526 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1213528, _1213530, _1213532, _1213534), _1213526) = c_Lazy__Sequence_Ohb__bind(_1213528, _1213530, hAPP(_1213532, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1213526), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1213528, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1213530))), _1213534), _1213526)))], (29228 ^ _779571) ^ [_1301865, _1301867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1301865, tc_HOL_Obool)), _1301867), c_Orderings_Obot__class_Obot(tc_fun(_1301865, tc_HOL_Obool))))], (2496 ^ _779571) ^ [_817339, _817341] : [_817341 = _817339, -(c_Divides_Oadjust(_817341) = c_Divides_Oadjust(_817339))], (32341 ^ _779571) ^ [_1368159, _1368161] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368161), _1368159)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1368159), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368161))))], (51537 ^ _779571) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (30283 ^ _779571) ^ [_1322587, _1322589, _1322591, _1322593] : [30284 ^ _779571 : [(30287 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1322587), _1322589), _1322593))], (30285 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1322587), _1322589), _1322591))]], -(hBOOL(hAPP(hAPP(c_member(_1322587), _1322589), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322587, tc_HOL_Obool)), _1322591), _1322593))))], (15396 ^ _779571) ^ [_1040236, _1040238, _1040240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040236), _1040238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040236), _1040240)), _1040238)))], (1372 ^ _779571) ^ [_799489, _799491] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_799489)), _799491 = _799489, class_Groups_Oordered__cancel__ab__semigroup__add(_799491)], (24719 ^ _779571) ^ [_1211239, _1211241] : [-(c_Code__Numeral_Onat__of__aux(_1211239, _1211241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211239)), _1211241))], (10606 ^ _779571) ^ [_955991, _955993, _955995] : [class_Rings_Olinordered__semidom(_955991), 10609 ^ _779571 : [(10616 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955993), _955995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955991), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_955991), _955993)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_955991), _955995))))], (10610 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955991), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_955991), _955993)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_955991), _955995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955993), _955995)))]]], (45101 ^ _779571) ^ [_1666248, _1666250, _1666252] : [c_Equiv__Relations_Oequiv(_1666248, _1666250, _1666252), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666248, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1666248), _1666250), _1666252)) = _1666250)], (11427 ^ _779571) ^ [_969209, _969211] : [11428 ^ _779571 : [(11429 ^ _779571) ^ [_969259] : [_969211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969209), _969259)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969209), _969211)))], (47045 ^ _779571) ^ [_1715168, _1715170, _1715172, _1715174, _1715176] : [class_Groups_Oab__group__add(_1715168), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1715168), hAPP(hAPP(c_List_Omap(_1715170, _1715168), hAPP(hAPP(c_COMBS(_1715170, _1715168, _1715168), hAPP(hAPP(c_COMBB(_1715168, tc_fun(_1715168, _1715168), _1715170), c_Groups_Ominus__class_Ominus(_1715168)), _1715172)), _1715174)), _1715176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1715168), hAPP(c_List_Omonoid__add__class_Olistsum(_1715168), hAPP(hAPP(c_List_Omap(_1715170, _1715168), _1715172), _1715176))), hAPP(c_List_Omonoid__add__class_Olistsum(_1715168), hAPP(hAPP(c_List_Omap(_1715170, _1715168), _1715174), _1715176))))], (43214 ^ _779571) ^ [_1620605, _1620607, _1620609, _1620611] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620605, _1620605)), hAPP(hAPP(c_Product__Type_OPair(_1620605, _1620605), _1620607), _1620609)), c_Transitive__Closure_Ortrancl(_1620605, _1620611))), hBOOL(hAPP(hAPP(c_member(_1620605), _1620609), c_Wellfounded_Oacc(_1620605, _1620611))), -(hBOOL(hAPP(hAPP(c_member(_1620605), _1620607), c_Wellfounded_Oacc(_1620605, _1620611))))], (50425 ^ _779571) ^ [_1792488, _1792490, _1792492, _1792494, _1792496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1792488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1792490), _1792492))), -(hAPP(hAPP(c_List_Onth(_1792494), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1792494), _1792496), c_List_Oupt(_1792492, _1792490))), _1792488) = hAPP(_1792496, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1792492), _1792488)))], (25836 ^ _779571) ^ [_1232073, _1232075] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1232075), _1232073))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232073), _1232075)))], (51699 ^ _779571) ^ [] : [-(v_P(v_Z, v_s))], (6021 ^ _779571) ^ [_876462, _876464, _876466] : [c_Com_Ocom_OCond(_876462, _876464, _876466) = c_Com_Ocom_OSKIP], (45183 ^ _779571) ^ [_1668426, _1668428] : [class_Complete__Lattice_Ocomplete__lattice(_1668426), -(c_Complete__Lattice_OSup__class_OSup(_1668426, hAPP(hAPP(c_Set_Oinsert(_1668426), _1668428), c_Orderings_Obot__class_Obot(tc_fun(_1668426, tc_HOL_Obool)))) = _1668428)], (16785 ^ _779571) ^ [_1067066, _1067068, _1067070] : [class_Rings_Ocomm__semiring__1(_1067066), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067066), _1067068), hAPP(c_Nat_OSuc, _1067070)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067066), _1067068), hAPP(hAPP(c_Power_Opower__class_Opower(_1067066), _1067068), _1067070)))], (23237 ^ _779571) ^ [_1183328, _1183330] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183328, _1183330) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1183328, _1183330)))], (1342 ^ _779571) ^ [_799114, _799116] : [-(class_Groups_Ouminus(_799114)), _799116 = _799114, class_Groups_Ouminus(_799116)], (24227 ^ _779571) ^ [_1201701, _1201703, _1201705, _1201707, _1201709, _1201711, _1201713] : [-(hAPP(c_Product__Type_Oapsnd(_1201701, _1201703, _1201705, _1201707), hAPP(c_Product__Type_Oapfst(_1201709, _1201705, _1201701, _1201711), _1201713)) = hAPP(hAPP(c_Product__Type_OPair(_1201705, _1201703), hAPP(_1201711, hAPP(c_Product__Type_Ofst(_1201709, _1201701), _1201713))), hAPP(_1201707, hAPP(c_Product__Type_Osnd(_1201709, _1201701), _1201713))))], (28599 ^ _779571) ^ [_1287407, _1287409, _1287411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1287407), _1287409)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287409), _1287411)) = 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, _1287407), _1287409)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287409), _1287411))))], (3732 ^ _779571) ^ [_837067, _837069, _837071, _837073, _837075, _837077] : [-(c_FunDef_Oin__rel(_837077, _837073, _837069) = c_FunDef_Oin__rel(_837075, _837071, _837067)), _837077 = _837075, _837073 = _837071, _837069 = _837067], (36710 ^ _779571) ^ [_1462377, _1462379, _1462381, _1462383] : [-(hBOOL(hAPP(hAPP(c_member(_1462377), _1462379), _1462381))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462377, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1462377), _1462379), _1462383)), _1462381) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462377, tc_HOL_Obool)), _1462383), _1462381))], (35559 ^ _779571) ^ [] : [-(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))], (28323 ^ _779571) ^ [_1282229] : [-(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)), _1282229)))], (12513 ^ _779571) ^ [_988439, _988441] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988439), _988441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988439)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _988441)))], (7996 ^ _779571) ^ [_912252, _912254] : [c_Option_Ooption_ONone(_912252) = hAPP(c_Option_Ooption_OSome(_912252), _912254)], (24317 ^ _779571) ^ [_1203402, _1203404, _1203406, _1203408] : [class_Orderings_Olinorder(_1203402), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203402), _1203404), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203402), _1203406), _1203408)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203402), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203402), _1203404), _1203406)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203402), _1203404), _1203408)))], (30333 ^ _779571) ^ [_1323525, _1323527, _1323529] : [hBOOL(hAPP(hAPP(c_member(_1323525), _1323527), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323525, tc_HOL_Obool)), _1323529))), hBOOL(hAPP(hAPP(c_member(_1323525), _1323527), _1323529))], (16955 ^ _779571) ^ [_1070561, _1070563, _1070565] : [class_Rings_Olinordered__idom(_1070561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070561), c_Groups_Ozero__class_Ozero(_1070561)), _1070563)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070561), hAPP(c_Groups_Oabs__class_Oabs(_1070561), _1070565)), _1070563) = hAPP(c_Groups_Oabs__class_Oabs(_1070561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070561), _1070565), _1070563)))], (36144 ^ _779571) ^ [_1449922, _1449924, _1449926, _1449928] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449922, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1449922, tc_fun(_1449922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449922)), _1449924)), hAPP(hAPP(c_COMBC(_1449922, tc_fun(_1449922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449922)), _1449926)), _1449928)), -(hBOOL(hAPP(hAPP(c_member(_1449922), _1449928), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449922, tc_HOL_Obool)), _1449924), _1449926))))], (50620 ^ _779571) ^ [_1797250, _1797252, _1797254] : [_1797252 = hAPP(hAPP(c_List_Olist_OCons(_1797250), _1797254), c_List_Olist_ONil(_1797250)), -(hAPP(c_List_Orev(_1797250), _1797252) = hAPP(hAPP(c_List_Olist_OCons(_1797250), _1797254), c_List_Olist_ONil(_1797250)))], (20649 ^ _779571) ^ [_1134369, _1134371, _1134373] : [class_Fields_Olinordered__field(_1134369), -(_1134371 = c_Groups_Ozero__class_Ozero(_1134369)), -(hAPP(c_Groups_Oabs__class_Oabs(_1134369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134369), _1134373), _1134371)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134369), hAPP(c_Groups_Oabs__class_Oabs(_1134369), _1134373)), hAPP(c_Groups_Oabs__class_Oabs(_1134369), _1134371)))], (33607 ^ _779571) ^ [_1393115, _1393117, _1393119, _1393121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1393115, _1393117)), c_Sum__Type_OPlus(_1393115, _1393117, _1393119, _1393121))), 33610 ^ _779571 : [(33613 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1393117), _1393121)))], (33611 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1393115), _1393119)))]]], (24095 ^ _779571) ^ [_1199131, _1199133, _1199135, _1199137, _1199139, _1199141] : [hBOOL(hAPP(_1199131, _1199133)), hBOOL(hAPP(_1199135, _1199137)), 24102 ^ _779571 : [(24105 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1199135, hAPP(c_Product__Type_Osnd(_1199139, _1199141), hAPP(hAPP(c_Product__Type_OPair(_1199139, _1199141), _1199133), _1199137)))))], (24103 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1199131, hAPP(c_Product__Type_Ofst(_1199139, _1199141), hAPP(hAPP(c_Product__Type_OPair(_1199139, _1199141), _1199133), _1199137)))))]]], (15993 ^ _779571) ^ [_1052213, _1052215, _1052217] : [hBOOL(hAPP(_1052213, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052215), _1052217))), 15996 ^ _779571 : [(16003 ^ _779571) ^ [_1052404] : [_1052215 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052217), _1052404), -(hBOOL(hAPP(_1052213, _1052404)))], (15997 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052215), _1052217)), -(hBOOL(hAPP(_1052213, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (6877 ^ _779571) ^ [_893088, _893090] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893088), _893090) = _893088, -(_893090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48716 ^ _779571) ^ [_1756323, _1756325, _1756327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756323)), _1756327)), _1756325)), -(hAPP(hAPP(c_List_Odrop(_1756323), _1756325), _1756327) = c_List_Olist_ONil(_1756323))], (5855 ^ _779571) ^ [_873417, _873419, _873421] : [5857 ^ _779571 : [(5860 ^ _779571) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_873417, hAPP(c_Nat_OSuc, _873421), 5856 ^ [_873417, _873419, _873421])], (5858 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_873417)), 5856 ^ [_873417, _873419, _873421]), _873419)))]], 5861 ^ _779571 : [(5862 ^ _779571) ^ [_873590] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_873417)), _873590), _873419)), -(c_Hoare__Mirabelle_Otriple__valid(_873417, _873421, _873590))]]], (36650 ^ _779571) ^ [_1460684, _1460686, _1460688, _1460690, _1460692] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460684, tc_HOL_Obool)), _1460686), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460688, tc_fun(_1460684, tc_HOL_Obool)), _1460690), _1460692)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460688, tc_fun(_1460684, tc_HOL_Obool)), _1460690), hAPP(hAPP(c_COMBB(tc_fun(_1460684, tc_HOL_Obool), tc_fun(_1460684, tc_HOL_Obool), _1460688), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460684, tc_HOL_Obool)), _1460686)), _1460692)))], (9676 ^ _779571) ^ [_940371, _940373, _940375] : [class_Rings_Olinordered__semiring__strict(_940371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940371), c_Groups_Ozero__class_Ozero(_940371)), _940373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940371), _940375), c_Groups_Ozero__class_Ozero(_940371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940371), _940375), _940373)), c_Groups_Ozero__class_Ozero(_940371))))], (15496 ^ _779571) ^ [_1041955, _1041957, _1041959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041955), _1041957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041955), _1041959)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041957), _1041959))))], (31846 ^ _779571) ^ [_1357821, _1357823, _1357825] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1357821), _1357823)), -(hAPP(c_Finite__Set_Ocard(_1357821), hAPP(hAPP(c_Set_Oinsert(_1357821), _1357825), _1357823)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1357821), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357821, tc_HOL_Obool)), _1357823), hAPP(hAPP(c_Set_Oinsert(_1357821), _1357825), c_Orderings_Obot__class_Obot(tc_fun(_1357821, tc_HOL_Obool)))))))], (30626 ^ _779571) ^ [_1329703, _1329705, _1329707, _1329709] : [hBOOL(hAPP(hAPP(c_member(_1329703), _1329705), _1329707)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329703, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1329703), _1329705), _1329709)), _1329707) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329703, tc_HOL_Obool)), _1329709), _1329707))], (39678 ^ _779571) ^ [_1528309, _1528311, _1528313, _1528315] : [c_Map_Odom(_1528309, _1528311, _1528313) = hAPP(hAPP(c_Set_Oinsert(_1528309), _1528315), c_Orderings_Obot__class_Obot(tc_fun(_1528309, tc_HOL_Obool))), -(_1528313 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1528309, tc_Option_Ooption(_1528311)), hAPP(c_COMBK(tc_Option_Ooption(_1528311), _1528309), c_Option_Ooption_ONone(_1528311))), _1528315), hAPP(c_Option_Ooption_OSome(_1528311), 39681 ^ [_1528309, _1528311, _1528313, _1528315])))], (23887 ^ _779571) ^ [_1194880, _1194882, _1194884, _1194886, _1194888] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194880, _1194882, _1194884), _1194886), _1194888) = hAPP(hAPP(_1194886, hAPP(c_Product__Type_Ofst(_1194880, _1194882), _1194888)), hAPP(c_Product__Type_Osnd(_1194880, _1194882), _1194888)))], (18541 ^ _779571) ^ [_1097665, _1097667] : [class_Int_Onumber__ring(_1097665), class_Rings_Olinordered__idom(_1097665), 18548 ^ _779571 : [(18555 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1097667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097665), c_Groups_Ozero__class_Ozero(_1097665)), hAPP(c_Int_Onumber__class_Onumber__of(_1097665), _1097667))))], (18549 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097665), c_Groups_Ozero__class_Ozero(_1097665)), hAPP(c_Int_Onumber__class_Onumber__of(_1097665), _1097667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1097667)))]]], (51197 ^ _779571) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (28563 ^ _779571) ^ [_1286753] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286753)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1286753))], (28238 ^ _779571) ^ [_1280529, _1280531, _1280533, _1280535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280529, tc_HOL_Obool)), _1280531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280529, tc_HOL_Obool)), _1280533), _1280535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280529, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280529, tc_HOL_Obool)), _1280531), _1280533)), _1280535)))], (50698 ^ _779571) ^ [_1798853, _1798855] : [-(c_List_Oconcat(_1798853, _1798855) = hAPP(c_List_Ofoldl(tc_List_Olist(_1798853), tc_List_Olist(_1798853), c_List_Oappend(_1798853), c_List_Olist_ONil(_1798853)), _1798855))], (51009 ^ _779571) ^ [_1806759, _1806761, _1806763, _1806765, _1806767] : [-(hBOOL(hAPP(_1806759, _1806761))), -(c_List_OtakeWhile(_1806763, _1806759, hAPP(hAPP(c_List_Oappend(_1806763), _1806765), hAPP(hAPP(c_List_Olist_OCons(_1806763), _1806761), _1806767))) = c_List_OtakeWhile(_1806763, _1806759, _1806765))], (25322 ^ _779571) ^ [_1223342, _1223344] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223342), _1223344)), -(_1223342 = _1223344), 25329 ^ _779571 : [(25332 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223344), _1223342))], (25330 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223342), _1223344)))]]], (24543 ^ _779571) ^ [_1207707, _1207709, _1207711] : [class_Orderings_Olinorder(_1207707), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207707), _1207709), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207707), _1207709), _1207711)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207707), _1207709), _1207711))], (44559 ^ _779571) ^ [_1652758, _1652760, _1652762, _1652764] : [44561 ^ _779571 : [(44564 ^ _779571) ^ [] : [hAPP(_1652764, 44560 ^ [_1652758, _1652760, _1652762, _1652764]) = c_Orderings_Otop__class_Otop(tc_fun(_1652760, tc_HOL_Obool))], (44562 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652758), 44560 ^ [_1652758, _1652760, _1652762, _1652764]), _1652762)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652758, tc_fun(_1652760, tc_HOL_Obool)), _1652762), _1652764) = c_Orderings_Otop__class_Otop(tc_fun(_1652760, tc_HOL_Obool)))], (25748 ^ _779571) ^ [_1230477, _1230479, _1230481, _1230483] : [class_Rings_Ocomm__semiring__1(_1230477), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230477), _1230479), _1230481)), _1230483)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230477), _1230481), _1230483)))], (42952 ^ _779571) ^ [_1613629, _1613631, _1613633, _1613635] : [-(c_Transitive__Closure_Otrancl(_1613629, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1613629, _1613629)), hAPP(hAPP(c_Product__Type_OPair(_1613629, _1613629), _1613631), _1613633)), _1613635)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1613629, _1613629), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613629, _1613635)), hAPP(c_Set_OCollect(tc_prod(_1613629, _1613629)), hAPP(c_Product__Type_Oprod_Oprod__case(_1613629, _1613629, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1613629, tc_fun(_1613629, tc_HOL_Obool), tc_fun(_1613629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1613629, tc_HOL_Obool), tc_fun(_1613629, tc_HOL_Obool)), _1613629), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1613629)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1613629), c_fconj), hAPP(hAPP(c_COMBC(_1613629, tc_fun(tc_prod(_1613629, _1613629), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1613629, _1613629), tc_fun(tc_fun(tc_prod(_1613629, _1613629), tc_HOL_Obool), tc_HOL_Obool), _1613629), c_member(tc_prod(_1613629, _1613629))), hAPP(hAPP(c_COMBC(_1613629, _1613629, tc_prod(_1613629, _1613629)), c_Product__Type_OPair(_1613629, _1613629)), _1613631))), c_Transitive__Closure_Ortrancl(_1613629, _1613635))))), hAPP(hAPP(c_COMBC(_1613629, tc_fun(tc_prod(_1613629, _1613629), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1613629, _1613629), tc_fun(tc_fun(tc_prod(_1613629, _1613629), tc_HOL_Obool), tc_HOL_Obool), _1613629), c_member(tc_prod(_1613629, _1613629))), hAPP(c_Product__Type_OPair(_1613629, _1613629), _1613633))), c_Transitive__Closure_Ortrancl(_1613629, _1613635)))))))], (6381 ^ _779571) ^ [_883355, _883357, _883359, _883361, _883363] : [c_Com_Ocom_OSemi(_883355, _883357) = c_Com_Ocom_OLocal(_883359, _883361, _883363)], (12351 ^ _779571) ^ [_985803] : [-(hAPP(c_Nat_OSuc, _985803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _985803))], (2326 ^ _779571) ^ [_814688, _814690, _814692, _814694] : [-(c_Nitpick_Onat__lcm(_814694, _814690) = c_Nitpick_Onat__lcm(_814692, _814688)), _814694 = _814692, _814690 = _814688], (12534 ^ _779571) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19203 ^ _779571) ^ [_1108859, _1108861] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1108859)), c_Int_OBit0(_1108861)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1108859), _1108861)))], (29017 ^ _779571) ^ [_1296999, _1297001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296999, tc_HOL_Obool)), _1297001), c_Orderings_Otop__class_Otop(tc_fun(_1296999, tc_HOL_Obool)))))], (26514 ^ _779571) ^ [_1245467, _1245469, _1245471, _1245473] : [class_Rings_Ocomm__ring(_1245467), class_Rings_Odvd(_1245467), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245467), _1245469), _1245471)), 26525 ^ _779571 : [(26532 ^ _779571) ^ [_1245893, _1245895] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245467), _1245469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1245467), _1245895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245467), _1245893), _1245471))), _1245473))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245467), _1245469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245467), _1245895), _1245473))))], (26526 ^ _779571) ^ [_1245720, _1245722] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245467), _1245469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245467), _1245722), _1245473))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245467), _1245469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1245467), _1245722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245467), _1245720), _1245471))), _1245473))))]]], (41786 ^ _779571) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (17367 ^ _779571) ^ [_1078231, _1078233] : [class_Groups_Omonoid__mult(_1078231), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078231), c_Groups_Oone__class_Oone(_1078231)), _1078233) = c_Groups_Oone__class_Oone(_1078231))], (51415 ^ _779571) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (46520 ^ _779571) ^ [_1699814, _1699816, _1699818] : [class_Orderings_Olinorder(_1699814), -(c_List_Oremove1(_1699814, _1699816, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699814, _1699814, c_COMBI(_1699814)), _1699816), _1699818)) = _1699818)], (678 ^ _779571) ^ [_790048, _790050, _790052, _790054] : [-(c_Wellfounded_Oacyclic(_790052, _790048)), c_Wellfounded_Oacyclic(_790054, _790050), _790054 = _790052, _790050 = _790048], (34581 ^ _779571) ^ [_1412755, _1412757, _1412759, _1412761, _1412763, _1412765, _1412767] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412755, tc_Option_Ooption(_1412757)), _1412759), _1412761), hAPP(c_Option_Ooption_OSome(_1412757), _1412763)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1412755, tc_Option_Ooption(_1412757)), _1412765), _1412761), hAPP(c_Option_Ooption_OSome(_1412757), _1412767)), -(_1412763 = _1412767)], (6045 ^ _779571) ^ [_876992, _876994, _876996, _876998] : [-(c_Com_Ocom_OWhile(_876992, _876994) = c_Com_Ocom_OWhile(_876996, _876998)), _876992 = _876996, _876994 = _876998], (16797 ^ _779571) ^ [_1067328, _1067330, _1067332] : [class_Rings_Ocomm__semiring__1(_1067328), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067328), hAPP(hAPP(c_Power_Opower__class_Opower(_1067328), _1067330), _1067332)), _1067330) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067328), _1067330), hAPP(c_Nat_OSuc, _1067332)))], (47099 ^ _779571) ^ [_1716708, _1716710, _1716712, _1716714] : [class_Groups_Ocomm__monoid__add(_1716708), hBOOL(hAPP(c_List_Odistinct(_1716710), _1716712)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716708), hAPP(hAPP(c_List_Omap(_1716710, _1716708), _1716714), _1716712)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1716710, _1716708), _1716714), hAPP(c_List_Oset(_1716710), _1716712)))], (37537 ^ _779571) ^ [_1480879, _1480881, _1480883, _1480885, _1480887, _1480889] : [c_Finite__Set_Ofolding(_1480879, _1480881, _1480883, _1480885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480879), _1480887)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480879), _1480889)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480879, tc_HOL_Obool)), _1480887), _1480889) = c_Orderings_Obot__class_Obot(tc_fun(_1480879, tc_HOL_Obool)), -(hAPP(_1480885, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480879, tc_HOL_Obool)), _1480887), _1480889)) = hAPP(c_Fun_Ocomp(_1480881, _1480881, _1480881, hAPP(_1480885, _1480887)), hAPP(_1480885, _1480889)))], (45666 ^ _779571) ^ [_1679350, _1679352, _1679354, _1679356, _1679358] : [-(c_Map_Omap__add(_1679350, _1679352, _1679354, c_Map_Omap__add(_1679350, _1679352, _1679356, _1679358)) = c_Map_Omap__add(_1679350, _1679352, c_Map_Omap__add(_1679350, _1679352, _1679354, _1679356), _1679358))], (47673 ^ _779571) ^ [_1730069, _1730071, _1730073, _1730075, _1730077] : [-(_1730069 = _1730071), -(hAPP(hAPP(c_List_Onth(_1730073), hAPP(hAPP(c_List_Olist__update(_1730073, _1730075), _1730069), _1730077)), _1730071) = hAPP(hAPP(c_List_Onth(_1730073), _1730075), _1730071))], (41087 ^ _779571) ^ [_1561900, _1561902, _1561904] : [-(hAPP(c_Set_OCollect(_1561900), hAPP(hAPP(c_COMBS(_1561900, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561900), c_fdisj), _1561902)), _1561904)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561900, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1561900), _1561902)), hAPP(c_Set_OCollect(_1561900), _1561904)))], (32438 ^ _779571) ^ [_1370715, _1370717, _1370719, _1370721, _1370723, _1370725] : [c_Finite__Set_Ofolding__image__simple(_1370715, _1370717, _1370719, _1370721, _1370723, _1370725), -(hAPP(_1370725, c_Orderings_Obot__class_Obot(tc_fun(_1370717, tc_HOL_Obool))) = _1370721)], (17855 ^ _779571) ^ [_1086888, _1086890] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086888) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086890), 17858 ^ _779571 : [(17865 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086888)))), 17868 ^ _779571 : [(17875 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086890)))), -(_1086888 = _1086890)], (17869 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086890))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086888) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17859 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086890)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (46873 ^ _779571) ^ [_1710212, _1710214, _1710216, _1710218] : [-(_1710212 = _1710214), -(c_List_Oremove1(_1710216, _1710212, hAPP(hAPP(c_List_Olist_OCons(_1710216), _1710214), _1710218)) = hAPP(hAPP(c_List_Olist_OCons(_1710216), _1710214), c_List_Oremove1(_1710216, _1710212, _1710218)))], (35543 ^ _779571) ^ [_1435623, _1435625, _1435627] : [class_Rings_Oring__1(_1435623), -(hAPP(c_Int_Oring__1__class_Oof__int(_1435623), 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), _1435625), _1435627)), 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(_1435623), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1435623), _1435625)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1435623), _1435627)))], (15508 ^ _779571) ^ [_1042201, _1042203] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042201), _1042203)), _1042201)))], (46282 ^ _779571) ^ [_1693915, _1693917] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1693915, _1693917)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1693915, _1693917))], (42728 ^ _779571) ^ [_1608615, _1608617, _1608619, _1608621, _1608623, _1608625] : [class_Rings_Ocomm__semiring__1(_1608615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608617), _1608619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608617, tc_HOL_Obool)), _1608621), _1608619)), 42742 ^ _779571 : [(42745 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1608615), hAPP(_1608623, 42741 ^ [_1608615, _1608617, _1608619, _1608621, _1608623, _1608625])), hAPP(_1608625, 42741 ^ [_1608615, _1608617, _1608619, _1608621, _1608623, _1608625])))], (42743 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608617), 42741 ^ [_1608615, _1608617, _1608619, _1608621, _1608623, _1608625]), _1608621)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1608615), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1608617, _1608615), _1608623), _1608621)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1608617, _1608615), _1608625), _1608619))))], (7203 ^ _779571) ^ [_898500, _898502, _898504, _898506, _898508] : [c_Hoare__Mirabelle_Otriple__valid(_898500, hAPP(c_Nat_OSuc, _898502), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898500), _898504), hAPP(c_Com_Ocom_OBODY, _898506)), _898508)), -(c_Hoare__Mirabelle_Otriple__valid(_898500, _898502, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898500), _898504), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _898506))), _898508)))], (46430 ^ _779571) ^ [_1697463, _1697465, _1697467, _1697469, _1697471, _1697473] : [-(hAPP(hAPP(c_List_Ozip(_1697463, _1697465), hAPP(hAPP(c_List_Omap(_1697467, _1697463), _1697469), _1697471)), _1697473) = hAPP(hAPP(c_List_Omap(tc_prod(_1697467, _1697465), tc_prod(_1697463, _1697465)), hAPP(c_Product__Type_Oprod_Oprod__case(_1697467, _1697465, tc_prod(_1697463, _1697465)), hAPP(hAPP(c_COMBB(_1697463, tc_fun(_1697465, tc_prod(_1697463, _1697465)), _1697467), c_Product__Type_OPair(_1697463, _1697465)), _1697469))), hAPP(hAPP(c_List_Ozip(_1697467, _1697465), _1697471), _1697473)))], (42233 ^ _779571) ^ [_1597035, _1597037] : [c_Wellfounded_OwfP(_1597035, _1597037), 42236 ^ _779571 : [(42237 ^ _779571) ^ [_1597099] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1597035, _1597037), _1597099)))]]], (11140 ^ _779571) ^ [_964593, _964595] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964593), _964595) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_964593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_964595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33649 ^ _779571) ^ [_1393888, _1393890, _1393892, _1393894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393888), _1393890)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393892), _1393894)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1393888, _1393892)), c_Sum__Type_OPlus(_1393888, _1393892, _1393890, _1393894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393888), _1393890)), hAPP(c_Finite__Set_Ocard(_1393892), _1393894)))], (14459 ^ _779571) ^ [_1023539, _1023541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023539)), 14462 ^ _779571 : [(14469 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023541), 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), _1023541), _1023539)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14463 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023541), _1023539)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023541), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17801 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8936 ^ _779571) ^ [_927652, _927654, _927656, _927658] : [class_Rings_Ocomm__semiring__1(_927652), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927652), _927654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927652), _927656), _927658)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927652), _927654), _927656)), _927658))], (39206 ^ _779571) ^ [_1517419, _1517421, _1517423, _1517425] : [c_Fun_Oinj__on(_1517419, _1517421, _1517423, c_Orderings_Otop__class_Otop(tc_fun(_1517419, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1517419, _1517421, c_Orderings_Otop__class_Otop(tc_fun(_1517419, tc_HOL_Obool)), _1517423), hAPP(_1517423, _1517425)) = _1517425)], (51321 ^ _779571) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (12690 ^ _779571) ^ [_991704, _991706, _991708, _991710] : [class_Rings_Olinordered__semiring(_991704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991704), _991706), _991708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991704), _991710), _991708))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991704), c_Groups_Ozero__class_Ozero(_991704)), _991708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991704), _991706), _991710)))], (32911 ^ _779571) ^ [_1380057, _1380059] : [class_Rings_Oring__1(_1380057), -(hBOOL(hAPP(hAPP(c_member(_1380057), hAPP(c_Int_Oring__1__class_Oof__int(_1380057), _1380059)), c_Int_Oring__1__class_OInts(_1380057))))], (41376 ^ _779571) ^ [_1570160, _1570162, _1570164] : [class_Orderings_Olinorder(_1570160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570160), _1570162)), -(_1570162 = c_Orderings_Obot__class_Obot(tc_fun(_1570160, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570160), _1570164)), -(_1570164 = c_Orderings_Obot__class_Obot(tc_fun(_1570160, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1570160), c_Big__Operators_Olattice_OSup__fin(_1570160, c_Orderings_Oord__class_Omax(_1570160), _1570162)), c_Big__Operators_Olattice_OSup__fin(_1570160, c_Orderings_Oord__class_Omax(_1570160), _1570164)) = c_Big__Operators_Olattice_OSup__fin(_1570160, c_Orderings_Oord__class_Omax(_1570160), hAPP(c_Set_OCollect(_1570160), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_HOL_Obool), tc_HOL_Obool, _1570160), c_HOL_OEx(_1570160)), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool)), tc_fun(_1570160, tc_HOL_Obool), _1570160), hAPP(c_COMBB(tc_fun(_1570160, tc_HOL_Obool), tc_HOL_Obool, _1570160), c_HOL_OEx(_1570160))), hAPP(hAPP(c_COMBC(_1570160, tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool)), tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_fun(tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool))), tc_fun(tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool)), tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool))), _1570160), c_COMBS(_1570160, tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_fun(_1570160, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1570160, tc_fun(tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool))), _1570160), hAPP(c_COMBB(tc_fun(_1570160, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool)), _1570160), c_COMBS(_1570160, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool)), tc_fun(_1570160, tc_fun(_1570160, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1570160), hAPP(c_COMBB(tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1570160), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570160), c_fconj))), hAPP(hAPP(c_COMBC(_1570160, tc_fun(_1570160, tc_fun(_1570160, _1570160)), tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1570160, _1570160), tc_fun(_1570160, tc_HOL_Obool)), tc_fun(tc_fun(_1570160, tc_fun(_1570160, _1570160)), tc_fun(_1570160, tc_fun(_1570160, tc_HOL_Obool))), _1570160), c_COMBB(tc_fun(_1570160, _1570160), tc_fun(_1570160, tc_HOL_Obool), _1570160)), hAPP(hAPP(c_COMBB(tc_fun(_1570160, tc_HOL_Obool), tc_fun(tc_fun(_1570160, _1570160), tc_fun(_1570160, tc_HOL_Obool)), _1570160), c_COMBB(_1570160, tc_HOL_Obool, _1570160)), c_fequal))), c_Orderings_Oord__class_Omin(_1570160)))))), hAPP(hAPP(c_COMBC(_1570160, tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570160, tc_HOL_Obool), tc_fun(_1570160, tc_HOL_Obool)), _1570160), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570160)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570160), c_fconj), hAPP(hAPP(c_COMBC(_1570160, tc_fun(_1570160, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570160)), _1570162)))), hAPP(hAPP(c_COMBC(_1570160, tc_fun(_1570160, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570160)), _1570164))))))))], (24879 ^ _779571) ^ [_1214744, _1214746, _1214748, _1214750, _1214752] : [-(hAPP(c_New__DSequence_Oneg__bind(_1214744, _1214746, _1214748, _1214750), _1214752) = c_Lazy__Sequence_Ohb__bind(_1214744, _1214746, hAPP(_1214748, _1214752), hAPP(hAPP(c_COMBC(_1214744, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1214746))), _1214750), _1214752)))], (18343 ^ _779571) ^ [_1094606] : [-(c_Int_Osucc(c_Int_Opred(_1094606)) = _1094606)], (19651 ^ _779571) ^ [_1116731, _1116733] : [class_Rings_Olinordered__idom(_1116731), 19654 ^ _779571 : [(19661 ^ _779571) ^ [] : [-(_1116733 = c_Groups_Ozero__class_Ozero(_1116731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116731), c_Groups_Ozero__class_Ozero(_1116731)), hAPP(hAPP(c_Power_Opower__class_Opower(_1116731), _1116733), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19655 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116731), c_Groups_Ozero__class_Ozero(_1116731)), hAPP(hAPP(c_Power_Opower__class_Opower(_1116731), _1116733), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1116733 = c_Groups_Ozero__class_Ozero(_1116731)]]], (45391 ^ _779571) ^ [_1673208, _1673210, _1673212] : [45393 ^ _779571 : [(45396 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673208, tc_HOL_Obool)), 45392 ^ [_1673208, _1673210, _1673212]), _1673212))], (45394 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1673208, tc_HOL_Obool)), 45392 ^ [_1673208, _1673210, _1673212]), _1673210)))]], -(_1673210 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1673208, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673208, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1673208, tc_HOL_Obool), _1673210)), _1673212)))], (48359 ^ _779571) ^ [_1746050, _1746052, _1746054, _1746056, _1746058] : [-(hAPP(hAPP(c_List_Otake(_1746050), _1746052), hAPP(hAPP(c_List_Omap(_1746054, _1746050), _1746056), _1746058)) = hAPP(hAPP(c_List_Omap(_1746054, _1746050), _1746056), hAPP(hAPP(c_List_Otake(_1746054), _1746052), _1746058)))], (6663 ^ _779571) ^ [_888615, _888617, _888619, _888621, _888623] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_888615, _888617, _888619)), _888621), _888623))), 6664 ^ _779571 : [(6671 ^ _779571) ^ [] : [-(hBOOL(hAPP(_888615, _888621))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888619), _888621), _888623))], (6665 ^ _779571) ^ [] : [hBOOL(hAPP(_888615, _888621)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888617), _888621), _888623))]]], (34138 ^ _779571) ^ [_1403787, _1403789, _1403791, _1403793, _1403795] : [class_Groups_Ocomm__monoid__mult(_1403787), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403789, _1403787), hAPP(hAPP(c_COMBS(_1403789, _1403787, _1403787), hAPP(hAPP(c_COMBB(_1403787, tc_fun(_1403787, _1403787), _1403789), c_Groups_Otimes__class_Otimes(_1403787)), _1403791)), _1403793)), _1403795) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403787), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403789, _1403787), _1403791), _1403795)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403789, _1403787), _1403793), _1403795)))], (51205 ^ _779571) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (42227 ^ _779571) ^ [_1596931, _1596933, _1596935] : [c_Wellfounded_OwfP(_1596931, _1596933), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1596931, _1596933), _1596935)))], (8874 ^ _779571) ^ [_926600, _926602, _926604, _926606] : [class_Rings_Ocomm__semiring__1(_926600), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926600), _926602), _926604)), _926606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926600), _926602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926600), _926604), _926606)))], (45259 ^ _779571) ^ [_1670194, _1670196] : [class_Complete__Lattice_Ocomplete__lattice(_1670194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670194), _1670196)), -(_1670196 = c_Orderings_Obot__class_Obot(tc_fun(_1670194, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1670194, _1670196) = c_Complete__Lattice_OSup__class_OSup(_1670194, _1670196))], (43345 ^ _779571) ^ [_1623946, _1623948, _1623950, _1623952, _1623954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623948, _1623946)), hAPP(hAPP(c_Product__Type_OPair(_1623948, _1623946), _1623952), _1623950)), _1623954)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623946, _1623948)), hAPP(hAPP(c_Product__Type_OPair(_1623946, _1623948), _1623950), _1623952)), hAPP(c_Relation_Oconverse(_1623948, _1623946), _1623954))))], (49844 ^ _779571) ^ [_1781306, _1781308, _1781310] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781306)), hAPP(c_List_Ofilter(_1781306, _1781308), _1781310)) = 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(_1781306)), _1781310)))), hAPP(hAPP(c_COMBB(_1781306, tc_HOL_Obool, tc_Nat_Onat), _1781308), hAPP(c_List_Onth(_1781306), _1781310))))))], (48710 ^ _779571) ^ [_1756204, _1756206, _1756208] : [hAPP(hAPP(c_List_Odrop(_1756204), _1756206), _1756208) = c_List_Olist_ONil(_1756204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756204)), _1756208)), _1756206)))], (11084 ^ _779571) ^ [_963519, _963521, _963523, _963525] : [class_Groups_Oordered__ab__semigroup__add(_963519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963519), _963521), _963523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963519), _963525), _963521)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963519), _963525), _963523))))], (18083 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (46492 ^ _779571) ^ [_1699142, _1699144, _1699146, _1699148] : [class_Orderings_Olinorder(_1699142), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699142, _1699142, c_COMBI(_1699142)), _1699144), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699142, _1699142, c_COMBI(_1699142)), _1699146), _1699148)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699142, _1699142, c_COMBI(_1699142)), _1699146), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699142, _1699142, c_COMBI(_1699142)), _1699144), _1699148)))], (13886 ^ _779571) ^ [_1012914, _1012916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012914), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012916), _1012914)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012914, _1012916) = _1012914)], (10874 ^ _779571) ^ [_960356, _960358, _960360] : [class_Orderings_Oorder(_960356), -(_960358 = _960360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960356), _960360), _960358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960356), _960360), _960358)))], (23883 ^ _779571) ^ [_1194784, _1194786, _1194788] : [-(_1194784 = hAPP(hAPP(c_Product__Type_OPair(_1194786, _1194788), hAPP(c_Product__Type_Ofst(_1194786, _1194788), _1194784)), hAPP(c_Product__Type_Osnd(_1194786, _1194788), _1194784)))], (47616 ^ _779571) ^ [_1728264, _1728266] : [class_Groups_Ocomm__monoid__add(_1728264), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1728264), _1728266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1728264), hAPP(c_List_Onth(_1728264), _1728266)), 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(_1728264)), _1728266))))], (46338 ^ _779571) ^ [_1694899, _1694901, _1694903] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1694899, tc_HOL_Obool)), hAPP(c_List_Oset(_1694899), c_List_Oremove1(_1694899, _1694901, _1694903))), hAPP(c_List_Oset(_1694899), _1694903))))], (42628 ^ _779571) ^ [_1606271, _1606273, _1606275] : [42630 ^ _779571 : [(42633 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1606271), 42629 ^ [_1606271, _1606273, _1606275]), c_Wellfounded_Oacc(_1606271, _1606275)))], (42631 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606271, _1606271)), hAPP(hAPP(c_Product__Type_OPair(_1606271, _1606271), 42629 ^ [_1606271, _1606273, _1606275]), _1606273)), _1606275)))]], -(hBOOL(hAPP(hAPP(c_member(_1606271), _1606273), c_Wellfounded_Oacc(_1606271, _1606275))))], (44027 ^ _779571) ^ [_1640703, _1640705, _1640707, _1640709] : [class_Orderings_Olinorder(_1640703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640703), _1640705)), hBOOL(hAPP(hAPP(c_member(_1640703), _1640707), _1640705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1640703), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1640703), _1640707), _1640709)), hAPP(hAPP(c_Finite__Set_Ofold(_1640703, _1640703, c_Orderings_Oord__class_Omax(_1640703)), _1640709), _1640705))))], (33745 ^ _779571) ^ [_1395897, _1395899, _1395901] : [class_Orderings_Olinorder(_1395897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395897), _1395899)), hBOOL(hAPP(hAPP(c_member(_1395897), _1395901), _1395899)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1395897), _1395901), c_Big__Operators_Olattice_OSup__fin(_1395897, c_Orderings_Oord__class_Omax(_1395897), _1395899)) = c_Big__Operators_Olattice_OSup__fin(_1395897, c_Orderings_Oord__class_Omax(_1395897), _1395899))], (4874 ^ _779571) ^ [_854886, _854888, _854890, _854892] : [-(c_Random_Opick(_854892, _854888) = c_Random_Opick(_854890, _854886)), _854892 = _854890, _854888 = _854886], (38733 ^ _779571) ^ [_1507376, _1507378, _1507380, _1507382, _1507384] : [c_Fun_Oinj__on(_1507376, _1507378, _1507380, c_Orderings_Otop__class_Otop(tc_fun(_1507376, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1507376, _1507378, _1507380), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507376, tc_HOL_Obool)), _1507382), _1507384)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507378, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1507376, _1507378, _1507380), _1507382)), hAPP(c_Set_Oimage(_1507376, _1507378, _1507380), _1507384)))], (13208 ^ _779571) ^ [_1000644, _1000646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000646)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1000644), _1000646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1000644)), hAPP(c_Int_Onat, _1000646)))], (44876 ^ _779571) ^ [_1661173, _1661175, _1661177, _1661179] : [hBOOL(hAPP(hAPP(c_member(_1661173), _1661175), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1661173, tc_HOL_Obool), _1661177))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1661173, tc_HOL_Obool)), _1661179), _1661177)), -(hBOOL(hAPP(hAPP(c_member(_1661173), _1661175), _1661179)))], (46895 ^ _779571) ^ [_1710678, _1710680, _1710682] : [hBOOL(hAPP(c_List_Odistinct(_1710678), hAPP(hAPP(c_List_Olist_OCons(_1710678), _1710680), _1710682))), 46898 ^ _779571 : [(46901 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1710678), _1710682)))], (46899 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1710678), _1710680), hAPP(c_List_Oset(_1710678), _1710682)))]]], (49567 ^ _779571) ^ [_1774997, _1774999, _1775001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774997), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774999)), _1775001))), -(c_List_Obutlast(_1774999, hAPP(hAPP(c_List_Otake(_1774999), _1774997), _1775001)) = hAPP(hAPP(c_List_Otake(_1774999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1774997), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1775001))], (19329 ^ _779571) ^ [_1111090, _1111092] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1111090)), c_Int_OBit1(_1111092)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1111090), _1111092)))], (34230 ^ _779571) ^ [_1405521, _1405523, _1405525, _1405527] : [class_Rings_Ocomm__semiring__1(_1405521), class_Rings_Ono__zero__divisors(_1405521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405523), _1405525)), 34241 ^ _779571 : [(34251 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405523, _1405521), _1405527), _1405525) = c_Groups_Ozero__class_Ozero(_1405521)), 34252 ^ _779571 : [(34253 ^ _779571) ^ [_1405899] : [hBOOL(hAPP(hAPP(c_member(_1405523), _1405899), _1405525)), hAPP(_1405527, _1405899) = c_Groups_Ozero__class_Ozero(_1405521)]]], (34242 ^ _779571) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405523, _1405521), _1405527), _1405525) = c_Groups_Ozero__class_Ozero(_1405521), 34246 ^ _779571 : [(34249 ^ _779571) ^ [] : [-(hAPP(_1405527, 34245 ^ [_1405521, _1405523, _1405525, _1405527]) = c_Groups_Ozero__class_Ozero(_1405521))], (34247 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405523), 34245 ^ [_1405521, _1405523, _1405525, _1405527]), _1405525)))]]]]], (24703 ^ _779571) ^ [_1210947] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1210947)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210947))], (50718 ^ _779571) ^ [_1799277, _1799279, _1799281] : [-(hAPP(c_List_Orev(_1799277), hAPP(hAPP(c_List_Oappend(_1799277), _1799279), _1799281)) = hAPP(hAPP(c_List_Oappend(_1799277), hAPP(c_List_Orev(_1799277), _1799281)), hAPP(c_List_Orev(_1799277), _1799279)))], (34630 ^ _779571) ^ [_1413880, _1413882, _1413884, _1413886, _1413888] : [-(c_Map_Orestrict__map(_1413880, _1413882, _1413884, hAPP(hAPP(c_Set_Oinsert(_1413880), _1413886), _1413888)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1413880, tc_Option_Ooption(_1413882)), c_Map_Orestrict__map(_1413880, _1413882, _1413884, _1413888)), _1413886), hAPP(_1413884, _1413886)))], (24995 ^ _779571) ^ [_1217784, _1217786] : [-(c_HOL_OThe(_1217784, hAPP(hAPP(c_COMBC(_1217784, _1217784, tc_HOL_Obool), c_fequal), _1217786)) = _1217786)], (43510 ^ _779571) ^ [_1628057, _1628059, _1628061, _1628063] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628057, _1628057)), _1628059), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1628057, _1628057), tc_HOL_Obool), _1628061), _1628063))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628057, _1628057)), _1628059), c_Transitive__Closure_Ortrancl(_1628057, _1628063))))], (48060 ^ _779571) ^ [_1739109, _1739111, _1739113, _1739115, _1739117] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739109), tc_List_Olist(_1739109))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739109), tc_List_Olist(_1739109)), _1739111), _1739113)), c_List_Olexord(_1739109, _1739115))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739109), tc_List_Olist(_1739109))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739109), tc_List_Olist(_1739109)), hAPP(hAPP(c_List_Oappend(_1739109), _1739117), _1739111)), hAPP(hAPP(c_List_Oappend(_1739109), _1739117), _1739113))), c_List_Olexord(_1739109, _1739115))))], (3416 ^ _779571) ^ [_832071, _832073] : [_832073 = _832071, -(c_Nitpick_Odenom(_832073) = c_Nitpick_Odenom(_832071))], (37906 ^ _779571) ^ [_1491194, _1491196, _1491198, _1491200, _1491202] : [c_Relation_Orefl__on(_1491194, _1491196, _1491198), c_Relation_Orefl__on(_1491194, _1491200, _1491202), -(c_Relation_Orefl__on(_1491194, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491194, tc_HOL_Obool)), _1491196), _1491200), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491194, _1491194), tc_HOL_Obool)), _1491198), _1491202)))], (46348 ^ _779571) ^ [_1695098, _1695100, _1695102] : [class_Orderings_Olinorder(_1695098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1695098), _1695100)), -(c_List_Olinorder__class_Osorted__list__of__set(_1695098, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1695098, tc_HOL_Obool)), _1695100), hAPP(hAPP(c_Set_Oinsert(_1695098), _1695102), c_Orderings_Obot__class_Obot(tc_fun(_1695098, tc_HOL_Obool))))) = c_List_Oremove1(_1695098, _1695102, c_List_Olinorder__class_Osorted__list__of__set(_1695098, _1695100)))], (24739 ^ _779571) ^ [_1211559] : [-(c_Code__Numeral_OSuc__code__numeral(_1211559) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1211559))))], (7095 ^ _779571) ^ [_896388, _896390, _896392, _896394] : [class_Groups_Ocancel__ab__semigroup__add(_896388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896388), _896390), _896392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_896388), _896390), _896394), -(_896392 = _896394)], (14864 ^ _779571) ^ [_1030192, _1030194, _1030196] : [-(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), _1030192), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030194), _1030192))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030194, _1030192))), _1030196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030194), _1030196))], (6750 ^ _779571) ^ [_890453] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _890453)], (24443 ^ _779571) ^ [_1205698, _1205700, _1205702] : [class_Orderings_Olinorder(_1205698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205698), _1205700), _1205702)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205698), _1205702), _1205700) = _1205702)], (51485 ^ _779571) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (39050 ^ _779571) ^ [_1514370, _1514372, _1514374, _1514376, _1514378, _1514380] : [c_Typedef_Otype__definition(_1514370, _1514372, _1514374, _1514376, _1514378), -(hAPP(_1514376, hAPP(_1514374, _1514380)) = _1514380)], (18459 ^ _779571) ^ [_1096327, _1096329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096327)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096329))), 18462 ^ _779571 : [(18463 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096327), _1096329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1096329)))], (18469 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096327), _1096329)))]]], (49789 ^ _779571) ^ [_1779701, _1779703, _1779705] : [49791 ^ _779571 : [(49794 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1779703, 49790 ^ [_1779701, _1779703, _1779705])))], (49792 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779701), 49790 ^ [_1779701, _1779703, _1779705]), hAPP(c_List_Oset(_1779701), _1779705))))]], -(hAPP(c_List_Ofilter(_1779701, _1779703), _1779705) = c_List_Olist_ONil(_1779701))], (50782 ^ _779571) ^ [_1800481, _1800483] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800481), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1800481))), c_List_Otranspose(_1800481, _1800483)))))], (41281 ^ _779571) ^ [_1567369, _1567371] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1567369)), 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)), _1567369))), 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, _1567371))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46973 ^ _779571) ^ [_1713291, _1713293, _1713295, _1713297, _1713299] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713291), tc_List_Olist(_1713291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713291), tc_List_Olist(_1713291)), hAPP(hAPP(c_List_Olist_OCons(_1713291), _1713293), _1713295)), _1713297)), c_List_Olistrel(_1713291, _1713299))), 46978 ^ _779571 : [(46983 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713291), tc_List_Olist(_1713291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713291), tc_List_Olist(_1713291)), _1713295), 46977 ^ [_1713291, _1713293, _1713295, _1713297, _1713299])), c_List_Olistrel(_1713291, _1713299))))], (46981 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713291, _1713291)), hAPP(hAPP(c_Product__Type_OPair(_1713291, _1713291), _1713293), 46976 ^ [_1713291, _1713293, _1713295, _1713297, _1713299])), _1713299)))], (46979 ^ _779571) ^ [] : [-(_1713297 = hAPP(hAPP(c_List_Olist_OCons(_1713291), 46976 ^ [_1713291, _1713293, _1713295, _1713297, _1713299]), 46977 ^ [_1713291, _1713293, _1713295, _1713297, _1713299]))]]], (35785 ^ _779571) ^ [_1442013, _1442015, _1442017] : [_1442015 = c_Orderings_Obot__class_Obot(tc_fun(_1442013, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442013), _1442015), _1442017) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1442013, tc_HOL_Obool), tc_HOL_Obool)))], (16070 ^ _779571) ^ [_1053919, _1053921, _1053923, _1053925, _1053927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053919), _1053921)), 16073 ^ _779571 : [(16080 ^ _779571) ^ [] : [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), _1053921), _1053919)), _1053923)), _1053925) = _1053927, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053921), _1053923)), _1053925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053919), _1053923)), _1053927))], (16074 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053921), _1053923)), _1053925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053919), _1053923)), _1053927), -(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), _1053921), _1053919)), _1053923)), _1053925) = _1053927)]]], (36814 ^ _779571) ^ [_1464906, _1464908, _1464910, _1464912, _1464914, _1464916, _1464918, _1464920] : [c_Equiv__Relations_Oequiv(_1464906, _1464908, _1464910), c_Equiv__Relations_Ocongruent2(_1464906, _1464912, _1464914, _1464910, _1464916, _1464918), hBOOL(hAPP(hAPP(c_member(_1464906), _1464920), _1464908)), -(c_Equiv__Relations_Ocongruent(_1464912, _1464914, _1464916, hAPP(_1464918, _1464920)))], (49726 ^ _779571) ^ [_1778534, _1778536, _1778538, _1778540] : [-(hBOOL(hAPP(_1778534, _1778536))), -(hAPP(c_List_Ofilter(_1778538, _1778534), hAPP(hAPP(c_List_Olist_OCons(_1778538), _1778536), _1778540)) = hAPP(c_List_Ofilter(_1778538, _1778534), _1778540))], (34713 ^ _779571) ^ [_1415876, _1415878, _1415880] : [class_Orderings_Olinorder(_1415876), hAPP(_1415878, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415876), 34718 ^ [_1415876, _1415878, _1415880]), 34719 ^ [_1415876, _1415878, _1415880])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415876), hAPP(_1415878, 34718 ^ [_1415876, _1415878, _1415880])), hAPP(_1415878, 34719 ^ [_1415876, _1415878, _1415880])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415876), _1415880)), -(_1415880 = c_Orderings_Obot__class_Obot(tc_fun(_1415876, tc_HOL_Obool))), -(hAPP(_1415878, c_Big__Operators_Olattice_OSup__fin(_1415876, c_Orderings_Oord__class_Omax(_1415876), _1415880)) = c_Big__Operators_Olattice_OSup__fin(_1415876, c_Orderings_Oord__class_Omax(_1415876), hAPP(c_Set_Oimage(_1415876, _1415876, _1415878), _1415880)))], (46825 ^ _779571) ^ [_1709240, _1709242, _1709244, _1709246, _1709248, _1709250] : [c_List_Olistrelp(_1709240, _1709242, hAPP(hAPP(c_List_Olist_OCons(_1709240), _1709244), _1709246), hAPP(hAPP(c_List_Olist_OCons(_1709240), _1709248), _1709250)), 46828 ^ _779571 : [(46831 ^ _779571) ^ [] : [-(c_List_Olistrelp(_1709240, _1709242, _1709246, _1709250))], (46829 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1709242, _1709244), _1709248)))]]], (5056 ^ _779571) ^ [_857715, _857717] : [_857717 = _857715, -(c_SetInterval_Oord__class_OatMost(_857717) = c_SetInterval_Oord__class_OatMost(_857715))], (15278 ^ _779571) ^ [_1038080, _1038082, _1038084] : [class_Groups_Oab__group__add(_1038080), 15281 ^ _779571 : [(15288 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038080), _1038082), _1038084) = c_Groups_Ozero__class_Ozero(_1038080), -(_1038082 = _1038084)], (15282 ^ _779571) ^ [] : [_1038082 = _1038084, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038080), _1038082), _1038084) = c_Groups_Ozero__class_Ozero(_1038080))]]], (25900 ^ _779571) ^ [_1233223, _1233225, _1233227] : [class_Groups_Ocomm__monoid__add(_1233223), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233223), _1233225), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233227))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1233223), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233223), _1233225), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1233227))), hAPP(_1233225, _1233227)))], (40150 ^ _779571) ^ [_1539984, _1539986, _1539988] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1539984, _1539986), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539984, _1539986), c_Orderings_Otop__class_Otop(tc_fun(_1539984, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1539986, tc_HOL_Obool), _1539984), _1539988))) = hAPP(hAPP(c_Product__Type_OSigma(_1539984, _1539986), c_Orderings_Otop__class_Otop(tc_fun(_1539984, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1539986, tc_HOL_Obool), _1539984), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1539986, tc_HOL_Obool)), _1539988))))], (50100 ^ _779571) ^ [_1786764, _1786766, _1786768] : [class_Orderings_Olinorder(_1786764), 50103 ^ _779571 : [(50122 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1786764, hAPP(hAPP(c_List_Oappend(_1786764), _1786766), _1786768))), c_List_Olinorder__class_Osorted(_1786764, _1786766), c_List_Olinorder__class_Osorted(_1786764, _1786768), 50132 ^ _779571 : [(50138 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1786764), 50131 ^ [_1786764, _1786766, _1786768]), 50134 ^ [_1786764, _1786766, _1786768]))], (50136 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786764), 50134 ^ [_1786764, _1786766, _1786768]), hAPP(c_List_Oset(_1786764), _1786768))))], (50133 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786764), 50131 ^ [_1786764, _1786766, _1786768]), hAPP(c_List_Oset(_1786764), _1786766))))]]], (50104 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1786764, hAPP(hAPP(c_List_Oappend(_1786764), _1786766), _1786768)), 50107 ^ _779571 : [(50112 ^ _779571) ^ [_1787000] : [hBOOL(hAPP(hAPP(c_member(_1786764), _1787000), hAPP(c_List_Oset(_1786764), _1786766))), 50115 ^ _779571 : [(50116 ^ _779571) ^ [_1787110] : [hBOOL(hAPP(hAPP(c_member(_1786764), _1787110), hAPP(c_List_Oset(_1786764), _1786768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1786764), _1787000), _1787110)))]]], (50110 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1786764, _1786768))], (50108 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1786764, _1786766))]]]]], (25802 ^ _779571) ^ [_1231460, _1231462] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231460), _1231462)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231460), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231462))))], (12177 ^ _779571) ^ [_982639, _982641] : [class_Rings_Olinordered__semidom(_982639), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982639), c_Groups_Ozero__class_Ozero(_982639)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_982639), _982641))))], (32637 ^ _779571) ^ [_1375029, _1375031, _1375033, _1375035, _1375037, _1375039] : [-(hBOOL(hAPP(hAPP(c_member(_1375029), _1375031), c_SetInterval_Oord_OgreaterThanAtMost(_1375029, _1375033, _1375035, _1375037, _1375039)))), hBOOL(hAPP(hAPP(_1375035, _1375037), _1375031)), hBOOL(hAPP(hAPP(_1375033, _1375031), _1375039))], (50392 ^ _779571) ^ [_1791883, _1791885] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1791883, _1791885) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1791883), hAPP(c_Nat_OSuc, _1791885))))], (17995 ^ _779571) ^ [_1089193] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089193)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1089193)))], (36782 ^ _779571) ^ [_1464122, _1464124] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464122, tc_HOL_Obool)), _1464124), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464122, tc_HOL_Obool)), _1464124)) = c_Orderings_Obot__class_Obot(tc_fun(_1464122, tc_HOL_Obool)))], (51139 ^ _779571) ^ [_1808896, _1808898] : [class_Orderings_Oorder(_1808896), -(class_Orderings_Oorder(tc_fun(_1808898, _1808896)))], (9560 ^ _779571) ^ [_938268, _938270, _938272, _938274] : [class_Rings_Olinordered__ring__strict(_938268), 9563 ^ _779571 : [(9578 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938268), _938270), _938272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938268), _938274), _938272)))), 9579 ^ _779571 : [(9586 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938272), c_Groups_Ozero__class_Ozero(_938268))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938274), _938270))], (9580 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), c_Groups_Ozero__class_Ozero(_938268)), _938272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938270), _938274))]]], (9564 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938268), _938270), _938272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938268), _938274), _938272))), 9569 ^ _779571 : [(9572 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938270), _938274)))], (9570 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), c_Groups_Ozero__class_Ozero(_938268)), _938272)))]], 9573 ^ _779571 : [(9576 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938274), _938270)))], (9574 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938268), _938272), c_Groups_Ozero__class_Ozero(_938268))))]]]]], (19135 ^ _779571) ^ [_1107738, _1107740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1107738)), c_Int_OBit0(_1107740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107738), _1107740)))], (49943 ^ _779571) ^ [_1783977, _1783979, _1783981, _1783983, _1783985] : [class_Orderings_Olinorder(_1783977), c_List_Olinorder__class_Osorted(_1783977, hAPP(hAPP(c_List_Omap(_1783979, _1783977), _1783981), _1783983)), -(c_List_Olinorder__class_Osorted(_1783977, hAPP(hAPP(c_List_Omap(_1783979, _1783977), _1783981), hAPP(c_List_Ofilter(_1783979, _1783985), _1783983))))], (19189 ^ _779571) ^ [_1108647] : [c_Int_OPls = _1108647, -(c_Int_OPls = c_Int_OBit0(_1108647))], (46620 ^ _779571) ^ [_1701866, _1701868] : [-(c_List_Olenlex(_1701866, _1701868) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1701866), tc_List_Olist(_1701866), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1701866), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), tc_List_Olist(_1701866)), c_COMBS(tc_List_Olist(_1701866), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1701866)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1701866)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701866), tc_fun(tc_List_Olist(_1701866), tc_Nat_Onat), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1701866), tc_Nat_Onat), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), tc_List_Olist(_1701866)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1701866))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1701866)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1701866))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1701866)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1701866), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), tc_List_Olist(_1701866)), c_COMBS(tc_List_Olist(_1701866), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1701866)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1701866)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701866), tc_fun(tc_List_Olist(_1701866), tc_Nat_Onat), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1701866), tc_Nat_Onat), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), tc_List_Olist(_1701866)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1701866))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1701866)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1701866))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1701866)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701866), tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701866), tc_HOL_Obool)), tc_List_Olist(_1701866)), c_COMBC(tc_List_Olist(_1701866), tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701866), tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866))), tc_fun(tc_List_Olist(_1701866), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1701866)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1701866)), c_member(tc_prod(tc_List_Olist(_1701866), tc_List_Olist(_1701866))))), c_Product__Type_OPair(tc_List_Olist(_1701866), tc_List_Olist(_1701866))))), c_List_Olex(_1701866, _1701868)))))))], (3998 ^ _779571) ^ [_841176, _841178] : [_841178 = _841176, -(c_Relation_OField(_841178) = c_Relation_OField(_841176))], (23785 ^ _779571) ^ [_1192835, _1192837, _1192839, _1192841] : [class_Orderings_Olinorder(_1192835), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192835), _1192837), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192835), _1192839), _1192841)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192835), _1192839), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192835), _1192837), _1192841)))], (41467 ^ _779571) ^ [_1574263, _1574265, _1574267] : [class_Groups_Olinordered__ab__semigroup__add(_1574263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574263), _1574265)), -(_1574265 = c_Orderings_Obot__class_Obot(tc_fun(_1574263, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1574263), _1574267), c_Big__Operators_Olinorder__class_OMin(_1574263, _1574265)) = c_Big__Operators_Olinorder__class_OMin(_1574263, hAPP(c_Set_OCollect(_1574263), hAPP(hAPP(c_COMBB(tc_fun(_1574263, tc_HOL_Obool), tc_HOL_Obool, _1574263), c_HOL_OEx(_1574263)), hAPP(hAPP(c_COMBC(_1574263, tc_fun(_1574263, tc_HOL_Obool), tc_fun(_1574263, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574263, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1574263, tc_HOL_Obool), tc_fun(_1574263, tc_HOL_Obool)), _1574263), c_COMBS(_1574263, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574263, tc_HOL_Obool), tc_fun(_1574263, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1574263), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574263), c_fconj)), hAPP(hAPP(c_COMBC(_1574263, tc_fun(_1574263, _1574263), tc_fun(_1574263, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574263, tc_HOL_Obool), tc_fun(tc_fun(_1574263, _1574263), tc_fun(_1574263, tc_HOL_Obool)), _1574263), c_COMBB(_1574263, tc_HOL_Obool, _1574263)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1574263), _1574267))))), hAPP(hAPP(c_COMBC(_1574263, tc_fun(_1574263, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574263)), _1574265))))))], (29286 ^ _779571) ^ [_1302969, _1302971, _1302973, _1302975] : [class_Complete__Lattice_Ocomplete__lattice(_1302969), -(_1302971 = c_Orderings_Obot__class_Obot(tc_fun(_1302973, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1302973, _1302969), _1302971), hAPP(c_COMBK(_1302969, _1302973), _1302975)) = _1302975)], (35452 ^ _779571) ^ [_1433128, _1433130, _1433132, _1433134, _1433136, _1433138] : [-(hAPP(hAPP(c_Fun_Ocomp(_1433128, _1433130, _1433132, _1433134), _1433136), _1433138) = hAPP(_1433134, hAPP(_1433136, _1433138)))], (34839 ^ _779571) ^ [] : [-(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)))], (51267 ^ _779571) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (19269 ^ _779571) ^ [_1110026, _1110028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110026), _1110028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1110026)), c_Int_OBit1(_1110028))))], (5724 ^ _779571) ^ [_871001, _871003] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _871001, _871003, _871001))], (36588 ^ _779571) ^ [_1459205, _1459207, _1459209] : [class_Lattices_Olattice(_1459205), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459205), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459205), _1459207), _1459209)), _1459209)))], (35239 ^ _779571) ^ [_1428436, _1428438] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1428436, tc_HOL_Obool)), hAPP(c_Set_OPow(_1428436), _1428438))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1428436), _1428438)))], (15380 ^ _779571) ^ [_1039954] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039954), _1039954) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8661 ^ _779571) ^ [_922532, _922534] : [class_Rings_Olinordered__idom(_922532), 8664 ^ _779571 : [(8671 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922532), c_Groups_Ozero__class_Ozero(_922532)), hAPP(c_Int_Oring__1__class_Oof__int(_922532), _922534))))], (8665 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922532), c_Groups_Ozero__class_Ozero(_922532)), hAPP(c_Int_Oring__1__class_Oof__int(_922532), _922534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922534)))]]], (7466 ^ _779571) ^ [_903451, _903453] : [-(_903451 = _903453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903451), _903453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903453), _903451)))], (28040 ^ _779571) ^ [_1276511, _1276513, _1276515] : [class_Lattices_Osemilattice__sup(_1276511), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276511), _1276513), _1276515) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276511), _1276515), _1276513))], (30455 ^ _779571) ^ [_1325783, _1325785, _1325787, _1325789, _1325791, _1325793] : [-(hBOOL(hAPP(hAPP(c_member(_1325783), _1325785), c_SetInterval_Oord_OatLeastLessThan(_1325783, _1325787, _1325789, _1325791, _1325793)))), hBOOL(hAPP(hAPP(_1325787, _1325791), _1325785)), hBOOL(hAPP(hAPP(_1325789, _1325785), _1325793))], (17753 ^ _779571) ^ [_1085362] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085362)))), -(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), _1085362)) = 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), _1085362))))], (30505 ^ _779571) ^ [_1326782, _1326784, _1326786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326782, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326782, tc_fun(_1326782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326782)), _1326784)), hAPP(hAPP(c_COMBC(_1326782, tc_fun(_1326782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326782)), _1326786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326782, tc_HOL_Obool)), _1326784), _1326786)))], (32584 ^ _779571) ^ [_1373883, _1373885, _1373887] : [-(hAPP(c_Finite__Set_Ocard(_1373883), _1373885) = hAPP(c_Nat_OSuc, _1373887)), 32585 ^ _779571 : [(32586 ^ _779571) ^ [_1373983, _1373985] : [_1373885 = hAPP(hAPP(c_Set_Oinsert(_1373883), _1373985), _1373983), -(hBOOL(hAPP(hAPP(c_member(_1373883), _1373985), _1373983))), hAPP(c_Finite__Set_Ocard(_1373883), _1373983) = _1373887, 32597 ^ _779571 : [(32600 ^ _779571) ^ [] : [_1373983 = c_Orderings_Obot__class_Obot(tc_fun(_1373883, tc_HOL_Obool))], (32598 ^ _779571) ^ [] : [-(_1373887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (6841 ^ _779571) ^ [_892388, _892390, _892392, _892394, _892396] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_892388, _892390), _892392, _892394, _892396), -(_892396 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _892392), _892388), hAPP(_892390, _892392)))], (9414 ^ _779571) ^ [_935709, _935711, _935713, _935715, _935717] : [class_Rings_Osemiring(_935709), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935709), _935711), _935713)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935709), _935715), _935713)), _935717)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935709), _935711), _935715)), _935713)), _935717))], (19165 ^ _779571) ^ [_1108285, _1108287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108285), _1108287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1108285)), c_Int_OBit0(_1108287))))], (39632 ^ _779571) ^ [_1527317, _1527319, _1527321, _1527323, _1527325, _1527327, _1527329, _1527331] : [class_Groups_Ocomm__monoid__mult(_1527317), c_Fun_Oinj__on(_1527319, _1527321, _1527323, _1527325), _1527327 = hAPP(c_Set_Oimage(_1527319, _1527321, _1527323), _1527325), 39646 ^ _779571 : [(39649 ^ _779571) ^ [] : [hAPP(_1527329, 39645 ^ [_1527317, _1527319, _1527321, _1527323, _1527325, _1527327, _1527329, _1527331]) = hAPP(hAPP(c_Fun_Ocomp(_1527321, _1527317, _1527319, _1527331), _1527323), 39645 ^ [_1527317, _1527319, _1527321, _1527323, _1527325, _1527327, _1527329, _1527331])], (39647 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527319), 39645 ^ [_1527317, _1527319, _1527321, _1527323, _1527325, _1527327, _1527329, _1527331]), _1527325)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1527321, _1527317), _1527331), _1527327) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1527319, _1527317), _1527329), _1527325))], (13236 ^ _779571) ^ [_1001134, _1001136] : [class_Rings_Oring__1(_1001134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001136)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1001134), hAPP(c_Int_Onat, _1001136)) = hAPP(c_Int_Oring__1__class_Oof__int(_1001134), _1001136))], (3422 ^ _779571) ^ [_832156, _832158] : [_832158 = _832156, -(c_Nitpick_Onum(_832158) = c_Nitpick_Onum(_832156))], (40702 ^ _779571) ^ [_1552357, _1552359, _1552361, _1552363, _1552365, _1552367] : [class_Groups_Ocomm__monoid__mult(_1552357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552359), _1552361)), 40712 ^ _779571 : [(40715 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552363), hAPP(_1552365, 40711 ^ [_1552357, _1552359, _1552361, _1552363, _1552365, _1552367])))], (40713 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552359), 40711 ^ [_1552357, _1552359, _1552361, _1552363, _1552365, _1552367]), _1552361)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552359, _1552357), hAPP(hAPP(c_COMBS(_1552359, tc_fun(_1552363, tc_HOL_Obool), _1552357), hAPP(hAPP(c_COMBB(tc_fun(_1552363, _1552357), tc_fun(tc_fun(_1552363, tc_HOL_Obool), _1552357), _1552359), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552363, _1552357)), _1552367)), _1552365)), _1552361) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1552359, _1552363), _1552357), hAPP(c_Product__Type_Oprod_Oprod__case(_1552359, _1552363, _1552357), _1552367)), hAPP(hAPP(c_Product__Type_OSigma(_1552359, _1552363), _1552361), _1552365)))], (29081 ^ _779571) ^ [_1298397] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298397)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298397)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1298397)))], (42686 ^ _779571) ^ [_1607577, _1607579, _1607581, _1607583] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1607577, tc_HOL_Obool), tc_fun(_1607577, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1607577, tc_HOL_Obool), tc_fun(_1607577, tc_HOL_Obool)), _1607579), _1607581)), c_Wellfounded_Omax__ext(_1607577, _1607583)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607577), _1607579)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607577), _1607581)), -(_1607581 = c_Orderings_Obot__class_Obot(tc_fun(_1607577, tc_HOL_Obool))), 42700 ^ _779571 : [(42703 ^ _779571) ^ [_1607982] : [hBOOL(hAPP(hAPP(c_member(_1607577), _1607982), _1607581)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1607577, _1607577)), hAPP(hAPP(c_Product__Type_OPair(_1607577, _1607577), 42699 ^ [_1607577, _1607579, _1607581, _1607583]), _1607982)), _1607583))], (42701 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607577), 42699 ^ [_1607577, _1607579, _1607581, _1607583]), _1607579)))]]], (13741 ^ _779571) ^ [_1010200, _1010202, _1010204, _1010206] : [class_Divides_Osemiring__div(_1010200), -(c_Divides_Odiv__class_Omod(_1010200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010200), _1010202), _1010204), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010200), _1010202), _1010206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010200), _1010202), c_Divides_Odiv__class_Omod(_1010200, _1010204, _1010206)))], (47382 ^ _779571) ^ [_1722303, _1722305] : [-(_1722303 = c_List_Olist_ONil(_1722305)), -(c_Random_Oselect__weight(_1722305, hAPP(hAPP(c_List_Omap(_1722305, tc_prod(tc_Code__Numeral_Ocode__numeral, _1722305)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1722305), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1722303)) = c_Random_Oselect(_1722305, _1722303))], (13000 ^ _779571) ^ [_997276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997276)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _997276)) = _997276)], (35811 ^ _779571) ^ [_1442611, _1442613, _1442615] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1442611), hAPP(hAPP(c_Set_Oinsert(_1442611), _1442613), c_Orderings_Obot__class_Obot(tc_fun(_1442611, tc_HOL_Obool)))), _1442615) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1442611, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442611, _1442611, _1442615), hAPP(hAPP(c_Set_Oinsert(_1442611), _1442613), c_Orderings_Obot__class_Obot(tc_fun(_1442611, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1442611, tc_HOL_Obool), tc_HOL_Obool))))], (24837 ^ _779571) ^ [_1213735, _1213737, _1213739] : [-(c_Nitpick_Oof__frac(_1213737, _1213735, _1213739) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213735), hAPP(c_Int_Oring__1__class_Oof__int(_1213735), hAPP(c_Nitpick_Onum(_1213737), _1213739))), hAPP(c_Int_Oring__1__class_Oof__int(_1213735), hAPP(c_Nitpick_Odenom(_1213737), _1213739)))), class_Rings_Oinverse(_1213735), class_Rings_Oring__1(_1213735)], (30886 ^ _779571) ^ [_1335446, _1335448] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335446), _1335448)), -(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)))), _1335448, _1335446) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (49708 ^ _779571) ^ [_1777983, _1777985, _1777987, _1777989, _1777991] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777983)), hAPP(c_List_Ofilter(_1777983, _1777985), hAPP(hAPP(c_List_Omap(_1777987, _1777983), _1777989), _1777991))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777987)), hAPP(c_List_Ofilter(_1777987, hAPP(c_Fun_Ocomp(_1777983, tc_HOL_Obool, _1777987, _1777985), _1777989)), _1777991)))], (43643 ^ _779571) ^ [_1631568, _1631570] : [-(c_Transitive__Closure_Ortrancl(_1631568, _1631570) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1631568, _1631568), 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(_1631568, _1631568), tc_HOL_Obool), tc_fun(tc_prod(_1631568, _1631568), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1631568, _1631568), tc_HOL_Obool)), _1631570)))], (10329 ^ _779571) ^ [_951634, _951636] : [_951634 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951634), _951636), -(_951636 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_951634 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46925 ^ _779571) ^ [_1711283, _1711285, _1711287] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711283)), hAPP(hAPP(c_List_Olist_OCons(_1711283), _1711285), _1711287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711283)), _1711287)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24909 ^ _779571) ^ [_1215437, _1215439, _1215441, _1215443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215437, tc_HOL_Obool)), _1215439), _1215441)), hBOOL(hAPP(_1215439, _1215443)), -(hBOOL(hAPP(_1215441, _1215443)))], (38353 ^ _779571) ^ [_1500009, _1500011, _1500013, _1500015, _1500017] : [c_Fun_Oinj__on(_1500009, _1500011, _1500013, c_Orderings_Otop__class_Otop(tc_fun(_1500009, tc_HOL_Obool))), c_Fun_Oinj__on(_1500015, _1500009, _1500017, c_Orderings_Otop__class_Otop(tc_fun(_1500015, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1500015, _1500011, hAPP(c_Fun_Ocomp(_1500009, _1500011, _1500015, _1500013), _1500017), c_Orderings_Otop__class_Otop(tc_fun(_1500015, tc_HOL_Obool))))], (39815 ^ _779571) ^ [_1531250, _1531252, _1531254, _1531256, _1531258] : [-(_1531250 = c_Option_Ooption_ONone(_1531252)), -(c_Map_Odom(_1531254, _1531252, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1531254, tc_Option_Ooption(_1531252)), _1531256), _1531258), _1531250)) = hAPP(hAPP(c_Set_Oinsert(_1531254), _1531258), c_Map_Odom(_1531254, _1531252, _1531256)))], (35301 ^ _779571) ^ [_1429848, _1429850, _1429852, _1429854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1429848), _1429850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429848, tc_HOL_Obool)), _1429850), _1429852)), hBOOL(hAPP(_1429854, c_Orderings_Obot__class_Obot(tc_fun(_1429848, tc_HOL_Obool)))), 35316 ^ _779571 : [(35317 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1429848), 35315 ^ [_1429848, _1429850, _1429852, _1429854])))], (35321 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1429848), 35314 ^ [_1429848, _1429850, _1429852, _1429854]), 35315 ^ [_1429848, _1429850, _1429852, _1429854]))], (35325 ^ _779571) ^ [] : [hBOOL(hAPP(_1429854, hAPP(hAPP(c_Set_Oinsert(_1429848), 35314 ^ [_1429848, _1429850, _1429852, _1429854]), 35315 ^ [_1429848, _1429850, _1429852, _1429854])))], (35323 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1429854, 35315 ^ [_1429848, _1429850, _1429852, _1429854])))], (35319 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429848), 35314 ^ [_1429848, _1429850, _1429852, _1429854]), _1429852)))]], -(hBOOL(hAPP(_1429854, _1429850)))], (26832 ^ _779571) ^ [_1251850, _1251852, _1251854] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251850, tc_Nat_Onat), _1251852), _1251854) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251850, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1251850), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1251852)), _1251854)))], (40380 ^ _779571) ^ [_1545424, _1545426, _1545428] : [c_Relation_Orefl__on(_1545424, _1545426, _1545428), 40383 ^ _779571 : [(40386 ^ _779571) ^ [_1545606] : [hBOOL(hAPP(hAPP(c_member(_1545424), _1545606), _1545426)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545424, _1545424)), hAPP(hAPP(c_Product__Type_OPair(_1545424, _1545424), _1545606), _1545606)), _1545428)))], (40384 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545424, _1545424), tc_HOL_Obool)), _1545428), hAPP(hAPP(c_Product__Type_OSigma(_1545424, _1545424), _1545426), hAPP(c_COMBK(tc_fun(_1545424, tc_HOL_Obool), _1545424), _1545426)))))]]], (25564 ^ _779571) ^ [_1227269, _1227271, _1227273] : [class_Orderings_Olinorder(_1227269), 25567 ^ _779571 : [(25574 ^ _779571) ^ [] : [_1227271 = _1227273, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1227269), _1227271) = hAPP(c_SetInterval_Oord__class_OlessThan(_1227269), _1227273))], (25568 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1227269), _1227271) = hAPP(c_SetInterval_Oord__class_OlessThan(_1227269), _1227273), -(_1227271 = _1227273)]]], (8157 ^ _779571) ^ [_914765, _914767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914765), _914767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914765)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914767))))], (48984 ^ _779571) ^ [_1762336, _1762338, _1762340] : [-(_1762336 = c_List_Olist_ONil(_1762338)), -(hAPP(c_List_Ohd(_1762338), hAPP(c_List_Orotate(_1762338, _1762340), _1762336)) = hAPP(hAPP(c_List_Onth(_1762338), _1762336), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1762340, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762338)), _1762336))))], (13615 ^ _779571) ^ [_1007701, _1007703, _1007705, _1007707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007703), _1007705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1007705), 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), _1007703), _1007701)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007703), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007707, _1007701))), _1007705))))], (9422 ^ _779571) ^ [_935948, _935950, _935952] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935950), _935952)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935948), _935950)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935948), _935952)))], (15156 ^ _779571) ^ [_1035759, _1035761, _1035763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035759)), 15162 ^ _779571 : [(15165 ^ _779571) ^ [] : [hBOOL(hAPP(_1035761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15161 ^ [_1035759, _1035761, _1035763]), _1035759)))], (15163 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1035761, 15161 ^ [_1035759, _1035761, _1035763])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035763)), 15170 ^ _779571 : [(15171 ^ _779571) ^ [_1036048] : [hBOOL(hAPP(_1035761, _1036048)), -(hBOOL(hAPP(_1035761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1036048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035763), _1035759)))))]]], (29464 ^ _779571) ^ [_1306310, _1306312, _1306314] : [class_Orderings_Oorder(_1306310), 29467 ^ _779571 : [(29474 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306310), _1306312), _1306314))), -(c_Orderings_Obot__class_Obot(tc_fun(_1306310, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306310, _1306312), _1306314))], (29468 ^ _779571) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1306310, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306310, _1306312), _1306314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306310), _1306312), _1306314))]]], (44678 ^ _779571) ^ [_1656145, _1656147, _1656149, _1656151, _1656153] : [_1656145 = c_Orderings_Obot__class_Obot(tc_fun(_1656147, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656149, tc_HOL_Obool)), _1656151), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656147, tc_fun(_1656149, tc_HOL_Obool)), _1656145), _1656153)) = _1656151)], (31476 ^ _779571) ^ [_1349284, _1349286, _1349288, _1349290, _1349292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1349284), hAPP(c_Set_Oimage(_1349286, _1349284, _1349288), c_Orderings_Otop__class_Otop(tc_fun(_1349286, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1349290), hAPP(c_Set_Oimage(_1349286, _1349290, hAPP(hAPP(c_COMBB(_1349284, _1349290, _1349286), _1349292), _1349288)), c_Orderings_Otop__class_Otop(tc_fun(_1349286, tc_HOL_Obool))))))], (43893 ^ _779571) ^ [_1637854, _1637856, _1637858, _1637860] : [-(hAPP(c_Finite__Set_Ofold__image(_1637854, _1637856, _1637858), _1637860) = c_Finite__Set_Ofold(_1637856, _1637854, hAPP(hAPP(c_COMBB(_1637854, tc_fun(_1637854, _1637854), _1637856), _1637858), _1637860)))], (51679 ^ _779571) ^ [_1814546, _1814548] : [v_P(_1814548, _1814546), 51682 ^ _779571 : [(51683 ^ _779571) ^ [_1814611] : [c_Natural_Oevaln(v_c, _1814546, v_n, _1814611), -(v_Q(_1814548, _1814611))]]], (47226 ^ _779571) ^ [_1719455, _1719457, _1719459, _1719461] : [hAPP(hAPP(c_List_Omap(_1719455, _1719457), _1719459), _1719461) = c_List_Olist_ONil(_1719457), -(_1719461 = c_List_Olist_ONil(_1719455))], (17603 ^ _779571) ^ [_1082594, _1082596] : [class_Power_Opower(_1082594), class_Rings_Osemiring__0(_1082594), 17610 ^ _779571 : [(17617 ^ _779571) ^ [] : [-(_1082596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082594), c_Groups_Ozero__class_Ozero(_1082594)), _1082596) = c_Groups_Ozero__class_Ozero(_1082594))], (17611 ^ _779571) ^ [] : [_1082596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082594), c_Groups_Ozero__class_Ozero(_1082594)), _1082596) = c_Groups_Oone__class_Oone(_1082594))]]], (14828 ^ _779571) ^ [_1029502, _1029504, _1029506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029502), _1029504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029506), 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), _1029504), _1029506)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029502), _1029506))))], (26346 ^ _779571) ^ [_1242376] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1242376), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1242376 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12253 ^ _779571) ^ [_984019, _984021, _984023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984019), _984021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984023), _984019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984023), _984021))))], (9408 ^ _779571) ^ [_935550, _935552, _935554, _935556] : [class_Rings_Ocomm__semiring(_935550), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935550), _935552), _935554)), _935556) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935550), _935552), _935556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935550), _935554), _935556)))], (36926 ^ _779571) ^ [_1467388, _1467390, _1467392, _1467394] : [class_Orderings_Olinorder(_1467388), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467388, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1467388), _1467390)), c_SetInterval_Oord__class_OatLeastAtMost(_1467388, _1467392, _1467394)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467388, _1467392, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1467388), _1467390), _1467394)))], (49742 ^ _779571) ^ [_1778816, _1778818, _1778820] : [49744 ^ _779571 : [(49747 ^ _779571) ^ [] : [hBOOL(hAPP(_1778818, 49743 ^ [_1778816, _1778818, _1778820]))], (49745 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778816), 49743 ^ [_1778816, _1778818, _1778820]), hAPP(c_List_Oset(_1778816), _1778820))))]], -(hAPP(c_List_Ofilter(_1778816, _1778818), _1778820) = _1778820)], (19373 ^ _779571) ^ [_1111858] : [-(c_Int_Opred(c_Int_OBit0(_1111858)) = c_Int_OBit1(c_Int_Opred(_1111858)))], (36296 ^ _779571) ^ [_1453683, _1453685, _1453687, _1453689] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453683, tc_HOL_Obool)), _1453685), _1453687), _1453689)), -(hBOOL(hAPP(_1453685, _1453689)))], (19211 ^ _779571) ^ [_1109028] : [c_Int_OBit0(_1109028) = c_Int_OMin], (33475 ^ _779571) ^ [_1389867, _1389869] : [-(hBOOL(hAPP(hAPP(c_member(_1389867), _1389869), c_Orderings_Otop__class_Otop(tc_fun(_1389867, tc_HOL_Obool)))))], (5258 ^ _779571) ^ [_860820, _860822, _860824, _860826, _860828, _860830, _860832, _860834] : [-(c_List_Olist_Olist__case(_860834, _860830, _860826, _860822) = c_List_Olist_Olist__case(_860832, _860828, _860824, _860820)), _860834 = _860832, _860830 = _860828, _860826 = _860824, _860822 = _860820], (6579 ^ _779571) ^ [_886958, _886960, _886962] : [6580 ^ _779571 : [(6581 ^ _779571) ^ [_887008] : [c_Natural_Oevaln(_886958, _886960, _887008, _886962)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886958), _886960), _886962)))], (30188 ^ _779571) ^ [_1320594, _1320596] : [hBOOL(hAPP(hAPP(c_member(_1320594), _1320596), c_Orderings_Obot__class_Obot(tc_fun(_1320594, tc_HOL_Obool))))], (48890 ^ _779571) ^ [_1760496, _1760498, _1760500, _1760502] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1760496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1760498), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1760496)), hAPP(hAPP(c_List_Olist_OCons(_1760498), _1760500), _1760502)) = hAPP(hAPP(c_List_Olist_OCons(_1760498), _1760500), _1760502))], (41800 ^ _779571) ^ [_1587379, _1587381, _1587383, _1587385] : [c_Wellfounded_Owf(_1587379, _1587381), -(c_Wellfounded_Owf(_1587383, hAPP(hAPP(c_Relation_Oinv__image(_1587379, _1587383), _1587381), _1587385)))], (46132 ^ _779571) ^ [_1690402, _1690404, _1690406, _1690408, _1690410] : [hAPP(c_Map_Omap__of(_1690402, _1690404, _1690406), _1690408) = hAPP(c_Option_Ooption_OSome(_1690404), _1690410), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1690402, _1690404)), hAPP(hAPP(c_Product__Type_OPair(_1690402, _1690404), _1690408), _1690410)), hAPP(c_List_Oset(tc_prod(_1690402, _1690404)), _1690406))))], (39072 ^ _779571) ^ [] : [-(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))))], (17783 ^ _779571) ^ [_1085808, _1085810] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085808)))), 17786 ^ _779571 : [(17793 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085810)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085810)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085810))))], (17787 ^ _779571) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085810))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085810)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085808))]]], (22272 ^ _779571) ^ [_1163787, _1163789, _1163791, _1163793] : [class_Groups_Ouminus(_1163787), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1163789, _1163787)), _1163791), _1163793) = hAPP(c_Groups_Ouminus__class_Ouminus(_1163787), hAPP(_1163791, _1163793)))], (35581 ^ _779571) ^ [_1436673, _1436675, _1436677, _1436679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436673), _1436679)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436677), _1436675))), -(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), _1436673), _1436675)), 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), _1436677), _1436679)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (39443 ^ _779571) ^ [_1522791, _1522793, _1522795, _1522797] : [-(hAPP(c_Set_Ovimage(_1522791, _1522793, _1522795), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1522793, tc_HOL_Obool)), _1522797)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1522791, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522791, _1522793, _1522795), _1522797)))], (51457 ^ _779571) ^ [_1811947] : [class_Finite__Set_Ofinite(_1811947), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1811947)))], (12293 ^ _779571) ^ [_984830, _984832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984830), hAPP(c_Nat_OSuc, _984832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984830), _984832)))], (29041 ^ _779571) ^ [_1297600, _1297602, _1297604, _1297606, _1297608] : [-(hAPP(c_Set_Oimage(_1297600, _1297602, hAPP(hAPP(c_COMBB(_1297604, _1297602, _1297600), _1297606), _1297608)), c_Orderings_Otop__class_Otop(tc_fun(_1297600, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1297604, _1297602, _1297606), hAPP(c_Set_Oimage(_1297600, _1297604, _1297608), c_Orderings_Otop__class_Otop(tc_fun(_1297600, tc_HOL_Obool)))))], (49646 ^ _779571) ^ [_1776616, _1776618, _1776620] : [-(c_List_Obutlast(_1776616, hAPP(hAPP(c_List_Oappend(_1776616), _1776618), hAPP(hAPP(c_List_Olist_OCons(_1776616), _1776620), c_List_Olist_ONil(_1776616)))) = _1776618)], (1182 ^ _779571) ^ [_797114, _797116] : [-(class_Groups_Oabs__if(_797114)), _797116 = _797114, class_Groups_Oabs__if(_797116)], (18421 ^ _779571) ^ [_1095758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095758), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095758)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42637 ^ _779571) ^ [_1606509, _1606511, _1606513, _1606515] : [class_Groups_Ocomm__monoid__mult(_1606509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1606511), _1606513)), 42647 ^ _779571 : [(42650 ^ _779571) ^ [] : [hAPP(_1606515, 42646 ^ [_1606509, _1606511, _1606513, _1606515]) = c_Groups_Oone__class_Oone(_1606509)], (42648 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606511), 42646 ^ [_1606509, _1606511, _1606513, _1606515]), _1606513)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1606509, _1606511, c_Groups_Otimes__class_Otimes(_1606509)), _1606515), c_Groups_Oone__class_Oone(_1606509)), _1606513) = c_Groups_Oone__class_Oone(_1606509))], (10670 ^ _779571) ^ [_957145, _957147] : [-(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), _957145), _957147)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _957145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _957147))], (20393 ^ _779571) ^ [_1130380, _1130382, _1130384, _1130386] : [class_Fields_Ofield__inverse__zero(_1130380), 20396 ^ _779571 : [(20397 ^ _779571) ^ [] : [_1130382 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130380), _1130384), _1130386), 20400 ^ _779571 : [(20407 ^ _779571) ^ [] : [_1130386 = c_Groups_Ozero__class_Ozero(_1130380), -(_1130382 = c_Groups_Ozero__class_Ozero(_1130380))], (20401 ^ _779571) ^ [] : [-(_1130386 = c_Groups_Ozero__class_Ozero(_1130380)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130380), _1130382), _1130386) = _1130384)]]], (20413 ^ _779571) ^ [] : [-(_1130382 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130380), _1130384), _1130386)), 20416 ^ _779571 : [(20419 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130380), _1130382), _1130386) = _1130384], (20417 ^ _779571) ^ [] : [_1130386 = c_Groups_Ozero__class_Ozero(_1130380)]], 20420 ^ _779571 : [(20423 ^ _779571) ^ [] : [_1130382 = c_Groups_Ozero__class_Ozero(_1130380)], (20421 ^ _779571) ^ [] : [-(_1130386 = c_Groups_Ozero__class_Ozero(_1130380))]]]]], (11925 ^ _779571) ^ [_978244, _978246, _978248] : [class_Rings_Oordered__cancel__semiring(_978244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978244), _978246), c_Groups_Ozero__class_Ozero(_978244))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978244), c_Groups_Ozero__class_Ozero(_978244)), _978248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978244), _978246), _978248)), c_Groups_Ozero__class_Ozero(_978244))))], (34674 ^ _779571) ^ [_1414980, _1414982, _1414984, _1414986] : [-(c_Map_Orestrict__map(_1414980, _1414982, _1414984, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414980, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1414980), _1414986), c_Orderings_Obot__class_Obot(tc_fun(_1414980, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414980, tc_Option_Ooption(_1414982)), _1414984), _1414986), c_Option_Ooption_ONone(_1414982)))], (47571 ^ _779571) ^ [_1727305, _1727307, _1727309] : [hBOOL(hAPP(hAPP(c_member(_1727305), _1727307), hAPP(c_List_Oset(_1727305), _1727309))), 47575 ^ _779571 : [(47578 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1727305), _1727309), 47574 ^ [_1727305, _1727307, _1727309]) = _1727307)], (47576 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47574 ^ [_1727305, _1727307, _1727309]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727305)), _1727309))))]]], (29339 ^ _779571) ^ [_1304111, _1304113, _1304115, _1304117] : [29341 ^ _779571 : [(29344 ^ _779571) ^ [] : [hAPP(_1304117, 29340 ^ [_1304111, _1304113, _1304115, _1304117]) = c_Orderings_Obot__class_Obot(tc_fun(_1304113, tc_HOL_Obool))], (29342 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304111), 29340 ^ [_1304111, _1304113, _1304115, _1304117]), _1304115)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304111, tc_fun(_1304113, tc_HOL_Obool)), _1304115), _1304117) = c_Orderings_Obot__class_Obot(tc_fun(_1304113, tc_HOL_Obool)))], (42872 ^ _779571) ^ [_1611591, _1611593] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1611591, _1611591)), c_Transitive__Closure_Otrancl(_1611591, _1611593))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1611591, _1611591)), _1611593)))], (46058 ^ _779571) ^ [_1688730, _1688732, _1688734, _1688736, _1688738] : [-(hAPP(hAPP(c_Option_Omap(_1688730, _1688732), _1688734), _1688736) = hAPP(c_Option_Ooption_OSome(_1688732), _1688738)), 46059 ^ _779571 : [(46060 ^ _779571) ^ [_1688798] : [_1688736 = hAPP(c_Option_Ooption_OSome(_1688730), _1688798), hAPP(_1688734, _1688798) = _1688738]]], (20941 ^ _779571) ^ [_1139874, _1139876, _1139878, _1139880] : [class_Fields_Olinordered__field__inverse__zero(_1139874), 20944 ^ _779571 : [(20945 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139874), _1139876), _1139878)), _1139880)), 20948 ^ _779571 : [(20955 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139878))), 20958 ^ _779571 : [(20965 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139878), c_Groups_Ozero__class_Ozero(_1139874)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139880)))], (20959 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139878), c_Groups_Ozero__class_Ozero(_1139874))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139874), _1139880), _1139878)), _1139876)))]]], (20949 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139874), _1139880), _1139878))))]]], (20971 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139874), _1139876), _1139878)), _1139880))), 20974 ^ _779571 : [(20977 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139874), _1139880), _1139878)))], (20975 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139878)))]], 20978 ^ _779571 : [(20981 ^ _779571) ^ [] : [20982 ^ _779571 : [(20985 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139874), _1139880), _1139878)), _1139876))], (20983 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139878), c_Groups_Ozero__class_Ozero(_1139874))))]], 20986 ^ _779571 : [(20989 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139880))], (20987 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), _1139878), c_Groups_Ozero__class_Ozero(_1139874)))]]], (20979 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139874), c_Groups_Ozero__class_Ozero(_1139874)), _1139878))]]]]], (49836 ^ _779571) ^ [_1780732, _1780734, _1780736] : [hBOOL(hAPP(c_List_Odistinct(_1780732), _1780734)), -(hAPP(c_List_Ofilter(_1780732, hAPP(hAPP(c_COMBC(_1780732, tc_fun(_1780732, tc_HOL_Obool), tc_HOL_Obool), c_member(_1780732)), hAPP(c_List_Oset(_1780732), c_List_Osublist(_1780732, _1780734, _1780736)))), _1780734) = c_List_Osublist(_1780732, _1780734, _1780736))], (11605 ^ _779571) ^ [_972412, _972414] : [class_Rings_Olinordered__idom(_972412), 11608 ^ _779571 : [(11615 ^ _779571) ^ [] : [_972414 = c_Groups_Ozero__class_Ozero(_972412), -(c_Groups_Osgn__class_Osgn(_972412, _972414) = c_Groups_Ozero__class_Ozero(_972412))], (11609 ^ _779571) ^ [] : [c_Groups_Osgn__class_Osgn(_972412, _972414) = c_Groups_Ozero__class_Ozero(_972412), -(_972414 = c_Groups_Ozero__class_Ozero(_972412))]]], (23113 ^ _779571) ^ [_1180486, _1180488, _1180490, _1180492, _1180494, _1180496] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1180486, _1180488, _1180490), _1180492), hAPP(hAPP(c_Product__Type_OPair(_1180486, _1180488), _1180494), _1180496)) = hAPP(hAPP(_1180492, _1180494), _1180496))], (38839 ^ _779571) ^ [_1509609] : [-(c_Fun_Oinj__on(_1509609, tc_fun(_1509609, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1509609, tc_fun(_1509609, tc_HOL_Obool), tc_fun(_1509609, tc_HOL_Obool)), c_Set_Oinsert(_1509609)), c_Orderings_Obot__class_Obot(tc_fun(_1509609, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1509609, tc_HOL_Obool))))], (29932 ^ _779571) ^ [_1315316, _1315318, _1315320, _1315322, _1315324] : [c_Hoare__Mirabelle_Ohoare__derivs(_1315316, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315316)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315316), _1315318), hAPP(c_Com_Ocom_OBODY, _1315320)), _1315322)), _1315324), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315316)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315316), _1315318), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1315320))), _1315322)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315316), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1315316, _1315324, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1315316)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1315316), _1315318), hAPP(c_Com_Ocom_OBODY, _1315320)), _1315322)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1315316), tc_HOL_Obool)))))], (35454 ^ _779571) ^ [_1433178, _1433180, _1433182, _1433184, _1433186, _1433188, _1433190, _1433192, _1433194] : [hAPP(c_Fun_Ocomp(_1433178, _1433180, _1433182, _1433184), _1433186) = hAPP(c_Fun_Ocomp(_1433188, _1433180, _1433182, _1433190), _1433192), -(hAPP(_1433184, hAPP(_1433186, _1433194)) = hAPP(_1433190, hAPP(_1433192, _1433194)))], (20105 ^ _779571) ^ [_1125395] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1125395)))], (29011 ^ _779571) ^ [_1296823, _1296825, _1296827, _1296829] : [-(hAPP(hAPP(c_Set_Oinsert(_1296823), _1296825), hAPP(hAPP(c_Set_Oinsert(_1296823), _1296827), _1296829)) = hAPP(hAPP(c_Set_Oinsert(_1296823), _1296827), hAPP(hAPP(c_Set_Oinsert(_1296823), _1296825), _1296829)))], (7560 ^ _779571) ^ [_904947, _904949, _904951, _904953, _904955] : [class_Groups_Oordered__cancel__ab__semigroup__add(_904947), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904947), _904949), _904951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904947), _904953), _904955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904947), _904949), _904953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904947), _904951), _904955))))], (2224 ^ _779571) ^ [_813029, _813031, _813033, _813035, _813037, _813039, _813041, _813043] : [-(c_Sum__Type_OSuml(_813043, _813039, _813035, _813031) = c_Sum__Type_OSuml(_813041, _813037, _813033, _813029)), _813043 = _813041, _813039 = _813037, _813035 = _813033, _813031 = _813029], (41742 ^ _779571) ^ [_1584543, _1584545, _1584547, _1584549, _1584551, _1584553, _1584555, _1584557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584543, _1584545), tc_HOL_Obool)), _1584547), hAPP(hAPP(c_Product__Type_OSigma(_1584543, _1584545), _1584549), hAPP(c_COMBK(tc_fun(_1584545, tc_HOL_Obool), _1584543), _1584551)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584545, _1584553), tc_HOL_Obool)), _1584555), hAPP(hAPP(c_Product__Type_OSigma(_1584545, _1584553), _1584551), hAPP(c_COMBK(tc_fun(_1584553, tc_HOL_Obool), _1584545), _1584557)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584543, _1584553), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584543, _1584545, _1584553), _1584547), _1584555)), hAPP(hAPP(c_Product__Type_OSigma(_1584543, _1584553), _1584549), hAPP(c_COMBK(tc_fun(_1584553, tc_HOL_Obool), _1584543), _1584557)))))], (20553 ^ _779571) ^ [_1132929, _1132931, _1132933, _1132935] : [class_Rings_Odivision__ring(_1132929), -(_1132931 = c_Groups_Ozero__class_Ozero(_1132929)), 20560 ^ _779571 : [(20567 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132929), _1132933), _1132931) = _1132935, -(_1132933 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132929), _1132935), _1132931))], (20561 ^ _779571) ^ [] : [_1132933 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132929), _1132935), _1132931), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132929), _1132933), _1132931) = _1132935)]]], (29840 ^ _779571) ^ [_1313247, _1313249, _1313251] : [class_Orderings_Olinorder(_1313247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313247), _1313249), _1313251)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313247, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1313247, _1313249, _1313251)), hAPP(hAPP(c_Set_Oinsert(_1313247), _1313251), c_Orderings_Obot__class_Obot(tc_fun(_1313247, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1313247, _1313249, _1313251))], (5868 ^ _779571) ^ [_873697, _873699, _873701, _873703] : [c_Natural_Oevaln(_873697, _873699, _873701, _873703), -(c_Natural_Oevaln(_873697, _873699, hAPP(c_Nat_OSuc, _873701), _873703))], (1432 ^ _779571) ^ [_800239, _800241] : [-(class_Groups_Oordered__comm__monoid__add(_800239)), _800241 = _800239, class_Groups_Oordered__comm__monoid__add(_800241)], (36150 ^ _779571) ^ [_1450121, _1450123, _1450125, _1450127] : [hBOOL(hAPP(hAPP(c_member(_1450121), _1450127), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450121, tc_HOL_Obool)), _1450123), _1450125))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450121, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1450121, tc_fun(_1450121, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450121)), _1450123)), hAPP(hAPP(c_COMBC(_1450121, tc_fun(_1450121, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450121)), _1450125)), _1450127)))], (26002 ^ _779571) ^ [_1236010, _1236012] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236010)), _1236012)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236010), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1236012)))))], (10792 ^ _779571) ^ [_959261, _959263, _959265] : [class_Orderings_Oorder(_959261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959261), _959263), _959265)), -(_959265 = _959263), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959261), _959263), _959265)))], (50308 ^ _779571) ^ [_1790213, _1790215, _1790217, _1790219, _1790221] : [class_Orderings_Olinorder(_1790213), c_List_Olinorder__class_Osorted(_1790213, hAPP(hAPP(c_List_Omap(_1790215, _1790213), _1790217), _1790219)), -(c_List_Olinorder__class_Osorted(_1790213, hAPP(hAPP(c_List_Omap(_1790215, _1790213), _1790217), c_List_Oremove1(_1790215, _1790221, _1790219))))], (18327 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (19931 ^ _779571) ^ [_1122019] : [_1122019 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1122019) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26906 ^ _779571) ^ [_1253240, _1253242, _1253244, _1253246, _1253248] : [class_Groups_Ocomm__monoid__add(_1253240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253244), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253240), _1253246), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1253242, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253244), _1253248))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253240), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253240), _1253246), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1253242, _1253244))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253240), _1253246), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253244), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253244), _1253248)))))], (16176 ^ _779571) ^ [_1055997, _1055999, _1056001, _1056003, _1056005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055997), _1055999)), 16179 ^ _779571 : [(16186 ^ _779571) ^ [] : [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), _1055999), _1055997)), _1056001)), _1056003)), _1056005)), -(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), _1055999), _1056001)), _1056003)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1055997), _1056001)), _1056005))))], (16180 ^ _779571) ^ [] : [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), _1055999), _1056001)), _1056003)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1055997), _1056001)), _1056005))), -(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), _1055999), _1055997)), _1056001)), _1056003)), _1056005)))]]], (6363 ^ _779571) ^ [_882800, _882802, _882804, _882806, _882808] : [c_Com_Ocom_OCall(_882800, _882802, _882804) = c_Com_Ocom_OWhile(_882806, _882808)], (41553 ^ _779571) ^ [_1577919, _1577921, _1577923] : [class_Orderings_Olinorder(_1577919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577919), _1577921)), -(_1577921 = c_Orderings_Obot__class_Obot(tc_fun(_1577919, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1577919), _1577923), c_Big__Operators_Olattice_OInf__fin(_1577919, c_Orderings_Oord__class_Omin(_1577919), _1577921)) = c_Big__Operators_Olattice_OInf__fin(_1577919, c_Orderings_Oord__class_Omin(_1577919), hAPP(c_Set_OCollect(_1577919), hAPP(hAPP(c_COMBB(tc_fun(_1577919, tc_HOL_Obool), tc_HOL_Obool, _1577919), c_HOL_OEx(_1577919)), hAPP(hAPP(c_COMBC(_1577919, tc_fun(_1577919, tc_HOL_Obool), tc_fun(_1577919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577919, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1577919, tc_HOL_Obool), tc_fun(_1577919, tc_HOL_Obool)), _1577919), c_COMBS(_1577919, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577919, tc_HOL_Obool), tc_fun(_1577919, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1577919), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577919), c_fconj)), hAPP(hAPP(c_COMBC(_1577919, tc_fun(_1577919, _1577919), tc_fun(_1577919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577919, tc_HOL_Obool), tc_fun(tc_fun(_1577919, _1577919), tc_fun(_1577919, tc_HOL_Obool)), _1577919), c_COMBB(_1577919, tc_HOL_Obool, _1577919)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1577919), _1577923))))), hAPP(hAPP(c_COMBC(_1577919, tc_fun(_1577919, tc_HOL_Obool), tc_HOL_Obool), c_member(_1577919)), _1577921))))))], (14335 ^ _779571) ^ [_1021274, _1021276, _1021278] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021274), _1021276)), _1021278) = 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), _1021274), _1021278)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021276), _1021278))), 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, _1021274, _1021278)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021276, _1021278))), _1021278)))], (22244 ^ _779571) ^ [_1163416, _1163418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1163416), _1163418)), -(c_Quickcheck_Obeyond(_1163416, _1163418) = _1163418)], (33527 ^ _779571) ^ [_1391250, _1391252, _1391254, _1391256, _1391258, _1391260, _1391262, _1391264] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1391250, _1391252), tc_prod(_1391250, _1391252))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1391250, _1391252), tc_prod(_1391250, _1391252)), hAPP(hAPP(c_Product__Type_OPair(_1391250, _1391252), _1391254), _1391256)), hAPP(hAPP(c_Product__Type_OPair(_1391250, _1391252), _1391258), _1391260))), c_Wellfounded_Olex__prod(_1391250, _1391252, _1391262, _1391264)))), 33528 ^ _779571 : [(33531 ^ _779571) ^ [] : [_1391254 = _1391258, hBOOL(hAPP(hAPP(c_member(tc_prod(_1391252, _1391252)), hAPP(hAPP(c_Product__Type_OPair(_1391252, _1391252), _1391256), _1391260)), _1391264))], (33529 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1391250, _1391250)), hAPP(hAPP(c_Product__Type_OPair(_1391250, _1391250), _1391254), _1391258)), _1391262))]]], (42280 ^ _779571) ^ [_1597955, _1597957, _1597959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1597955, _1597957)), _1597959)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1597955), hAPP(c_Relation_ODomain(_1597955, _1597957), _1597959))))], (3976 ^ _779571) ^ [_840857, _840859, _840861, _840863] : [-(c_HOL_OThe(_840863, _840859) = c_HOL_OThe(_840861, _840857)), _840863 = _840861, _840859 = _840857], (48114 ^ _779571) ^ [_1740199, _1740201, _1740203] : [_1740199 = hAPP(hAPP(c_List_Oappend(_1740201), _1740203), _1740199), -(_1740203 = c_List_Olist_ONil(_1740201))], (32079 ^ _779571) ^ [_1363145, _1363147, _1363149, _1363151, _1363153, _1363155] : [hBOOL(hAPP(hAPP(_1363145, _1363147), _1363149)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363151, tc_fun(_1363153, tc_HOL_Obool))), _1363145), _1363155), _1363147), _1363149)))], (26172 ^ _779571) ^ [_1239054, _1239056, _1239058, _1239060] : [class_Divides_Osemiring__div(_1239054), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239054), _1239056), _1239058)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239054), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239054), _1239058), _1239056)), _1239060) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1239054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239054), _1239058), _1239060)), _1239056))], (34887 ^ _779571) ^ [_1419869, _1419871, _1419873, _1419875] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419869), _1419875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419873), _1419871), -(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), _1419869), _1419871)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1419873), _1419875))), c_Int_Ointrel)))], (31347 ^ _779571) ^ [_1346263, _1346265] : [c_Nat__Transfer_Ois__nat(_1346263), c_Nat__Transfer_Onat__set(_1346265), 31354 ^ _779571 : [(31361 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1346263)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1346265))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1346263), _1346265)))], (31355 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1346263), _1346265)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1346263)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1346265))))]]], (8848 ^ _779571) ^ [_925875, _925877, _925879, _925881, _925883] : [class_Rings_Ocomm__semiring__1(_925875), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), _925877), _925879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), _925881), _925883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), _925877), _925881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925875), _925879), _925883)))], (4960 ^ _779571) ^ [_856195, _856197, _856199, _856201, _856203, _856205, _856207, _856209, _856211, _856213] : [-(c_List_Olinorder__class_Oinsort__insert__key(_856213, _856209, _856205, _856201, _856197) = c_List_Olinorder__class_Oinsort__insert__key(_856211, _856207, _856203, _856199, _856195)), _856213 = _856211, _856209 = _856207, _856205 = _856203, _856201 = _856199, _856197 = _856195], (13450 ^ _779571) ^ [_1004836, _1004838, _1004840, _1004842] : [class_Orderings_Oord(_1004836), 13453 ^ _779571 : [(13462 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1004838, _1004836)), _1004840), _1004842))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004838, _1004836)), _1004840), _1004842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004838, _1004836)), _1004842), _1004840)))], (13454 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1004838, _1004836)), _1004840), _1004842)), 13457 ^ _779571 : [(13460 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004838, _1004836)), _1004842), _1004840))], (13458 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004838, _1004836)), _1004840), _1004842)))]]]]], (42711 ^ _779571) ^ [_1608210, _1608212, _1608214, _1608216, _1608218, _1608220] : [class_Groups_Oab__semigroup__mult(_1608210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608212), _1608214)), 42721 ^ _779571 : [(42724 ^ _779571) ^ [] : [hAPP(_1608216, 42720 ^ [_1608210, _1608212, _1608214, _1608216, _1608218, _1608220]) = hAPP(_1608218, 42720 ^ [_1608210, _1608212, _1608214, _1608216, _1608218, _1608220])], (42722 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608212), 42720 ^ [_1608210, _1608212, _1608214, _1608216, _1608218, _1608220]), _1608214)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1608210, _1608212, c_Groups_Otimes__class_Otimes(_1608210)), _1608216), _1608220), _1608214) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1608210, _1608212, c_Groups_Otimes__class_Otimes(_1608210)), _1608218), _1608220), _1608214))], (13855 ^ _779571) ^ [_1012403, _1012405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012405, _1012403)), _1012403)))], (16855 ^ _779571) ^ [_1068526, _1068528, _1068530] : [class_Int_Onumber__ring(_1068526), class_Rings_Olinordered__idom(_1068526), 16862 ^ _779571 : [(16869 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068528), _1068530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068526), hAPP(c_Int_Onumber__class_Onumber__of(_1068526), _1068528)), hAPP(c_Int_Onumber__class_Onumber__of(_1068526), _1068530))))], (16863 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068526), hAPP(c_Int_Onumber__class_Onumber__of(_1068526), _1068528)), hAPP(c_Int_Onumber__class_Onumber__of(_1068526), _1068530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068528), _1068530)))]]], (50979 ^ _779571) ^ [_1806288, _1806290, _1806292] : [hBOOL(hAPP(c_List_Odistinct(_1806288), _1806290)), -(hBOOL(hAPP(c_List_Odistinct(_1806288), c_List_OtakeWhile(_1806288, _1806292, _1806290))))], (37148 ^ _779571) ^ [_1472566, _1472568, _1472570, _1472572, _1472574] : [c_Finite__Set_Ofolding__one(_1472566, _1472568, _1472570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472566), _1472572)), -(_1472572 = c_Orderings_Obot__class_Obot(tc_fun(_1472566, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472566), _1472574)), -(_1472574 = c_Orderings_Obot__class_Obot(tc_fun(_1472566, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472566, tc_HOL_Obool)), _1472572), _1472574) = c_Orderings_Obot__class_Obot(tc_fun(_1472566, tc_HOL_Obool)), -(hAPP(_1472570, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472566, tc_HOL_Obool)), _1472572), _1472574)) = hAPP(hAPP(_1472568, hAPP(_1472570, _1472572)), hAPP(_1472570, _1472574)))], (25450 ^ _779571) ^ [_1225388, _1225390] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225388), _1225390)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225390), _1225388))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225390), _1225388)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225388), _1225390)))], (17687 ^ _779571) ^ [_1084083, _1084085, _1084087, _1084089] : [class_Rings_Olinordered__semidom(_1084083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084085), _1084087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084083), c_Groups_Oone__class_Oone(_1084083)), _1084089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084083), hAPP(hAPP(c_Power_Opower__class_Opower(_1084083), _1084089), _1084085)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084083), _1084089), _1084087))))], (28028 ^ _779571) ^ [_1276261, _1276263, _1276265] : [class_Lattices_Olattice(_1276261), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276261), _1276263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276261), _1276263), _1276265)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276261), _1276263), _1276265))], (8233 ^ _779571) ^ [_916123, _916125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916123), _916125)), -(_916125 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _916123), 8236 ^ [_916123, _916125])))], (48682 ^ _779571) ^ [_1755331, _1755333, _1755335, _1755337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755331), tc_List_Olist(_1755331))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755331), tc_List_Olist(_1755331)), _1755333), _1755335)), c_List_Olistrel1(_1755331, _1755337))), 48687 ^ _779571 : [(48694 ^ _779571) ^ [] : [-(_1755335 = hAPP(hAPP(c_List_Oappend(_1755331), 48689 ^ [_1755331, _1755333, _1755335, _1755337]), hAPP(hAPP(c_List_Olist_OCons(_1755331), 48686 ^ [_1755331, _1755333, _1755335, _1755337]), 48690 ^ [_1755331, _1755333, _1755335, _1755337])))], (48692 ^ _779571) ^ [] : [-(_1755333 = hAPP(hAPP(c_List_Oappend(_1755331), 48689 ^ [_1755331, _1755333, _1755335, _1755337]), hAPP(hAPP(c_List_Olist_OCons(_1755331), 48685 ^ [_1755331, _1755333, _1755335, _1755337]), 48690 ^ [_1755331, _1755333, _1755335, _1755337])))], (48688 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755331, _1755331)), hAPP(hAPP(c_Product__Type_OPair(_1755331, _1755331), 48685 ^ [_1755331, _1755333, _1755335, _1755337]), 48686 ^ [_1755331, _1755333, _1755335, _1755337])), _1755337)))]]], (41101 ^ _779571) ^ [_1562131, _1562133] : [-(hAPP(c_Set_OCollect(_1562131), hAPP(hAPP(c_COMBC(_1562131, tc_fun(_1562131, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562131)), _1562133)) = _1562133)], (7065 ^ _779571) ^ [] : [-(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))], (6764 ^ _779571) ^ [_890760, _890762, _890764, _890766, _890768] : [c_Com_Ocom_OCond(_890760, _890762, _890764) = c_Com_Ocom_OAss(_890766, _890768)], (24423 ^ _779571) ^ [_1205358, _1205360, _1205362, _1205364] : [class_Orderings_Olinorder(_1205358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205358), _1205360), _1205362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205358), _1205360), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205358), _1205364), _1205362))))], (10806 ^ _779571) ^ [_959435, _959437, _959439] : [class_Orderings_Oorder(_959435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959435), _959437), _959439)), -(_959437 = _959439), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959435), _959437), _959439)))], (33581 ^ _779571) ^ [_1392526, _1392528, _1392530, _1392532, _1392534] : [hBOOL(hAPP(hAPP(c_member(_1392526), _1392528), _1392530)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1392526, _1392532)), hAPP(c_Sum__Type_OInl(_1392526, _1392532), _1392528)), c_Sum__Type_OPlus(_1392526, _1392532, _1392530, _1392534))))], (49610 ^ _779571) ^ [_1775945, _1775947, _1775949] : [_1775945 = c_List_Olist_ONil(_1775947), -(c_List_Obutlast(_1775947, hAPP(hAPP(c_List_Olist_OCons(_1775947), _1775949), _1775945)) = c_List_Olist_ONil(_1775947))], (32657 ^ _779571) ^ [_1375396, _1375398] : [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)))), _1375396, _1375398), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375396), _1375398)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375398), _1375396)))], (44013 ^ _779571) ^ [_1640436, _1640438, _1640440, _1640442] : [class_Orderings_Olinorder(_1640436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640436), _1640438)), hBOOL(hAPP(hAPP(c_member(_1640436), _1640440), _1640438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1640436), hAPP(hAPP(c_Finite__Set_Ofold(_1640436, _1640436, c_Orderings_Oord__class_Omin(_1640436)), _1640442), _1640438)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1640436), _1640440), _1640442))))], (16491 ^ _779571) ^ [_1061693] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061693)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061693))], (3546 ^ _779571) ^ [_834072, _834074, _834076, _834078, _834080, _834082, _834084, _834086] : [-(c_Fun_Othe__inv__into(_834086, _834082, _834078, _834074) = c_Fun_Othe__inv__into(_834084, _834080, _834076, _834072)), _834086 = _834084, _834082 = _834080, _834078 = _834076, _834074 = _834072], (27608 ^ _779571) ^ [_1267785, _1267787] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1267785), _1267787)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1267785)), hAPP(c_Nat_OSuc, _1267787)))], (30884 ^ _779571) ^ [_1335413] : [-(c_Option_Oset(_1335413, c_Option_Ooption_ONone(_1335413)) = c_Orderings_Obot__class_Obot(tc_fun(_1335413, tc_HOL_Obool)))], (36784 ^ _779571) ^ [_1464171, _1464173] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464171, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464171, tc_HOL_Obool)), _1464173)), _1464173) = c_Orderings_Obot__class_Obot(tc_fun(_1464171, tc_HOL_Obool)))], (17953 ^ _779571) ^ [_1088545, _1088547] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088545))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088545)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088547)) = 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), _1088547)))], (47137 ^ _779571) ^ [_1717601, _1717603, _1717605] : [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, _1717601), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1717601)), _1717603)))), -(hBOOL(hAPP(hAPP(c_member(_1717601), hAPP(c_Product__Type_Ofst(_1717601, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1717601, _1717603), _1717605))), hAPP(c_List_Oset(_1717601), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1717601), _1717601), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1717601)), _1717603)))))], (42465 ^ _779571) ^ [_1602562] : [-(_1602562 = hAPP(c_Int_OAbs__Integ, 42463 ^ [_1602562]))], (41320 ^ _779571) ^ [_1568603, _1568605, _1568607, _1568609, _1568611, _1568613] : [hBOOL(hAPP(hAPP(c_member(_1568603), _1568605), _1568607)), -(hAPP(c_Fun_Ooverride__on(_1568603, _1568609, _1568611, _1568613, _1568607), _1568605) = hAPP(_1568613, _1568605))], (7333 ^ _779571) ^ [_901253, _901255, _901257, _901259] : [hAPP(c_Sum__Type_OInl(_901253, _901255), _901257) = hAPP(c_Sum__Type_OInl(_901253, _901255), _901259), -(_901257 = _901259)], (49074 ^ _779571) ^ [_1764150, _1764152] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764150)), hAPP(c_List_Otl(_1764150), _1764152)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764150)), _1764152)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42112 ^ _779571) ^ [_1593897, _1593899] : [-(hAPP(c_Relation_ORange(_1593897, _1593899), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593897, _1593899), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1593899, tc_HOL_Obool)))], (9970 ^ _779571) ^ [_945584, _945586] : [class_Int_Oring__char__0(_945584), 9973 ^ _779571 : [(9980 ^ _779571) ^ [] : [_945586 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_945584), _945586) = c_Groups_Ozero__class_Ozero(_945584))], (9974 ^ _779571) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_945584), _945586) = c_Groups_Ozero__class_Ozero(_945584), -(_945586 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (49479 ^ _779571) ^ [_1773069, _1773071] : [-(_1773069 = c_List_Olist_ONil(_1773071)), -(hBOOL(hAPP(hAPP(c_member(_1773071), c_List_Olast(_1773071, _1773069)), hAPP(c_List_Oset(_1773071), _1773069))))], (47881 ^ _779571) ^ [_1734977, _1734979, _1734981, _1734983, _1734985] : [hAPP(hAPP(c_List_Oappend(_1734977), _1734979), hAPP(hAPP(c_List_Olist_OCons(_1734977), _1734981), c_List_Olist_ONil(_1734977))) = hAPP(hAPP(c_List_Oappend(_1734977), _1734983), hAPP(hAPP(c_List_Olist_OCons(_1734977), _1734985), c_List_Olist_ONil(_1734977))), 47884 ^ _779571 : [(47887 ^ _779571) ^ [] : [-(_1734981 = _1734985)], (47885 ^ _779571) ^ [] : [-(_1734979 = _1734983)]]], (8090 ^ _779571) ^ [_913676] : [-(c_Option_Ois__none(_913676, c_Option_Ooption_ONone(_913676)))], (24215 ^ _779571) ^ [_1201418, _1201420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1201418)), -(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(_1201418), _1201420))), _1201418)))], (47336 ^ _779571) ^ [_1721355, _1721357] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721355), tc_List_Olist(_1721355))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721355), tc_List_Olist(_1721355)), c_List_Olist_ONil(_1721355)), c_List_Olist_ONil(_1721355))), c_List_Olistrel(_1721355, _1721357))))], (5292 ^ _779571) ^ [_861355, _861357, _861359, _861361] : [-(c_Product__Type_Osnd(_861361, _861357) = c_Product__Type_Osnd(_861359, _861355)), _861361 = _861359, _861357 = _861355], (46753 ^ _779571) ^ [_1706679, _1706681, _1706683] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706679), tc_List_Olist(_1706679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706679), tc_List_Olist(_1706679)), _1706681), _1706681)), c_List_Olistrel(_1706679, c_Transitive__Closure_Ortrancl(_1706679, _1706683)))))], (28252 ^ _779571) ^ [_1280879, _1280881, _1280883, _1280885] : [class_Orderings_Olinorder(_1280879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280879), _1280881), _1280883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280879), _1280883), _1280885)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280879, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1280879, _1280881, _1280883)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1280879, _1280883, _1280885)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1280879, _1280881, _1280885))], (22158 ^ _779571) ^ [_1162051, _1162053] : [-(_1162051 = _1162053), -(c_Random_Oinc__shift(_1162051, _1162053) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1162053), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28876 ^ _779571) ^ [_1293590, _1293592, _1293594, _1293596, _1293598, _1293600] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293590, tc_fun(_1293592, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293594, tc_fun(_1293590, tc_HOL_Obool)), _1293596), _1293598)), _1293600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293594, tc_fun(_1293592, tc_HOL_Obool)), _1293596), hAPP(hAPP(c_COMBC(_1293594, tc_fun(_1293590, tc_fun(_1293592, tc_HOL_Obool)), tc_fun(_1293592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293590, tc_HOL_Obool), tc_fun(tc_fun(_1293590, tc_fun(_1293592, tc_HOL_Obool)), tc_fun(_1293592, tc_HOL_Obool)), _1293594), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293590, tc_fun(_1293592, tc_HOL_Obool))), _1293598)), _1293600)))], (31259 ^ _779571) ^ [_1343662, _1343664, _1343666, _1343668, _1343670, _1343672] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343662, tc_fun(_1343664, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1343662, tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_fun(_1343664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343664, tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_fun(_1343664, tc_HOL_Obool)), _1343662), c_COMBC(_1343664, tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343664, tc_prod(_1343662, _1343664)), tc_fun(_1343664, tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), _1343662), hAPP(c_COMBB(tc_prod(_1343662, _1343664), tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool), _1343664), c_member(tc_prod(_1343662, _1343664)))), c_Product__Type_OPair(_1343662, _1343664)))), _1343666)), hAPP(hAPP(c_COMBC(_1343662, tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_fun(_1343664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343664, tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_fun(_1343664, tc_HOL_Obool)), _1343662), c_COMBC(_1343664, tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343664, tc_prod(_1343662, _1343664)), tc_fun(_1343664, tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool)), _1343662), hAPP(c_COMBB(tc_prod(_1343662, _1343664), tc_fun(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool), tc_HOL_Obool), _1343664), c_member(tc_prod(_1343662, _1343664)))), c_Product__Type_OPair(_1343662, _1343664)))), _1343668)), _1343670), _1343672)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1343662, _1343664)), hAPP(hAPP(c_Product__Type_OPair(_1343662, _1343664), _1343670), _1343672)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1343662, _1343664), tc_HOL_Obool)), _1343666), _1343668))))], (23391 ^ _779571) ^ [_1185563, _1185565, _1185567, _1185569] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185563, _1185565), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185567), _1185569))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185563), _1185565), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1185569), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185567)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185567)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1185569), 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), _1185565), _1185569))))))], (7394 ^ _779571) ^ [_902321] : [7395 ^ _779571 : [(7396 ^ _779571) ^ [_902369] : [hAPP(c_Com_Obody, _902321) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _902369)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _902321))))], (16152 ^ _779571) ^ [_1055658, _1055660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055658), _1055660)), -(c_Nat__Transfer_Otsub(_1055660, _1055658) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055660), _1055658))], (15778 ^ _779571) ^ [_1047496, _1047498, _1047500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047496), _1047498)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047498), _1047496)), _1047500) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047498), _1047500)), _1047496))], (30612 ^ _779571) ^ [_1329401, _1329403, _1329405, _1329407] : [-(hBOOL(hAPP(hAPP(c_member(_1329401), hAPP(_1329403, _1329405)), hAPP(c_Set_Oimage(_1329407, _1329401, _1329403), c_Orderings_Otop__class_Otop(tc_fun(_1329407, tc_HOL_Obool))))))], (48148 ^ _779571) ^ [_1740791, _1740793, _1740795] : [-(c_List_Olist_ONil(_1740791) = hAPP(hAPP(c_List_Oappend(_1740791), _1740793), _1740795)), _1740793 = c_List_Olist_ONil(_1740791), _1740795 = c_List_Olist_ONil(_1740791)], (10 ^ _779571) ^ [_779694, _779696, _779698] : [-(_779698 = _779694), _779698 = _779696, _779696 = _779694], (41121 ^ _779571) ^ [_1562513, _1562515, _1562517] : [hBOOL(hAPP(hAPP(c_member(_1562513), _1562515), hAPP(c_Set_OCollect(_1562513), _1562517))), -(hBOOL(hAPP(_1562517, _1562515)))], (1602 ^ _779571) ^ [_802364, _802366] : [-(class_Nat_Osemiring__char__0(_802364)), _802366 = _802364, class_Nat_Osemiring__char__0(_802366)], (50694 ^ _779571) ^ [_1798738, _1798740, _1798742, _1798744] : [-(hAPP(c_List_Orev(_1798738), hAPP(hAPP(c_List_Omap(_1798740, _1798738), _1798742), _1798744)) = hAPP(hAPP(c_List_Omap(_1798740, _1798738), _1798742), hAPP(c_List_Orev(_1798740), _1798744)))], (43826 ^ _779571) ^ [_1636163, _1636165, _1636167, _1636169, _1636171] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636163, _1636163)), hAPP(hAPP(c_Product__Type_OPair(_1636163, _1636163), _1636165), _1636167)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636163, _1636163), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1636169)), _1636171))), 43830 ^ _779571 : [(43833 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636163, _1636163)), hAPP(hAPP(c_Product__Type_OPair(_1636163, _1636163), 43829 ^ [_1636163, _1636165, _1636167, _1636169, _1636171]), _1636167)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636163, _1636163), tc_HOL_Obool), _1636169), _1636171))))], (43831 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636163, _1636163)), hAPP(hAPP(c_Product__Type_OPair(_1636163, _1636163), _1636165), 43829 ^ [_1636163, _1636165, _1636167, _1636169, _1636171])), _1636171)))]]], (16150 ^ _779571) ^ [_1055602, _1055604] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1055602), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1055604), _1055602)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055604), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055604, _1055602)))], (51193 ^ _779571) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (45862 ^ _779571) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (35157 ^ _779571) ^ [_1426291, _1426293] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426291), _1426293)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1426291, tc_HOL_Obool)), hAPP(c_Set_OPow(_1426291), _1426293)) = 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(_1426291), _1426293)))], (10163 ^ _779571) ^ [_948883] : [_948883 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _948883) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18363 ^ _779571) ^ [_1094908, _1094910] : [class_Int_Onumber__ring(_1094908), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094908), _1094910), hAPP(c_Int_Onumber__class_Onumber__of(_1094908), c_Int_OPls)) = _1094910)], (46041 ^ _779571) ^ [_1688335] : [-(hAPP(c_Option_Omap(_1688335, _1688335), c_Fun_Oid(_1688335)) = c_Fun_Oid(tc_Option_Ooption(_1688335)))], (42982 ^ _779571) ^ [_1615134, _1615136] : [-(c_Transitive__Closure_Otrancl(_1615134, _1615136) = hAPP(hAPP(c_Relation_Orel__comp(_1615134, _1615134, _1615134), _1615136), c_Transitive__Closure_Ortrancl(_1615134, _1615136)))], (34957 ^ _779571) ^ [_1421959, _1421961, _1421963] : [class_Orderings_Olinorder(_1421959), hAPP(_1421961, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1421959), 34962 ^ [_1421959, _1421961, _1421963]), 34963 ^ [_1421959, _1421961, _1421963])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1421959), hAPP(_1421961, 34962 ^ [_1421959, _1421961, _1421963])), hAPP(_1421961, 34963 ^ [_1421959, _1421961, _1421963])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421959), _1421963)), -(_1421963 = c_Orderings_Obot__class_Obot(tc_fun(_1421959, tc_HOL_Obool))), -(hAPP(_1421961, c_Big__Operators_Olinorder__class_OMin(_1421959, _1421963)) = c_Big__Operators_Olinorder__class_OMin(_1421959, hAPP(c_Set_Oimage(_1421959, _1421959, _1421961), _1421963)))], (45273 ^ _779571) ^ [_1670366, _1670368, _1670370] : [class_Complete__Lattice_Ocomplete__lattice(_1670366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670366), _1670368)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1670366), _1670370), c_Complete__Lattice_OInf__class_OInf(_1670366, _1670368)) = hAPP(hAPP(c_Finite__Set_Ofold(_1670366, _1670366, c_Lattices_Osemilattice__inf__class_Oinf(_1670366)), _1670370), _1670368))], (49558 ^ _779571) ^ [_1774747, _1774749, _1774751, _1774753] : [49560 ^ _779571 : [(49563 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1774751, 49559 ^ [_1774747, _1774749, _1774751, _1774753])), hAPP(_1774753, 49559 ^ [_1774747, _1774749, _1774751, _1774753])))], (49561 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774747), 49559 ^ [_1774747, _1774749, _1774751, _1774753]), hAPP(c_List_Oset(_1774747), _1774749))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1774747, _1774751, _1774749)), c_List_Olist_Olist__size(_1774747, _1774753, _1774749))))], (48772 ^ _779571) ^ [_1757535, _1757537] : [-(hAPP(hAPP(c_List_Odrop(_1757535), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1757537) = _1757537)], (48796 ^ _779571) ^ [_1758092, _1758094, _1758096, _1758098] : [-(hAPP(hAPP(c_List_Odrop(_1758092), _1758094), hAPP(hAPP(c_List_Otake(_1758092), _1758096), _1758098)) = hAPP(hAPP(c_List_Otake(_1758092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1758096), _1758094)), hAPP(hAPP(c_List_Odrop(_1758092), _1758094), _1758098)))], (50932 ^ _779571) ^ [_1805167, _1805169] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1805167), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1805167))), _1805169))), -(c_List_Otranspose(_1805167, c_List_Otranspose(_1805167, _1805169)) = c_List_OtakeWhile(tc_List_Olist(_1805167), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1805167)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1805167), tc_List_Olist(_1805167), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1805167))), _1805169))], (50600 ^ _779571) ^ [_1796782, _1796784, _1796786] : [-(c_List_Oconcat(_1796782, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1796782)), _1796784), _1796786)) = hAPP(hAPP(c_List_Oappend(_1796782), _1796784), c_List_Oconcat(_1796782, _1796786)))], (49694 ^ _779571) ^ [_1777583, _1777585] : [-(_1777583 = c_List_Olist_ONil(_1777585)), -(hAPP(hAPP(c_List_Oappend(_1777585), c_List_Obutlast(_1777585, _1777583)), hAPP(hAPP(c_List_Olist_OCons(_1777585), c_List_Olast(_1777585, _1777583)), c_List_Olist_ONil(_1777585))) = _1777583)], (8526 ^ _779571) ^ [_920749, _920751, _920753] : [class_Orderings_Oorder(_920749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920749), _920751), _920753)), _920751 = _920753], (6167 ^ _779571) ^ [_879201, _879203, _879205, _879207] : [-(hAPP(c_Nat_Onat_Onat__rec(_879201, _879203, _879205), hAPP(c_Nat_OSuc, _879207)) = hAPP(hAPP(_879205, _879207), hAPP(c_Nat_Onat_Onat__rec(_879201, _879203, _879205), _879207)))], (16473 ^ _779571) ^ [_1061324, _1061326] : [class_Groups_Oordered__ab__group__add__abs(_1061324), -(hAPP(c_Groups_Oabs__class_Oabs(_1061324), hAPP(c_Groups_Ouminus__class_Ouminus(_1061324), _1061326)) = hAPP(c_Groups_Oabs__class_Oabs(_1061324), _1061326))], (3920 ^ _779571) ^ [_840019, _840021, _840023, _840025] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_840025, _840021) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_840023, _840019)), _840025 = _840023, _840021 = _840019], (36408 ^ _779571) ^ [_1456075, _1456077, _1456079, _1456081, _1456083] : [class_Lattices_Olattice(_1456075), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456077, _1456075)), _1456079), _1456081), _1456083) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456075), hAPP(_1456079, _1456083)), hAPP(_1456081, _1456083)))], (46088 ^ _779571) ^ [_1689442, _1689444, _1689446, _1689448, _1689450] : [hAPP(hAPP(c_List_Omap(_1689442, _1689444), _1689446), _1689448) = hAPP(hAPP(c_List_Omap(_1689442, _1689444), _1689446), _1689450), c_Fun_Oinj__on(_1689442, _1689444, _1689446, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689442, tc_HOL_Obool)), hAPP(c_List_Oset(_1689442), _1689448)), hAPP(c_List_Oset(_1689442), _1689450))), -(_1689448 = _1689450)], (38547 ^ _779571) ^ [_1503739, _1503741, _1503743, _1503745, _1503747] : [c_Fun_Oinj__on(_1503739, _1503741, _1503743, c_Orderings_Otop__class_Otop(tc_fun(_1503739, tc_HOL_Obool))), hAPP(_1503743, _1503745) = hAPP(_1503743, _1503747), -(_1503745 = _1503747)], (14475 ^ _779571) ^ [_1023798, _1023800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023798), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14478 ^ _779571 : [(14485 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023800), _1023798)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14479 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023800), _1023798)), 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)), _1023800)))]]], (25384 ^ _779571) ^ [_1224305, _1224307, _1224309] : [_1224305 = _1224307, 25395 ^ _779571 : [(25398 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224309), _1224305))], (25396 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224305), _1224309)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224307), _1224309)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224309), _1224307)))], (30024 ^ _779571) ^ [_1317545, _1317547] : [-(hBOOL(hAPP(hAPP(c_member(_1317545), _1317547), c_Orderings_Otop__class_Otop(tc_fun(_1317545, tc_HOL_Obool)))))], (7426 ^ _779571) ^ [_902787, _902789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902787), _902789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902787)), hAPP(c_Nat_OSuc, _902789))))], (11621 ^ _779571) ^ [_972638] : [class_Groups_Osgn__if(_972638), -(c_Groups_Osgn__class_Osgn(_972638, c_Groups_Ozero__class_Ozero(_972638)) = c_Groups_Ozero__class_Ozero(_972638))], (42439 ^ _779571) ^ [_1601923, _1601925] : [-(c_Nitpick_Owf_H(_1601923, _1601925)), c_Wellfounded_Oacyclic(_1601923, _1601925), 42444 ^ _779571 : [(42447 ^ _779571) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (42445 ^ _779571) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601923, _1601923)), _1601925))]]], (24507 ^ _779571) ^ [_1206851, _1206853, _1206855, _1206857] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1206851), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206851), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206851), _1206853), _1206855)), _1206857) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206851), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206851), _1206853), _1206857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206851), _1206855), _1206857)))], (29910 ^ _779571) ^ [_1314763, _1314765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314763), _1314765)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1314765, _1314763) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (48600 ^ _779571) ^ [_1752931, _1752933, _1752935, _1752937, _1752939, _1752941] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752931), tc_List_Olist(_1752931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752931), tc_List_Olist(_1752931)), hAPP(hAPP(c_List_Olist_OCons(_1752931), _1752933), _1752935)), hAPP(hAPP(c_List_Olist_OCons(_1752931), _1752937), _1752939))), c_List_Olistrel1(_1752931, _1752941)))), 48601 ^ _779571 : [(48608 ^ _779571) ^ [] : [_1752933 = _1752937, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752931), tc_List_Olist(_1752931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752931), tc_List_Olist(_1752931)), _1752935), _1752939)), c_List_Olistrel1(_1752931, _1752941)))], (48602 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1752931, _1752931)), hAPP(hAPP(c_Product__Type_OPair(_1752931, _1752931), _1752933), _1752937)), _1752941)), _1752935 = _1752939]]], (51037 ^ _779571) ^ [_1807306, _1807308, _1807310, _1807312, _1807314] : [-(c_Map_Omap__upds(_1807306, _1807308, _1807310, _1807312, _1807314) = c_Map_Omap__add(_1807306, _1807308, _1807310, c_Map_Omap__of(_1807306, _1807308, hAPP(c_List_Orev(tc_prod(_1807306, _1807308)), hAPP(hAPP(c_List_Ozip(_1807306, _1807308), _1807312), _1807314)))))], (13934 ^ _779571) ^ [_1013706, _1013708, _1013710] : [class_Lattices_Oab__semigroup__idem__mult(_1013706), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013706), _1013708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013706), _1013708), _1013710)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013706), _1013708), _1013710))], (32859 ^ _779571) ^ [_1379145, _1379147, _1379149] : [class_Rings_Oring__1(_1379145), hBOOL(hAPP(hAPP(c_member(_1379145), _1379147), c_Int_Oring__1__class_OInts(_1379145))), hBOOL(hAPP(hAPP(c_member(_1379145), _1379149), c_Int_Oring__1__class_OInts(_1379145))), -(hBOOL(hAPP(hAPP(c_member(_1379145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379145), _1379147), _1379149)), c_Int_Oring__1__class_OInts(_1379145))))], (41818 ^ _779571) ^ [_1587676, _1587678] : [c_Wellfounded_Owf(_1587676, _1587678), -(c_Wellfounded_Owf(_1587676, hAPP(hAPP(c_Relation_Orel__comp(_1587676, _1587676, _1587676), _1587678), _1587678)))], (26880 ^ _779571) ^ [_1252679, _1252681, _1252683, _1252685] : [class_Groups_Ocomm__monoid__add(_1252679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1252681), _1252683)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252679), _1252685), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1252681, _1252683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252679), hAPP(_1252685, _1252681)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252679), _1252685), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1252681), _1252683))))], (15194 ^ _779571) ^ [_1036571, _1036573, _1036575, _1036577, _1036579] : [class_Groups_Oab__group__add(_1036571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1036571), _1036573), _1036575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1036571), _1036577), _1036579), 15201 ^ _779571 : [(15208 ^ _779571) ^ [] : [_1036577 = _1036579, -(_1036573 = _1036575)], (15202 ^ _779571) ^ [] : [_1036573 = _1036575, -(_1036577 = _1036579)]]], (48698 ^ _779571) ^ [_1755830, _1755832, _1755834, _1755836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755830), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755832)), _1755834))), -(hAPP(hAPP(c_List_Olist__update(_1755832, _1755834), _1755830), _1755836) = hAPP(hAPP(c_List_Oappend(_1755832), hAPP(hAPP(c_List_Otake(_1755832), _1755830), _1755834)), hAPP(hAPP(c_List_Olist_OCons(_1755832), _1755836), hAPP(hAPP(c_List_Odrop(_1755832), hAPP(c_Nat_OSuc, _1755830)), _1755834))))], (36974 ^ _779571) ^ [_1468456, _1468458, _1468460] : [class_Orderings_Oorder(_1468456), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468456, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1468456, _1468458, _1468460)), hAPP(c_SetInterval_Oord__class_OatLeast(_1468456), _1468460)) = c_Orderings_Obot__class_Obot(tc_fun(_1468456, tc_HOL_Obool)))], (36312 ^ _779571) ^ [_1453990, _1453992, _1453994] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453990, tc_HOL_Obool)), _1453992), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453990, tc_HOL_Obool)), _1453992), _1453994)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453990, tc_HOL_Obool)), _1453992), _1453994))], (48568 ^ _779571) ^ [_1751881, _1751883, _1751885, _1751887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751881), tc_List_Olist(_1751881))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751881), tc_List_Olist(_1751881)), _1751883), _1751885)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1751881), tc_List_Olist(_1751881)), c_List_Olistrel1(_1751881, _1751887)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751881), tc_List_Olist(_1751881))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751881), tc_List_Olist(_1751881)), _1751883), _1751885)), c_List_Olistrel1(_1751881, hAPP(c_Relation_Oconverse(_1751881, _1751881), _1751887)))))], (47604 ^ _779571) ^ [_1728064, _1728066, _1728068, _1728070] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1728064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1728066), hAPP(hAPP(c_List_Olist_OCons(_1728066), _1728068), _1728070)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1728064)) = _1728068)], (41850 ^ _779571) ^ [_1588421] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1588421)))], (40130 ^ _779571) ^ [_1539550, _1539552, _1539554] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1539550, _1539552), _1539554), hAPP(c_COMBK(tc_fun(_1539552, tc_HOL_Obool), _1539550), c_Orderings_Obot__class_Obot(tc_fun(_1539552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1539550, _1539552), tc_HOL_Obool)))], (41449 ^ _779571) ^ [_1573403, _1573405, _1573407] : [-(c_Map_Oran(_1573403, _1573405, _1573407) = hAPP(c_Set_OCollect(_1573405), hAPP(hAPP(c_COMBB(tc_fun(_1573403, tc_HOL_Obool), tc_HOL_Obool, _1573405), c_HOL_OEx(_1573403)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1573405), tc_fun(_1573403, tc_HOL_Obool), _1573405), hAPP(c_COMBC(_1573403, tc_Option_Ooption(_1573405), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1573405), tc_fun(tc_Option_Ooption(_1573405), tc_HOL_Obool), _1573403), c_fequal), _1573407))), c_Option_Ooption_OSome(_1573405)))))], (17959 ^ _779571) ^ [_1088662, _1088664] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088662)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088662)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088664)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088662)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088664))))], (19399 ^ _779571) ^ [_1112229] : [-(c_Int_Osucc(c_Int_OBit1(_1112229)) = c_Int_OBit0(c_Int_Osucc(_1112229)))], (42030 ^ _779571) ^ [_1592073, _1592075, _1592077, _1592079] : [c_FunDef_Oreduction__pair(_1592073, _1592075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool)), _1592077), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool), tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool)), _1592075))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool)), _1592079), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool), tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool)), _1592075))), c_Wellfounded_Owf(_1592073, _1592079), -(c_Wellfounded_Owf(_1592073, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592073, _1592073), tc_HOL_Obool)), _1592077), _1592079)))], (7987 ^ _779571) ^ [_912094] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _912094))), -(hAPP(c_Com_Obody, _912094) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7990 ^ [_912094]))], (9780 ^ _779571) ^ [_942296, _942298, _942300, _942302] : [class_Rings_Olinordered__semiring__strict(_942296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942296), _942298), _942300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942296), c_Groups_Ozero__class_Ozero(_942296)), _942302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942296), _942302), _942298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942296), _942302), _942300))))], (5911 ^ _779571) ^ [_874471, _874473, _874475, _874477] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_874471, _874473), _874475, _874477, _874475), hBOOL(hAPP(_874471, _874475)), 5919 ^ _779571 : [(5922 ^ _779571) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_874471, _874473), 5918 ^ [_874471, _874473, _874475, _874477], _874477, _874475))], (5920 ^ _779571) ^ [] : [-(c_Natural_Oevaln(_874473, _874475, _874477, 5918 ^ [_874471, _874473, _874475, _874477]))]]], (40360 ^ _779571) ^ [_1545080, _1545082] : [class_Orderings_Olinorder(_1545080), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545080), _1545082)), -(c_Big__Operators_Olattice_OInf__fin(_1545080, c_Orderings_Oord__class_Omin(_1545080), _1545082) = hAPP(c_Finite__Set_Ofold1(_1545080, c_Orderings_Oord__class_Omin(_1545080)), _1545082))], (5568 ^ _779571) ^ [_865553, _865555, _865557, _865559] : [-(tc_fun(_865559, _865555) = tc_fun(_865557, _865553)), _865559 = _865557, _865555 = _865553], (41638 ^ _779571) ^ [_1581456, _1581458] : [-(hAPP(c_Set_Oimage(_1581456, _1581456, c_Fun_Oid(_1581456)), _1581458) = _1581458)], (29216 ^ _779571) ^ [_1301621, _1301623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301621, tc_HOL_Obool)), _1301623), c_Orderings_Obot__class_Obot(tc_fun(_1301621, tc_HOL_Obool)))), -(_1301623 = c_Orderings_Obot__class_Obot(tc_fun(_1301621, tc_HOL_Obool)))], (15402 ^ _779571) ^ [_1040347, _1040349, _1040351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040347), _1040349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040347), _1040351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040351), _1040349)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040351), _1040347))))], (6169 ^ _779571) ^ [_879253, _879255, _879257, _879259, _879261, _879263, _879265, _879267, _879269] : [-(c_Com_Ocom_Ocom__rec(_879253, _879255, _879257, _879259, _879261, _879263, _879265, _879267, _879269, c_Com_Ocom_OSKIP) = _879255)], (47029 ^ _779571) ^ [_1714744, _1714746, _1714748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1714744, tc_HOL_Obool)), hAPP(c_List_Oset(_1714744), c_List_Osublist(_1714744, _1714746, _1714748))), hAPP(c_List_Oset(_1714744), _1714746))))], (48242 ^ _779571) ^ [_1743000, _1743002, _1743004, _1743006, _1743008, _1743010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743000)), _1743002)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743004)), _1743006))), -(c_Map_Omap__upds(_1743000, _1743004, _1743008, hAPP(hAPP(c_List_Oappend(_1743000), _1743002), hAPP(hAPP(c_List_Olist_OCons(_1743000), _1743010), c_List_Olist_ONil(_1743000))), _1743006) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1743000, tc_Option_Ooption(_1743004)), c_Map_Omap__upds(_1743000, _1743004, _1743008, _1743002, _1743006)), _1743010), hAPP(c_Option_Ooption_OSome(_1743004), hAPP(hAPP(c_List_Onth(_1743004), _1743006), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743000)), _1743002)))))], (16208 ^ _779571) ^ [_1056788, _1056790] : [_1056788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1056788), _1056790) = _1056790)], (8068 ^ _779571) ^ [_913291, _913293, _913295, _913297, _913299] : [-(hAPP(c_Option_Ooption_Ooption__case(_913291, _913293, _913295, _913297), hAPP(c_Option_Ooption_OSome(_913293), _913299)) = hAPP(_913297, _913299))], (46068 ^ _779571) ^ [_1688942, _1688944, _1688946, _1688948] : [-(hAPP(hAPP(c_Option_Omap(_1688942, _1688944), _1688946), hAPP(c_Option_Ooption_OSome(_1688942), _1688948)) = hAPP(c_Option_Ooption_OSome(_1688944), hAPP(_1688946, _1688948)))], (25344 ^ _779571) ^ [_1223691, _1223693, _1223695] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223691), _1223693)), _1223693 = _1223695, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223691), _1223695)))], (646 ^ _779571) ^ [_789586, _789588, _789590, _789592] : [-(c_Relation_Oirrefl(_789590, _789586)), c_Relation_Oirrefl(_789592, _789588), _789592 = _789590, _789588 = _789586], (28489 ^ _779571) ^ [_1285483, _1285485, _1285487] : [class_Orderings_Olinorder(_1285483), 28492 ^ _779571 : [(28499 ^ _779571) ^ [] : [_1285485 = _1285487, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1285483), _1285485) = hAPP(c_SetInterval_Oord__class_OatLeast(_1285483), _1285487))], (28493 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1285483), _1285485) = hAPP(c_SetInterval_Oord__class_OatLeast(_1285483), _1285487), -(_1285485 = _1285487)]]], (18717 ^ _779571) ^ [_1100738, _1100740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100738)), c_Int_OBit1(_1100740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100738), _1100740)))], (28645 ^ _779571) ^ [_1288370, _1288372, _1288374] : [class_Orderings_Olinorder(_1288370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288370), _1288372), _1288374)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288370, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1288370), _1288372)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288370, _1288372, _1288374)) = hAPP(c_SetInterval_Oord__class_OatMost(_1288370), _1288374))], (3890 ^ _779571) ^ [_839564, _839566, _839568, _839570, _839572, _839574] : [-(c_Predicate_ORangeP(_839574, _839570, _839566) = c_Predicate_ORangeP(_839572, _839568, _839564)), _839574 = _839572, _839570 = _839568, _839566 = _839564], (23062 ^ _779571) ^ [_1179434, _1179436, _1179438, _1179440, _1179442, _1179444] : [-(hAPP(c_Product__Type_Oapsnd(_1179434, _1179436, _1179438, _1179440), hAPP(hAPP(c_Product__Type_OPair(_1179438, _1179434), _1179442), _1179444)) = hAPP(hAPP(c_Product__Type_OPair(_1179438, _1179436), _1179442), hAPP(_1179440, _1179444)))], (8185 ^ _779571) ^ [_915274] : [class_Rings_Osemiring__1(_915274), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915274), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_915274))], (45825 ^ _779571) ^ [_1682827, _1682829] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1682827), _1682829) = c_Smallcheck_Osmall_H(_1682827, hAPP(c_Code__Numeral_Oint__of, _1682829), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1682829))))], (4764 ^ _779571) ^ [_853207, _853209, _853211, _853213] : [-(c_List_Olexord(_853213, _853209) = c_List_Olexord(_853211, _853207)), _853213 = _853211, _853209 = _853207], (46193 ^ _779571) ^ [_1691911, _1691913, _1691915, _1691917] : [hBOOL(hAPP(c_List_Odistinct(_1691911), hAPP(hAPP(c_List_Omap(_1691913, _1691911), _1691915), _1691917))), 46196 ^ _779571 : [(46199 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1691913, _1691911, _1691915, hAPP(c_List_Oset(_1691913), _1691917)))], (46197 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1691913), _1691917)))]]], (43457 ^ _779571) ^ [_1626749, _1626751, _1626753] : [hAPP(hAPP(c_Relation_Orel__comp(_1626749, _1626749, _1626749), hAPP(c_Relation_Oconverse(_1626749, _1626749), _1626751)), _1626751) = _1626751, hAPP(c_Relation_ODomain(_1626749, _1626749), _1626751) = _1626753, -(c_Equiv__Relations_Oequiv(_1626749, _1626753, _1626751))], (1838 ^ _779571) ^ [_805394, _805396, _805398, _805400, _805402, _805404, _805406, _805408] : [-(c_Natural_Oevaln(_805406, _805402, _805398, _805394)), c_Natural_Oevaln(_805408, _805404, _805400, _805396), _805408 = _805406, _805404 = _805402, _805400 = _805398, _805396 = _805394], (14170 ^ _779571) ^ [_1018091, _1018093, _1018095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018091)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018093, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018095), _1018091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018095), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018093), _1018095), _1018091))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018093, _1018095)))], (33349 ^ _779571) ^ [_1387653, _1387655, _1387657] : [class_Orderings_Olinorder(_1387653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387653), _1387655)), -(_1387657 = c_Orderings_Obot__class_Obot(tc_fun(_1387653, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387653, tc_HOL_Obool)), _1387657), _1387655)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387653), c_Big__Operators_Olinorder__class_OMin(_1387653, _1387657)), c_Big__Operators_Olinorder__class_OMin(_1387653, _1387655)) = c_Big__Operators_Olinorder__class_OMin(_1387653, _1387655))], (48946 ^ _779571) ^ [_1761896, _1761898, _1761900] : [-(hAPP(c_List_Ohd(_1761896), hAPP(hAPP(c_List_Olist_OCons(_1761896), _1761898), _1761900)) = _1761898)], (49846 ^ _779571) ^ [_1781386, _1781388, _1781390, _1781392] : [-(c_List_Omap__filter(_1781386, _1781388, _1781390, _1781392) = hAPP(hAPP(c_List_Omap(_1781386, _1781388), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1781388), _1781388, _1781386, c_Option_Othe(_1781388)), _1781390)), hAPP(c_List_Ofilter(_1781386, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1781386), c_fNot), hAPP(hAPP(c_COMBC(_1781386, tc_Option_Ooption(_1781388), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1781388), tc_fun(tc_Option_Ooption(_1781388), tc_HOL_Obool), _1781386), c_fequal), _1781390)), c_Option_Ooption_ONone(_1781388)))), _1781392)))], (47232 ^ _779571) ^ [_1719558, _1719560, _1719562, _1719564] : [_1719564 = c_List_Olist_ONil(_1719558), -(hAPP(hAPP(c_List_Omap(_1719558, _1719560), _1719562), _1719564) = c_List_Olist_ONil(_1719560))], (31185 ^ _779571) ^ [_1341368, _1341370, _1341372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341368, tc_HOL_Obool)), _1341370), _1341372)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341368), _1341372)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341368), _1341370)))], (18445 ^ _779571) ^ [_1096114] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096114) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096114), c_Int_OPls)))], (4490 ^ _779571) ^ [_849048, _849050, _849052, _849054, _849056, _849058, _849060, _849062] : [-(c_Map_Orestrict__map(_849062, _849058, _849054, _849050) = c_Map_Orestrict__map(_849060, _849056, _849052, _849048)), _849062 = _849060, _849058 = _849056, _849054 = _849052, _849050 = _849048], (22688 ^ _779571) ^ [_1172132, _1172134] : [class_Rings_Oring__1(_1172132), 22691 ^ _779571 : [(22698 ^ _779571) ^ [] : [-(_1172134 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22701 ^ _779571 : [(22708 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172134), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1172132), _1172134) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1172132), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1172132, _1172132)), tc_fun(tc_Int_Oint, _1172132)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1172132, _1172132), _1172132), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1172132, _1172132)), tc_fun(tc_Int_Oint, _1172132)), tc_Int_Oint), c_COMBB(tc_fun(_1172132, _1172132), _1172132, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1172132, tc_fun(tc_fun(_1172132, _1172132), _1172132), tc_Int_Oint), c_HOL_OLet(_1172132, _1172132)), c_Int_Oring__1__class_Oof__int(_1172132)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1172132, _1172132), tc_fun(_1172132, _1172132)), hAPP(hAPP(c_COMBB(tc_fun(_1172132, tc_fun(_1172132, _1172132)), tc_fun(tc_fun(_1172132, _1172132), tc_fun(_1172132, _1172132)), tc_Int_Oint), c_COMBS(_1172132, _1172132, _1172132)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1172132, _1172132), tc_fun(_1172132, tc_fun(_1172132, _1172132))), hAPP(hAPP(c_COMBB(tc_fun(_1172132, tc_fun(_1172132, _1172132)), tc_fun(tc_fun(_1172132, _1172132), tc_fun(_1172132, tc_fun(_1172132, _1172132))), tc_Int_Oint), c_COMBB(_1172132, tc_fun(_1172132, _1172132), _1172132)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1172132, tc_fun(_1172132, _1172132)), tc_Int_Oint), c_If(_1172132)), 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(_1172132, _1172132, _1172132), c_Groups_Oplus__class_Oplus(_1172132)), c_COMBI(_1172132))))), hAPP(hAPP(c_COMBC(_1172132, _1172132, _1172132), hAPP(hAPP(c_COMBB(_1172132, tc_fun(_1172132, _1172132), _1172132), c_Groups_Oplus__class_Oplus(_1172132)), hAPP(hAPP(c_COMBS(_1172132, _1172132, _1172132), c_Groups_Oplus__class_Oplus(_1172132)), c_COMBI(_1172132)))), c_Groups_Oone__class_Oone(_1172132))))), c_Divides_Odivmod__int(_1172134, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (22702 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172134), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1172132), _1172134) = hAPP(c_Groups_Ouminus__class_Ouminus(_1172132), hAPP(c_Int_Oring__1__class_Oof__int(_1172132), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1172134))))]]], (22692 ^ _779571) ^ [] : [_1172134 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1172132), _1172134) = c_Groups_Ozero__class_Ozero(_1172132))]]], (4568 ^ _779571) ^ [_850267, _850269, _850271, _850273] : [-(c_Finite__Set_Ofold1(_850273, _850269) = c_Finite__Set_Ofold1(_850271, _850267)), _850273 = _850271, _850269 = _850267], (44317 ^ _779571) ^ [_1646193, _1646195, _1646197, _1646199, _1646201, _1646203] : [c_Finite__Set_Ofun__left__comm(_1646193, _1646195, _1646197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646193), _1646199)), -(hBOOL(hAPP(hAPP(c_member(_1646193), _1646201), _1646199))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1646193, _1646195, _1646197), _1646203), hAPP(hAPP(c_Set_Oinsert(_1646193), _1646201), _1646199)) = hAPP(hAPP(_1646197, _1646201), hAPP(hAPP(c_Finite__Set_Ofold(_1646193, _1646195, _1646197), _1646203), _1646199)))], (46086 ^ _779571) ^ [_1689330, _1689332, _1689334, _1689336, _1689338, _1689340, _1689342] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1689330), tc_Option_Ooption(_1689332), _1689334, hAPP(c_Option_Omap(_1689330, _1689332), _1689336)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1689334, tc_Option_Ooption(_1689330)), _1689338), _1689340), hAPP(c_Option_Ooption_OSome(_1689330), _1689342))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1689334, tc_Option_Ooption(_1689332)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1689330), tc_Option_Ooption(_1689332), _1689334, hAPP(c_Option_Omap(_1689330, _1689332), _1689336)), _1689338)), _1689340), hAPP(c_Option_Ooption_OSome(_1689332), hAPP(_1689336, _1689342))))], (30766 ^ _779571) ^ [_1332701, _1332703, _1332705, _1332707, _1332709] : [hBOOL(hAPP(hAPP(c_member(_1332701), _1332703), _1332705)), -(hAPP(c_Set_Oimage(_1332701, _1332707, hAPP(c_COMBK(_1332707, _1332701), _1332709)), _1332705) = hAPP(hAPP(c_Set_Oinsert(_1332707), _1332709), c_Orderings_Obot__class_Obot(tc_fun(_1332707, tc_HOL_Obool))))], (46969 ^ _779571) ^ [_1712633, _1712635, _1712637, _1712639] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1712633), tc_List_Olist(_1712633), c_List_Olistrel(_1712633, _1712635)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1712633)), hAPP(hAPP(c_List_Olist_OCons(_1712633), _1712637), _1712639)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1712633), tc_HOL_Obool)))) = c_List_Oset__Cons(_1712633, hAPP(c_Relation_OImage(_1712633, _1712633, _1712635), hAPP(hAPP(c_Set_Oinsert(_1712633), _1712637), c_Orderings_Obot__class_Obot(tc_fun(_1712633, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1712633), tc_List_Olist(_1712633), c_List_Olistrel(_1712633, _1712635)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1712633)), _1712639), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1712633), tc_HOL_Obool))))))], (8402 ^ _779571) ^ [_918781, _918783, _918785] : [class_Orderings_Opreorder(_918781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918781), _918783), _918785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918781), _918785), _918783))], (36006 ^ _779571) ^ [_1446981, _1446983, _1446985, _1446987, _1446989] : [c_Equiv__Relations_Oequiv(_1446981, _1446983, _1446985), hBOOL(hAPP(hAPP(c_member(tc_prod(_1446981, _1446981)), hAPP(hAPP(c_Product__Type_OPair(_1446981, _1446981), _1446987), _1446989)), _1446985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446981, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446981, _1446981, _1446985), hAPP(hAPP(c_Set_Oinsert(_1446981), _1446987), c_Orderings_Obot__class_Obot(tc_fun(_1446981, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1446981, _1446981, _1446985), hAPP(hAPP(c_Set_Oinsert(_1446981), _1446989), c_Orderings_Obot__class_Obot(tc_fun(_1446981, tc_HOL_Obool)))))))], (46671 ^ _779571) ^ [_1703775, _1703777, _1703779, _1703781, _1703783] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703775)), _1703777) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703779)), _1703781), 46674 ^ _779571 : [(46682 ^ _779571) ^ [] : [46683 ^ _779571 : [(46684 ^ _779571) ^ [_1704063] : [hAPP(c_Map_Omap__of(_1703775, _1703779, hAPP(hAPP(c_List_Ozip(_1703775, _1703779), _1703777), _1703781)), _1703783) = hAPP(c_Option_Ooption_OSome(_1703779), _1704063)]], -(hBOOL(hAPP(hAPP(c_member(_1703775), _1703783), hAPP(c_List_Oset(_1703775), _1703777))))], (46675 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1703775), _1703783), hAPP(c_List_Oset(_1703775), _1703777))), -(hAPP(c_Map_Omap__of(_1703775, _1703779, hAPP(hAPP(c_List_Ozip(_1703775, _1703779), _1703777), _1703781)), _1703783) = hAPP(c_Option_Ooption_OSome(_1703779), 46678 ^ [_1703775, _1703777, _1703779, _1703781, _1703783]))]]], (13356 ^ _779571) ^ [_1003224, _1003226, _1003228, _1003230, _1003232] : [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), _1003224), _1003226)), _1003228)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003224), _1003230)), _1003232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1003232), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003224), _1003232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003224), _1003228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1003230), _1003226)))], (51623 ^ _779571) ^ [_1813838, _1813840] : [hBOOL(hAPP(hAPP(c_fconj, _1813838), _1813840)), -(hBOOL(_1813840))], (51065 ^ _779571) ^ [_1807893, _1807895] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807893)), c_List_Oremdups(_1807893, c_List_Oconcat(_1807893, _1807895))) = hAPP(c_Finite__Set_Ocard(_1807893), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1807893), tc_fun(_1807893, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1807893)), _1807895)), c_List_Oset(_1807893))))], (44646 ^ _779571) ^ [_1655349, _1655351, _1655353, _1655355, _1655357] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655349, tc_fun(_1655351, tc_HOL_Obool)), _1655353), hAPP(hAPP(c_COMBB(tc_fun(_1655351, tc_HOL_Obool), tc_fun(_1655351, tc_HOL_Obool), _1655349), hAPP(c_Set_Oinsert(_1655351), _1655355)), _1655357)) = hAPP(hAPP(c_Set_Oinsert(_1655351), _1655355), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655349, tc_fun(_1655351, tc_HOL_Obool)), _1655353), _1655357)))], (40042 ^ _779571) ^ [_1537259, _1537261, _1537263, _1537265, _1537267, _1537269] : [-(hAPP(c_Set_Oimage(_1537259, tc_prod(_1537261, _1537263), hAPP(hAPP(c_COMBS(_1537259, _1537263, tc_prod(_1537261, _1537263)), hAPP(hAPP(c_COMBB(_1537261, tc_fun(_1537263, tc_prod(_1537261, _1537263)), _1537259), c_Product__Type_OPair(_1537261, _1537263)), _1537265)), _1537267)), _1537269) = hAPP(hAPP(c_Product__Type_OSigma(_1537261, _1537263), hAPP(c_Set_Oimage(_1537259, _1537261, _1537265), _1537269)), hAPP(hAPP(c_COMBB(tc_fun(_1537259, tc_HOL_Obool), tc_fun(_1537263, tc_HOL_Obool), _1537261), c_Set_Oimage(_1537259, _1537263, _1537267)), hAPP(hAPP(c_COMBC(_1537261, tc_fun(_1537259, tc_HOL_Obool), tc_fun(_1537259, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537259, tc_HOL_Obool), tc_fun(tc_fun(_1537259, tc_HOL_Obool), tc_fun(_1537259, tc_HOL_Obool)), _1537261), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537259, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1537261, tc_HOL_Obool), tc_fun(_1537259, tc_HOL_Obool), _1537261), c_Set_Ovimage(_1537259, _1537261, _1537265)), hAPP(hAPP(c_COMBC(_1537261, tc_fun(_1537261, tc_HOL_Obool), tc_fun(_1537261, tc_HOL_Obool)), c_Set_Oinsert(_1537261)), c_Orderings_Obot__class_Obot(tc_fun(_1537261, tc_HOL_Obool)))))), _1537269))))], (204 ^ _779571) ^ [_782507, _782509, _782511, _782513, _782515, _782517, _782519, _782521, _782523, _782525, _782527, _782529] : [-(c_Nitpick_Ofold__graph_H(_782527, _782523, _782519, _782515, _782511, _782507)), c_Nitpick_Ofold__graph_H(_782529, _782525, _782521, _782517, _782513, _782509), _782529 = _782527, _782525 = _782523, _782521 = _782519, _782517 = _782515, _782513 = _782511, _782509 = _782507], (33575 ^ _779571) ^ [_1392387, _1392389, _1392391, _1392393, _1392395] : [hBOOL(hAPP(hAPP(c_member(_1392387), _1392389), _1392391)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1392393, _1392387)), hAPP(c_Sum__Type_OInr(_1392387, _1392393), _1392389)), c_Sum__Type_OPlus(_1392393, _1392387, _1392395, _1392391))))], (45133 ^ _779571) ^ [_1667238, _1667240, _1667242, _1667244] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1667238, tc_HOL_Obool), tc_fun(_1667240, tc_HOL_Obool)), _1667242), hAPP(hAPP(c_COMBC(tc_fun(_1667238, tc_HOL_Obool), tc_fun(_1667238, tc_fun(_1667240, tc_HOL_Obool)), tc_fun(_1667240, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667238, tc_fun(_1667240, tc_HOL_Obool))), _1667244)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667238, tc_fun(_1667240, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667238, tc_HOL_Obool), _1667242)), _1667244))], (48347 ^ _779571) ^ [_1745837, _1745839, _1745841, _1745843, _1745845, _1745847] : [-(hBOOL(hAPP(hAPP(c_member(_1745837), _1745839), hAPP(c_List_Oset(_1745837), _1745841)))), -(hAPP(c_Map_Omap__upds(_1745837, _1745843, _1745845, _1745841, _1745847), _1745839) = hAPP(_1745845, _1745839))], (12812 ^ _779571) ^ [_994046, _994048, _994050, _994052] : [class_Rings_Olinordered__ring__strict(_994046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994046), c_Groups_Ozero__class_Ozero(_994046)), _994048)), 12819 ^ _779571 : [(12826 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994046), _994050), _994052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994046), _994048), _994050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994046), _994048), _994052))))], (12820 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994046), _994048), _994050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994046), _994048), _994052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994046), _994050), _994052)))]]], (47312 ^ _779571) ^ [_1720973, _1720975, _1720977] : [c_List_Olist_ONil(_1720973) = hAPP(hAPP(c_List_Olist_OCons(_1720973), _1720975), _1720977)], (18747 ^ _779571) ^ [_1101212] : [c_Int_OBit1(_1101212) = c_Int_OMin, -(_1101212 = c_Int_OMin)], (3296 ^ _779571) ^ [_830165, _830167, _830169, _830171, _830173, _830175] : [-(c_SetInterval_Oord_OgreaterThan(_830175, _830171, _830167) = c_SetInterval_Oord_OgreaterThan(_830173, _830169, _830165)), _830175 = _830173, _830171 = _830169, _830167 = _830165], (33079 ^ _779571) ^ [_1382733, _1382735, _1382737] : [class_Orderings_Olinorder(_1382733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382733), _1382735)), -(_1382737 = c_Orderings_Obot__class_Obot(tc_fun(_1382733, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382733, tc_HOL_Obool)), _1382737), _1382735)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1382733), c_Big__Operators_Olinorder__class_OMax(_1382733, _1382737)), c_Big__Operators_Olinorder__class_OMax(_1382733, _1382735)) = c_Big__Operators_Olinorder__class_OMax(_1382733, _1382735))], (12269 ^ _779571) ^ [_984349, _984351, _984353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984351), _984353)), -(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, _984349)), _984351)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984349)), _984353))))], (51491 ^ _779571) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (43403 ^ _779571) ^ [_1625210, _1625212, _1625214] : [-(hAPP(c_Relation_ODomain(_1625210, _1625212), hAPP(c_Relation_Oconverse(_1625212, _1625210), _1625214)) = hAPP(c_Relation_ORange(_1625212, _1625210), _1625214))], (6099 ^ _779571) ^ [_877886, _877888, _877890, _877892, _877894, _877896] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_877886, _877888, _877890, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877886), _877892), _877894), _877896)) = hAPP(hAPP(hAPP(_877890, _877892), _877894), _877896))], (42064 ^ _779571) ^ [_1592752, _1592754, _1592756, _1592758] : [42066 ^ _779571 : [(42069 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1592754, hAPP(_1592756, 42065 ^ [_1592752, _1592754, _1592756, _1592758]))), hAPP(_1592754, 42065 ^ [_1592752, _1592754, _1592756, _1592758])))], (42067 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1592752, 42065 ^ [_1592752, _1592754, _1592756, _1592758])))]], -(c_Wellfounded_Owf(_1592758, hAPP(c_Set_OCollect(tc_prod(_1592758, _1592758)), hAPP(c_Product__Type_Oprod_Oprod__case(_1592758, _1592758, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1592758, tc_HOL_Obool), tc_fun(_1592758, tc_HOL_Obool), _1592758), hAPP(c_COMBS(_1592758, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1592758), c_fconj), _1592752))), hAPP(hAPP(c_COMBC(_1592758, tc_fun(_1592758, _1592758), tc_fun(_1592758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592758, tc_HOL_Obool), tc_fun(tc_fun(_1592758, _1592758), tc_fun(_1592758, tc_HOL_Obool)), _1592758), c_COMBB(_1592758, tc_HOL_Obool, _1592758)), c_fequal)), _1592756))))))], (29606 ^ _779571) ^ [] : [-(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)))], (15430 ^ _779571) ^ [_1040740, _1040742] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040740), _1040742)), _1040742) = _1040740)], (14134 ^ _779571) ^ [_1017358, _1017360, _1017362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017358), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14137 ^ _779571 : [(14138 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1017360, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017362), _1017358)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017362, _1017358))), 14141 ^ _779571 : [(14142 ^ _779571) ^ [_1017568, _1017570] : [-(hBOOL(hAPP(hAPP(_1017360, _1017570), _1017568))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017358), _1017568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017568), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1017362 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017358), _1017570)), _1017568)]]], (14156 ^ _779571) ^ [] : [14159 ^ _779571 : [(14162 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14158 ^ [_1017358, _1017360, _1017362]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14164 ^ _779571) ^ [] : [-(_1017362 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017358), 14157 ^ [_1017358, _1017360, _1017362])), 14158 ^ [_1017358, _1017360, _1017362]))], (14166 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(_1017360, 14157 ^ [_1017358, _1017360, _1017362]), 14158 ^ [_1017358, _1017360, _1017362]))], (14160 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017358), 14158 ^ [_1017358, _1017360, _1017362])))]], -(hBOOL(hAPP(hAPP(_1017360, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017362), _1017358)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017362, _1017358))))]]], (19377 ^ _779571) ^ [_1111907, _1111909] : [class_Int_Onumber__ring(_1111907), class_Int_Oring__char__0(_1111907), 19384 ^ _779571 : [(19391 ^ _779571) ^ [] : [c_Int_Oiszero(_1111907, hAPP(c_Int_Onumber__class_Onumber__of(_1111907), _1111909)), -(c_Int_Oiszero(_1111907, hAPP(c_Int_Onumber__class_Onumber__of(_1111907), c_Int_OBit0(_1111909))))], (19385 ^ _779571) ^ [] : [c_Int_Oiszero(_1111907, hAPP(c_Int_Onumber__class_Onumber__of(_1111907), c_Int_OBit0(_1111909))), -(c_Int_Oiszero(_1111907, hAPP(c_Int_Onumber__class_Onumber__of(_1111907), _1111909)))]]], (35381 ^ _779571) ^ [_1431401, _1431403, _1431405, _1431407, _1431409] : [class_Groups_Ocomm__monoid__add(_1431401), class_Groups_Oordered__cancel__ab__semigroup__add(_1431401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431403), _1431405)), -(_1431405 = c_Orderings_Obot__class_Obot(tc_fun(_1431403, tc_HOL_Obool))), 35399 ^ _779571 : [(35402 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431401), hAPP(_1431407, 35398 ^ [_1431401, _1431403, _1431405, _1431407, _1431409])), hAPP(_1431409, 35398 ^ [_1431401, _1431403, _1431405, _1431407, _1431409])))], (35400 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1431403), 35398 ^ [_1431401, _1431403, _1431405, _1431407, _1431409]), _1431405)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431401), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431403, _1431401), _1431407), _1431405)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431403, _1431401), _1431409), _1431405))))], (44738 ^ _779571) ^ [_1658088, _1658090, _1658092, _1658094, _1658096] : [-(_1658088 = c_Orderings_Obot__class_Obot(tc_fun(_1658090, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658090, tc_fun(_1658092, tc_HOL_Obool)), _1658088), hAPP(hAPP(c_COMBB(tc_fun(_1658092, tc_HOL_Obool), tc_fun(_1658092, tc_HOL_Obool), _1658090), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658092, tc_HOL_Obool)), _1658094)), _1658096)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658092, tc_HOL_Obool)), _1658094), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658090, tc_fun(_1658092, tc_HOL_Obool)), _1658088), _1658096)))], (6476 ^ _779571) ^ [_885147, _885149, _885151, _885153, _885155] : [hBOOL(hAPP(_885147, _885149)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885151), _885149), _885153)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_885147, _885151, _885155)), _885149), _885153)))], (516 ^ _779571) ^ [_787491, _787493, _787495, _787497, _787499, _787501, _787503, _787505, _787507, _787509, _787511, _787513] : [-(c_Finite__Set_Ofolding__image__simple(_787511, _787507, _787503, _787499, _787495, _787491)), c_Finite__Set_Ofolding__image__simple(_787513, _787509, _787505, _787501, _787497, _787493), _787513 = _787511, _787509 = _787507, _787505 = _787503, _787501 = _787499, _787497 = _787495, _787493 = _787491], (43092 ^ _779571) ^ [_1617854, _1617856] : [-(hAPP(c_Relation_ORange(_1617854, _1617854), c_Transitive__Closure_Ortrancl(_1617854, _1617856)) = c_Orderings_Otop__class_Otop(tc_fun(_1617854, tc_HOL_Obool)))], (25426 ^ _779571) ^ [_1224996, _1224998] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224996), _1224998)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224998), _1224996))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224998), _1224996)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224996), _1224998)))], (13012 ^ _779571) ^ [_997420, _997422] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _997420) = _997422, 13015 ^ _779571 : [(13018 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997422)))], (13016 ^ _779571) ^ [] : [-(_997420 = hAPP(c_Int_Onat, _997422))]]], (22772 ^ _779571) ^ [_1174186, _1174188, _1174190] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1174186, _1174188), _1174190)), 22775 ^ _779571 : [(22776 ^ _779571) ^ [_1174271] : [hBOOL(hAPP(hAPP(_1174188, _1174271), _1174190)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1174186, _1174188), _1174271)))]]], (49712 ^ _779571) ^ [_1778110, _1778112, _1778114] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778110)), hAPP(c_List_Ofilter(_1778110, _1778112), _1778114))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778110)), _1778114))))], (22986 ^ _779571) ^ [_1177982, _1177984] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177982), _1177984)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177982), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1177984)))], (7063 ^ _779571) ^ [_895942] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _895942) = _895942)], (44041 ^ _779571) ^ [_1640970, _1640972, _1640974] : [class_Lattices_Oab__semigroup__idem__mult(_1640970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640970), _1640972)), -(hAPP(c_Finite__Set_Ofold1(_1640970, c_Groups_Otimes__class_Otimes(_1640970)), hAPP(hAPP(c_Set_Oinsert(_1640970), _1640974), _1640972)) = hAPP(hAPP(c_Finite__Set_Ofold(_1640970, _1640970, c_Groups_Otimes__class_Otimes(_1640970)), _1640974), _1640972))], (29804 ^ _779571) ^ [_1312469, _1312471] : [class_Orderings_Olinorder(_1312469), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312469, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1312469), _1312471), c_Orderings_Obot__class_Obot(tc_fun(_1312469, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1312469), _1312471)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1312469), _1312471))], (46771 ^ _779571) ^ [_1707247, _1707249, _1707251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1707247, _1707247), tc_HOL_Obool)), _1707249), _1707251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1707247), tc_List_Olist(_1707247)), tc_HOL_Obool)), c_List_Olistrel(_1707247, _1707249)), c_List_Olistrel(_1707247, _1707251))))], (13679 ^ _779571) ^ [_1008821, _1008823, _1008825, _1008827] : [class_Divides_Osemiring__div(_1008821), 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tc_HOL_Obool), _1560932), c_fconj), _1560934)), _1560936)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1560932, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1560932), _1560934)), hAPP(c_Set_OCollect(_1560932), _1560936)))], (45037 ^ _779571) ^ [_1665080, _1665082, _1665084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1665080, tc_HOL_Obool), tc_HOL_Obool)), _1665082), _1665084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1665080, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665080, tc_HOL_Obool), _1665082)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665080, tc_HOL_Obool), _1665084))))], (33759 ^ _779571) ^ [_1396144, _1396146] : [class_Orderings_Olinorder(_1396144), -(c_Big__Operators_Olattice_OInf__fin(_1396144, c_Orderings_Oord__class_Omin(_1396144), hAPP(hAPP(c_Set_Oinsert(_1396144), _1396146), c_Orderings_Obot__class_Obot(tc_fun(_1396144, tc_HOL_Obool)))) = _1396146)], (23105 ^ _779571) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (17087 ^ _779571) ^ [_1073232, _1073234, _1073236, _1073238] : [class_Rings_Olinordered__semidom(_1073232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073232), _1073234), _1073236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073232), c_Groups_Ozero__class_Ozero(_1073232)), _1073234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073232), hAPP(hAPP(c_Power_Opower__class_Opower(_1073232), _1073234), _1073238)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073232), _1073236), _1073238))))], (32091 ^ _779571) ^ [_1363399, _1363401, _1363403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363399)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1363401), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1363403)), 32098 ^ _779571 : [(32099 ^ _779571) ^ [_1363607] : [32101 ^ _779571 : [(32107 ^ _779571) ^ [] : [-(_1363607 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32103 ^ [_1363399, _1363401, _1363403, _1363607]), 32100 ^ [_1363399, _1363401, _1363403, _1363607]))], (32105 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32103 ^ [_1363399, _1363401, _1363403, _1363607]), _1363403)))], (32102 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32100 ^ [_1363399, _1363401, _1363403, _1363607]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1363399))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1363607), _1363401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1363607), _1363399)), _1363401)))]]], (7794 ^ 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hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094288), _1094290)))], (15436 ^ _779571) ^ [_1040865, _1040867, _1040869] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040865), _1040867)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040865), _1040869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040867), _1040869))], (18387 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (12982 ^ _779571) ^ [_997001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997001), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _997001) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14628 ^ _779571) ^ [_1026285, _1026287, _1026289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1026285)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026285), _1026287)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026285), _1026289)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026287), _1026289))], (35329 ^ _779571) ^ [_1430513, _1430515, _1430517, _1430519, _1430521] : [c_Finite__Set_Ofolding__one__idem(_1430513, _1430515, _1430517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430513), _1430519)), -(_1430521 = c_Orderings_Obot__class_Obot(tc_fun(_1430513, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430513, tc_HOL_Obool)), _1430521), _1430519)), -(hAPP(hAPP(_1430515, hAPP(_1430517, _1430521)), hAPP(_1430517, _1430519)) = hAPP(_1430517, _1430519))], (46304 ^ _779571) ^ [_1694263, _1694265, _1694267] : [hBOOL(hAPP(c_List_Odistinct(_1694263), _1694265)), -(hAPP(c_List_Oset(_1694263), c_List_Oremove1(_1694263, _1694267, _1694265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1694263, tc_HOL_Obool)), hAPP(c_List_Oset(_1694263), _1694265)), hAPP(hAPP(c_Set_Oinsert(_1694263), _1694267), c_Orderings_Obot__class_Obot(tc_fun(_1694263, tc_HOL_Obool)))))], (22454 ^ _779571) ^ [_1167673, _1167675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167673)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167675))), -(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(_1167675))), 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), _1167673)), c_Int_Onat))))))], (13685 ^ _779571) ^ [_1008956, _1008958, _1008960, _1008962] : [class_Divides_Osemiring__div(_1008956), -(c_Divides_Odiv__class_Omod(_1008956, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008956), _1008958), _1008960), _1008962) = c_Divides_Odiv__class_Omod(_1008956, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008956), c_Divides_Odiv__class_Omod(_1008956, _1008958, _1008962)), _1008960), _1008962))], (24885 ^ _779571) ^ [_1214873, _1214875, _1214877, _1214879, _1214881, _1214883, _1214885] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1214873, _1214875, _1214877, _1214879), _1214881), _1214883), _1214885) = c_New__DSequence_Oneg__bind(_1214873, _1214875, hAPP(hAPP(hAPP(_1214877, _1214881), _1214883), _1214885), hAPP(hAPP(c_COMBC(_1214873, 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(_1214875)))), hAPP(hAPP(c_COMBC(_1214873, 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(_1214875))))), hAPP(hAPP(c_COMBC(_1214873, 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(_1214875)))))), _1214879), _1214881)), _1214883)), _1214885)))], (18207 ^ _779571) ^ [_1092571, _1092573] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1092571), hAPP(hAPP(c_Power_Opower__class_Opower(_1092571), hAPP(c_Int_Onumber__class_Onumber__of(_1092571), c_Int_OMin)), _1092573)) = c_Groups_Oone__class_Oone(_1092571)), class_Int_Onumber__ring(_1092571), class_Rings_Olinordered__idom(_1092571)], (15700 ^ _779571) ^ [_1046090, _1046092] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046090), _1046092) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046090), _1046092)))], (49237 ^ _779571) ^ [_1767634, _1767636, _1767638, _1767640] : [class_Complete__Lattice_Ocomplete__lattice(_1767634), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1767636, _1767634), hAPP(c_List_Oset(_1767636), _1767638)), _1767640) = hAPP(c_List_Ofoldl(_1767634, _1767636, hAPP(c_COMBC(_1767636, _1767634, _1767634), hAPP(hAPP(c_COMBB(_1767634, tc_fun(_1767634, _1767634), _1767636), c_Lattices_Osemilattice__inf__class_Oinf(_1767634)), _1767640)), c_Orderings_Otop__class_Otop(_1767634)), _1767638))], (28756 ^ _779571) ^ [_1290516, _1290518] : [class_Orderings_Oorder(_1290516), 28763 ^ _779571 : [(28766 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290516), hAPP(_1290518, 28761 ^ [_1290516, _1290518])), hAPP(_1290518, 28762 ^ [_1290516, _1290518])))], (28764 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 28761 ^ [_1290516, _1290518]), 28762 ^ [_1290516, _1290518])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1290516, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290518))], (10586 ^ _779571) ^ [_955686, _955688, _955690, _955692, _955694] : [class_Orderings_Oord(_955686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955688, _955686)), _955690), _955692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955686), hAPP(_955690, _955694)), hAPP(_955692, _955694))))], (3458 ^ _779571) ^ [_832696, _832698, _832700, _832702, _832704, _832706] : [-(c_Com_Ocom_OCond(_832706, _832702, _832698) = c_Com_Ocom_OCond(_832704, _832700, _832696)), _832706 = _832704, _832702 = _832700, _832698 = _832696], (29762 ^ _779571) ^ [_1311743, _1311745, _1311747] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1311743, _1311745) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1311747), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1311743 = _1311745, _1311745 = _1311747], (39519 ^ _779571) ^ [_1524654, _1524656, _1524658, _1524660] : [-(hAPP(c_Set_Oimage(_1524654, _1524656, _1524658), hAPP(c_Set_Ovimage(_1524654, _1524656, _1524658), _1524660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524656, tc_HOL_Obool)), _1524660), hAPP(c_Set_Oimage(_1524654, _1524656, _1524658), c_Orderings_Otop__class_Otop(tc_fun(_1524654, tc_HOL_Obool)))))], (8824 ^ _779571) ^ [_925359, _925361, _925363] : [class_Rings_Oring(_925359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925359), hAPP(c_Groups_Ouminus__class_Ouminus(_925359), _925361)), hAPP(c_Groups_Ouminus__class_Ouminus(_925359), _925363)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925359), _925361), _925363))], (42381 ^ _779571) ^ [_1601034, _1601036, _1601038] : [c_Wellfounded_Oacyclic(_1601034, _1601036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601034, _1601034), tc_HOL_Obool)), _1601038), _1601036)), -(c_Wellfounded_Oacyclic(_1601034, _1601038))], (40320 ^ _779571) ^ [_1544452, _1544454] : [class_Lattices_Olattice(_1544452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544452), _1544454)), -(c_Big__Operators_Olattice__class_OSup__fin(_1544452, _1544454) = hAPP(c_Finite__Set_Ofold1(_1544452, c_Lattices_Osemilattice__sup__class_Osup(_1544452)), _1544454))], (51577 ^ _779571) ^ [_1813226, _1813228, _1813230, _1813232, _1813234, _1813236] : [-(hAPP(hAPP(hAPP(c_COMBS(_1813226, _1813228, _1813230), _1813232), _1813234), _1813236) = hAPP(hAPP(_1813232, _1813236), hAPP(_1813234, _1813236)))], (7067 ^ _779571) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34330 ^ _779571) ^ [_1407185, _1407187, _1407189, _1407191, _1407193] : [class_Groups_Ocomm__monoid__mult(_1407185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407187), _1407189)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407187, _1407185), hAPP(hAPP(c_COMBS(_1407187, _1407185, _1407185), hAPP(hAPP(c_COMBB(_1407185, tc_fun(_1407185, _1407185), _1407187), c_Groups_Otimes__class_Otimes(_1407185)), _1407191)), _1407193)), _1407189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407185), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407187, _1407185), _1407191), _1407189)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407187, _1407185), _1407193), _1407189)))], (42994 ^ _779571) ^ [_1615378, _1615380, _1615382, _1615384, _1615386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615378, _1615378)), hAPP(hAPP(c_Product__Type_OPair(_1615378, _1615378), _1615380), _1615382)), c_Transitive__Closure_Ortrancl(_1615378, _1615384))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615378, _1615378)), hAPP(hAPP(c_Product__Type_OPair(_1615378, _1615378), _1615382), _1615386)), c_Transitive__Closure_Ortrancl(_1615378, _1615384))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615378, _1615378)), hAPP(hAPP(c_Product__Type_OPair(_1615378, _1615378), _1615380), _1615386)), c_Transitive__Closure_Ortrancl(_1615378, _1615384))))], (10111 ^ _779571) ^ [_948053, _948055] : [class_Groups_Osgn__if(_948053), 10114 ^ _779571 : [(10121 ^ _779571) ^ [] : [-(_948055 = c_Groups_Ozero__class_Ozero(_948053)), 10124 ^ _779571 : [(10131 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948053), c_Groups_Ozero__class_Ozero(_948053)), _948055))), -(c_Groups_Osgn__class_Osgn(_948053, _948055) = hAPP(c_Groups_Ouminus__class_Ouminus(_948053), c_Groups_Oone__class_Oone(_948053)))], (10125 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948053), c_Groups_Ozero__class_Ozero(_948053)), _948055)), -(c_Groups_Osgn__class_Osgn(_948053, _948055) = c_Groups_Oone__class_Oone(_948053))]]], (10115 ^ _779571) ^ [] : [_948055 = c_Groups_Ozero__class_Ozero(_948053), -(c_Groups_Osgn__class_Osgn(_948053, _948055) = c_Groups_Ozero__class_Ozero(_948053))]]], (16170 ^ _779571) ^ [_1055900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1055900)), -(_1055900 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055900), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (31748 ^ _779571) ^ [_1355734, _1355736, _1355738] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1355734), _1355736)), -(hBOOL(hAPP(hAPP(c_member(_1355734), _1355738), _1355736))), -(hAPP(c_Finite__Set_Ocard(_1355734), hAPP(hAPP(c_Set_Oinsert(_1355734), _1355738), _1355736)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1355734), _1355736)))], (30044 ^ _779571) ^ [_1317960, _1317962, _1317964, _1317966] : [hBOOL(hAPP(hAPP(c_member(_1317960), _1317962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317960, tc_HOL_Obool)), _1317964), _1317966))), -(hBOOL(hAPP(hAPP(c_member(_1317960), _1317962), _1317964))), -(hBOOL(hAPP(hAPP(c_member(_1317960), _1317962), _1317966)))], (44886 ^ _779571) ^ [_1661370, _1661372, _1661374, _1661376] : [hBOOL(hAPP(hAPP(c_member(_1661370), _1661372), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1661370, tc_HOL_Obool), _1661374))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1661370, tc_HOL_Obool)), _1661376), _1661374)), -(hBOOL(hAPP(hAPP(c_member(_1661370), _1661372), _1661376)))], (9948 ^ _779571) ^ [_945271] : [class_Rings_Oring__1(_945271), -(hAPP(c_Int_Oring__1__class_Oof__int(_945271), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_945271))], (47121 ^ _779571) ^ [_1717193, _1717195, _1717197, _1717199] : [class_Rings_Osemiring__1(_1717193), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717193), hAPP(hAPP(c_List_Omap(_1717195, _1717193), hAPP(c_COMBK(_1717193, _1717195), _1717197)), _1717199)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1717193), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1717193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717195)), _1717199))), _1717197))], (44625 ^ _779571) ^ [_1654744, _1654746, _1654748, _1654750, _1654752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654744, tc_HOL_Obool)), _1654746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654748, tc_fun(_1654744, tc_HOL_Obool)), _1654750), _1654752))), 44628 ^ _779571 : [(44629 ^ _779571) ^ [_1654877] : [hBOOL(hAPP(hAPP(c_member(_1654748), _1654877), _1654750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654744, tc_HOL_Obool)), _1654746), hAPP(_1654752, _1654877))))]]], (49710 ^ _779571) ^ [_1778057, _1778059, _1778061] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1778057, tc_HOL_Obool)), hAPP(c_List_Oset(_1778057), hAPP(c_List_Ofilter(_1778057, _1778059), _1778061))), hAPP(c_List_Oset(_1778057), _1778061))))], (32931 ^ _779571) ^ [_1380387, _1380389] : [class_Orderings_Olinorder(_1380387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380387), _1380389)), -(_1380389 = c_Orderings_Obot__class_Obot(tc_fun(_1380387, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1380387), c_Big__Operators_Olinorder__class_OMax(_1380387, _1380389)), _1380389)))], (4982 ^ _779571) ^ [_856584, _856586, _856588, _856590, _856592, _856594] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_856594, _856590, _856586) = c_SetInterval_Oord__class_OatLeastAtMost(_856592, _856588, _856584)), _856594 = _856592, _856590 = _856588, _856586 = _856584], (19051 ^ _779571) ^ [_1106023, _1106025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1106023)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106025)), _1106023) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1106025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1106023), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (38579 ^ _779571) ^ [_1504310, _1504312, _1504314, _1504316, _1504318] : [c_Fun_Oinj__on(_1504310, _1504312, _1504314, _1504316), c_Fun_Oinj__on(_1504310, _1504312, _1504314, _1504318), -(c_Fun_Oinj__on(_1504310, _1504312, _1504314, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1504310, tc_HOL_Obool)), _1504316), _1504318)))], (28825 ^ _779571) ^ [_1291988, _1291990, _1291992, _1291994, _1291996] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1291988, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291990, tc_fun(_1291988, tc_HOL_Obool)), _1291992), _1291994)), _1291996) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291990, tc_fun(_1291988, tc_HOL_Obool)), _1291992), hAPP(hAPP(c_COMBC(_1291990, tc_fun(_1291988, tc_HOL_Obool), tc_fun(_1291988, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1291988, tc_HOL_Obool), tc_fun(tc_fun(_1291988, tc_HOL_Obool), tc_fun(_1291988, tc_HOL_Obool)), _1291990), c_Groups_Ominus__class_Ominus(tc_fun(_1291988, tc_HOL_Obool))), _1291994)), _1291996)))], (19845 ^ _779571) ^ [_1120303, _1120305] : [class_Rings_Oring__1(_1120303), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1120303), hAPP(c_Groups_Ouminus__class_Ouminus(_1120303), c_Groups_Oone__class_Oone(_1120303))), 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)))), _1120305)) = c_Groups_Oone__class_Oone(_1120303))], (28770 ^ _779571) ^ [_1290811, _1290813, _1290815, _1290817, _1290819] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290811, tc_fun(_1290813, tc_HOL_Obool)), _1290815), _1290817), _1290819)), 28774 ^ _779571 : [(28777 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(_1290817, 28773 ^ [_1290811, _1290813, _1290815, _1290817, _1290819]), _1290819)))], (28775 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290811), 28773 ^ [_1290811, _1290813, _1290815, _1290817, _1290819]), _1290815)))]]], (42114 ^ _779571) ^ [_1593959, _1593961, _1593963] : [hAPP(c_Relation_ORange(_1593959, _1593961), _1593963) = c_Orderings_Obot__class_Obot(tc_fun(_1593961, tc_HOL_Obool)), -(_1593963 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593959, _1593961), tc_HOL_Obool)))], (43194 ^ _779571) ^ [_1620261] : [-(c_Relation_Orefl__on(_1620261, c_Orderings_Otop__class_Otop(tc_fun(_1620261, tc_HOL_Obool)), c_Relation_OId(_1620261)))], (27584 ^ _779571) ^ [_1267380, _1267382] : [class_Groups_Oordered__ab__group__add(_1267380), -(hAPP(c_Set_Oimage(_1267380, _1267380, c_Groups_Ouminus__class_Ouminus(_1267380)), hAPP(c_SetInterval_Oord__class_OlessThan(_1267380), _1267382)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1267380), hAPP(c_Groups_Ouminus__class_Ouminus(_1267380), _1267382)))], (51545 ^ _779571) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (30267 ^ _779571) ^ [_1322281, _1322283, _1322285, _1322287] : [hBOOL(hAPP(hAPP(c_member(_1322281), _1322283), _1322285)), -(hBOOL(hAPP(hAPP(c_member(_1322281), _1322283), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322281, tc_HOL_Obool)), _1322285), _1322287))))], (30935 ^ _779571) ^ [_1336477, _1336479, _1336481] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336477, tc_HOL_Obool)), _1336479), hAPP(hAPP(c_Set_Oinsert(_1336477), _1336481), c_Orderings_Obot__class_Obot(tc_fun(_1336477, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1336477, _1336481, _1336479) = c_HOL_OThe(_1336477, hAPP(hAPP(c_COMBC(_1336477, tc_fun(_1336477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1336477)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336477, tc_HOL_Obool)), _1336479), hAPP(hAPP(c_Set_Oinsert(_1336477), _1336481), c_Orderings_Obot__class_Obot(tc_fun(_1336477, tc_HOL_Obool)))))))], (24795 ^ _779571) ^ [_1212797, _1212799, _1212801, _1212803, _1212805, _1212807] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1212797, _1212799, _1212801, _1212803, _1212805), hAPP(c_Sum__Type_OInr(_1212801, _1212797), _1212807)) = hAPP(_1212805, _1212807))], (36728 ^ _779571) ^ [_1462707, _1462709, _1462711, _1462713] : [-(hBOOL(hAPP(hAPP(c_member(_1462707), _1462709), _1462711))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462707, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1462707), _1462709), _1462713)), _1462711) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462707, tc_HOL_Obool)), _1462713), _1462711))], (29922 ^ _779571) ^ [_1314915, _1314917, _1314919, _1314921, _1314923] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1314915, _1314917, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1314915)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1314915), hAPP(hAPP(c_COMBC(_1314915, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1314915), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1314919)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1314921)), _1314923))), c_Com_Ocom_OAss(_1314921, _1314923)), _1314919)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1314915), tc_HOL_Obool)))))], (30860 ^ _779571) ^ [_1334924, _1334926, _1334928, _1334930] : [hBOOL(hAPP(hAPP(c_member(_1334924), _1334926), _1334928)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334924, tc_Nat_Onat), _1334930), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334924, tc_HOL_Obool)), _1334928), hAPP(hAPP(c_Set_Oinsert(_1334924), _1334926), c_Orderings_Obot__class_Obot(tc_fun(_1334924, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334924, tc_Nat_Onat), _1334930), _1334928)), hAPP(_1334930, _1334926)))], (50340 ^ _779571) ^ [_1790817, _1790819, _1790821, _1790823] : [-(c_List_Oupt(_1790817, _1790819) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1790821), _1790823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790817), _1790819)), _1790817 = _1790821, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790817), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1790819) = _1790823], (17983 ^ _779571) ^ [_1089030, _1089032] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089030)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089030)), _1089032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1089030))), _1089032))], (14616 ^ _779571) ^ [_1026075, _1026077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1026075)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026077), _1026075)), _1026075) = _1026077)], (18101 ^ _779571) ^ [_1091062] : [class_Rings_Osemiring__1(_1091062), -(c_Int_Oiszero(_1091062, c_Groups_Ozero__class_Ozero(_1091062)))], (38507 ^ _779571) ^ [_1503072, _1503074, _1503076, _1503078] : [c_Equiv__Relations_Oequivp(_1503072, _1503074), hBOOL(hAPP(hAPP(_1503074, _1503076), _1503078)), -(hBOOL(hAPP(hAPP(_1503074, _1503078), _1503076)))], (11897 ^ _779571) ^ [_977720, _977722, _977724, _977726] : [class_Rings_Oordered__semiring(_977720), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977720), _977722), _977724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977720), c_Groups_Ozero__class_Ozero(_977720)), _977726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977720), _977722), _977726)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977720), _977724), _977726))))], (22850 ^ _779571) ^ [_1175686, _1175688, _1175690, _1175692, _1175694, _1175696, _1175698] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175686, _1175688), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175690), _1175692))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175694, _1175688), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175696), _1175698))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175688)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175686), _1175694), _1175688), 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), _1175690), _1175696)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175692), _1175698)), _1175688))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175692), _1175698), _1175688)))))], (10516 ^ _779571) ^ [_954575, _954577, _954579, _954581] : [class_Orderings_Oorder(_954575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954575), _954577), _954579)), _954577 = _954581, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954575), _954581), _954579)))], (33185 ^ _779571) ^ [_1384526, _1384528, _1384530] : [class_Orderings_Olinorder(_1384526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384526), _1384528)), 33192 ^ _779571 : [(33199 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384526, tc_HOL_Obool)), _1384528), hAPP(hAPP(c_Set_Oinsert(_1384526), _1384530), c_Orderings_Obot__class_Obot(tc_fun(_1384526, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1384526, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1384526, hAPP(hAPP(c_Set_Oinsert(_1384526), _1384530), _1384528)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384526), _1384530), c_Big__Operators_Olinorder__class_OMax(_1384526, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384526, tc_HOL_Obool)), _1384528), hAPP(hAPP(c_Set_Oinsert(_1384526), _1384530), c_Orderings_Obot__class_Obot(tc_fun(_1384526, tc_HOL_Obool)))))))], (33193 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384526, tc_HOL_Obool)), _1384528), hAPP(hAPP(c_Set_Oinsert(_1384526), _1384530), c_Orderings_Obot__class_Obot(tc_fun(_1384526, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1384526, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1384526, hAPP(hAPP(c_Set_Oinsert(_1384526), _1384530), _1384528)) = _1384530)]]], (43835 ^ _779571) ^ [_1636471, _1636473, _1636475, _1636477, _1636479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636471, _1636471)), hAPP(hAPP(c_Product__Type_OPair(_1636471, _1636471), _1636473), _1636475)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636471, _1636471), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1636477)), _1636479))), 43839 ^ _779571 : [(43842 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636471, _1636471)), hAPP(hAPP(c_Product__Type_OPair(_1636471, _1636471), 43838 ^ [_1636471, _1636473, _1636475, _1636477, _1636479]), _1636475)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636471, _1636471), tc_HOL_Obool), _1636477), _1636479))))], (43840 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636471, _1636471)), hAPP(hAPP(c_Product__Type_OPair(_1636471, _1636471), _1636473), 43838 ^ [_1636471, _1636473, _1636475, _1636477, _1636479])), _1636479)))]]], (17647 ^ _779571) ^ [_1083322, _1083324, _1083326, _1083328] : [class_Rings_Olinordered__semidom(_1083322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083322), c_Groups_Oone__class_Oone(_1083322)), _1083324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083322), hAPP(hAPP(c_Power_Opower__class_Opower(_1083322), _1083324), _1083326)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083322), _1083324), _1083328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083326), _1083328)))], (21729 ^ _779571) ^ [_1154052, _1154054, _1154056, _1154058] : [class_Fields_Olinordered__field__inverse__zero(_1154052), class_Int_Onumber(_1154052), 21736 ^ _779571 : [(21737 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154052), _1154056), _1154058))), 21740 ^ _779571 : [(21747 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), c_Groups_Ozero__class_Ozero(_1154052)), _1154058))), 21750 ^ _779571 : [(21757 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154058), c_Groups_Ozero__class_Ozero(_1154052)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), c_Groups_Ozero__class_Ozero(_1154052))))], (21751 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154058), c_Groups_Ozero__class_Ozero(_1154052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), _1154058))))]]], (21741 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), c_Groups_Ozero__class_Ozero(_1154052)), _1154058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), _1154058)), _1154056)))]]], (21763 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154052), _1154056), _1154058)))), 21766 ^ _779571 : [(21769 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), _1154058)), _1154056))], (21767 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), c_Groups_Ozero__class_Ozero(_1154052)), _1154058)))]], 21770 ^ _779571 : [(21773 ^ _779571) ^ [] : [21774 ^ _779571 : [(21777 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), _1154058)))], (21775 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154058), c_Groups_Ozero__class_Ozero(_1154052))))]], 21778 ^ _779571 : [(21781 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), hAPP(c_Int_Onumber__class_Onumber__of(_1154052), _1154054)), c_Groups_Ozero__class_Ozero(_1154052)))], (21779 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), _1154058), c_Groups_Ozero__class_Ozero(_1154052)))]]], (21771 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154052), c_Groups_Ozero__class_Ozero(_1154052)), _1154058))]]]]], (50142 ^ _779571) ^ [_1787612, _1787614, _1787616] : [class_Orderings_Olinorder(_1787612), c_List_Olinorder__class_Osorted(_1787612, _1787614), -(c_List_Olinorder__class_Osorted(_1787612, hAPP(hAPP(c_List_Odrop(_1787612), _1787616), _1787614)))], (42831 ^ _779571) ^ [_1610779, _1610781] : [c_Wellfounded_Owf(_1610779, _1610781), -(c_Wellfounded_Owf(_1610779, c_Transitive__Closure_Otrancl(_1610779, _1610781)))], (39831 ^ _779571) ^ [_1531482, _1531484, _1531486, _1531488, _1531490] : [hBOOL(hAPP(hAPP(c_member(_1531482), _1531484), c_Map_Oran(_1531486, _1531482, c_Map_Orestrict__map(_1531486, _1531482, _1531488, _1531490)))), 39835 ^ _779571 : [(39838 ^ _779571) ^ [] : [-(hAPP(_1531488, 39834 ^ [_1531482, _1531484, _1531486, _1531488, _1531490]) = hAPP(c_Option_Ooption_OSome(_1531482), _1531484))], (39836 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531486), 39834 ^ [_1531482, _1531484, _1531486, _1531488, _1531490]), _1531490)))]]], (35367 ^ _779571) ^ [_1431185, _1431187, _1431189, _1431191, _1431193] : [c_Finite__Set_Ofolding__one__idem(_1431185, _1431187, _1431189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431185), _1431191)), -(_1431191 = c_Orderings_Obot__class_Obot(tc_fun(_1431185, tc_HOL_Obool))), -(hAPP(_1431189, hAPP(hAPP(c_Set_Oinsert(_1431185), _1431193), _1431191)) = hAPP(hAPP(_1431187, _1431193), hAPP(_1431189, _1431191)))], (39483 ^ _779571) ^ [_1523744, _1523746, _1523748, _1523750, _1523752] : [-(hAPP(c_Set_Ovimage(_1523744, _1523746, _1523748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523746, tc_HOL_Obool)), _1523750), _1523752)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523744, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1523744, _1523746, _1523748), _1523750)), hAPP(c_Set_Ovimage(_1523744, _1523746, _1523748), _1523752)))], (28232 ^ _779571) ^ [_1280368, _1280370, _1280372, _1280374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280368, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280368, tc_HOL_Obool)), _1280370), _1280372)), _1280374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280368, tc_HOL_Obool)), _1280370), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280368, tc_HOL_Obool)), _1280372), _1280374))))], (10572 ^ _779571) ^ [_955453, _955455, _955457, _955459] : [class_Orderings_Oorder(_955453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955453), _955455), _955457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955453), _955459), _955455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955453), _955459), _955457)))], (43467 ^ _779571) ^ [_1626928, _1626930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1626928, _1626928)), _1626930)), c_Wellfounded_Oacyclic(_1626928, _1626930), -(c_Wellfounded_Owf(_1626928, hAPP(c_Relation_Oconverse(_1626928, _1626928), _1626930)))], (50394 ^ _779571) ^ [_1791924, _1791926, _1791928] : [class_Orderings_Olinorder(_1791924), 50397 ^ _779571 : [(50410 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1791924, hAPP(hAPP(c_List_Olist_OCons(_1791924), _1791926), _1791928))), 50414 ^ _779571 : [(50417 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791924), _1791926), 50413 ^ [_1791924, _1791926, _1791928]))], (50415 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791924), 50413 ^ [_1791924, _1791926, _1791928]), hAPP(c_List_Oset(_1791924), _1791928))))]], c_List_Olinorder__class_Osorted(_1791924, _1791928)], (50398 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1791924, hAPP(hAPP(c_List_Olist_OCons(_1791924), _1791926), _1791928)), 50401 ^ _779571 : [(50402 ^ _779571) ^ [_1792092] : [hBOOL(hAPP(hAPP(c_member(_1791924), _1792092), hAPP(c_List_Oset(_1791924), _1791928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791924), _1791926), _1792092)))], (50408 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1791924, _1791928))]]]]], (43724 ^ _779571) ^ [_1633557, _1633559, _1633561, _1633563, _1633565] : [c_Relation_Osingle__valued(_1633557, _1633559, _1633561), c_Relation_Osingle__valued(_1633559, _1633563, _1633565), -(c_Relation_Osingle__valued(_1633557, _1633563, hAPP(hAPP(c_Relation_Orel__comp(_1633557, _1633559, _1633563), _1633561), _1633565)))], (51513 ^ _779571) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (11288 ^ _779571) ^ [_967062, _967064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967062), hAPP(c_Nat_OSuc, _967064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967062), _967064))), -(_967062 = hAPP(c_Nat_OSuc, _967064))], (34853 ^ _779571) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (36648 ^ _779571) ^ [_1460594, _1460596, _1460598, _1460600, _1460602] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460594, tc_HOL_Obool)), _1460596), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460598, tc_fun(_1460594, tc_HOL_Obool)), _1460600), _1460602)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460598, tc_fun(_1460594, tc_HOL_Obool)), _1460600), hAPP(hAPP(c_COMBB(tc_fun(_1460594, tc_HOL_Obool), tc_fun(_1460594, tc_HOL_Obool), _1460598), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460594, tc_HOL_Obool)), _1460596)), _1460602)))], (36804 ^ _779571) ^ [_1464739, _1464741] : [c_Nat__Transfer_Onat__set(_1464739), c_Nat__Transfer_Onat__set(_1464741), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1464739), _1464741) = 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), _1464739)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1464741))))], (30495 ^ _779571) ^ [_1326577, _1326579, _1326581, _1326583, _1326585] : [-(hBOOL(hAPP(hAPP(c_member(_1326577), _1326579), c_SetInterval_Oord_OatLeastAtMost(_1326577, _1326581, _1326583, _1326585)))), hBOOL(hAPP(hAPP(_1326581, _1326583), _1326579)), hBOOL(hAPP(hAPP(_1326581, _1326579), _1326585))], (20213 ^ _779571) ^ [_1127104, _1127106, _1127108, _1127110] : [class_Fields_Olinordered__field__inverse__zero(_1127104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127104), _1127106), _1127108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127104), c_Groups_Ozero__class_Ozero(_1127104)), _1127110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127104), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127104), _1127106), _1127110)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127104), _1127108), _1127110))))], (47857 ^ _779571) ^ [_1734202, _1734204, _1734206, _1734208] : [-(hAPP(hAPP(c_List_Onth(_1734202), hAPP(hAPP(c_List_Oappend(_1734202), _1734204), hAPP(hAPP(c_List_Olist_OCons(_1734202), _1734206), _1734208))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734202)), _1734204)) = _1734206)], (24569 ^ _779571) ^ [_1208230, _1208232, _1208234, _1208236, _1208238, _1208240] : [hAPP(c_Product__Type_Oapfst(_1208230, _1208232, _1208234, _1208236), _1208238) = hAPP(c_Product__Type_Oapfst(_1208230, _1208232, _1208234, _1208240), _1208238), -(hAPP(_1208236, hAPP(c_Product__Type_Ofst(_1208230, _1208234), _1208238)) = hAPP(_1208240, hAPP(c_Product__Type_Ofst(_1208230, _1208234), _1208238)))], (24705 ^ _779571) ^ [_1210994, _1210996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1210994), _1210996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210994)), hAPP(c_Code__Numeral_Onat__of, _1210996))))], (46694 ^ _779571) ^ [_1704310, _1704312, _1704314] : [-(hBOOL(hAPP(hAPP(c_member(_1704310), _1704312), hAPP(c_List_Oset(_1704310), _1704314)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704310)), c_List_Oremove1(_1704310, _1704312, _1704314)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704310)), _1704314))], (24113 ^ _779571) ^ [_1199541] : [class_Orderings_Oord(_1199541), -(c_Orderings_Oord__class_Omin(_1199541) = c_Orderings_Oord_Omin(_1199541, c_Orderings_Oord__class_Oless__eq(_1199541)))], (33317 ^ _779571) ^ [_1387139, _1387141, _1387143] : [class_Orderings_Olinorder(_1387139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387139, tc_HOL_Obool)), _1387141), _1387143)), -(_1387141 = c_Orderings_Obot__class_Obot(tc_fun(_1387139, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387139), _1387143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387139), c_Big__Operators_Olinorder__class_OMin(_1387139, _1387143)), c_Big__Operators_Olinorder__class_OMin(_1387139, _1387141))))], (27808 ^ _779571) ^ [_1272058, _1272060, _1272062] : [class_Lattices_Olattice(_1272058), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272058), _1272060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272058), _1272062), _1272060))))], (39897 ^ _779571) ^ [_1533452, _1533454, _1533456, _1533458] : [hBOOL(hAPP(hAPP(c_member(_1533452), _1533454), c_Wellfounded_Oacc(_1533452, _1533456))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1533452, _1533452)), hAPP(hAPP(c_Product__Type_OPair(_1533452, _1533452), _1533458), _1533454)), _1533456)), -(hBOOL(hAPP(hAPP(c_member(_1533452), _1533458), c_Wellfounded_Oacc(_1533452, _1533456))))], (50160 ^ _779571) ^ [_1787903, _1787905, _1787907] : [class_Orderings_Olinorder(_1787903), c_List_Olinorder__class_Osorted(_1787903, _1787905), -(c_List_Olinorder__class_Osorted(_1787903, c_List_Olinorder__class_Oinsort__insert__key(_1787903, _1787903, c_COMBI(_1787903), _1787907, _1787905)))], (26998 ^ _779571) ^ [_1255219, _1255221] : [27006 ^ _779571 : [(27009 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1255221, 27005 ^ [_1255219, _1255221])))], (27007 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27005 ^ [_1255219, _1255221]), _1255219)))]], 26999 ^ _779571 : [(27000 ^ _779571) ^ [_1255287] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1255287), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1255219))), hBOOL(hAPP(_1255221, _1255287))]]], (30892 ^ _779571) ^ [_1335560, _1335562] : [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)))), _1335560, _1335562) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335560), _1335562)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335562), _1335560)))], (28868 ^ _779571) ^ [_1293262, _1293264, _1293266, _1293268, _1293270, _1293272] : [class_Complete__Lattice_Ocomplete__lattice(_1293262), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293264, _1293262), _1293266), hAPP(hAPP(c_COMBB(tc_fun(_1293268, _1293262), _1293262, _1293264), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293268, _1293262), _1293270)), _1293272)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293268, _1293262), _1293270), hAPP(hAPP(c_COMBB(tc_fun(_1293264, _1293262), _1293262, _1293268), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293264, _1293262), _1293266)), hAPP(c_COMBC(_1293264, _1293268, _1293262), _1293272))))], (4 ^ _779571) ^ [_779621, _779623] : [_779623 = _779621, -(_779621 = _779623)], (24799 ^ _779571) ^ [_1212899, _1212901, _1212903, _1212905, _1212907, _1212909, _1212911] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1212899, _1212901, _1212903, _1212905), _1212907), _1212909), _1212911) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1212901, _1212903, _1212905), _1212909), hAPP(_1212907, _1212911)))], (18941 ^ _779571) ^ [] : [-(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)))], (29742 ^ _779571) ^ [_1311297, _1311299] : [class_Orderings_Oorder(_1311297), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311297, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1311297), _1311299), c_Orderings_Obot__class_Obot(tc_fun(_1311297, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1311297), _1311299)) = hAPP(hAPP(c_Set_Oinsert(_1311297), _1311299), c_Orderings_Obot__class_Obot(tc_fun(_1311297, tc_HOL_Obool))))], (50025 ^ _779571) ^ [_1785400, _1785402, _1785404, _1785406] : [class_Orderings_Olinorder(_1785400), 50028 ^ _779571 : [(50037 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1785400, hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785402), hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785404), _1785406)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1785400), _1785402), _1785404)), c_List_Olinorder__class_Osorted(_1785400, hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785404), _1785406))], (50029 ^ _779571) ^ [] : [c_List_Olinorder__class_Osorted(_1785400, hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785402), hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785404), _1785406))), 50032 ^ _779571 : [(50035 ^ _779571) ^ [] : [-(c_List_Olinorder__class_Osorted(_1785400, hAPP(hAPP(c_List_Olist_OCons(_1785400), _1785404), _1785406)))], (50033 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1785400), _1785402), _1785404)))]]]]], (17385 ^ _779571) ^ [_1078594] : [-(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), _1078594)) = 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), _1078594))))], (18323 ^ _779571) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47510 ^ _779571) ^ [_1725692, _1725694] : [47512 ^ _779571 : [(47516 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47514 ^ [_1725692, _1725694]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725692)), _1725694))))], (47518 ^ _779571) ^ [] : [47511 ^ [_1725692, _1725694] = 47514 ^ [_1725692, _1725694]], (47520 ^ _779571) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1725692), _1725694), 47511 ^ [_1725692, _1725694]) = hAPP(hAPP(c_List_Onth(_1725692), _1725694), 47514 ^ [_1725692, _1725694]))], (47513 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47511 ^ [_1725692, _1725694]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725692)), _1725694))))]], -(hBOOL(hAPP(c_List_Odistinct(_1725692), _1725694)))], (41626 ^ _779571) ^ [_1581199, _1581201, _1581203, _1581205, _1581207, _1581209, _1581211] : [hAPP(c_Fun_Ocomp(_1581199, _1581201, _1581203, _1581205), _1581207) = hAPP(c_Fun_Ocomp(_1581201, _1581201, _1581203, c_Fun_Oid(_1581201)), _1581209), -(hAPP(_1581205, hAPP(_1581207, _1581211)) = hAPP(_1581209, _1581211))], (4476 ^ _779571) ^ [_848827, _848829, _848831, _848833, _848835, _848837] : [-(c_Map_Odom(_848837, _848833, _848829) = c_Map_Odom(_848835, _848831, _848827)), _848837 = _848835, _848833 = _848831, _848829 = _848827], (14371 ^ _779571) ^ [_1022099, _1022101] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022099), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022101)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022099)), _1022101))], (2698 ^ _779571) ^ [_820482, _820484] : [_820484 = _820482, -(c_Code__Numeral_OSuc__code__numeral(_820484) = c_Code__Numeral_OSuc__code__numeral(_820482))], (6434 ^ _779571) ^ [_884461, _884463, _884465, _884467, _884469, _884471, _884473, _884475, _884477, _884479] : [-(c_Com_Ocom_Ocom__case(_884461, _884463, _884465, _884467, _884469, _884471, _884473, _884475, _884477, hAPP(c_Com_Ocom_OBODY, _884479)) = hAPP(_884475, _884479))], (24853 ^ _779571) ^ [_1214153, _1214155, _1214157] : [c_Nitpick_Oless__frac(_1214153, _1214155, _1214157), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1214153), c_Nitpick_Oplus__frac(_1214153, _1214155, c_Nitpick_Ouminus__frac(_1214153, _1214157)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (908 ^ _779571) ^ [_793549, _793551, _793553, _793555, _793557, _793559] : [-(c_Relation_Orefl__on(_793557, _793553, _793549)), c_Relation_Orefl__on(_793559, _793555, _793551), _793559 = _793557, _793555 = _793553, _793551 = _793549], (51255 ^ _779571) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (29686 ^ _779571) ^ [_1310024, _1310026, _1310028, _1310030, _1310032] : [-(_1310024 = c_Orderings_Obot__class_Obot(tc_fun(_1310026, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310028, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310026, tc_fun(_1310028, tc_HOL_Obool)), _1310024), _1310030)), _1310032) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310026, tc_fun(_1310028, tc_HOL_Obool)), _1310024), hAPP(hAPP(c_COMBC(_1310026, tc_fun(_1310028, tc_HOL_Obool), tc_fun(_1310028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310028, tc_HOL_Obool), tc_fun(tc_fun(_1310028, tc_HOL_Obool), tc_fun(_1310028, tc_HOL_Obool)), _1310026), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310028, tc_HOL_Obool))), _1310030)), _1310032)))], (36796 ^ _779571) ^ [_1464564, _1464566, _1464568, _1464570] : [class_Orderings_Oorder(_1464564), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464564, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1464564, _1464566, _1464568)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1464564, _1464568, _1464570)) = c_Orderings_Obot__class_Obot(tc_fun(_1464564, tc_HOL_Obool)))], (49773 ^ _779571) ^ [_1779315, _1779317, _1779319, _1779321] : [-(hAPP(c_List_Ofilter(_1779315, _1779317), c_List_Oremove1(_1779315, _1779319, _1779321)) = c_List_Oremove1(_1779315, _1779319, hAPP(c_List_Ofilter(_1779315, _1779317), _1779321)))], (23335 ^ _779571) ^ [_1184610, _1184612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184610), 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)), _1184612)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184610, _1184612) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1184610, _1184612)))], (12159 ^ _779571) ^ [_982385, _982387] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982385), _982387) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12162 ^ _779571 : [(12165 ^ _779571) ^ [] : [-(_982387 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12163 ^ _779571) ^ [] : [-(_982385 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (41992 ^ _779571) ^ [_1591080, _1591082, _1591084] : [c_Wellfounded_Owf(_1591080, _1591082), c_Wellfounded_Owf(_1591080, _1591084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591080, _1591080), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1591080, _1591080, _1591080), _1591082), _1591084)), _1591082)), -(c_Wellfounded_Owf(_1591080, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1591080, _1591080), tc_HOL_Obool)), _1591082), _1591084)))], (28827 ^ _779571) ^ [_1292097, _1292099, _1292101, _1292103, _1292105] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292097, tc_fun(_1292099, tc_HOL_Obool)), _1292101), hAPP(hAPP(c_COMBC(_1292097, tc_fun(_1292099, tc_HOL_Obool), tc_fun(_1292099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292099, tc_HOL_Obool), tc_fun(tc_fun(_1292099, tc_HOL_Obool), tc_fun(_1292099, tc_HOL_Obool)), _1292097), c_Groups_Ominus__class_Ominus(tc_fun(_1292099, tc_HOL_Obool))), _1292103)), _1292105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292099, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292097, tc_fun(_1292099, tc_HOL_Obool)), _1292101), _1292103)), _1292105))], (4010 ^ _779571) ^ [_841346, _841348] : [_841348 = _841346, -(c_Equiv__Relations_Oquotient(_841348) = c_Equiv__Relations_Oquotient(_841346))], (35448 ^ _779571) ^ [_1433011, _1433013, _1433015, _1433017, _1433019, _1433021] : [-(hAPP(hAPP(c_Fun_Ocomp(_1433011, _1433013, _1433015, _1433017), _1433019), _1433021) = hAPP(_1433017, hAPP(_1433019, _1433021)))], (38197 ^ _779571) ^ [_1496590, _1496592, _1496594, _1496596, _1496598, _1496600] : [c_Finite__Set_Ofolding__idem(_1496590, _1496592, _1496594, _1496596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496590), _1496598)), hBOOL(hAPP(hAPP(c_member(_1496590), _1496600), _1496598)), -(hAPP(c_Fun_Ocomp(_1496592, _1496592, _1496592, hAPP(_1496596, _1496598)), hAPP(_1496594, _1496600)) = hAPP(_1496596, _1496598))], (24133 ^ _779571) ^ [_1199920, _1199922] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199920, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199920, tc_HOL_Obool)), _1199922)) = _1199922)], (40016 ^ _779571) ^ [_1536505, _1536507, _1536509, _1536511, _1536513] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1536505, _1536507, hAPP(hAPP(c_Set_Oinsert(_1536505), _1536509), _1536511)), _1536513))), 40017 ^ _779571 : [(40018 ^ _779571) ^ [_1536609, _1536611] : [hAPP(hAPP(c_Set_Oinsert(_1536505), _1536509), _1536511) = hAPP(hAPP(c_Set_Oinsert(_1536505), _1536611), _1536609), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1536505, _1536505, _1536507, _1536611, _1536609), _1536513)), -(hBOOL(hAPP(hAPP(c_member(_1536505), _1536611), _1536609)))]]], (25196 ^ _779571) ^ [_1221300, _1221302, _1221304, _1221306] : [class_Rings_Ocomm__semiring__1(_1221300), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221300), _1221302), _1221304)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221300), _1221302), _1221306)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221300), _1221302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221300), _1221304), _1221306))))], (44281 ^ _779571) ^ [_1645463, _1645465, _1645467, _1645469, _1645471] : [c_Finite__Set_Ofun__left__comm(_1645463, _1645465, _1645467), -(hAPP(c_Fun_Ocomp(_1645465, _1645465, _1645465, hAPP(_1645467, _1645469)), hAPP(_1645467, _1645471)) = hAPP(c_Fun_Ocomp(_1645465, _1645465, _1645465, hAPP(_1645467, _1645471)), hAPP(_1645467, _1645469)))], (46971 ^ _779571) ^ [_1712756, _1712758, _1712760] : [-(c_List_Oset__Cons(_1712756, _1712758, _1712760) = hAPP(c_Set_OCollect(tc_List_Olist(_1712756)), hAPP(hAPP(c_COMBB(tc_fun(_1712756, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1712756)), c_HOL_OEx(_1712756)), hAPP(hAPP(c_COMBB(tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_fun(_1712756, tc_HOL_Obool), tc_List_Olist(_1712756)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_HOL_Obool, _1712756), c_HOL_OEx(tc_List_Olist(_1712756)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712756), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1712756, tc_fun(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), tc_fun(tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), tc_List_Olist(_1712756)), c_COMBS(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1712756, tc_fun(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), tc_List_Olist(_1712756)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1712756), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), _1712756), c_COMBS(tc_List_Olist(_1712756), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1712756)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1712756), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1712756)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712756), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_List_Olist(_1712756))), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1712756), tc_List_Olist(_1712756)), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_fun(tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_List_Olist(_1712756))), tc_fun(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool))), tc_List_Olist(_1712756)), c_COMBB(tc_fun(tc_List_Olist(_1712756), tc_List_Olist(_1712756)), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), _1712756)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1712756), tc_List_Olist(_1712756)), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), tc_List_Olist(_1712756)), c_COMBB(tc_List_Olist(_1712756), tc_HOL_Obool, tc_List_Olist(_1712756))), c_fequal))), c_List_Olist_OCons(_1712756)))))), hAPP(hAPP(c_COMBC(_1712756, tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool)), _1712756), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1712756))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1712756), c_fconj), hAPP(hAPP(c_COMBC(_1712756, tc_fun(_1712756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1712756)), _1712758)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712756), tc_fun(tc_List_Olist(_1712756), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1712756))), _1712760)))))))], (2542 ^ _779571) ^ [_818020, _818022, _818024, _818026] : [-(c_Divides_Odivmod__int__rel(_818026, _818022) = c_Divides_Odivmod__int__rel(_818024, _818020)), _818026 = _818024, _818022 = _818020], (29970 ^ _779571) ^ [_1316520, _1316522, _1316524, _1316526] : [_1316520 = _1316522, 29975 ^ _779571 : [(29978 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316524), _1316526), _1316522)))], (29976 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316524), _1316526), _1316520)))]], 29979 ^ _779571 : [(29982 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1316524), _1316526), _1316522))], (29980 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1316524), _1316526), _1316520))]]], (10596 ^ _779571) ^ [_955871, _955873, _955875] : [class_Orderings_Olinorder(_955871), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955871), _955873), _955875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955871), _955875), _955873)))], (30110 ^ _779571) ^ [_1319285, _1319287, _1319289] : [hBOOL(hAPP(hAPP(c_member(_1319285), _1319287), _1319289)), -(hAPP(hAPP(c_Set_Oinsert(_1319285), _1319287), _1319289) = _1319289)], (1662 ^ _779571) ^ [_803114, _803116] : [-(class_Rings_Osemiring__1(_803114)), _803116 = _803114, class_Rings_Osemiring__1(_803116)], (24041 ^ _779571) ^ [_1198111, _1198113, _1198115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1198111, tc_HOL_Obool)), _1198113), _1198115))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198111, tc_HOL_Obool)), _1198113), _1198115)), -(_1198113 = _1198115)], (46398 ^ _779571) ^ [_1696504, _1696506, _1696508, _1696510, _1696512, _1696514] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696504, _1696506)), hAPP(hAPP(c_Product__Type_OPair(_1696504, _1696506), _1696508), _1696510)), hAPP(c_List_Oset(tc_prod(_1696504, _1696506)), hAPP(hAPP(c_List_Ozip(_1696504, _1696506), _1696512), _1696514)))), -(hBOOL(hAPP(hAPP(c_member(_1696506), _1696510), hAPP(c_List_Oset(_1696506), _1696514))))], (19275 ^ _779571) ^ [_1110145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1110145)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110145), c_Int_OPls)))], (6189 ^ _779571) ^ [_879831, _879833, _879835] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_879831, _879833, _879835))), 6192 ^ _779571 : [(6195 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879835)))], (6193 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879833)))]]], (47394 ^ _779571) ^ [_1722425, _1722427, _1722429] : [-(hAPP(c_Map_Omap__of(_1722425, _1722427, c_List_Olist_ONil(tc_prod(_1722425, _1722427))), _1722429) = c_Option_Ooption_ONone(_1722427))], (46386 ^ _779571) ^ [_1695945, _1695947, _1695949, _1695951, _1695953, _1695955, _1695957, _1695959] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1695945, _1695947), _1695949), _1695951), hAPP(hAPP(c_List_Ozip(_1695945, _1695947), _1695953), hAPP(hAPP(c_List_Omap(_1695955, _1695947), _1695957), _1695959))) = hAPP(hAPP(c_List_Omap(tc_prod(_1695945, _1695955), _1695949), hAPP(c_Product__Type_Oprod_Oprod__case(_1695945, _1695955, _1695949), hAPP(hAPP(c_COMBB(tc_fun(_1695955, tc_prod(_1695945, _1695947)), tc_fun(_1695955, _1695949), _1695945), hAPP(c_COMBB(tc_prod(_1695945, _1695947), _1695949, _1695955), _1695951)), hAPP(hAPP(c_COMBC(_1695945, tc_fun(_1695955, _1695947), tc_fun(_1695955, tc_prod(_1695945, _1695947))), hAPP(hAPP(c_COMBB(tc_fun(_1695947, tc_prod(_1695945, _1695947)), tc_fun(tc_fun(_1695955, _1695947), tc_fun(_1695955, tc_prod(_1695945, _1695947))), _1695945), c_COMBB(_1695947, tc_prod(_1695945, _1695947), _1695955)), c_Product__Type_OPair(_1695945, _1695947))), _1695957)))), hAPP(hAPP(c_List_Ozip(_1695945, _1695955), _1695953), _1695959)))], (6768 ^ _779571) ^ [_890848, _890850, _890852, _890854] : [c_Com_Ocom_OAss(_890848, _890850) = c_Com_Ocom_OSemi(_890852, _890854)], (14339 ^ _779571) ^ [_1021403, _1021405] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021403), _1021405)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1021403)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1021405)))], (19833 ^ _779571) ^ [_1119981, _1119983, _1119985] : [class_Rings_Ocomm__semiring__1(_1119981), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119981), _1119983), 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)))), _1119985))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119981), _1119983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119981), hAPP(hAPP(c_Power_Opower__class_Opower(_1119981), _1119983), _1119985)), hAPP(hAPP(c_Power_Opower__class_Opower(_1119981), _1119983), _1119985))))], (26020 ^ _779571) ^ [_1236364, _1236366] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1236364))), _1236366)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236364), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236366))))], (7826 ^ _779571) ^ [_909385, _909387] : [class_Groups_Olinordered__ab__group__add(_909385), 7829 ^ _779571 : [(7836 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909385), _909387), c_Groups_Ozero__class_Ozero(_909385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909385), _909387), _909387)), c_Groups_Ozero__class_Ozero(_909385))))], (7830 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909385), _909387), _909387)), c_Groups_Ozero__class_Ozero(_909385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909385), _909387), c_Groups_Ozero__class_Ozero(_909385))))]]], (6752 ^ _779571) ^ [_890488] : [hAPP(c_Com_Ocom_OBODY, _890488) = c_Com_Ocom_OSKIP], (40370 ^ _779571) ^ [_1545243, _1545245] : [class_Orderings_Olinorder(_1545243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545243), _1545245)), -(c_Big__Operators_Olattice_OSup__fin(_1545243, c_Orderings_Oord__class_Omax(_1545243), _1545245) = hAPP(c_Finite__Set_Ofold1(_1545243, c_Orderings_Oord__class_Omax(_1545243)), _1545245))], (24149 ^ _779571) ^ [_1200273, _1200275, _1200277] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1200273, _1200275), _1200277)), 24152 ^ _779571 : [(24161 ^ _779571) ^ [] : [-(_1200275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24164 ^ _779571 : [(24173 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200275))), 24176 ^ _779571 : [(24179 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200277)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24177 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1200275), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200277))))]]], (24165 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200275)), 24168 ^ _779571 : [(24171 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200277)), _1200275)))], (24169 ^ _779571) ^ [] : [-(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), _1200277))))]]]]], (24155 ^ _779571) ^ [] : [_1200275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1200277) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24153 ^ _779571) ^ [] : [-(_1200273 = 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), _1200277)), _1200275)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1200277)))]]], (6776 ^ _779571) ^ [_891075, _891077, _891079, _891081, _891083] : [c_Com_Ocom_OAss(_891075, _891077) = c_Com_Ocom_OLocal(_891079, _891081, _891083)], (47821 ^ _779571) ^ [_1733232, _1733234, _1733236] : [class_Orderings_Olinorder(_1733232), -(hBOOL(hAPP(hAPP(c_member(_1733232), _1733234), hAPP(c_List_Oset(_1733232), _1733236)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1733232, _1733232, c_COMBI(_1733232), _1733234, _1733236) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733232, _1733232, c_COMBI(_1733232)), _1733234), _1733236))], (42329 ^ _779571) ^ [_1599553, _1599555, _1599557, _1599559] : [hBOOL(hAPP(c_Predicate_ODomainP(_1599553, _1599555, hAPP(hAPP(c_COMBC(_1599553, tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_fun(_1599555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599555, tc_fun(tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_fun(_1599555, tc_HOL_Obool)), _1599553), c_COMBC(_1599555, tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599555, tc_prod(_1599553, _1599555)), tc_fun(_1599555, tc_fun(tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_HOL_Obool)), _1599553), hAPP(c_COMBB(tc_prod(_1599553, _1599555), tc_fun(tc_fun(tc_prod(_1599553, _1599555), tc_HOL_Obool), tc_HOL_Obool), _1599555), c_member(tc_prod(_1599553, _1599555)))), c_Product__Type_OPair(_1599553, _1599555)))), _1599557)), _1599559)), -(hBOOL(hAPP(hAPP(c_member(_1599553), _1599559), hAPP(c_Relation_ODomain(_1599553, _1599555), _1599557))))], (7235 ^ _779571) ^ [_899192, _899194, _899196] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899192), _899194), _899196)), -(c_Natural_Oevaln(_899192, _899194, 7238 ^ [_899192, _899194, _899196], _899196))], (49700 ^ _779571) ^ [_1777645, _1777647, _1777649, _1777651] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777645)), _1777647))), c_List_Ofoldr(tc_List_Olist(_1777649), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1777649)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1777649))), _1777651, 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(_1777645)), _1777647)), c_List_Ofoldr(tc_List_Olist(_1777649), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1777649)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1777649), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1777649)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1777649)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1777649), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1777649)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1777649), tc_List_Olist(_1777649), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1777649)))), _1777651), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (41927 ^ _779571) ^ [_1589879] : [-(c_Wellfounded_Owf(tc_fun(_1589879, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1589879)))], (18955 ^ _779571) ^ [] : [-(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)))))], (29049 ^ _779571) ^ [_1297765, _1297767] : [class_Lattices_Obounded__lattice__top(_1297765), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1297765), _1297767), c_Orderings_Otop__class_Otop(_1297765)) = c_Orderings_Otop__class_Otop(_1297765))], (24323 ^ _779571) ^ [_1203561, _1203563, _1203565, _1203567] : [class_Orderings_Olinorder(_1203561), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203561), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203561), _1203563), _1203565)), _1203567) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1203561), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203561), _1203563), _1203567)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1203561), _1203565), _1203567)))], (21513 ^ _779571) ^ [_1149851, _1149853, _1149855, _1149857] : [class_Fields_Olinordered__field(_1149851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149851), c_Groups_Ozero__class_Ozero(_1149851)), _1149853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149851), _1149855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149851), _1149857), _1149853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149851), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149851), _1149855), _1149853)), _1149857)))], (48333 ^ _779571) ^ [_1745512, _1745514, _1745516] : [hBOOL(hAPP(c_List_Odistinct(_1745512), _1745514)), -(hBOOL(hAPP(c_List_Odistinct(_1745512), hAPP(hAPP(c_List_Otake(_1745512), _1745516), _1745514))))], (24849 ^ _779571) ^ [_1213974, _1213976] : [-(c_Nitpick_Ouminus__frac(_1213974, _1213976) = c_Nitpick_OAbs__Frac(_1213974, 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(_1213974), _1213976))), hAPP(c_Nitpick_Odenom(_1213974), _1213976))))], (30582 ^ _779571) ^ [_1328745, _1328747, _1328749, _1328751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328745, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328745), _1328747), _1328749)), _1328751)), 30585 ^ _779571 : [(30588 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328745, tc_HOL_Obool)), _1328749), _1328751)))], (30586 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328745), _1328747), _1328751)))]]], (6780 ^ _779571) ^ [_891184, _891186] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_891184, _891186)], (25334 ^ _779571) ^ [_1223538, _1223540, _1223542] : [_1223538 = _1223540, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223540), _1223542)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223538), _1223542)))], (50942 ^ _779571) ^ [_1805443] : [-(c_List_Oreturn__list(_1805443) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1805443))], (13821 ^ _779571) ^ [_1011832, _1011834, _1011836, _1011838] : [class_Divides_Osemiring__div(_1011832), -(c_Divides_Odiv__class_Omod(_1011832, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011832), _1011834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011832), _1011836), _1011838)), _1011838) = c_Divides_Odiv__class_Omod(_1011832, _1011834, _1011838))], (7377 ^ _779571) ^ [_902072, _902074, _902076, _902078, _902080] : [-(hAPP(c_Sum__Type_OSuml(_902072, _902074, _902076, _902078), hAPP(c_Sum__Type_OInl(_902072, _902076), _902080)) = hAPP(_902078, _902080))], (21673 ^ _779571) ^ [_1152983, _1152985, _1152987, _1152989] : [class_Fields_Olinordered__field__inverse__zero(_1152983), class_Int_Onumber(_1152983), 21680 ^ _779571 : [(21681 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152983), _1152985), _1152987)), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989))), 21684 ^ _779571 : [(21691 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), _1152987))), 21694 ^ _779571 : [(21701 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152987), c_Groups_Ozero__class_Ozero(_1152983)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989))))], (21695 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152987), c_Groups_Ozero__class_Ozero(_1152983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152983), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)), _1152987)), _1152985)))]]], (21685 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), _1152987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152983), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)), _1152987))))]]], (21707 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152983), _1152985), _1152987)), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)))), 21710 ^ _779571 : [(21713 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152983), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)), _1152987)))], (21711 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), _1152987)))]], 21714 ^ _779571 : [(21717 ^ _779571) ^ [] : [21718 ^ _779571 : [(21721 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152983), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)), _1152987)), _1152985))], (21719 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152987), c_Groups_Ozero__class_Ozero(_1152983))))]], 21722 ^ _779571 : [(21725 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), hAPP(c_Int_Onumber__class_Onumber__of(_1152983), _1152989)))], (21723 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), _1152987), c_Groups_Ozero__class_Ozero(_1152983)))]]], (21715 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152983), c_Groups_Ozero__class_Ozero(_1152983)), _1152987))]]]]], (13178 ^ _779571) ^ [_1000228, _1000230] : [hAPP(c_Int_Onat, _1000228) = _1000230, 13181 ^ _779571 : [(13188 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000228))), -(_1000230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13182 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000228)), -(_1000228 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1000230))]]], (45545 ^ _779571) ^ [_1676769, _1676771, _1676773, _1676775, _1676777, _1676779, _1676781, _1676783] : [c_Finite__Set_Ofolding__image__simple__idem(_1676769, _1676771, _1676773, _1676775, _1676777, _1676779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1676771), _1676781)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1676771), _1676783)), -(hAPP(_1676779, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1676771, tc_HOL_Obool)), _1676781), _1676783)) = hAPP(hAPP(_1676773, hAPP(_1676779, _1676781)), hAPP(_1676779, _1676783)))], (46476 ^ _779571) ^ [_1698860, _1698862, _1698864] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698860)), _1698862) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698860)), _1698864)), _1698862 = _1698864], (15884 ^ _779571) ^ [_1049603, _1049605] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049603), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049605)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049603), _1049605)))], (38909 ^ _779571) ^ [_1511130, _1511132, _1511134, _1511136, _1511138] : [-(c_Fun_Oinj__on(_1511130, _1511132, _1511134, hAPP(hAPP(c_Set_Oinsert(_1511130), _1511136), _1511138))), c_Fun_Oinj__on(_1511130, _1511132, _1511134, _1511138), -(hBOOL(hAPP(hAPP(c_member(_1511132), hAPP(_1511134, _1511136)), hAPP(c_Set_Oimage(_1511130, _1511132, _1511134), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511130, tc_HOL_Obool)), _1511138), hAPP(hAPP(c_Set_Oinsert(_1511130), _1511136), c_Orderings_Obot__class_Obot(tc_fun(_1511130, tc_HOL_Obool))))))))], (22564 ^ _779571) ^ [_1170072, _1170074] : [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), _1170072))), 22567 ^ _779571 : [(22574 ^ _779571) ^ [] : [-(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), _1170074)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170074), 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), _1170072)))))], (22568 ^ _779571) ^ [] : [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), _1170074)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072)) = 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), _1170074)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170072))))]]], (14411 ^ _779571) ^ [_1022809, _1022811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1022809), _1022811)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1022809), _1022811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4402 ^ _779571) ^ [_847688, _847690, _847692, _847694] : [-(c_List_Olistset(_847694, _847690) = c_List_Olistset(_847692, _847688)), _847694 = _847692, _847690 = _847688], (26282 ^ _779571) ^ [_1241197, _1241199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241197), _1241199)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241199), _1241197))], (47602 ^ _779571) ^ [_1727923, _1727925] : [-(hAPP(c_List_Oset(_1727923), _1727925) = hAPP(c_Set_OCollect(_1727923), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1727923), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1727923, 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)), _1727923), 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)), _1727923), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1727923, tc_fun(tc_Nat_Onat, _1727923), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1727923, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1727923), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1727923), c_COMBB(_1727923, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1727923), _1727925))))), 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(_1727923)), _1727925))))))], (9430 ^ _779571) ^ [_936130] : [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, _936130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _936130)))], (27592 ^ _779571) ^ [_1267544, _1267546, _1267548] : [class_Orderings_Olinorder(_1267544), 27595 ^ _779571 : [(27602 ^ _779571) ^ [] : [_1267546 = _1267548, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1267544), _1267546) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1267544), _1267548))], (27596 ^ _779571) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1267544), _1267546) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1267544), _1267548), -(_1267546 = _1267548)]]], (42335 ^ _779571) ^ [_1599904, _1599906, _1599908, _1599910] : [hBOOL(hAPP(hAPP(c_member(_1599904), _1599910), hAPP(c_Relation_ODomain(_1599904, _1599906), _1599908))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1599904, _1599906, hAPP(hAPP(c_COMBC(_1599904, tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_fun(_1599906, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599906, tc_fun(tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_fun(_1599906, tc_HOL_Obool)), _1599904), c_COMBC(_1599906, tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599906, tc_prod(_1599904, _1599906)), tc_fun(_1599906, tc_fun(tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_HOL_Obool)), _1599904), hAPP(c_COMBB(tc_prod(_1599904, _1599906), tc_fun(tc_fun(tc_prod(_1599904, _1599906), tc_HOL_Obool), tc_HOL_Obool), _1599906), c_member(tc_prod(_1599904, _1599906)))), c_Product__Type_OPair(_1599904, _1599906)))), _1599908)), _1599910)))], (16671 ^ _779571) ^ [_1064962, _1064964] : [class_Groups_Oordered__ab__group__add__abs(_1064962), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064962), hAPP(c_Groups_Ouminus__class_Ouminus(_1064962), _1064964)), hAPP(c_Groups_Oabs__class_Oabs(_1064962), _1064964))))], (47416 ^ _779571) ^ [_1723235, _1723237, _1723239, _1723241, _1723243] : [-(hAPP(hAPP(c_List_Ozip(_1723235, _1723237), _1723239), hAPP(hAPP(c_List_Olist_OCons(_1723237), _1723241), _1723243)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1723235, _1723237)), _1723235, c_List_Olist_ONil(tc_prod(_1723235, _1723237)), hAPP(hAPP(c_COMBC(_1723235, tc_fun(tc_List_Olist(_1723235), tc_List_Olist(tc_prod(_1723235, _1723237))), tc_fun(tc_List_Olist(_1723235), tc_List_Olist(tc_prod(_1723235, _1723237)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1723235, _1723237)), tc_List_Olist(tc_prod(_1723235, _1723237))), tc_fun(tc_fun(tc_List_Olist(_1723235), tc_List_Olist(tc_prod(_1723235, _1723237))), tc_fun(tc_List_Olist(_1723235), tc_List_Olist(tc_prod(_1723235, _1723237)))), _1723235), c_COMBB(tc_List_Olist(tc_prod(_1723235, _1723237)), tc_List_Olist(tc_prod(_1723235, _1723237)), tc_List_Olist(_1723235))), hAPP(hAPP(c_COMBB(tc_prod(_1723235, _1723237), tc_fun(tc_List_Olist(tc_prod(_1723235, _1723237)), tc_List_Olist(tc_prod(_1723235, _1723237))), _1723235), c_List_Olist_OCons(tc_prod(_1723235, _1723237))), hAPP(hAPP(c_COMBC(_1723235, _1723237, tc_prod(_1723235, _1723237)), c_Product__Type_OPair(_1723235, _1723237)), _1723241)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723235), tc_List_Olist(_1723237), tc_List_Olist(tc_prod(_1723235, _1723237))), c_List_Ozip(_1723235, _1723237)), _1723243))), _1723239))], (15662 ^ _779571) ^ [_1045405, _1045407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045405), _1045407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1045405), _1045407)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24931 ^ _779571) ^ [_1215884, _1215886, _1215888] : [-(c_HOL_OThe(tc_prod(_1215884, _1215886), hAPP(c_Product__Type_Oprod_Oprod__case(_1215884, _1215886, tc_HOL_Obool), _1215888)) = c_HOL_OThe(tc_prod(_1215884, _1215886), hAPP(hAPP(c_COMBS(tc_prod(_1215884, _1215886), _1215886, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1215884, tc_fun(_1215886, tc_HOL_Obool), tc_prod(_1215884, _1215886)), _1215888), c_Product__Type_Ofst(_1215884, _1215886))), c_Product__Type_Osnd(_1215884, _1215886))))], (24747 ^ _779571) ^ [_1211731, _1211733] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1211731), _1211733) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211731)), hAPP(c_Code__Numeral_Onat__of, _1211733))))], (10888 ^ _779571) ^ [_960572, _960574, _960576] : [class_Orderings_Oorder(_960572), -(_960574 = _960576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960572), _960574), _960576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960572), _960574), _960576)))], (10022 ^ _779571) ^ [_946473, _946475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946473)), hAPP(c_Int_Onat, _946475)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946473), _946475))], (3344 ^ _779571) ^ [_830913, _830915, _830917, _830919, _830921, _830923, _830925, _830927, _830929, _830931] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_830931, _830927, _830923, _830919, _830915) = c_SetInterval_Oord_OgreaterThanAtMost(_830929, _830925, _830921, _830917, _830913)), _830931 = _830929, _830927 = _830925, _830923 = _830921, _830919 = _830917, _830915 = _830913], (41141 ^ _779571) ^ [_1562892, _1562894, _1562896, _1562898] : [hBOOL(hAPP(hAPP(c_member(_1562892), _1562894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562892, tc_HOL_Obool)), _1562896), hAPP(c_Set_OCollect(_1562892), _1562898)))), 41144 ^ _779571 : [(41147 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1562898, _1562894)))], (41145 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562892), _1562894), _1562896)))]]], (47175 ^ _779571) ^ [_1718440, _1718442, _1718444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718440), tc_List_Olist(_1718440))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718440), tc_List_Olist(_1718440)), _1718442), c_List_Olist_ONil(_1718440))), c_List_Olistrel(_1718440, _1718444))), -(_1718442 = c_List_Olist_ONil(_1718440))], (31155 ^ _779571) ^ [_1340839, _1340841, _1340843] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1340839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340839, tc_HOL_Obool)), _1340841), _1340843)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340839), _1340841)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340839), _1340843))], (51093 ^ _779571) ^ [_1808293, _1808295] : [class_Lattices_Olattice(_1808293), -(class_Lattices_Osemilattice__sup(tc_fun(_1808295, _1808293)))], (12189 ^ _779571) ^ [_982860, _982862] : [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), _982860), _982862))), 12192 ^ _779571 : [(12195 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982862)))], (12193 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982860)))]]], (48916 ^ _779571) ^ [_1761139, _1761141, _1761143, _1761145, _1761147] : [-(hAPP(hAPP(c_List_Ozip(_1761139, _1761141), _1761143), hAPP(hAPP(c_List_Oappend(_1761141), _1761145), _1761147)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1761139, _1761141)), hAPP(hAPP(c_List_Ozip(_1761139, _1761141), hAPP(hAPP(c_List_Otake(_1761139), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761141)), _1761145)), _1761143)), _1761145)), hAPP(hAPP(c_List_Ozip(_1761139, _1761141), hAPP(hAPP(c_List_Odrop(_1761139), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761141)), _1761145)), _1761143)), _1761147)))], (38605 ^ _779571) ^ [_1504796, _1504798, _1504800, _1504802] : [c_Fun_Oinj__on(_1504796, _1504798, _1504800, c_Orderings_Otop__class_Otop(tc_fun(_1504796, tc_HOL_Obool))), 38608 ^ _779571 : [(38622 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504798), _1504802), hAPP(c_Set_Oimage(_1504796, _1504798, _1504800), c_Orderings_Otop__class_Otop(tc_fun(_1504796, tc_HOL_Obool)))))), 38623 ^ _779571 : [(38624 ^ _779571) ^ [_1505199] : [_1504802 = hAPP(_1504800, _1505199), 38628 ^ _779571 : [(38631 ^ _779571) ^ [] : [38627 ^ [_1504796, _1504798, _1504800, _1504802, _1505199] = _1505199], (38629 ^ _779571) ^ [] : [-(_1504802 = hAPP(_1504800, 38627 ^ [_1504796, _1504798, _1504800, _1504802, _1505199]))]]]]], (38609 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504798), _1504802), hAPP(c_Set_Oimage(_1504796, _1504798, _1504800), c_Orderings_Otop__class_Otop(tc_fun(_1504796, tc_HOL_Obool))))), 38613 ^ _779571 : [(38616 ^ _779571) ^ [_1505061] : [_1504802 = hAPP(_1504800, _1505061), -(_1505061 = 38612 ^ [_1504796, _1504798, _1504800, _1504802])], (38614 ^ _779571) ^ [] : [-(_1504802 = hAPP(_1504800, 38612 ^ [_1504796, _1504798, _1504800, _1504802]))]]]]], (7069 ^ _779571) ^ [_896004, _896006] : [class_Groups_Ozero(_896004), 7072 ^ _779571 : [(7079 ^ _779571) ^ [] : [_896006 = c_Groups_Ozero__class_Ozero(_896004), -(c_Groups_Ozero__class_Ozero(_896004) = _896006)], (7073 ^ _779571) ^ [] : [c_Groups_Ozero__class_Ozero(_896004) = _896006, -(_896006 = c_Groups_Ozero__class_Ozero(_896004))]]], (5648 ^ _779571) ^ [_866761, _866763, _866765, _866767, _866769, _866771] : [-(c_COMBS(_866771, _866767, _866763) = c_COMBS(_866769, _866765, _866761)), _866771 = _866769, _866767 = _866765, _866763 = _866761], (9690 ^ _779571) ^ [_940626, _940628, _940630] : [class_Rings_Olinordered__semiring__strict(_940626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940626), c_Groups_Ozero__class_Ozero(_940626)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940626), _940628), _940630))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940626), c_Groups_Ozero__class_Ozero(_940626)), _940628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940626), c_Groups_Ozero__class_Ozero(_940626)), _940630)))], (51271 ^ _779571) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (22400 ^ _779571) ^ [_1166412, _1166414, _1166416, _1166418] : [-(c_Nat_Onat_Onat__case(_1166412, _1166414, _1166416, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166418)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1166412), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1166418))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1166412, _1166412), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1166412, tc_fun(_1166412, _1166412)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1166412, tc_fun(_1166412, _1166412)), tc_Int_Oint), c_If(_1166412)), c_Nat__Numeral_Oneg)), _1166414)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1166412, tc_Int_Oint), _1166416), c_Int_Onat))))], (25122 ^ _779571) ^ [_1220075] : [_1220075 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220075), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (40392 ^ _779571) ^ [_1545741, _1545743, _1545745] : [-(c_Relation_Orefl__on(_1545741, _1545743, _1545745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545741, _1545741), tc_HOL_Obool)), _1545745), hAPP(hAPP(c_Product__Type_OSigma(_1545741, _1545741), _1545743), hAPP(c_COMBK(tc_fun(_1545741, tc_HOL_Obool), _1545741), _1545743)))), 40398 ^ _779571 : [(40401 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545741, _1545741)), hAPP(hAPP(c_Product__Type_OPair(_1545741, _1545741), 40397 ^ [_1545741, _1545743, _1545745]), 40397 ^ [_1545741, _1545743, _1545745])), _1545745))], (40399 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545741), 40397 ^ [_1545741, _1545743, _1545745]), _1545743)))]]], (43333 ^ _779571) ^ [_1623584, _1623586, _1623588, _1623590, _1623592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623584, _1623586)), hAPP(hAPP(c_Product__Type_OPair(_1623584, _1623586), _1623588), _1623590)), _1623592)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623586, _1623584)), hAPP(hAPP(c_Product__Type_OPair(_1623586, _1623584), _1623590), _1623588)), hAPP(c_Relation_Oconverse(_1623584, _1623586), _1623592))))], (5446 ^ _779571) ^ [_863758, _863760, _863762, _863764] : [-(c_List_Obutlast(_863764, _863760) = c_List_Obutlast(_863762, _863758)), _863764 = _863762, _863760 = _863758], (39421 ^ _779571) ^ [_1522250, _1522252, _1522254, _1522256, _1522258, _1522260] : [-(hAPP(c_Set_Ovimage(_1522250, _1522252, hAPP(c_Fun_Ocomp(_1522254, _1522252, _1522250, _1522256), _1522258)), _1522260) = hAPP(c_Set_Ovimage(_1522250, _1522254, _1522258), hAPP(c_Set_Ovimage(_1522254, _1522252, _1522256), _1522260)))], (78 ^ _779571) ^ [_780592, _780594, _780596, _780598, _780600, _780602, _780604, _780606] : [-(c_Nat__Transfer_Otransfer__morphism(_780604, _780600, _780596, _780592)), c_Nat__Transfer_Otransfer__morphism(_780606, _780602, _780598, _780594), _780606 = _780604, _780602 = _780600, _780598 = _780596, _780594 = _780592], (19457 ^ _779571) ^ [_1113356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1113356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1113356)))], (1874 ^ _779571) ^ [_806678, _806680, _806682, _806684, _806686, _806688, _806690, _806692] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_806692, _806688, _806684, _806680) = c_Hoare__Mirabelle_Otriple_Otriple__case(_806690, _806686, _806682, _806678)), _806692 = _806690, _806688 = _806686, _806684 = _806682, _806680 = _806678], (6732 ^ _779571) ^ [_889991, _889993, _889995] : [c_Com_Ocom_OWhile(_889991, _889993) = hAPP(c_Com_Ocom_OBODY, _889995)], (32450 ^ _779571) ^ [_1370939, _1370941, _1370943, _1370945, _1370947, _1370949, _1370951, _1370953] : [c_Finite__Set_Ofolding__image__simple(_1370939, _1370941, _1370943, _1370945, _1370947, _1370949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370941), _1370951)), -(hBOOL(hAPP(hAPP(c_member(_1370941), _1370953), _1370951))), -(hAPP(_1370949, hAPP(hAPP(c_Set_Oinsert(_1370941), _1370953), _1370951)) = hAPP(hAPP(_1370943, hAPP(_1370947, _1370953)), hAPP(_1370949, _1370951)))], (9184 ^ _779571) ^ [_931581, _931583, _931585] : [class_Groups_Oordered__ab__group__add(_931581), 9187 ^ _779571 : [(9194 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931581), _931585), _931583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931581), hAPP(c_Groups_Ouminus__class_Ouminus(_931581), _931583)), hAPP(c_Groups_Ouminus__class_Ouminus(_931581), _931585))))], (9188 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931581), hAPP(c_Groups_Ouminus__class_Ouminus(_931581), _931583)), hAPP(c_Groups_Ouminus__class_Ouminus(_931581), _931585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931581), _931585), _931583)))]]], (46390 ^ _779571) ^ [_1696269, _1696271, _1696273, _1696275, _1696277, _1696279] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696269, _1696271)), hAPP(hAPP(c_Product__Type_OPair(_1696269, _1696271), _1696273), _1696275)), hAPP(c_List_Oset(tc_prod(_1696269, _1696271)), hAPP(hAPP(c_List_Ozip(_1696269, _1696271), _1696277), _1696279)))), 46393 ^ _779571 : [(46396 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696271), _1696275), hAPP(c_List_Oset(_1696271), _1696279))))], (46394 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696269), _1696273), hAPP(c_List_Oset(_1696269), _1696277))))]]], (38295 ^ _779571) ^ [_1499002, _1499004, _1499006, _1499008, _1499010, _1499012] : [c_Fun_Oinj__on(_1499002, _1499004, _1499006, _1499008), hBOOL(hAPP(hAPP(c_member(_1499002), _1499010), _1499008)), hBOOL(hAPP(hAPP(c_member(_1499002), _1499012), _1499008)), 38306 ^ _779571 : [(38313 ^ _779571) ^ [] : [_1499010 = _1499012, -(hAPP(_1499006, _1499010) = hAPP(_1499006, _1499012))], (38307 ^ _779571) ^ [] : [hAPP(_1499006, _1499010) = hAPP(_1499006, _1499012), -(_1499010 = _1499012)]]], (16723 ^ _779571) ^ [_1065875, _1065877, _1065879] : [class_Rings_Olinordered__idom(_1065875), 16726 ^ _779571 : [(16735 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), hAPP(c_Groups_Oabs__class_Oabs(_1065875), _1065877)), _1065879))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), _1065877), _1065879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), hAPP(c_Groups_Ouminus__class_Ouminus(_1065875), _1065877)), _1065879))], (16727 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), hAPP(c_Groups_Oabs__class_Oabs(_1065875), _1065877)), _1065879)), 16730 ^ _779571 : [(16733 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), hAPP(c_Groups_Ouminus__class_Ouminus(_1065875), _1065877)), _1065879)))], (16731 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065875), _1065877), _1065879)))]]]]], (6528 ^ _779571) ^ [_886087, _886089] : [hAPP(c_Com_Ocom_OBODY, _886087) = hAPP(c_Com_Ocom_OBODY, _886089), -(_886087 = _886089)], (36674 ^ _779571) ^ [_1461537, _1461539] : [class_Lattices_Oboolean__algebra(_1461537), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461537), hAPP(c_Groups_Ouminus__class_Ouminus(_1461537), _1461539)), _1461539) = c_Orderings_Obot__class_Obot(_1461537))], (39685 ^ _779571) ^ [_1528494, _1528496, _1528498, _1528500] : [39686 ^ _779571 : [(39687 ^ _779571) ^ [_1528583] : [_1528498 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1528494, tc_Option_Ooption(_1528496)), hAPP(c_COMBK(tc_Option_Ooption(_1528496), _1528494), c_Option_Ooption_ONone(_1528496))), _1528500), hAPP(c_Option_Ooption_OSome(_1528496), _1528583))]], -(c_Map_Odom(_1528494, _1528496, _1528498) = hAPP(hAPP(c_Set_Oinsert(_1528494), _1528500), c_Orderings_Obot__class_Obot(tc_fun(_1528494, tc_HOL_Obool))))], (37229 ^ _779571) ^ [_1474590, _1474592, _1474594, _1474596, _1474598] : [class_Groups_Oab__group__add(_1474590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474592), _1474594)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474592), _1474596)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474592, _1474590), _1474598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474592, tc_HOL_Obool)), _1474594), _1474596)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1474590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1474590), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474592, _1474590), _1474598), _1474594)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474592, _1474590), _1474598), _1474596))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474592, _1474590), _1474598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474592, tc_HOL_Obool)), _1474594), _1474596))))], (35659 ^ _779571) ^ [_1438811] : [-(_1438811 = 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), 35656 ^ [_1438811]), 35657 ^ [_1438811])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (51395 ^ _779571) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (24939 ^ _779571) ^ [_1216111, _1216113, _1216115, _1216117] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1216111), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1216113, _1216115, _1216111, _1216117) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1216113, 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(_1216113)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1216115, _1216117)), 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(_1216113)))), 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(_1216113)))), 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(_1216113)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1216113, 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(_1216113)))), 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(_1216113)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1216113, _1216115, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1216111), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1216117))), 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(_1216113)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113)))), 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(_1216113)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1216113, 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(_1216113)))), 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(_1216113)))), 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(_1216113))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113)))), 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(_1216113)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113))))), tc_prod(_1216113, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1216113)), hAPP(hAPP(c_COMBB(_1216113, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1216113)))), tc_prod(_1216113, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1216113)), c_Product__Type_Ofst(_1216113, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (32353 ^ _779571) ^ [_1368382, _1368384] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368382), _1368384)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1368382), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368384))))], (24877 ^ _779571) ^ [_1214627, _1214629, _1214631, _1214633, _1214635, _1214637, _1214639] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1214627, _1214629, _1214631, _1214633, _1214635, _1214637, _1214639) = c_New__DSequence_Oneg__decr__bind(_1214627, _1214629, hAPP(hAPP(hAPP(_1214631, _1214635), _1214637), _1214639), hAPP(hAPP(c_COMBC(_1214627, 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(_1214629)))), hAPP(hAPP(c_COMBC(_1214627, 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(_1214629))))), hAPP(hAPP(c_COMBC(_1214627, 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(_1214629)))))), _1214633), _1214635)), _1214637)), _1214639)))], (41806 ^ _779571) ^ [_1587478, _1587480, _1587482, _1587484] : [c_Wellfounded_Owf(_1587478, _1587480), c_Wellfounded_Owf(_1587482, _1587484), -(c_Wellfounded_Owf(tc_prod(_1587478, _1587482), c_Wellfounded_Olex__prod(_1587478, _1587482, _1587480, _1587484)))], (19063 ^ _779571) ^ [_1106287, _1106289] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1106287), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106289)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1106287), 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)))), _1106289)))], (7634 ^ _779571) ^ [_906097, _906099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906097), hAPP(c_Nat_OSuc, _906099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906097), _906099))), -(_906097 = _906099)], (18057 ^ _779571) ^ [_1090411, _1090413, _1090415] : [class_Int_Onumber__ring(_1090411), 18060 ^ _779571 : [(18067 ^ _779571) ^ [] : [c_Int_Oiszero(_1090411, hAPP(c_Int_Onumber__class_Onumber__of(_1090411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1090413), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1090415)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1090411), _1090413) = hAPP(c_Int_Onumber__class_Onumber__of(_1090411), _1090415))], (18061 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1090411), _1090413) = hAPP(c_Int_Onumber__class_Onumber__of(_1090411), _1090415), -(c_Int_Oiszero(_1090411, hAPP(c_Int_Onumber__class_Onumber__of(_1090411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1090413), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1090415)))))]]], (1072 ^ _779571) ^ [_795739, _795741] : [-(class_Rings_Olinordered__ring(_795739)), _795741 = _795739, class_Rings_Olinordered__ring(_795741)], (25094 ^ _779571) ^ [_1219519, _1219521, _1219523, _1219525] : [class_Groups_Oordered__ab__group__add__abs(_1219519), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219519), hAPP(c_Groups_Oabs__class_Oabs(_1219519), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1219521, _1219519), _1219523), _1219525))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1219521, _1219519), hAPP(hAPP(c_COMBB(_1219519, _1219519, _1219521), c_Groups_Oabs__class_Oabs(_1219519)), _1219523)), _1219525))))], (20783 ^ _779571) ^ [_1136839, _1136841, _1136843] : [class_Fields_Olinordered__field(_1136839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136839), c_Groups_Ozero__class_Ozero(_1136839)), _1136841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136839), c_Groups_Ozero__class_Ozero(_1136839)), _1136843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136839), c_Groups_Ozero__class_Ozero(_1136839)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136839), _1136841), _1136843))))], (19365 ^ _779571) ^ [_1111728] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111728))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111728)))))], (51191 ^ _779571) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (42467 ^ _779571) ^ [_1602590] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42463 ^ [_1602590]), c_Int_OInteg)))], (17285 ^ _779571) ^ [_1076732, _1076734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1076732)), -(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), _1076732), _1076734))))], (21473 ^ _779571) ^ [_1149089, _1149091, _1149093, _1149095] : [class_Fields_Olinordered__field(_1149089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149089), c_Groups_Ozero__class_Ozero(_1149089)), _1149091)), 21480 ^ _779571 : [(21487 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149089), _1149093), _1149091)), _1149095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149089), _1149093), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149089), _1149095), _1149091))))], (21481 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149089), _1149093), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149089), _1149095), _1149091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149089), _1149093), _1149091)), _1149095)))]]], (24433 ^ _779571) ^ [_1205537, _1205539, _1205541] : [class_Orderings_Olinorder(_1205537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205537), _1205539), _1205541)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205537), _1205539), _1205541) = _1205541)], (49901 ^ _779571) ^ [_1783021, _1783023] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1783021))), c_List_Otranspose(_1783021, _1783023)) = c_List_Ofoldr(tc_List_Olist(_1783021), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1783021)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1783021))), _1783023, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25982 ^ _779571) ^ [_1235680, _1235682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235682)), 25989 ^ _779571 : [(25996 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235680), _1235682)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1235680)), hAPP(c_Int_Onat, _1235682))))], (25990 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1235680)), hAPP(c_Int_Onat, _1235682))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235680), _1235682)))]]], (48138 ^ _779571) ^ [_1740609, _1740611] : [-(hAPP(hAPP(c_List_Oappend(_1740609), _1740611), c_List_Olist_ONil(_1740609)) = _1740611)], (44714 ^ _779571) ^ [_1657256, _1657258, _1657260, _1657262, _1657264] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657256, tc_fun(_1657258, tc_HOL_Obool)), _1657260), hAPP(hAPP(c_COMBB(tc_fun(_1657258, tc_HOL_Obool), tc_fun(_1657258, tc_HOL_Obool), _1657256), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657258, tc_HOL_Obool)), _1657262)), _1657264)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657258, tc_HOL_Obool)), _1657262), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657256, tc_fun(_1657258, tc_HOL_Obool)), _1657260), _1657264)))], (27650 ^ _779571) ^ [_1268658, _1268660] : [-(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)), _1268658)), 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), _1268660), _1268658))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1268658), _1268660))], (50846 ^ _779571) ^ [_1802789, _1802791, _1802793, _1802795] : [class_Orderings_Olinorder(_1802789), c_List_Olinorder__class_Osorted(_1802789, hAPP(c_List_Orev(_1802789), _1802791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1802793), _1802795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802795), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802789)), _1802791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1802789), hAPP(hAPP(c_List_Onth(_1802789), _1802791), _1802795)), hAPP(hAPP(c_List_Onth(_1802789), _1802791), _1802793))))], (36450 ^ _779571) ^ [_1456790, _1456792, _1456794, _1456796] : [class_Lattices_Osemilattice__inf(_1456790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456790), _1456792), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456790), _1456794), _1456796))), 36457 ^ _779571 : [(36460 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456790), _1456792), _1456796)))], (36458 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456790), _1456792), _1456794)))]]], (1332 ^ _779571) ^ [_798989, _798991] : [-(class_Orderings_Obot(_798989)), _798991 = _798989, class_Orderings_Obot(_798991)], (31271 ^ _779571) ^ [_1344994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1344994)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1344994), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1344994), c_Orderings_Otop__class_Otop(tc_fun(_1344994, tc_HOL_Obool)))))], (28282 ^ _779571) ^ [_1281478, _1281480, _1281482, _1281484] : [class_Orderings_Olinorder(_1281478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281478), _1281480), _1281482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281478), _1281482), _1281484)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281478, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1281478, _1281480, _1281482)), c_SetInterval_Oord__class_OatLeastAtMost(_1281478, _1281482, _1281484)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1281478, _1281480, _1281484))], (41115 ^ _779571) ^ [_1562406, _1562408, _1562410] : [hBOOL(hAPP(hAPP(c_member(_1562406), _1562408), hAPP(c_Set_OCollect(_1562406), _1562410))), -(hBOOL(hAPP(_1562410, _1562408)))], (35677 ^ _779571) ^ [_1439280, _1439282, _1439284, _1439286, _1439288, _1439290] : [c_Finite__Set_Ofolding(_1439280, _1439282, _1439284, _1439286), -(hAPP(c_Fun_Ocomp(_1439282, _1439282, _1439282, hAPP(_1439284, _1439288)), hAPP(_1439284, _1439290)) = hAPP(c_Fun_Ocomp(_1439282, _1439282, _1439282, hAPP(_1439284, _1439290)), hAPP(_1439284, _1439288)))], (42187 ^ _779571) ^ [_1596130, _1596132, _1596134, _1596136] : [42188 ^ _779571 : [(42189 ^ _779571) ^ [_1596184] : [hBOOL(hAPP(hAPP(_1596134, _1596184), _1596136))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1596130, _1596132, _1596134), _1596136)))], (42749 ^ _779571) ^ [_1609111, _1609113, _1609115] : [class_Orderings_Olinorder(_1609111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609111), _1609113)), 42759 ^ _779571 : [(42762 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609111), _1609115), 42758 ^ [_1609111, _1609113, _1609115]))], (42760 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609111), 42758 ^ [_1609111, _1609113, _1609115]), _1609113)))]], hBOOL(hAPP(hAPP(c_member(_1609111), _1609115), _1609113)), -(c_Big__Operators_Olinorder__class_OMin(_1609111, _1609113) = _1609115)], (34668 ^ _779571) ^ [_1414757, _1414759, _1414761, _1414763, _1414765, _1414767] : [hBOOL(hAPP(hAPP(c_member(_1414757), _1414759), _1414761)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414757, tc_Option_Ooption(_1414763)), c_Map_Orestrict__map(_1414757, _1414763, _1414765, _1414761)), _1414759), _1414767) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1414757, tc_Option_Ooption(_1414763)), c_Map_Orestrict__map(_1414757, _1414763, _1414765, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414757, tc_HOL_Obool)), _1414761), hAPP(hAPP(c_Set_Oinsert(_1414757), _1414759), c_Orderings_Obot__class_Obot(tc_fun(_1414757, tc_HOL_Obool)))))), _1414759), _1414767))], (29850 ^ _779571) ^ [_1313456, _1313458] : [-(c_Set_Othe__elem(_1313456, _1313458) = c_HOL_OThe(_1313456, hAPP(hAPP(c_COMBB(tc_fun(_1313456, tc_HOL_Obool), tc_HOL_Obool, _1313456), hAPP(c_fequal, _1313458)), hAPP(hAPP(c_COMBC(_1313456, tc_fun(_1313456, tc_HOL_Obool), tc_fun(_1313456, tc_HOL_Obool)), c_Set_Oinsert(_1313456)), c_Orderings_Obot__class_Obot(tc_fun(_1313456, tc_HOL_Obool))))))], (8165 ^ _779571) ^ [_914936, _914938] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914936)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914938)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914936), _914938)))], (35163 ^ _779571) ^ [_1426418, _1426420, _1426422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426418), _1426420)), hBOOL(hAPP(_1426422, _1426420)), 35174 ^ _779571 : [(35177 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426418), 35172 ^ [_1426418, _1426420, _1426422]), 35173 ^ [_1426418, _1426420, _1426422])))], (35179 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1426422, 35173 ^ [_1426418, _1426420, _1426422])))], (35181 ^ _779571) ^ [] : [hBOOL(hAPP(_1426422, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426418, tc_HOL_Obool)), 35173 ^ [_1426418, _1426420, _1426422]), hAPP(hAPP(c_Set_Oinsert(_1426418), 35172 ^ [_1426418, _1426420, _1426422]), c_Orderings_Obot__class_Obot(tc_fun(_1426418, tc_HOL_Obool))))))], (35175 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1426418), 35173 ^ [_1426418, _1426420, _1426422])))]], -(hBOOL(hAPP(_1426422, c_Orderings_Obot__class_Obot(tc_fun(_1426418, tc_HOL_Obool)))))], (22168 ^ _779571) ^ [_1162170, _1162172] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1162170), _1162172) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1162170), _1162172))], (27349 ^ _779571) ^ [_1262225, _1262227, _1262229, _1262231] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262225), _1262227)), 27352 ^ _779571 : [(27353 ^ _779571) ^ [_1262383] : [27355 ^ _779571 : [(27361 ^ _779571) ^ [] : [-(_1262383 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27357 ^ [_1262225, _1262227, _1262229, _1262231, _1262383]), 27354 ^ [_1262225, _1262227, _1262229, _1262231, _1262383]))], (27359 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27357 ^ [_1262225, _1262227, _1262229, _1262231, _1262383]), _1262229)))], (27356 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27354 ^ [_1262225, _1262227, _1262229, _1262231, _1262383]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1262227))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262383), _1262231)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1262225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262383), _1262227)), _1262231)))]]], (45175 ^ _779571) ^ [_1668263, _1668265, _1668267] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668263, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1668263, tc_HOL_Obool), tc_HOL_Obool)), _1668265), _1668267)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668263, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668263, tc_HOL_Obool), _1668265)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668263, tc_HOL_Obool), _1668267)))], (10902 ^ _779571) ^ [_960788, _960790, _960792] : [class_Orderings_Olinorder(_960788), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960788), _960790), _960792))), 10909 ^ _779571 : [(10916 ^ _779571) ^ [] : [_960790 = _960792, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960788), _960790), _960792)))], (10910 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960788), _960790), _960792)), -(_960790 = _960792)]]], (44061 ^ _779571) ^ [_1641350, _1641352, _1641354] : [class_Lattices_Olattice(_1641350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641350), _1641352)), -(c_Big__Operators_Olattice__class_OInf__fin(_1641350, hAPP(hAPP(c_Set_Oinsert(_1641350), _1641354), _1641352)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641350, _1641350, c_Lattices_Osemilattice__inf__class_Oinf(_1641350)), _1641354), _1641352))], (36652 ^ _779571) ^ [_1460774, _1460776, _1460778, _1460780, _1460782] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460774, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460776, tc_fun(_1460774, tc_HOL_Obool)), _1460778), _1460780)), _1460782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1460776, tc_fun(_1460774, tc_HOL_Obool)), _1460778), hAPP(hAPP(c_COMBC(_1460776, tc_fun(_1460774, tc_HOL_Obool), tc_fun(_1460774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460774, tc_HOL_Obool), tc_fun(tc_fun(_1460774, tc_HOL_Obool), tc_fun(_1460774, tc_HOL_Obool)), _1460776), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460774, tc_HOL_Obool))), _1460780)), _1460782)))], (6235 ^ _779571) ^ [_880656, _880658, _880660, _880662, _880664, _880666] : [-(c_Com_Ocom_OCall(_880656, _880658, _880660) = c_Com_Ocom_OCall(_880662, _880664, _880666)), _880656 = _880662, _880658 = _880664, _880660 = _880666], (42924 ^ _779571) ^ [_1612879, _1612881, _1612883, _1612885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612879, _1612879)), _1612881), c_Transitive__Closure_Otrancl(_1612879, _1612883))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1612879, _1612879), tc_HOL_Obool)), _1612883), _1612885)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612879, _1612879)), _1612881), c_Transitive__Closure_Otrancl(_1612879, _1612885))))], (14530 ^ _779571) ^ [_1024705, _1024707] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1024705), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1024707)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024705, _1024707)))], (9344 ^ _779571) ^ [_934214] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934214)) = _934214)], (24997 ^ _779571) ^ [_1217822, _1217824] : [-(c_HOL_OThe(_1217822, hAPP(c_fequal, _1217824)) = _1217824)], (24985 ^ _779571) ^ [_1217456, _1217458, _1217460] : [-(c_HOL_OThe(tc_prod(_1217456, _1217458), _1217460) = c_HOL_OThe(tc_prod(_1217456, _1217458), hAPP(c_Product__Type_Oprod_Oprod__case(_1217456, _1217458, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1217458, tc_prod(_1217456, _1217458)), tc_fun(_1217458, tc_HOL_Obool), _1217456), hAPP(c_COMBB(tc_prod(_1217456, _1217458), tc_HOL_Obool, _1217458), _1217460)), c_Product__Type_OPair(_1217456, _1217458)))))], (50491 ^ _779571) ^ [_1793872, _1793874, _1793876, _1793878] : [class_Orderings_Olinorder(_1793872), c_List_Olinorder__class_Osorted(_1793872, _1793874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1793876), _1793878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1793878), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793872)), _1793874))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793872), hAPP(hAPP(c_List_Onth(_1793872), _1793874), _1793876)), hAPP(hAPP(c_List_Onth(_1793872), _1793874), _1793878))))], (13508 ^ _779571) ^ [_1005825, _1005827, _1005829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005825)), 13511 ^ _779571 : [(13518 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005827), _1005829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005825), _1005827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005825), _1005829))))], (13512 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005825), _1005827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005825), _1005829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005827), _1005829)))]]], (46655 ^ _779571) ^ [_1703476, _1703478, _1703480, _1703482, _1703484] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703476)), _1703478) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703480)), _1703482), 46658 ^ _779571 : [(46665 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703476), _1703484), hAPP(c_List_Oset(_1703476), _1703478)))), -(hAPP(c_Map_Omap__of(_1703476, _1703480, hAPP(hAPP(c_List_Ozip(_1703476, _1703480), _1703478), _1703482)), _1703484) = c_Option_Ooption_ONone(_1703480))], (46659 ^ _779571) ^ [] : [hAPP(c_Map_Omap__of(_1703476, _1703480, hAPP(hAPP(c_List_Ozip(_1703476, _1703480), _1703478), _1703482)), _1703484) = c_Option_Ooption_ONone(_1703480), hBOOL(hAPP(hAPP(c_member(_1703476), _1703484), hAPP(c_List_Oset(_1703476), _1703478)))]]], (32059 ^ _779571) ^ [_1362770, _1362772, _1362774, _1362776, _1362778, _1362780] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362770, tc_fun(_1362772, tc_HOL_Obool))), _1362774), _1362776), _1362778), _1362780)), -(hBOOL(hAPP(hAPP(_1362774, _1362778), _1362780))), -(hBOOL(hAPP(hAPP(_1362776, _1362778), _1362780)))], (31147 ^ _779571) ^ [_1340692, _1340694, _1340696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340692), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340692, tc_HOL_Obool)), _1340694), _1340696))), 31150 ^ _779571 : [(31153 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1340692), _1340696)))], (31151 ^ _779571) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1340692), _1340694)))]]], (28395 ^ _779571) ^ [_1283570] : [c_Nat__Transfer_Onat__set(_1283570), -(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), _1283570)) = _1283570)], (39312 ^ _779571) ^ [_1519604, _1519606, _1519608, _1519610, _1519612] : [class_Groups_Ocomm__monoid__mult(_1519604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519606), _1519608)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519606), _1519610)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1519604), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519604, _1519606, c_Groups_Otimes__class_Otimes(_1519604)), _1519612), c_Groups_Oone__class_Oone(_1519604)), _1519608)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519604, _1519606, c_Groups_Otimes__class_Otimes(_1519604)), _1519612), c_Groups_Oone__class_Oone(_1519604)), _1519610)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1519604), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519604, _1519606, c_Groups_Otimes__class_Otimes(_1519604)), _1519612), c_Groups_Oone__class_Oone(_1519604)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519606, tc_HOL_Obool)), _1519608), _1519610))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519604, _1519606, c_Groups_Otimes__class_Otimes(_1519604)), _1519612), c_Groups_Oone__class_Oone(_1519604)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519606, tc_HOL_Obool)), _1519608), _1519610))))], (22632 ^ _779571) ^ [_1171243, _1171245] : [-(c_Divides_OposDivAlg(_1171243, _1171245) = hAPP(c_Divides_Oadjust(_1171245), c_Divides_OposDivAlg(_1171243, 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)))), _1171245)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171243), _1171245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171245), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6734 ^ _779571) ^ [_890042, _890044, _890046, _890048] : [hAPP(c_Com_Ocom_OBODY, _890042) = c_Com_Ocom_OCond(_890044, _890046, _890048)], (30548 ^ _779571) ^ [_1328044, _1328046, _1328048] : [hBOOL(hAPP(hAPP(c_member(_1328044), _1328046), hAPP(hAPP(c_Set_Oinsert(_1328044), _1328048), c_Orderings_Obot__class_Obot(tc_fun(_1328044, tc_HOL_Obool))))), -(_1328046 = _1328048)], (28296 ^ _779571) ^ [_1281743, _1281745] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1281743, _1281745)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1281745), _1281743))], (28635 ^ _779571) ^ [_1288171, _1288173, _1288175] : [class_Orderings_Olinorder(_1288171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288171), _1288173), _1288175)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288171, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288171, _1288173), _1288175)), hAPP(c_SetInterval_Oord__class_OatLeast(_1288171), _1288175)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1288171), _1288173))], (30208 ^ _779571) ^ [_1321019, _1321021, _1321023, _1321025] : [hBOOL(hAPP(hAPP(c_member(_1321019), _1321021), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321019, tc_HOL_Obool)), _1321023), _1321025))), 30211 ^ _779571 : [(30214 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1321019), _1321021), _1321025))], (30212 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321019), _1321021), _1321023)))]]], (23607 ^ _779571) ^ [_1189508, _1189510, _1189512, _1189514] : [class_Orderings_Olinorder(_1189508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189508), _1189510), _1189512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189508), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189508), _1189514), _1189510)), _1189512)))], (41686 ^ _779571) ^ [_1582392, _1582394, _1582396, _1582398, _1582400] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582392, _1582394, _1582396), _1582398), _1582400) = hAPP(c_Set_OCollect(tc_prod(_1582392, _1582396)), hAPP(c_Product__Type_Oprod_Oprod__case(_1582392, _1582396, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1582396, tc_fun(_1582394, tc_HOL_Obool)), tc_fun(_1582396, tc_HOL_Obool), _1582392), hAPP(c_COMBB(tc_fun(_1582394, tc_HOL_Obool), tc_HOL_Obool, _1582396), c_HOL_OEx(_1582394))), hAPP(hAPP(c_COMBC(_1582392, tc_fun(_1582396, tc_fun(_1582394, tc_HOL_Obool)), tc_fun(_1582396, tc_fun(_1582394, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1582394, tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), tc_fun(tc_fun(_1582396, tc_fun(_1582394, tc_HOL_Obool)), tc_fun(_1582396, tc_fun(_1582394, tc_HOL_Obool))), _1582392), c_COMBB(tc_fun(_1582394, tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool), _1582396)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1582394, tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), _1582392), c_COMBS(_1582394, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_HOL_Obool), tc_fun(_1582394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1582392), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1582394), c_fconj)), hAPP(hAPP(c_COMBC(_1582392, tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_fun(tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), _1582392), c_COMBC(_1582394, tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_prod(_1582392, _1582394)), tc_fun(_1582394, tc_fun(tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_HOL_Obool)), _1582392), hAPP(c_COMBB(tc_prod(_1582392, _1582394), tc_fun(tc_fun(tc_prod(_1582392, _1582394), tc_HOL_Obool), tc_HOL_Obool), _1582394), c_member(tc_prod(_1582392, _1582394)))), c_Product__Type_OPair(_1582392, _1582394)))), _1582398))))), hAPP(hAPP(c_COMBC(_1582396, tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_fun(tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_fun(_1582394, tc_HOL_Obool)), _1582396), c_COMBC(_1582394, tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582394, tc_prod(_1582394, _1582396)), tc_fun(_1582394, tc_fun(tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_HOL_Obool)), _1582396), hAPP(c_COMBB(tc_prod(_1582394, _1582396), tc_fun(tc_fun(tc_prod(_1582394, _1582396), tc_HOL_Obool), tc_HOL_Obool), _1582394), c_member(tc_prod(_1582394, _1582396)))), hAPP(c_COMBC(_1582394, _1582396, tc_prod(_1582394, _1582396)), c_Product__Type_OPair(_1582394, _1582396))))), _1582400))))))], (6035 ^ _779571) ^ [_876818, _876820, _876822, _876824, _876826] : [c_Com_Ocom_OWhile(_876818, _876820) = c_Com_Ocom_OCond(_876822, _876824, _876826)], (47097 ^ _779571) ^ [_1716624, _1716626] : [-(c_Random_Oselect__weight(_1716624, _1716626) = 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(_1716624, 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, _1716624), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1716624)), _1716626)))), hAPP(hAPP(c_COMBB(_1716624, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1716624, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1716624, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1716624, _1716626))))], (42936 ^ _779571) ^ [_1613149, _1613151, _1613153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613149, _1613149), tc_HOL_Obool)), _1613151), hAPP(hAPP(c_Product__Type_OSigma(_1613149, _1613149), _1613153), hAPP(c_COMBK(tc_fun(_1613149, tc_HOL_Obool), _1613149), _1613153)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613149, _1613149), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613149, _1613151)), hAPP(hAPP(c_Product__Type_OSigma(_1613149, _1613149), _1613153), hAPP(c_COMBK(tc_fun(_1613149, tc_HOL_Obool), _1613149), _1613153)))))], (6760 ^ _779571) ^ [_890645, _890647, _890649, _890651] : [c_Com_Ocom_OWhile(_890645, _890647) = c_Com_Ocom_OAss(_890649, _890651)], (3106 ^ _779571) ^ [_827192, _827194, _827196, _827198] : [-(c_Divides_Odivmod__nat(_827198, _827194) = c_Divides_Odivmod__nat(_827196, _827192)), _827198 = _827196, _827194 = _827192], (16995 ^ _779571) ^ [_1071531, _1071533] : [class_Groups_Oordered__ab__group__add__abs(_1071531), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071531), _1071533), c_Groups_Ozero__class_Ozero(_1071531))), -(hAPP(c_Groups_Oabs__class_Oabs(_1071531), _1071533) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071531), _1071533))], (35737 ^ _779571) ^ [_1440678, _1440680, _1440682, _1440684, _1440686, _1440688] : [c_Finite__Set_Ofolding(_1440678, _1440680, _1440682, _1440684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440678), _1440686)), -(hBOOL(hAPP(hAPP(c_member(_1440678), _1440688), _1440686))), -(hAPP(_1440684, hAPP(hAPP(c_Set_Oinsert(_1440678), _1440688), _1440686)) = hAPP(c_Fun_Ocomp(_1440680, _1440680, _1440680, hAPP(_1440684, _1440686)), hAPP(_1440682, _1440688)))], (19565 ^ _779571) ^ [_1115184] : [class_Rings_Osemiring__1(_1115184), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1115184), c_Groups_Oone__class_Oone(_1115184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1115184))], (17233 ^ _779571) ^ [_1075961] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075961)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1075961)))], (36716 ^ _779571) ^ [_1462450, _1462452, _1462454, _1462456] : [-(hBOOL(hAPP(hAPP(c_member(_1462450), _1462452), _1462454))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462450, tc_HOL_Obool)), _1462454), hAPP(hAPP(c_Set_Oinsert(_1462450), _1462452), _1462456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462450, tc_HOL_Obool)), _1462454), _1462456))], (3282 ^ _779571) ^ [_829944, _829946, _829948, _829950, _829952, _829954] : [-(c_SetInterval_Oord_OlessThan(_829954, _829950, _829946) = c_SetInterval_Oord_OlessThan(_829952, _829948, _829944)), _829954 = _829952, _829950 = _829948, _829946 = _829944], (25364 ^ _779571) ^ [_1223993, _1223995] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223993), _1223995)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223995), _1223993)), -(_1223993 = _1223995)], (3666 ^ _779571) ^ [_836056, _836058] : [_836058 = _836056, -(c_Wellfounded_Omeasure(_836058) = c_Wellfounded_Omeasure(_836056))], (50380 ^ _779571) ^ [_1791609, _1791611, _1791613, _1791615] : [class_Groups_Ocomm__monoid__add(_1791609), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1791609), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1791609), _1791611), c_List_Oupt(_1791613, _1791615))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1791609), _1791611), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1791613, _1791615))))], (732 ^ _779571) ^ [_790863, _790865, _790867, _790869, _790871, _790873] : [-(c_Finite__Set_Ofolding__one(_790871, _790867, _790863)), c_Finite__Set_Ofolding__one(_790873, _790869, _790865), _790873 = _790871, _790869 = _790867, _790865 = _790863], (43783 ^ _779571) ^ [_1634902, _1634904, _1634906, _1634908, _1634910] : [c_Relation_Osingle__valued(_1634902, _1634902, _1634904), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634902, _1634902)), hAPP(hAPP(c_Product__Type_OPair(_1634902, _1634902), _1634906), _1634908)), c_Transitive__Closure_Ortrancl(_1634902, _1634904))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634902, _1634902)), hAPP(hAPP(c_Product__Type_OPair(_1634902, _1634902), _1634906), _1634910)), c_Transitive__Closure_Ortrancl(_1634902, _1634904))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634902, _1634902)), hAPP(hAPP(c_Product__Type_OPair(_1634902, _1634902), _1634908), _1634910)), c_Transitive__Closure_Ortrancl(_1634902, _1634904)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634902, _1634902)), hAPP(hAPP(c_Product__Type_OPair(_1634902, _1634902), _1634910), _1634908)), c_Transitive__Closure_Ortrancl(_1634902, _1634904))))], (8780 ^ _779571) ^ [_924733, _924735, _924737] : [class_Rings_Oidom(_924733), 8783 ^ _779571 : [(8784 ^ _779571) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924733), _924735), _924735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924733), _924737), _924737), -(_924735 = _924737), -(_924735 = hAPP(c_Groups_Ouminus__class_Ouminus(_924733), _924737))], (8794 ^ _779571) ^ [] : [8795 ^ _779571 : [(8798 ^ _779571) ^ [] : [_924735 = hAPP(c_Groups_Ouminus__class_Ouminus(_924733), _924737)], (8796 ^ _779571) ^ [] : [_924735 = _924737]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924733), _924735), _924735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924733), _924737), _924737))]]], (51275 ^ _779571) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (46863 ^ _779571) ^ [_1709995, _1709997, _1709999] : [_1709995 = hAPP(hAPP(c_List_Olist_OCons(_1709997), _1709999), _1709995)], (16653 ^ _779571) ^ [_1064493, _1064495, _1064497] : [class_Groups_Oordered__ab__group__add__abs(_1064493), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064493), hAPP(c_Groups_Oabs__class_Oabs(_1064493), _1064495)), hAPP(c_Groups_Oabs__class_Oabs(_1064493), _1064497))), hAPP(c_Groups_Oabs__class_Oabs(_1064493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064493), _1064497), _1064495)))))], (51527 ^ _779571) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (28403 ^ _779571) ^ [_1283696, _1283698] : [c_Nat__Transfer_Onat__set(_1283696), c_Nat__Transfer_Onat__set(_1283698), 28410 ^ _779571 : [(28417 ^ _779571) ^ [] : [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), _1283696)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1283696), _1283698)))], (28411 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1283696), _1283698)), -(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), _1283696)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283698))))]]], (45971 ^ _779571) ^ [_1686391, _1686393, _1686395, _1686397, _1686399, _1686401, _1686403] : [-(c_List_Ofoldr(_1686391, _1686393, _1686395, hAPP(hAPP(c_List_Omap(_1686397, _1686391), _1686399), _1686401), _1686403) = c_List_Ofoldr(_1686397, _1686393, hAPP(c_Fun_Ocomp(_1686391, tc_fun(_1686393, _1686393), _1686397, _1686395), _1686399), _1686401, _1686403))], (16449 ^ _779571) ^ [_1060838, _1060840] : [class_Rings_Olinordered__idom(_1060838), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060838), hAPP(c_Groups_Oabs__class_Oabs(_1060838), _1060840)), hAPP(c_Groups_Oabs__class_Oabs(_1060838), _1060840)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060838), _1060840), _1060840))], (34150 ^ _779571) ^ [_1404097, _1404099, _1404101, _1404103, _1404105, _1404107] : [-(_1404097 = _1404099), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404101, _1404103), _1404105), _1404099), _1404107), _1404097) = hAPP(_1404105, _1404097))], (51305 ^ _779571) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (12517 ^ _779571) ^ [_988546, _988548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988546), _988548)), -(_988548 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _988546), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12520 ^ [_988546, _988548])))], (17813 ^ _779571) ^ [_1086252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086252)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086252))], (3856 ^ _779571) ^ [_839045, _839047, _839049, _839051] : [-(c_New__DSequence_Opos__single(_839051, _839047) = c_New__DSequence_Opos__single(_839049, _839045)), _839051 = _839049, _839047 = _839045], (27618 ^ _779571) ^ [_1268036] : [-(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)), _1268036)) = _1268036)], (6821 ^ _779571) ^ [_891943, _891945] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_891943, _891945)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_891943)), c_Com_Ocom_Ocom__size(_891945))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24091 ^ _779571) ^ [_1199007, _1199009] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1199007)), hAPP(c_Nat_OSuc, _1199009)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1199007))), 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)), _1199009)))))], (34994 ^ _779571) ^ [_1422692, _1422694] : [-(c_Relation_OId__on(_1422692, _1422694) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1422692, tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool)), _1422694), hAPP(hAPP(c_COMBC(_1422692, tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool), tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1422692, _1422692), tc_fun(tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool), tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool)), _1422692), c_Set_Oinsert(tc_prod(_1422692, _1422692))), hAPP(hAPP(c_COMBS(_1422692, _1422692, tc_prod(_1422692, _1422692)), c_Product__Type_OPair(_1422692, _1422692)), c_COMBI(_1422692)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1422692, _1422692), tc_HOL_Obool)))))], (24757 ^ _779571) ^ [_1211925, _1211927, _1211929, _1211931] : [-(c_Sum__Type_Osum_Osum__case(_1211925, _1211927, _1211929, hAPP(hAPP(c_COMBB(tc_sum(_1211925, _1211929), _1211927, _1211925), _1211931), c_Sum__Type_OInl(_1211925, _1211929)), hAPP(hAPP(c_COMBB(tc_sum(_1211925, _1211929), _1211927, _1211929), _1211931), c_Sum__Type_OInr(_1211929, _1211925))) = _1211931)], (36090 ^ _779571) ^ [_1448964, _1448966, _1448968, _1448970] : [hBOOL(hAPP(hAPP(c_member(_1448964), _1448966), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448964, tc_HOL_Obool)), _1448968), _1448970))), 36093 ^ _779571 : [(36096 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1448964), _1448966), _1448970)))], (36094 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1448964), _1448966), _1448968)))]]], (43144 ^ _779571) ^ [_1619115, _1619117, _1619119, _1619121] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619115, _1619115)), hAPP(hAPP(c_Product__Type_OPair(_1619115, _1619115), _1619117), _1619119)), c_Transitive__Closure_Ortrancl(_1619115, _1619121))), -(_1619117 = _1619119), 43151 ^ _779571 : [(43154 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619115, _1619115)), hAPP(hAPP(c_Product__Type_OPair(_1619115, _1619115), _1619117), _1619119)), c_Transitive__Closure_Otrancl(_1619115, _1619121))))], (43152 ^ _779571) ^ [] : [_1619117 = _1619119]]], (46070 ^ _779571) ^ [_1689014, _1689016, _1689018, _1689020] : [hAPP(hAPP(c_Option_Omap(_1689014, _1689016), _1689018), _1689020) = c_Option_Ooption_ONone(_1689016), -(_1689020 = c_Option_Ooption_ONone(_1689014))], (1652 ^ _779571) ^ [_802989, _802991] : [-(class_Groups_Omonoid__add(_802989)), _802991 = _802989, class_Groups_Omonoid__add(_802991)], (29250 ^ _779571) ^ [_1302330, _1302332, _1302334, _1302336] : [_1302336 = c_Orderings_Obot__class_Obot(tc_fun(_1302332, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1302330, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1302332, _1302330, _1302334), _1302336))], (24289 ^ _779571) ^ [_1202846, _1202848, _1202850, _1202852] : [class_Orderings_Olinorder(_1202846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202846), _1202848), _1202850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202846), _1202848), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202846), _1202850), _1202852))))], (42367 ^ _779571) ^ [_1600785, _1600787] : [c_Wellfounded_OwfP(_1600785, _1600787), -(c_Wellfounded_Oacyclic(_1600785, hAPP(c_Set_OCollect(tc_prod(_1600785, _1600785)), hAPP(c_Product__Type_Oprod_Oprod__case(_1600785, _1600785, tc_HOL_Obool), _1600787))))], (9342 ^ _779571) ^ [] : [-(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))], (26128 ^ _779571) ^ [_1238188, _1238190, _1238192, _1238194] : [class_Divides_Osemiring__div(_1238188), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238188), _1238190), _1238192)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238188), _1238190), _1238194)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238188), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238188), _1238192), _1238194)), _1238190) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238188), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238188), _1238192), _1238190)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1238188), _1238194), _1238190)))], (47298 ^ _779571) ^ [_1720706, _1720708] : [hAPP(c_List_Oset(_1720706), _1720708) = c_Orderings_Obot__class_Obot(tc_fun(_1720706, tc_HOL_Obool)), -(_1720708 = c_List_Olist_ONil(_1720706))], (42073 ^ _779571) ^ [] : [-(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))))], (51365 ^ _779571) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (50682 ^ _779571) ^ [_1798514, _1798516] : [_1798516 = c_List_Olist_ONil(_1798514), -(c_List_Olist_ONil(_1798514) = hAPP(c_List_Orev(_1798514), _1798516))], (43308 ^ _779571) ^ [_1622839, _1622841, _1622843, _1622845, _1622847] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622839, _1622839)), hAPP(hAPP(c_Product__Type_OPair(_1622839, _1622839), hAPP(_1622841, hAPP(c_Nat_OSuc, 43309 ^ [_1622839, _1622841, _1622843, _1622845, _1622847]))), hAPP(_1622841, 43309 ^ [_1622839, _1622841, _1622843, _1622845, _1622847]))), c_Transitive__Closure_Ortrancl(_1622839, _1622843))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622839, _1622839)), hAPP(hAPP(c_Product__Type_OPair(_1622839, _1622839), hAPP(_1622841, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1622845), _1622847))), hAPP(_1622841, _1622845))), c_Transitive__Closure_Ortrancl(_1622839, _1622843))))], (13779 ^ _779571) ^ [_1011025, _1011027, _1011029, _1011031] : [class_Divides_Oring__div(_1011025), c_Divides_Odiv__class_Omod(_1011025, _1011027, _1011029) = c_Divides_Odiv__class_Omod(_1011025, _1011031, _1011029), -(c_Divides_Odiv__class_Omod(_1011025, hAPP(c_Groups_Ouminus__class_Ouminus(_1011025), _1011027), _1011029) = c_Divides_Odiv__class_Omod(_1011025, hAPP(c_Groups_Ouminus__class_Ouminus(_1011025), _1011031), _1011029))], (8227 ^ _779571) ^ [_915988, _915990, _915992] : [class_Rings_Osemiring__1(_915988), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915988), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915990), _915992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915988), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915988), _915990)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915988), _915992)))], (40570 ^ _779571) ^ [_1549787, _1549789, _1549791] : [class_Lattices_Oab__semigroup__idem__mult(_1549787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549787), _1549789)), -(_1549789 = c_Orderings_Obot__class_Obot(tc_fun(_1549787, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549787), _1549791)), -(_1549791 = c_Orderings_Obot__class_Obot(tc_fun(_1549787, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1549787, c_Groups_Otimes__class_Otimes(_1549787)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1549787, tc_HOL_Obool)), _1549789), _1549791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1549787), hAPP(c_Finite__Set_Ofold1(_1549787, c_Groups_Otimes__class_Otimes(_1549787)), _1549789)), hAPP(c_Finite__Set_Ofold1(_1549787, c_Groups_Otimes__class_Otimes(_1549787)), _1549791)))], (32335 ^ _779571) ^ [_1368058, _1368060] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1368058), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368060))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1368060), _1368058)))], (36226 ^ _779571) ^ [_1452056, _1452058, _1452060, _1452062] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452056, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452056, tc_HOL_Obool)), _1452058), _1452060)), _1452062) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452056, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452056, tc_HOL_Obool)), _1452058), _1452062)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452056, tc_HOL_Obool)), _1452060), _1452062)))], (10281 ^ _779571) ^ [_950879, _950881, _950883] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950879), _950881)), _950883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950881), _950883)))], (32267 ^ _779571) ^ [_1366760, _1366762, _1366764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366760)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1366762), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1366764)), 32277 ^ _779571 : [(32283 ^ _779571) ^ [] : [-(_1366762 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32279 ^ [_1366760, _1366762, _1366764]), 32276 ^ [_1366760, _1366762, _1366764]))], (32281 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32279 ^ [_1366760, _1366762, _1366764]), _1366764)))], (32278 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32276 ^ [_1366760, _1366762, _1366764]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1366760))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1366762), _1366760) = _1366762)], (39469 ^ _779571) ^ [_1523417, _1523419, _1523421, _1523423, _1523425] : [hBOOL(hAPP(hAPP(c_member(_1523417), hAPP(_1523419, _1523421)), _1523423)), -(hBOOL(hAPP(hAPP(c_member(_1523425), _1523421), hAPP(c_Set_Ovimage(_1523425, _1523417, _1523419), _1523423))))], (33119 ^ _779571) ^ [_1383396, _1383398] : [class_Int_Oring__char__0(_1383396), hBOOL(hAPP(hAPP(c_member(_1383396), _1383398), c_Int_Oring__1__class_OInts(_1383396))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383396), c_Groups_Oone__class_Oone(_1383396)), _1383398)), _1383398) = c_Groups_Ozero__class_Ozero(_1383396)], (51309 ^ _779571) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (49680 ^ _779571) ^ [_1777337, _1777339, _1777341, _1777343] : [-(hAPP(hAPP(c_List_Oappend(_1777337), _1777339), hAPP(hAPP(c_List_Olist_OCons(_1777337), _1777341), c_List_Olist_ONil(_1777337))) = _1777343), -(_1777343 = c_List_Olist_ONil(_1777337)), c_List_Obutlast(_1777337, _1777343) = _1777339, c_List_Olast(_1777337, _1777343) = _1777341], (41041 ^ _779571) ^ [_1561123] : [-(c_Finite__Set_Ofun__left__comm__idem(_1561123, tc_fun(_1561123, tc_HOL_Obool), c_Set_Oinsert(_1561123)))], (21259 ^ _779571) ^ [_1145306, _1145308, _1145310, _1145312] : [class_Fields_Ofield__inverse__zero(_1145306), class_Int_Onumber(_1145306), 21266 ^ _779571 : [(21267 ^ _779571) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145306), _1145308), hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310)) = _1145312, 21270 ^ _779571 : [(21277 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310) = c_Groups_Ozero__class_Ozero(_1145306), -(_1145312 = c_Groups_Ozero__class_Ozero(_1145306))], (21271 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310) = c_Groups_Ozero__class_Ozero(_1145306)), -(_1145308 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145306), _1145312), hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310)))]]], (21283 ^ _779571) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145306), _1145308), hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310)) = _1145312), 21286 ^ _779571 : [(21289 ^ _779571) ^ [] : [_1145308 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145306), _1145312), hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310))], (21287 ^ _779571) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310) = c_Groups_Ozero__class_Ozero(_1145306)]], 21290 ^ _779571 : [(21293 ^ _779571) ^ [] : [_1145312 = c_Groups_Ozero__class_Ozero(_1145306)], (21291 ^ _779571) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1145306), _1145310) = c_Groups_Ozero__class_Ozero(_1145306))]]]]], (4316 ^ _779571) ^ [_846325, _846327] : [_846327 = _846325, -(c_Groups_Ouminus__class_Ouminus(_846327) = c_Groups_Ouminus__class_Ouminus(_846325))], (42866 ^ _779571) ^ [_1611454] : [-(c_Transitive__Closure_Otrancl(_1611454, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1611454, _1611454), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1611454, _1611454), tc_HOL_Obool)))], (18665 ^ _779571) ^ [_1099767, _1099769] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1099767)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099769)) = 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)))), _1099767)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099769)))], (24865 ^ _779571) ^ [_1214399, _1214401, _1214403] : [c_Nitpick_Oless__eq__frac(_1214399, _1214401, _1214403), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1214399), c_Nitpick_Oplus__frac(_1214399, _1214401, c_Nitpick_Ouminus__frac(_1214399, _1214403)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45864 ^ _779571) ^ [_1683913, _1683915, _1683917, _1683919, _1683921, _1683923, _1683925] : [c_Fun_Oinj__on(_1683913, _1683915, _1683917, c_Orderings_Otop__class_Otop(tc_fun(_1683913, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1683913, _1683919, _1683921), _1683923) = hAPP(c_Option_Ooption_OSome(_1683919), _1683925), -(hAPP(c_Map_Omap__of(_1683915, _1683919, hAPP(hAPP(c_List_Omap(tc_prod(_1683913, _1683919), tc_prod(_1683915, _1683919)), hAPP(c_Product__Type_Oprod_Oprod__case(_1683913, _1683919, tc_prod(_1683915, _1683919)), hAPP(hAPP(c_COMBB(_1683915, tc_fun(_1683919, tc_prod(_1683915, _1683919)), _1683913), c_Product__Type_OPair(_1683915, _1683919)), _1683917))), _1683921)), hAPP(_1683917, _1683923)) = hAPP(c_Option_Ooption_OSome(_1683919), _1683925))], (7652 ^ _779571) ^ [_906367, _906369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _906367)), hAPP(c_Nat_OSuc, _906369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906367), _906369)))], (972 ^ _779571) ^ [_794489, _794491] : [-(class_Lattices_Obounded__lattice(_794489)), _794491 = _794489, class_Lattices_Obounded__lattice(_794491)], (18935 ^ _779571) ^ [_1104205] : [class_Int_Onumber__ring(_1104205), c_Int_Oiszero(_1104205, hAPP(c_Int_Onumber__class_Onumber__of(_1104205), c_Int_OBit1(c_Int_OPls)))], (10864 ^ _779571) ^ [_960196, _960198, _960200] : [class_Orderings_Olinorder(_960196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960196), _960198), _960200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960196), _960200), _960198))], (41420 ^ _779571) ^ [_1572394, _1572396, _1572398, _1572400] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572394), hAPP(c_Set_OCollect(_1572394), _1572396))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572398), hAPP(c_Set_OCollect(_1572398), hAPP(hAPP(c_COMBB(tc_fun(_1572394, tc_HOL_Obool), tc_HOL_Obool, _1572398), c_HOL_OEx(_1572394)), hAPP(hAPP(c_COMBC(_1572398, tc_fun(_1572394, tc_HOL_Obool), tc_fun(_1572394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1572394, tc_HOL_Obool), tc_fun(_1572394, tc_HOL_Obool)), _1572398), c_COMBS(_1572394, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572394, tc_HOL_Obool), tc_fun(_1572394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1572398), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572394), c_fconj)), hAPP(hAPP(c_COMBC(_1572398, tc_fun(_1572394, _1572398), tc_fun(_1572394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572398, tc_HOL_Obool), tc_fun(tc_fun(_1572394, _1572398), tc_fun(_1572394, tc_HOL_Obool)), _1572398), c_COMBB(_1572398, tc_HOL_Obool, _1572394)), c_fequal)), _1572400)))), _1572396))))))], (11457 ^ _779571) ^ [_969807, _969809, _969811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969807), _969809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969807), _969811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969809), _969811))))], (43108 ^ _779571) ^ [_1618179, _1618181, _1618183] : [_1618181 = _1618183, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618179, _1618179)), hAPP(hAPP(c_Product__Type_OPair(_1618179, _1618179), _1618181), _1618183)), c_Relation_OId(_1618179))))], (44644 ^ _779571) ^ [_1655265, _1655267, _1655269, _1655271, _1655273] : [-(hAPP(hAPP(c_Set_Oinsert(_1655265), _1655267), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655269, tc_fun(_1655265, tc_HOL_Obool)), _1655271), _1655273)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655269, tc_fun(_1655265, tc_HOL_Obool)), _1655271), hAPP(hAPP(c_COMBB(tc_fun(_1655265, tc_HOL_Obool), tc_fun(_1655265, tc_HOL_Obool), _1655269), hAPP(c_Set_Oinsert(_1655265), _1655267)), _1655273)))], (46082 ^ _779571) ^ [_1689226, _1689228, _1689230] : [-(hAPP(hAPP(c_Option_Omap(_1689226, _1689228), _1689230), c_Option_Ooption_ONone(_1689226)) = c_Option_Ooption_ONone(_1689228))], (49542 ^ _779571) ^ [_1774381, _1774383, _1774385] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1774381)), _1774383), c_List_Olists(_1774381, _1774385)))), 49543 ^ _779571 : [(49546 ^ _779571) ^ [_1774509, _1774511] : [_1774383 = hAPP(hAPP(c_List_Olist_OCons(_1774381), _1774511), _1774509), hBOOL(hAPP(hAPP(c_member(_1774381), _1774511), _1774385)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1774381)), _1774509), c_List_Olists(_1774381, _1774385)))], (49544 ^ _779571) ^ [] : [_1774383 = c_List_Olist_ONil(_1774381)]]], (3508 ^ _779571) ^ [_833519, _833521] : [_833521 = _833519, -(c_Random__Sequence_Osingle(_833521) = c_Random__Sequence_Osingle(_833519))], (6925 ^ _779571) ^ [_893829, _893831] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893829), _893831) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6926 ^ _779571 : [(6933 ^ _779571) ^ [] : [_893829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _893831 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6927 ^ _779571) ^ [] : [_893829 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (14794 ^ _779571) ^ [_1028915, _1028917, _1028919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028915), 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)), _1028917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028917), _1028919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028915), _1028917)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028915), _1028919))))], (10313 ^ _779571) ^ [_951391, _951393] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951391), _951393)), _951391 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _951393 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (44762 ^ _779571) ^ [_1658773, _1658775, _1658777, _1658779, _1658781] : [-(_1658773 = c_Orderings_Obot__class_Obot(tc_fun(_1658775, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658775, tc_fun(_1658777, tc_HOL_Obool)), _1658773), hAPP(hAPP(c_COMBC(_1658775, tc_fun(_1658777, tc_HOL_Obool), tc_fun(_1658777, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1658777, tc_HOL_Obool), tc_fun(tc_fun(_1658777, tc_HOL_Obool), tc_fun(_1658777, tc_HOL_Obool)), _1658775), c_Groups_Ominus__class_Ominus(tc_fun(_1658777, tc_HOL_Obool))), _1658779)), _1658781)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658777, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658775, tc_fun(_1658777, tc_HOL_Obool)), _1658773), _1658779)), _1658781))], (47745 ^ _779571) ^ [_1731700, _1731702, _1731704, _1731706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731702)), _1731704))), -(hAPP(hAPP(c_List_Onth(_1731702), hAPP(hAPP(c_List_Olist__update(_1731702, _1731704), _1731700), _1731706)), _1731700) = _1731706)], (4754 ^ _779571) ^ [_853058, _853060, _853062, _853064] : [-(c_List_Olistrel1(_853064, _853060) = c_List_Olistrel1(_853062, _853058)), _853064 = _853062, _853060 = _853058], (36062 ^ _779571) ^ [_1448447, _1448449, _1448451, _1448453] : [hBOOL(hAPP(_1448447, _1448449)), hBOOL(hAPP(_1448451, _1448449)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448453, tc_HOL_Obool)), _1448447), _1448451), _1448449)))], (16983 ^ _779571) ^ [_1071157, _1071159, _1071161, _1071163, _1071165] : [class_Groups_Oordered__ab__group__add__abs(_1071157), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071157), hAPP(c_Groups_Oabs__class_Oabs(_1071157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071157), _1071159), _1071161)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071157), _1071163), _1071165)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071157), hAPP(c_Groups_Oabs__class_Oabs(_1071157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071157), _1071159), _1071163))), hAPP(c_Groups_Oabs__class_Oabs(_1071157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071157), _1071161), _1071165))))))], (14086 ^ _779571) ^ [_1016504, _1016506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016504)), -(c_SMT_Oz3mod(_1016506, _1016504) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016506, _1016504))], (34184 ^ _779571) ^ [_1404691, _1404693, _1404695, _1404697, _1404699] : [hAPP(_1404695, _1404697) = _1404699, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1404691, _1404693), _1404695), _1404697), _1404699) = _1404695)], (41127 ^ _779571) ^ [_1562620] : [class_Orderings_Olinorder(_1562620), -(c_Finite__Set_Ofun__left__comm__idem(_1562620, _1562620, c_Orderings_Oord__class_Omax(_1562620)))], (8013 ^ _779571) ^ [_912498, _912500] : [-(_912498 = c_Option_Ooption_ONone(_912500)), -(_912498 = hAPP(c_Option_Ooption_OSome(_912500), 8016 ^ [_912498, _912500]))], (3514 ^ _779571) ^ [_833604, _833606] : [_833606 = _833604, -(c_SetInterval_Oord__class_OatLeast(_833606) = c_SetInterval_Oord__class_OatLeast(_833604))], (48668 ^ _779571) ^ [_1754898, _1754900, _1754902, _1754904] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754898), tc_List_Olist(_1754898))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754898), tc_List_Olist(_1754898)), _1754900), _1754902)), c_List_Olistrel1(_1754898, _1754904)))), 48669 ^ _779571 : [(48670 ^ _779571) ^ [_1755031, _1755033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1754898, _1754898)), hAPP(hAPP(c_Product__Type_OPair(_1754898, _1754898), hAPP(hAPP(c_List_Onth(_1754898), _1754900), _1755031)), _1755033)), _1754904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755031), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754898)), _1754900))), _1754902 = hAPP(hAPP(c_List_Olist__update(_1754898, _1754900), _1755031), _1755033)]]], (50246 ^ _779571) ^ [_1789206, _1789208] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1789206, _1789208)))], (47424 ^ _779571) ^ [_1723644, _1723646, _1723648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723644), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723646)), _1723648))), -(hAPP(c_Random_Opick(_1723646, hAPP(hAPP(c_List_Omap(_1723646, tc_prod(tc_Code__Numeral_Ocode__numeral, _1723646)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1723646), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1723648)), hAPP(c_Code__Numeral_Oof__nat, _1723644)) = hAPP(hAPP(c_List_Onth(_1723646), _1723648), _1723644))], (7165 ^ _779571) ^ [_897715, _897717, _897719, _897721] : [class_Rings_Ocomm__semiring__1(_897715), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897715), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897715), _897717), _897719)), _897721) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897715), _897717), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897715), _897719), _897721)))], (10942 ^ _779571) ^ [_961331, _961333, _961335] : [class_Orderings_Oorder(_961331), 10945 ^ _779571 : [(10946 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961331), _961333), _961335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961331), _961333), _961335))), -(_961333 = _961335)], (10956 ^ _779571) ^ [] : [10957 ^ _779571 : [(10960 ^ _779571) ^ [] : [_961333 = _961335], (10958 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961331), _961333), _961335))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961331), _961333), _961335)))]]], (51391 ^ _779571) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (47314 ^ _779571) ^ [_1721010, _1721012, _1721014, _1721016] : [class_Orderings_Olinorder(_1721010), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721012, _1721010, _1721014), _1721016), c_List_Olist_ONil(_1721012)) = hAPP(hAPP(c_List_Olist_OCons(_1721012), _1721016), c_List_Olist_ONil(_1721012)))], (40300 ^ _779571) ^ [_1544084, _1544086, _1544088, _1544090] : [-(_1544084 = c_Orderings_Obot__class_Obot(tc_fun(_1544086, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1544088, _1544086), _1544088, c_Product__Type_Ofst(_1544088, _1544086)), hAPP(hAPP(c_Product__Type_OSigma(_1544088, _1544086), _1544090), hAPP(c_COMBK(tc_fun(_1544086, tc_HOL_Obool), _1544088), _1544084))) = _1544090)], (49265 ^ _779571) ^ [_1768510, _1768512] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1768510), hAPP(c_List_Oset(tc_Nat_Onat), _1768512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768510), 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)), _1768512))))], (14353 ^ _779571) ^ [_1021744] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021744) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14298 ^ _779571) ^ [_1020572, _1020574, _1020576] : [hBOOL(hAPP(_1020572, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020574), _1020576))), 14303 ^ _779571 : [(14306 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1020572, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14304 ^ _779571) ^ [] : [-(_1020576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14308 ^ _779571 : [(14313 ^ _779571) ^ [] : [-(hBOOL(hAPP(_1020572, 14307 ^ [_1020572, _1020574, _1020576])))], (14311 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020576), hAPP(c_Nat_OSuc, 14307 ^ [_1020572, _1020574, _1020576])))))], (14309 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020576), 14307 ^ [_1020572, _1020574, _1020576])), _1020574)))]]], (11368 ^ _779571) ^ [_968331, _968333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968331), _968333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968331), _968333))), -(_968331 = _968333)], (51345 ^ _779571) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (25928 ^ _779571) ^ [_1233973, _1233975, _1233977] : [class_Groups_Ocomm__monoid__add(_1233973), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1233975, _1233973), hAPP(c_COMBK(_1233973, _1233975), c_Groups_Ozero__class_Ozero(_1233973))), _1233977) = c_Groups_Ozero__class_Ozero(_1233973))], (43124 ^ _779571) ^ [_1618575, _1618577, _1618579, _1618581, _1618583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618575, _1618575)), hAPP(hAPP(c_Product__Type_OPair(_1618575, _1618575), _1618577), _1618579)), c_Transitive__Closure_Otrancl(_1618575, _1618581))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618575, _1618575)), hAPP(hAPP(c_Product__Type_OPair(_1618575, _1618575), _1618579), _1618583)), c_Transitive__Closure_Ortrancl(_1618575, _1618581))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618575, _1618575)), hAPP(hAPP(c_Product__Type_OPair(_1618575, _1618575), _1618577), _1618583)), c_Transitive__Closure_Otrancl(_1618575, _1618581))))], (264 ^ _779571) ^ [_783427, _783429, _783431, _783433, _783435, _783437] : [-(c_Hoare__Mirabelle_Ohoare__valids(_783435, _783431, _783427)), c_Hoare__Mirabelle_Ohoare__valids(_783437, _783433, _783429), _783437 = _783435, _783433 = _783431, _783429 = _783427], (31836 ^ _779571) ^ [_1357552, _1357554, _1357556, _1357558, _1357560] : [class_Groups_Ocomm__monoid__add(_1357552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357554), _1357556)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357554, _1357552), _1357558), hAPP(hAPP(c_Set_Oinsert(_1357554), _1357560), _1357556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357552), hAPP(_1357558, _1357560)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357554, _1357552), _1357558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357554, tc_HOL_Obool)), _1357556), hAPP(hAPP(c_Set_Oinsert(_1357554), _1357560), c_Orderings_Obot__class_Obot(tc_fun(_1357554, tc_HOL_Obool)))))))], (46985 ^ _779571) ^ [_1713680, _1713682, _1713684, _1713686, _1713688] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713680), tc_List_Olist(_1713680))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713680), tc_List_Olist(_1713680)), _1713682), hAPP(hAPP(c_List_Olist_OCons(_1713680), _1713684), _1713686))), c_List_Olistrel(_1713680, _1713688))), 46990 ^ _779571 : [(46995 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713680), tc_List_Olist(_1713680))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713680), tc_List_Olist(_1713680)), 46989 ^ [_1713680, _1713682, _1713684, _1713686, _1713688]), _1713686)), c_List_Olistrel(_1713680, _1713688))))], (46993 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713680, _1713680)), hAPP(hAPP(c_Product__Type_OPair(_1713680, _1713680), 46988 ^ [_1713680, _1713682, _1713684, _1713686, _1713688]), _1713684)), _1713688)))], (46991 ^ _779571) ^ [] : [-(_1713682 = hAPP(hAPP(c_List_Olist_OCons(_1713680), 46988 ^ [_1713680, _1713682, _1713684, _1713686, _1713688]), 46989 ^ [_1713680, _1713682, _1713684, _1713686, _1713688]))]]], (41177 ^ _779571) ^ [_1563712, _1563714, _1563716] : [hBOOL(hAPP(_1563712, _1563714)), -(hAPP(c_Set_OCollect(_1563716), hAPP(hAPP(c_COMBS(_1563716, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563716), c_fconj), hAPP(hAPP(c_COMBC(_1563716, _1563716, tc_HOL_Obool), c_fequal), _1563714))), _1563712)) = hAPP(hAPP(c_Set_Oinsert(_1563716), _1563714), c_Orderings_Obot__class_Obot(tc_fun(_1563716, tc_HOL_Obool))))], (10369 ^ _779571) ^ [_952255, _952257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952255), _952257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952257), _952255)), -(_952255 = _952257)], (9244 ^ _779571) ^ [_932708, _932710, _932712] : [class_Groups_Ogroup__add(_932708), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932708), _932710), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932708), hAPP(c_Groups_Ouminus__class_Ouminus(_932708), _932710)), _932712)) = _932712)], (45809 ^ _779571) ^ [_1682541, _1682543, _1682545] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1682541), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1682543), _1682545)))), 45812 ^ _779571 : [(45819 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1682543), _1682545))), -(c_Smallcheck_Osmall_H(_1682541, _1682543, _1682545) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1682541, _1682543, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1682545), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1682541, _1682545)))], (45813 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1682543), _1682545)), -(c_Smallcheck_Osmall_H(_1682541, _1682543, _1682545) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (12243 ^ _779571) ^ [_983838, _983840, _983842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983838), _983840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983838), _983842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983840), _983842))))], (25500 ^ _779571) ^ [_1226190, _1226192, _1226194] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226190), _1226192)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226192), _1226190))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226192), _1226194)), 25511 ^ _779571 : [(25514 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226194), _1226190))], (25512 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226190), _1226194)))]]], (47240 ^ _779571) ^ [_1719698, _1719700] : [-(c_List_Olistrelp(_1719698, _1719700, c_List_Olist_ONil(_1719698), c_List_Olist_ONil(_1719698)))], (14844 ^ _779571) ^ [_1029788, _1029790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1029790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029788), _1029790)), _1029788)))], (43288 ^ _779571) ^ [_1622379, _1622381, _1622383, _1622385, _1622387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622379, _1622379)), hAPP(hAPP(c_Product__Type_OPair(_1622379, _1622379), _1622381), _1622383)), c_Transitive__Closure_Ortrancl(_1622379, _1622385))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1622379, _1622379), tc_HOL_Obool)), _1622385), hAPP(hAPP(c_Product__Type_OSigma(_1622379, _1622379), _1622387), hAPP(c_COMBK(tc_fun(_1622379, tc_HOL_Obool), _1622379), _1622387)))), -(_1622381 = _1622383), -(hBOOL(hAPP(hAPP(c_member(_1622379), _1622381), _1622387)))], (38635 ^ _779571) ^ [_1505426, _1505428, _1505430, _1505432] : [-(_1505426 = c_Orderings_Obot__class_Obot(tc_fun(_1505428, tc_HOL_Obool))), 38638 ^ _779571 : [(38639 ^ _779571) ^ [] : [-(hAPP(c_Set_Oimage(_1505430, _1505428, 38646 ^ [_1505426, _1505428, _1505430, _1505432]), _1505432) = _1505426), 38640 ^ _779571 : [(38641 ^ _779571) ^ [_1505567] : [c_Fun_Oinj__on(_1505428, _1505430, _1505567, _1505426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505430, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1505428, _1505430, _1505567), _1505426)), _1505432))]]], (38650 ^ _779571) ^ [] : [38651 ^ _779571 : [(38652 ^ _779571) ^ [_1505759] : [hAPP(c_Set_Oimage(_1505430, _1505428, _1505759), _1505432) = _1505426]], 38654 ^ _779571 : [(38657 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505430, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1505428, _1505430, 38653 ^ [_1505426, _1505428, _1505430, _1505432]), _1505426)), _1505432)))], (38655 ^ _779571) ^ [] : [-(c_Fun_Oinj__on(_1505428, _1505430, 38653 ^ [_1505426, _1505428, _1505430, _1505432], _1505426))]]]]], (13815 ^ _779571) ^ [_1011705, _1011707, _1011709, _1011711] : [class_Divides_Osemiring__div(_1011705), -(c_Divides_Odiv__class_Omod(_1011705, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011705), _1011707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011705), _1011709), _1011711)), _1011709) = c_Divides_Odiv__class_Omod(_1011705, _1011707, _1011709))], (32945 ^ _779571) ^ [_1380567, _1380569, _1380571] : [class_Lattices_Olattice(_1380567), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380567), _1380569)), hBOOL(hAPP(hAPP(c_member(_1380567), _1380571), _1380569)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1380567), _1380571), c_Big__Operators_Olattice__class_OSup__fin(_1380567, _1380569)) = c_Big__Operators_Olattice__class_OSup__fin(_1380567, _1380569))], (34075 ^ _779571) ^ [_1402459, _1402461, _1402463, _1402465, _1402467] : [class_Groups_Oordered__ab__group__add(_1402459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402461), _1402463)), 34085 ^ _779571 : [(34088 ^ _779571) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402459), c_Groups_Ozero__class_Ozero(_1402459)), hAPP(_1402465, 34084 ^ [_1402459, _1402461, _1402463, _1402465, _1402467])))], (34086 ^ _779571) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402461), 34084 ^ [_1402459, _1402461, _1402463, _1402465, _1402467]), _1402463)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1402461, _1402459), _1402465), _1402463) = c_Groups_Ozero__class_Ozero(_1402459), hBOOL(hAPP(hAPP(c_member(_1402461), _1402467), _1402463)), -(hAPP(_1402465, _1402467) = c_Groups_Ozero__class_Ozero(_1402459))]], input).
% 45.12/44.04  ncf('1',plain,[v_R(v_Z, v_s_H)],start(51705 ^ 0)).
% 45.12/44.04  ncf('1.1',plain,[-(v_R(v_Z, v_s_H)), 51693 : c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H), 51693 : v_Q(v_Z, v_s1)],extension(51689 ^ 1,bind([[_1814698, _1814700, _1814763], [v_s1, v_Z, v_s_H]]))).
% 45.12/44.04  ncf('1.1.1',plain,[-(c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H))],extension(51703 ^ 4)).
% 45.12/44.04  ncf('1.1.2',plain,[-(v_Q(v_Z, v_s1)), 51683 : c_Natural_Oevaln(v_c, v_s, v_n, v_s1), 51683 : v_P(v_Z, v_s)],extension(51679 ^ 2,bind([[_1814546, _1814548, _1814611], [v_s, v_Z, v_s1]]))).
% 45.12/44.04  ncf('1.1.2.1',plain,[-(c_Natural_Oevaln(v_c, v_s, v_n, v_s1))],extension(51701 ^ 5)).
% 45.12/44.04  ncf('1.1.2.2',plain,[-(v_P(v_Z, v_s))],extension(51699 ^ 3)).
% 45.12/44.04  %-----------------------------------------------------
% 45.12/44.04  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------